X-Planes: Bell X-14

The previous article in this series used two numbers it could not justify. Discussing the Ryan X-13 Vertijet, it asked whether the aircraft’s control surfaces were adequate, and to answer that it needed a standard of adequacy. It used half a radian per second squared in pitch and one radian per second squared in roll, the roll figure rounded up from the three quarters that Garren et al. 1965 found to be the lower limit of satisfactory control power, flagged both in its epistemic state as figures the field settled on after the X-13 had finished flying, and named the aircraft that produced them. This article is about that aircraft. The Bell X-14 is the machine that turned the question of how much control a hovering aeroplane needs from a matter of opinion into a number in a specification. It is the fifteenth article in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, and the X-13.

It is also the strangest aircraft the series has met so far, and the strangeness is not in how it looks. The X-14 was built to be a bad aeroplane on demand. In the standard account its wings, ailerons, and landing gear came from a Beechcraft Bonanza and its tail from a T-34 Mentor. It had an open cockpit and fixed gear. Its fastest recorded flight was 172 miles per hour, in NASA’s inventory of the X-vehicles by Jenkins, Landis and Miller. None of that was carelessness, because none of it was the point. The point was a control system whose authority and whose damping could be dialled to arbitrary values in flight, so that a pilot could be handed a deliberately deficient aircraft and asked how bad it was. The standard inventory entry remains Jenkins Landis and Miller 2003 American X-Vehicles, An Inventory X-1 to X-50, the vehicle compilation is Miller 2001 The X-Planes, X-1 to X-45, and the vertical take-off context is Rogers 1989 VTOL, Military Research Aircraft.

One more thing separates it from everything before it in this series. It flew for twenty-four years on one airframe, from a first flight on 17 February 1957 to a last flight on 29 May 1981, both dates from the same inventory by Jenkins, Landis and Miller, and the research it did in its last decade would have been unintelligible to the people who built it.

The Research Question

Every article in this series so far has been about an aircraft built to go somewhere. The X-1 went faster than sound, the X-2 faster still, the X-13 went from a hover to wingborne flight and back. The X-14 was built to go nowhere in particular. Its research question is not about a region of the flight envelope at all. It is this.

How much attitude control authority does a hovering aircraft need?

Why This Could Not Be Calculated

A designer in 1955 laying out a vertical take-off aeroplane had to choose the size of its attitude control system, and there was nothing to choose it from. The physics gives an inequality but not a threshold. The aircraft must be able to arrest any disturbance it will meet, which sets a floor, and it must not spend so much of its propulsion on control that it cannot lift anything, which sets a ceiling. Writing the control power as CP, the worst disturbance the vehicle must overpower as $\ddot{\theta}_{d}$, and the thrust the control system may consume as a fraction $\beta$ of the whole,

\[\ddot{\theta}_{d} \;<\; \text{CP} \;<\; \text{CP}\big(\beta_{\max}\big), \qquad \beta_{\max} = \frac{T - W}{T} \tag{1}\]

where the upper bound is whatever control power the remaining thrust margin can buy. Between those two bounds, over more than an order of magnitude, the answer depends on whether a human being can fly it.

That is not a rhetorical difficulty. It is a structural one. The quantity being sought is a property of a closed loop containing a person, and the person’s transfer characteristics are not derivable from the airframe. Anderson 1960a examines handling-qualities criteria for vertical and short take-off aircraft at this moment, proposes a preliminary set adapted from the helicopter and aeroplane requirements, and finds the information inadequate to set a firm quantitative requirement for control power and damping about all axes. Tapscott 1960c attempts to state them and is explicit that the supporting data are thin.

The absence persisted long enough to generate a literature about the absence. Clark 1964 and Westbrook 1964 both report research on vertical take-off handling-qualities criteria rather than the criteria themselves. Curry et al. 1965 offers suggested requirements, the qualifier doing real work. Goldberger 1966 asks, four years after the X-14A’s first results, about the relative importance of the low-speed control requirement, which is not a question a settled field asks. Carpenter and Jenny 1964 proposes a statistical approach to low-speed control criteria, in effect admitting that the deterministic approach had not produced one. The same problem was recognised for spacecraft attitude control at the same time in Besco 1964, where the aerodynamic term is absent for a different reason and the human term is identical.

Why the Question Forces an Instrument

If the answer is a threshold in a human response, then locating it requires crossing it. A pilot flying an aircraft with adequate control power reports that the aircraft is adequate, which establishes an upper bound on the requirement and nothing else. To find where adequacy ends, the aircraft must be made inadequate while the pilot is flying it, and then made adequate again, and the pilot must be asked about both.

No ordinary aeroplane can do this. Its control power is a fixed consequence of its nozzle sizes, its bleed capacity, and its inertias. Changing it means rebuilding it, and rebuilding it changes twenty other things at the same time, so that a difference in pilot opinion cannot be attributed to the variable of interest.

What is required is an aircraft in which control power is an adjustable parameter and everything else is held constant. That combination defines a variable-stability aircraft. Key et al. 1965 states the case for the type directly, treating variable-stability aeroplanes as research instruments rather than as aircraft. The X-14A, the X-14 as Ames converted it, is an early instance of the type applied to the vertical take-off problem, and Hegarty et al. 1965 describes its conversion.

The technique was not new. Harper and Robert P. 1955 reports flight evaluations of longitudinal handling qualities in a variable-stability jet fighter two years before the X-14 first hovered, so the method existed and had been applied to conventional flight. What had not been done was applying it where the aerodynamic terms vanish, and the parallel attempt on a rotorcraft is Garren and Kelly 1965, which applied a model-following technique to a variable-stability helicopter for the same purpose. McGregor and Smith 1965 describes the same programme pursued independently in Canada with airborne simulators.

The Inversion This Represents

This is unusual enough to state with care, because it inverts the relationship between a research aircraft and its research question that the rest of this series has taken for granted.

In the ordinary case the aircraft is dimensioned so that it can reach the condition of interest. The X-1 carries the propellant and the structure it needs to exceed the speed of sound, and every subsystem is sized against that. The aircraft is the means and the flight condition is the end.

In the X-14 the flight condition is trivial. Hovering ten feet above a ramp at Moffett Field is not a frontier. The aircraft is not the means of reaching a condition. It is the apparatus in which a variable is swept, and the frontier it approaches is not aerodynamic but experimental. What it must do well is not fly, but change, repeatably, on command, while a pilot who knows what is being changed forms an opinion about it.

This has a consequence that runs through the article. A research aircraft built as an instrument has no mission to fail at. The flight-test record of the X-1 is a record of speeds reached. The flight-test record of the X-14 is a record of experiments run, and the interesting question about it is not whether it flew well but whether the numbers it produced were right.

Programme Origin

In the secondary account of the Virtual Aircraft Museum, Bell Aircraft received an Air Force contract for research into vertical take-off and landing in July 1955, and assembly of the Bell Model 68 prototype began within about three months. The aircraft was assigned the designation X-14 and the serial 56-4022 in the Bell X-14 entry, and only one was built, which NASA’s inventory confirms in describing the single X-14.

The Cheapest Possible Airframe

The design decisions read as parsimony and are better read as focus. Bell took the wings, ailerons, and landing gear from a Beechcraft Bonanza and the tail surfaces from a T-34 Mentor, in the secondary account of the Bell X-14 entry, and built a new fuselage of duralumin around two turbojets mounted side by side, with their thrust diverters at the centre of mass. NASA’s own history of Ames flight research, by Borchers, Franklin and Fletcher, describes the configuration instead as built from a Beech T-34 wing and tail. The T-34 was derived from the Bonanza, so the two accounts may name one wing by two parents, and the record available here does not settle which part numbers were used. The cockpit was open. The undercarriage was fixed.

Every one of those choices removes a variable that the experiment does not care about and would have had to pay for. A retractable undercarriage would have added weight to an aircraft whose research programme was bounded by its thrust margin, and would have bought speed the programme had no use for. Borrowed wings from a light aircraft in production removed a design and stress-analysis task whose outcome the experiment was indifferent to.

The contrast with the X-13 is instructive. Ryan built a purpose-designed delta airframe to demonstrate a manoeuvre, and the airframe was the demonstration. Bell built a parts-bin airframe to carry a control system, and the control system was the point. Both are correct engineering, and the difference between them is entirely a difference in what was being asked.

The Two Institutions

The programme has a clean division. The Air Force paid for an aircraft that could hover and transition, and Bell delivered one that had completed hovering and transitional flight before its transfer, as Rolls 1965b records. What the aircraft then did for twenty-two years was decided elsewhere.

Rolls 1965b places the transfer to the Ames Research Center of NASA, the National Aeronautics and Space Administration, at Moffett Field in late 1959. The Virtual Aircraft Museum gives the date as 2 October 1959. It stayed at Ames for the rest of its flying life. Ames was not interested in the X-14 as a vertical take-off aeroplane. It was interested in it as a flying laboratory for handling qualities, the purpose Rolls 1960 gives for its conversion, and handling qualities were a subject Ames had already been pursuing with fixed-wing aircraft. Creer et al. 1959 is a pilot-opinion study of lateral control requirements for fighters published the same year the X-14 arrived, and stands as the methodological ancestor of everything the X-14 subsequently did. The method was established. What was missing was a vehicle that could apply it to hovering.

The Aircraft Was Not Alone

The X-14A was an early variable-stability aircraft applied to the hovering problem and it was not the last. Naming the family it belongs to establishes that the method rather than the aircraft was the durable contribution.

Key et al. 1965 treats the flight research use of variable-stability aeroplanes for vertical take-off flying qualities. Eney 1967 reports Navy variable-stability studies of longitudinal handling qualities, and Rhoads 1967 an in-flight simulation and pilot evaluation of landing approach handling qualities, extended in Rhoads 1970 to cockpit controller configurations. Newell et al. 1963 describes a variable-drag device fitted to a variable-stability aircraft, which indicates how far the technique was pushed beyond attitude dynamics.

The type spread to large aircraft as well as small. Person and Robbins 1965 and Baska and Robbins 1966 describe the variable-stability simulation system fitted to a Boeing 367-80, first for a supersonic transport programme and then for a large transport programme, and Condit et al. 1966 compares in-flight against ground-based simulation of the handling qualities of very large aeroplanes in landing approach. Motyka 1975 assesses a T-2 as a high-angle-of-attack in-flight simulator, carrying the technique into a third regime where the aerodynamics misbehave.

The control law itself became a subject. Merrick 1977 studies an implicit model-following controller applied to lift-fan vertical take-off aircraft, Deets 1978 compares optimal-regulator and conventional setup techniques for a model-following simulator control system, and Takahashi et al. 1994 develops a model-following law for in-flight simulation two decades later. The X-14B’s digital system sits in the middle of that development rather than at the end of it.

The direct successor for the vertical take-off problem was the X-22A, a tilting-ducted-propeller research aircraft described in Marchese 1963 and whose variable-stability capabilities for flying-qualities work are reported in Aiken et al. 1977. Smith et al. 1973 reports a flight investigation of longitudinal short-term dynamics for short take-off landing approaches using it, and Smith 1974 summarises the flying-qualities research the aircraft supported. The X-22A could do what the X-14 did, and its existence from the late 1960s onward is plausibly part of why the X-14B’s later work moved toward control-law concepts rather than toward refining the original criteria, although no source here states that motive.

The helicopter branch of the same family is reviewed in Hindson 1982, which considers past applications and future potential of variable-stability research helicopters, and continues in Watson and Hindson 1988 on rotorcraft pitch-roll cross coupling. A helicopter has aerodynamic damping a jet-lift aircraft lacks, so the two branches are not interchangeable, but the method is identical.

What the Field Already Knew in 1955

What was and was not available when Bell began needs recording, because the X-14’s contribution is easy to overstate.

The configuration question had been worked over thoroughly. Boeing Co Morton Pa Vertol Div 1956 and Irvin and Swan 1956 compare types and estimate weights for competing vertical take-off transport layouts, and McCormick and Mallen 1956 treats tilt-wing design considerations. The field had a textbook within a few years in Campbell 1962, a conference compilation in Conference on V/Stol Aircraft 1960, the aerodynamics of propeller-driven configurations in Kirby 1961, and a survey of low-disc-loading designs in Brown 1965. The tilt-wing branch alone supported Nichols 1963, Martin 1963a, Tosti 1961, and Longhurst 1966. Everyone knew how to lay out a vertical take-off aircraft. Nobody knew how to size its control system.

The hovering-stability problem had also been posed cleanly, though for rotorcraft rather than for jets. Miller 1948 treats helicopter control and stability in hovering flight, and the subject was worked over through Payne 1955 and Bramwell 1956. The flying-platform experiments of Albachten 1956 and Sissingh 1956 address hovering stability for a vehicle with no wing at all. What none of these could supply is the jet-lift case, in which there is no rotor to provide damping and no propeller slipstream to provide control.

The problem of attitude control on a jet-lift aircraft was recognised and named. Baxter and Finvold 1958 addresses jet engine control and attitude control in vertical-attitude aircraft, the same problem in the tail-sitting configuration the X-13 used. Scale-model work was underway, including the free-flight tests of a one-fifth-scale Ryan X-13 model reported in Smith 1958b.

The X-14 supplied what was missing, and Anderson 1960a and Tapscott 1960b both say so in the same year, the first by proposing preliminary criteria and finding the information too thin to fix control power and damping quantitatively, and the second by proposing criteria and being explicit about the thinness of the supporting data.

Sizing From First Principles

The keystone relationship is short enough to write in one line and deserves care, because almost everything that follows is a consequence of it.

Control Power Is an Acceleration

The moment a control system can produce is a force multiplied by a distance. What matters to the pilot is not that moment but the angular acceleration it produces, because the pilot is closing a loop on attitude. So the quantity of interest is

\[\text{CP} = \frac{M_{\text{control}}}{I} \tag{2}\]

where $M_{\text{control}}$ is the maximum moment the control system can generate about an axis and $I$ is the moment of inertia about that axis. The units are radians per second squared. Greif et al. 1972 defines it in these terms, as control moment divided by moment of inertia.

The inertias and derivatives that populate this relation were themselves a measurement problem. Rampy 1966 identifies which stability derivatives matter in hover and transition, and the techniques for obtaining them are treated in Barzda 1966 on low-frequency oscillation methods, Owen and Cox 1966 on measuring oscillatory derivatives on jet-blowing models, and Williams and Butler 1964 on the wind-tunnel techniques the field depended on.

For a pair of nozzles acting differentially at a distance $\ell$ either side of the centre of mass, the moment is

\[M_{\text{control}} = 2 F \ell \tag{3}\]

so the control power delivered by a given nozzle thrust is

\[\text{CP} = \frac{2 F \ell}{I} \tag{4}\]

This normalisation is the reason the X-14’s results transfer to other aircraft at all. A moment expressed in newton metres is a fact about one airframe. The same moment divided by that airframe’s inertia describes how quickly attitude responds, and a pilot flying two different aircraft with the same control power and the same damping is, to a first approximation, flying the same aircraft. The criterion is stated in radians per second squared precisely so that it can be carried from the vehicle that measured it to vehicles that did not.

The claim being made is that the pair of numbers is sufficient. Two aircraft whose attitude dynamics satisfy

\[\ddot{\theta}_{1} = \text{CP} \, u - \frac{D}{I}\dot{\theta}_{1}, \qquad \ddot{\theta}_{2} = \text{CP} \, u - \frac{D}{I}\dot{\theta}_{2} \tag{5}\]

with the same CP and the same $D/I$ produce identical attitude histories for identical inputs, whatever their masses, spans, or nozzle arrangements. The whole transferability of the criterion rests on that statement and on nothing else, and the places where it fails are the subject of a later section.

The Second Variable Is Damping

Control power alone does not determine the response. An aircraft whose attitude rate is opposed by a restoring effect behaves differently from one whose attitude rate is opposed by nothing. In hovering flight the aerodynamic damping is negligible, because damping in pitch and roll comes from the change in local incidence produced by rotation, and at zero airspeed there is no incidence to change. So the damping present in a hover is whatever the control system synthesises.

Writing the attitude dynamics about one axis with a rate-proportional term,

\[I \ddot{\theta} = M_{\text{control}} - D \dot{\theta} \tag{6}\]

and dividing by the inertia,

\[\ddot{\theta} = \text{CP} \, u - \frac{D}{I} \dot{\theta} \tag{7}\]

where $u$ is the normalised control input between minus one and one and $D/I$ has units of inverse seconds. The pair of numbers CP and $D/I$ specifies the attitude response, and the X-14A’s experimental programme was a sweep over that pair.

Transforming gives the attitude response to control as

\[\frac{\theta(s)}{u(s)} = \frac{\text{CP}}{s\left(s + \dfrac{D}{I}\right)} \tag{8}\]

which has a pole at the origin and a second at the damping value, so the system carries a characteristic time

\[\tau = \frac{I}{D} = \left(\frac{D}{I}\right)^{-1} \tag{9}\]

The three dampings the X-14A flew in its lateral experiments, listed in table II of Drinkwater et al. 1965 as 0.55, 1.75, and 2.9 per second, correspond to

\[\tau = \frac{1}{0.55} = 1.82 \text{ s}, \qquad \tau = \frac{1}{1.75} = 0.571 \text{ s}, \qquad \tau = \frac{1}{2.9} = 0.345 \text{ s} \tag{10}\]

The angular rate following a step of full control approaches its limit exponentially,

\[\dot{\theta}(t) = \frac{\text{CP}}{D/I}\left(1 - e^{-t/\tau}\right) \tag{11}\]

and the steady rate reached at full control is the ratio of the two,

\[\dot{\theta}_{\text{max}} = \frac{\text{CP}}{D/I} \tag{12}\]

a relation that prevents the two parameters from being varied entirely independently in their effect on what the pilot sees. Raising the damping at fixed control power lowers the achievable rate. At the maximum control power the three flown dampings give

\[\frac{2.0}{0.55} = 3.64 \text{ rad/s}, \qquad \frac{2.0}{1.75} = 1.14 \text{ rad/s}, \qquad \frac{2.0}{2.9} = 0.690 \text{ rad/s} \tag{13}\]

or 208, 65.5, and 39.5 degrees per second. At the lowest damping the steady rate is far beyond anything a hovering pilot would use, so there the damping acts only through the transient. At the highest damping it does not, because the steady rate itself is modest, and the damping then limits the rate the pilot can reach as well as shaping how it is reached.

With no damping at all the attitude is a pure double integrator,

\[\ddot{\theta} = \text{CP} \, u \quad \Longrightarrow \quad \theta(t) = \tfrac{1}{2}\,\text{CP}\, t^{2} \tag{14}\]

so a second of full control at 2.0 radians per second squared banks the aircraft through

\[\tfrac{1}{2} \times 2.0 \times 1^{2} = 1.0 \text{ rad} = 57.3 \text{ degrees} \tag{15}\]

This is the condition a hovering jet-lift aircraft is in unless something synthesises damping for it, and it should be kept in mind, because it decides the order of the loop the pilot is closing.

What the Control Power Was Bought With

On the X-14 the attitude control moments came from compressed air bled from the compressors of the turbojets and ejected through nozzles at the wingtips and the tail. Drinkwater et al. 1965 describes the arrangement and Hegarty et al. 1965 gives its design, and Keller 1969 and Friend 1964 treat reaction controls for jet-lift aircraft as a design problem in their own right. Patierno and Asdurian 1965 states the trade in its title, addressing the impact of control provisions on the mission performance of jet vertical take-off aircraft using reaction control systems, which is the subject of the next several pages here. The effectiveness of such jets was still being measured in the wind tunnel a quarter of a century later in Riley et al. 1989, for the hover and transition of a short take-off vertical landing fighter concept.

One property of a reaction control system that this article does not otherwise treat deserves naming, because it bears on the fan result below. A nozzle valve that is effectively on or off rather than proportional makes the closed loop a relay system, and relay systems limit-cycle. Dahl et al. 1962 analyses limit cycles in reaction-jet attitude control subject to external torques, the failure mode a bang-bang attitude control invites.

The thrust of a reaction nozzle follows from the mass flow through it and the velocity at which that mass leaves,

\[F = \dot{m} \, v_{e} \tag{16}\]

and for a choked convergent nozzle supplied at total temperature $T_{0}$ the exit velocity is set by the temperature and the gas properties,

\[v_{e} = \sqrt{\frac{2 \gamma}{\gamma + 1} R T_{0}} \tag{17}\]

so that hotter bleed gives more thrust per unit of mass flow. The mass flow, for a choked convergent nozzle of throat area $A$ supplied at total pressure $p_{0}$, is

\[\dot{m} = A \, p_{0} \sqrt{\frac{\gamma}{R T_{0}}} \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{2(\gamma - 1)}} \tag{18}\]

and the thrust per unit mass flow, the figure of merit for the arrangement, is just the exit velocity,

\[\frac{F}{\dot{m}} = v_{e} \tag{19}\]

The design freedom ends there, and it amounts to little, because the bleed temperature is whatever the compressor stage delivers. The X-14A’s figures are given in the design report of its variable-stability system by Hegarty et al. 1965. A constant ten percent of the 85.0 pounds per second flowing through both engines, or 8.5 pounds per second, was bled for all reaction control, which the report notes was more than the engine manufacturer recommended and was judged permissible for short flights. After the losses in ports, valves and ducts the air reached the nozzles at 76.0 pounds per square inch absolute and 939 degrees Rankine. A sonic nozzle discharging to the atmosphere also produces a pressure thrust beyond $\dot{m}\,v_{e}$, and the report’s relation, which includes it, is

\[F = C_{v}\,C_{d}\,A\,p_{0}\left(1.268 - \frac{p_{a}}{p_{0}}\right) \tag{20}\]

with a discharge coefficient $C_{d}$ of 0.90 and a velocity coefficient $C_{v}$ of 0.95, both from test data, a total exit area $A$ of 7.17 square inches, and an atmospheric pressure $p_{a}$ of 14.7 pounds per square inch. It gives

\[F = 0.95 \times 0.90 \times 7.17 \times 76 \times \left(1.268 - \frac{14.7}{76}\right) = 500.7 \text{ pounds} \tag{21}\]

So the whole of the X-14A’s attitude control in a hover, in all three axes and for the pilot’s nozzles and the variable-stability nozzles together, came to about five hundred pounds of reaction force bought with a tenth of the engines’ airflow.

The important point is not how the nozzle works but where the mass flow comes from. It comes out of the engine, and the engine was going to use it to make lift.

The Price of Control, Fixed by an Experiment

The cost of bleed in thrust is hard to isolate by measurement, because separating it from every other installation effect requires running the same engine in the same aircraft with two different bleed schedules. The X-14A programme did something close to that, for a different reason, and the result bounds the price.

Gerdes and Rolls 1969 reports flight tests of tip-turbine-driven fans fitted at the wingtips as an alternative lateral control effector. The fans were rejected, for reasons taken up later in this article, but the report states that for equal thrust they required less than half the bleed air of the reaction nozzles, that the total bleed requirement would therefore fall by about 20 percent, and that the engines would then produce 4 percent more thrust.

Those statements can be combined with the ten percent bleed of the design report. The bleed removed is

\[\Delta\beta = 0.20 \times 0.10 = 0.020 \tag{22}\]

of the engines’ airflow. Writing the thrust as falling linearly with the bled fraction $\beta$ at a rate $s$,

\[T = T_{0}\,(1 - s\,\beta) \tag{23}\]

the reported gain $\delta$ on reducing the bleed by $\Delta\beta$ satisfies

\[\frac{1 - s\,(\beta - \Delta\beta)}{1 - s\,\beta} = 1 + \delta \quad \Longrightarrow \quad s = \frac{\delta}{\Delta\beta + \delta\,\beta} \tag{24}\]

and substituting the reported four percent,

\[s = \frac{0.04}{0.020 + 0.04 \times 0.10} = \frac{0.04}{0.024} = \frac{5}{3} = 1.67 \tag{25}\]

Each percent of airflow bled cost about one and two thirds percent of thrust. That is the expected direction, because bled air has been compressed at the engine’s expense and then leaves without passing through the turbine and the propelling nozzle. Assuming the same rate holds over the whole bleed, which neither report states, the full ten percent cost

\[s\,\beta = \frac{5}{3} \times 0.10 = \frac{1}{6} = 0.167 \tag{26}\]

of the thrust the engines would otherwise have produced. Had the thrust fallen only in proportion to the air removed, the cost would have been 0.10, and that is a floor. So the reaction control system on the X-14A consumed between a tenth and a sixth of the engines’ thrust, with a sixth the better estimate. The rest of the analysis in this article uses both figures, and the linear rate behind the larger is listed among the article’s assumptions.

What a Sixth of the Thrust Costs a Hovering Aircraft

A sixth of the thrust sounds tolerable. For a hovering aircraft it is not, and the reason is that a hovering aircraft’s useful output is not its thrust but the difference between its thrust and its weight,

\[\Delta T = T - W \tag{27}\]

which for a machine with a thrust-to-weight ratio near unity is a small difference of two large numbers and is therefore extremely sensitive to any deduction from either.

During the lateral control experiments the X-14A weighed 3,700 pounds and had a thrust-to-weight ratio available of 1.1 to 1.2, which Drinkwater et al. 1965 states directly. Its two General Electric J85-GE-5 engines were rated at 2,680 pounds of thrust each in the General Electric J85 entry, or 5,360 pounds together, so the uninstalled thrust-to-weight ratio was

\[\frac{T_{\text{uninstalled}}}{W} = \frac{5{,}360}{3{,}700} = 1.449 \tag{28}\]

against an available 1.1 to 1.2. Defining the installation efficiency as the ratio of what the aircraft got to what the engines were rated at,

\[\eta_{\text{inst}} = \frac{T_{\text{available}}}{T_{\text{uninstalled}}} \tag{29}\]

the two reported bounds give

\[\eta_{\text{inst}} = \frac{1.1 \times 3{,}700}{5{,}360} = 0.759, \qquad \frac{1.2 \times 3{,}700}{5{,}360} = 0.828 \tag{30}\]

The installation therefore lost between 17.2 and 24.1 percent of the engines’ rated thrust, and the bleed for the attitude controls is most of that loss. The thrust diverters cost the rest. Loscutoff et al. 1973 reports a diverter efficiency $\eta_{d}$ of 0.91 for the X-14B, and applying it to the earlier aircraft, which is an assumption, the bleed estimate and the diverters together leave

\[\eta_{d}\,(1 - s\,\beta) = 0.91 \times \left(1 - \tfrac{1}{6}\right) = 0.758 \tag{31}\]

matching the lower of the two reported bounds.

Now take the margin. At a thrust-to-weight ratio of 1.2 the aircraft can lift 740 pounds beyond its own weight. On the estimate the bleed costs

\[\tfrac{1}{6} \times 5{,}360 = 893 \text{ pounds of thrust} \tag{32}\]

so without it the margin would have been 1,633 pounds. The attitude control system consumed 54.7 percent of the aircraft’s hover margin. At a thrust-to-weight ratio of 1.1 the margin after bleed is 370 pounds, the margin before bleed would have been 1,263, and the control system consumed 70.7 percent of it.

\[\frac{893}{1{,}263} = 0.707, \qquad \frac{893}{1{,}633} = 0.547 \tag{33}\]

On the proportional floor the bleed costs $0.10 \times 5{,}360 = 536$ pounds and the shares become

\[\frac{536}{906} = 0.592, \qquad \frac{536}{1{,}276} = 0.420 \tag{34}\]

A designer would use the general form rather than the two numbers, so it is given here. If the control system takes a fraction $\beta$ of the uninstalled thrust and the aircraft is left with a thrust-to-weight ratio $r$, the share of the pre-bleed margin that the control system consumed is

\[\Phi = \frac{\beta \, T_{0}}{(r - 1) W + \beta \, T_{0}} \tag{35}\]

The denominator contains $r - 1$, and the difficulty lies there. As the thrust-to-weight ratio approaches unity the margin vanishes while the bleed does not, so $\Phi$ approaches one and the control system consumes everything.

This is the central result of the article’s sizing analysis and it deserves stating plainly. More than half of everything the X-14A could lift beyond its own weight was spent on being controllable, and not less than two fifths even on the most favourable reading. Not on payload, not on fuel, not on range. On the ability to point.

Hoffman 1971 treats this cost as a separate subject under the title of control power costs, which indicates that by 1971 the field understood the trade as central rather than incidental.

The Floor Set by Disturbances

The analysis so far gives the price of control power. It does not say how much is needed, and the lower bound comes from a different place, which is that the aircraft must be able to overpower whatever is trying to upset it.

A hovering aircraft in a wind experiences a moment it did not ask for. The control system must be able to cancel that moment and still have authority left over for the pilot to manoeuvre with, so the requirement is not that control power exceed the disturbance but that it exceed it by enough.

How large was that moment? The answer is not what the framing suggests. A steady wind of speed $V_{w}$ acting on a side area $S_{s}$ produces a force

\[F_{w} = \tfrac{1}{2}\rho V_{w}^{2} S_{s} C_{D} \tag{36}\]

and at ten metres per second on a representative eight square metres at a drag coefficient of 0.8 that is

\[F_{w} = \tfrac{1}{2} \times 1.225 \times 100 \times 8 \times 0.8 = 392 \text{ N} \tag{37}\]

As an attitude disturbance this is modest. Acting through an offset of a metre on the roll inertia of 1,586 kilogramme metres squared that the design report gives, taken up below, it produces

\[\frac{392 \times 1.0}{1{,}586} = 0.247 \text{ rad/s}^{2} \tag{38}\]

which is 12.4 percent of the maximum control power. The flight reports say the same thing qualitatively. Drinkwater et al. 1965 notes that the X-14A, which is not self-disturbing in a hover, could be held over a spot using a small fraction of the control power required for manoeuvres. As a translational disturbance it is not trivial at all. The same force accelerates the aircraft at

\[a_{w} = \frac{392}{1{,}678} = 0.234 \text{ m/s}^{2} \tag{39}\]

and holding station against it requires a permanent tilt into wind of

\[\theta_{\text{trim}} = \arctan\frac{a_{w}}{g} = \arctan\frac{0.234}{9.807} = 1.36^{\circ} \tag{40}\]

while leaving it uncorrected for ten seconds costs

\[\tfrac{1}{2} \times 0.234 \times 100 = 11.7 \text{ m} \tag{41}\]

The wind is a position problem and not an attitude problem, the same conclusion the previous article reached for the X-13 by a different route and on a differently shaped aircraft. The disturbance that sizes the control power is therefore the gust and the manoeuvre rather than the steady wind, and the experimental ratio below encodes that.

The field settled on a working ratio and it can be read off the experimental design. Greif et al. 1972 held peak disturbance strength at 0.32 radians per second squared against a maximum roll control power of 0.8, and states the ratio explicitly as four tenths of the maximum. Writing the disturbance as a fraction $\sigma$ of the available control power,

\[\ddot{\theta}_{\text{disturbance}} = \sigma \, \text{CP}, \qquad \sigma = 0.4 \tag{42}\]

the authority available to the pilot is what remains,

\[\text{CP}_{\text{pilot}} = (1 - \sigma) \, \text{CP} \tag{43}\]

Sixty percent of the control power reaches the pilot and forty percent is spent standing still. At the X-14A’s maximum of 2.0 radians per second squared this leaves 1.2, and at its minimum of 0.8 it leaves 0.48.

\[0.6 \times 2.0 = 1.2, \qquad 0.6 \times 0.8 = 0.48 \tag{44}\]

This compounds with the bleed cost in an unpleasant way. The aircraft surrenders between two fifths and seven tenths of its hover margin to buy control power, and then surrenders two fifths of the control power it bought to the disturbance. The two fractions multiply,

\[\Phi \times (1 - \sigma) \tag{45}\]

giving, at the two reported thrust-to-weight ratios,

\[0.707 \times 0.6 = 0.424, \qquad 0.547 \times 0.6 = 0.328 \tag{46}\]

on the estimate of the bleed cost. So between 33 and 42 percent of the aircraft’s pre-bleed hover margin was spent on manoeuvring authority in the pilot’s hands, a further $0.4\,\Phi$, or 22 to 28 percent, on standing still against disturbances, and only the remaining $1 - \Phi$, or 29 to 45 percent, was left as margin. The pilot’s share is small through two independent multiplications rather than one.

The Inertias, From the Design Report

The article needs the aircraft’s inertias to say anything quantitative about what the tested control powers meant in terms of force, and the design report of the variable-stability system states them. Hegarty et al. 1965 sizes every nozzle from

\[F = \frac{I\,\alpha}{L} \tag{47}\]

where $F$ is the net reaction force a nozzle produces about an axis, $I$ the moment of inertia about that axis, $\alpha$ the angular acceleration wanted, and $L$ the moment arm. It uses a roll inertia of 1,170 slug square feet, a pitch inertia of 1,990, and a yaw inertia of 2,920, with a wingtip arm of 16.9 feet and a tail arm of 18.75 feet. In SI units the roll inertia is

\[I_{x} = 1{,}170 \times 1.356 = 1{,}586 \text{ kg m}^{2} \tag{48}\]

The report divides its 500.7 pounds of reaction force so that the pilot’s nozzles give 1.84 radians per second squared in roll, 0.92 in pitch, and 0.52 in yaw, and the variable-stability nozzles nine tenths of each, 1.66, 0.83, and 0.47. Its roll figure checks against the relation,

\[F_{r} = \frac{1{,}170 \times 1.84}{16.9} = 127.4 \text{ pounds} \tag{49}\]

against the 127.2 pounds the report lists.

At the 3,700 pound test weight, a mass of 115.0 slugs, the roll radius of gyration is

\[k_{x} = \sqrt{\frac{I_{x}}{m}} = \sqrt{\frac{1{,}170}{115.0}} = 3.19 \text{ ft} \tag{50}\]

or, against the span of 33.83 feet that Hoffman et al. 1972 gives,

\[\frac{k_{x}}{b} = \frac{3.19}{33.83} = 0.094 \tag{51}\]

The second primary source disagrees by a factor of two. Hoffman et al. 1972, which writes the X-14’s equations of motion at a weight of 4,182 pounds in the X-14B period, gives a roll inertia of 2,340 slug square feet, with 3,400 in pitch and 5,400 in yaw. At its mass of 129.9 slugs that is a radius of gyration of

\[k_{x} = \sqrt{\frac{2{,}340}{129.9}} = 4.24 \text{ ft}, \qquad \frac{k_{x}}{b} = \frac{4.24}{33.83} = 0.125 \tag{52}\]

The two weights differ by 482 pounds, which cannot obviously account for a doubling of the roll inertia, and neither report explains its value, so this article carries both. The 1965 figures belong to the aircraft that flew the lateral experiments and are used below. Every force derived from them would be larger by the ratio of the inertias if the later value applied to the earlier aircraft.

The tip-fan report does not support reading the fans as sized to the maximum tested control power. Gerdes and Rolls 1969 specified each fan at 150 pounds of thrust on minimum bleed, and the X-14A with the fans installed reached a maximum roll control power of 0.65 radians per second squared, against 0.70 for the basic reaction nozzles without the variable-stability nozzles. The report attributes the lost roll performance to the lag of the fan control system and to the increase in roll inertia that the fans added at the wingtips. The 0.70 it gives for the basic nozzles is also well below the 1.84 of the 1965 design, a difference the sources consulted leave unexplained. What the report does state is the motive, which was to supply sufficient control power without the severe performance penalty that large amounts of bleed impose. Bleed, and not control power, was understood as the binding constraint, and the fan programme is the evidence of it.

Why Control Power Gets Harder as Aircraft Get Bigger

The relation for control power can be pushed through a scaling argument, and the result explains a great deal about why jet-lift vertical take-off never grew.

With reaction nozzles at the wingtips the control moment is the differential force multiplied by the span,

\[M = F b \tag{53}\]

and the inertia is the mass multiplied by the square of a radius of gyration that is itself proportional to span,

\[I_{x} = m k_{x}^{2}, \qquad k_{x} \propto b \tag{54}\]

so the control power is

\[\text{CP} = \frac{M}{I_{x}} \propto \frac{F b}{m b^{2}} = \frac{F}{m b} \tag{55}\]

A hovering aircraft has thrust proportional to weight and therefore to mass,

\[T \approx W = m g \quad \Longrightarrow \quad T \propto m \tag{56}\]

and at a fixed bleed fraction the reaction force is proportional to thrust,

\[F = \beta \, T \propto \beta \, m g \tag{57}\]

so $F \propto m$ and

\[\text{CP} \propto \frac{1}{b} \tag{58}\]

Control power at a fixed bleed fraction is inversely proportional to span. Doubling the linear size of a jet-lift aircraft halves its control power, and holding the control power fixed requires doubling the bleed fraction.

The consequences are severe and they are arithmetic. The pilot’s nozzles on the X-14A carried 97.8 pounds of pitch force and 127.2 pounds of roll and yaw force out of the 500.7 pounds in the design report of Hegarty et al. 1965. At a common pressure and temperature both the force and the airflow of a sonic nozzle are proportional to its exit area, so the pilot’s set used a share

\[\frac{97.8 + 127.2}{500.7} = 0.449 \tag{59}\]

of the bleed, or 4.49 percent of the airflow, and at the estimated rate $s$ it cost

\[1.67 \times 0.0449 = 0.0749 \tag{60}\]

of the thrust, to give 1.84 radians per second squared in roll at a span of 10.31 metres. Holding that control power, the same accounting at twice the span costs 15.0 percent, at three times 22.5 percent, and at four times 30.0 percent.

\[\beta(b) = 0.0749 \times \frac{b}{10.31} \tag{61}\]

Set that against the thrust margin available. Take a jet-lift aircraft with twenty percent of thrust to spare over its weight, a generous figure assumed here rather than taken from any aircraft. The bleed consumes the whole of the margin at

\[b = 10.31 \times \frac{0.20}{0.0749} = 27.5 \text{ m} \tag{62}\]

or at 45.9 metres on the proportional floor. A jet-lift aircraft with bleed-fed reaction controls at the wingtips runs out of aircraft somewhere between about twenty-eight and forty-six metres of span.

The largest jet-lift aircraft that NASA flight-tested did not pay this price, and the way it avoided it is the confirmation. The Dornier Do 31 spanned 17.0 metres and weighed about 45,000 pounds, according to Holzhauser et al. 1972, and at that span the relation demands 12.3 percent of thrust for 1.84 radians per second squared. The Do 31 produced its rolling moments instead by differential thrust between two wingtip pods, each holding four lift engines of 4,200 pounds, and used bleed reaction controls only for pitch. It installed 0.8 radians per second squared in roll, the bottom of the X-14A’s range, which its pilots rated satisfactory with its attitude-command stabilisation engaged, and the report recommends no significant reduction for its class. The type answered the scaling problem by putting engines at the wingtips and by stabilising attitude, not by bleeding more air.

The contemporary literature took up the same question. Johnston and Friend 1965 is titled for the effect of size on hover and low-speed handling qualities, and Johnston et al. 1965 reports a study of size effects on vertical take-off handling-qualities criteria in the same year. Two papers on the size dependence within three years of the X-14A’s first results is not a coincidence, and it indicates the field had recognised the scaling problem as soon as it had a criterion to scale.

The reappraisals that followed carry the same concern. Smith 1966c revisits the requirements four years after they were determined, Hoffman 1971 treats the cost of control power as a subject in itself, and Stevens and Roskam 1985 is still investigating vertical-axis control power requirements for shipboard landing two decades later.

What the Criterion Costs an Arbitrary Aircraft

The scaling relation can be turned into the calculation a designer would have performed, the calculation the X-14A’s number existed to enable.

Take an aircraft of mass $m$ and span $b$ whose roll radius of gyration is a fraction $\kappa_{r}$ of its span, with reaction nozzles at the wingtips acting through a moment arm of half the span, as the X-14A’s 16.9 foot arm on a 33.83 foot span nearly is. Meeting a control power CP requires a net differential tip force of

\[F_{\text{tip}} = \frac{\text{CP} \, m \, \kappa_{r}^{2} b^{2}}{b/2} = 2\,\text{CP}\, m \, \kappa_{r}^{2}\, b \tag{63}\]

The force grows with the product of mass and span, the scaling result in the form a designer meets it. With the value of $\kappa_{r}$ from the 1965 inertias, 0.0943, this reproduces the X-14A’s 127.2 pounds of roll force at 1.84 radians per second squared. The agreement checks consistency and adds no new result, because the constant comes from that aircraft.

Applied to larger aircraft the numbers become difficult very quickly. At the Do 31’s span of 17.0 metres and its landing mass of about 18,500 kilogrammes, with the X-14A’s proportions,

\[F_{\text{tip}} = 2 \times 2.0 \times 18{,}500 \times 0.0943^{2} \times 17.0 = 11{,}187 \text{ N} = 2{,}515 \text{ pounds} \tag{64}\]

for 2.0 radians per second squared, and 1,006 pounds for the 0.8 the Do 31 actually installed. Hoffman’s later inertias would raise both by a factor of 1.77. That is a small jet engine at the end of each wing, purely to point the aircraft, and the Do 31 carried such engines, four to a pod. The conclusion drawn earlier from the bleed fraction is the same conclusion reached from the force, and reaching it twice by different routes is the reason this article treats the scaling result as the most durable thing the X-14’s numbers imply.

What the Bleed Bought

One ratio states the efficiency of the arrangement. The X-14A surrendered an estimated 893 pounds of engine thrust, and at least 536, to obtain 500.7 pounds of reaction force across all three axes and both nozzle sets.

\[\frac{500.7}{893} = 0.561, \qquad \frac{500.7}{536} = 0.934 \tag{65}\]

Between a half and nine tenths of a pound of control force for every pound of thrust given up. It is a poor exchange rate, and the tip-turbine fans were built to improve it.

Dependent Systems

Each subsystem was dimensioned against the keystone, and the ordering below follows dependency, not convention. The propulsion determines the control authority available, the control authority determines what the variable-stability system can synthesise, and what it can synthesise determines the experiment.

Propulsion and the Diverter

The aircraft was re-engined twice, and neither change was about performance in the ordinary sense.

The original X-14 flew on two Armstrong Siddeley Viper ASV.8 turbojets, as Rolls 1960 names them, and NASA’s later history by Borchers, Franklin and Fletcher calls them Bristol-Siddeley Vipers. Sources disagree on their rating. The Armstrong Siddeley Viper entry rates the ASV.8 at 1,750 pounds of thrust, and the Virtual Aircraft Museum gives 707 kilogrammes, or about 1,560 pounds. The disagreement matters, and this article does not resolve it, because both figures produce the same conclusion.

At 1,750 pounds each the pair gives 3,500 pounds. At 1,560 each the pair gives 3,120. Against the 3,700 pound weight at which the aircraft later did its research, those are thrust-to-weight ratios of

\[\frac{3{,}500}{3{,}700} = 0.946, \qquad \frac{3{,}120}{3{,}700} = 0.843 \tag{66}\]

Both are below one. The original X-14 could not have hovered at the weight the X-14A hovered at, on either reading of its engine rating, and that is before any allowance for bleed or for the losses in turning the exhaust. Whatever the aircraft did in 1957 and 1958, it did light, and the margin was not a margin in any useful sense.

Replacing the Vipers with two General Electric J85-GE-5 engines at 2,680 pounds each raised the uninstalled ratio to 1.449, and the later J85-GE-19 installation at 3,015 pounds each raised it to 1.630, on the ratings in the General Electric J85 entry. The re-engining was not an upgrade to an aircraft that already worked. It was the precondition for the research programme existing at all, and the primary record says so. Rolls 1960 reports that the original X-14 lacked sufficient control power because of the limited bleed air available, and that the conversion to a variable-stability aircraft was possible because of the greater bleed capacity of the J85-5, which also gave more thrust for less weight. Hegarty et al. 1965 puts the gain at 25 percent more thrust for about 400 pounds less weight, and Borchers, Franklin and Fletcher gives the purpose as increasing the thrust margin for hover. A variable-stability aircraft must be able to give away control power to the experiment and still fly, and an aircraft with no bleed and no thrust margin has nothing to give away.

The exhaust was turned by cascade-type diverters at the centre of mass, which the pilot could set for any direction between vertical and horizontal thrust, as Rolls 1960 describes. The device had a research literature, including Erwin et al. 1964 on a tandem cascade thrust-vectoring programme and Davis and Spicer 1965 on determining the thrust vector of a fixed-nozzle engine on a six-component stand, the measurement problem that turning the exhaust creates. The wider principle of an engine that supplies both lift and thrust is set out in Denning 1962, and the control of engines used this way in Sellers and Szuch 1973. The propulsion requirements of the configuration as a class are treated in Kohn 1972 on military propulsion system design and Ciepluch et al. 1979 on propulsion technology.

Turning a jet through ninety degrees is not free. Writing the turning efficiency as $\eta$, the vertical thrust available is

\[T_{v} = \eta \, T \tag{67}\]

and combining that with the bleed gives the thrust available for lifting,

\[T_{\text{lift}} = \eta \, (1 - s\,\beta) \, T \tag{68}\]

During the transition the diverter sits at intermediate angles, and the thrust splits into components. At a deflection $\delta$ measured from the vertical,

\[T_{v} = \eta \, T \cos\delta, \qquad T_{h} = \eta \, T \sin\delta \tag{69}\]

so the vertical component the aircraft still needs to support itself and the horizontal component that accelerates it are not independent,

\[\left(\frac{T_{v}}{\eta T}\right)^{2} + \left(\frac{T_{h}}{\eta T}\right)^{2} = 1 \tag{70}\]

The aircraft cannot accelerate forward without giving up lift, which is why the transition has to be flown as a trajectory rather than as a switch, and why a thrust-to-weight ratio comfortably above one is needed to fly it at all.

At the diverter efficiency of 0.91 that Loscutoff et al. 1973 reports for the X-14B, and the estimated bleed cost of a sixth, the J85-GE-5 installation yields

\[\frac{T_{\text{lift}}}{W} = 0.91 \times \left(1 - \tfrac{1}{6}\right) \times \frac{5{,}360}{3{,}700} = 1.099 \tag{71}\]

against a reported available ratio of 1.1 to 1.2. The product lands at the bottom of the reported band, and inlet losses, ambient conditions, and the accessory loads not accounted for here would move it further down. On the proportional floor the same product is

\[0.91 \times (1 - 0.10) \times \frac{5{,}360}{3{,}700} = 1.186 \tag{72}\]

which also lies in the band. The check therefore confirms that the bleed cost is of the right size without choosing between the estimate and the floor.

The same arithmetic applied to the later engines shows what the second re-engining bought. The J85-GE-19 installation gives an uninstalled ratio of

\[\frac{6{,}030}{3{,}700} = 1.630 \tag{73}\]

and after the same two deductions, assuming the later engines bled the same fraction,

\[0.91 \times \left(1 - \tfrac{1}{6}\right) \times \frac{6{,}030}{3{,}700} = 1.236 \tag{74}\]

The X-14B could therefore afford roughly 0.14 more in thrust-to-weight ratio than the X-14A, which at a constant weight is about 508 pounds of additional lift, and that margin, not the digital computer, set how much authority the later experiments could give away.

Rolls 1965a reports the powerplant experience from the X-14A flight test programme directly, and is the primary source on how the installation behaved in service, although its full text is not retrievable from the NASA Technical Reports Server and only its title and abstract are relied on here.

There is a further loss that this article accounts for only qualitatively. A jet directed downward beneath a wing entrains air, lowers the pressure on the surfaces above it, and produces a download that subtracts from the thrust. Gentry and Margason 1966 measured jet-induced lift losses on vertical take-off configurations hovering both in and out of ground effect, and the effect is a few percent of thrust for a configuration like the X-14’s.

This matters for the argument only in that it makes the accounting worse. The bleed for the attitude controls is the largest identifiable single deduction from the hover thrust budget, and the induced loss, the cascade turning loss, and the inlet loss are additional. Every one of them competes with payload, and the article’s conclusion that control consumed more than half of the margin is a lower bound on the total burden rather than an upper one.

Operating close to the ground adds effects to which the jet-lift aircraft is the most exposed, because of its high jet velocities, in the experience of Rolls 1965b. Dent 1966 addresses ground erosion in the operation of jet lift aircraft, the source of the practical objection that a jet-lift aircraft requires a prepared surface.

The Reaction Control System

The reaction controls were the aircraft’s only means of attitude control in a hover and they were the experimental variable. Hegarty et al. 1965 describes two sets. The pilot’s nozzles were linked mechanically to the stick and pedals. A pitch nozzle at the tail discharged through variable areas top and bottom, and the wingtip nozzles gave roll through the difference between the left and right exit areas and yaw by rotating the two tip thrust vectors in opposite directions, so that roll and yaw drew on one force. The variable-stability nozzles that Ames added were driven by servomotors and put roll at the wingtips and pitch and yaw at the tail. The total exit area of each set was constant, so the bleed flowed whatever the command, and the pilot’s set was required to give at least ten percent more moment in each axis than the variable-stability set, so that the pilot could always override it.

The moment arms and the inertias differ between axes, which means the axes are not equally cheap. The report gives a wingtip arm of 16.9 feet and a tail arm of 18.75 feet,

\[\frac{L_{w}}{L_{t}} = \frac{16.9}{18.75} = 0.901 \tag{75}\]

and which axis is cheaper in control power depends on the product of the arm ratio and the inertia ratio,

\[\frac{F_{\text{pitch}}}{F_{\text{roll}}} = \frac{I_{y}}{I_{x}} \times \frac{L_{w}}{L_{t}} = \frac{1{,}990}{1{,}170} \times 0.901 = 1.53 \tag{76}\]

so the pitch nozzle must be about half again as strong as the roll nozzle for the same control power, because the pitch inertia is 1.70 times the roll inertia while its arm is only about eleven percent longer. The design did not ask for equal control powers. It changed the proportions of maximum angular acceleration in roll, pitch, and yaw from the original aircraft’s 10 to 3.2 to 2.8 to 10 to 5 to 2.8, which is why the pilot’s pitch nozzle gave 0.92 radians per second squared against 1.84 in roll.

With the design report’s roll inertia and wingtip arm, the net roll force needed for each tested control power follows from

\[F_{r} = \frac{\text{CP} \times I_{x}}{L_{w}} \tag{77}\]

giving 55.4 pounds at 0.8 radians per second squared, 96.9 pounds at 1.4, and 138.5 pounds at 2.0. These are small forces. The X-14A’s entire lateral control authority at its most generous setting was about 140 pounds of net differential force at the wingtips, out of 500.7 pounds of reaction force for all axes and both sets, bought with a tenth of the engines’ airflow. The efficiency of the conversion from engine thrust to control force is poor, and the fan experiment set out to improve it.

The Variable Stability System and Its Budget

The system that made the aircraft an instrument was installed by Ames after the aircraft arrived, in analogue form on the X-14A and in digital form on the X-14B, the latter described by Gallagher et al. 1972 as a model-following system.

The analogue system has a dedicated paper and it is easy to miss, because its title names the configuration rather than the aircraft. Hegarty et al. 1965 describes a system for varying the stability and control of a deflected-jet fixed-wing vertical take-off aircraft. That aircraft is the X-14A and no other machine, and the paper is the primary description of the apparatus that produced every number in this article.

The principle is feedback through effectors in parallel with the pilot’s. To synthesise a damping derivative that the airframe does not possess, the system measures the angular rate and commands a control moment opposing it. To synthesise a different control power, it adds a moment proportional to the pilot’s stick position. The report lists its modes as rate damping, cross-coupling cancellation, augmented pilot control, and stiffness with a manoeuvrability cutout, and a button on the stick returned the aircraft to its basic configuration.

The two functions are not independent, because they share an authority budget. The variable-stability nozzles can produce a bounded moment, which the design puts at 1.66 radians per second squared in roll. Every newton metre the feedback loop spends opposing rate is a newton metre the augmentation cannot add. Writing the synthesised damping as $D/I$, the roll rate as $p$, and the authority of the variable-stability set as $\text{CP}_{v}$, the authority left after the damping loop has taken its share is

\[\text{CP}_{\text{left}} = \text{CP}_{v} - \frac{D}{I} \, p \tag{78}\]

and the rate at which the damping loop exhausts the set on its own is

\[p_{\text{sat}} = \frac{\text{CP}_{v}}{D/I} \tag{79}\]

At the three dampings flown this is

\[\frac{1.66}{0.55} = 3.02, \qquad \frac{1.66}{1.75} = 0.949, \qquad \frac{1.66}{2.9} = 0.572 \text{ rad/s} \tag{80}\]

or 173, 54.3, and 32.8 degrees per second. Reserving a fraction $\lambda$ of the set for augmentation caps the damping that can be synthesised at a working roll rate,

\[\left(\frac{D}{I}\right)_{\max} = \frac{(1 - \lambda)\,\text{CP}_{v}}{p} \tag{81}\]

and reserving half at thirty degrees per second caps it at

\[\frac{0.5 \times 1.66}{0.5236} = 1.59 \text{ per second} \tag{82}\]

which the highest damping flown, 2.9 per second, exceeds. At that damping half the set is already spent at

\[\frac{0.5 \times 1.66}{2.9} = 0.286 \text{ rad/s} = 16.4 \text{ degrees per second} \tag{83}\]

The instrument could not simultaneously offer high damping and high augmented control power at large rates, and the ceiling is set by the nozzles rather than by the electronics.

This bears on a qualifier in the source. Drinkwater et al. 1965 says the tested conditions covered, to the ability of the X-14A, a high, medium, and low control power for each of a high, medium, and low damping. Its table II shows that every one of the nine combinations was flown and rated by both pilots at each of the three stick travels, so the grid itself was complete. What the qualifier records is that the levels were set by what the aircraft could do, with 2.0 radians per second squared at the top. The relations above add that in the high-damping and high-control-power corner the damping loop saturates at modest roll rates, which is an inference from the design figures and assumes that the design values held in the 1965 tests, and not a statement in the report.

The Position Loop the Pilot Actually Closed

The variable being measured was attitude authority, and the task the pilots were rated on was holding a position. Those are not the same thing, and the relation between them is what makes hovering hard.

The previous article established the structure for the X-13, and writing it as a transfer function rather than as a chain of integrals shows it needs one correction and gains a result the X-14 is uniquely placed to supply.

A hovering aircraft has no aerodynamic restoring moment, so with the damping set to zero attitude is a double integrator driven by control,

\[\ddot{\theta} = \text{CP} \, u \tag{84}\]

and horizontal position is driven by attitude,

\[\ddot{x} = g \tan\theta \approx g \theta \tag{85}\]

Composing the two,

\[\frac{x(s)}{u(s)} = \frac{g \, \text{CP}}{s^{4}} \tag{86}\]

Position is the fourth integral of the pilot’s control input, not the third. The previous article described this as a third-order loop, on the reasoning that attitude is the integral of what the control does. That is the step to check. A reaction nozzle produces a moment, and a moment produces angular acceleration, so attitude is the double integral of control rather than the single integral, and the loop from stick to position is fourth order.

The reconciliation is that the earlier description holds at low frequency and only there, and the parameter that decides where the boundary falls is the damping. Restoring the rate term,

\[\frac{x(s)}{u(s)} = \frac{g \, \text{CP}}{s^{3}\left(s + \dfrac{D}{I}\right)} \tag{87}\]

Below the break frequency $D/I$ the bracket is dominated by the constant, and the loop behaves as

\[\frac{x(s)}{u(s)} \approx \frac{g \, \text{CP}}{(D/I)\, s^{3}} \qquad \text{for} \quad \omega \ll \frac{D}{I} \tag{88}\]

which is third order and is the case the previous article described. Above it the bracket is dominated by $s$ and the loop is fourth order. So hovering is a third-order problem or a fourth-order one depending on how much damping the aircraft has, and an aircraft with no aerodynamic damping and no artificial damping is in the harder case.

This is not a quibble about counting. The two cases differ in what the pilot must supply. A fourth-order plant requires the pilot to generate two derivatives of lead to stabilise it rather than one, and a human being generating lead is a human being working hard. It is the clearest available explanation of why Greif et al. 1972 found that attitude stabilisation gives the best handling qualities for the least control power, because attitude stabilisation does not merely help the pilot, it removes two orders from the plant they are closing around.

The X-14A is the only aircraft in this series that could have demonstrated the distinction, because it is the only one whose damping was a dial.

The loop closure was observed rather than merely postulated. Lollar and Matous 1963 reports observed pilot-vehicle loop-closure characteristics for hovering aircraft control, the measurement whose shape the analysis above predicts. The engineering response was to stop asking the pilot to close it unaided, and that response has a continuous literature, running from Elliott and Schreiber 1964 on improving the stability of hovering aircraft, Dukes 1970 on feedback control of vertical take-off aircraft, Kelly et al. 1977 on a vertical-velocity command system, and Stapleford 1980 on velocity command with position hold, which by then had become the recommended concept for hovering. Merrick 1982 is the same idea reported from the X-14B itself. The sequence is a retreat from the raw fourth-order plant toward something a person can fly, and every step buys that with control authority.

Two consequences follow, and both bear on how the criterion should be read.

The first is that attitude errors do not merely make the aircraft look untidy. They integrate twice into position. Holding a mean tilt of one degree for ten seconds moves the aircraft

\[\tfrac{1}{2} \times 9.807 \times 0.01745 \times 100 = 8.6 \text{ m} \tag{89}\]

which is a long way for a machine meant to land on a marked spot.

The second is that the pilot’s control power requirement is not set by the size of the attitude excursions but by how quickly they must be reversed. This is why control power and not control sensitivity dominated the ratings. Sensitivity determines how much attitude a given stick displacement commands. Control power determines how fast the aircraft can stop doing something. In a loop where errors integrate twice before the pilot sees them as position, the ability to stop counts for more than the ability to start.

The Other Half of the Loop Is Visual

The pilot closing that loop needs to see the position error, and this turns out to be the operational problem the programme actually struggled with.

Rolls 1965b divides five and a half years of operating problems into two categories, and one of them is restrictions imposed on the pilot by reduced visual reference. The aircraft’s difficulties were not the ones its experiments were measuring. Garren et al. 1965 conducted a visual flight investigation of hovering and low-speed control requirements because the visual environment turns out to be a variable in its own right.

It became a research subject with a separate literature. Lemons and Dukes 1975 studied the information requirements for precision hovering directly, asking not how much control the pilot needs but how much information, and Fry et al. 1969 used a six-degrees-of-freedom motion simulator for hovering tasks to separate the motion cues from the visual ones. The two questions are the same question approached from opposite ends of the loop, and the X-14A’s criterion answers only one of them.

The engineering answer was to supply the information artificially. Schwartz and Shearer 1964a sets out control and display subsystem requirements for high-performance vertical take-off aircraft, Gold and Walchli 1974 reports a head-up display for all-weather approach and landing, and Moen and Yenni 1975 an approach profile indicator. A display is cheaper than control power and it addresses a different half of the same loop, a trade the control-power criterion cannot express. The line runs on through Merrick 1981 and Merrick 1984 on control and display systems for instrument approach and shipboard landing, Farris et al. 1983 on shipboard operations, Foster et al. 1987 and Foster et al. 1988 on integrated control and display for transition and vertical flight, and Dorr et al. 1992 and Dorr et al. 1994 on head-up display guidance for Harrier approach transitions. Earlier display work that framed the problem includes Behan and Siciliani 1965, Vallerie 1967, and Roscoe et al. 1975.

What happens when the cues are removed rather than supplied is the controlled experiment, and it was run. Howard 1976 measures the influence of losing visual cues on pilot performance in the final approach and landing of a remotely piloted vehicle, Haines 1980 observes head-up transition behaviour in low visibility, and Hoh 1985 investigates which outside visual cues are required for low-speed flight and hover. How much of the cue can be supplied by a simulator at all is the question of Sinacori 1986 and Parrish and Bowles 1983.

The difficulty is structural rather than incidental. Position error is not directly sensed. It is inferred from the apparent motion of the ground, and the precision of that inference depends on texture, on lighting, on height, and on where the pilot is sitting. A criterion measured with good visual cues is not a criterion for flying with poor ones, and an aircraft that meets it on a marked ramp in daylight at Moffett Field may not meet it elsewhere. This limitation is inherited by every number the programme produced and is taken up again below.

A Deliberately Uninteresting Airframe

The borrowed wing gave a span $b$ of 33.83 feet, or 10.31 metres, over an area $S$ of 182.69 square feet, or 16.97 square metres, in Hoffman et al. 1972. The aspect ratio and, at the 3,700 pound test weight, the wing loading follow as

\[\frac{b^{2}}{S} = \frac{33.83^{2}}{182.69} = 6.26, \qquad \frac{W}{S} = \frac{3{,}700}{182.69} = 20.25 \text{ lb/ft}^{2} = 970 \text{ N/m}^{2} \tag{90}\]

These are light-aircraft numbers and they were chosen to be. Rolls 1965b notes the consequence that mattered in flight, that with its light wing loading the aircraft could recover from attitude excursions of more than 180 degrees, which pilots unable to see their drift at altitude did make, with only a nominal loss of height.

In a hover the wing does nothing except add inertia and catch the exhaust. In the transition it does what a light-aircraft wing does. The X-14 was not asked to fly fast, and its fastest recorded flight, the 172 miles per hour of Jenkins, Landis and Miller, is a consequence of not caring rather than a limit that was pushed against.

There is one respect in which the airframe was not neutral. It is quantitative, so it is treated here and not in the epistemic state. The inertia the wing contributes is the denominator of every control-power figure the aircraft produced. An aircraft with the same nozzles and heavier wings would have measured lower control powers for the same hardware. The criterion the X-14A produced is expressed in radians per second squared to remove this dependence, and the removal is exact only to the extent that pilot opinion depends on angular acceleration alone.

The Ground Beneath the Hover

This article treats ground effects only where they bear on control, and one point is taken up here because it constrained where the experiments could be run.

A jet-lift aircraft hovering close to a surface directs its entire exhaust at that surface. The downwash impingement problem was studied contemporaneously and at length, in White et al. 1960, Morse and Newhouse 1960, and Morse and Newhouse 1961a, the last extending to duct adapter testing, and it had hardened into stated design criteria by George et al. 1964. The efflux is reviewed in Garner 1967 and its aerodynamics treated in Skifstad 1970, and the outflows of competing configurations are compared in Michaelsen 1971, which finds the jet-lift case the most severe of the three. The underlying fluid mechanics were pursued in parallel, in Donaldson et al. 1966 on the structure of an impinging free jet, Strand 1967 on the inviscid theory of a round jet striking the ground, Binion 1970b on the recirculation region a jet in ground effect creates with crossflow, and Lissaman 1967 on the related jet-flap case. Ground-effect machines supplied a neighbouring body of measurements in Foltz 1962 and Walker et al. 1965, and the ingestion hazard was characterised as a dust problem as early as Hafer and Skinner 1960. Estimating the loss from a single jet remained a live problem into Christiansen et al. 1985.

The aircraft also loses lift to its own jet before it ever reaches the ground. McLemore 1966b measures jet-induced lift loss in the hovering condition and Margason 1966 the induced effects in transition, with the theoretical treatment in Levinsky et al. 1968. The operational consequences run from prepared surfaces in Butler and Thomas 1964 through spray in Kuhn 1979 and deck temperatures in Fluk 1981 to shipboard operation in Kamman and Hall 1978, with the flow field modelled in Kotansky 1982 and still being visualised in Mourtos et al. 1995. Hot gas returning to the inlet is the related hazard, treated in Johns et al. 1989b and Johns et al. 1990a.

The consequence for the X-14 programme is that out-of-ground-effect experiments and in-ground-effect experiments are different experiments, and Drinkwater et al. 1965 is explicit that its hovering evaluations were conducted out of ground effect. That is the correct choice for isolating the control variable, and it means the criterion was established in the condition least like a landing.

The Instrumentation Was a Rating Scale

The measuring instrument in this aircraft was not a transducer. It was a numbered scale of pilot opinion, and the aircraft’s output was an integer.

Drinkwater et al. 1965 reproduces the rating schedule it used, running from excellent through satisfactory with mildly unpleasant characteristics, then to acceptable but with unpleasant characteristics, then to unacceptable for normal operation and acceptable only for emergency conditions. This is the Cooper scale in the form current before the revision that produced the Cooper-Harper scale.

Two properties of this instrument shape everything the programme could conclude.

It is ordinal rather than interval. The distance between ratings three and four is not known to equal the distance between four and five, so averaging ratings is not obviously meaningful, and fitting a curve through them to find where it crosses a boundary imports an assumption the scale does not support. The scale’s own authors returned to this two decades later in Harper and Cooper 1984, and the methodological difficulties of evaluation in the hover are the subject of Harper and Sardanowsky 1969.

Its dependence on how the evaluation is run was known and measured. Kidd and Bull 1963 examines how handling-qualities requirements are influenced by pilot evaluation time and sample size, the same objection this article raises below about two pilots, published two years before the lateral control experiments. The ambition to predict the rating rather than collect it runs from Adams and Hatch 1970 and Adams 1972 through Levison 1982b to Hess 1981b and Hess 1984b, the last proposing a unifying theory. None of them removed the pilot from the procedure.

Its resolution is set by the sampling, not by the scale. The X-14A tested three control powers, 0.8, 1.4, and 2.0 radians per second squared, spaced 0.6 apart, in Drinkwater et al. 1965. A threshold lying between two of them is located only to within that spacing. If the satisfactory boundary sits near 1.4, the experiment locates it to within 42.9 percent of its own value. If it sits near 2.0, to within 30.0 percent.

\[\frac{0.6}{1.4} = 0.429, \qquad \frac{0.6}{2.0} = 0.300 \tag{91}\]

This is the article’s least comfortable number and it is not a criticism of the programme. Three points was what an aircraft with a finite authority budget and a finite flight-test programme could deliver, and three points across a factor of two and a half in the variable is a respectable experiment. But a criterion stated to two significant figures rests, at its origin, on a grid whose spacing was thirty to forty percent of the answer.

The Other Way of Measuring the Same Pilot

The rating scale treats the pilot as an oracle who returns a number. A parallel literature, running through the same years and the same institutions, treats the pilot as a dynamic system to be identified.

Elkind and Forgie 1959 characterises the human operator in simple manual control systems, and the subject was developed continuously through a long conference series, of which Second Annual NASA-University Conference 1966, Second Annual NASA-University Conference, Third Annual NASA University 1967, Fourth Annual NASA-University Conference 1969, Fifth Annual NASA-University Conference 1970, and Seventh Annual Conference 1972 are successive proceedings. Mitchell 1964 surveys the operator models available, Young et al. 1964 treats the operator’s adaptive response, and Costello 1968 proposes a specific model form.

The most directly relevant of these is Smith 1966b, which measured human describing functions in flight and on simulators, because that is the comparison the X-14A’s justification rested on. Mooij 1973 measured the pitch-axis describing function and remnant in flight.

The hovering case was singled out for this treatment, which matters because the loop structure derived above says hovering should be the hardest case for an adaptive operator. Vinje 1968 analyses pilot adaptation in a simulated multiloop vertical take-off hovering task, and Andrisani 1982 determines pilot models experimentally from hovering flight data rather than from a simulator. The identification methods themselves developed through Washizu et al. 1978 on the effect of forcing-function characteristics, Tomizuka and Whitney 1976 on preview tracking, Dey 1972 on prediction displays, and Biezad and Schmidt 1984 on time-series modelling, with the field’s proceedings continuing through Eleventh Annual Conference 1975, Proceedings, 13th Annual Conference, and Proceedings of the Seventeenth 1981.

The two literatures met in Hess 1977b, which predicts pilot opinion ratings using an optimal pilot model. If that programme had fully succeeded, the variable-stability aircraft would have become unnecessary, because a rating could be computed from the dynamics rather than obtained from a person. It did not fully succeed, and the reason it did not is the reason a Cooper-Harper rating is still collected by asking someone.

There is a tension here the X-14’s programme never resolved and mostly did not need to. A rating is a scalar summary of a closed-loop interaction whose dynamics the same field was busy measuring in detail. The criterion the X-14A produced is expressed in terms of the plant alone, which is only defensible if the pilot’s contribution is approximately constant across the configurations compared, and the adaptive-operator literature was simultaneously establishing that it is not.

The Flight Test Record

The X-14’s flight record divides into a short period in which it was an aeroplane and a long period in which it was an instrument, and the two have almost nothing to do with each other.

The Aeroplane, 1957 and 1958

The aircraft first hovered in February 1957. Sources give either the seventeenth or the nineteenth. NASA’s inventory by Jenkins, Landis and Miller gives a first flight on 17 February 1957, and the abstract of the project pilot’s retrospective, Gerdes 1981, gives the first free-hover flight as 19 February 1957. The two dates may describe different events, a first hover and a first untethered hover, but neither source says so, and this article does not choose between them. Whichever it was, the first hover was made on the Viper engines, at a thrust-to-weight ratio that the arithmetic above shows to have been marginal at any realistic weight.

A partial transition followed, and the first full transition from vertical to horizontal flight was made on 24 May 1958, in the Bell X-14 entry and the account of the Virtual Aircraft Museum. That completed the hover and transition whose demonstration the same entry gives as the project’s main objective. The X-14 had shown that a jet-lift aircraft with vectored thrust and reaction controls could take off vertically, fly, and land vertically, which the X-13 had also shown by a different means the previous year.

At that point the aircraft had discharged its stated purpose and there was no obvious reason to keep flying it.

The Instrument, 1959 to 1981

The aircraft came to NASA Ames in late 1959 and first flew a brief programme there on its Vipers, which Rolls 1960 summarises. Three problems dominated. Ground suction meant that breaking contact with the ground took excess thrust of the order of 12 percent of the gross weight. Because the reaction nozzles drew directly on the compressors, control power fell steeply with engine speed, to about 90 percent of the maximum at the normal hovering speeds of 93 to 97 percent and to 70 percent during momentary drops to 90 percent. And the engines’ gyroscopic coupling between pitch and yaw left the pilot unable to hold the aircraft level at yaw rates above 15 degrees per second. Transition, by contrast, presented no great problems. The aircraft was then re-engined with the J85-GE-5, becoming the X-14A, and the variable-stability system followed. From that point the flight record is a record of experiments.

The two that matter most to this article are the ones already drawn on. Drinkwater and Rolls 1962 used the variable-stability and control X-14A to determine attitude control power and damping requirements for a visual hovering task, and is the origin of the criteria. Drinkwater et al. 1965 extended the work by separating control power from control sensitivity, testing three total control powers at three stick travels, and reported a result that is easy to state and was not obvious in advance.

Total control power dominated. Control sensitivity barely mattered. Changing the control power per inch of stick travel had only a minor effect across the range investigated, while changing the maximum moment available had a predominant effect on the pilots’ ratings during visual hovering out of ground effect, in the summary of Drinkwater et al. 1965. This matters because sensitivity is nearly free and control power is expensive. The experiment found that the expensive parameter was the one that counted.

The report’s table II gives the ratings themselves. At 2.0 radians per second squared and the highest damping, 2.9 per second, the two pilots’ ratings ran from 2 to 3-1/2 across the three stick travels, inside the satisfactory region of the scale. At 0.8 radians per second squared and the lowest damping, 0.55 per second, they ran from 5 to 7, from unsatisfactory to unacceptable for normal operation. The report compares them with boundaries at ratings of 3-1/2 and 6-1/2 derived in the 1962 tests, and notes that the two pilots disagreed most at the lowest damping, where the pilot more familiar with the aircraft rated it more favourably because he valued its greater responsiveness.

Rolls 1965b reports the operational experience of five and a half years of flight research with the aircraft, grouping the problems into effects of the jet engine and its operation, and restrictions imposed on the pilot by reduced visual reference. Those two categories are the ones the wider field also found, and the operational literature that grew around them covers terminal-area operation in Schade 1968, shipboard compatibility in Daffer and Rogers 1973 and guidance to a small ship in Goka et al. 1980, noise in Cole and England 1967, the sensing problem a vehicle with no reliable airspeed has in McElreath 1972 and Wachtell 1970, and the consequences of losing the pilot in Harvey and Waugh 1976. Whether vertical take-off was worth its costs at all was assessed commercially in Fry 1967 for rotor and propeller lift, and against competing layouts in Englar and Kirkpatrick 1969 and Detore and Gaffey 1969. Low-speed control improvement generally is Kesselyak 1974. Neither category is about control power, which is a useful corrective. The thing the aircraft was measuring was not the thing that made it difficult to operate.

Gerdes and Rolls 1969 reports the tip-turbine fan experiment. The fans worked thermodynamically and failed dynamically, and the failure is instructive enough to be taken up separately below.

The experiments were not confined to control power. Gerdes 1964 investigated height-control requirements. Height control is the vertical axis of the same problem and has a different character because thrust responds through engine dynamics rather than through a nozzle valve. The aircraft’s inability to change its own thrust quickly is a limitation the criterion for attitude does not address at all. Feistel et al. 1969 tested a direct side-force manoeuvring system on the aircraft, which translates it sideways without banking, and NASA’s inventory names that system as one of the aircraft’s uses as a testbed.

By 1971, when the Virtual Aircraft Museum records its first flight with the new engines, the aircraft had been re-engined again with J85-GE-19 engines and fitted with a programmable digital computer and a fly-by-wire control system, becoming the X-14B in the Bell X-14 entry. Borchers, Franklin and Fletcher records that Richard Greif and Terry Gossett directed this modification, that Ronald Gerdes then became the sole project pilot, and that the later experiments set criteria for pitch and roll attitude command, which had become the preferred augmentation for precision hover. Loscutoff et al. 1973 modelled the re-engined aircraft and reports that it hovered with its engines at 98 to 99 percent of maximum speed. Gallagher et al. 1972 describes the model-following variable-stability system. The digital system did what the analogue system had done, but it could be reprogrammed between flights rather than rewired, which changed the economics of running an experiment. Corliss et al. 1977 reports an in-flight simulation of hover control concepts, and Merrick 1982 a translational velocity command system, both of which are experiments the analogue aircraft could not have hosted.

Over the whole period more than 25 pilots flew the aircraft, many of them to preview vertical take-off handling qualities before flying other designs, in NASA’s inventory. Borchers, Franklin and Fletcher names Fred Drinkwater and Ronald Gerdes as the principal pilots of the research programme. The same history notes that in 1965 Neil Armstrong flew it to evaluate control characteristics in vertical flight representative of the Apollo lunar module during final descent.

The Ending

The X-14B made its last flight on 29 May 1981, the date Jenkins, Landis and Miller give. Borchers, Franklin and Fletcher records that during an experiment phase in 1981 the aircraft made a hard landing as a consequence of a lateral control software design flaw that led to a pilot-induced oscillation, and that it was never flown again. That attribution is NASA’s own, in its history of Ames flight research, but no investigation report is available to show the evidence behind it. The Virtual Aircraft Museum adds that the pilot, Ronald Gerdes, escaped uninjured. The airframe was not destroyed. The inventory states that it was retired to the Army Aviation Museum at Fort Rucker and is in storage in a private collection in Indiana.

If the attribution is correct, the ending is exact. An aircraft whose entire purpose was to make itself deliberately deficient in the lateral axis so that pilots could report on the consequences was ended by an unintended deficiency in the lateral axis that a pilot could not fly out of. The instrument was consumed by the phenomenon it existed to measure. It had been flying for twenty-four years and it was not flown again.

Comparison With Ground Prediction

The X-14A’s results can be set against three kinds of prediction, and the comparison is unusually informative because in this case the ground-based method eventually replaced the aircraft rather than merely preceding it.

Against Ground Simulators

Ames ran motion-base simulators on the same questions throughout the period. Gerdes 1964 investigated height-control requirements on a piloted motion simulator, and Garren et al. 1965 conducted a visual flight investigation of hovering and low-speed control requirements. Greif et al. 1972 used a motion simulator to study the effect of stabilisation on control power requirements, comparing no stabilisation, rate stabilisation, and attitude stabilisation. The same approach was applied to other configurations in Breul 1963 for tilt-wing handling qualities and in McCormick 1969 through moving-base simulation, with the equations of motion that such simulations required set out in McIntyre 1963 and the attitude representation problem in Greenwood 1960.

The most useful evidence of agreement is that the 1972 simulator study swept the same range the 1965 aircraft had. Greif et al. 1972 reports results across control powers from 0.8 to 2.0 radians per second squared and states its disturbance correlation as valid at least within that range. A decade after the flight experiment, the simulator work was still anchored to the interval the aircraft had established. That is either strong corroboration or strong path dependence, and the two are not easy to separate from outside.

The 1972 study also reports a finding the aircraft could not have produced. An attitude-stabilised system gives the best handling qualities for the least control power, a trade between two things the X-14A could vary but could not vary cheaply enough to map densely. A simulator can run far more configurations than a flight programme can. The aircraft’s 1965 lateral experiment rated twenty-seven conditions per pilot, nine combinations of control power and damping at each of three stick travels.

Whether the two agree in general is a question the field kept returning to and never closed. Innis and Anderson 1972 compares simulator and flight results directly for an augmentor-wing research aircraft, Condit et al. 1966 does the same for large transports in landing approach, Mitchell and Hart 1993 examines how simulator motion and visual characteristics change rotorcraft handling-qualities evaluations, and Brandon et al. 1995 compares ground and flight assessments for a high-performance aeroplane. That the comparison was still being made in 1995 is the answer to whether the X-14A’s premise had been superseded.

Against the Scaling Argument

The scaling relation derived above, that control power at fixed bleed fraction falls inversely with span, is a prediction this article makes from the X-14A’s numbers. It can be checked against the contemporary literature rather than against a wind tunnel.

Johnston and Friend 1965 addresses the effect of size on hover and low-speed handling qualities directly. The existence of that paper, in that year, is the corroboration. The field asked the size question within three years of the X-14A’s first control-power results, which is what one would expect if the practitioners had noticed the same inverse dependence the algebra gives.

The check that can be made numerically is the Dornier Do 31, which spanned 17.0 metres and is the largest vertical take-off aircraft NASA flight-tested. The relation demands 12.3 percent of thrust at that span for the 1.84 radians per second squared of the X-14A’s pilot nozzles. Holzhauser et al. 1972 shows that the Do 31 did not pay it, because it rolled by differential thrust of wingtip lift engines rather than by bleed, and that it flew satisfactorily with 0.8 radians per second squared and attitude stabilisation. The prediction is not falsified by the one large data point available, and the designers’ choice of a different effector is consistent with it. That is weaker than confirmation, and it is as far as the evidence goes.

Against the Model That Replaced the Aircraft

The most consequential comparison is with what came after. Smith 1966c reappraises control power requirements only four years after the original determination, which indicates the numbers were contested almost immediately.

The eventual resolution was not a better number. It was a change of variable, taken up below.

What the Data Changed

This section usually asks whether an aircraft’s data mattered. In the X-14’s case the answer is unusually definite, and it is definite because the data became a specification.

It Became a Requirement Document

Military Specification MIL-F-83300, Flying Qualities of Piloted V/STOL Aircraft is dated 31 December 1970. It is the document that turned handling-qualities research on vertical take-off aircraft into a contractual obligation on manufacturers, and its hovering requirements descend from the flight and simulator work of the preceding decade, of which the X-14A’s is the principal flight component. NASA’s history of Ames flight research by Borchers, Franklin and Fletcher states the link in so many words, that research with this aircraft, together with experiments on the new six-degrees-of-freedom hover simulator, contributed to the military flying qualities specification for vertical and short take-off aircraft, and adds that it played an important role in the control system development of the Hawker P.1127.

The generation of the specification is documented separately. Key 1971 describes how MIL-F-83300 was produced, published the year after adoption, and is the primary source for the lineage this section claims. The conventional-aircraft counterpart is documented the same way in Chalk et al. 1969, the background and user guide for MIL-F-8785B. The specification then attracted the work any specification attracts. Vinje and Miller 1973 reports flight simulator experiments in support of its further development, Hutchings 1977 reviews the Navy requirements against it, Anderson 1979 compares an actual aircraft’s handling qualities against both it and the corresponding report of the Advisory Group for Aerospace Research and Development, and Goldstein 1982 gives an overview of where the specifications stood a decade on. The short take-off case followed in Hoh and Mitchell 1983. A research aircraft whose output can be traced into a numbered document that contractors must satisfy has had an unusual kind of effect.

This is rare among X-planes. The X-1 changed what engineers believed about transonic drag. The X-5 changed what they believed about variable sweep. Belief is the usual output. A number in a military specification that a contractor must demonstrate compliance with is a different kind of output, and among the fourteen aircraft this series has covered, only the X-14 produced one directly.

It Set the Range Everyone Else Worked In

The interval from 0.8 to 2.0 radians per second squared appears in the X-14A lateral control report of 1965, which compares its ratings with boundaries from the 1962 flights, in the Ames simulator work of 1972, and in the discussion of control power requirements throughout the period. A research aircraft that fixes the axis limits of everyone else’s plots has had an effect that is easy to miss because it does not look like a result.

It Fed the Lunar Programme, Partially

Armstrong’s 1965 flights connect the X-14A to Apollo, and the connection is real but narrower than the popular account suggests. Hewes 1967 reports flight evaluations of lunar landing vehicle attitude control systems, and McCabe et al. 1967 reports piloted lunar module landing simulation studies. The X-14A could contribute to the attitude problem. It could not contribute to the whole problem, for a reason that is exactly quantifiable and is taken up in the next section.

The Criteria Were Applied Far Beyond the Aircraft That Produced Them

A criterion expressed in radians per second squared can be carried to any vehicle, the purpose the normalisation served, and the record shows it being carried.

The lift-fan branch runs through Przedpelski 1965, Hill and Waters 1974, Bland et al. 1976, and Sellers et al. 1977, and reaches an integrated flight and propulsion treatment in Chung et al. 1995b. Rotorcraft response requirements were settled the same way in Mitchell et al. 1987, A flight investigation of helicopt and Mitchell et al. 1989, with hovering dynamics and pilot performance in Aponso et al. 1987 and control and display dynamics for hover in Eshow 1990. Even vehicles with no wing at all inherited the framework, in Putman et al. 1977 and Curtiss and Sumantran 1985 on hovering airships, with the rotor case in Curtiss 1973.

The configuration the X-14 vindicated acquired an operating literature, on how to fly it rather than whether to build it, in Huntley 1972 on minimising landing transition distance, Karemaa 1971 on hybrid jet-lift take-off and landing, Nishimura 1980 on the fuel-minimal take-off path, and Morello et al. 1972 on a flight evaluation of a vectored-thrust aeroplane during simulated instrument approaches. The inlet problem the configuration creates for itself is Grahame 1968 and Grahame 1969, the configuration management the transition demands is Johnson and Craig 1974, and the development is reviewed from a distance in Anderson 1983.

The most pointed instance is the one that returns to where the previous article left off. The tail-sitting layout came back for piloted simulation in Hill 1981 and Hill 1983, the X-13’s configuration re-examined a quarter of a century after it was abandoned, using criteria that the aircraft standing beside it in the designation sequence had supplied.

It Established the Method More Firmly Than the Number

The number the X-14A produced was reappraised within four years by Smith 1966c and superseded within twenty by the shift to bandwidth criteria. The method outlived both.

Many handling-qualities questions since have been settled the same way, by building a vehicle or a simulator whose dynamics are adjustable, sweeping the parameter of interest across a boundary, and asking a trained pilot for an ordinal judgement. Aiken et al. 1977 on the X-22A, Hindson 1982 on research helicopters, and Corliss et al. 1977 on the X-14B itself are all the same experiment with different plants.

That legacy is stronger than a number, and the X-14 has the best claim to it, because it was among the early vehicles to apply the method to the hover.

It Did Not Save Jet Lift

The X-14’s data made jet-lift vertical take-off aircraft designable. It did not make them worth designing. The scaling relation above is the reason, and it was not something better criteria could fix. Knowing precisely how much control power a hovering aircraft needs does not make that control power cheaper, and the history of the configuration after 1970 is the history of an idea that worked and did not pay.

The Contemporary Literature

Cluster	Records
Handling-qualities criteria, ratings and specifications	617
Electric vertical take-off aircraft, urban air mobility and vertiports	573
Lunar landing, planetary flight and the gravity a simulator cannot change	454
The human operator and pilot models	437
Tiltrotors, tiltwings and tail-sitters through the transition	486
Helicopter hover, stability and flight dynamics	427
Multirotor and quadrotor attitude control	427
Control allocation, attainable moments and effector failure	322
Ground simulators and their fidelity	318
Ground effect, jet-induced flow and hot gas ingestion	301
Lift fans, lift engines and jet-lift aircraft	241
Variable-stability aircraft and in-flight simulation	227
System identification, model testing and flight-test method	222
Vertical take-off aircraft design, propulsion and configurations	227
Attitude command, augmentation and flight control of hovering vehicles	167
Vertical take-off operations, terminal areas, ships and noise	176
Pilot-induced oscillation, bandwidth and time delay	147
Reaction controls, bleed and thrust deflection	141
Visual cues, displays and the hover task	168
Shared control, workload and the division of authority	92
Other vertical take-off and handling-qualities literature	31
Total	6,201

The X-14’s question is live, in a field that does not usually cite it. The review that follows the table is of recent scholarship rather than recent history. It opens with arithmetic before turning to the literature, because running this article’s relations forward on a modern vehicle changes what the literature then has to say.

Running the Article’s Relations on a Vehicle With No Bleed

A multirotor makes its attitude moments by running some rotors harder than others. The accounting therefore differs from the X-14’s, and the difference is derived here rather than asserted.

Take a vehicle of mass $m$ with $n$ rotors at radius $R$, hovering with each rotor at $mg/n$, and a thrust-to-weight ratio limit $r$. Each rotor can be pushed up by $(r-1)mg/n$ and pulled down by $mg/n$ before it reaches zero, so a symmetric differential is bounded by the smaller of the two,

\[\delta = \min(r - 1,\, 1)\,\frac{mg}{n} \tag{92}\]

Summing over the rotors with a geometry factor $c_{g}$ that accounts for their not all lying on the control axis, the moment and the control power are

\[M = c_{g}\, n\, \delta\, R = c_{g} \min(r-1,\,1)\, m g R \tag{93}\]

The rotor count has already cancelled, so the number of rotors does not by itself buy authority. Dividing by the inertia gives the control power.

\[\text{CP} = \frac{M}{m k^{2}} = \frac{c_{g} \min(r-1,\,1)\, g R}{k^{2}} \tag{94}\]

The mass cancels. Putting $k = \kappa b$ and $R = b/2$ gives

\[\text{CP} = \frac{c_{g} \min(r-1,\,1)\, g}{2 \kappa^{2} b} \tag{95}\]

which is inversely proportional to span. That is the same law this article derived for bleed-fed reaction nozzles, with the same exponent, by a mechanism that shares no hardware with it. The inverse-span dependence therefore does not arise from reaction controls as such. It follows from making moments with forces at the extremities of a vehicle whose thrust scales with its weight, and it survives the complete replacement of the propulsion system.

Evaluating for three representative vehicles, taking $c_{g} = 0.707$ for a cross configuration and $\kappa = 0.2$, gives control powers far above anything the X-14A could offer.

Vehicle	Mass	Span	Thrust-to-weight	Control power	Against X-14A
Small research quadrotor	1.2 kg	0.50 m	3.0	173 rad/s²	87 times
Medium cargo multirotor	25 kg	1.60 m	2.0	54.2 rad/s²	27 times
Electric air taxi	2,200 kg	8.0 m	1.4	4.33 rad/s²	2.2 times

The small vehicle is overprovided with attitude authority by a factor of nearly ninety, and the scaling law, not any advance in control technology, accounts for it. These figures are representative, not taken from real vehicles, and the conclusions drawn from them are ratios and orders.

The Cost Changed Character, Not Merely Magnitude

The more consequential difference is not the size of the control power but what it costs.

The X-14A’s reaction controls consumed an estimated sixth of engine thrust, and at least a tenth, and the design report of Hegarty et al. 1965 makes the total nozzle exit area constant so that the bleed flowed whether or not the pilot was commanding anything. The tax was standing rather than incurred. A multirotor’s differential is zero-sum. One rotor rises exactly as much as another falls, so

\[\sum_{i} \Delta T_{i} = 0 \tag{96}\]

and the mean cost of attitude control is zero. What the vehicle pays instead is the headroom $\min(r-1,1)$, which it needs anyway for climb and for gust rejection, so the attitude requirement is frequently not the binding one at all.

The design constraint that dominated the X-14 has been dissolved rather than solved. That is the same verdict the previous article reached about the X-13’s hovering control problem, by a different route, and the agreement matters because the two aircraft solved the vertical take-off problem in opposite ways.

The standing character of the X-14A’s bleed is a design fact rather than an assumption. The report states that the characteristics of the engines made it essential that the total bleed be constant, that the flow through the pilot’s nozzles was constant, and that the added variable-stability nozzles were therefore given a constant flow too. What remains uncertain is the size of the tax, between a tenth and a sixth of thrust, not its character.

The Constraint Moved Rather Than Vanishing

The inverse-span law has a consequence that the enthusiasm around small vehicles obscures. Setting the multirotor relation equal to the X-14A’s maximum,

\[b^{*} = \frac{c_{g} \min(r-1,\,1)\, g}{2 \kappa^{2} \times 2.0} \tag{97}\]

gives 17.3 metres of span at a thrust-to-weight ratio of 1.4, 26.0 metres at 1.6, and 43.3 metres at 2.0. A modern vehicle with an air-taxi thrust margin falls to the X-14A’s control power at about seventeen metres, compared with the twenty-eight to forty-six metre span at which this article found bleed-fed jet lift exhausting a twenty percent margin. The two constraints bite at comparable size for comparable margin. Large hovering aircraft are still hard, and they are hard for a reason the X-14A measured.

The Authority Budget Became a Geometry Problem

The X-14A met its authority limit at the top of its experimental grid, whose levels its 1965 report, Drinkwater et al. 1965, sets by the ability of the aircraft. The modern statement of the same limit is explicit and geometric.

Antonakis 2025a sizes handling qualities using control moment polytopes, which represent the achievable moments as a convex region in three-dimensional moment space, and the attainable moment set is computed directly in Han et al. 2025b and used as a controller constraint in Han et al. 2024. The equivalent construction for a multirotor is the attainable control set of Strampe and Klingauf 2026 and Yoon et al. 2025b. In those terms the X-14A’s problem was that the polytope did not contain the required corner, and casting it this way makes the multi-axis case tractable, which the scalar criterion never was, because an aircraft demanding simultaneous roll and pitch authority is asking about a diagonal rather than about either axis alone.

Control Allocation Is the Modern Form of the Handover

The X-14A’s pilot nozzles were connected mechanically to the stick and pedals, in Hegarty et al. 1965, so any blending of reaction and aerodynamic control was done by linkage and pilot technique. The modern equivalent is a least-squares problem solved many times a second.

The general over-actuated formulation is treated in Scordamaglia et al. 2025, Jafari et al. 2022, and Singh et al. 2024, and specifically for vertical take-off configurations in Enenakpogbe et al. 2025 and Enenakpogbe et al. 2024b on vectored-thrust vehicles, Yılmaz and German 2024 on a tandem tiltwing, Qin et al. 2023a on a distributed-electric-propulsion test platform, Davi Antônio dos Santos et al. 2024 and Ruggia 2025 on fully actuated multirotors, and Mohammadi et al. 2023 and Asghari and Tayefi 2026 on the transition itself. Pfeifle and Fichter 2023b is the one that rhymes with this article, since it allocates control so as to minimise power, the X-14A’s bleed trade with electricity substituted for compressed air. Spadão et al. 2026 treats the blending of control authority through a lift-plus-cruise transition, and so reproduces the handover the previous article analysed for the X-13 with an allocator in place of the pilot. Attitude control of an over-actuated fixed-wing aircraft is Chen et al. 2026b, and saturation and failure of the effectors are the subject of Wang et al. 2026b, Zhang et al. 2024a, and Yang 2023. The allocation extends to several multirotors sharing one payload in Wahba and Hönig 2024, and the same mathematics appears outside aviation in Lan et al. 2025 for an over-actuated spacecraft, Lin et al. 2024 for a road vehicle, and Rüddenklau and Schitter 2026 for satellite laser communication.

The Loop Order Was Designed Out

This article derived that a hovering aircraft with no damping presents a fourth-order plant from stick to position, third order only below the damping break frequency, and that the X-14A’s synthesised dampings of 0.55 to 2.9 per second put that break between 0.55 and 2.9 radians per second, at periods of 11.4 to 2.17 seconds.

On a band assumed here for a small modern vehicle, an attitude loop closes between roughly ten and thirty radians per second, which is 3.4 times the highest break frequency the X-14A was flown with and 18 times the lowest. At its lowest damping the aircraft was in its fourth-order regime above about half a radian per second, and at that damping the ratings of the pilot less familiar with the aircraft were his worst at every control power and stick travel in table II of Drinkwater et al. 1965, while the more familiar pilot’s were not. That is consistent with the loop-order explanation of why it was hard to fly, although the ratings alone cannot separate the loop order from the lost damping itself.

The modern answer is not more control power but attitude command, which makes the outer loop second order. Attitude and position architectures for hovering vehicles are Zhang et al. 2024a and the cascaded treatments in Wang et al. 2026g, with disturbance rejection in Wang et al. 2026f and Kato and Suzuki 2019. The 1972 Ames finding that attitude stabilisation gives the best handling qualities for the least control power is now not a finding but a design assumption, built into the attitude-command architectures just cited before anyone flies them.

The Criterion Moved to Bandwidth and Then to Certification

MIL-F-83300 obliged a military contractor to demonstrate compliance. Many of the vehicles now being built to hover are civil, and what they must satisfy is a certification basis.

Favaro et al. 2025b is written from inside that problem and asks what makes a flight model credible enough to certify against by simulation rather than by flight. This closes a loop the X-14 opened. The X-14A was converted because a hovering handling-qualities question was wanted under realistic flight conditions, as Hegarty et al. 1965 argues in making the case for variable-stability aircraft. The modern question is what evidence would justify trusting one, because flying every configuration is no longer affordable and the number of configurations has grown enormously. Li et al. 2024d proposes an objective assessment framework for electric vertical take-off vehicles, Wang et al. 2025g models wake interference within quadrotor handling qualities, and Zanoni et al. 2022a pulls handling qualities forward into conceptual design. Uncertainty in the assessment is Saetti and Rogers 2024, and automating the assessment is Antonakis 2025b. The certification architecture around all of it is Pleffken 2026 and Kieß et al. 2026, and the accident record that will discipline it is already being surveyed in Shubert et al. 2026.

Pilot-induced oscillation, the cause NASA’s history of Ames flight research gives for the end of the X-14B’s flying, remains an open criterion problem. Bidinotto et al. 2021 surveys the pilot models used to predict it, Wang et al. 2023d proposes criteria for the nonlinear lateral-directional case that fly-by-wire systems produce, Efremov et al. 2022b and Newton and Kroo 2025 treat suppression, and Rezaei and Khosravi 2023 attacks it through the actuator saturation that causes it. The failure mode that ended the X-14B’s flying is still being written about seriously forty years later.

Handling Qualities for Vehicles With No Pilot Aboard

The X-14A’s criterion assumed a pilot in the seat. A large part of the modern literature does not.

Ivler et al. 2022 develops and flight-validates handling-qualities requirements for unmanned systems, Herrington et al. 2023 assesses them for systems and operators together, Ioannis and Ioannis 2026 applies the Cooper-Harper scale to a small uncrewed aircraft through simulation, and Jusko and Berger 2026 develops new mission task elements for low-level flight. Kozhanov et al. 2022 predicts hover and low-speed handling qualities for a helicopter with its augmentation system, Yuan et al. 2022 does it for a tiltrotor by inverse simulation, and Wang and Chen 2024 for a helicopter whose plant changes with its slung load. Turbulence, which the X-14A’s out-of-ground-effect calm-air testing excluded by design, is now modelled explicitly in Henriquez Huecas et al. 2022 and enters the pilot model in Ji et al. 2022.

The most direct descendant of the X-14’s pilot problem is the decision to stop requiring a pilot’s skill at all. Janetzko et al. 2026 measures the flight performance of novices and system designers under a simplified vehicle operations concept, which asks whether people who are not pilots can fly the vehicle. The X-14A asked an experienced test pilot to do something at the edge of what a person can do, and the field’s eventual answer was to change the aircraft rather than to train the person.

The Pilot Is Still Measured, and Now So Is the Division of Authority

Where a human remains in the loop, the question has become how authority is shared rather than how much of it there is.

Xu et al. 2025c models shared control between a human pilot and an autopilot for a carrier landing, structurally the X-14A’s problem with a second controller added. Allocation of authority between the two is Liu et al. 2026b, Chen et al. 2026f, and Liu and Kaber 2025, with haptic implementations in Qin et al. 2025, Sato and Wada 2025, and Turco et al. 2026. The X-14A’s variable-stability system was an early and unusually literal instance of shared control, since its synthesised damping and its pilot drew on one fixed budget of nozzle moment, and the modern treatment of shared control when the second controller is remote and delayed, in Liu et al. 2026a, Prakash et al. 2026, Zhang et al. 2026b, and Li et al. 2026c, says the delay is the thing to attack.

Workload, which the Cooper scale summarised as an integer, is now instrumented directly in Xu et al. 2026, Procházková and Juračka 2026, and Mohan et al. 2024, and treated as a quantity to design for in Stephenson et al. 2026. None of this has removed the rating, which is still collected by asking a person.

In-Flight Simulation, Subscale Testing, and Identification

The variable-stability aircraft has not disappeared, but it now shares the work.

Yi and Feng 2025 describes a variable-stability operating method for a simulator control mechanism, the technique migrating back to the ground. Identification from flight data, the inverse of what the X-14 did, is Matt and Altamirano 2026 on an octocopter in hover, Juhasz et al. 2025 on a hovering biplane tail-sitter, Perry et al. 2023 on a distributed-electric-propulsion aircraft, Abdul Rashid et al. 2025 and Chornyi et al. 2026 on small aircraft, and Simmons et al. 2023 and Grauer and Morelli 2023 on the methods generally.

Subscale flight testing is how the expensive part is avoided, in Pan et al. 2026, Comer et al. 2026c on a transitioning vehicle, and Shen and Chen 2025 on model-in-the-loop validation. The economic change matters most. The X-14 cost an airframe, two engines, a control system, and twenty-four years of a flight-test organisation. A subscale vehicle that answers a narrower version of the same question costs far less and can be replaced when it crashes, which changes not only the price of an experiment but the acceptable probability of losing one.

Gravity Is Still Not Adjustable, and Someone Flew on Mars

The article’s sharpest limitation on the X-14 was that it could reproduce lunar attitude dynamics exactly and lunar translation 2.46 times too fast, because gravity is in the plant rather than in the controller.

That limitation is unchanged and the field still works around it the same way. Aldosari and Feron 2025 reports acceleration flight control for reduced-gravity flight in a large fixed-wing aircraft, the parabolic-trajectory descendant of the Lunar Landing Research Vehicle’s weight cancellation, and Li et al. 2024b designs a low-gravity simulation scheme for a Mars ascent vehicle. The alternative is to stop simulating and go, and Ågren et al. 2026 reports in-flight system identification of the Ingenuity Mars helicopter, which is the first time the dynamics of a hovering vehicle have been identified in another planet’s gravity from that planet’s surface. Its ground effect is treated in Caprace et al. 2025.

The guidance problem the X-14A could only partly rehearse now has a large literature, in Inoue et al. 2026, Sasaki et al. 2025, Zhang et al. 2025a, Ito et al. 2025b, Wang et al. 2024g, Robbiani et al. 2025, Sandoval et al. 2024, and Abdhul Rahuman and Lee 2026.

Ground Effect Became a Vertiport Problem

A jet-lift aircraft needing a prepared surface was held against it, and Rolls 1965b sought to free the jet from operating only over concrete. A modern vertical take-off aircraft needing a licensed vertiport is treated as infrastructure.

The aerodynamics are Lee et al. 2026a on rotor-rotor interaction in ground effect, Sagaga and Lee 2025 on side-by-side rotors, Zhu et al. 2024b on staggered rotors, Georgiev 2025 on low-Reynolds-number rotors near the ground, Shirbhate et al. 2025 and Boschetti et al. 2022 on wings, and the control consequence is Kato and Suzuki 2019. The ingestion and erosion problems the X-14 programme met are Li et al. 2025d, Ghosh and Rajagopalan 2022, Bardera Mora and Matías García 2022, and Sharma et al. 2021, and the prepared surface is Guleria et al. 2023.

What has changed is whose problem it is. The infrastructure literature is now large, in Li et al. 2026g, Lyu and Feng 2026, Mirković et al. 2026, Zhou et al. 2026a, and Rajendran et al. 2023, with noise in Rizzi et al. 2026 and Pascioni et al. 2026, risk in Hu et al. 2026d, Chen et al. 2026e, and Dai et al. 2024, and crashworthiness and battery safety in Schatrow et al. 2025 and Bosch et al. 2025. The requirement did not go away. The expectation did.

The Tip-Fan Failure Mode Survives, and Was Beaten by the Drive

The most transferable single result in this article is that the X-14A’s tip-turbine fans delivered nearly the control power of the reaction nozzles they replaced, 0.65 against 0.70 radians per second squared, and were unflyable because of their time constants.

A multirotor changes its attitude moment by changing rotor speed, the mechanism that failed in 1969. The rotors are of comparable size, since the X-14A’s fans were 12.8 inches in diameter in Gerdes and Rolls 1969 and a small quadrotor’s rotors are of that order. What changed is the drive. An electric motor delivers far more torque per unit of rotor inertia than a bleed-fed tip turbine, so the same geometry has a much shorter time constant, and the failure mode is avoided rather than removed. The electric propulsion and power literature that sets those limits is Litt 2024, Xiao et al. 2024, Jing et al. 2025, Park 2026, Nakayama et al. 2026, Li and Jiang 2026, Critchfield and Ning 2026, and Liu et al. 2024a, with the configuration space explored and compared in Chen et al. 2026d. Morphing and reconfiguration, which changes the plant in flight the way the X-14A’s system changed it artificially, is Zhu et al. 2025b. Cyber integrity and software validation now sit alongside, in Emeto et al. 2026 on a cyber-resilient flight architecture and Ide and Landman 2025 on validating multirotor flight-time prediction by flight test, and the near-ground aerodynamics of small inclined plates is Pieris et al. 2023.

What Has Not Changed

Four of this article’s findings have no modern remedy.

Control power still falls inversely with span, by the same exponent, through a mechanism that shares no hardware with the one that produced it. Large hovering vehicles are still hard.

Attitude authority is still taken from lift on any vehicle that produces both from the same source. The multirotor’s advantage is that its differential is zero-mean rather than that its control is free.

The threshold is still a property of the person. No amount of modelling has removed the need to ask a human being whether a vehicle is acceptable, which is why a rating scale descended from the Cooper scale of 1957 is still in use.

And gravity is still not adjustable. Every argument in this article about what the X-14 could not simulate applies unchanged to any Earth-based simulator for any other body, which is why reduced-gravity flight remains a live engineering subject rather than a historical one.

Handling-qualities criteria, ratings and specifications

The criterion the X-14 produced, and the discipline it belongs to. Handling-qualities and flying-qualities criteria, pilot rating and its scales, the military specifications and the Aeronautical Design Standard 33 for rotorcraft that carry the criteria, and the design methods that aim at them. Only 211 of its 617 titles name a vertical or short take-off aircraft, a helicopter, a tilting configuration or the hover, and the rest concern conventional aeroplanes, which is the parent discipline from which the X-14’s method was carried into the hover rather than a literature of its own.

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al. 1984] [Lantzsch et al. 2014] [Larrabee and Tymczyszyn 1968] [Lateral Control Power Rolling 2003] [Lateral-Directional Flying Qualities 2002b] [Lateral-Directional Flying Qualities 2002a] [Lawrence and Padfield 2003] [Lawrence and Padfield 2005] [Lawrence and Padfield 2006] [Lawrence et al. 2016b] [Lawrence et al. 2016a] [Lawrence et al. 2018] [Lebacqz and Forrest 1982] [Lebacqz and Scott 1984] [Lebacqz et al. 1982b] [Lee et al. 2001] [Leggett and Cord 1994] [Leggett et al. 1990] [Lemaignan 2005] [Levison 1982b] [Levison 1982a] [Levison and Rickard 1981] [Lewis et al. 1987] [Liang et al. 2025b] [Lind and Tamplin 1981] [Lollar and Kriechbaum 1968] [Lollar et al. 1965] [Longitudinal Flying Qualities 2002b] [Longitudinal Flying Qualities 2002a] [Low and Garrard 1991] [Low and Garrard 1993] [Luria et al. 2012] [Lusardi 2023] [Lusardi et al. 2004] [Lusardi et al. 2010] [Macedo et al. 2020] [Malaek and Karimi 2008] [Malpica and Lusardi 2013] [Malpica et al. 2015] [Mavris et al. 1998] [Memon et al. 2021] [Meyer 1983] [Meyer and Husband 1990] [Miller 1969] [Miller 1970] [Miller and Franklin 1968] [Mitchell 2019] [Mitchell and Hoh 1982] [Mitchell and Hoh 1983] [Mitchell and Hoh 1985] [Mitchell et al. 1987, A flight investigation of helicopt] [Mitchell et al. 1989] [Mitchell et al. 1992] [Mitchell et al. 1995] [Mitchell et al. 2003] [Mitchell et al. 2009b] [Moennich and Dalldorff 1993] [Momiyama 1977] [Montgomery 1971] [Mooij 1985a] [Mooij 1985d] [Mooij 1985c] [Moorhouse 1979] [Moorhouse 1990] [Moorhouse 1995] [Moorhouse et al. 1989] [Morris et al. 2013] [Mudd 1969] [Musso et al. 2026] [Neal and Smith 1970] [Neal and Smith 1971] [Neighbor and Wiler 1978] [Nettleton 1965] [Newell 1963] [Newton 2025] [Nichols 1960] [Nicoll and Mitchell 2009] [Ockier 1993] [Ockier 1996] [Oelker et al. 2009] [Ohta et al. 1977] [Orra et al. 2013] [Padfield 1998] [Padfield 2006] [Padfield 2013] [Padfield and Wilkinson 1997] [Page and Gillette 1994] [Pasha et al. 1982] [Patton 1972] [Pauli et al. 1974] [Perfect et al. 2014] [Perhinschi 2000] [Peterson and Grant 2011] [Pitt and Heacock 1979] [Place et al. 1974] [Portapas et al. 2017] [Potsdam and Hodgkinson 1990] [Potvin and Grant 2026] [Prabhakar et al. 2019] [Price 1964b] [Pritchard et al. 2016] [Puig - Navarro et al 2019] [Quigley and Holzhauser 1974] [Radford and Andrisani 1984] [Radford and Andrisani 1980] [Raffel et al. 2021b] [Raffel et al. 2021a] [Ranaudo et al. 2000] [Ransone 1970] [Raol and Singh 2023] [Reeder 1958] [Reeder 1960a] [Requirements of V/STOL Systems 1992] [Reschak 1970] [Reschak 1971] [Riboldi et al. 2026] [Riccardi et al. 2025] [Rich 1969b] [Rickard and Levison 1981] [Riley and Drajeske 1991] [Riley and Wilson 1990] [Risse et al. 2010] [Ritter et al. 1971] [Robbins 1967] [Rodchenko et al. 2003] [Rogalski and Dołęga 2006] [Rohling 1968] [Rohling 1969] [Rotorcraft Handling Qualities Design 2011] [Rowan and Dogan 2023] [Ruflin and Grantham 1984] [Rynaski 1985] [Rynaski 1994] [Rynaski et al. 1986] [Rysdyk and Calise 2005] [Ryu and Andrisani 2000a] [Ryu and Andrisani 2000b] [Ryu and Andrisani 2003] [Sachs 1990] [Sachs 1999] [Saetti and Rogers 2020] [Saetti and Rogers 2024] [Saetti et al. 2020c] [Sahasrabudhe and Celi 1997] [Salem et al. 2014] [Saporito et al. 2021] [Sarrafian and Powers 1988] [Saucez] [Schaum 1977] [Schmidt 1981] [Schmidt 1983a] [Schneider and Wilkerson 1990] [Schrage and Meyer 1986] [Schuck et al. 2013] [Schuler 1983] [Schy 1972] [Schönenberg 2011] [Schönenberg 2013] [Scroggs et al. 2023] [Shibata et al. 1987] [Shomber and Gertsen 1967] [Sissingh 2015] [Slaughter 1958] [Smetana et al. 1973] [Smit et al. 2022] [Smith 1966c] [Smith 1977] [Smith 2020] [Smith 2023] [Soban et al] [Solies 1995] [Srinathkumar 2011] [Srinathkumar 2015] [Stability Control and Handling 2024] [Stapleford and Walton 1966] [Stengel 1981] [Stengel 1985] [Stengel and Miller 1978] [Stepniewski and Schneider 1964] [Stettner and Voss 2002] [Stevens and Roskam 1985] [Stinton 1987] [Strand and Ennis 2012] [Suchomel 1987] [Sun et al. 2020] [Swaim 1970] [Swaim 1978] [Swaim 1979] [Swaim 1980] [Swaim 1981] [Swaim and Poopaka 1982] [Swaim and Yen 1979] [Tajar et al. 2015] [Tapscott 1960b] [Tapscott 1960a] [Tapscott 1960c] [Tapscott 1964] [Taschner 1995] [Teofilatto 2001] [Teper and Stapleford 1965] [Teper and Stapleford 1966] [Teplitz 1971] [Thome et al. 1999] [Thomson and Bradley 1997] [Thomson et al. 2005] [Thukral and Innocenti 1992] [Tigges et al. 2011] [Tischler and Hoh 1982] [Tomczyk 2001] [Tomczyk 2002] [Tomczyk 2008b] [Tomczyk 2008a] [Tseng et al] [Tseng et al. 2006a] [Turner et al. 2002] [Uybarreta et al. 2024] [Van Dam et al. 1980] [van Dam et al. 1981] [Vijaya Kumar et al. 2008] [Walker et al. 2007] [Walsh 1993] [Wang and Chen 2024] [Wang et al. 2021a] [Wanner 1973] [Warner and Onstott 1986] [Waszak and Schmidt 1985] [Wei 1985] [Wei et al. 2023] [Wendel 1987] [Wernecke 1958] [Westbrook 1964] [Westbrook 1965] [Whalley 1993] [Whitbeck and Hofmann 1978] [White and Innis 1959] [Wilcox and Quigley 1978] [Wilhelm and Schafranek 1986] [Wilson and Riley 1989] [Wilson et al. 1993a] [Wilson et al. 1993b] [Wilson et al. 1994] [Wolfram et al. 2008] [Woodcock and Browne 1986] [Wright and Lappos 1979] [Wright and Lappos 1981] [Wu 2025] [Wynosky and Szyszko 1973] [Yen and Swaim 1977] [Yue and Postlethwaite 1990] [Zanoni et al. 2022a]

Electric vertical take-off aircraft, urban air mobility and vertiports

The modern hovering aircraft and the ground it needs. Electric vertical take-off aircraft and their lift-plus-cruise, tilting and multirotor configurations, their propulsion, batteries and crashworthiness, urban air mobility operations, and the design, siting and capacity of vertiports. Vertiports are named in 107 titles and handling or flying qualities in 18, which bears out the review’s statement that the requirement has become an infrastructure problem as much as a control one. Its median publication year of 2024 is the latest of any cluster.

573 records. [Jacob da Motta 2020] [Abergo et al. 2026a] [Abraham et al. 2026] [Acheson et al] [Adebimpe 2023] [Adeline et al. 2023] [Agustinho and Bento 2022] [Ahmed] [Akash et al. 2021] [Al labbad] [Alcañiz-Brull et al. 2026b] [Alcañiz-Brull et al. 2026a] [Altamirano et al] [Altamirano et al. 2022] [An et al. 2022] [Ariante and Papa 2024] [Ariante et al. 2022] [Asfour et al. 2025] [Ayalew et al] [Ayyaswamy et al. 2023] [Bacchini et al. 2021] [Bahr et al. 2020] [Bahr et al. 2021a] [Bai et al. 2024] [Bapat et al. 2025] [Bapat et al. 2026] [Barakos 2024] [Barbarino et al. 2022] [Barrett et al. 2023] [Bassey 2025] [Bauer 2021] [Begault] [Bernyk et al. 2023] [Bhandari et al. 2023] [Bhandari et al. 2024] [Bickmeier and Levitt] [Bills et al. 2023] [Bisht et al. 2024] [Blume 2026] [Bosch et al. 2025] [Boyd n.d.] [Bridgelall et al. 2023] [Brignardello 2023] [Bris and Nguyen 2022] [Le Bris and Nguyen 2023a] [Brito] [Brown and Harris 2020] [Bullock et al. 2024] [Busan et al. 2021] [Bustamante Alarcon et al. 2023] [Cacciavillani and Ielmini 2019] [Cai et al. 2026] [Campbell et al] [Casanova et al. 2025] [Cha et al. 2023] [Cha et al. 2024] [Cha et al. 2025] [Chahba] [Chakraborty and Mishra 2021] [Chakraborty and Mishra 2022] [Chakraborty and Mishra 2023a] [Chakraborty et al. 2022] [Chakraborty et al. 2023a] [Chakraborty et al. 2024a] [Chamberlain et al. 2026] [Chan 2019] [Chandravanshi et al. 2026] [Chang et al. 2022] [Chang et al. 2023a] [Chang et al. 2026] [Chaohui et al. 2026] [Chapman 2019] [Charnsethikul et al. 2025] [Chatterji] [Chatterji 2020] [Chen et al. 2022c] [Chen et al. 2024a] [Chen et al. 2026a] [Chen et al. 2026d] [Chen et al. 2026e] [Cheng et al. 2025b] [Cheyno 1967] [Choi et al. 2021] [Choi et al. 2026b] [Christy et al] [Christy et al. 2026] [Ci̇zreli̇oğullari et al 2022] [Clare 2026] [Cohen 1996] [Cokorilo 2020] [Cole et al. 2021] [Comer and Chakraborty 2024] [Comer et al. 2024a] [Comer et al. 2024b] [Conrad et al. 2023] [Conrad et al. 2024] [Cornelius] [Cornes 2019] [Cox-Gross and Collins 2025] [Critchfield and Ning 2026] [Cureton 2020] [Dai] [Darmstadt et al. 2021b] [Darrah et al. 2022] [Daskilewicz et al. 2018] [Datta 2021] [Dawe et al. 2025] [Demers Bouchard et al. 2015] [Deng et al. 2024] [Deng et al. 2026a] [DeVore et al. 2022] [Ding et al. 2025] [Dixit 2023] [Doff-Sotta et al. 2022] [Donateo and Çinar 2022] [Doo et al. 2021] [Dožić et al. 2026] [Duffy and Samaritano 2015] [Eißfeldt 2020] [Elahi Kahooker and Liu 2026] [Ellis et al. 2023] [Enenakpogbe et al. 2022] [Fardin et al. 2026] [Farides 2025] [Feroskhan et al. 2025] [Ferrare] [Finger et al. 2018] [Fisler and Datta 2019] [Fredericks et al. 2013a] [Fredericks et al. 2013b] [Fregnani and Balvedi 2026] [Furlan et al. 2026] [Gao et al. 2025a] [Garcia et al. 2026] [García Crespillo et al. 2024] [Garg and Moon 2026] [Gawenda 2025] [German et al] [Gilmore 2025] [Goldschmidt and Ukeiley 2023] [Gómez et al. 2021] [Aviation et al. 2025] [Goodrich] [Goodrich] [Goshtasbi et al. 2024] [Gottschalg et al. 2025] [Gottschall et al. 2022] [Gouveia et al. 2022] [Granata et al. 2024] [Grauer et al] [Greenfeld 2020] [Gress 2024] [Guerrero and Clarke 2026] [Guida 2023] [Guo et al. 2025b] [Guo et al. 2025d] [Guruswamy 2020] [Gutierrez] [Galffy et al. 2023] [Ha et al. 2024] [Ha et al. 2026] [Hakim 2024] [Halder and Gandhi 2026] [Han et al. 2025c] [Han et al. 2026] [Dabaghian and Halder 2025] [Hasselmann 2026] [Hatherall et al. 2024] [Haworth et al] [He et al. 2023] [He et al. 2024] [He et al. 2025] [Hearn et al. 2023] [Heidary and Kosari 2024] [Heilein and Crespillo 2024] [Hendricks et al. 2019] [Heo et al. 2026] [Hess 2019] [Hess et al. 2024] [Higgins et al. 2020] [Higgins et al. 2021] [Hijazeen et al. 2026] [Hirschberg 2023] [Hoffelner et al. 2023] [Hsu et al. 2023] [Hsu et al. 2024] [Hu] [Hu et al. 2025b] [Hu et al. 2025c] [Hu et al. 2026a] [Hu et al. 2026d] [Tech et al. 2025] [Huangfu et al. 2024] [Hui et al. 2024] [Hwang et al. 2024] [Hyodo and Lei 2024] [Hyun et al. 2023] [Ilapuram] [Ito and Adachi 2023] [Jensen 1990] [Jeon et al. 2024b] [Jeong et al. 2024] [Ji et al. 2026] [Jiang and Pakmehr 2022] [Jiao and Yang 2026] [Johnsen et al. 2022] [Johnson and Silva 2022] [Jones et al] [Josephson 2020] [Kadhiresan and Duffy 2019] [Kai et al. 2022] [Kaneko and Martins 2023] [Kaneshige et al. 2023] [Kang 2025] [Kang et al. 2024a] [Kang et al. 2025b] [Kang et al. 2025a] [Kang et al. 2026a] [Kang et al. 2026b] [Karimli and Marano 2025] [Karklin 2026] [Keller et al. 2024] [Keller et al. 2026b] [Keller et al. 2026a] [Li and Lee 2021] [Keçeci and Oktal 2026] [Kim and Hong 2024] [Kim and Park 2022] [Kim et al. 2024b] [Kim et al. 2024a] [Kim et al. 2025c] [Kim et al. 2025a] [Kim et al. 2026a] [Kirste and Stumpf 2025] [Kopyt and Ogrodnik 2026] [Kopyt et al. 2024] [Kou et al. 2021] [Kraenzler et al. 2019] [Kukla 2026] [Kumar 2026] [Kunwar et al. 2026] [Kwak et al. 2026] [Köse and Özuysal 2023] [Vu et al. 2025] [Laghrib et al. 2024] [Lampl and Armanini 2023] [Landi and Caccetta 2025] [Le Bris and Nguyen 2023b] [Lee and Park 2022] [Lee and Yee 2024] [Lee et al. 2024a] [Lee et al. 2024b] [Lee et al. 2025a] [Lee et al. 2025b] [Lee et al. 2026c] [Lepe and Huynh 2026] [Lerro 2020] [Letica and Rizzi 2024] [Li 2026] [Li and Jiang 2026] [Li et al. 2023b] [Li et al. 2024d] [Li et al. 2025c] [Li et al. 2025b] [Li et al. 2026a] [Li et al. 2026b] [Li et al. 2026g] [Liang et al. 2025a] [Lim] [Lim et al. 2023] [Lin 2023] [Lin et al. 2027] [Lippoldt et al. 2023] [Littell 2019] [Littell and Putnam] [Littell and Putnam] [Littell and Putnam 2023] [Littell et al] [Littell et al] [Littell et al] [Littell et al. 2019] [Littell et al. 2021] [Liu and Hupy 2025] [Liu and Wang 2024] [Liu et al. 2023] [Liu et al. 2025b] [Liu et al. 2026e] [Lombaerts et al. 2019] [Lombaerts et al. 2020b] [Love 2022] [Lowry 2018] [Luo and Chen 2026] [Lyu and Feng 2026] [Ma and Liu 2025] [Ma et al. 2025a] [Ma et al. 2025c] [Maksoud et al. 2025] [Maleki et al. 2024] [Maleki et al. 2025] [Malpica et al. 2023] [Malpica et al. 2024] [Mannan and Hassanalian 2024] [Marepally et al. 2025] [Marvakov et al. 2024] [Marzouk 2025] [Matveev et al. 2023] [Mbikayi et al. 2024] [McKercher] [McKercher et al. 2024] [McKillip et al. 2025] [McQueen 2021b] [McQueen 2021a] [Mendonca et al. 2022] [Menton 2026] [Mercan et al. 2024] [Mercan et al. 2025] [Mikic et al. 2021] [MirkoviĆ and Sindik 2024] [Mirković et al. 2026] [Mishra and Chakraborty 2024b] [Mishra and Chakraborty 2024a] [Misiorowski et al. 2019] [Mitchell et al. 2022] [Mitici et al. 2023] [Mo et al. 2026] [Mohana Sundaram and Kavya Santhoshi 2024] [Monk et al. 2025] [Moore and Hassanalian 2025] [Mpala and Chakraborty 2025] [Mukherjee et al. 2022] [Mukherjee et al. 2023] [Mulyanto et al. 2026] [Mumford et al. 2023] [Murphy et al] [Nakayama et al. 2026] [Naru 2025] [Naseer et al. 2026] [Nassir Tafreshi 2026] [Neogi et al] [Neogi et al. 2025] [Ng and Datta 2018] [Ng and Datta 2019] [Ng et al. 2020] [Nguyen 2025] [Nguyen and Webb] [Nguyen and Webb 2025] [Nguyen and Xiong] [Nguyen and Xiong 2026] [Nguyen et al. 2023] [Niemiec et al. 2020] [Ning et al. 2023] [Norsetter and Smith 2024] [North et al] [North et al. 2021] [Nunes et al. 2025c] [Nunes et al. 2025b] [Obertino et al. 2023] [Ogden 2023] [Oh et al. 2025] [Oh et al. 2026] [Paek 2025] [Paek et al. 2021] [Palaia et al. 2021] [Panish and Bacic 2025] [Park 2025] [Park 2026] [Park and Kim 2022] [Park and Kim 2026] [Park and Park 2025b] [Park and Park 2026] [Park et al. 2022] [Park et al. 2025b] [Park et al. 2025a] [Parvaz Afraz Hava Sanat et al. 2023] [Pascioni et al. 2026] [Patterson 2025] [Patterson et al. 2023] [Pavel 2022] [Paw and Ang 2023] [Pedrioli et al. 2024] [Peng et al. 2022] [Perry et al. 2019] [Perry et al. 2023] [Peryea 2026] [Pflüger et al. 2026] [Pham et al. 2022] [Pleffken 2026] [Pons-Prats et al. 2022] [Prabhakar et al. 2026] [Preis and Cheng 2022] [Preis and Hornung 2022a] [Preis and Hornung 2022b] [Pressburger et al. 2023] [Putnam] [Putnam and Littell] [Putnam and Littell] [Putnam and Littell 2020] [Putnam and Littell 2023] [Putnam et al] [Putnam et al. 2026] [Qiao and Zhou 2026] [Qiao et al. 2026a] [Qin et al. 2026] [Qu et al. 2024] [Rakas 2022] [Rakas et al. 2021] [Rathinasamy et al. 2024] [Rigby and Von Hardenberg 2024] [Rimjha and Trani 2021] [Rister and Bartling 2023] [Rizzi 2020] [Rizzi and Rafaelof 2021] [Rizzi et al. 2026] [Rogers and Holdstock 2022] [Rohrmeier et al. 2025] [Roiati et al. 2022] [Rosen 2026] [Rozman and Grace 2025] [Ruh et al. 2023] [Russo and Tan 2023] [Rylko et al. 2025] [Saberi et al. 2026] [Saetti et al. 2020b] [Saetti et al. 2022] [Safwat et al. 2026] [Sagaga and Lee 2020] [Sarkar et al] [Sarker et al. 2026a] [Savino and Zanotti 2025] [Schatrow et al. 2025] [Scherer et al. 2024] [Schier-Morgenthal et al. 2025] [Schrage et al. 2018] [Schuchardt et al. 2025] [Schuet et al. 2020] [Schweiger and Knabe 2023] [Schweiger and Preis 2022] [Schweiger et al. 2023] [Scott 2021] [Seren and Hornung 2020] [Shah 2025] [Shan et al. 2026] [Shapiro and Healy 1968] [Shaw-Lecerf et al] [Sheng and Zhao 2026] [Sherman 2019] [Sheth 2023] [Shi et al. 2023] [Shin 2025] [Shin et al. 2022] [Shin et al. 2024] [Shinozuka et al. 2024] [Shon and Lee 2025] [Shubert et al. 2026] [Simmons] [Simmons 2022b] [Simmons 2023b] [Simmons 2023a] [Simmons and Ackerman 2026] [Simmons and Busan] [Simmons and Hatke 2021] [Simmons and Murphy] [Simmons et al] [Simmons et al] [Simmons et al. 2025b] [Singh 2023] [Smith 2025] [Smith and Geddes 1979] [Snyder 2020] [Song 2022] [Song and Yeo 2021] [Song et al. 2021b] [Spraggett et al. 2026] [Standard Specification for Vertiport] [Staruk et al. 2023] [Stewart et al. 2026a] [Stoll and Bevirt 2022] [Su and Xu 2025] [Suh et al] [Suiçmez and Kutay 2023] [Sun et al. 2026] [Surmann et al. 2022] [Szafranski et al. 2014] [Tacke 2026] [Takacs and Haidegger 2022] [Tanabe et al. 2024] [Tang et al. 2023] [Taylor et al. 2020] [Thomas et al] [Tinney and Valdez 2024] [Tinney and Valdez 2025] [Torens et al. 2024] [Valente et al. 2023] [Tumuluru Ramesh and Pandurangi 2022] [Turchetti and Condé Rocha Murça 2024] [Ugwueze et al. 2023] [Unal and Yavrucuk 2021] [Unverricht et al. 2024] [Vandy 2026] [Vascik and Hansman 2019] [Verberne et al. 2024] [Vertiports - Infrastructure and] [Vieira et al. 2019] [Vincent] [Volakakis and Mahmassani 2024] [Vrdoljak et al. 2023] [Wachspress et al. 2019] [Wang et al. 2021c] [Wang et al. 2023c] [Wang et al. 2023a] [Wang et al. 2024h] [Wang et al. 2025g] [Wang et al. 2025a] [Wang et al. 2025b] [Wang et al. 2025h] [Wang et al. 2026c] [Wang et al. 2026l] [Wasson et al. 2022] [Wei et al. 2025] [Wen et al. 2020] [Westcott et al. 2023] [Westcott et al. 2025b] [Westcott et al. 2025a] [Whiteside and Welstead] [Whitt and Gandhi 2023] [Withrow-Maser et al] [Withrow-Maser et al] [Withrow-Maser et al. 2020] [Withrow-Maser et al. 2021] [Wong 2008] [Wyzykowski 2025] [Xie et al. 2026] [Xiong et al. 2023] [Xu et al. 2024] [Xue 2020] [Yan et al. 2023b] [Yang and Morales 2021] [Yang and Wei 2021] [Yang et al. 2026c] [Yilmaz et al. 2019] [Yokoyama et al. 2025] [Yoon et al. 2025a] [Young and Rajagopalan 2013] [Yu 2023] [Yu et al. 2023] [Yunus et al. 2024] [Zahn et al. 2024] [Zahn et al. 2025] [Zanotti and Algarotti 2022] [Zanotti et al. 2024] [Zelinski 2020] [Zhang and Hwang 2025] [Zhang et al. 2021c] [Zhang et al. 2023d] [Zhang et al. 2023a] [Zhang et al. 2024b] [Zhang et al. 2025b] [Zhang et al. 2025g] [Zhao and Han 2026] [Zhao et al. 2024b] [Zhao et al. 2024d] [Zhao et al. 2025a] [Zhao et al. 2025g] [Zhao et al. 2025e] [Zhao et al. 2025d] [Zheng et al. 2024] [Zhou et al. 2026a] [Zhou et al. 2026b] [Zhu et al. 2022b] [Ziakkas 2026] [Zong et al. 2021] [Zong et al. 2022] [Zuo et al. 2025]

Lunar landing, planetary flight and the gravity a simulator cannot change

The gravity a terrestrial simulator cannot change, and the vehicles built because of it. Lunar landing simulation and the vehicles that trained for it, the Apollo lunar module and its touchdown, piloted and automatic lunar landing, powered descent guidance on the Moon and Mars, reduced-gravity flight, and flight on Mars. Powered descent is named in 117 titles, and the Mars helicopter and Martian rotorcraft in 56, against 17 that name handling qualities, so the modern literature treats the landing as a guidance problem far more often than as a piloting one.

454 records. [Aagren et al] [Abelson 1963] [Acikmese and Ploen 2005] [Acikmese and Ploen 2007] [Acikmese et al. 2008] [Adams et al. 1970] [Aklan 2025] [Aldosari and Feron 2025] [Ali et al] [Ali et al] [Allen and Levin 1965] [Allen et al. 1965] [Amato 2021] [Anand et al. 2025] [Anzaline et al. 2019] [Arai et al. 2020] [Armstrong and Nassiff 1968] [Arthur et al. 2008] [Arthur et al. 2010] [Aung 2019] [Aung 2020a] [Aung 2020b] [Azimov 2013] [Azimov 2016] [Azimov and Bishop 2018] [Azimov and Bishop 2025a] [Azimov and Bishop 2025b] [Azimov and Bishop 2025c] [Azimov and Bishop 2025d] [Azimov and Bishop 2026] [Ramya et al. 2025] [Bailey et al. 2009] [Bailey et al. 2025] [Balaram 2018] [Balaram 2020] [Balaram et al. 2018] [Banerjee and Padhi 2015] [Banerjee and Padhi 2017] [Banerjee and Padhi 2018] [Banerjee et al. 2016] [Barabush 1962] [Barker and Queijo 1964] [Bartos and Greenberg 1963] [Basar and Ghosh 2023] [Bellman and Matranga 1965] [Benito et al. 2017] [Benton 2026] [Berning et al. 2023] [Besco 1964] [Bigham 1970] [Bilimoria 2008] [Bilimoria 2009] [Bilimoria 2019] [Blackmore et al. 2010] [Blanchard 1969] [Boyd et al. 1967] [Bozajian 1964] [Bozajian 1965] [Brady and Paschall 2010] [Brady et al. 2009] [Briden et al. 2025] [Bu et al. 2010] [Buckner et al. 2026] [Cai et al. 2014b] [Calkins et al. 2024] [Cappucci 2020] [Cappucci 2021] [Cappucci and Pauken 2021] [Caprace et al. 2025] [Caros et al. 2026] [Carson et al. 2011] [Ceresoli 2026] [Chae et al. 2023] [Chambers and Korzun] [Cheatham and Hackler 1966] [Chen et al. 2010a] [Cheng and Pfeffer 1962] [Cheng et al. 2006] [Cheng et al. 2019b] [Chengchao et al. 2018] [Chenoweth et al. 1963] [Cho et al. 2024] [Choi and Kim 2024] [Choi and Kim 2025] [Choi et al. 2026a] [Chu et al. 2017] [Chua and Major 2009] [Chua et al. 2010] [Clark et al. 2011] [Cohanim 2008] [Cohanim and Collins 2009] [Cohen 2012] [Condoleo et al. 2017] [Corker and Reger 1984] [Cortés-Martínez et al. 2021] [Crane and Rock 2012] [Crues et al. 2024] [Cummings et al] [D’Souza and D’Souza 1997] [Dan Tuckness 1994] [Davami et al. 2025] [Davis et al. 2010] [de Lafontaine et al. 2008] [Delaune et al. 2010] [Desiderio and Lovera 2010] [Digesu 1963] [Ding and Wang 2016] [Do 2014a] [Do 2014b] [Do and Paxman 2013] [Doiron and Zupp 2000] [Donahue 1996] [Donahue 1997] [Drinkwater and Rolls 1963b] [Drinkwater et al. 1963] [Duda et al. 2010] [Duda et al. 2026] [Dueri et al. 2017] [Dull et al] [Duncan 2020] [Durling and Walton 1967] [Durling et al. 1964] [Edwards et al. 1997] [Eichler 1967] [Elango et al. 2022] [Elena 2026] [Engle 2004] [Erzberger 1967] [Erzberger 1968a] [Escobar et al. 2019] [Excerpts from Test Films 1968] [Fan et al. 2021] [Feng and Wasynczuk 1967] [Fletcher and Miller 1965] [Ford 1969] [Forest et al. 2008] [Fox 2021] [Gao et al. 2024] [Gao et al. 2025b] [Gaudet and Furfaro 2022] [Ge and Cui 2018] [Gelino et al] [Geller and Christensen 2009] [Gelzer 2006] [Gelzer 2009] [Gentile et al] [Ginosar et al. 2023] [Gong et al. 2014] [Gong et al. 2024] [Goodworth and Fontes] [Gorton] [Grady 2021] [Greene and Russo 1967] [Grenier et al. 2022] [Grip 2021] [Grip et al. 2020] [Guo et al. 2016] [Hall et al. 1964] [Han 2026] [Hayes and Pei 2024] [Hayner et al. 2025] [He et al. 2026] [Henderson 1963] [Hengeveld et al. 2018] [Herr and Leonard 1964] [Herr and Leonard 1967] [Hewes 1967] [Hewes and Obryan 1967] [Hilderman et al. 1966] [Hildreth and Burton 1983] [Hornus et al. 2026] [Huertas et al. 2011] [Idan and Grunwald 1999] [Strohl et al] [Ikeda et al. 2001] [Ingenuity 2022] [Ingenuity Operations 2022] [Inoue et al. 2026] [Irwin 1966] [Ito 2017] [Ito and Sakai 2023] [Ito et al. 2025b] [Ito et al. 2025a] [Koning et al. 2018c] [Jang et al. 2025] [Jaquet 1964] [Jaquet and Riley 1964] [Jarvis 1966] [Jarvis 1967b] [Jarvis 1967a] [Jeon et al. 2024a] [Ji and Liang 2021] [Jiang et al. 2018] [Jing-Yang et al. 2006] [Johnson and Montgomery 2008] [Johnson et al. 2015] [Johnson et al. 2020] [Johnston et al. 2020] [Kelly 1992] [Kim et al. 2021] [Kluever 1967] [Klumpp 1968] [Klumpp 2003] [Koning and Dominguez 2024] [Koning et al] [Koning et al. 2018b] [Koning et al. 2018a] [Koning et al. 2024] [Korzun et al. 2020] [Kozynchenko 2010] [Kramer et al] [Kramer et al. 2009] [Kramer et al. 2023] [Kumar et al. 2025] [Kumar et al. 2026] [Kuo et al. 2020] [Kwon et al. 2021] [Lan et al. 2025] [Land and Scholl 1969] [LANDER Program Manual 1988] [Latyshev et al. 2020] [Lavender 1965] [Lawrence and Scofield 1971] [Lee 1964] [Lee and Mesbahi 2012] [Li et al. 2016a] [Li et al. 2021b] [Li et al. 2023f] [Li et al. 2024b] [Li et al. 2024e] [Liang et al. 2011] [Liever and West] [Liu et al. 2013] [Liu et al. 2014b] [Liu et al. 2017a] [Liu et al. 2021b] [Liu et al. 2026d] [LLRV/Apollo 11 25th Anniversary 1994] [Lona and Swaminathan 2025] [Long 1968] [Lonner et al. 2024] [Lovas 2026] [Lu 2018] [Lu 2019] [Lu 2020a] [Lu 2020b] [Lu 2026a] [Lu 2026b] [Lu and Callan 2023] [Lu and Davami 2024] [Lu and Sandoval 2021] [Lu et al. 2018] [Lugo et al] [Lugo et al] [Lugo et al] [Lugo et al. 2022] [Lugo et al. 2025] [Lunar Lander 2006] [Lunar landing] [Lunar Landing 2026a] [Lunar Landing 2026b] [Lunar Landing and Launch 1988] [Lunar Landing Rehearsal 1969] [Lunar Landing Research Facility 1962] [Luo and Bao 2023] [Luo et al. 2006] [Lysandrou and Braun 2021] [Ma et al. 2022a] [Maeda et al. 2014] [Markson et al. 1963] [Mason and Brainin 1962] [Mason and Nordmeyer 1969] [Mathavaraj et al. 2017] [McCabe et al. 1967] [McGuire and Oleson 2010] [Mehta et al. 2010] [Meissinger 1963] [Menou et al. 2022] [Merchant and Sawdy 1970] [Merchant and Sawdy 1971] [Mikhaylyuk et al. 2021] [Moghe and Zanetti 2020] [Mu et al. 2023] [Mueller et al. 2009] [Mueller et al. 2010] [Mueller et al. 2011] [Mueller et al. 2012] [Mukhopadhyay 1969] [Murphy 2010] [Myers et al. 1982] [NASA’s Ingenuity Mars Helicopter 2020] [Obryan 1966a] [Obryan 1966b] [Olsen 2024] [Orphee et al. 2019] [Orr and Shtessel 2008] [Pascucci et al. 2015] [Pastorelli 2013] [Pei et al] [Perez et al] [Petersen et al. 2020] [Phillips 1988] [Pino and Condon] [Pipenberg et al. 2019] [Planning the lunar landing] [Ploen et al. 2006] [Pollack et al. 1967] [Pontani et al. 2022] [Pontani et al. 2023] [Powers 1984] [Powers 1986a] [Preliminary Landing Tests 1962] [Qiao et al. 2020] [Radotich et al] [Abdhul Rahuman and Lee 2026] [Rea and Bishop 2010] [Remesh et al. 2021] [Reynolds and Mesbahi 2020] [Reynolds et al. 2020b] [Reynolds et al. 2020a] [Reynolds et al. 2021] [Rhodes and Morehead 2025] [Ridderhof and Tsiotras 2018] [Ridderhof and Tsiotras 2021] [Rimer and Sperling 1965] [Robbiani et al. 2025] [Roberts 1964] [Rogerson 2021] [Ruan and Aagren 2025] [Ryken 1966] [Mathavaraj and Padhi 2017] [Pontani and Caruso 2025] [Sachan and Padhi 2015] [Sachan and Padhi 2019] [Sadraey 2017] [Saeki et al. 2015] [Sagliano 2018b] [Sagliano 2018a] [Sagliano 2019] [San Martin et al. 2017] [Sandoval et al. 2024] [Saripalli and Sukhatme] [Sasaki et al. 2025] [Scharf et al. 2015] [Scharf et al. 2017] [Schatzman et al] [Schuiling 2001] [Scorsoglio et al. 2020] [Scorsoglio et al. 2022] [Shan and Duan 2006] [Shen et al. 2010a] [Shields et al. 1982] [Shoemaker et al. 2022] [Shuang and Pingyuan 2006] [Siddhardha 2019] [Siddhardha and Manathara 2022] [Singh] [Singh et al. 2007] [Smith 1981] [Smith et al. 2008] [Song et al. 2020] [Song et al. 2021a] [Sostaric and Rea 2005] [Spada et al. 2023] [Starkweather 1971] [Steffes et al. 2023] [Stegall 1965] [Stengel 1979] [Su et al. 2023] [Swaminathan and Lona 2025] [Swaminathan et al. 2020] [Szmuk et al. 2017] [Szmuk et al. 2020] [Talekar et al. 2021] [Tang et al. 2026] [Testing and Delivering Ingenuity 2022] [Topcu et al. 2005] [Topcu et al. 2007] [Trawny et al. 2015] [Tucker 1967] [Tzanetos 2021] [Ueda et al. 2018] [Ueda et al. 2024] [Ueda et al. 2025] [Ueno and Yamaguchi 1998] [Ueno and Yamaguchi 1999] [Ulybyshev 2019] [Ulybyshev 2021] [Uzun et al. 2025] [Valdez 2021] [van Susante and Metzger 2016] [Varga and Young 1966] [Varga and Young 1967] [Veismann et al. 2021] [von Ehrenfried 2022] [Wagner 2019] [Wan et al. 2010] [Wan et al. 2020] [Wan et al. 2022] [Wang et al. 2008] [Wang et al. 2013] [Wang et al. 2024f] [Wang et al. 2024c] [Wang et al. 2024g] [Wang et al. 2026f] [Weaver et al] [Weiss et al. 2026] [Williams et al. 2008] [Williams et al. 2022] [Wiston and Yan 2025] [Withrow-Maser et al] [Withrow-Maser et al] [Woicke and Mooij 2016] [Wright et al] [Wu] [Wu et al. 2007] [Wu et al. 2026b] [Xiao et al. 2026a] [Ximenes 2010] [Xu et al. 2015b] [Xu et al. 2018a] [Yan et al. 2026] [Yang and Liu 2020] [Yiyu et al. 2015] [You et al. 2020] [You et al. 2021a] [You et al. 2021b] [You et al. 2022] [Young 2017a] [Young 2017b] [Young et al. 2000] [Yu et al. 2021b] [Yu et al. 2021a] [Yuan et al. 2018] [Zahn 2023] [Zenk et al. 2019] [Zhang and Duan 2013] [Zhang and Li 2016] [Zhang et al. 2016c] [Zhang et al. 2017a] [Zhang et al. 2021b] [Zhang et al. 2021a] [Zhang et al. 2025a] [Zhang et al. 2026d] [Zhao et al. 2017] [Zhao et al. 2022] [Zhao et al. 2023b] [Zheng and Cui 2015] [Zhiyuan Li and Hongjue Li 2014] [Zhou et al. 2009] [Zhou et al. 2011] [Zhou et al. 2022b] [Zhou et al. 2023] [Ågren et al. 2026]

The human operator and pilot models

The pilot as a dynamic system to be identified. The human operator in manual control, describing functions and their remnant, the crossover and structural models, the optimal control model of the pilot, adaptation to changing dynamics, and the proceedings of the manual control conferences. Compensatory or pursuit tracking is named in 40 titles and the optimal control pilot model in 22, which is the parallel literature the article describes as running through the same years and institutions as the rating scale.

437 records. [Abdel-Malek and Marmarelis] [Abdessameud and Janabi-Sharifi 2013] [Abdessameud and Tayebi 2013b] [Adams 1972] [Adams 1976] [Adams 1983] [Adams and Bergeron 1963] [Adams and Moore 1976] [Adams et al. 1978] [Afloare et al. 2018] [Agarwal et al. 1982] [Ailon] [Akashi and Mahmood 1965] [Al-barzinji] [Alex et al. 1969] [Amato et al] [Amin and Li 2017] [Amit Ailon 2006] [An Experimental Study 1961] [Anderson] [Anderson 1994b] [Anderson and Page 1995] [Andrisani 1982] [Andrisani and Gau 1985] [Andrisani 1983] [Angel 1967] [Angué et al. 1978] [Aponso et al. 1987] [Application of the Optimal 1974] [Arif and Inooka 1999] [Arnold 2015] [Bachelder and Aponso 2017] [Bachelder and Aponso 2021a] [Bachelder and Aponso 2022] [Bachelder et al. 2023c] [Bachelder et al. 2023b] [Baron 1973b] [Baron 1973a] [Baron 1984] [Baron and Kleinman 1972] [Baron and Levison 1977] [Bartram et al. 1985] [Baty 1969] [Bekey 1969] [Bekey and Merritt 1967] [Bekey and Neal 1971] [Bekey and Phatak 1969] [Bekey et al. 1966] [Bekey et al. 1967] [Benoit et al. 2014] [Benosman et al. 2007] [Berger and Meyer 1974] [Bergeron 1970] [Bernard and Cruz Neira 2002] [Bidinotto et al. 2021] [Biezad and Schmidt 1984] [Biezad and Schmidt 1985] [Bliss 1967] [Bocola et al. 2015] [Bogart and Waller 1985] [Bottasso et al. 2009] [Bragado Aldana et al. 2025] [Brauser 1982] [Brauser 1983] [Brieger et al. 2008] [Brooks and Ransbury 2012] [Broussard and Berry 1982] [Buck et al. 1978] [Burgett 1969b] [Burgett 1969a] [Burton et al. 2026] [Cameron et al. 2003] [Campos et al. 2021] [Cavalli 1977] [Cavalli 1978] [Cerchie 1989] [Chambers 1963] [Chang et al. 2023b] [Chase 1997] [Chen and Horn 2025] [Chen et al. 2019a] [Chen et al. 2019b] [Chernikoff and Taylor 1957] [Chernikoff et al. 1955] [Christensen et al. 1981] [Cohen and Ferrell 1969] [Colburn 1978] [Collins et al. 1968] [Compensatory Tracking 2010] [Consolini and Tosques 2006] [Control Characteristics 2023] [Costello 1968] [Craig and Heffley 1972] [Craun et al. 2013a] [Curry et al. 1976] [Dai et al. 2024] [Damos and Lintern 1979] [Dantzig 1975] [Davenport et al. 1981] [Davidson and Schmidt 1992] [Deng et al. 2023] [Devasia 1997] [Dey 1972] [Deyuan et al. 2018] [Dillow et al. 1975] [Do et al] [Do et al. 2003] [Dolhyi et al. 2026] [Doman 1995] [Doman 1999] [Doman and Anderson 1996] [Doman and Anderson 2000] [Doman et al. 1997] [Dong et al. 2016] [Drewiacki et al. 2018] [Du 2025] [Durak et al. 2016] [Durrett 1973] [Edmunds and Vangaasbeek 1984] [Edwards and Wingrove 1968] [Effects of Modes 2016] [Efremov et al. 2019a] [Efremov et al. 2022a] [Elkind and Darley 1963] [Elkind and Forgie 1959] [Ema and Mizukura 1999b] [Engler et al. 1980] [Erturk et al. 2022] [Farmer et al. 1989] [Faulkner and Onstott 1977] [Fegely et al. 2017b] [Fogel and Moore 1968] [Fu and Gould 1966] [Fu et al. 2011] [Gagne and Wierwille 1966a] [Gagne and Wierwille 1966b] [Gao and Lu 2024] [Garg and Schmidt 1988] [Gestwa 2011] [Goto et al. 1994] [Grantham and Williams 1987] [Gray 2008] [Guo et al. 2013] [Guédon et al. 1995] [Habboush and Yildiz 2022] [Habboush and Yildiz 2026] [Hachem et al. 2026] [Haffley 1982] [Hahn 1965] [Hanson 2012] [Harden et al. 2006] [Teknik Dirgantatara FTMD et al. 2019] [Harshavarthini et al. 2019] [Harvey and Dillow 1974] [Heffley and Schulman 1981] [Hess 1971] [Hess 1976] [Hess 1977b] [Hess 1979a] [Hess 1979b] [Hess 1980b] [Hess 1980a] [Hess 1981a] [Hess 1982] [Hess 1985] [Hess 1987] [Hess 1995b] [Hess 2007] [Hess 2016a] [Hess 2021] [Hess and Chan 1988] [Hess and Marchesi 2008] [Hess and Moore 2013] [Hess and Teichgraber 1974] [Hirsch and McCormick 1965] [Hirsch and McCORMICK 1966] [Hoffman et al. 2018] [Holden and Shinners 1973] [Holzapfel et al. 2004] [Hoppe 1974] [Horn 2014] [Horn 2016] [Howard 1976] [Huggins et al. 1973] [Inaba and Matsuo 1995] [Inaba and Matsuo 1997] [Inbar 1991] [Innocenti 1985] [Invernizzi et al. 2018] [Islam et al. 2020] [Ito et al. 1973] [Jacinto and Cunha 2025] [Jagacinski and Flach 2018] [Jagacinski et al. 1978] [Jakimovska et al. 2023] [Jalovecký and Janů 2010] [Jarvis et al. 2008] [Jenkins and Hackett 1975] [Ji et al. 2022] [Jin et al. 2026] [Johannsen 1972] [Johannsen and Govindaraj 1978] [Johnson 1995] [Jones and Hunter 1991a] [Jones and Hunter 1991b] [Kao 1976] [Kao 1977] [Kao and Smith 1978] [Kashler 1961] [Keller et al. 2026c] [Kelley 1967] [Kelley et al. 1967] [Kessler and Mohr 1978] [Kim et al. 2020b] [Kleinman 1976] [Kleinman and Curry 1976] [Kleinman and Curry 1977] [Kleinman and Killingsworth 1974] [Klyde et al. 2020d] [Korn and Kleinan 1982] [Krishnakumar et al. 1995] [Kroemer 1982] [Kuang and Chen 2024] [Kucuk 1988] [Kurochkin and Mal’tsev 1982] [Kusmirek et al. 2024] [Lang and Vacroux 1969] [Lathrop 1965] [Leacock and Thomson 1998] [Levine et al. 1985] [Levison 1986] [Lin et al. 2024] [Lind and Beck 1991] [Liu 2021] [Liu and Kaber 2025] [Liu and Wang 2023] [Liu et al. 2006] [Liu et al. 2010] [Liu et al. 2021a] [Liu et al. 2026c] [Lopez Matos et al. 2018] [Lu and Jump 2014] [Lundberg and Johansson 2020] [Lyshevski and Smith 2023] [Ma et al. 2020] [Madeiras et al. 2026] [Maggiore and Consolini] [Mai et al. 2025] [Malaek and Sajjadi Kia 2004] [Mandal and Gu 2016b] [Manso and Bourne 2014] [Manual Control Devices 2006] [Marantos et al. 2013b] [Martin et al] [Martin et al. 1996] [Masarati et al. 2014] [McCord 1991] [McKissick et al. 1983] [McRuer 1965] [McRuer 1972] [Mekel and Peruo 1972] [Meraglia et al. 2023] [Merhav 1989] [Merritt 1966] [Middlebrooks et al. 1999] [Miller 1965a] [Miller et al. 1977] [Miller et al. 2022] [Miller and Riley 1976] [Mitchell 1964] [Mooij 1973] [Mooij 1985b] [Muckler 1961] [Muralidharan and Baron 1978] [Muralidharan et al. 1979] [Murphy 1976] [Muscarello and Quaranta 2021] [Second Annual NASA-University Conference 1966, Second Annual NASA-University Conference] [Third Annual NASA University 1967] [Fourth Annual NASA-University Conference 1969] [Fifth Annual NASA-University Conference 1970] [Seventh Annual Conference 1972] [Eleventh Annual Conference 1975] [Hart and Hartzell 1984] [Howard 1975] [Jirgl et al. 2019] [Kelly et al. 1973] [Litt et al. 2012] [Miller and Jagacinski 1986] [Proceedings, 13th Annual Conference] [Proceedings of the Seventeenth 1981] [Nelson] [Ninz 1982] [Nithya and Rashmi 2019] [North and Lomnicki 1961] [Ntuen 1992] [Olivari et al. 2012] [Onur et al. 2016] [Pal et al. 2025] [Perhinschi 1998] [Perhinschi and Prasad 1995] [Phatak and Weinert 1973] [Phatak and Weir 1966] [Phatak and Weir 1967] [Phatak et al. 1976] [Piloted Simulation and Pilot 2014] [Pollard and Hannen 1974] [Pool et al. 2012] [Portapas and Cooke 2020] [Poulton 1963] [Poulton 1981] [Prakash et al. 2026] [Prasad et al. 2006] [Qiao et al. 2026b] [Ramp and Papadopoulos 2018] [Rawson 1963] [Reedy 1987] [Repperger and Junker 1978] [Repperger et al. 1997] [Ridge and Bayes Identification 1976] [Rong et al. 2026] [Roscoe 1948] [Rosen and Enciu 2014] [Sagoo et al. 2008] [Sampson and Elkin 1965] [Santiago 2015] [Schiess and Roland 1975] [Schiess et al. 1972] [Schmidt 1978a] [Schmidt 1979a] [Schmidt 1979b] [Schmidt 1980] [Schmidt 1982] [Schmidt 1983b] [Schroeder 1993] [Schroeder and Grant 2010] [Schumacher and Geiser 1978] [Schwithal et al. 2025] [Seeley and Bliss 1966] [Sen et al. 2025] [Seok-Jae Lee and Joon Lyou 2007] [Setlur et al] [Shannon and Wang 1973] [Shaw 1993] [Sheng et al. 2019b] [Shipman 2014a] [Shipman 2014b] [Shirley 1969] [Shirley 1978] [Shunxiang and Rui 2017] [Siapkara and Sheridan 1981] [Siegel and Wolf 1979] [Simha and Ambroziak 2025] [Sinacori 1986] [Sinha 1982] [Sirouspour and Salcudean 2003] [Smith 1966b] [Wickens et al. 2015] [Stapleford et al. 1967] [Strieb 1979] [Su and Lin 2011a] [Su and Lin 2011b] [Su and Lin 2012] [Suenaga 1996] [Suenaga and Ihara 1991] [Suzuki et al. 2006] [Tada 1993] [Takase et al. 2020] [Takashima et al. 1980] [Tanaka and Washizu 1982] [The 14th Annual Conference 1978] [The Effects of Impacts 1984] [The Effects of Sustained 1977] [Theunissen 1993] [Thomas 1984] [Thompson and McRuer 1988] [Tohidi and Yildiz 2019] [Tohidi and Yildiz 2022] [Tomizuka and Whitney 1976] [Trujillo] [Trujillo and Gregory 2012] [Trujillo et al. 2015] [ul Amin et al 2016] [Vahdanipour and Khodabandeh 2023] [Vanlunteren 1977] [Vepa 2023] [Villa et al] [Vinje 1968] [Vinje and Pitkin 1972] [Vrdoljak et al. 2017] [Waller 1979] [Wang et al. 2009b] [Wang et al. 2016c] [Wang et al. 2016b] [Wang et al. 2023b] [Wargo 1967] [Washizu et al. 1978] [Wasicko et al. 1966] [Way 1978] [Wei and Jiang 2023] [Weissenberger and Sheridan 1962] [Wherry 1976] [White et al. 2004] [Wickens et al. 2009] [Wierenga 1969] [Wierwille 1965] [Willis and Beard 2021] [Wilson et al. 1990] [Witte et al. 2003] [Wu and Zhu 2024] [Wu et al. 2019] [Xu and Zhang 2024] [Xu et al. 2019b] [Xu et al. 2022] [Xu et al. 2025c] [Yoshizawa and Takeda 1983] [Young et al. 1964] [Yu et al. 2024] [Zaal and Sweet 2011] [Zaitceva et al. 2022] [Zaychik and Cardullo 2012] [Zewei et al. 2015] [Zhang and Cai 2011] [Zhang and Ji 2020] [Zhang et al. 2019d] [Zhang et al. 2026a] [Zhao et al. 2018c] [Zhaoying et al. 2021] [Zhou and Deng 2024] [Zhu and Wang 2022] [Zhu et al. 2010] [Zolner et al. 2010] [Zou and Devasia 2006] [Zou et al. 2017] [Zou et al. 2023b] [Zou et al. 2024] [Zou et al. 2025]

Tiltrotors, tiltwings and tail-sitters through the transition

The other ways of making a wing hover. Tiltrotors, tiltwings, tilting ducts and tail-sitters, their dynamics and control in hover, and above all the conversion between hover and wingborne flight. Tail-sitters are named in 150 titles and the transition in 150, so the tail-sitting layout the X-13 flew has returned in large numbers as an uncrewed vehicle, and the transition the X-13 and X-14 demonstrated is now chiefly a problem in automatic control.

486 records. [Ajel et al. 2021] [Akhtar and Maqsood 2024] [Akturk and Camcı 2014] [Alam et al. 2016] [Alexander et al. 1973] [Ansari et al. 2018] [Anusonti-Inthra 2010] [Aoyagi and Aiken 1979] [Apkarian 2018] [Argyle et al. 2014] [Arias et al. 2025] [Athayde et al. 2024a] [Athayde et al. 2024b] [Babac and Domitran 2023] [Bachelder et al. 2023a] [Bachmaier and Anderson 2021] [Banazadeh and Taymourtash 2016] [Basgall et al. 2024] [Bauersfeld and Ducard 2020] [Belák and Hromčík 2023] [Beppu and Curtiss 1966] [Berger et al. 2010] [AvMC et al. 2020b] [Berger et al. 2022b] [Betzina and Kita 1979] [Betzina and Kita 1980] [Bhardwaj and Holzapfel 2024] [Bhardwaj et al. 2019] [Bian et al. 2025] [Bilodeau and Wong 2010] [Binz et al. 2019] [Builta et al. 1995] [Burley 1979] [Burton et al. 2023] [Burton et al. 2024] [Cai and Lovera 2026b] [Cameron and Padfield 2007a] [Cameron and Padfield 2007b] [Campbell and Quinn 1973] [Campbell and Quinn 1974] [Cao and Qi 2018] [Carlson and Zhao 2003] [Carnes and Coder 2019] [Carnes and Coder 2022] [Casau et al. 2011a] [Casau et al. 2011b] [Chambers and Grafton 1970] [Champine 1971] [Chen and Guo 2025] [Chen and He 2023] [Chen et al. 2013] [Chen et al. 2016b] [Chen et al. 2016a] [Chen et al. 2023b] [Chen et al. 2026c] [Cheng and Pei 2020] [Cheng and Pei 2022] [Cheng and Pei 2023] [Cheng and Pei 2024] [Cheng et al. 2020b] [Choi et al. 2022] [Clark et al. 1963] [Clark et al. 1982] [Comer et al. 2026c] [Crawford et al. 1996] [Curtiss and Howard C. 1969] [Curtiss et al. 1967] [Czinczenheim 1977] [Dalwadi et al. 2021] [Dalwadi et al. 2023] [Dancik et al. 1958] [Darabi and Wygnanski 2003] [Daud Filho] [de Madrid et al. 2007] [De Wagter and Meulenbeld 2019] [deBrun et al 2003] [Deng et al. 2026b] [Detore and Sambell 1975] [Yoo 2005] [Deyuan et al. 2017] [Dickeson et al] [Dickeson et al. 2007a] [Dillenius and Mendenhall 1979] [DiMaggio et al. 2026] [Doff-Sotta et al. 2023] [Doff-Sotta et al. 2025] [Doman and Andrisani 1994] [Droandi et al. 2014] [Droandi et al. 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Helicopter hover, stability and flight dynamics

The rotorcraft case of the same problem. Helicopter stability and control near the hover, flight dynamics models, hover control laws, slung loads, and the aerodynamics and performance of rotors in hover. The hover is named in 213 of its 427 titles, which is the branch of the subject in which aerodynamic damping exists and the X-14’s synthesised damping does not have to.

427 records. 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Multirotor and quadrotor attitude control

The vehicle the review runs the article’s relations on. Multirotor and quadrotor attitude and position control, identification of their dynamics, and the first handling-qualities requirements written for uncrewed vehicles.

427 records. [3D Path-Following Control 2017] [Abdessameud 2019] [Abdessameud and Tayebi 2013a] [Abdugulova et al. 2024] [Abdul Ghaffar et al. 2021] [Abdul Rashid et al. 2025] [Abdulrahim et al. 2017] [Abdulrahim et al. 2019b] [Abdulrahim et al. 2019a] [Abryandoko et al. 2026] [Ackerman et al. 2019] [Aclécio J. Santos et al. 2024] [Adamski et al. 2014] [Ahmed and Katupitiya 2021] [Ahmed and Pota 2009] [Ahmed and Xiong 2024] [Ahmed Snikdha and Chen 2023] [Ai and Yu 2019] [Akshat Deshpande and Shyamkant Limaye 2016] [Alblooshi et al. 2025] [Alcan and Unel 2017] [Alexis et al. 2014] [Ansari 2023] [Araar et al. 2017] [Armani et al. 2025] [Aroussi 2025] [Azid et al. 2021] [Bachelder 2026] [Baek and Jung 2020] [Bagdai 2025] [Bahnemann et al. 2017] [Baldini et al. 2018] [Bangura and Mahony 2017] [BaniAsad et al. 2024] [Bannwarth et al. 2024] [Barcelos 2021] [Barrett 2017] [Baughman and Longeauay 2015] [Beharie et al. 2015] [Ben Jabeur and Seddik 2022] [Benzaid et al. 2016] [AvMC et al. 2020a] [Berrios et al. 2017] [Bingaman 2012] [Blas et al. 2022] [Bona et al. 2026] [Boschma 1998] [Bressan et al. 2018] [Bucherelli et al. 2025] [Buratti et al. 2019] [Callaghan and Kunz 2019] [Callaghan and Kunz 2021] [Cao et al. 2022a] [Capello et al. 2011] [Capocchiano et al. 2018] [Cardenas 2022] [Castañeda and Gordillo 2019] [Castillo et al. 2019] [Chang et al. 2024] [Charla et al. 2024] [Chebbi and Briere 2021] [Chebbi and Briere 2022] [Chekari et al. 2026] [Chen et al. 2018] [Chen et al. 2022b] [Cheng and Wang 2023] [Chipade et al. 2018] [Chiu] [Chodnicki et al. 2019] [Chopra et al. 2022] [Chowdhary and Lorenz 2005] [Chung and Son 2023] [Chung et al. 2019] [Classification for Unmanned Aircraft] [Combey et al. 2026] [Conley and Shirazi] [Corban et al. 2000] [Cotting 2009] [Cotting 2011] [Crombie and Moorhouse 1980] [Cunningham and Hubbard 2018] [Czyba et al. 2021] [Cárdenas et al. 2009] [Céspedes and Lopez 2019] [Dalei Song et al. 2010] [Dantsker 2024] [Dauer et al. 2013] [De Blauwe et al. 2007] [Delbecq et al. 2021] [Denuelle et al. 2015] [Derawi et al. 2015] [Design of Avionics System 2015] [Yoo 2004] [Myoung-Hyun 2006] [Dong et al. 2022] [Dou and Wen 2022] [Dragos Daniel et al. 2026] [Du et al. 2016] [Du et al. 2026] [Duman and Demirci 2026] [Duranti and Conte 2007] [Dydek et al. 2010a] [Dydek et al. 2010b] [Kim 2008] [聂 2017] [Edmonds and Yi 2021] [Elbasueny et al. 2019] [Emeto et al. 2026] [Erasmus and Jordaan 2020] [Ertugrul and Koyuncu 2023] [Escareño et al] [Faizal et al. 2018] [Fell et al. 2015] [Fiorucci et al. 2025] [Flight control system for] [Flight Tests of Multirotor 2017] [Foster and Bowman 2005] [Foster and Hartman 2017] [Foster et al. 2020] [Fourie and Jones 2015] [Fu et al. 2025a] [Raza and Gueaieb 2009] [Gamble 2023] [Gardecki et al. 2017] [Gargioli et al. 2013] [Ga̧sior et al 2018] [Ghanchi and Gururajan 2026] [Ghignoni et al. 2021] [Gill and D’Andrea 2020] [Gong et al. 2023] [Gordillo et al. 2025] [Graham and Bhandari 2022] [Greene et al. 2014] [Grzes et al. 2019] [Gu et al. 2017] [Guerrero-Castellanos et al. 2021] [Güner et al. 2021] [Guo 2012] [Gün 2023] [Hai-Rui and Bo 2017] [Han and Choi 2023] [Harada et al. 2012] [Hatamleh et al. 2009] [Haus et al. 2016] [Haus et al. 2018] [Hazawa et al] [He et al. 2016] [Healy et al. 2022] [Heidarian and Memon 2012] [Herisanu and Marinca 2020] [Herrington et al. 2023] [High Altitude Long Endurance 2005] [Hnidka and Rozehnal 2019] [Hoffman et al. 2017] [Hoffmann et al. 2007] [Hongxi Yang and Qingbo Geng 2011] [Hoshu et al. 2022] [Howard et al. 1996] [Hrishikeshavan et al. 2013] [Hrishikeshavan et al. 2015] [Hu et al. 2026b] [Huang and Meng 2021] [Huang and Zhang 2026] [Huang et al. 2009] [Huang et al. 2025] [Ide and Landman 2025] [Imumbhon et al. 2021] [Invernizzi et al. 2020b] [Iosifidis et al. 2018] [Ispiryan 2024] [Iswanto et al. 2016] [Ivler et al. 2019a] [Ivler et al. 2019b] [Ivler et al. 2021] [Ivler et al. 2022] [Işık and Tosun 2023] [Jan and Lin 2011] [Jaramillo et al. 2025] [Jarrah and Rawashdeh 2026] [Jehangir 2014] [Jiajin et al. 2017] [Jiande Wu et al. 2010] [Jiang et al. 2024b] [Jiang et al. 2025a] [Johnsen et al. 2021] [Johnson and Kannan 2002] [Ju et al. 2023] [Jumiyatun 2017] [Jun et al. 2026b] [Junior and Santos 2023] [Kahn and Foch 2003] [Kaila et al. 2016] [Kannan et al. 2025] [Kapitanova et al. 2025] [Karas] [Karimoddini et al. 2011] [Kasac et al. 2019] [Kazemi and Tarighi 2024] [Kellen and Benedict 2018] [Khadhraoui et al. 2025] [Kim and Kunz 2016] [Kim et al. 2009] [Kim et al. 2023c] [Kim et al. 2023b] [Klyde et al. 2018] [Kocamer et al. 2025] [Kong et al. 2023] [Koning et al. 2018d] [Kose 2024] [Kotarski et al. 2017b] [Kottenstette and Porter 2009] [Krammer et al. 2023] [Kubo 2018] [Kurenda et al. 2025] [Kurniawan 2014] [Kwon and Yang 2026] [Laddusaw et al. 2020] [Laddusaw et al. 2021] [Lai and Le Tri 2017] [Lee et al. 2010] [Lee et al. 2021] [Lee et al. 2022b] [Lee et al. 2025c] [Lee et al. 2026d] [Lei et al. 2020] [Lei et al. 2021] [Lei et al. 2023] [Lesiário and Hagström 2010] [Letalenet and Morin 2020] [Li and Tan 2023] [Li et al. 2014a] [Li et al. 2022b] [Li et al. 2023g] [Liao et al. 2010] [Limaico et al. 2025] [Lin et al. 2020a] [Liu 2024] [Liu and Wang 2015] [Liu Bo and Li Ping 2010] [Liu et al. 2014a] [Liu et al. 2020b] [Louw and Jordaan 2021] [Loyaga et al. 2025] [Lu 2024] [Lu et al. 2017b] [Lu et al. 2020] [Luo 2016] [Luo et al. 2019] [Luo et al. 2025] [Ma et al. 2024] [Macdonald] [Mahajani and Arya 2011] [Makhdoom and Shi-Yin Qin 2010] [Marantos et al. 2013a] [Maria-Agneta and Stef 2011] [Masuda and Uchiyama 2024] [Matt and Altamirano 2026] [McFarlane et al. 2008] [Mehmood and Johnson 2017] [Messaoui et al. 2023] [Michel et al. 2022] [Minh-Duc Hua et al. 2009b] [Minh-Duc Hua et al. 2009a] [Mishra et al. 2019] [Moeini et al. 2021] [Mogorosi et al. 2021] [Mokhtari and Abdelaziz 2016] [Nagabhushan and Tomlinson 1982a] [Nascimento and Saska 2019] [Nayak et al. 2026] [Ni 2024] [Niemiec et al. 2022] [Niki Maleki et al. 2024] [Novák and Chudý 2023] [Nowak et al. 2017] [Nugroho et al. 2022] [Olawoye et al. 2025] [Orozco-Soto et al. 2018] [Osman et al. 2026] [Oumlik and Dai 2026] [Panayotov and Zikyamov 2026] [Panayotov et al. 2020] [Parkala and Kandath 2026] [Patial et al. 2025] [Peters et al. 1997] [Pham et al. 2019] [Pines 2014] [Practice for Commercial Unmanned] [Pérez et al. 2019] [Pérez Gordillo et al. 2019] [Qi et al. 2024a] [Raharja et al. 2014] [Ramirez and Nahon 2021] [Rathjen] [Rathore and Sinha 2005] [Rebai 2022] [Recommendations for UAS Crew 2005] [Regan et al. 2020] [Renkert and Alleyne 2023] [Renó Peixoto de Azevedo Silva and Antônio dos Santos 2021] [Republic Aviation Corp Mineola Ny 1963] [Riboldi and Rolando 2023] [Ricardo and Santos 2023b] [Ricardo and Santos 2023a] [Ricci et al. 2022a] [Ricci et al. 2022b] [Rinaldi et al. 2013] [Rithirun and Sooraksa 2013] [Romero and Salazar 2013] [Roy et al. 2022] [Ruangwiset 2019] [Ruiz et al. 2023] [Ruiz-Sanchez 2016] [Russell et al. 2016] [Saderla et al. 2018] [Safe Coordinated Maneuvering 2016] [Saied et al. 2017] [Saifuddin et al. 2025] [Saito and Kurose 2025] [Saji 2026] [Sanchez and Kali 2026] [Sandino et al. 2013] [Sansou et al. 2024] [Santos and Gonçalves 2016] [Santos et al. 2024] [Satoh and Ohno 2025] [Schmidt and Swik 1974] [Scott 2017] [Setiawan] [Shen and Chen 2025] [Shin et al. 2003] [Shiotsuka et al. 2024] [Sikora and Czyba 2018] [Silva and Santos 2023] [Silva and Santos 2024] [Silva et al. 2024] [Simsek and Tekinalp 2015] [Sisák and Škultéty 2020] [Song et al. 2019] [Spitzer and Michael 2019] [Srigrarom and Holzapfel 2019] [Su et al. 2025] [Sun et al. 2021] [Sun et al. 2022a] [Supsukbaworn and Lin 2014] [Sönmez] [Taamallah 2011] [Taamallah 2013] [Takita and Kashitani 2016] [Tal and Karaman 2021] [Tamayo et al. 2018] [Tan et al. 2010] [Tarighi et al. 2021] [Tatenda and Qiang 2023] [Tayebi and McGilvray 2006] [Tian et al. 2026] [Tobing] [Tolba and Shirinzadeh 2022] [Turkoglu and Najafi 2015] [Uybarreta et al. 2025b] [Walter et al. 2020] [Walter et al. 2021] [Walter et al. 2022] [Walter et al. 2023] [Wang] [Wang 2019] [Wang 2025] [Wang and Low 2021] [Wang et al. 2014] [Wang et al. 2016a] [Wang et al. 2019c] [Wang et al. 2024b] [Wang et al. 2024d] [Wang et al. 2026j] [Wang et al. 2026a] [Wang et al. 2026d] [Watanabe et al. 2025] [Webb and Rogers 2021] [Wei et al. 2021] [Whidborne et al. 2022] [Wijerathna and Annasiwaththa 2025] [Wilson and Prazenica 2021] [Wu et al. 2010] [Wu et al. 2016] [Wu et al. 2024] [Xiaodong Wang and Xiaoguang Zhao 2008] [Xing and Xi 2024] [Xu and Zhang 2017] [Xu and Zhang 2025] [Xu et al. 2020a] [Xu et al. 2023] [Xu et al. 2025b] [Yang 2021] [Yang et al. 2012] [Yang et al. 2022] [Yang et al. 2024b] [Yang et al. 2025a] [Yi et al. 2014] [Yuan and Duan 2021] [Yuan and Zhu 2014] [Yuan et al. 2024] [Yuksel 2023] [Yun et al. 2005] [Zaki and Unel 2018] [Zaludin and Harituddin 2019] [Zangarini et al. 2020] [Zhang and Ran 2023] [Zhang et al. 2017d] [Zhang et al. 2017f] [Zhang et al. 2019f] [Zhang et al. 2019a] [Zhang et al. 2019b] [Zhang et al. 2019c] [Zhang et al. 2023c] [Zhang et al. 2025e] [Zhao and Anvar 2012] [Zhao et al. 2018a] [Zhao et al. 2024e] [Zhe Jiang et al] [Zheng et al. 2025] [Zhong et al. 2026b] [Zhou et al. 2019c] [Zhou Fang et al. 2008] [Zhu et al. 2017] [Zwiener et al. 2026] [Çakici and Leblebi̇ci̇oğlu 2016] [Szabolcsi 2019]

Control allocation, attainable moments and effector failure

The modern form of the handover the X-14 managed by linkage. Control allocation for over-actuated aircraft and multirotors, the attainable moment set, actuator saturation, and fault tolerance. Faults or failures are named in 127 titles and the attainable set in 17, so the allocation literature is concerned more with losing an effector than with the geometry of what the effectors can reach, which is the case the review argues makes the multi-axis requirement tractable.

322 records. [Abouselima et al. 2019] [Abouselima et al. 2021] [向 et al. 2023] [Agrawal et al. 2024] [Ahmadi Dastgerdi and Nabavi-Chashmi 2026] [Akbari et al. 2024] [Akram et al. 2020] [Akram et al. 2022] [Akumalla et al. 2024] [Alberghini and Lee 2018] [Almutairi and Aouf 2017] [Alwi and Edwards 2007] [Alwi and Edwards 2009] [Ang et al. 2014] [Antonakis 2025a] [Antonakis and Biannic 2024] [asadi 2022] [Asadi 2023] [Asaro et al. 2025] [Asghari and Tayefi 2026] [Asper et al. 2026] [Ayati et al. 2022] [Aymene et al. 2024] [Azinheira and Moutinho 2008] [Baggi et al. 2020] [Baggi et al. 2022] [Bai and Dong 2025] [Bakori and Moncayo 2020] [benghezal et al 2022] [Berger et al. 2025] [Bezerra and Antônio dos Santos 2021] [Bezerra and Santos 2022b] [Bezerra and Santos 2022a] [Bian et al. 2018] [Bian et al. 2019] [Binwen Lu et al. 2016] [Bodson 2000] [Bolander et al. 2022] [Bole et al. 2010] [Bolender and Doman] [Bolender and Doman 2004] [Bondyra et al. 2018] [Boskovic et al] [Boskovic et al. 1998] [Brady and Gururajan 2026] [Buffington 1997] [Vidya and Kandath 2024] [Candido et al. 2014] [Carlson et al. 2022] [Casavola and Garone 2007] [Casavola and Garone 2008b] [Casavola and Garone 2008a] [Casavola and Garone 2010] [Castaldi et al. 2016] [Chamseddine et al. 2013] [Chang et al. 2020] [Chen 2016] [Chen et al. 2024b] [Chen et al. 2026b] [Chen et al. 2026f] [Cheng and Pei 2021] [Cheng et al. 2019a] [Cheng et al. 2025a] [Christensen et al. 2009] [Chung and Son 2020] [ChunSheng Liu et al. 2012] [Ciresola et al. 2026] [Cong et al. 2023] [Control Allocation and Flight 2016] [Cristofaro and Johansen 2014] [Cristofaro et al. 2017] [Cui et al. 2021] [Córdoba G. 2007] [Darmstad et al. 2024] [Darmstadt et al] [Darmstadt et al. 2021a] [de Vries and Van Kampen 2019] [Demenkov 2011] [Diget et al. 2022] [Doman and Oppenheimer 2002] [Dong et al. 2024] [Dou et al. 2025] [Ducard and Kryenbuhl 2020] [Dudgeon et al. 1998] [Durham 1994b] [Durham 1994a] [Durham et al. 2016] [Dutta et al. 2019] [Dzygadlo et al. 2003] [Enns and Si 2002] [Enns and Si 2003] [Falconi et al. 2016] [Farconi et al. 2019] [Frame-Wise Control Allocation 2016] [Franze et al. 2013] [Fuhrer et al. 2019] [Fulton et al. 2026] [Furci et al. 2020] [Gai and Wang 2013] [Gibbard and Reid 1996] [Giribet et al. 2019] [Goff et al. 2022] [Gong et al. 2019] [Goodarzi et al. 2025] [Guan et al. 2025] [Guiatni et al. 2019] [Guo et al. 2025a] [Guo et al. 2025c] [Hafner et al. 2025] [Hafner et al. 2026] [Hamadi] [Han and Pei 2026] [Han et al. 2024] [Han et al. 2025b] [Han et al. 2025a] [Hansen et al. 2020] [Hansen et al. 2022] [Hariharan et al. 2020] [Harkegard] [Harkegard 2003] [Harshavarthini et al. 2020] [Hartman et al. 2025] [Heer et al. 2023] [Heinz and Takahashi 2024] [Hindson et al. 1990] [Hodel and Shtessel 2002] [Horn et al. 2014] [Hu et al. 2021] [Huang et al. 1996] [Härkegård and Glad 2005] [Immersion and Invariance Adaptive 2026] [Iriarte et al. 2020] [Jafari et al. 2022] [Jianjun Ma et al. 2008] [Jing and Ma 2025] [Jing et al. 2025] [Jothiraj et al. 2020] [Kang and Choi 2022] [Ke et al. 2026] [Kefayat and Kamali 2024] [Kelm and Myschik 2023] [Kim et al. 2024c] [Kirchengast et al. 2018] [Kobayashi and Takahashi 2011] [Kotarski and Kasać 2018] [Kun et al. 2011] [Lee et al. 2024c] [Lee et al. 2024d] [Li and Pei 2024] [Li and Zhu 2023] [Li et al. 2011] [Li et al. 2012] [Li et al. 2020a] [Li et al. 2021a] [Li et al. 2023e] [Li et al. 2023c] [Li et al. 2023h] [Li et al. 2024a] [Li et al. 2025a] [Liao et al. 2014] [Liao et al. 2025] [Liao et al. 2026] [Lin et al. 2019] [Lin et al. 2020b] [Lingyu et al. 2006] [Litt 2024] [Litt 2026] [Liu and Crespo 2010] [Liu and Xu 2026] [Liu et al. 2018d] [Liu et al. 2018a] [Liu et al. 2019a] [Liu et al. 2022b] [Liu et al. 2026b] [Lou et al. 2024] [Lu et al. 2019] [Lu et al. 2024] [Lu et al. 2026] [Ma and Wang 2009] [Ma et al. 2010] [Ma et al. 2012] [Ma et al. 2025b] [Mallavalli and Fekih 2017] [Mallavalli and Fekih 2018] [Mallavalli and Fekih 2019] [Man Wang et al. 2013] [Mario Andres Cordoba 2001] [Martin 2025] [Mashud and Bera 2022] [Matamoros and de Visser 2018] [Mazeh et al. 2021] [Meskin and Khorasani 2007] [Mohammadi et al. 2023] [Monteiro et al. 2016] [Moralez et al. 2006] [Murata et al. 2025b] [Murata et al. 2025a] [Naskar et al. 2015] [Naskar et al. 2016] [Nery and Antônio dos Santos 2025] [Nguyen et al. 2018] [Nnamdi-Nwosu and Liscouët 2023] [Nunes et al. 2025a] [Oberschwendtner and Hornung 2024] [Oliva 2000] [Osmic et al. 2018] [Panza and Lovera 2014] [Pfeifle and Fichter 2021] [Pfeifle and Fichter 2023b] [Pfeifle and Fichter 2023a] [Polesel et al. 2014] [Prochazka et al. 2018] [Puchalski et al. 2022] [Qin et al. 2023a] [Qin et al. 2023b] [Qu et al. 2023] [Rajendran et al. 2023] [Rajput et al. 2015] [Ranjan and Majhi 2024] [Razvi et al. 2023] [Ruggia 2025] [Rüddenklau and Schitter 2026] [Sadeghzadeh et al. 2012] [Sadien et al. 2019] [Sagan et al. 2025] [Saied et al. 2019] [Sajjadi et al. 2025] [Sanjuan et al. 2019] [Santos and Bezerra 2022] [Sarker et al. 2026b] [Schoenfeld et al. 2023] [Schofield 2008] [Scordamaglia et al. 2025] [Sharma and Aldeen 2007] [Shearwood et al. 2020b] [Shearwood et al. 2020a] [Shearwood et al. 2021] [Sheng et al. 2019a] [Shi and Zhang 2013] [Singh] [Singh et al. 2024] [Sinha and Patra 2026] [Siwakosit et al. 2000] [Spaans et al. 2024] [Stam and de Visser 2025] [Stephan 2025] [Strampe and Klingauf 2026] [Su et al. 2021] [Sun et al. 2022b] [Suzuki et al. 2013] [Swaid et al. 2023] [Tang and Patton 2012] [Tang et al. 2020b] [Tang et al. 2025] [Tariq and Nahon 2020] [Taylor and Yoo 2011] [The Geometry of Control 2016] [Theilliol et al. 2015] [Thomas and Malone] [Tjonnas and Johansen 2007] [Tohidi et al. 2017] [Tohidy and Sedigh 2013] [Tsagkaris et al. 2026] [Varriale and Voskuijl 2021] [Varriale et al. 2020] [Veldhuizen et al. 2026] [Vermillion et al. 2007] [Vey and Lunze 2015] [Vey and Lunze 2016] [Vile et al. 2019b] [Vile et al. 2019a] [Vile et al. 2020] [Wahba and Hönig 2024] [Wahler et al. 2023] [Wang and Hu 2026] [Wang et al. 2017a] [Wang et al. 2018b] [Wang et al. 2019a] [Wang et al. 2021d] [Wang et al. 2025c] [Wang et al. 2025e] [Wang et al. 2026i] [Wang et al. 2026b] [Ward et al. 1999] [Willis and Beard 2022] [Xiao et al. 2022] [Xiao et al. 2024] [Xing and Ruan 2021] [Xu et al. 2019c] [Xu et al. 2020b] [Xulin and Yuying 2018] [Yan and Shi 2024] [Yang 2023] [Yang and Gao 2020] [Yang and Shen 2007] [Yang et al. 2009a] [Yang et al. 2024c] [Yang et al. 2026a] [Yao et al. 2020] [Yiming et al. 2019] [Yin et al. 2019b] [Yoon et al. 2025b] [Yu et al. 2016] [Yuanqing et al. 2014] [Yuwei et al. 2016] [Yılmaz and German 2024] [Zaki et al. 2017] [Zare et al. 2025] [Zhang and Holzapfel 2021] [Zhang et al. 2007] [Zhang et al. 2008] [Zhang et al. 2018a] [Zhang et al. 2024a] [Zhang et al. 2024c] [Zhang et al. 2025f] [Zhang et al. 2025h] [Zhao et al. 2026b] [Zhen and Cui 2023] [Zheng and Li 2019] [Zhong et al. 2009] [Zhou and Wang 2026] [Zou et al. 2012]

Ground simulators and their fidelity

The ground-based alternative whose fidelity the X-14 existed to test. Piloted ground simulators, their motion and visual systems, simulator fidelity and its measurement, and piloted simulation studies of vertical take-off aircraft. Motion is named in 46 titles, which reflects the question the comparison with ground prediction leaves open, of what a simulator must reproduce before its ratings can be trusted.

318 records. [A Piloted Simulator Investigation 1979] [Abbott et al. 1982] [Advani and Djavdan 1996] [Advani et al. 1995] [Advani et al. 2002] [Agha et al. 2017] [Agnerian et al. 2006] [Ahad and Graham 2007] [Aiken 1982] [Alagic et al. 1996] [Albion et al. 1969] [Alfred et al. 2013] [Alfred et al. 2017] [Altamirano et al] [Altamirano et al. 2023b] [Alvarez et al. 2013] [Anderson and Biezad 1998] [Andre and Johnson] [Aponso et al. 2009] [Arjun et al. 2022] [Asadi et al. 2016] [Bahr et al. 2021b] [Barker et al. 1970] [Barnes et al. 2025] [Baron 1983] [Becerra-Vargas and Morgado Belo 2015] [Becerra-Vargas et al. 2009] [Begichev et al. 2001] [Benmoussa and Gamboa 2024] [Berger et al. 2015] [Birckelbaw and Corliss 1994] [Bischof et al. 1985] [Blake 1996] [Bland et al. 1976] [Blanton 1988] [Blok 1992] [Boldovici 1992] [Braun and Galloway 2004] [Bray 1963] [Bray 1985] [Bray 1986] [Breul 1963] [Brown] [Bruce et al. 1998] [Bussolari et al. 1989] [Butter et al. 1996] [Caleffi and Belo 1993] [Cardullo 1981] [Carpenter and Whalley 1992] [Caseria 1966] [Caudle et al] [Chakraborty et al. 2023b] [Chakraborty et al. 2024b] [Chalk 1963] [Chalk 1964] [Chen and Ji 2017] [Chen et al. 1978] [Chen et al. 2008] [Cheng et al. 2026] [Cho and Nagati 1995] [Chung et al. 1995a] [Chung et al. 1995b] [Chung et al. 1996] [Chung et al. 2020] [Clement et al. 1990] [Corliss and Dugan 1972] [Crosbie and Kiefer 1985] [Crosbie and Eyth 1981] [Curtis et al. 2005] [Dalang-Secretan and Ballin 1990] [Dander 1962] [Davis 1974] [Design of an Engineering 2022] [Dietz and Hebert 1996] [Douglas Aircraft Co Long Beach Ca 1963] [Drewiacki et al. 2025] [Drinkwater et al. 1964] [Duda et al. 2013] [Durak et al. 2014] [Durak et al. 2015] [Dursun and Erturk 2021] [Erkelens 1987] [Eskey and Wilson 1989] [Eyth and Heffner 1992] [Fanciullo et al. 2001] [Faye 1960] [Feather and Joshi 1981] [Field et al. 2004a] [Fielding and Southworth 2001] [Fontaine and Johnson 2001] [Forrest and Lebacqz 1980] [Forrest et al. 1979] [Forsstrom et al. 1985] [Fouladi and Audonnet 2026] [Franklin 1997b] [Franklin and Stortz 1993] [Freeman and Klunk 2018] [Fry et al. 1966] [Fry et al. 1969] [Fry et al. 1973] [Fuad et al. 2024] [Gaertner 1972] [Gaffey and Maisel 1974] [Gallagher 1970] [Gallagher 1971] [Garrood and Reid 1993] [Gerdes 1964] [Gerdes 1977] [Gilbert and Nguyen 1978] [Gladfelter et al] [Goodrich et al. 2008] [Gouverneur et al. 2003] [Grant and Schroeder 2010] [Gray and Kemper 2009] [Greenwood 1960] [Groeneweg 1998] [Gu 2025] [Guozhu and Zhehao 2020] [Han and Dang 2016] [Hartley 2024] [Hastings and Keyser 1982] [Hays 1980] [He and Xin 2003] [Hebbar et al. 2023] [Henriquez Huecas et al. 2022] [Hess 1993] [Hess and Siwakosit 2001] [Hill 1981] [Hill 1983] [Hofmann and Riedel 1979] [Hon et al. 2022] [Horri and Pietraszko 2022] [Howe 1987] [Hsieh 1979] [Hughes et al. 2002] [Humphreys-Jennings et al. 2020] [Idan and Sahar 1996] [Iliff and Taylor 1969] [Innis and Anderson 1972] [Innocenti 1999] [Introduction to the Flight 2007] [Introduction to the Flight 2018] [Ioannis and Ioannis 2026] [Iseler et al. 1995] [Jansen 1980] [Jansen 1988] [Jewell et al. 1978] [Johnson et al. 2024] [Joosten et al. 2023] [Juhasz et al. 2021] [Junker et al] [Jusko and Berger 2024] [Kanki et al. 2017] [Kaye and Freeman 1989] [Kelley 1978] [Kemper and Cotting 2016] [Kereliuk and Sinclair 1979] [Key and Heffley 2002] [Kiefer and Calvert 1992] [Kimball 1993] [Klyde et al. 2013] [Klyde et al. 2023] [Knaak] [Koekebakker et al. 1998] [Krabs and Naumes 2003] [Krishnamurthi and Gandhi 2017] [Krumenacker and Pellicano 1992] [Kuehn et al. 1998] [Kunwar and Chakraborty 2025] [Laforce and Bunnell 1992] [Landis and Aiken 1982] [Landis and Aiken 1984] [Landis et al. 1985] [Lapins et al. 1982] [Lebacqz et al. 1982a] [Lehmer and Chung 1999] [Lemons and Dukes 1975] [Lewis et al. 1991] [Litt et al. 2022] [Liu et al. 2009] [Lombaerts et al] [Lombaerts et al] [Lombaerts et al. 2025] [Longbridge et al. 2001] [Longo 1995] [Lord 1985] [Malhotra et al. 2019] [Marchesini 2000] [Markov et al. 1981] [Martin 2007] [Matějů 2019] [McCormick 1969] [McCormick et al. 1963] [McGregor and Smith 1965] [McKeehen et al. 1996] [Mendela 1970] [Mendela 1971] [Merrick and Gerdes 1978] [Merriken et al. 1987] [Metodiev 2024] [Mihaloew et al. 1981] [Miletović et al. 2017] [Miller 1979] [Mitchell and Hart 1993] [Modeling Atmospheric Effects 1989] [Modelling Helicopter Flight Dynamics 2007a] [Modelling Helicopter Flight Dynamics 2018a] [Mohan et al. 2024] [Morris et al. 1964] [Ng 2018] [Nichols 1994] [Nieuwenhuijse and Franklin 1974] [Norlin 1995] [Nusseck et al. 2008] [Ockier and Butter 2000] [Ohara 1964] [Paulino et al. 2019] [Pausch et al. 2017] [Pavel 2007] [Pavel 2021] [Pedrioli et al. 2026] [Peters et al. 2003] [Plumpton] [Podzus et al. 2022] [Pool et al. 2010] [Portapas 2025] [Postlethwaite et al. 1999] [Postlethwaite et al. 2000] [Putting Flight Simulator 1998] [Qu et al. 2025] [Raab 2026] [Ratvasky et al. 2003] [Ray 1996] [Reay 1977] [Reid and Nahon 1987] [Research and Analysis 2022] [Reynolds and Hall 1978] [Garrott 1994] [Robinson and Mania 2007] [Robinson et al. 1989] [Rogalski et al. 2009] [Rolfe 1973] [Rosenstein et al. 1973b] [Sachs et al. 1994] [Sadoff 1958] [Sagoo] [Salinas 1994] [Sarathy and Murthy 1993b] [Sarathy and Murthy 1993a] [Sarrafian 1984] [Scafetta 1983] [Scalera and Durham 1999] [Schroeder et al. 1994] [Sharkey and McCauley 1992] [Shepherd et al. 2009] [Shi 2021] [Shupeng Zheng et al. 2009] [Sinacori 1970b] [Sinacori 1970a] [Somerville et al. 2025] [Soparkar and Reid 2003] [Soparkar and Reid 2006] [Spitzer et al. 1972] [Staley 1976] [Steurs et al. 2004] [Stewart 1998] [Stewart 2008] [Strassacker et al. 2013] [Stroosma et al. 2010] [Suh et al. 2025] [Sullivan and Soukup 1996] [Swaine] [Tafs and Kraft 1985] [Tashiro et al. 1985] [Tian and Zhao 2017] [Torelli et al. 2023] [Townsend] [Uybarreta et al. 2025a] [V/STOL Flight Simulation 1979] [Van Gaasbeek 1980] [Van Gool and Mooij 1979] [Vinje 1973] [Vinje 1974] [Vinje and Miller 1973] [Visual Simulation for General] [Wachspress et al. 2008] [Walker and Tischler 2022] [Wang and Yue 2012] [Wang et al. 2009a] [Warner 1993] [Watanabe et al. 1989] [Wechner et al. 2022] [Wei 2020] [Wei 2021] [Wei et al. 2019] [White et al. 2021] [Whiteside 1977] [Whiteside and Iffland 1977] [Wirth 1972] [Withrow-Maser et al] [Wood 1984] [Wuwer et al. 2026] [Yang et al. 2025b] [Yoon et al. 2016] [Yuska 1972] [Zammit and Zwaanenburg 1989] [Zanoni et al. 2022b] [Zeyada and Hess 1999] [Zeyada and Hess 2002] [Zhang et al. 2012a] [Zhao et al. 2020] [Zhao et al. 2024a] [Zheng et al. 2019] [Zhixin 2022] [Zinchiak] [Zintl et al. 2022] [Zintl et al. 2024b] [Zuccaro 1970]

Ground effect, jet-induced flow and hot gas ingestion

What the exhaust does near the ground. Jet-induced lift loss and suckdown, fountains, the ground vortex, hot gas ingestion and recirculation, surface erosion and downwash impingement, and rotors in ground effect. Hot gas ingestion is named in 55 titles and the fountain in 24, the hazards that made in-ground-effect and out-of-ground-effect experiments different experiments for the X-14.

301 records. [Adarkar and Hall 1968] [Adarkar and Hall 1969] [Agarwal and Deese 1985] [Aircraft in Ground Effect 1997] [Allen 2004] [Amuedo et al. 1989] [Amuedo et al. 1991] [Andronikos et al. 2021] [Arledge et al. 1996] [Asdurian 1967] [Bai and Zhou 2023] [Bai and Zhou 2024] [Barata 1991] [Barata 1993] [Barata 2013] [Bardera Mora and Matías García 2022] [Barrack and Kirk 1968b] [Barrack and Kirk 1970] [Barton and Edwards 1968] [Bauer 1987] [Bellavia et al. 1991a] [Bellavia et al. 1991b] [Bevilaqua et al. 2007] [Bevilaqua et al. 2010] [Bhattacharyya and Conlisk 2003] [Binion 1970b] [Blake and Laughrey 1987] [Blake and Stewart 1993] [Bolanovich and Marks 1959] [Boschetti et al. 2022] [Brun et al. 2011] [Cabrita et al. 2005] [Campbell et al. 1978] [Carangui et al. 2016] [Castells and Mishler 1973] [Chaderjian et al. 2002b] [Chaderjian et al. 2002a] [Childs and Nixon 1986] [Childs and Nixon 1987] [Chilukuri 2019] [Christiansen 1984] [Christiansen et al. 1985] [Cimbala et al. 1993] [Cook et al. 2005] [Cosgrove and Ryan 1969] [Cosgrove et al. 1968] [Curtis 2002] [Curtiss 1965b] [Davidson et al. 1972] [Dawson and Omar 1977] [Deneke and Carter 2025] [Deng 2019] [Dent 1966] [Design Concepts for Minimizing 1981] [Donaldson et al. 1966] [Donaldson et al. 1971] [Dos Santos et al. 2024] [Dudley et al. 1981] [Dudley et al. 1986] [DuWaldt 1966] [Eshleman et al. 1986] [Eshlemen 1985] [Fanucci et al. 1969] [Foley and Finlay 1980] [Foltz 1962] [Fricker et al. 1992] [Fricker et al. 1994] [Ganesh and Komerath 2006] [Gao and Agarwal 2019] [Gentry and Margason 1966] [George et al. 1964] [Georgiev 2025] [Gilbert 1985] [Goland and Pruyn 1962] [Gonzalez-Guerrero et al. 2022] [Greco et al. 1997] [Green and Zanine 1984] [Greene 1977] [Greene 2020] [Grotz 1961] [Grunwald 1961b] [Grunwald 1961a] [Grunwald 1966] [Guleria et al. 2023] [Hafer and Skinner 1960] [Hall 1967] [Hall 1968b] [Hall 1970] [Hall 1971b] [Hammond and McLemore 1967] [Hange and Wardwell 1992] [Hange and Wardwell 1993] [Hange et al. 1996b] [Hange et al. 1996a] [Harman et al. 1994] [He and Leang 2020] [He and Leang 2024] [He et al. 2019] [Heathcote et al. 2026] [Hemeter et al. 1970] [Heyson 1961] [Heyson 1962b] [Heyson 1962a] [Higgins and Wainwright 1964] [Higgins et al. 1966] [Hill et al. 1982b] [Hoad and Gentry 1975] [Hoad and Gentry 1977] [Holdeman and Vukits 2004] [Holder and Tritschler 2019] [Hot Gas Ingestion 1984] [Hot-Gas Ingestion 2007] [Houlihan and Thompson 1972] [Huggett 1959] [Huston and Winston 1960] [Hwang 1990] [Hwang and Kwon 2019] [Hwang and Tsou 1981] [Hwang et al. 1991] [Hwang et al. 2016] [Ing and Zhang 1993] [Ing and Zhang 1994] [Ison 2024] [Jackson and House 1981] [Jackson and House 1982] [Jang et al. 2022a] [Johns 1989] [Johns et al. 1987] [Johns et al. 1989b] [Johns et al. 1989a] [Joshi and Compton 1984] [Kaemming and Smith 1984] [Kalra et al. 2013] [Kamman and Hall 1978] [Karemaa et al. 1979] [Kato and Suzuki 2019] [Kemmerly 1989] [Kemp 1967] [Kemp 1969] [Kim et al. 2018] [Kirk and Barrack 1969] [Koc¸er et al 2008] [Kotansky 1978] [Kotansky 1982] [Kotansky 1986] [Kotansky and Bower 1977b] [Kotansky and Bower 1977a] [Kotansky and Bower 1978] [Kotansky and Glaze 1978] [Kotansky and Glaze 1980] [Kotansky and Glaze 1981] [Krishnamoorthy 1971] [Kristy 1995] [Kuhlman and Warcup 1977] [Kuhlman and Warcup 1979] [Kuhlman and Warcup 1980] [Kuhlman et al. 1978] [Kuhn 1965] [Kuhn 1982] [Kuhn 1986] [Kuhn 1987] [Kuhn 1998] [Kuhn and Grunwald 1960] [Kuhn and Grunwald 1961] [Kuhn et al. 1991] [Kuhn et al. 1993a] [Kuhn et al. 1993b] [Lavi 1967b] [Lee et al. 2026a] [Lehman 1971] [Levin and Wardwell 1997] [Levinsky et al. 1968] [Lewis and Hurd 1980] [Li et al. 2020c] [Li et al. 2025d] [Lift Loss in Hover 2007] [Lissaman 1967] [Lissaman 1968] [Lissaman 1969] [Liu et al. 2016] [Louisse and Marshall 1974] [Louisse and Marshall 1976] [Maclean 1991] [Margason 1966] [Margason 2002] [Marques Goncalves et al. 2024] [McLemore 1966b] [McLemore 1966a] [McLemore and Smith 1968] [Mehrabi and Davari 2020] [Miesner et al. 2020] [Migdal et al. 1979] [Morse and Newhouse 1960] [Morse and Newhouse 1961a] [Morse and Newhouse 1961b] [Moushegian et al. 2021] [Murman et al. 2001] [Mylapore and Schmitz 2015] [Narducci and Hariharan 2023] [Newsom 1957] [Newsom 1960] [O’Bryan 1961] [Obryan 1960] [Oliver and Stanzione 1993] [Pamadi 1980] [Pandya et al. 2002] [Pandya et al. 2003] [Penrose 1987] [Penrose and Smith 1996] [Perrotta 2015] [Pieris et al. 2023] [Porcacchia et al. 2023] [Preston 1994] [Prewitt et al. 2023] [Pruyn and Taylor 1970] [Pruyn and Taylor 1971] [Pulla and Conlisk 2005] [Quackenbush et al. 2018] [Radhakrishnan and Schmitz 2003] [Radhakrishnan and Schmitz 2005] [Radhakrishnan and Schmitz 2006] [Vijayaraj et al. 2025] [Richardson et al. 2005] [Richardson et al. 2006] [Richardson et al. 2007] [Rizk and Menon 1989] [Rogers and Belluomini 2026] [Rovere et al. 2020] [Saddington and Knowles 2013] [Saddington et al. 2002] [Saddington et al. 2009] [Sagaga and Lee 2025] [Sandlin and Howard 1991] [Saripalli 1985] [Saripalli 1987a] [Saripalli 1987b] [Saripalli and Kroutil 1985] [Saripalli et al. 1997] [Sharma et al. 2021] [Sharon 1975] [Shirbhate et al. 2025] [Shishir et al. 2001] [Shollenberger 1978] [Shollenberger and Smyth 1978] [Shumpert and Tibbetts 1969] [Siclari et al. 1980] [Silwal et al. 2022] [Smith et al. 1991] [Smith et al. 1993b] [Smith et al. 1993a] [Smith et al. 2021] [Soderlund and Matveev 2010] [Spong et al. 1979] [Stahl and Gaitonde 2021] [Stewart 1979b] [Stewart 1988] [Stewart et al. 1995] [STOL Operation Transition-in-Ground Effect 2007] [Strand 1967] [Su et al. 2024] [Suresh 2020] [Tafti and Vanka 1990] [Tan et al. 2018] [Tanabe et al. 2009] [Tatom et al. 1972b] [Thipyopas and Moschetta 2010] [Transition out-of-Ground Effect 2007] [Tritschler et al. 2019] [Van Dalsem et al. 1987] [Vanka 1998] [VanOverbeke and Holdeman 1990] [Vaughn 1970] [Vidal 1962] [Vidal 1963] [Vogler 1966] [Von Glahn and Groesbeck 1979] [Wachspress et al. 2026] [Wadcock et al. 2008] [Walker et al. 1965] [Wang 2003] [Wang et al. 2024a] [Wang et al. 2026k] [Wardwell and Hange 1993] [Wardwell et al. 1992] [Wardwell et al. 1993] [Wareing 1968] [Watson et al. 1967] [Weber 1973] [Weber and Gay 1975] [White et al. 1960] [Wichita State Univ Ks 1962] [Wohllebe and Migdal 1979] [Xin et al. 1998] [Xin et al. 1999] [Yon and Li 2026] [Zhang and Agarwal 2020] [Zhang and Ing 1993] [Zhang and Ing 1994] [Zhang et al. 2019e] [Zhao et al. 2023c] [Zhu et al. 2024b]

Lift fans, lift engines and jet-lift aircraft

The jet-lift configurations the X-14 was sized for. Lift fans, tip-turbine and lift/cruise fans, lift engines, deflected-jet and vectored-thrust aircraft and the Harrier line. Lift fans, cruise fans and tip turbines are named in 95 titles. Its median publication year of 1973 is the earliest of any named cluster, which is consistent with the article’s conclusion that jet lift was made designable without being made worth designing.

241 records. [Abdullah and Husi 2026] [Al-Gilani et al. 2009] [Albang and Roberts 1974] [Alford et al. 1963] [Anderson 1990] [Anderson and Foster 1984] [Anderson and Petersen 1977] [Anderson et al. 1983] [Aoyagi 1979] [Asmus 1963] [Atencio et al. 1973] [Auer et al. 1971] [Bagby 1963] [Barrack and Kirk 1968a] [Barrack and Kirk 1972] [Baxter and Finvold 1958] [Beeler 1965] [Beeler and Volk 1965] [Berger et al. 2012] [Berger et al. 2013] [Berger et al. 2017] [Biggers et al. 1964] [Birckelbaw et al. 1995] [Blackburn 1965] [Blackburn and Whitfield 1965] [Bode et al. 1978] [Boling and Zha 2021] [Boling et al. 2020] [Brogan et al. 1961] [Butler and Thomas 1964] [Caffee 1985] [Capone 1969] [Capone 1972] [Capone et al. 1971] [Casado et al. 2002] [Cavage 1975] [Chang et al. 2009] [Chopra 2002] [Chow 1993] [Cleveland 1971] [Cole et al. 1980] [Conceptual Design 1973] [Conceptual Design Studies 1974] [Coplin 1965] [Coplin 1966] [Davis and Ela 1969] [Deckert 1993] [Deckert 1995] [Deckert and Rolls 1974] [Denham and Paines 2008] [Design Definition Study 1975] [Diedrich 1971] [Diedrich 1975] [Duan 2022] [Dudley et al. 1990] [Dugan et al. 1971] [Eccles 1983] [El-Okda and Telionis 2002] [Eldridge et al. 1973] [Elliott 1976] [Englar 1974] [Everett 1965] [Feistel et al. 1969] [Flemming 1968] [Flemming and Scholten 1969] [Fletcher 1962] [Gambucci et al. 1976] [Garner 1967] [Gaston et al. 1984] [Gea et al. 1991] [General Electric Co Cincinnati Oh 1964] [Gentry and Margason 1968] [Gerdes 1981] [Gerdes 1993a] [Gerdes 1993b] [Gerdes and Hynes 1972] [Gerdes and Hynes 1975] [Gleiter 1976] [Gotlieb 1977] [Grahame 1968] [Grahame 1969] [Haas et al. 1976] [Haas et al. 1978a] [Haas et al. 1978b] [Hackett et al. 1976] [Hahn and Wilson 1985] [Hall 1968a] [Hall 1971a] [Hall and Hodder 1971] [Hall et al. 1967] [Hall et al. 1970] [Hammond 1966] [Harris 1968] [Head 1981] [Henderson 1971] [Hewson 1959] [Heyson 1973] [Hickey and Kirk 1966] [Hickey and Kirk 1993] [Hickey et al. 1966] [Hill and Waters 1974] [Hoffert 1964] [Hoffman et al. 1972] [Holden 1964] [Hollingsworth et al. 1977] [Huang et al. 2018] [Hudson 1977] [Hudson and Gee 1977] [Hunt et al. 1977] [Huntley 1972] [Jacobson 1964] [Jacobson 1965] [Jaklitsch et al. 1971] [Jang et al. 2022b] [Jiang and Zhang 2016b] [Jiang and Zhang 2016a] [Jiang and Zhang 2018] [Kappus 1969] [Karemaa 1971] [Kelly and Tolhurst 1966] [Kirk et al. 1972] [Knight et al. 1973] [Konsewicz 1977] [Krebs 1972] [Kuhn and McKinney 1965] [Kuhn and Vogler 1965] [Kutney 1964b] [Kutney 1964a] [Laskowitz 1963] [Lavi 1966] [Lee et al. 2016] [Lieblein 1970b] [Lieblein 1970a] [Lieblein and Stockman 1969] [Lieblein et al. 1973] [Linnell 1963] [Lipera and Sandlin 1984] [Liubov et al. 2023] [Loscutoff et al. 1973] [Lowe and Sanger 1972] [Marchionna 1971] [Marder 2002] [McBreen et al. 2023] [McJones 1953] [McKinney et al. 1964] [McNally 1986] [Mehus 1965] [Merrick et al. 1991] [Michaelsen 1971] [Myers et al. 2019] [Mysko et al. 1993] [Naumowicz et al. 1998] [Nishimura 1980] [Novak 1975] [O’Malley 1959] [Obrien 1976a] [Obrien 1976b] [Ornelas 1985] [Ostroukhov and Chumakova 2019] [Otis 1962] [Owen and Cox 1966] [Pauli 1964] [Pauli 1965] [Hegarty et al. 1965] [Pauli et al. 1970] [Paxhia and Cord 1963] [Peterson 1964] [Peterson 1965] [Prasad and Choi 2017] [Pratt et al. 1971] [Przedpelski 1965] [Przedpelski 1967] [Pulk and Stolarik 1977] [Quigley and Franklin 1977] [Rabone and Paulson 1973] [Rauch 1972] [Remote Lift Fan Study 1973] [Robins et al. 1994] [Roelke and Zigan 1972] [Rogers et al. 1969] [Rolls 1960] [Rolls 1965b] [Rolls 1965a] [Gerdes and Rolls 1969] [Drinkwater et al. 1965] [Rolls et al. 1976] [Saari 1958] [Saddington and Knowles 2001] [Schmeer and Runckel 1962] [Sellers and Szuch 1973] [Sellers et al. 1977] [Shanks and Smith 1959] [Shanks and Smith 1960] [Shanks et al. 2018] [Shumpert and Harris 1969] [Sissingh 1960] [Smith 1958a] [Smith 1959] [Smith 1961] [Smith 1971] [Speth 1993] [Spillman 1965] [Spillman 1967] [Spreemann 1960] [Spreemann 1961] [Stanley and Hood 1981] [Stewart 1979a] [Stewart 1980] [Stewart and Blake 1992] [Stimpert 1973] [Stimpert and Fogg 1973] [Stockman et al. 1973b] [Szuch 1973] [Tauber et al. 1976] [The Jet Lift Controversy 1962] [True 1967] [Truong et al. 2023] [Turkmen and Altug 2020] [Vogler 1970] [Volk 1969] [VSTOL Systems Research Aircraft 1994] [Welter 1966] [Weng et al. 2026] [Whitfield and Blackburn 1965] [Wilson and Liperra 1984] [Wilson and Wurts 1985] [Wind Tunnel and Ground 1976] [Winston et al. 1975] [Xu and Zha 2021] [Yin et al. 2023] [Yuan 1969] [Yuan 1970] [Yuska and Diedrich 1972] [Zabinsky et al. 1974] [Zha 2023] [Zha and Ren 2023] [Zha et al. 2019] [Zha et al. 2024] [Zhang et al. 2013b] [Zheng et al. 2011b] [Zheng et al. 2011a]

Variable-stability aircraft and in-flight simulation

The instrument itself. Variable-stability aircraft and helicopters, in-flight and airborne simulators, and the model-following control laws that make one aircraft fly like another. Model following is named in 99 titles and the X-22A in 19, the aircraft the article identifies as the X-14’s direct successor for the vertical take-off problem.

227 records. [Lee 2017a] [Aiken et al. 1977] [Alag 1987] [Alag and Kaufman 1974a] [Alag and Kaufman 1974b] [Alag and Kaufman 1975] [Alag et al. 1973] [Alag et al. 1986] [Alexander and Höfinger 2013] [Anderson and Schmidt 1991] [Arendt et al. 1966] [Armstrong 1974] [Arterburn 2002] [Arterburn et al. 2002] [Baillie et al. 1997] [Barker 1966] [Baron et al. 1980] [Baska and Robbins 1966] [Bauschat 2002] [Becerra-Vargas 2015] [Beilman 1965] [Beilman 1983] [Berens and Biezad 1988] [Berry and Deets 1966] [Borah and Young 1983] [Bouwer 1987] [Bouwer and Hilbert 1984] [Bouwer and Hilbert 1986] [Bridges et al. 2005] [Buethe and Lebacqz 1984] [Cao et al. 2017] [Cetin and Kutay 2016] [Chakraborty and Comer 2024] [Chandrasekaran et al. 2021] [Chen and Gau 1987] [Chen et al. 1986] [Chen et al. 2023a] [Chetty and Henschel 1987] [Clark 1977] [Comer 2024] [Comer et al. 2024c] [Cook 1988] [Corliss et al. 1977] [Corliss et al. 1978] [Creer and McNeill 1956] [Crosbie and Eyth 1983] [Curran 1971b] [Curran 1971a] [Deets 1978] [Dickeson et al. 2007b] [Dittmar 1988] [Dong xinmin et al 2003] [Duda et al. 1997b] [Duda et al. 1997a] [Durham and Lutze 1991] [Edwards et al. 1995] [Ehlers et al. 2011] [Ellis and Miller 1967] [Ellis and Tilak 1975] [Ellis et al. 2002] [Eney 1967] [Eney 1969] [Erzberger 1968b] [Fang et al. 2022] [Jw et al. 1995] [Fossard 1993] [Fujizawa] [Fujizawa et al. 2016] [Gallagher et al. 1972] [Garren and Kelly 1965] [Gmelin 2017] [Gracio et al. 2011] [Hamel 2017b] [Hamidani and Kunz 2018] [Hanke and Hahn 2017] [Harper and Robert P. 1955] [Hasdorff et al. 1970] [Hellmann et al. 1988] [Henderson 1964] [Henderson and Lavretsky 1999] [Hilbert and Bouwer 1984] [Hilbert et al. 1986] [Hindson 1982] [Hosman and Van Der Steen 1993] [Huber and Reynolds 1976] [Huguenin 1981] [Hamel 2017a] [Ishitobi and Nishi 2010] [Ishitobi et al. 2010] [Iyer et al. 2003] [Jackson 1993] [Johnson et al. 1992] [Kaletka 2017] [Kaletka and von Grünhagen 1989] [Kanai and Nikiforuk 1982] [Kanai et al. 1985] [Kanai et al. 1986] [Key et al. 1965] [Kim et al. 2002] [Klopfstein 1968] [Kluever et al. 1966] [Klüssendorf and Lorenz 2011] [Knotts and Bailey 1988] [Knotts and Parrag 1983] [Ko and Park 2014] [Kocurek et al. 1997] [Komoda et al. 1988] [Komoda et al. 1989] [Kumar and Pradeep 2007] [Köhne 1982] [Lancraft et al. 1981] [Landau and Courtiol 1972] [Lavretsky 2019] [Lebacqz 1974] [Lebacqz and Aiken 1975a] [Lebacqz and Aiken 1975b] [Lebacqz and Govindaraj 1980] [Lebacqz et al. 1972] [Lebacqz et al. 1974] [Lee 1997b] [Lee 1997a] [Leissling et al. 2003] [Lewis and Johnson 2020] [Li et al. 2024c] [Lee 2017c] [Lorenz 2008] [Lutze 1989] [Malcom 1969] [Marchese 1963] [Markman 1993] [McCarley and Lindak 2016] [McFarland 1987] [McKillip 1987a] [McKillip 1987b] [Merrick 1977] [Meyer et al. 2012] [Michaels 1969] [Mirfakhraie and Garrard 1994] [Mitsuaki Ishitobi et al. 2007] [Model Following Control Systems 2011] [;;; 2003] [Moon et al. 2005] [Moralez et al. 2000] [Morgan 1985] [Moro et al. 2025] [Morse and Ossman 1990] [Motyka 1972] [Motyka 1974] [Motyka 1975] [Motyka and Reynolds 1971] [Newell et al. 1963] [Nield and Powell 1981] [Niessen 1969] [Nonlinear Model Following Control 1989] [Ouyang et al. 2001] [Padfield and Bradley 1993] [Pahle 1990] [Park and Ko 2008] [Pausder et al. 1988] [Person and Robbins 1965] [Pfeiff 1965] [Picardi et al. 2016] [Pieper et al] [Pieper et al. 1996] [Pineiro and Biezad] [Porter and Hicks] [Porter and Hicks] [Porter and Hicks 1993] [Porter and Othman 1989] [Porter and Xin-Guo Zhang] [Porter and Xin-Guo Zhang] [Porter et al. 1988] [Reynolds 1983] [Rhoads 1967] [Rhoads 1970] [Rhodes 1969] [Rhodes 1970] [Rohlf et al. 1988] [Drinkwater and Rolls 1962] [Roy and Winsor 1970] [Saetti et al. 2018] [Saetti et al. 2020a] [Sato 2006] [Sato and Satoh 2007] [Sattler 1986] [Scamps and Gibbens 2003] [Schmidt 1987b] [Schmidt and Schierman 1990] [Schmidt and Young 1998] [Scholten et al. 2020a] [Scholten et al. 2020b] [Schuchardt 2015] [Shafer 1991] [Shafer 1992] [Shafer 1994] [Shibasaki and Ishida 2016] [Sims and Kimberlin 1995] [Sinclair and Morgan 1987] [Smith 1974] [Smith et al. 1973] [Spires and Horn 2015] [Spires and Horn 2021] [Stengel 1973] [Stern et al. 1988] [Stevens 1995] [Swanson] [Szalai 1967] [Takahashi et al. 1994] [The Bell X-22A V/STOL 1990] [Tidwell 1989] [Tiroshi and Elliott 1973] [Trentini and Pieper] [Van Gool and Weingarten 1981] [Wang Xiaoqing et al. 2008] [Wasserman and Mitchell 1973] [Watson and Hindson 1988] [Watson et al. 2003] [Weingarten 2003] [Weingarten 2004] [Wilhelm 2017] [Xue et al. 2017] [Yang et al. 2009b] [Yi and Feng 2025] [Yongliang et al. 2013] [You 2020] [Young 1978] [Zugaj and Narkiewicz 2010]

System identification, model testing and flight-test method

Identification from flight data, which is the inverse of what the X-14 did. System and parameter identification of aircraft and rotorcraft, stability derivatives, subscale and scale-model testing, and flight-test method. Identification is named in 80 titles.

222 records. [Air Force Test Pilot School Edwards Afb Ca 1991a] [Air Force Test Pilot School Edwards Afb Ca 1992] [Aircraft and Rotorcraft System 2008] [Aircraft and Rotorcraft System 2016] [Aircraft Stability Derivatives 1998] [Aircraft Stability Derivatives 2002] [Akagi et al. 2024] [Al-Sharman et al. 2018] [Alscher et al. 1966] [Anderson and Vincent 1985] [Armstrong 1970] [Asper and Simmons 2022] [Babcock and Arena 2004] [Bachelder et al. 2011] [Bachfischer et al. 2024] [Baker et al. 1980] [Balasa et al. 2026] [Barzda 1966] [Berrigan et al. 2020] [Bilodeau et al. 2010] [Binion 1970a] [Binion 1971] [Binion 1975] [Blake and Lunn 1980] [Boirun 1979] [Boothe et al. 1974] [Botez and Rotaru 2007] [Burton and Bischoff 1976] [Butler and Ham 1991] [Chambers et al. 1981] [Cho et al. 2019] [Clarke and Roskam 1982] [Comer et al. 2025] [Comer et al. 2026a] [Corsiglia et al. 1989] [Courtin et al. 2020] [Cox et al. 2012] [Craig et al. 2004] [Damveld 2004] [De Jesus Mota and Botez 2009] [Development of a Continuous 2012] [Dias 2022] [Dias 2023] [Drinkwater and Feistel 1965] [Duan et al. 2024] [Duval 1981] [Eilertson 1977] [Ellis and Gubbels 1999] [Ericsson and Beyers 2003] [Falarski et al. 1981] [Fenwick 1967] [Ferrell et al. 1974] [Finnestead et al. 1970] [Fletcher 1993] [Fletcher 1995] [Fletcher 2008] [Flight Test 1979] [Flying Qualities and Flight 1998] [Fujimori and Ljung] [Gainer et al. 1967] [Garland 1980] [Garratt et al. 2013] [Gee et al. 1976] [Ghazi et al. 2020] [Grafton and Anglin 1972] [Grafton and Anglin 1975] [Grauer and Morelli 2023] [Gresham et al. 2023] [Ground Tests of Piasecki 1958] [Gustafson et al. 1960] [Hackett and Justice 1973] [Hageman et al. 2003] [Hall et al. 1978] [Ham et al. 1995] [Hanks and Ham 1992] [Hansen 1983] [Hansen 1984] [Harris et al. 2016] [Hebbar et al. 1999b] [Heyson 1978] [Hiliuta and Botez 2006] [Hill et al. 1982a] [Hindson 1987] [Höfinger and Blanken 2012] [Hutto 1975a] [Hutto 1975b] [Harasani 2015] [Vigouroux et al. 2013] [Iliff and Powers 1969] [Initial Flight Test 1989] [Integration and Simulated Flight 1977] [Irmawan 2026] [Ivler et al. 2014] [Jayaraman et al. 2022] [Jordan and Bailey 2008] [Jouannet et al. 2012] [Jung et al. 2017] [Kieß et al. 2026] [Klyde et al. 2007] [Knott 1977] [Knott 1978] [Kochuk et al. 2021] [Koenig et al. 1977] [Koeniguer and Spear 2018] [Koratkar and Chopra 2001] [Kuehme et al. 2014] [Kumar et al. 2006] [Kumar et al. 2022] [Kuppuswamy and Kiran 1981] [Langham 1979] [Larsson 2019] [Laudeman 1972] [Lawler et al. 2006] [Layton 1986] [Lebacqz and Chen 1977] [Lichota 2023] [Lo 1971] [Londono and Leonhardt 2012] [Lopez et al. 2021] [Lykins and Keshmiri 2010] [Marshall et al. 2005] [McKinney and Lysle 1954] [McNally and Bach 1988] [Mertaugh 1998] [Molusis 1973] [Morelli 1998] [Morris et al] [Mouritsen 1994] [Murch et al. 2009] [Murphy et al. 2004] [Nagata et al. 1973] [Nagy and Kirsten 1976] [Nepomuceno et al. 2022] [Newsom and Anglin 1975] [Newsom and Tosti 1959] [Nicolosi et al. 2010] [Nieuwenhuizen et al. 2007] [Oelker and Friehmelt 1998] [Okumoto and Elsanker 1973] [Optimization and Flight-Test Evaluation 2017] [Oreg et al. 2019] [Padfield 1986] [Padfield and Duval 1982] [Pan et al. 2026] [Parlett and Kirby 1964] [Pausder and Gerdes 1982] [Paw] [Payne and Henry E. 1961] [Petit 2024] [Plaetschke and Weiss 1988] [Pollini et al. 2014] [Position Estimation for Autonomous 2014] [Prasad et al. 2011] [Qianqian and Yi 2010] [Queijo et al. 1953c] [Remple and Tischler 2006] [Riesenfeld 1968] [Rothman] [Runco and Benedict 2018] [Runco and Benedict 2021] [Runco and Benedict 2023] [Saetti et al. 2019] [Sarigul-Klijn et al. 2008] [Saripalli 1995] [Schillings et al. 2010] [Schkolnik et al. 1995] [Schmidt and Jusko 2025] [Schmidt and Jusko 2026] [Schwanz and Grimes 1980] [Seher-Weiß et al. 2020] [Shubert and Jones 2025] [Shubert et al. 1994] [Simmons et al] [Simmons et al. 2021] [Simmons et al. 2023] [Singh and Girija 1998] [Smith and Parsons 1970] [Sobron 2018] [Sobron et al. 2021] [Sobrón Rueda 2021] [Spencer and He 2025] [Stange 1959] [Stark 2003] [Stratton and Spyropoulos 2024] [Stratton et al. 2023] [Strelkov and Bozhko 2026] [Suit and Williams 1973] [Sun et al. 2019] [Nusrath et al. 2020] [Tangler 1979] [Tatoglu 2017] [Terceiro 1976] [Thibault 1964] [Tischler 2018] [Tischler and Cauffman 1992] [Tischler and Remple 2012] [Tischler and Tumashofski 2002] [Toha et al. 2015] [Tomaine et al. 1978] [Trankle and Rabin 1983] [Tritschler and O’Connor 2016] [Umapathy et al. 2021] [Vagianos and Rooney 1964] [Vincent and Franklin 1981] [Wang et al. 1986] [Wang et al. 2020a] [Wang et al. 2022a] [Wang et al. 2025d] [Weiss 1983] [Widmayer and Tomassoni 1971] [Williams and Butler 1964] [Wolkovitch and Hoffman 1971] [Woodrow et al. 2013] [Wu et al. 2026a] [Yamauchi et al. 1988] [Young and Patton 1988] [Yu et al. 2013] [Yuan 2026] [Yuan and Katupitiya 2012] [Zhu et al. 2025b] [Zosimovych 2022] [Öhrle et al. 2019]

Vertical take-off aircraft design, propulsion and configurations

The configuration question the field had answered before the X-14 flew. Vertical take-off aircraft design, sizing and propulsion, transport and fighter concepts, and the reviews of the configuration as a class.

227 records. [Adamson 1968] [Adesh and Arun 2024] [Akturk and Camci 2022] [Albers 1972] [American Helicopter Society INC Washington DC 1965] [Anderson 1981] [Anderson 1983] [Anderson and Lebacqz 1997] [Apkarian 2017] [Asher 1969] [Axten and Johnson 2021] [Batterton and Blaha 1987] [Batterton and Blaha 1988] [Beatty and Worthey 1984] [Bianco et al. 2024] [Biesiadny et al. 1993] [Bland 1971] [Bloomfield 1959] [Boeing Co Morton Pa Vertol Div 1956] [Borland 1959] [Borst 1965] [Bower 1978] [Brown 1965] [Brown and Fisher 1968] [Burley 1984] [Burley and Hwang 1982] [Campbell 1959] [Campbell 1960] [Chana 2002] [Chance Vought Corp Dallas Tx 1963] [Chapman et al] [Chapman et al. 2023] [Chen et al. 2021] [Chichester-Miles 1965] [Civinskas 1973] [Connors and Swaim 1968] [Coplin 1967] [Coty and Kesling 1967] [Cowels 2023a] [Cowels 2023b] [Culpepper et al. 1979] [Curtiss 1965a] [Cäsar et al. 2025] [Davis et al. 1961] [DE Decker 1966] [Defense Science Board Washington Dc 1979] [Denning 1962] [Diekmann 2019] [Dikshit et al. 2022] [Scientific and Technical Information Division 1966] [Durbin and McGeer 1982] [Egerton and Fitzpatrick 1967] [Emerson et al. 2023] [Fatima et al. 2020] [Feddersen and Cea 1977] [Fu et al. 2025b] [Fu et al. 2026] [Gertsma and Zigan 1973] [Gladfelter et al] [Gokce and Camci 2010] [Goldsmith and Hickey 1963] [Govindarajan and Sridharan 2021] [Green and Andrews 1989] [Green and Oh 2006] [Technology et al. 2025] [Hasbrook 1957] [Hays and Schultz 2025] [Hazen 1963] [Hebbar et al. 1999a] [Hebert et al. 1970] [Hesse 1965] [Hill 1969] [Hill 1971] [Hill and Schmitt 1964] [Hobson et al. 2004] [Hoffrichter] [Hovering on One Engine 1968] [Howze 1969] [Hu et al. 2026c] [Irvin and Swan 1956] [Jacobsen and Greif 1972] [Jain and Mukkamala 2016] [Johnston 1964] [Johnston 1965] [Jou and Metcalfe 1984] [Kalemaris and Cea 1977] [Kappus 1959] [Kesling and Hyde 1968] [Kibens et al. 1987] [Kibens et al. 1988] [Kim et al. 2023d] [Kirby 1961] [Kleinman 1975] [Klingloff et al. 1965] [Kress 1980] [Kuhn 1980] [Kuhn and McKinney 1961] [LaBiche 2003] [Lavi 1967a] [Leutzinger 1968] [Lewis 1989] [Lewis 1990] [Lewis and Lewis 1981] [Li et al. 2013] [Lichten 1959] [Lindenbaum 1976] [Lockheed-Georgia Co Marietta 1969] [Loh and Jacob 2014] [Louma 1961] [MacPhail et al. 1993] [Madureira and de Almeida 2026] [Margason and Kuhn 1988] [Marino et al. 2017] [Mathur and Atkins 2026] [May and Widdison 1971] [McElreath 1972] [McIntire and Monson 1970] [McKinney and Newsom 1962] [Mendenhall and Spangler 1976] [Migdal 1973] [Milde 2003] [Milde et al. 2003] [Miller 1965b] [Miller 1984] [Moller 1985] [Muse 1961] [Musselwhite 1978] [Conference on V/Stol Aircraft 1960] [Cox et al. 1990] [Deckert and Holzhauser 1973] [Driggers 1978] [Fernandez et al. 2026] [Frey 2011] [Gainutdinov et al. 2026] [Gerhardt and Chen 1978] [Giurca 2025] [Kanishk Mahaveer Jain 2025] [Kidwell and Rapp 1985] [Krenkel and Salzman 1968] [Lee et al. 2022a] [Liu et al. 2022c] [Loth et al. 1974] [Lovell and Parlett 1957] [Ma et al. 2022b] [Magee et al. 1975] [Mihalik and Keane 2022] [Miller et al. 1981] [NASA Conference on V/STOL 1960] [Naumowicz and Smith 1992] [Nelms and Anderson 1984] [Nelms and Durston 1980] [Nelms et al. 1980] [Nelms et al. 1981] [Nicholson and lowry 1966] [O’Mallei 1957] [Paulson et al. 1988] [Peaker 1974] [Peciak et al. 2023] [Pedro et al. 2021] [Philhower 2002] [PlCKERELL and Cresswell 1968] [Pour Razzaghi et al. 2025] [Pour Razzaghi et al. 2026] [Price 1964a] [Qin 2023] [Ramirez et al. 1980] [Raymer 1988] [Rich 1969a] [Richardson 1959] [Ringland 1977] [Ringland and Craig 1977a] [Roberts and Deckert 1982] [Robinson 1959] [Robinson 2015] [Saboe 1963] [Sadey] [Saelman 1963] [Salkind 1973] [Salter 1975] [Samuels and Payne 1990] [Sanders 1964] [Sawata and Dinu 2025] [Schmitz 1969] [Seckel 1964] [Serovy and Kavanagh 1974] [Silva and Johnson 2021] [Simpson 1968] [Simpson 1969] [Skifstad 1970] [Snyder and Tong 2019] [Spitzer 1972] [Stanzione and Schrage 2023] [Statler 1966] [Stepniewski 1959] [Stewart et al. 2026b] [Stockman 1975] [Strack 1973] [Sulkoske et al. 1977] [Swaim 1969] [Swaim and Connor 1968] [Szlenkier 1970] [Tatom et al. 1972a] [Trenka 1966] [Turkel and Frost 1980] [Uehara and Matthies 2019] [Uehara et al. 2019] [Unsworth and Sutton 1984] [Vertical Take-off Aircraft 2001] [Virasak 2022] [Walz 1976] [Welsch and Fichter 2021] [Wernicke 1993] [West 1969] [White et al. 1985] [Wilson and Mahoney 1987] [Winborn 1969] [Wood 1967] [Woolard 1974] [Yang and Wang 2017] [Young 1961] [Zabinsky and Burnham 1977] [Zhou et al. 2019a] [Zhou et al. 2020a] [Zhu et al. 2024a] [Zhu et al. 2025a] [Zimmerman 1957] [Çelik et al. 2023]

Attitude command, augmentation and flight control of hovering vehicles

The retreat from the raw plant toward something a person can fly. Attitude command, stability augmentation, automatic flight control and fly-by-wire for hovering and vertical take-off aircraft, including the planar vertical take-off aircraft that control theory uses as a benchmark.

167 records. [Tan Nin 2022] [Ailon 2007] [Ailon 2009] [Aircraft Hovering Control 2007] [Albachten 1956] [Alford and Luoma 1960] [Anderson 1967] [Anderson and Innis 1965] [Anderson and Schroers 1972a] [Avanzini et al. 2003] [Axten and Johnson 2020] [Axten et al. 2024b] [Axten et al. 2024a] [Beattie 1975] [Berry and Broussard 1979] [Bilodeau et al. 2009] [Broussard and Stengel 1977] [Butler et al. 1966] [Cabarbaye] [Campbell and Abramovitz 1975] [Carpenter and Hodgkinson 1981] [Chen 2011] [Chen and Huo 2019] [Chen and Pérez-Arancibia 2024] [Cicolani et al. 1979] [Corliss and Gossett 1969] [Costandin et al. 2018] [Crim 1959] [Cunningham 1976] [Curtiss 1970] [Curtiss and Sumantran 1985] [Curtiss 1969] [Czyba and Kronhof 2020] [Dagal and Erol 2025] [Dendy and Tribken 1968] [Design of the Circulation 1979] [Digital Engine Control 1982] [Dukes 1970] [Efremov et al. 2024] [Elliott and Schreiber 1964] [Englar 1975] [Englar 1987a] [Englar 1987b] [Englar et al. 1977] [Englar et al. 1981] [Escareno et al. 2006] [Experimental Development 1981] [Feng Lin et al. 1999] [Filatov and Unbehauen 2004] [Franke and Hafer 1963] [Franklin 1986] [Franklin 2018] [Franklin and Engelland 1991] [Franklin and Stortz 1989] [Franklin et al. 1990] [Gallagher and O’Donnell 1965] [Gao et al. 2020] [Garren and Kelly 1966] [Gatley et al. 2001] [Gerardi et al. 2010] [Goland et al. 1964] [Gotleib 1977] [Greif et al. 1972] [Gress 2018] [Griffith and Crosby 1970] [Grunwald 2005] [Haisheng and Jinkun 2012] [Ham 1986] [Hart 1956] [Hartmann and Stein 1978] [Hartmann et al. 1979] [Hauser et al. 1992] [Henderson and Walters 1981] [Hendrick 1977] [Herrera et al. 2017] [Hess 2009c] [Hess 2009b] [Hill 1966] [Houghton et al] [Hu et al. 2000] [Ilyas et al. 2025] [Ioan and Adrian 2011] [Jackson and Patch 1968] [Jenkins 1973] [Kai 2024] [Kamalasadan 2007] [Kamarulzaman and Yasunobu 2015] [Kaplan 1959] [Kaufman 1965] [Kaufman and Schultz 1963] [Kaup et al. 2025] [Kazan and Krause 1968] [Kazan and Krause 1967] [Kelly et al. 1977] [Kesselyak 1974] [Kirby 1957] [Kirk and Pitt 1969] [Ko et al. 2024] [Krekeler et al. 1987] [LaRue 2026] [Lenox 1972] [Lepicovsky 2008] [Liming et al. 2015] [Liu et al. 2025a] [Lollar and Matous 1963] [Makarov 2019] [Mandal] [McLean and Naseem 1977] [McManus 1978] [Merrick 1982] [Mihaloew 1987] [Moralez et al. 1987] [Morris 1962] [Mueller 1964] [Mueller 1965] [Nagabhushan and Tomlinson 1982b] [Nakamura 1986] [Naldi et al. 2008] [Nichols and Englar 1981] [Nichols and Englar 1980] [Niessen 1971] [Pauli 1969] [Pauli 1971] [Portlock and Cubero] [Putman et al. 1977] [Reid 1976b] [Reid 1976a] [Ren et al. 2017] [Ringland and Craig 1977b] [Roltgen and Byrnes 1991] [Rosas et al. 2012] [Roth et al. 1980] [Saeki and Sakaue] [Schmidt 1978b] [Schmidt and Innocenti 1981] [Schroeder 1987] [Selman 2023] [Simko and Tatoglu 2019] [Sissingh 1956] [Stapleford 1980] [Stauffer et al. 1990] [Steils 1966] [Steils 1965] [Stengel et al. 1976] [Stengel et al. 1978] [Su 2014] [Switched Control 2006] [Tan et al. 2014] [Turner et al. 2001] [Uchida et al. 1988] [Vincent and Anex 1990] [Vogt et al. 1989] [VTOL Aircraft Control Design 2010] [Walters and Henderson 1983] [Wang and Ma 2021] [Wang et al. 2022c] [Weber 1982] [Wenqian et al. 2016] [Whitaker et al. 1977] [Xu et al. 2018b] [Zabinsky 1978] [Zabinsky 1979] [Zhang et al. 2025c] [Zhao 2017] [Zhao and Liu 2018] [Zhong et al. 2026a] [Zipf 1989]

Vertical take-off operations, terminal areas, ships and noise

The operational literature the article says grew around the configuration. Terminal-area operation and guidance, steep and instrument approaches, shipboard landing, noise, safety and airworthiness, and escape systems. Ships and decks are named in 22 titles.

176 records. [Abergo et al. 2026b] [Advanced Short Takeoff 1995] [Afilipoae et al. 2024] [Al-radhi and El-Metwally 2023] [Avionics 1969a] [Avionics 1969b] [Azinheira et al. 2006] [Bagan 1967] [Baitis 1977] [Barlow et al. 2009] [Barriage and Brandewie 1968] [Barton 1966] [Bhardwaj and Holzapfel 2025] [Bodson and Athans 1985] [Boothe and Ledder 1973] [Boothe and Ledder 1974] [Botre et al. 2023] [Brady and Gururajan 2025] [Brenckmann 1964] [Bryson et al. 1970] [Caldwell and Lafavor 1980] [Calise and Kramer 1982] [Calise and Kramer 1984] [Calvano and Harney 1998] [Camacho 1991] [Campbell 1962] [Capen 1971] [Casau et al. 2012] [Chaitanya et al. 2025] [Choi and Hampton 2020] [Ciepluch et al. 1979] [Clarke et al. 1973] [Clero et al. 2024] [Clough 1990] [Cole and England 1967] [Cook and Gregory] [Cornish 1965] [Craig 1961] [Craig and Heffley 1973] [Daffer and Rogers 1973] [Do 2021] [Douglas et al. 1990] [Dyke 1963] [Eilertson 1975a] [Eilertson 1975b] [Erickson and John C. 1969] [Erickson et al. 1965] [Erk et al. 2026] [Fluk 1981] [Fortenbaugh 1980] [Franklin and Innis 1977] [Fredericks et al. 2016] [Fredericks et al. 2018] [Gerdes et al. 1971] [Goka et al. 1980] [Guy 1976] [Haugen 1966] [Henschel et al. 1974] [Hoffman et al. 1971] [Hollister 1969] [Hollister et al. 1970] [Hsin 1974] [Jensen and Pera 1977] [Jia and Lee 2020] [Jia and Lee 2021] [Dalamagkidis 2006] [Kalemaris 1983] [Kejik et al. 2026] [Kelly et al. 1979] [Kesselring 1969] [Klein 1970] [Kohn 1972] [Kuhn 1979] [Kurylowich and Ritter 1970a] [Kurylowich and Ritter 1970b] [LaRue and Rivera 2026] [Li 2021] [Liseitsev 2025] [Love 2020] [Lozano et al. 2021] [Lozano et al. 2022] [Lozano et al. 2024] [McCormack and Poteate 1965] [McGee 1977] [McGee et al. 1978] [McMuldroch 1979] [McMuldroch et al. 1979] [Merrick and Gerdes 1977] [Merrick and Gerdes 1983] [Minsk 1970] [Mo et al. 2024] [Moen and Yenni 1975] [Mohd Ali et al. 2023] [Mondal and Mahanta 2013] [Mondal et al. 2012] [Neuman and Lee 1975] [Okoduwa et al. 2025] [Overfield and Crawford 1967] [Oyewola 2026] [Papadales and Basil S. 1979] [Park and Park 2025a] [Paulk and Phatak 1984] [Pilot Training and Certification] [Podguzov et al. 2024] [Pogust 1969] [Posner 1967] [Poteate and Solomonides 1964] [Prabhakar et al. 2023] [Ramaveerapathiran et al. 2025] [Representative Operations of V/STOL 2002] [Rigatos 2021] [Rosenthal et al. 1988] [Rudolph 1972] [Rupert 2008] [Anoop and Sharma 2018] [K.А. 2025] [Comeau et al. 2022] [de Paula et al. 2026] [Di et al. 2022] [Garren et al. 1969] [Huang et al. 2019] [Kang et al. 2024b] [Kelly et al. 1974] [Kolosov et al. 2020] [Kownacki et al. 2023] [León et al. 2021] [Leon et al. 2021] [Owen et al. 2021] [Renselaer 1974] [Rogers 1993] [Sadik Aboud et al. 2023] [Schade 1968] [Schmidt 1963] [Schmitz and Stepniewski 1973] [Schneider 1989] [Schrage and Van 2015] [Sloman 2019] [Sloman and Scott 2018] [Smith 1996b] [Smith 1997a] [Smith 1997b] [Smith and Meyer 1981] [Sonkar et al. 2021] [Sorensen et al. 1980] [Stamper 1973] [Sternfeld et al. 1972] [Sturdevant 1962] [Tang et al. 2020a] [Tiberio fernandez] [Toader et al. 2018] [Tuck 1970a] [Tuck 1970b] [Turner 1969] [Udroiu and Blaj 2016] [Vasiloff and Forbes 1963] [Warner et al. 1986] [Watson et al. 2019] [Watson et al. 2020] [Wen et al. 2021] [Whyte 1979] [Willis 1980] [Wilson et al. 1981] [Windolph 1969] [Wolkovitch et al. 1971] [Wu 2024] [Wu et al. 2022b] [Xie et al. 2015] [Yang et al. 2026b] [Ye et al. 2011] [Ye et al. 2020] [Yu et al. 2020] [Zabinsky 1964] [Zhang 2017] [Zhang et al. 2014c] [Zhu et al. 2022a] [Zou et al. 2026]

Pilot-induced oscillation, bandwidth and time delay

The failure mode that ended the X-14B’s flying. Pilot-induced oscillation and aircraft-pilot coupling, its prediction and suppression, actuator rate limiting, and the bandwidth and time-delay criteria that replaced the magnitude criterion. Pilot-induced oscillation or pilot coupling is named in 113 titles and rate limiting in 20, a form of the actuator saturation the review names as a cause.

147 records. [A Comparative Study 2015] [A’Harrah 1994] [Adams 1978] [Adams 1980] [Aharrah 1995] [Ali 1997] [Alvarez-Munoz et al. 2019] [Andreea-Irina and Achim 2014] [Bachelder and Aponso 2023] [Bachelder et al. 2024] [Bailey and Smith 1982] [Bailey et al. 1987] [Bechelder et al. 2025] [Blanken and Pausder 1994] [Boskovic and Mehra] [Cai et al. 2014a] [Chen and Hindson 1985] [Chen and Hindson 1986] [Crane 1981] [Crane 1983] [Craun et al. 2013b] [Duda et al. 1998] [Efremov et al. 2020a] [Efremov et al. 2022b] [Eichler 1970] [Ema et al. 1997] [Fan et al. 2024] [Gatley et al. 2006] [Gilbreath and Markofski 2001] [Green 1988] [Han and Liu 2026] [Hanke 2003] [Hess] [Hess 1981c] [Hess 1984a] [Hess 1994] [Hess 1997] [Hess and Hess 1997] [Hess and Kalteis 1989] [Hess and Stout 1998] [Hess et al. 1997] [Hodgkinson et al. 1982] [Iloputaife and Iloputaife 1997] [Ionita 1996] [Jeram and Prasad 2003b] [Jeram and Prasad 2003a] [Funk et al. 1993] [Jones 2020] [Jones and Jump 2013] [Junfeng et al. 2017] [Kartal et al. 2024] [Katayanagi 2001] [Katayanagi 2004] [Kempel 1971a] [Kendall 2005] [Kish et al. 1996] [Kish et al. 1997a] [Kish et al. 1997b] [Klyde and Mitchell 1999] [Klyde and Mitchell 2003] [Klyde and Mitchell 2004] [Klyde et al. 1997b] [Klyde et al. 2020b] [Klyde et al. 2020a] [Koivo et al] [Kurttisi et al. 2023] [Leonard 2013] [Levi and Nelson 1963] [Levi and Nelson 1964] [Levison and Papazian 1987] [Li 2005] [Li et al. 2014b] [Li et al. 2026c] [Liebst et al. 2002] [Liu and Gao 2010] [Liu and Lone 2013] [Liu et al. 2021c] [Liu et al. 2026a] [Mandal and Gu 2016a] [Mariano et al. 2011] [Markofski and Bailey 1999] [McFarland and Bunnell 1990] [McKay 1994] [McRuer 1995] [Mitchell 2000] [Mitchell and Klyde 2001] [Mitchell and Klyde 2008] [Mitchell et al] [Mitchell et al. 1991] [Muscarello et al. 2017] [Neal 1970] [Newton and Kroo 2023] [Newton and Kroo 2024] [Newton and Kroo 2025] [Nguyen and Cord 1999] [Nguyen et al. 1997] [Nguyen et al. 2021] [Pausder and Blanken 1992] [Pausder and Blanken 1993] [Powers 1980] [Powers 1982] [Powers 1986b] [Quan 2013] [Rezaei and Khosravi 2023] [Rzucidło and Tomczyk 2007] [Schroeder 2001] [Schroeder and Chung 2000] [Schroeder et al. 1998] [Schroeder et al. 2001] [Shafer and Steinmetz 2001a] [Shafer and Steinmetz 2001b] [Shafer et al. 1983] [Shafer et al. 1984] [Shams] [Shams et al. 2023] [Shweyk and Weltz 2005] [Smith 1979] [Smith 1982] [Smith 1986] [Smith 1991] [Smith and Berry 1975] [Smith and Edwards 1980] [Tabassum and Bai 2022] [Tohidi et al. 2018] [Tran et al. 2017] [Twisdale and Kirsten 1984] [Valentin 2011] [Walker and Postlthewaite] [Wang et al. 2012] [Wang et al. 2021b] [Wang et al. 2023d] [Weltz et al. 2007] [Wu and Perng 2004] [Xu and Wu 2021] [Yildiz 2010] [Yildiz and Kolmanovsky 2010] [Yin and Wang 2017] [Yin et al. 2019a] [Yu and Liu 2013] [Zaytseva et al. 2021] [Zeyada et al. 1998] [Zeyada et al. 1999] [Zhang et al. 2017b] [Zhang et al. 2023b] [Zhang et al. 2026b] [Zhou et al. 2012] [Ünen and Yıldız 2025]

Reaction controls, bleed and thrust deflection

What the control power was bought with. Reaction controls, engine bleed and its cost, thrust deflection and vectoring for vertical take-off. Thrust vectoring is named in 99 titles and reaction controls in 8, so the bleed-fed reaction control that dominated the X-14 is a small literature beside the vectored-thrust vehicles that replaced it.

141 records. [Abdelmageed et al. 2024] [AIR Bleed Objective for] [Ale Isaac Khoueini] [Aroussi 2026] [Aygun 2023] [Aygun 2024] [Baldini et al. 2026] [Barrett 1965] [Beard and Foley 1983] [Beck et al] [Borchers et al. 1994] [Bose et al. 2014] [Carr 1984] [Carr 1986] [Casau et al. 2016] [Cheatham et al. 1990] [Chen et al. 2011] [Cheng et al. 2020a] [Clark 1965] [Coles 1968] [Conan and Savarese 2001] [Crandall et al. 1973] [Cunningham and Boytos 1981] [Cunningham and Boytos 1983] [Dahl et al. 1962] [Davi Antônio dos Santos et al. 2024] [Davis and Spicer 1965] [Denton et al. 2021] [Dhanya et al. 2023] [Di et al. 2025] [Dinca and Corcau 2021] [Dinca et al. 2019] [Do Nascimento and Pilidis 1991] [dos Santos et al 2013] [Durán-Delfín et al. 2026] [Enenakpogbe et al. 2024b] [Enenakpogbe et al. 2024a] [Enenakpogbe et al. 2025] [Englar 1987c] [Erwin et al. 1964] [Esker and McArdle 1993] [Esker and Sedrick 1972] [Eulopa-Hernandez et al. 2026] [Flight Characteristics of Quad 2014] [Friend 1964] [Frost and Bishop 1963] [Frost and Bishop 1965] [Garcia et al. 2009] [Gasior et al. 2017] [Gerber and Tsao 2018] [Hall 1965] [Hang et al. 2013] [Hill and Jenkins 1980] [Hill and Jenkins 1979] [Hooker 1981] [Hoshu et al. 2019] [Hoskin et al. 1991] [Hou et al. 2024] [Huber et al. 2024] [Huo et al. 2025] [Huo et al. 2026] [Invernizzi et al. 2020a] [Jiang et al. 2014] [Kantner et al] [Kara-Mohamed 2023] [Keller 1969] [Kentfield 1967] [Koru and Wan 2025] [Krase 1967] [Kuang and Zhu 2015] [Kumon et al. 2010] [Kumon et al. 2011] [Lam 1998] [Lampard 1978] [Leovan 2019] [Lewis and Simpkin 1981] [Li et al. 2016b] [Liu et al. 2018b] [Liu et al. 2022a] [Liu et al. 2024a] [Liu et al. 2024b] [Lowe 1985] [Mansell 1987] [Mao et al. 2026] [Martinez et al. 2025] [Marubashi and Miwa 2014] [Marubashi and Miwa 2015] [Marubashi and Miwa 2016] [Matveev and Wheeler 2019] [McNown and Yih 1953] [Merceruio] [Mishra et al. 2025] [Miwa 2021] [Miwa and Maruhashi 2016] [Miyazaki and Tsubakino 2017] [Molyneux 1983] [Morello et al. 1972] [Nagabhushan and Faiss 1984] [Nery et al. 2024] [Nishino and Osaki 1961] [Aerojet-General Corp., Sacramento, Calif. (USA) 1975] [Petit and Scholey 1973b] [Petit and Scholey 1973c] [Petit and Scholey 1973a] [Rahman and Whidborne 2008] [Ren and Zha 2024] [Riley et al. 1989] [Robins et al. 1985] [Rolls and Aoyagi 1977] [Russo et al. 2011] [Saghafi and Banazadeh 2006] [Saghafi and Banazadeh 2007] [Sherbaum and Lichtsinder 1998] [Simmons 2022a] [Simmons et al. 2025a] [Smith 1966a] [Sotheran 1982] [Sully and Whittley 1987] [Sørensen et al. 1996] [Thames 1965] [The Hawker P1127 Vectored 1990] [Tich 1991] [Tsubakino and Saito 2020] [Van Nieuwstadt and Murray 1998] [Vectored Thrust 1992] [Wang et al. 2017d] [Wang et al. 2018a] [Wang et al. 2020b] [Wang et al. 2022d] [Wang et al. 2026e] [Ward and Lewis 1987] [Ward and Penrose 1983] [Wei Yuan and Katupitiya 2013] [Witting and Sneck 1991] [Xu and Zhang 2019] [YAV-8B Reaction Control System 1993] [Yuhas and Ray 1992] [Zafirov 2010] [Zhang et al. 2013a] [Zhijie et al. 2026] [Zhou et al. 2022a]

Visual cues, displays and the hover task

The other half of the hover task. Visual cues, displays and symbology for hover and approach, and flight in degraded visual environments. Degraded or reduced visibility is named in 17 titles, the operational problem that the X-14’s own five and a half years of operating experience placed beside the engine.

168 records. [Aires et al] [Aires et al. 2022b] [Aires et al. 2022a] [Alshbatat 2021] [Anderson 1966] [Anderson and Schroers 1972b] [Bachelder and Hansman] [Bachelder and McRuer 2002] [Bachelder et al. 2002] [Bailey 1986] [Baillie et al. 1995] [Behan and Siciliani 1965] [Beilman et al. 1975] [Bhargavapuri et al. 2019] [Birckelbaw and Nelson 1992] [Blanken et al. 1991] [Blundell et al. 2020] [Brown et al] [Burke and Ferris 1981] [Chalk and Wilson 1968] [Chalk and Wilson 1969] [Chase 1976] [Chen 1982] [Chen et al. 2020] [Chitrakaran et al. 2005] [Chittaluri 2022] [Chu et al. 2022] [Comandur et al. 2020] [Control Augmentation and Cockpit 2002] [Dare and Burley 1992] [Davi Antônio dos Santos et al. 2016] [De Wagter et al. 2018] [Deal et al. 1967] [Di Carlo et al. 1971] [Dorr et al. 1992] [Dorr et al. 1994] [Dukes 1969] [Efremov et al. 2020b] [Eshow 1990] [Eshow and Schroeder 1993] [Eshow et al. 1987] [Eulrich and Lebacqz 1978] [J. Victor Lebacqz; Edwin W. Aiken 1978] [Farris et al. 1983] [Flaig 1977] [Flow Visualization Studies 1991] [Foster et al. 1987] [Foster et al. 1988] [Franceschini et al. 2023] [Franklin 1997a] [Franklin and Nicholas 1992] [Franklin et al. 1996] [Frost et al. 2002] [Garcia-Pardo et al. 2001] [Garg and Schmidt 1989] [Garren et al. 1965] [Ge et al. 2023] [General Electric Co Cincinnati Oh 1962] [Ghosh and Rajagopalan 2022] [Gillingham 1984] [Godfroy-Cooper et al. 2017] [Gold and Walchli 1974] [González-Tejeda et al. 2026] [Haider 2018] [Haines 1980] [Haworth et al. 2001] [Heo and Lee 2024] [Hess 1977a] [Hess 1988] [Hoh 1985] [Hoh and Ashkenas 1979a] [Hoh and Ashkenas 1979b] [Hoh and Ashkenas 1981a] [Hoh and Ashkenas 1981b] [Hoh et al. 1983] [Hoh et al. 1987] [Holzhauser et al. 1971] [Holzhauser et al. 1972] [Irmawan et al. 2023] [Janetzko et al. 2024] [Janetzko et al. 2025] [Johns et al. 1988] [Johns et al. 1990a] [Johns et al. 1990b] [Johnson and Andre 1993] [Johnson and Montgomery 2005] [Jones et al. 2018] [Jung and Kim 2024] [Kawamura et al. 2024] [Keipour et al. 2022] [Klein et al. 1974] [Krammer et al. 2021] [Krammer et al. 2022] [Kurdel et al. 2024] [Lebacqz and Radford 1978] [Lebacqz and Radford 1979] [Lebacqz et al. 1981] [Li et al. 2023a] [Liu et al. 2019b] [Llerena Caña et al. 2022] [Llerena et al. 2022] [Martin et al. 1999] [Marut et al. 2023] [Mayfield et al. 2026] [Meng et al. 2022] [Merrick 1981] [Merrick 1984] [Milam et al. 2019] [Minor et al. 2017] [Mitchell et al. 2004] [Mitchell et al. 2014] [Mourtos et al. 1995] [Nasiri and Rezazade 2006] [Newton et al. 2024] [O’Donnell et al. 1988] [Omorodion 2023] [Osterman and Mulley 1977] [Otsuka et al. 2024] [Ouerdane and Mysorewala 2024] [Parrish and Bowles 1983] [Parrish and Williams 1990] [Patierno and Asdurian 1965] [Priambodo et al. 2022] [Procházková and Juračka 2026] [Reid and Sattler 2001] [Richards et al. 2014] [Rogers et al. 2017] [Roscoe et al. 1975] [Roscoe et al. 2001] [Schmidt 1987a] [Schroeder and Merrick 1990] [Schwartz and Shearer 1964a] [Schwartz and Shearer 1964b] [Sevostyanov and Devitt 2021] [Sevostyanov et al. 2022] [Shaik 2026] [Stereopsis Cueing Effects 1989] [Stockman et al. 1973a] [Swanson 1993] [Sykora 2009] [Szoboszlay et al. 2021] [Sözer and Kumbasar 2023] [Tapia and Intano 1976] [Taylor 2009] [The Role of Human 1986] [Theodore et al. 2014] [Tritschler et al. 2015] [Tritschler et al. 2020] [Trusfus and Abdullin 2021] [Tsai 2008] [Tuck 1985] [Vallerie 1967] [Viertler and Hajek 2016] [Viertler and Hajek 2017] [Walters et al. 2022] [Wang et al. 2020c] [Whalley et al. 1999] [Willis and Genever-Watling 1977] [Xiao et al. 2026c] [Xie et al. 2017] [Xin et al. 2022] [Xu et al. 2019d] [Yang et al. 2025c] [Zahmatkesh et al. 2026] [Zhang et al. 2025d] [Zhang et al. 2026e] [Zhong et al. 2021] [Zurn et al. 2016]

Shared control, workload and the division of authority

How authority is divided once a second controller exists. Pilot workload and its measurement, shared and blended control between pilot and automation, and the simplified vehicle operations concept. Workload is named in 40 titles and simplified vehicle operations in 18.

92 records. [Angelov and Holzapfel 2022] [Arnegard and Comstock 1991] [Bachelder and Aponso 2021b] [Bachelder et al. 2018] [Bachelder et al. 2019] [Belak and Hromcik 2024] [Bittner et al. 2013] [Bolat and Avci 2025] [Khalaj et al. 2024] [Bridges et al. 2006] [Casali and Wierwille 1983] [Casali and Wierwille 1984b] [Casali and Wierwille 1984a] [Chai et al] [Chakraborty et al. 2025] [Chakraborty et al. 2026] [Chandarana et al] [Chevalier and Burke 1972] [Chisom 1984] [Choi et al. 2025] [Chornyi et al. 2026] [Comer 2026] [Comer and Chakraborty 2023] [Comer et al. 2026b] [Control Authority Assessment 1993] [Degani and Heymann 2002] [Dollinger et al. 2021] [Feary et al] [Feary et al] [Goodrich 2016] [Griffiths et al. 2024] [Hanson et al. 2014] [Hart and Hauser 1987] [Hoh 2003] [Homola and Tiwari 2023] [Govers 2024] [Janetzko et al. 2026] [Jones et al. 2022] [Kalra and Greiwe 2026] [Kamath et al. 2025] [Kaneshige et al] [Kaneshige et al. 2024] [Kannan et al] [Kantowitz 1992] [Kim and Kunz 2017] [Kish et al. 2021] [Klein et al. 2017] [Krebs et al. 1977] [Krois et al. 2024] [Liang 2026] [Licata 2024] [Lombaerts et al. 2020a] [Louis-Ferdinand et al. 2025] [Mansikka et al. 2019] [Mao et al. 2022] [Matni and Meeko Oishi 2008] [Mora-Soto et al. 2021] [Muhammad 2021] [Nagami et al] [Papa and Stoliker 1988] [Pepitone et al. 1988] [Qin et al. 2025] [Rault 1979] [Roscoe 1989] [Rzucidło and Chudý 2011] [Santhosh 2023] [Sato and Wada 2025] [Scerbo et al. 2002] [Shish et al] [Shively et al. 1987] [Singh et al. 2021] [Song et al. 2025] [Spadão et al. 2026] [Spyker et al. 1971] [Stephenson et al. 2026] [Suppiah et al. 2020] [Suyatinov et al. 2022] [Suzuki et al. 2010] [Taheri Gorji et al. 2023] [Turco et al. 2026] [Türe et al. 2015] [Tvaryanas 2006] [Warr et al. 1986] [Willebeek-LeMair and Rhinehart 2023] [Wing et al. 2020] [Xu et al. 2026] [Yan and Chen 2019] [Yan et al. 2023a] [Yin and Fu 2014] [Zhang et al. 2026c] [Zikmund et al. 2019] [Zintl et al. 2024a]

Other vertical take-off and handling-qualities literature

The residual, reported and not hidden. General surveys of vertical take-off of the 1960s, single-word or general titles on hover and vertical flight, and works on hovering mechanisms that belong to no single cluster.

31 records. [Altoscan Co Landsdowne Pa 1957] [Altoscan Co Landsdowne Pa 1958] [Alvarez muñoz] [Bertelsen 2016] [Campbell 1964] [Cook 1985] [Coolican 2002] [Cotton 1967] [Equations of Motion 2002] [Freymuth 1990] [García Carrillo et al. 2013] [Gillmore 1960] [Gluhareff 1959] [Goto and Miwa 2017] [Gowanlock 2025] [Hafer and Sachs 1982] [Harvey and Waugh 1976] [Hellyar 1970] [Hollister 1970] [Introduction to Hovering 2014] [Lightfoot 1968] [Naval Air Development Center Warminsterpa 1978] [Rand and Khromov 2017] [Schwaiger and Wills 2016] [Shafer 1970] [Sherman 1964] [STOL VTOL and V/STOL 1971] [V/STOL 1971] [VTOL 1971] [VTOL 1969] [Yehia et al. 2026]

Where the Framing Breaks Down

Treating the X-14 through the keystone of control-power measurement is the right frame, and there are five places where it misleads.

The Criterion Specified Magnitude and the Problem Was Bandwidth

This is the most important limitation and the aircraft’s own programme demonstrated it.

The tip-turbine fans of Gerdes and Rolls 1969 produced their thrust for less than half the bleed, and gave the aircraft 0.65 radians per second squared of roll control power against 0.70 for the reaction nozzles, which by the criterion the aircraft itself had established should have been close to a straightforward improvement. They were rejected because of their time constants. A fan has rotational inertia and takes time to spin up, so the moment arrives late. The report gives a first-order time constant of 0.58 seconds open loop and 0.34 seconds with the closed-loop speed control fitted for flight, against 0.08 seconds for the reaction nozzles, and it rated the fans 6-1/2 to 7-1/2 against 4-1/2 to 5-1/2 for the nozzles. For a first-order lag of time constant $\tau_{c}$ the fraction of a commanded moment present a time $t$ after a step is

\[1 - e^{-t/\tau_{c}} \tag{98}\]

so at the 0.2 seconds within which the military and Advisory Group for Aerospace Research and Development recommendations of the day required the aircraft to begin moving the right way,

\[1 - e^{-0.2/0.58} = 0.292, \qquad 1 - e^{-0.2/0.34} = 0.445, \qquad 1 - e^{-0.2/0.08} = 0.918 \tag{99}\]

The report adds that a full command saturates the closed loop, so the fan reverts to its open-loop constant exactly when the pilot asks for the most, and that the aircraft took about 1.0 second to stop and begin moving in the direction of the control. It is explicit that this resulted in pilot-induced oscillations and long lags between control initiation and the aircraft following.

So a control system nearly matching the control power of the one it replaced was unflyable. The criterion was incomplete, and the experiment that revealed the incompleteness was run on the same aircraft that had produced the criterion. What was missing was any statement about how quickly the moment must appear, a bandwidth requirement rather than an authority requirement.

The field’s eventual answer was to change the variable. Modern handling-qualities criteria are stated in terms of attitude-response bandwidth and phase delay rather than in terms of maximum angular acceleration alone, and the experiments that established those criteria are a direct methodological descendant of the X-14A’s. Pausder and Blanken 1992, Pausder and Blanken 1993, and Blanken and Pausder 1994 investigate the effects of bandwidth and time delay on roll-axis handling qualities, sweeping two parameters across a boundary and collecting pilot ratings. The procedure is the X-14A’s, with the independent variables replaced. The state of the subject at that point is collected in Blanken and Whalley 1993. The X-14’s number survived as a floor and stopped being the criterion.

The two framings can be connected, and connecting them shows why the older one was not simply wrong. Tracking an attitude oscillation of amplitude $A$ at frequency $\omega$ on a double integrator requires an angular acceleration of

\[\ddot{\theta} = A \omega^{2} \tag{100}\]

so saturation at the available control power caps the frequency at

\[\omega_{\text{max}} = \sqrt{\frac{\text{CP}}{A}} \tag{101}\]

Authority and bandwidth are therefore the same statement at a specified amplitude and different statements otherwise. At five degrees of amplitude the X-14A’s lowest tested control power of 0.8 radians per second squared supports 3.03 radians per second and its highest supports 4.79.

\[\sqrt{\frac{0.8}{0.0873}} = 3.03, \qquad \sqrt{\frac{2.0}{0.0873}} = 4.79 \tag{102}\]

Turning it the other way, a control power of 0.8 sustains a bandwidth of two radians per second up to an amplitude of 11.5 degrees, and 2.0 sustains it up to 28.6 degrees.

\[A_{\text{max}} = \frac{\text{CP}}{\omega^{2}} = \frac{0.8}{4} = 0.2 \text{ rad} \tag{103}\]

So the magnitude criterion is a bandwidth criterion evaluated at large amplitude. The X-14A’s numbers are adequate for the large corrections and become uninformative for the small rapid ones, the regime in which a laggy actuator ruins an aircraft while satisfying the magnitude requirement. The tip-turbine fans failed in the regime the criterion did not describe.

Two Pilots

The lateral control results rest on the flight performance of two NASA research pilots, both experienced in helicopters and vertical take-off aircraft, in Drinkwater et al. 1965. That is the sample.

Nothing about this was unreasonable in 1965, and the alternative was no data at all. But a criterion that a contractor must design to, derived from two experienced test pilots’ opinions, carries an assumption that the population of pilots who will fly production aircraft resembles those two. Experienced test pilots are the population least representative of the difficulty a task presents, because they are selected for being able to fly things other people cannot.

One Airframe’s Inertias

Every control power the X-14A reported is a moment divided by the X-14A’s inertia. The normalisation is intended to make the result transferable, and it does so exactly if pilot opinion depends on angular acceleration and nothing else.

It does not, quite. The pilot sees the aircraft’s attitude and also its position, and the mapping from attitude to position depends on the aircraft’s height above the ground, its visual surroundings, and the pilot’s viewing position. The X-14 had an open cockpit and the pilot sat forward of the wing, an unusually good viewing position, and Rolls 1965b identifies reduced visual reference as one of the two principal operational problem categories. A criterion measured in one visual environment and applied in another is being extrapolated on a variable nobody recorded.

Gravity Was Not Adjustable

The variable-stability system could synthesise any attitude dynamics within its authority budget. It could not synthesise gravity, and this bounds what the aircraft could simulate in a way that is exactly computable.

The attitude dynamics contain no gravitational term,

\[\ddot{\theta} = \frac{M}{I} \tag{104}\]

so the X-14A could reproduce a lunar module’s attitude response exactly. The translational dynamics do contain one. A hovering vehicle holding height and tilted by $\theta$ accelerates horizontally at

\[\ddot{x} = g \tan\theta \tag{105}\]

so the same attitude produces different translation under different gravity. The ratio of terrestrial to lunar gravity is

\[\frac{g_{e}}{g_{m}} = \frac{9.807}{1.62} = 6.05 \tag{106}\]

and since a distance covered under constant acceleration goes as the square of time, the lunar translation timescale is longer by

\[\sqrt{\frac{g_{e}}{g_{m}}} = 2.46 \tag{107}\]

The X-14A therefore simulated the inner loop exactly and the outer loop 2.46 times too fast. Concretely, holding five degrees of tilt for five seconds moves an aircraft 10.7 metres on Earth and 1.8 metres on the Moon.

\[\tfrac{1}{2} \times 9.807 \times 0.0873 \times 25 = 10.7 \text{ m} \tag{108}\]

The same input on the Moon produces a translation the pilot would have to work to notice.

\[\tfrac{1}{2} \times 1.62 \times 0.0873 \times 25 = 1.8 \text{ m} \tag{109}\]

Two further consequences follow and both are quantitative. A vehicle hovering on the Moon needs

\[\frac{T_{\text{moon}}}{T_{\text{earth}}} = \frac{g_{m}}{g_{e}} = 0.165 \tag{110}\]

of the thrust it would need on Earth, so the thrust margin is not the binding constraint there that it is here. And to obtain the same horizontal acceleration the lunar vehicle must tilt very much further, since

\[g_{m} \tan\theta_{m} = g_{e} \tan\theta_{e} \quad \Longrightarrow \quad \tan\theta_{m} = 6.05 \tan\theta_{e} \tag{111}\]

so that five degrees on Earth corresponds to

\[\theta_{m} = \arctan\left(6.05 \times \tan 5^{\circ}\right) = 27.9^{\circ} \tag{112}\]

A lunar lander manoeuvres at attitudes that would be alarming in a terrestrial hover, and no amount of adjustment to a terrestrial aircraft’s control system reproduces that, because the aircraft would simply translate away.

The mismatch is large, and it lies in the plant rather than in the controller, so no adjustment of the control system can correct it. It is the reason the Lunar Landing Research Vehicle had to exist.

The lineage is documented and it reads as a sequence of admissions that the previous simulator was insufficient. Henderson 1963 compares control systems for the final descent and landing manoeuvre, and Markson et al. 1963 reports simulation of the manned lunar landing. Obryan 1966a reports flight tests of a manned rocket-powered vehicle using the Langley lunar landing facility, which suspended the vehicle to cancel most of its weight. Greene and Russo 1967 and McCabe et al. 1967 report piloted lunar module landing simulation studies, and Hewes 1967 reports flight evaluations of lunar landing vehicle attitude control systems.

The document that states the problem most directly is Kluever 1967, which assesses ground and flight simulators for examining the manned lunar landing, because that is the question of what each kind of simulator can and cannot represent. The training programme that resulted is described in Armstrong and Nassiff 1968 and the vehicle itself in Bigham 1970. Jarvis 1967b is the most directly comparable document, reporting fly-by-wire flight control experience with a free-flight lunar-landing research vehicle, a report of the same class as the X-14B papers for a machine built because the X-14 could not do the job. The landing simulations themselves are reported in Pollack et al. 1967, the automatic alternative to a piloted landing is Rimer and Sperling 1965, and the surface interaction that made the final phase hazardous is Roberts 1964. That vehicle cancelled five sixths of its weight with a gimballed vertical jet so that the residual translational dynamics were lunar, in the Lunar Landing Research Vehicle entry. The fraction it had to support is

\[1 - \frac{g_{m}}{g_{e}} = 1 - 0.165 = 0.835 \tag{113}\]

so the jet carried 83.5 percent of the vehicle and the remaining 16.5 percent was flown, a far more expensive and dangerous way to build a simulator, accepted because the cheaper way could not reproduce lunar translation.

The X-14’s contribution to Apollo was therefore real and bounded. It could teach the attitude task. It could not teach the landing.

Diminishing Returns the Criterion Does Not Show

A last point that the framing obscures. The criterion is a threshold, which suggests that more control power is better until the threshold is met and irrelevant afterwards. The dynamics say something more graded.

Consider correcting a position error of three metres. The pilot tilts, waits, and tilts back. Establishing an attitude $\theta$ by a symmetric accelerate-and-arrest input at angular acceleration CP takes $2\sqrt{\theta/\text{CP}}$, and the tilt must be put in and taken out twice. Covering the distance at that tilt takes $2\sqrt{d/(g\tan\theta)}$. So the total is approximately

\[t(\theta) = 4\sqrt{\frac{\theta}{\text{CP}}} + 2\sqrt{\frac{d}{g \tan\theta}} \tag{114}\]

which has an interior minimum, because a larger tilt translates faster but takes longer to establish. In the small-angle form the stationarity condition is

\[\frac{dt}{d\theta} = \frac{2}{\sqrt{\text{CP}\,\theta}} - \sqrt{\frac{d}{g}}\;\theta^{-3/2} = 0 \tag{115}\]

which solves to

\[\theta^{*} = \tfrac{1}{2}\sqrt{\frac{\text{CP}\, d}{g}} \tag{116}\]

and substituting that back has a pleasant consequence. The attitude term and the translation term become equal,

\[4\sqrt{\frac{\theta^{*}}{\text{CP}}} = 2\sqrt{\frac{d}{g\,\theta^{*}}} \tag{117}\]

An optimally flown hover correction spends exactly half its time changing attitude and half translating, whatever the control power and whatever the distance. The numerical optimum with the exact tangent runs a little above the small-angle value, at 24.6 degrees against 22.4 for a three metre correction at the maximum control power, and the split is 1.85 seconds against 1.63.

Minimising over $\theta$ for a three metre correction gives 4.42 seconds at a control power of 0.8 and 3.49 seconds at 2.0.

Two and a half times the control power buys 21.2 percent less time. The local exponent is

\[\frac{d \ln t}{d \ln \text{CP}} = -0.26 \tag{118}\]

which is close to a quarter-power law. Control power has sharply diminishing returns, and this is a structural reason why the pilot ratings improved so much less than proportionally across the tested range, and why a threshold criterion is the right shape of answer even though the underlying physics is continuous.

What the X-14 Was Worth

The X-14 is the first aircraft in this series whose value cannot be stated as a capability.

It did not fly fast, high, or far. It demonstrated a transition that another aircraft in the same series had already demonstrated by a different method a year earlier. Its entire contribution is a set of numbers, and the numbers are about people.

The case for it is that the numbers were not otherwise obtainable and that they were needed. Between 1955 and 1970 every serious vertical take-off design in the West had to choose an attitude control system size, and before the X-14A the choice had little flight measurement behind it, as Anderson 1960a found, and afterwards it had measurement. The measurement was coarse, resting on three sampled control powers and two pilots, and it was incomplete, specifying magnitude where bandwidth also mattered. It was still better than what it replaced, which was nothing.

The second part of the case is the twenty-four years. An aircraft built for a 1955 question was still producing publishable results in 1982, in Merrick 1982, on subjects its designers had no concept of, because what had been built was reprogrammable. The X-14 is the strongest argument in this series for building research aircraft as instruments rather than as demonstrations, and the argument is economic rather than aesthetic. A demonstration is worth what it demonstrates, once. An instrument is worth whatever anyone subsequently thinks to measure with it.

An Unremarkable Designation

There is nothing anomalous about the X-14 designation. It was assigned in sequence, to one aircraft in the Bell X-14 entry, which was built and flown and kept the designation with suffix changes through two major reconfigurations.

One asymmetry in the record should be set down, because the contrast says something about how each programme was run. The tail-sitting alternative is far better documented in the scale-model literature. The X-13 was preceded by free-flight model work in Smith 1958a and derivative measurements in Shanks and Smith 1959 and Shanks and Smith 1960, and the earlier Convair tail-sitter by Lovell et al. 1953 and the four-part derivative series beginning at Queijo et al. 1953c. The X-14’s control-power question could not be attacked that way at all, because the quantity being sought resides in a pilot and a model has no pilot in it.

The point that does deserve comment is the pairing. The X-13 and the X-14 are consecutive designations covering two solutions to the same problem, a jet aircraft that takes off vertically. The X-13 solved it by standing the whole aircraft on its tail and the X-14 by turning the exhaust while the aircraft stayed level. The second approach is the one that survived, in the Harrier and everything descended from it, and the NASA inventory of Jenkins, Landis and Miller credits the X-14 with showing the vectored-thrust concept viable for it. The designation sequence records the comparison without comment.

The Source Base

The primary record for this article is concentrated at Ames and has one significant hole.

The keystone document is Drinkwater and Rolls 1962, NASA Technical Note D-1328, which is the Ames determination of attitude control power and damping requirements using the variable-stability and control X-14A. The full text of the underlying technical note is not retrievable. The NASA Technical Reports Server holds the record with a one-line abstract, and its download link returns no document.

This article therefore relies on its successors for its numbers. Drinkwater et al. 1965, NASA Technical Note D-2701, is read in full. It states the control powers, dampings, and stick travels tested, the test weight, and the thrust-to-weight ratio, and it gives every pilot rating in its table II. Hegarty et al. 1965, NASA Technical Note D-2700, is read in its design sections and its appendix, and gives the bleed, the nozzle arrangement, the inertias, and the moment arms on which the sizing analysis rests. Gerdes and Rolls 1969, NASA Technical Note D-5491, is read in full and gives the fan results and the thrust gain from reduced bleed. Greif et al. 1972 gives the simulator comparison. Rolls 1960 and Rolls 1965b, the latter read in the compilation of the 1965 NASA conference on aircraft operating problems, give the early and the operational experience. Hoffman et al. 1972 and Loscutoff et al. 1973, contractor reports from the University of California at Davis, give the later mass properties, the span, and the diverter efficiency, and Holzhauser et al. 1972 gives the Do 31 comparison. Gallagher et al. 1972, Corliss et al. 1977, Rolls 1965a, and Gerdes 1981 are not retrievable in full from the NASA Technical Reports Server and are relied on only for what their titles and abstracts state. Merrick 1982 covers the digital era in full.

Where the primary documents disagree, both values are given. The 1965 design report and the 1972 equations of motion differ by a factor of two in roll inertia, and the 1969 fan report gives a basic roll control power well below the 1965 design value. Neither difference is explained in the record available here.

The programme history comes from two NASA publications, the history of Ames flight research by Borchers, Franklin and Fletcher and the inventory of X-vehicles by Jenkins, Landis and Miller, and from secondary compilations for the contract date, the Bell model number, the serial, the date of the first transition, and the engine ratings. The sources disagree on the Viper engine rating, on the date of the first hover, and on whether the wing came from the Bonanza or the T-34, and all three disagreements are reported in the text rather than resolved. The 1981 accident cause is given by NASA’s history of Ames flight research, and no investigation report is available to show the evidence behind it.

The survey rests on 6,201 research records drawn from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center, of which 1,241 are report primaries by the identifier rule set out under The Definition of Primary, being 20.0 percent. Of those primaries, 970 are Technical Reports Server records and 271 are Defense Technical Information Center reports. The survey includes the 365 research records cited in the argument above, each placed in the cluster its title describes, and 160 of those are report primaries. The median publication year of the dated records is 2010, and of those records 1,498, or 25.1 percent, appeared in or before 1981, the year the X-14 last flew, 2,467, or 40.9 percent, appeared before 2000, and 2,637, or 43.8 percent, appeared in 2015 or later.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when it is a NASA Technical Reports Server url or carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. The same report can be reachable through Crossref and through the Defense Technical Information Center under two different labels, and a rule keyed on where a record was found rather than on what it is would count such a report as secondary.

The rule reaches the programme’s own documents. The Ames reports on the X-14A and X-14B and the contractor studies of the aircraft’s dynamics are Technical Reports Server records and so are report primaries by this rule. Journal papers by the engineers who did the work are not primaries by this rule, so 20.0 percent is a lower bound on how much of this survey is first-hand.

Thin Subjects

Ten subjects that this article’s derivations and conclusions depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with every hyphen and slash read as a space.

Subject	Title terms counted	Records
the X-14 and its two rebuilds	x 14, x 14a, x 14b, bell model 68	8
control power as a named quantity	control power	23
the thrust cost of compressor bleed	engine bleed, compressor bleed, bleed air extraction, effect of bleed air, reaction control system bleed	5
synthesised damping	damping	4
the effect of size and inertia on control	effect of size, size effect, size effects, radius of gyration, moment of inertia, moments of inertia	6
the thrust diverter and the turning of the jet	diverter, jet deflector, cascade thrust, thrust deflection	5
the thrust margin in hover	thrust to weight, thrust weight, thrust margin, thrust margins	4
the Dornier Do 31	do 31, dornier	3
the number of pilots and the spread of their ratings	pilot evaluation time, sample size, rating variability	5
the order of the position loop	fourth order, loop order	0

The aircraft is named in eight titles, and every one of them is a Technical Reports Server record. Its keystone reports on lateral control, on the design of the variable-stability system and on the tip-turbine fans name the configuration rather than the aircraft, which is why the X-14 is nearly invisible to a search on its own designation.

The quantity the article is about is named in 23 titles, and four of those are the quarterly and final reports of a single study of the control power requirements of vertical take-off aircraft. What the control power was bought with is thinner still. Five records name the thrust cost of engine bleed, and two of them carry the title of one report on the bleed and control power usage of the YAV-8B Harrier, so the price this article derives for the X-14A’s reaction controls rests on the X-14A’s own fan report rather than on a literature of the trade. Four records name damping, the second variable the X-14A swept.

The scaling argument has almost no titled literature. Three records name the effect of size, two of them the 1965 studies the article cites, and three name a moment of inertia, all of them as an uncertainty in quadrotor control rather than as the denominator of a requirement. Four records name the thrust margin or the thrust-to-weight ratio, three name the Do 31 that the scaling relation is checked against, and no record names a diverter, so the turning efficiency the sizing analysis uses rests on the contractor report alone.

The objections the article raises to its own criterion are the thinnest subjects of all. Five records concern the number of pilots, the evaluation time or the spread of pilot ratings, against the two pilots on whom the lateral results rest, and no record names the order of the position loop, which the article derives from the transfer functions rather than finds in the literature.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject, which is the hovering aircraft and the requirement located in its pilot, being vertical and short take-off aircraft of every lifting scheme and their control, handling qualities and pilot rating, variable-stability and ground simulation, the human operator, reaction controls and lift propulsion, the flow of the exhaust near the ground, the visual task, the landing on bodies of other gravity, and the multirotor and electric vertical take-off aircraft and vertiports that inherited the problem. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. A hovercraft rides on an air cushion and a hovering insect flaps its wings. A pilot study is a trial in medicine and a pilot plant a process facility. A spacecraft hovers at an asteroid, a satellite has an attitude control system, and an airborne simulator can be a remote sensing instrument. Hot gas ingestion is also a problem of turbine rim seals, ground effect also lifts a wing-in-ground-effect craft, and compensatory tracking is also a tool of psychology and physiology. Thrust vectoring and thrust reversers belong to fighters and rockets as well, bleed air also supplies an aircraft’s cabin, and handling qualities are also a property of road vehicles. Studies of demand, public acceptance and equity in urban air mobility, and the aeroelastic stability, structural loads and vibration of rotor blades, are excluded as outside the vehicle’s flight. Removal notices, records whose titles are a subject index or a single unqualified word, and news items are excluded as well, because a survey counts research works and those are editorial events or not works at all.

Reviews of books, reference and definition entries and notices are not admitted, and a document deposited twice is admitted once. An authored encyclopedia article of more than two pages and a chapter of a textbook are research works and are kept, and where one document is held twice the journal or report version is the one admitted.

Some records of doubtful relevance are kept. The handling qualities of conventional aeroplanes, which are 406 of the handling-qualities titles, the aerodynamics and performance of rotors in hover, powered descent guidance for landing on the Moon and Mars, the general literature of control allocation for over-actuated systems, and the siting and operation of vertiports each share a construct, a method or a contrast with this article’s argument, so each is kept and a reader may weigh it accordingly. The road vehicle, robotics, teleoperation and satellite studies that the review cites as the same allocation and shared-control mathematics outside aviation are kept for the same reason.

Every research title in the survey has been read for relevance, so the off-topic share that remains is a matter of reading judgement. A reading of titles cannot show that a work is relevant in substance, so this is a statement about titles only.

Epistemic State

Historical fact, from primary sources. The X-14A weighed 3,700 pounds during the lateral control experiments with a thrust-to-weight ratio available of 1.1 to 1.2. Lateral control power was tested at 0.8, 1.4, and 2.0 radians per second squared, damping at 0.55, 1.75, and 2.9 per second, and stick travel at 4.5, 3.5, and 3.0 inches either way, by two pilots who rated all twenty-seven conditions, and total control power dominated their ratings while control sensitivity had only a minor effect. Attitude control in a hover was by two parallel sets of reaction nozzles at the wingtips and tail, fed by a constant bleed of ten percent of the engines’ 85.0 pounds per second of airflow and producing 500.7 pounds of reaction force in all. The 1965 design inertias were 1,170, 1,990, and 2,920 slug square feet in roll, pitch, and yaw, with arms of 16.9 and 18.75 feet, and the X-14B-period model gives 2,340, 3,400, and 5,400 slug square feet at 4,182 pounds, a span of 33.83 feet, and a diverter efficiency of 0.91. The exhaust was turned by cascade diverters. The original aircraft lacked control power for want of bleed, and the J85 engines were fitted to supply more bleed and thrust. Tip-turbine fans of 150 pounds thrust were flown, needed less than half the bleed of the reaction nozzles for the same thrust, would have cut the total bleed by about 20 percent and returned four percent more engine thrust, gave 0.65 against 0.70 radians per second squared, had time constants of 0.58 and 0.34 seconds against 0.08, and were rejected. The 1965 operating report records the late-1959 transfer. NASA’s history of Ames flight research records the principal pilots, Armstrong’s 1965 flights, the X-14B modification, the aircraft’s contribution to the military specification, and the 1981 hard landing and its attributed cause. NASA’s inventory records the first flight on 17 February 1957, the last on 29 May 1981, the 172 miles per hour, the more than 25 pilots, and the airframe’s survival.

Historical fact, from secondary sources. The July 1955 Air Force contract, the Bell Model 68 designation and 56-4022 serial, the Bonanza wing, the date of 2 October 1959, the J85-GE-5 and J85-GE-19 ratings, the first transition on 24 May 1958, and that the pilot in 1981 was uninjured.

Contested in the sources and left contested. The Viper rating, given as either 1,750 or 1,560 pounds of thrust each. The first hover date, given as 17 February 1957 for the first flight in NASA’s inventory and as 19 February 1957 for the first free hover in the abstract of Gerdes’s retrospective, which may be different events. The wing, given as a Bonanza wing in the secondary account and as a T-34 wing in NASA’s history. The roll inertia, given as 1,170 and as 2,340 slug square feet by two primary reports seven years apart.

Engineering analysis, derived in this article and reproducible from the stated inputs. The thrust lost per unit of airflow bled, 1.67, and the bleed cost of 0.167 of thrust, with 0.10 as a floor. The consequent 893 pounds of thrust, or 536 on the floor, and the finding that this consumed 54.7 to 70.7 percent of the hover margin, or 42.0 to 59.2 percent on the floor. The installation loss of 17.2 to 24.1 percent and its reproduction by the bleed estimate and the diverter efficiency. The Viper thrust-to-weight ratios of 0.843 and 0.946, both below unity at the 3,700 pound test weight. The roll radius of gyration of 0.094 or 0.125 of the span. The saturation rates of the damping loop. The scaling relation that control power falls inversely with span at fixed bleed fraction, and the resulting span limit between 27.5 and 45.9 metres for a twenty percent margin. The repositioning time analysis and its exponent of minus 0.26. The lunar timescale mismatch of 2.46.

A correction to the previous article, derived here. The X-13 article described hovering as a third-order position loop. Composing the transfer functions shows the loop from control input to position is fourth order when the damping is zero, and third only below the damping break frequency. Both articles are describing the same physics and the earlier phrasing is the low-frequency case. The distinction matters because a fourth-order plant demands two derivatives of lead from the pilot rather than one, and this article treats that as the explanation for why attitude stabilisation buys so much.

Inference, stated as such. That the damping loop saturated at modest roll rates in the high-damping and high-control-power corner rests on the 1965 design authorities and assumes they held in the 1965 tests. That the X-14A’s tested range set the range used by later simulator studies is an inference from the coincidence of intervals and could equally be independent convergence. That the field recognised the size-scaling problem within three years is inferred from the existence and title of a 1965 paper rather than from its content, which was not read in full.

Claims the record does not settle. Whether MIL-F-83300’s hovering requirements derive specifically from the X-14A’s numbers rather than from the broader flight and simulator corpus of the 1960s. NASA’s history states that the aircraft’s research contributed to the specification, and the article claims descent from that corpus, of which the X-14A is the principal flight component, but does not claim a direct numerical inheritance. Whether the 1981 accident was as described, since the attribution is NASA’s but the evidence behind it is not available here. Whether the X-14 is the longest-serving X-plane, which its 1957 to 1981 span suggests but which this article has not verified against all seventy-two designations in the series and therefore does not assert.

Anachronism, flagged. The bandwidth and phase-delay framing used in the discussion of what the criterion missed postdates the X-14A’s principal results by decades. It is applied here because the tip-fan failure of 1969 is unintelligible without it, and the aircraft’s own programme produced the evidence that the magnitude criterion was incomplete before the vocabulary existed to say so.

The three modern reference vehicles are representative rather than actual. Their masses, rotor radii, thrust-to-weight ratios, and radii of gyration were chosen as plausible for their classes rather than taken from any particular aircraft, and the radius of gyration fraction used for all three is 0.2 rather than the 0.094 to 0.125 that the X-14’s two primary inertia sets give. The conclusions drawn from them are ratios and orders and are insensitive to reasonable variation. The specific control powers are not, and a reader who substitutes a real vehicle’s inertia should expect the third significant figure to move.

Assumptions, stated as such. The thrust lost per unit of airflow bled is assumed to stay at 1.67 over the whole ten percent bleed, which neither source states, and the proportional floor of 0.10 is reported beside every figure that depends on it. The diverter efficiency of 0.91 reported for the X-14B is assumed to apply to the X-14A. The twenty percent thrust margin in the scaling argument is an assumed figure for a generous design. The wind speed, side area, drag coefficient, and offset in the disturbance example are representative values, not measurements. The Do 31 force example applies the X-14A’s proportions to the Do 31’s span and mass.

The claim that the modern attitude loop closes well above the X-14A’s damping break is a comparison of a stated range against reported values. The ten to thirty radians per second figure is an assumed band for a small vehicle’s inner loop, not taken from a cited source or measured here, and the X-14A’s synthesised dampings of 0.55 to 2.9 per second are the reported values in table II of the 1965 lateral control report.

Out of Scope

The transition aerodynamics of jet-lift aircraft, including induced lift loss and the ground vortex, are treated only where they bear on control. Hot gas ingestion and ground erosion, which the sources identify as significant operational problems, are noted and not analysed. The Cooper-Harper scale’s development and its statistical properties are not this article’s subject and are treated only far enough to state why an ordinal scale limits what the experiment concluded. The Lunar Landing Research Vehicle and Lunar Landing Training Vehicle are discussed only as the answer to a limitation of the X-14 and not on their own terms. The Hawker P.1127 and the Harrier line are the obvious descendants of vectored-thrust jet lift and are out of scope here. The detailed thermodynamics of compressor bleed extraction, including the stage from which air is taken and the effect on surge margin, is not treated.

Conclusion

The X-14 answered the question of how much attitude control a hovering aircraft needs, and the answer was a number between 0.8 and 2.0 radians per second squared with the boundary somewhere inside that interval.

The more durable results are the ones around the number. Attitude control on a jet-lift aircraft is bought with lift, at a price this article puts at about a sixth of the X-14A’s thrust and not less than a tenth, which consumed more than half of everything the aircraft could lift beyond its own weight. That price scales badly, growing linearly with span at fixed control power, and the largest jet-lift aircraft NASA tested, at 17.0 metres of span, avoided it by putting engines at its wingtips and stabilising its attitude.

The aircraft also demonstrated the limits of its own criterion. The tip-turbine fan experiment produced a control system that nearly matched the control power of the nozzles it replaced and was unflyable, which showed that magnitude without bandwidth is not a specification, and the field eventually changed the variable rather than the number.

And it could not simulate gravity. That single unadjustable parameter bounds what any Earth-based hovering simulator can teach about landing anywhere else, by a factor of 2.46 in the translational timescale, and it explains why a far more dangerous vehicle had to be built to finish the job.

What the X-14 is worth is not what it did but what was done with it. It was built as an instrument, kept for twenty-four years, rebuilt twice, and used for experiments nobody had conceived when it was ordered. Among the fourteen aircraft this series has examined, it is the only one whose principal output was a number that a contractor was later obliged to meet.

The next article takes up the North American X-15, the opposite of this aircraft in every respect that matters.

Equations

This section collects the 118 display equations of the article in the order they appear, each under its number and reproduced exactly as it stands in the text. A title in bold names an established result, and a title in italics beginning with the word Bespoke names a construction made for this analysis. Of the 118, 68 are established and 50 are bespoke. Control power CP is an angular acceleration in radians per second squared, the forces and weights are mostly in pounds while the disturbance and multirotor relations are in newtons and metres, $T_{0}$ is the total temperature of the bleed air in the nozzle relations but the uninstalled thrust in the bleed and margin relations, $\beta$ is a fraction of thrust in the opening bound and a bled fraction of airflow thereafter, and $\delta$, $A$ and $R$ each carry more than one meaning.

Equation 1, Bespoke Bounds on Control Power. The article frames the requirement as an inequality, with control power above the worst disturbance acceleration and below what the thrust margin fraction $\beta_{\max} = (T - W)/T$ can buy.

\[\ddot{\theta}_{d} \;<\; \text{CP} \;<\; \text{CP}\big(\beta_{\max}\big), \qquad \beta_{\max} = \frac{T - W}{T} \tag{1}\]

Equation 2, Control Power as Moment over Inertia. Control power is the maximum control moment about an axis divided by the moment of inertia about that axis. Greif et al. 1972

\[\text{CP} = \frac{M_{\text{control}}}{I} \tag{2}\]

Equation 3, Moment of a Differential Nozzle Pair. Two nozzles acting differentially at a distance $\ell$ either side of the centre of mass produce a moment of $2 F \ell$.

\[M_{\text{control}} = 2 F \ell \tag{3}\]

Equation 4, Control Power of a Differential Nozzle Pair. The control power of the nozzle pair is twice the nozzle force times the arm over the inertia.

\[\text{CP} = \frac{2 F \ell}{I} \tag{4}\]

Equation 5, Identical Attitude Dynamics of Two Aircraft. Two aircraft with the same control power and the same damping per unit inertia obey the same attitude equation and so respond identically to identical inputs.

\[\ddot{\theta}_{1} = \text{CP} \, u - \frac{D}{I}\dot{\theta}_{1}, \qquad \ddot{\theta}_{2} = \text{CP} \, u - \frac{D}{I}\dot{\theta}_{2} \tag{5}\]

Equation 6, Single-Axis Attitude Dynamics with Rate Damping. The inertia times the angular acceleration equals the control moment less a damping moment proportional to the angular rate.

\[I \ddot{\theta} = M_{\text{control}} - D \dot{\theta} \tag{6}\]

Equation 7, Normalised Attitude Dynamics. Dividing by the inertia writes the angular acceleration as the control power times the normalised input less the damping per unit inertia times the rate.

\[\ddot{\theta} = \text{CP} \, u - \frac{D}{I} \dot{\theta} \tag{7}\]

Equation 8, Attitude Transfer Function. The Laplace transform of the normalised dynamics gives a transfer function from input to attitude with a pole at the origin and a pole at the damping value.

\[\frac{\theta(s)}{u(s)} = \frac{\text{CP}}{s\left(s + \dfrac{D}{I}\right)} \tag{8}\]

Equation 9, Characteristic Time of the Damped Attitude Response. The characteristic time is the inertia over the damping, the reciprocal of the damping per unit inertia.

\[\tau = \frac{I}{D} = \left(\frac{D}{I}\right)^{-1} \tag{9}\]

Equation 10, Characteristic Times at the Three Flown Dampings. The dampings of 0.55, 1.75 and 2.9 per second flown in the lateral experiments give characteristic times of 1.82, 0.571 and 0.345 seconds. Drinkwater et al. 1965

\[\tau = \frac{1}{0.55} = 1.82 \text{ s}, \qquad \tau = \frac{1}{1.75} = 0.571 \text{ s}, \qquad \tau = \frac{1}{2.9} = 0.345 \text{ s} \tag{10}\]

Equation 11, Rate Response to a Step of Full Control. After a step of full control the angular rate approaches its limit exponentially with the characteristic time.

\[\dot{\theta}(t) = \frac{\text{CP}}{D/I}\left(1 - e^{-t/\tau}\right) \tag{11}\]

Equation 12, Steady Rate at Full Control. The steady angular rate at full control is the control power over the damping per unit inertia.

\[\dot{\theta}_{\text{max}} = \frac{\text{CP}}{D/I} \tag{12}\]

Equation 13, Steady Rates at Maximum Control Power. At the maximum control power of 2.0 radians per second squared the three flown dampings give steady rates of 3.64, 1.14 and 0.690 radians per second. Drinkwater et al. 1965

\[\frac{2.0}{0.55} = 3.64 \text{ rad/s}, \qquad \frac{2.0}{1.75} = 1.14 \text{ rad/s}, \qquad \frac{2.0}{2.9} = 0.690 \text{ rad/s} \tag{13}\]

Equation 14, Undamped Double Integrator. With no damping the attitude after a step of full control grows as half the control power times the square of the time.

\[\ddot{\theta} = \text{CP} \, u \quad \Longrightarrow \quad \theta(t) = \tfrac{1}{2}\,\text{CP}\, t^{2} \tag{14}\]

Equation 15, Bank Angle After One Second Undamped. One second of full control at 2.0 radians per second squared with no damping banks the aircraft through one radian.

\[\tfrac{1}{2} \times 2.0 \times 1^{2} = 1.0 \text{ rad} = 57.3 \text{ degrees} \tag{15}\]

Equation 16, Nozzle Thrust from Mass Flow and Exit Velocity. The momentum thrust of a reaction nozzle is the mass flow times the exit velocity.

\[F = \dot{m} \, v_{e} \tag{16}\]

Equation 17, Exit Velocity of a Choked Convergent Nozzle. For a choked convergent nozzle the exit velocity is the sonic velocity at the throat, set by the ratio of specific heats, the gas constant and the total temperature.

\[v_{e} = \sqrt{\frac{2 \gamma}{\gamma + 1} R T_{0}} \tag{17}\]

Equation 18, Choked Mass Flow. The mass flow through a choked nozzle is the throat area times the total pressure times a function of the total temperature and the ratio of specific heats.

\[\dot{m} = A \, p_{0} \sqrt{\frac{\gamma}{R T_{0}}} \left(\frac{2}{\gamma + 1}\right)^{\frac{\gamma + 1}{2(\gamma - 1)}} \tag{18}\]

Equation 19, Thrust per Unit Mass Flow. The thrust per unit mass flow of the momentum term is the exit velocity.

\[\frac{F}{\dot{m}} = v_{e} \tag{19}\]

Equation 20, Sonic Nozzle Thrust Including Pressure Thrust. The design report writes the thrust of a sonic nozzle with velocity and discharge coefficients and a pressure term relative to the atmosphere. Hegarty et al. 1965

\[F = C_{v}\,C_{d}\,A\,p_{0}\left(1.268 - \frac{p_{a}}{p_{0}}\right) \tag{20}\]

Equation 21, Total Reaction Force of the X-14A. The report’s coefficients, exit area and supply pressure give a total reaction force of 500.7 pounds. Hegarty et al. 1965

\[F = 0.95 \times 0.90 \times 7.17 \times 76 \times \left(1.268 - \frac{14.7}{76}\right) = 500.7 \text{ pounds} \tag{21}\]

Equation 22, Bleed Removed by the Tip-Turbine Fans. A 20 percent reduction of the ten percent bleed removes two percent of the engines’ airflow. Gerdes and Rolls 1969

\[\Delta\beta = 0.20 \times 0.10 = 0.020 \tag{22}\]

Equation 23, Bespoke Linear Bleed Thrust Model. The article assumes that thrust falls linearly with the bled fraction of airflow $\beta$ at a rate $s$.

\[T = T_{0}\,(1 - s\,\beta) \tag{23}\]

Equation 24, Bespoke Bleed Cost Rate from the Reported Gain. Under the linear bleed model the reported thrust gain $\delta$ on removing a bleed $\Delta\beta$ fixes the rate $s$.

\[\frac{1 - s\,(\beta - \Delta\beta)}{1 - s\,\beta} = 1 + \delta \quad \Longrightarrow \quad s = \frac{\delta}{\Delta\beta + \delta\,\beta} \tag{24}\]

Equation 25, Bespoke Evaluated Bleed Cost Rate. Substituting the reported four percent thrust gain into the linear model gives a rate of five thirds.

\[s = \frac{0.04}{0.020 + 0.04 \times 0.10} = \frac{0.04}{0.024} = \frac{5}{3} = 1.67 \tag{25}\]

Equation 26, Bespoke Thrust Cost of the Full Bleed. Assuming that the same linear rate holds over the whole ten percent bleed, the reaction controls cost a sixth of the thrust.

\[s\,\beta = \frac{5}{3} \times 0.10 = \frac{1}{6} = 0.167 \tag{26}\]

Equation 27, Hover Thrust Margin. A hovering aircraft’s useful output is the excess of its thrust over its weight.

\[\Delta T = T - W \tag{27}\]

Equation 28, Uninstalled Thrust-to-Weight Ratio. The rated 5,360 pounds of the two J85-GE-5 engines over the 3,700 pound test weight gives 1.449. General Electric J85

\[\frac{T_{\text{uninstalled}}}{W} = \frac{5{,}360}{3{,}700} = 1.449 \tag{28}\]

Equation 29, Bespoke Installation Efficiency. The article defines the installation efficiency as the thrust the aircraft actually had available over the rated uninstalled thrust.

\[\eta_{\text{inst}} = \frac{T_{\text{available}}}{T_{\text{uninstalled}}} \tag{29}\]

Equation 30, Bespoke Installation Efficiency at the Reported Bounds. The reported available thrust-to-weight ratios of 1.1 and 1.2 give installation efficiencies of 0.759 and 0.828.

\[\eta_{\text{inst}} = \frac{1.1 \times 3{,}700}{5{,}360} = 0.759, \qquad \frac{1.2 \times 3{,}700}{5{,}360} = 0.828 \tag{30}\]

Equation 31, Bespoke Diverter and Bleed Product. Applying the X-14B diverter efficiency of 0.91 to the earlier aircraft and the estimated bleed cost of a sixth gives 0.758. Loscutoff et al. 1973

\[\eta_{d}\,(1 - s\,\beta) = 0.91 \times \left(1 - \tfrac{1}{6}\right) = 0.758 \tag{31}\]

Equation 32, Bespoke Thrust Spent on Bleed. The estimated bleed cost of a sixth of the rated thrust is 893 pounds.

\[\tfrac{1}{6} \times 5{,}360 = 893 \text{ pounds of thrust} \tag{32}\]

Equation 33, Bespoke Share of the Pre-Bleed Margin on the Estimate. The estimated 893 pounds of bleed consumes 70.7 percent of the pre-bleed margin at a thrust-to-weight ratio of 1.1 and 54.7 percent at 1.2.

\[\frac{893}{1{,}263} = 0.707, \qquad \frac{893}{1{,}633} = 0.547 \tag{33}\]

Equation 34, Bespoke Share of the Pre-Bleed Margin on the Proportional Floor. If thrust falls only in proportion to the air removed, the 536 pound bleed consumes 59.2 and 42.0 percent of the pre-bleed margin.

\[\frac{536}{906} = 0.592, \qquad \frac{536}{1{,}276} = 0.420 \tag{34}\]

Equation 35, Bespoke Margin Share Consumed by Control. The article defines $\Phi$ as the bleed thrust over the pre-bleed margin, the share of that margin spent on control.

\[\Phi = \frac{\beta \, T_{0}}{(r - 1) W + \beta \, T_{0}} \tag{35}\]

Equation 36, Wind Side Force. A steady wind on a side area produces a force equal to the dynamic pressure of the wind times the area times the drag coefficient.

\[F_{w} = \tfrac{1}{2}\rho V_{w}^{2} S_{s} C_{D} \tag{36}\]

Equation 37, Bespoke Side Force in a Ten Metre per Second Wind. The side force is evaluated at a representative side area of eight square metres and a drag coefficient of 0.8, giving 392 newtons.

\[F_{w} = \tfrac{1}{2} \times 1.225 \times 100 \times 8 \times 0.8 = 392 \text{ N} \tag{37}\]

Equation 38, Bespoke Roll Disturbance from the Wind. The wind force acting through an assumed offset of one metre on the design roll inertia gives 0.247 radians per second squared.

\[\frac{392 \times 1.0}{1{,}586} = 0.247 \text{ rad/s}^{2} \tag{38}\]

Equation 39, Bespoke Translational Acceleration from the Wind. The wind force from the representative side area and drag coefficient accelerates the 1,678 kilogramme aircraft at 0.234 metres per second squared.

\[a_{w} = \frac{392}{1{,}678} = 0.234 \text{ m/s}^{2} \tag{39}\]

Equation 40, Bespoke Station-Keeping Tilt. Holding station against the wind acceleration from the representative side area requires a tilt of 1.36 degrees.

\[\theta_{\text{trim}} = \arctan\frac{a_{w}}{g} = \arctan\frac{0.234}{9.807} = 1.36^{\circ} \tag{40}\]

Equation 41, Bespoke Uncorrected Wind Drift. Leaving the wind acceleration uncorrected for ten seconds costs 11.7 metres.

\[\tfrac{1}{2} \times 0.234 \times 100 = 11.7 \text{ m} \tag{41}\]

Equation 42, Disturbance as a Fraction of Control Power. The experimental design held the peak disturbance at four tenths of the available control power. Greif et al. 1972

\[\ddot{\theta}_{\text{disturbance}} = \sigma \, \text{CP}, \qquad \sigma = 0.4 \tag{42}\]

Equation 43, Bespoke Control Power Left to the Pilot. The article treats the disturbance as taking a fixed share $\sigma$ of the control power, so the pilot has the remaining $(1 - \sigma)$.

\[\text{CP}_{\text{pilot}} = (1 - \sigma) \, \text{CP} \tag{43}\]

Equation 44, Bespoke Pilot Authority at the Tested Extremes. With the fixed disturbance share, the maximum and minimum control powers leave 1.2 and 0.48 radians per second squared to the pilot.

\[0.6 \times 2.0 = 1.2, \qquad 0.6 \times 0.8 = 0.48 \tag{44}\]

Equation 45, Bespoke Product of the Two Fractions. The share of the pre-bleed margin reaching the pilot is the margin share spent on control times the share of control power not spent on disturbances.

\[\Phi \times (1 - \sigma) \tag{45}\]

Equation 46, Bespoke Pilot Share of the Pre-Bleed Margin. On the estimated bleed cost the pilot receives 42.4 and 32.8 percent of the pre-bleed margin at the two reported thrust-to-weight ratios.

\[0.707 \times 0.6 = 0.424, \qquad 0.547 \times 0.6 = 0.328 \tag{46}\]

Equation 47, Nozzle Sizing Relation of the Design Report. The report sizes each nozzle by the inertia times the wanted angular acceleration over the moment arm. Hegarty et al. 1965

\[F = \frac{I\,\alpha}{L} \tag{47}\]

Equation 48, Roll Inertia in Kilogramme Square Metres. The design report’s roll inertia of 1,170 slug square feet is 1,586 kilogramme square metres. Hegarty et al. 1965

\[I_{x} = 1{,}170 \times 1.356 = 1{,}586 \text{ kg m}^{2} \tag{48}\]

Equation 49, Check of the Report’s Roll Force. The report’s roll inertia, roll control power and wingtip arm give 127.4 pounds against the 127.2 it lists. Hegarty et al. 1965

\[F_{r} = \frac{1{,}170 \times 1.84}{16.9} = 127.4 \text{ pounds} \tag{49}\]

Equation 50, Roll Radius of Gyration from the 1965 Inertia. The 1965 roll inertia at the 3,700 pound test weight gives a roll radius of gyration of 3.19 feet.

\[k_{x} = \sqrt{\frac{I_{x}}{m}} = \sqrt{\frac{1{,}170}{115.0}} = 3.19 \text{ ft} \tag{50}\]

Equation 51, Roll Radius of Gyration as a Fraction of Span. Against the 33.83 foot span the roll radius of gyration is 0.094 of the span. Hoffman et al. 1972

\[\frac{k_{x}}{b} = \frac{3.19}{33.83} = 0.094 \tag{51}\]

Equation 52, Roll Radius of Gyration from the 1972 Inertia. The later roll inertia of 2,340 slug square feet at 129.9 slugs gives 4.24 feet, or 0.125 of the span. Hoffman et al. 1972

\[k_{x} = \sqrt{\frac{2{,}340}{129.9}} = 4.24 \text{ ft}, \qquad \frac{k_{x}}{b} = \frac{4.24}{33.83} = 0.125 \tag{52}\]

Equation 53, Moment of Wingtip Nozzles. With nozzles at the wingtips the control moment is the differential force times the span.

\[M = F b \tag{53}\]

Equation 54, Roll Inertia Under Geometric Similarity. The roll inertia is the mass times the square of a radius of gyration that is proportional to the span for geometrically similar aircraft.

\[I_{x} = m k_{x}^{2}, \qquad k_{x} \propto b \tag{54}\]

Equation 55, Scaling of Control Power with Force, Mass and Span. Combining the wingtip moment with the scaled inertia makes control power vary as the force over the mass times the span.

\[\text{CP} = \frac{M}{I_{x}} \propto \frac{F b}{m b^{2}} = \frac{F}{m b} \tag{55}\]

Equation 56, Hover Thrust Proportional to Mass. A hovering aircraft has thrust approximately equal to its weight and therefore proportional to its mass.

\[T \approx W = m g \quad \Longrightarrow \quad T \propto m \tag{56}\]

Equation 57, Bespoke Reaction Force at a Fixed Bleed Fraction. The article holds the bleed fraction fixed across sizes, so the reaction force is proportional to the thrust and hence to the mass.

\[F = \beta \, T \propto \beta \, m g \tag{57}\]

Equation 58, Bespoke Inverse-Span Law for Control Power. At a fixed bleed fraction under geometric similarity control power is inversely proportional to the span.

\[\text{CP} \propto \frac{1}{b} \tag{58}\]

Equation 59, Share of Bleed Used by the Pilot’s Nozzles. The pilot’s 97.8 pounds of pitch force and 127.2 pounds of roll and yaw force are 0.449 of the 500.7 pound total. Hegarty et al. 1965

\[\frac{97.8 + 127.2}{500.7} = 0.449 \tag{59}\]

Equation 60, Bespoke Thrust Cost of the Pilot’s Nozzles. The pilot’s 4.49 percent of airflow at the estimated bleed cost rate of 1.67 costs 0.0749 of the thrust.

\[1.67 \times 0.0449 = 0.0749 \tag{60}\]

Equation 61, Bespoke Bleed Fraction Required as a Function of Span. Holding the pilot’s roll control power under the inverse-span law and the estimated bleed cost rate makes the thrust cost grow linearly with span.

\[\beta(b) = 0.0749 \times \frac{b}{10.31} \tag{61}\]

Equation 62, Bespoke Span at Which Bleed Consumes the Margin. For an assumed thrust margin of twenty percent the bleed consumes the whole margin at a span of 27.5 metres.

\[b = 10.31 \times \frac{0.20}{0.0749} = 27.5 \text{ m} \tag{62}\]

Equation 63, Bespoke Tip Force for a Required Control Power. Taking the roll radius of gyration as a fixed fraction $\kappa_{r}$ of span and the arm as half the span, the net tip force grows with the product of mass and span.

\[F_{\text{tip}} = \frac{\text{CP} \, m \, \kappa_{r}^{2} b^{2}}{b/2} = 2\,\text{CP}\, m \, \kappa_{r}^{2}\, b \tag{63}\]

Equation 64, Bespoke Tip Force at the Do 31 Span. Applying the X-14A proportions to the Do 31 span and landing mass at 2.0 radians per second squared gives 11,187 newtons. Holzhauser et al. 1972

\[F_{\text{tip}} = 2 \times 2.0 \times 18{,}500 \times 0.0943^{2} \times 17.0 = 11{,}187 \text{ N} = 2{,}515 \text{ pounds} \tag{64}\]

Equation 65, Bespoke Control Force per Pound of Thrust Given Up. The 500.7 pounds of reaction force bought with an estimated 893 or a floor of 536 pounds of thrust gives 0.561 and 0.934.

\[\frac{500.7}{893} = 0.561, \qquad \frac{500.7}{536} = 0.934 \tag{65}\]

Equation 66, Thrust-to-Weight Ratios of the Original Vipers. Either Viper rating gives a pair thrust below the 3,700 pound test weight, at ratios of 0.946 and 0.843. Armstrong Siddeley Viper Virtual Aircraft Museum

\[\frac{3{,}500}{3{,}700} = 0.946, \qquad \frac{3{,}120}{3{,}700} = 0.843 \tag{66}\]

Equation 67, Vertical Thrust Through the Diverter. The vertical thrust available is the turning efficiency times the thrust.

\[T_{v} = \eta \, T \tag{67}\]

Equation 68, Bespoke Thrust Available for Lifting. The thrust available for lifting combines the turning efficiency with the linear bleed model.

\[T_{\text{lift}} = \eta \, (1 - s\,\beta) \, T \tag{68}\]

Equation 69, Thrust Components at a Diverter Deflection. At a deflection $\delta$ from the vertical the turned thrust splits into vertical and horizontal components by the cosine and sine.

\[T_{v} = \eta \, T \cos\delta, \qquad T_{h} = \eta \, T \sin\delta \tag{69}\]

Equation 70, Constraint Between Thrust Components. The squares of the normalised vertical and horizontal components sum to one.

\[\left(\frac{T_{v}}{\eta T}\right)^{2} + \left(\frac{T_{h}}{\eta T}\right)^{2} = 1 \tag{70}\]

Equation 71, Bespoke Lifting Thrust-to-Weight Ratio on the Estimate. Applying the X-14B diverter efficiency and the estimated bleed cost of a sixth to the J85-GE-5 rating gives 1.099. Loscutoff et al. 1973

\[\frac{T_{\text{lift}}}{W} = 0.91 \times \left(1 - \tfrac{1}{6}\right) \times \frac{5{,}360}{3{,}700} = 1.099 \tag{71}\]

Equation 72, Bespoke Lifting Thrust-to-Weight Ratio on the Floor. The same product on the proportional bleed floor of 0.10 gives 1.186.

\[0.91 \times (1 - 0.10) \times \frac{5{,}360}{3{,}700} = 1.186 \tag{72}\]

Equation 73, Uninstalled Ratio of the J85-GE-19. The rated 6,030 pounds of the two later engines over the 3,700 pound weight gives 1.630. General Electric J85

\[\frac{6{,}030}{3{,}700} = 1.630 \tag{73}\]

Equation 74, Bespoke Lifting Ratio of the X-14B. Assuming the later engines bled the same fraction at the estimated cost, the diverter and bleed deductions leave 1.236.

\[0.91 \times \left(1 - \tfrac{1}{6}\right) \times \frac{6{,}030}{3{,}700} = 1.236 \tag{74}\]

Equation 75, Ratio of the Wingtip and Tail Arms. The report’s wingtip arm of 16.9 feet over its tail arm of 18.75 feet is 0.901. Hegarty et al. 1965

\[\frac{L_{w}}{L_{t}} = \frac{16.9}{18.75} = 0.901 \tag{75}\]

Equation 76, Pitch to Roll Nozzle Force for Equal Control Power. For equal control power the pitch nozzle force over the roll nozzle force is the inertia ratio times the arm ratio, 1.53. Hegarty et al. 1965

\[\frac{F_{\text{pitch}}}{F_{\text{roll}}} = \frac{I_{y}}{I_{x}} \times \frac{L_{w}}{L_{t}} = \frac{1{,}990}{1{,}170} \times 0.901 = 1.53 \tag{76}\]

Equation 77, Net Roll Force for a Tested Control Power. The net roll force needed is the control power times the roll inertia over the wingtip arm.

\[F_{r} = \frac{\text{CP} \times I_{x}}{L_{w}} \tag{77}\]

Equation 78, Bespoke Authority Left After the Damping Loop. The article budgets the variable-stability set so that the authority left for augmentation is its total less the damping per unit inertia times the roll rate.

\[\text{CP}_{\text{left}} = \text{CP}_{v} - \frac{D}{I} \, p \tag{78}\]

Equation 79, Bespoke Saturation Rate of the Damping Loop. The roll rate at which the damping loop alone exhausts the variable-stability set is its authority over the synthesised damping.

\[p_{\text{sat}} = \frac{\text{CP}_{v}}{D/I} \tag{79}\]

Equation 80, Bespoke Saturation Rates at the Flown Dampings. The authority budget gives saturation rates of 3.02, 0.949 and 0.572 radians per second at the three flown dampings.

\[\frac{1.66}{0.55} = 3.02, \qquad \frac{1.66}{1.75} = 0.949, \qquad \frac{1.66}{2.9} = 0.572 \text{ rad/s} \tag{80}\]

Equation 81, Bespoke Damping Ceiling with Reserved Authority. Reserving a fraction $\lambda$ of the set for augmentation caps the damping that can be synthesised at a working roll rate $p$.

\[\left(\frac{D}{I}\right)_{\max} = \frac{(1 - \lambda)\,\text{CP}_{v}}{p} \tag{81}\]

Equation 82, Bespoke Damping Ceiling at Thirty Degrees per Second. Reserving an assumed half of the set at an assumed working rate of thirty degrees per second caps the damping at 1.59 per second.

\[\frac{0.5 \times 1.66}{0.5236} = 1.59 \text{ per second} \tag{82}\]

Equation 83, Bespoke Rate at Which Half the Set Is Spent. At the highest flown damping half of the variable-stability set is spent at 16.4 degrees per second.

\[\frac{0.5 \times 1.66}{2.9} = 0.286 \text{ rad/s} = 16.4 \text{ degrees per second} \tag{83}\]

Equation 84, Undamped Attitude Response to Control. With zero damping the angular acceleration is the control power times the normalised input.

\[\ddot{\theta} = \text{CP} \, u \tag{84}\]

Equation 85, Horizontal Acceleration from Tilt. A hovering aircraft tilted by $\theta$ accelerates horizontally at $g \tan\theta$, approximately $g \theta$ at small angles.

\[\ddot{x} = g \tan\theta \approx g \theta \tag{85}\]

Equation 86, Undamped Position Transfer Function. Composing the undamped attitude and translation relations makes position the fourth integral of the control input.

\[\frac{x(s)}{u(s)} = \frac{g \, \text{CP}}{s^{4}} \tag{86}\]

Equation 87, Damped Position Transfer Function. Restoring the rate damping places one of the four poles at the damping value.

\[\frac{x(s)}{u(s)} = \frac{g \, \text{CP}}{s^{3}\left(s + \dfrac{D}{I}\right)} \tag{87}\]

Equation 88, Low-Frequency Form of the Position Transfer Function. Below the break frequency set by the damping the position loop behaves as a third-order integrator.

\[\frac{x(s)}{u(s)} \approx \frac{g \, \text{CP}}{(D/I)\, s^{3}} \qquad \text{for} \quad \omega \ll \frac{D}{I} \tag{88}\]

Equation 89, Drift from One Degree of Tilt over Ten Seconds. A mean tilt of one degree held for ten seconds moves the aircraft 8.6 metres.

\[\tfrac{1}{2} \times 9.807 \times 0.01745 \times 100 = 8.6 \text{ m} \tag{89}\]

Equation 90, Aspect Ratio and Wing Loading. The span and wing area give an aspect ratio of 6.26 and at the test weight a wing loading of 970 newtons per square metre. Hoffman et al. 1972

\[\frac{b^{2}}{S} = \frac{33.83^{2}}{182.69} = 6.26, \qquad \frac{W}{S} = \frac{3{,}700}{182.69} = 20.25 \text{ lb/ft}^{2} = 970 \text{ N/m}^{2} \tag{90}\]

Equation 91, Bespoke Resolution of the Control Power Grid. The article measures the resolution of the experiment as the 0.6 grid spacing over a candidate threshold of 1.4 or 2.0.

\[\frac{0.6}{1.4} = 0.429, \qquad \frac{0.6}{2.0} = 0.300 \tag{91}\]

Equation 92, Bespoke Symmetric Rotor Differential. The article bounds the symmetric differential of each rotor by the smaller of the upward headroom and the downward reserve at the hover thrust $mg/n$.

\[\delta = \min(r - 1,\, 1)\,\frac{mg}{n} \tag{92}\]

Equation 93, Bespoke Multirotor Control Moment. Summing the bounded differentials with a geometry factor $c_{g}$ at rotor radius $R$ gives a moment in which the rotor count cancels.

\[M = c_{g}\, n\, \delta\, R = c_{g} \min(r-1,\,1)\, m g R \tag{93}\]

Equation 94, Bespoke Multirotor Control Power. Dividing the moment by the inertia written with a radius of gyration $k$ gives a control power in which the mass cancels.

\[\text{CP} = \frac{M}{m k^{2}} = \frac{c_{g} \min(r-1,\,1)\, g R}{k^{2}} \tag{94}\]

Equation 95, Bespoke Inverse-Span Law for a Multirotor. Putting the radius of gyration at a fraction $\kappa$ of span and the rotor radius at half the span makes multirotor control power inversely proportional to span.

\[\text{CP} = \frac{c_{g} \min(r-1,\,1)\, g}{2 \kappa^{2} b} \tag{95}\]

Equation 96, Zero-Sum Differential Thrust. A pure moment command on a multirotor raises some rotors exactly as much as it lowers others, so the thrust changes sum to zero.

\[\sum_{i} \Delta T_{i} = 0 \tag{96}\]

Equation 97, Bespoke Span at Which a Multirotor Falls to the X-14A Maximum. Setting the multirotor relation equal to 2.0 radians per second squared gives the span at which a vehicle of given margin falls to the X-14A maximum.

\[b^{*} = \frac{c_{g} \min(r-1,\,1)\, g}{2 \kappa^{2} \times 2.0} \tag{97}\]

Equation 98, First-Order Lag Response. For a first-order lag of time constant $\tau_{c}$ the fraction of a commanded moment present after a time $t$ is $1 - e^{-t/\tau_{c}}$.

\[1 - e^{-t/\tau_{c}} \tag{98}\]

Equation 99, Moment Fraction at 0.2 Seconds. At 0.2 seconds the open-loop fan, the closed-loop fan and the reaction nozzles deliver 29.2, 44.5 and 91.8 percent of the commanded moment. Gerdes and Rolls 1969

\[1 - e^{-0.2/0.58} = 0.292, \qquad 1 - e^{-0.2/0.34} = 0.445, \qquad 1 - e^{-0.2/0.08} = 0.918 \tag{99}\]

Equation 100, Angular Acceleration of a Sinusoidal Attitude. Tracking an attitude oscillation of amplitude $A$ at frequency $\omega$ requires a peak angular acceleration of $A \omega^{2}$.

\[\ddot{\theta} = A \omega^{2} \tag{100}\]

Equation 101, Bandwidth Cap at the Available Control Power. Saturation at the available control power caps the trackable frequency at the square root of the control power over the amplitude.

\[\omega_{\text{max}} = \sqrt{\frac{\text{CP}}{A}} \tag{101}\]

Equation 102, Bandwidth Caps at Five Degrees of Amplitude. At five degrees of amplitude control powers of 0.8 and 2.0 support 3.03 and 4.79 radians per second.

\[\sqrt{\frac{0.8}{0.0873}} = 3.03, \qquad \sqrt{\frac{2.0}{0.0873}} = 4.79 \tag{102}\]

Equation 103, Amplitude Cap at Two Radians per Second. A control power of 0.8 sustains two radians per second up to an amplitude of 0.2 radians.

\[A_{\text{max}} = \frac{\text{CP}}{\omega^{2}} = \frac{0.8}{4} = 0.2 \text{ rad} \tag{103}\]

Equation 104, Attitude Dynamics Without Gravity. The angular acceleration is the moment over the inertia and contains no gravitational term.

\[\ddot{\theta} = \frac{M}{I} \tag{104}\]

Equation 105, Horizontal Acceleration of a Tilted Hover. A vehicle holding height and tilted by $\theta$ accelerates horizontally at $g \tan\theta$.

\[\ddot{x} = g \tan\theta \tag{105}\]

Equation 106, Ratio of Terrestrial to Lunar Gravity. Terrestrial gravity is 6.05 times lunar gravity.

\[\frac{g_{e}}{g_{m}} = \frac{9.807}{1.62} = 6.05 \tag{106}\]

Equation 107, Lunar Translation Timescale Ratio. Because distance under constant acceleration goes as the square of time, the lunar translation timescale is longer by the square root of the gravity ratio, 2.46.

\[\sqrt{\frac{g_{e}}{g_{m}}} = 2.46 \tag{107}\]

Equation 108, Terrestrial Drift at Five Degrees for Five Seconds. Five degrees of tilt held for five seconds moves a vehicle 10.7 metres on Earth.

\[\tfrac{1}{2} \times 9.807 \times 0.0873 \times 25 = 10.7 \text{ m} \tag{108}\]

Equation 109, Lunar Drift at Five Degrees for Five Seconds. The same tilt and time move a vehicle 1.8 metres on the Moon.

\[\tfrac{1}{2} \times 1.62 \times 0.0873 \times 25 = 1.8 \text{ m} \tag{109}\]

Equation 110, Lunar to Terrestrial Hover Thrust. A vehicle hovering on the Moon needs the gravity ratio, 0.165, of the thrust it needs on Earth.

\[\frac{T_{\text{moon}}}{T_{\text{earth}}} = \frac{g_{m}}{g_{e}} = 0.165 \tag{110}\]

Equation 111, Equal Horizontal Acceleration Under Two Gravities. Equal horizontal acceleration requires the tangent of the lunar tilt to be 6.05 times that of the terrestrial tilt.

\[g_{m} \tan\theta_{m} = g_{e} \tan\theta_{e} \quad \Longrightarrow \quad \tan\theta_{m} = 6.05 \tan\theta_{e} \tag{111}\]

Equation 112, Lunar Tilt Equivalent to Five Degrees on Earth. Five degrees of terrestrial tilt corresponds to 27.9 degrees on the Moon.

\[\theta_{m} = \arctan\left(6.05 \times \tan 5^{\circ}\right) = 27.9^{\circ} \tag{112}\]

Equation 113, Weight Fraction Carried by the Lunar Landing Research Vehicle Jet. Cancelling five sixths of the weight leaves the jet carrying 83.5 percent of the vehicle. Lunar Landing Research Vehicle

\[1 - \frac{g_{m}}{g_{e}} = 1 - 0.165 = 0.835 \tag{113}\]

Equation 114, Bespoke Time for a Hover Position Correction. The article models a correction as two symmetric accelerate-and-arrest attitude changes at full control power plus a constant-tilt translation over a distance $d$.

\[t(\theta) = 4\sqrt{\frac{\theta}{\text{CP}}} + 2\sqrt{\frac{d}{g \tan\theta}} \tag{114}\]

Equation 115, Bespoke Stationarity Condition for the Correction Time. Differentiating the small-angle form of the correction time with respect to tilt and setting it to zero gives the stationarity condition.

\[\frac{dt}{d\theta} = \frac{2}{\sqrt{\text{CP}\,\theta}} - \sqrt{\frac{d}{g}}\;\theta^{-3/2} = 0 \tag{115}\]

Equation 116, Bespoke Optimal Correction Tilt. The stationarity condition of the correction model solves to an optimal tilt of half the square root of the control power times the distance over gravity.

\[\theta^{*} = \tfrac{1}{2}\sqrt{\frac{\text{CP}\, d}{g}} \tag{116}\]

Equation 117, Bespoke Equal Split of the Correction Time. At the optimal tilt of the correction model the attitude term and the translation term are equal.

\[4\sqrt{\frac{\theta^{*}}{\text{CP}}} = 2\sqrt{\frac{d}{g\,\theta^{*}}} \tag{117}\]

Equation 118, Bespoke Elasticity of Correction Time to Control Power. Across the tested range the correction model gives a local exponent of about minus a quarter for the time with respect to control power.

\[\frac{d \ln t}{d \ln \text{CP}} = -0.26 \tag{118}\]

Notation

• $\text{CP}$, the control power, the angular acceleration the control system can produce
• $M_{\text{control}}$, the maximum control moment about an axis
• $I$, the moment of inertia about the axis considered
• $F$, the nozzle force
• $\ell$, the distance of each nozzle from the centre of mass
• $u$, the normalised control input between minus one and one
• $D/I$, the damping per unit inertia in inverse seconds
• $\tau$, the characteristic time of the damped attitude response
• $\dot{m}$, the nozzle mass flow
• $v_{e}$, the nozzle exit velocity
• $\gamma$, the ratio of specific heats, taken as 1.4 for air
• $T_{0}$, the total temperature of the bleed air, and in the bleed and margin relations the uninstalled thrust
• $p_{0}$, the total pressure at the nozzle
• $p_{a}$, the atmospheric pressure
• $C_{v}$, the nozzle velocity coefficient
• $C_{d}$, the nozzle discharge coefficient
• $\beta$, the fraction of airflow bled for control, and in the opening bound a fraction of thrust
• $s$, the fractional thrust lost per unit fraction of airflow bled
• $T$, the thrust
• $W$, the aircraft weight
• $r$, the thrust-to-weight ratio
• $\eta_{\text{inst}}$, the installation efficiency
• $\eta_{d}$, the thrust diverter efficiency
• $\Phi$, the share of the pre-bleed hover margin consumed by the control system
• $V_{w}$, the wind speed
• $S_{s}$, the side area exposed to the wind
• $C_{D}$, the drag coefficient
• $\sigma$, the disturbance as a fraction of the available control power
• $I_{x}$, the moment of inertia in roll
• $I_{y}$, the moment of inertia in pitch
• $k_{x}$, the roll radius of gyration
• $b$, the wing span
• $m$, the aircraft mass
• $L_{w}$, the wingtip nozzle arm
• $L_{t}$, the tail nozzle arm
• $\kappa_{r}$, the roll radius of gyration as a fraction of span
• $\text{CP}_{v}$, the authority of the variable-stability nozzle set
• $p$, the roll rate
• $\lambda$, the fraction of the variable-stability set reserved for augmentation
• $c_{g}$, the geometry factor of a multirotor layout
• $n$, the number of rotors
• $\tau_{c}$, the first-order time constant of a control effector
• $g_{e}$, the gravitational acceleration at the surface of the Earth
• $g_{m}$, the gravitational acceleration at the surface of the Moon
• $\theta^{*}$, the tilt that minimises the time of a hover position correction
• $d$, the distance of a hover position correction

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