X-Planes: Lockheed Martin X-35

The Lockheed Martin X-35 won, which makes it the only aircraft in this series so far whose demonstrator became a production programme, and it won partly on one flight. On 20 July 2001 the X-35B took off in a few hundred feet, climbed to twenty-five thousand feet, accelerated past the speed of sound in level flight, returned to the field and landed vertically. No aircraft had ever done those three things in one sortie, the rival demonstrator could not, and the contract followed three months later. This is the thirty-sixth 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, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, the X-24, the X-25, the X-26, the X-27, the X-28, the X-29, the X-30, the X-31, the X-32, the X-33, and the X-34.

That sortie is called Mission X, the most famous single flight any aircraft in this series ever made. A flight that famous invites one question, the question can be answered, and this article exists to answer it. What did it establish?

The Research Question

The Sortie Has a Reputation and the Reputation Is Doing Work

The short version, repeated in almost every account, is that the X-35B did in one flight what the X-32 could not do at all, that the rival had to be physically reconfigured between the hovering and supersonic parts of its envelope, and that the fly-off was therefore decided by a capability one team had and the other did not. The rival’s own record bears out the middle clause, since Boeing demonstrated hovering and supersonic flight in separate configurations.

Every clause of that is true and the conclusion still does not follow from it, because the flight was not the experiment. A demonstration that three regimes can be flown in sequence is a demonstration about sequencing. Whether sequencing was the hard part is a separate question. Nobody asks it, because the answer feels obvious and is not.

What This Article Will Not Do

The previous article on the losing side of this competition already made the argument that neither demonstrator was the aircraft being bought, and made it at length. The X-32 and the X-35 were concept demonstrators and not fighter prototypes, and the machines that flew in 2000 and 2001 differed from the production aircraft in structure, in systems, in weight and in purpose. That construct-validity argument is correct and has been made. It will not be remade here.

What remains is a different question, the winner’s. Granting that the demonstrator was a demonstrator, what did its most celebrated flight actually demonstrate?

The Question, Stated So That It Can Be Answered Wrongly

A sortie that performs three manoeuvres in sequence tests something the same three manoeuvres flown on three separate days do not, if and only if the three place demands on the same hardware that interfere. If they do interfere, sequencing them is an existence proof and the flight is evidence. If they do not, sequencing them is scheduling and the flight is a display.

So the keystone of this article is an answerable coupling question. For each of the three events, and for the transitions between them, the article asks what physical quantity was scarce, and computes it. It does not reach the answer the reputation implies, and a later section states the case against its answer openly.

A preview, because a reader is entitled to know where an argument is going. Two of the three events turn out to have been cheap, one of them very cheap indeed, and the expensive thing is not one of the three. It is the conversion between modes, which is not in the name of the trick. Worse for the reputation, and central to the argument, the first in-flight conversion had already been flown eleven days earlier, on a sortie that also went faster than Mission X did.

Programme Origin

What Was Being Bought

The Joint Strike Fighter programme sought a single airframe family for three services and two navies, with a conventional variant, a carrier variant and a short-takeoff and vertical-landing variant sharing enough structure and systems to be affordable. The short-takeoff and vertical-landing requirement constrains everything else, because it demands that an aircraft otherwise sized for supersonic combat also hover, and hovering is the most thrust-hungry thing an aeroplane can do.

The competition ran as a fly-off between two concept demonstrator teams. Each built and flew aircraft covering the three variants, and each demonstrated a different answer to the hovering problem. Neither team started from nothing. The technology base both drew on had been accumulating for four decades, a great deal of it in reports of the National Aeronautics and Space Administration and its predecessor, and most of the period literature this article cites comes from that base, not from the competition itself.

The Invention

The X-35’s answer is due to Paul Bevilaqua and Paul Shumpert at the Lockheed Skunk Works, who set it out in their patent for a propulsion system for a vertical and short takeoff and landing aircraft, granted in 1993. The inventor described the cycle himself in a 1996 paper on dual cycle operation of the shaft driven lift fan and gave the programme’s own account of its origins in the 2009 Wright Brothers Lecture, the genesis of the F-35, and in a companion paper on inventing it. Those are the primary sources for this architecture and the article leans on them.

The idea is unusual enough to state in one sentence. Instead of pointing the engine’s own exhaust downward, take mechanical power off the engine’s shaft, run it forward through a clutch and a bevel gearbox, and use it to drive a separate fan that blows cold air straight down.

Almost every reader’s first reaction is that this is a worse deal, because the fan’s thrust has to come out of the engine’s thrust and a shaft cannot create energy. The reaction is correct about the energy and wrong about the thrust, for a reason given by the most important relation in this article.

One detail of the inventor’s record shows what the fan replaced. Bevilaqua spent the preceding fifteen years on thrust-augmenting ejectors, publishing a lifting surface theory for them in 1977, an evaluation of hypermixing in 1974 and two reviews of advances in ejector thrust augmentation in the 1980s. The ejector is the other way of adding mass flow to a lift system, entraining ambient air into a high-velocity primary jet and not driving a fan with a shaft. The man who displaced it had spent much of his earlier career on it.

The Three Aircraft

Two airframes were built. The X-35A flew first, in the conventional configuration, and was then rebuilt as the X-35B by installing the lift system. The X-35C was a separate aircraft with the larger wing and the strengthened structure of the carrier variant. So the aircraft that flew Mission X is the same airframe that had earlier flown as a conventional fighter, which matters later, because it means the conventional and hovering configurations differed by an installation, not by an airframe.

Sizing From First Principles

The Relation That Makes a Fan Worth Carrying

The relation is the one the X-32 article derives. A jet that accelerates a mass flow $\dot{m}$ from rest to a velocity $v$ produces a thrust and carries away a kinetic power,

\[T = \dot{m} v \qquad \text{and} \qquad P = \tfrac{1}{2} \dot{m} v^{2} \tag{1}\]

and eliminating the velocity between them gives the relation that governs every lift system ever built,

\[T = \sqrt{2 P \dot{m}} \tag{2}\]

At a fixed power, thrust rises as the square root of the mass flow.

The argument for a lift fan follows from this. A shaft cannot create power, so the fan’s power does come out of the engine. But the fan moves air that the engine never touched, and adding mass flow at fixed power raises thrust. Doubling the mass flow multiplies the thrust by the square root of two even though not one extra joule was spent.

Said the other way round, in the form that makes the design decision obvious, thrust per unit power is inversely proportional to jet velocity. Dividing the two definitions, not eliminating between them,

\[\frac{T}{P} = \frac{\dot{m} v}{\tfrac{1}{2} \dot{m} v^{2}} = \frac{2}{v} \tag{3}\]

A hovering aeroplane wants the slowest, fattest jet it can arrange. A supersonic aeroplane wants the opposite. The lift fan exists because those two wants are irreconcilable in one nozzle and reconcilable in two.

The Fan as an Actuator Disc

Three published numbers fix the fan completely and none of them was published in order to. The Rolls-Royce LiftFan is fifty inches in diameter, produces twenty thousand pounds force of thrust, and absorbs twenty-nine thousand shaft horsepower.

Writing $D$ for the diameter, the disc area is

\[A = \frac{\pi D^{2}}{4} = \frac{\pi \times 1.27^{2}}{4} = 1.2668 \ \text{m}^{2} \tag{4}\]

Momentum theory treats the fan as a disc across which pressure jumps, with air arriving at rest and leaving at a velocity that is twice the velocity through the disc itself. Writing $v_i$ for the induced velocity at the disc and $\rho$ for sea-level density, thrust and mass flow give

\[T = 2 \rho A v_i^{2} \qquad \Rightarrow \qquad v_i = \sqrt{\frac{T}{2 \rho A}} \tag{5}\]

and substituting twenty thousand pounds force, which is 88,964 newtons,

\[v_i = \sqrt{\frac{88{,}964}{2 \times 1.225 \times 1.2668}} = 169.3 \ \text{m/s} \tag{6}\]

so the fully developed jet runs at 338.6 metres per second and the mass flow through the disc is

\[\dot{m} = \rho A v_i = 1.225 \times 1.2668 \times 169.3 = 262.7 \ \text{kg/s} \tag{7}\]

which is 579.2 pounds per second. The figure is nearly twice the engine core flow that the inversion in a later section recovers. Far from being an accessory, the fan is the larger air handler of the two.

The ideal power such a disc requires is the thrust times the induced velocity,

\[P_{\text{ideal}} = T v_i = 88{,}964 \times 169.3 = 15.06 \ \text{MW} \tag{8}\]

against the 21.63 megawatts that twenty-nine thousand shaft horsepower delivers, so the fan’s figure of merit is

\[\mathrm{FM} = \frac{P_{\text{ideal}}}{P_{\text{shaft}}} = \frac{15.06}{21.63} = 0.697 \tag{9}\]

The previous article recovered the same 0.697 while examining the rival, from the same three numbers, and it belongs to the X-35’s fan and not the X-32’s. A figure of merit near seven tenths is respectable for a heavily loaded fan in a short duct with louvred exit vanes and no time to be elegant.

The same figure follows if the power is taken as the kinetic flux of the fully developed jet, $\tfrac{1}{2} \dot{m} \left(2 v_i\right)^{2} = 2 \dot{m} v_i^{2} = T v_i$, rather than as thrust times induced velocity. The two forms are algebraically identical, so their agreement is a check on the arithmetic and not on the physics.

What the Whole System Multiplies

The lift system’s three published contributors are the fan at twenty thousand pounds force, the three-bearing swivel module at eighteen thousand, and two roll posts at 1,950 pounds force each, giving

\[T_{\text{total}} = 20{,}000 + 18{,}000 + 2 \times 1{,}950 = 41{,}900 \ \text{lbf} \tag{10}\]

Those are the figures published for the production LiftSystem, and the 2001 company releases credit the X-35B with nearly 40,000 pounds of vertical force. The total stands against an engine whose dry thrust is twenty-five thousand pounds force. A direct-lift installation of the same engine, which is what the rival built, has that dry thrust and nothing else to hover on. So the shaft-driven arrangement multiplies the available vertical thrust by

\[\frac{41{,}900}{25{,}000} = 1.676 \tag{11}\]

and it does so without burning any more fuel. The engine is producing the same power either way.

An Unpublished Number Recovered From Three Published Ones

The square-root law shows where that factor came from, and inverting it yields a number the manufacturer never released. If the augmentation is entirely the mass-flow effect, then

\[\frac{T_{\text{total}}}{T_{\text{dry}}} = \sqrt{\frac{\dot{m}_{\text{fan}} + \dot{m}_{\text{core}}}{\dot{m}_{\text{core}}}} \tag{12}\]

and solving for the core mass flow, which no source cited here gives,

\[\dot{m}_{\text{core}} = \frac{\dot{m}_{\text{fan}}}{r^{2} - 1} = \frac{579.2}{1.676^{2} - 1} = 320.2 \ \text{lb/s} \tag{13}\]

Because no cited source gives an airflow figure for the engine, the inversion cannot be checked against a published value. It is reached from three numbers about thrust and one about a fan, none of which concerns engine airflow.

The figure should not be read for more than it is. The relation assumes the total power is unchanged between the two arrangements, that both jets are ideal, and that the roll posts belong in the numerator, and each of those holds only approximately. It is the core flow the mass-flow mechanism alone would require, and it has not measured the engine.

The Identity the Article Was Already Printing

Momentum theory hands over a second quantity for free, as the X-32 article also shows. The disc loading is thrust over disc area,

\[\frac{T}{A} = \frac{88{,}964}{1.2668} = 70.2 \ \text{kPa} \tag{14}\]

and the dynamic pressure in the fully developed jet is

\[q_{\text{jet}} = \tfrac{1}{2} \rho \left(2 v_i\right)^{2} = 2 \rho v_i^{2} = \frac{T}{A} \tag{15}\]

so the dynamic pressure the jet puts on the ground is the disc loading, exactly. The equality is an algebraic identity of the ideal disc and holds for any thrust, area and density.

This matters because it converts a propulsion number into a facilities number without any further modelling. A fifty-inch fan making twenty thousand pounds force is also a machine that presses on whatever it is standing over at 70.2 kilopascals, which is about ten pounds per square inch.

Why Cold Matters More Than the Thrust Does

The core stream is a different animal. Its footprint pressure needs the nozzle exit area, which is not published, so it is reached from the mass flow already recovered. For a jet expanded to ambient pressure at exit temperature $T_e$, continuity gives the area and the footprint follows,

\[\rho_e = \frac{p_0}{R T_e} \qquad \text{and} \qquad A_e = \frac{\dot{m}_{\text{core}}}{\rho_e v_e} \tag{16}\]

so the pressure the core jet applies to the surface below it is

\[\frac{T_r}{A_e} = \frac{T_r \, \rho_e v_e}{\dot{m}_{\text{core}}} \tag{17}\]

At roughly nine hundred kelvin the exit density is 0.3922 kilograms per cubic metre, and taking a dry military exit velocity between 550 and 650 metres per second,

Assumed exit velocity, m/s	Implied exit area, m²	Footprint pressure, kPa	Ratio to the fan
550	0.6733	118.9	1.69
600	0.6172	129.7	1.85
650	0.5697	140.5	2.00

Across the bracket the core jet presses between 1.69 and 2.00 times as hard as the fan does, and it does so at roughly three times the absolute temperature. The fan’s efflux leaves at ambient temperature plus the 46.8 kelvin the compression adds. For the fan pressure ratio $\Pi$ derived under The Torque Nobody Mentions, the isentropic relation gives the exit temperature directly,

\[T_{\text{fan}} = T_0 \, \Pi^{\frac{\gamma - 1}{\gamma}} = 288.15 \times 1.693^{0.2857} = 334.9 \ \text{K} \tag{18}\]

The core’s is taken here to leave at about nine hundred kelvin.

So the fan contributes more than thrust. It places a large volume of cold air under the front of the aeroplane, which does two things a hotter, faster jet cannot. It reduces the pressure and temperature the landing surface sees, and it puts a barrier of ambient-temperature air between the hot core efflux and the inlet. The previous article treated hot gas ingestion as the rival’s central difficulty. The X-35’s architecture attacks it at the source.

The Torque Nobody Mentions

The fan is described as two-stage counter-rotating, and the phrase is usually read as a refinement. In fact counter-rotation makes the aircraft controllable.

A single-rotation fan absorbing shaft power $P$ at angular velocity $\omega$ applies a reaction torque to the airframe of

\[Q = \frac{P}{\omega} \tag{19}\]

and in a hover there is nothing to react it against except the roll posts, which exist to control the aircraft and not to trim it. The roll posts supply a couple of

\[C = 2 F_{\text{post}} \ell \tag{20}\]

where $\ell$ is the distance from the centreline. The fan’s rotational speed is not given in any source cited here, so the relation is inverted, not evaluated. Asking what speed would make the reaction torque consume the entire roll-post couple gives

Roll-post arm, m	Roll-post couple, N·m	Threshold speed, rpm
2.5	43,370	4,761
3.0	52,044	3,968
3.5	60,718	3,401
4.0	69,392	2,976

Every threshold in that table is an ordinary fan speed. An independent estimate of the fan’s actual speed can be built from quantities already computed. The fan raises total pressure by the jet’s dynamic head, giving a pressure ratio of

\[\Pi = \frac{p_0 + q_{\text{jet}}}{p_0} = \frac{101{,}325 + 70{,}229}{101{,}325} = 1.693 \tag{21}\]

For an isentropic compression the total temperature rise follows from the pressure ratio,

\[\Delta T_0 = T_0 \left(\Pi^{\frac{\gamma - 1}{\gamma}} - 1\right) = 288.15 \times \left(1.693^{0.2857} - 1\right) = 46.8 \ \text{K} \tag{22}\]

so the fan does specific work of

\[w = c_p \Delta T_0 = 1004.7 \times 46.8 = 47.0 \ \text{kJ/kg} \tag{23}\]

and the air leaves it at 334.9 kelvin, which is the number the ground-environment argument above relies on. Writing $\psi$ for the stage loading coefficient and taking the work as shared between two stages, the blade speed follows from

\[U = \sqrt{\frac{c_p \Delta T_0}{2 \psi}} = \sqrt{\frac{47{,}002}{2 \times 0.40}} = 242.4 \ \text{m/s} \tag{24}\]

which is a tip Mach number of 0.712, comfortable for a transonic stage and a check that the assumed loading coefficient is not absurd. The rotational speed is then

\[N = \frac{60 U}{\pi D} = \frac{60 \times 242.4}{\pi \times 1.27} = 3{,}645 \ \text{rpm} \tag{25}\]

That estimate sits inside the threshold band and near its middle. The supportable claim is therefore not that counter-rotation saved a stated percentage, but that across every plausible roll-post location a single-rotation fan of this power would have consumed somewhere between three quarters and all of the aircraft’s roll authority merely to stand still. Without counter-rotation there would be no usable control system to improve.

The Clutch and the Halving Identity

The fan is not always running. In conventional flight it is stopped, its doors are closed, and it is carried as dead weight. Entering the hovering mode means opening the doors and engaging a clutch between a running engine and a stationary fan. The article’s thesis holds that this was the hard event, so its cost should be computed exactly.

Consider a source held at a constant angular velocity $\omega_s$ driving an inertia $I$ initially at rest, through a slipping clutch transmitting a torque $Q$ that may vary however it likes. The source does work at a rate $Q \omega_s$. The inertia receives work at a rate $Q \omega$. The difference is destroyed in the clutch. Over the whole engagement the impulse fixes the total,

\[\int Q \, dt = I \omega_s \qquad \Rightarrow \qquad W_{\text{in}} = \omega_s \int Q \, dt = I \omega_s^{2} \tag{26}\]

while the inertia ends up holding

\[E_{\text{fan}} = \tfrac{1}{2} I \omega_s^{2} \tag{27}\]

so the energy destroyed is the difference,

\[E_{\text{clutch}} = I \omega_s^{2} - \tfrac{1}{2} I \omega_s^{2} = \tfrac{1}{2} I \omega_s^{2} \tag{28}\]

Exactly half of the energy drawn from the engine during the engagement is destroyed as heat in the clutch, and nothing about that fraction depends on how the engagement is managed. A slow, gentle engagement destroys exactly as much as a violent one. Integrating the equations of motion under a constant torque, a linearly rising torque and an exponentially decaying torque gives a dissipated fraction of 0.5 in all three cases, as the impulse argument requires.

The magnitude needs the fan’s polar moment of inertia, which is not published, so it is bracketed.

Assumed inertia, kg·m²	Fan kinetic energy, MJ	Clutch dissipation, MJ	Stored energy as a time, s
25	1.82	1.82	0.084
37	2.70	2.70	0.125
50	3.64	3.64	0.168

The last column is the useful one, and the bracket does not weaken it. It is

\[\tau = \frac{E_{\text{fan}}}{P_{\text{shaft}}} = \frac{I \omega_s^{2}}{2 P_{\text{shaft}}} \tag{29}\]

the fan’s stored kinetic energy divided by the power it absorbs when running, which has the dimensions of time, and across the bracket it stays under a fifth of a second. The fan stores less than a fifth of a second of its operating power.

The heat has to go somewhere, and the same bracket gives its effect on the clutch. For a plate pack of mass $m_p$ and specific heat $c_p$, an adiabatic engagement raises its temperature by

\[\Delta T_p = \frac{E_{\text{clutch}}}{m_p c_p} = \frac{I \omega_s^{2}}{2 m_p c_p} \tag{30}\]

and for an assumed twenty kilograms of carbon at 710 joules per kilogram kelvin that is 128.3, 189.8 and 256.5 kelvin across the three inertias. Those are ordinary friction-material temperatures, which is the first sign that the engagement is thermally modest.

What the Bound Rules Out

The cited sources give no engagement time for the X-35B’s clutch, so the bound is taken for an assumed engagement time $t$ of nine seconds. Combining that time with the rated shaft power gives a bound that assumes nothing about the fan. At most the rated power can flow for at most that time, and at most half of it can be destroyed, so

\[E_{\text{clutch}} \le \tfrac{1}{2} P t = \tfrac{1}{2} \times 21.63 \times 10^{6} \times 9 = 97.3 \ \text{MJ} \tag{31}\]

That bound is absurd and its absurdity is the finding. Ninety-seven megajoules deposited into an assumed twenty kilograms of carbon would raise its temperature by about 6,853 kelvin, which is beyond the vaporisation point of anything. The engagement therefore cannot be anywhere near power-limited.

Comparing the bound with the bracket gives the size of the margin. Spreading the bracketed dissipation over the assumed nine seconds and dividing by the bound’s rate, which is half the shaft power, gives

\[\frac{E_{\text{clutch}} / t}{\tfrac{1}{2} P} = \frac{E_{\text{clutch}}}{\tfrac{1}{2} P t} = \frac{1.82}{97.3} = 0.0187 \quad \text{to} \quad \frac{3.64}{97.3} = 0.0374 \tag{32}\]

across the inertia bracket, so the mean dissipation is between 1.9 and 3.7 percent of the most the shaft could feed into the clutch. The bound exceeds the dissipation across the inertia bracket for any engagement longer than about a third of a second, so the conclusion does not rest on the assumed time. The energy does not set an engagement of that length. If anything in the clutch sets it, the heat does, and that difference explains why a mode change on this aircraft is a scheduled sequence of doors opening, the clutch engaging and the clutch locking, not the flick of a switch.

The Force That Appears the Moment the Fan Engages

The conversion’s largest single effect is a force that most descriptions of this aeroplane do not mention. A lift fan running in forward flight ingests air travelling at the aircraft’s speed and discharges it vertically. All of that horizontal momentum has to be destroyed, and the reaction is a drag force.

Writing $\dot{m}$ for the fan’s mass flow and $V$ for true airspeed,

\[D_{\text{mom}} = \dot{m} V \tag{33}\]

which is exact and needs nothing beyond the flow the disc analysis already produced. The same mass flow follows from thrust over jet velocity, since the ideal disc has $T = \dot{m} v_j$ identically.

Speed, kt	Momentum drag, lbf	As a share of the swivel module’s thrust	As a share of weight
60	1,823	10.1 percent	5.4 percent
80	2,431	13.5 percent	7.2 percent
120	3,646	20.3 percent	10.7 percent
150	4,558	25.3 percent	13.4 percent
180	5,469	30.4 percent	16.1 percent

The X-35B made its first in-flight conversion at 180 knots, and at that speed engaging the fan costs 5,469 pounds force of drag. That is 30.4 percent of everything the rear nozzle can produce, and on its own it would decelerate the aircraft at

\[a = \frac{D_{\text{mom}}}{m} = \frac{24{,}329}{15{,}422} = 1.578 \ \text{m/s}^{2} = 0.1609 \, g \tag{34}\]

These figures give quantitative content to the claim that the conversion was the hard event. Nothing about hovering, going supersonic or landing vertically produces a step change of that size. Opening the doors and letting the clutch in does.

Where That Drag Acts

The fan sits ahead of the centre of gravity and its inlet doors are on top of the fuselage, so the momentum drag is a horizontal force applied above and forward of the centre of mass, and it therefore pitches the aircraft as well as decelerating it.

The inlet’s height above the centre of gravity is unpublished, so the relation is solved for the height that would matter. Pitch control in the hover comes from shifting thrust between the fan and the rear nozzle, and an authority of ten percent of the fan’s thrust acting on its moment arm gives

\[M_{\text{avail}} = 0.10 \, T_f x_f = 0.10 \times 88{,}964 \times 3.553 = 31{,}606 \ \text{N m} \tag{35}\]

Setting that equal to the momentum-drag moment gives the height at which the two are equal,

\[h^{*} = \frac{M_{\text{avail}}}{D_{\text{mom}}} = \frac{31{,}606}{24{,}329} = 1.299 \ \text{m} \tag{36}\]

If the dorsal fan inlet sits roughly a metre above the centre of gravity, which is an estimate and not a published figure, the threshold is not comfortably far away. What can be said is that the momentum drag’s pitching moment is of the same order as the trim authority available to oppose it, which is why a conversion is flown as a scheduled and gradual event rather than as a switch.

The Hover Balance Fixes the Centre of Gravity

In wing-borne flight an aeroplane trims by moving a control surface. In a hover it cannot, because there is no airflow to work against. The only vertical forces are the fan ahead of the centre of gravity and the rear nozzle behind it, and in steady hover their moments must cancel,

\[T_f x_f = T_r x_r \tag{37}\]

Both thrusts are fixed by the hardware, so this equation does not determine the trim. It determines where the centre of gravity has to be. Writing $L$ for the separation between the two,

\[\frac{x_f}{L} = \frac{T_r}{T_f + T_r} = \frac{18{,}000}{38{,}000} = 0.4737 \tag{38}\]

The centre of gravity must sit at 47.37 percent of the distance from the fan to the rear nozzle, and for an assumed separation of 7.5 metres that is 3.553 metres behind the fan and 3.947 metres ahead of the nozzle. The ratio of the two arms is fixed at 0.9 by the ratio of the two thrusts and by nothing else.

How tightly that is fixed is the useful question. Modulating the split in opposite directions moves the balance point across the following band.

Split modulation	Reachable station, fraction from the fan	Travel
2 percent	0.4637 to 0.4837	5.89 inches
5 percent	0.4488 to 0.4987	14.72 inches
10 percent	0.4241 to 0.5238	29.45 inches

A few percent of thrust split yields a few inches of centre-of-gravity travel. That is a tight band for an aeroplane whose fuel and stores move the centre of gravity by considerably more, and it is a cost of the architecture that does not ease as the aircraft gets lighter, unlike every other margin in this article.

What an Inlet Temperature Rise Costs, in Kelvin

The lift fan is shaft-driven, which means every pound of vertical thrust in this aircraft is ultimately core thrust. The fan has no combustor of its own. So an engine that swallows its own hot exhaust loses the fan and the rear nozzle together, and the ground-environment argument made earlier can now be quantified.

At a fixed corrected operating point the physical mass flow, and with it the thrust, falls as the inverse of inlet total temperature. This relation needs a thrust and a temperature in the same expression, and the article has used $T$ for thrust throughout, so thrust is written $F$ here and only here.

\[\frac{F}{F_{0}} = \frac{T_{\text{amb}}}{T_{\text{amb}} + \Delta T} \tag{39}\]

Inlet rise, K	Thrust retained	Vertical thrust, lbf	Hover margin
0	1.000	41,900	1.232
10	0.966	40,495	1.191
20	0.935	39,181	1.152
30	0.906	37,949	1.116
50	0.852	35,705	1.050

The losses are 3.354, 6.490, 9.430 and 14.786 percent respectively. Inverting for the rise that consumes the margin entirely gives

\[\Delta T_{\text{crit}} = T_{\text{amb}} \left(\frac{F_{\text{total}}}{W} - 1\right) = 288.15 \times 0.2324 = 66.95 \ \text{K} \tag{40}\]

At 34,000 pounds the X-35B could tolerate a 66.95 kelvin inlet temperature rise before it could no longer hold itself up. That single number measures the value of the cold fan. It accounts for the architecture’s choice to place a large volume of ambient air between the hot core efflux and the inlets instead of managing ingestion afterwards, and it converts a comparison with the rival from a matter of adjectives into a matter of kelvin.

The Vehicle

Two airframes covered three configurations. The X-35A flew as a conventional fighter from 24 October 2000, was then rebuilt with the lift system installed, and flew again as the X-35B. The X-35C was a separate aircraft carrying the carrier variant’s larger wing and heavier structure.

The demonstrators were deliberately simpler than the production aircraft. They carried no weapons bays, no radar, no mission systems and no low-observable treatment of the kind the product would need, and they used off-the-shelf components wherever schedule allowed. The X-35A’s published empty weight of 26,500 pounds belongs to a machine built to answer a question, not to fight. The maximum takeoff weight of fifty thousand pounds printed beside it is the figure of the 1998 operational requirement.

Dependent Systems

The Three-Bearing Swivel Module

The rear nozzle redirects the core exhaust downward through a jointed pipe whose three canted bearings, rotated relative to one another, sweep the nozzle through ninety-five degrees in 2.5 seconds, a mean slew rate of

\[\dot{\delta} = \frac{\Delta \delta}{\Delta t} = \frac{95^{\circ}}{2.5 \ \text{s}} = 38.0 \ \text{deg/s} \tag{41}\]

The elegance is that a purely rotational mechanism produces a large angular deflection, so the sealing problem is a set of rotating joints rather than a set of sliding ones, at a station carrying the full core efflux.

The number of bearings is not a styling choice, and the geometry fixes the count at three. Take a single joint whose mating plane is inclined at an angle $\beta$ to the duct axis. Rolling one side relative to the other by $\phi$ deflects the downstream axis by $\delta$, where

\[\cos\delta = \cos^{2}\beta + \sin^{2}\beta \cos\phi \tag{42}\]

At half a turn it reduces to $\delta = 2\beta$, so one joint can bend the duct by twice its cant angle and no more.

\[\beta_{\text{single}} = \frac{95^{\circ}}{2} = 47.5^{\circ} \tag{43}\]

A single bearing would therefore need its mating plane canted at 47.5 degrees, which is an extraordinary angle for a pressure-tight rotating seal carrying the full exhaust of an augmented turbofan. Such a joint would be impractical.

Putting joints in series helps only if their cants alternate, and this condition is not obvious. A numerical search over the roll angles found that two joints canted the same way reach $2\beta$ and no more, because the second can only undo what the first did. Mirror the second joint and the two add to $4\beta$, and three alternating joints reach $6\beta$, which the search confirmed to the grid resolution at a cant of fifteen degrees.

\[\beta_{\text{three}} = \frac{95^{\circ}}{6} = 15.83^{\circ} \tag{44}\]

Sixteen degrees is an ordinary cant for a rotating duct joint. So the count of bearings follows from the angle a sealed joint can tolerate, divided into the deflection the aircraft needs. The actual cant angles and the gearing between the three rings are not published, and this article claims only the requirement and leaves the mechanism open.

The Inlet

The inlet is a diverterless supersonic design, replacing the boundary-layer diverter of a conventional installation with a fixed compression surface that pushes the boundary layer sideways. It removes weight, moving parts and radar return at once, and it does so at the cost of being optimised for one region of the envelope rather than adjustable across it. For a demonstrator flown to about Mach 1.2 that cost is invisible, a point to bear in mind when reading the supersonic leg of Mission X.

Roll Posts and Control Power

Bleed from the engine’s fan is ducted to nozzles in each wing, giving 1,950 pounds force each, which is half of the 3,900 pounds force published for the pair combined. In a hover an aeroplane has no aerodynamic control at all, so every axis must be held by thrust modulation. Pitch comes from splitting thrust between the lift fan and the rear nozzle, yaw from vectoring the rear nozzle laterally, and roll from the posts.

The earlier counter-rotation result can be turned from a fraction into something a pilot would feel. The posts supply a couple, and dividing by the roll moment of inertia gives an angular acceleration,

\[\dot{p} = \frac{2 F_{\text{post}} \ell}{I_{xx}} \tag{45}\]

The inertia is not published, so it is estimated from a radius of gyration taken as a fraction of span and reported across a bracket. At 0.22 of the span,

\[I_{xx} = m k_x^{2} = 15{,}422 \times 2.213^{2} = 75{,}400 \ \text{kg m}^{2} \tag{46}\]

which is 75,400 kilogram metres squared, and with the posts at 3.5 metres from the centreline the couple of 60,718 newton metres gives

\[\dot{p} = \frac{60{,}718}{75{,}400} = 0.805 \ \text{rad/s}^{2} = 46.07 \ \text{deg/s}^{2} \tag{47}\]

which is a healthy figure for a hovering aircraft. Across the plausible bracket of radius of gyration and post position it runs from 30.6 to 55.7 degrees per second squared.

Now subtract what a single-rotation fan would have taken. Its reaction torque at the speed estimated above is 56,655 newton metres, which is 93.31 percent of the couple, leaving 4,063 newton metres and

\[\dot{p}_{\text{residual}} = \frac{4{,}063}{75{,}400} = 3.083 \ \text{deg/s}^{2} \tag{48}\]

Three degrees per second squared is not a degraded control system. It is not a control system. A pilot holding a hover in a crosswind would have had about one fifteenth of the roll acceleration the aircraft has. That difference is the return on the counter-rotating fan, expressed in the units the handling-qualities literature uses, and it makes a stronger statement than the percentage the earlier section could make.

Structure and the Variant Problem

The three variants share a fuselage cross-section and a great deal of structure, and differ in wing area, in landing gear, and in whether a lift fan occupies the volume immediately behind the cockpit. That shared volume is the hardest constraint in the design, because the conventional and carrier variants carry fuel where the short-takeoff and vertical-landing variant, or STOVL variant, carries a fan, and the airframe has to be the same airframe for the commonality argument to pay. The STOVL variant trades fuel volume for vertical flight systems, and the carrier variant has a larger wing and stronger landing gear.

The size of that constraint can be estimated. The fan bay is at least the swept volume of the fan itself,

\[V = \frac{\pi D^{2}}{4} \ell \tag{49}\]

and for the fifty-inch fan over an assumed bay length between 1.2 and 1.6 metres that is 1.52 to 2.03 cubic metres. Filled with fuel at 800 kilograms per cubic metre instead,

\[W_{\text{fuel}} = \rho_f V = 800 \times 1.773 = 1{,}419 \ \text{kg} = 3{,}128 \ \text{lb} \tag{50}\]

so the hovering variant gives up roughly three thousand pounds of internal fuel to the fan, running from 2,681 pounds at the short bay to 3,575 at the long one. That is the commonality argument’s bill, paid in range by the variant that can least afford it. The estimate is a lower bound, since the bay must also house doors, the drive shaft and the clutch.

The Flight Test Record

The Precedents

Two aircraft had already solved parts of this problem. The Harrier made vertical landing an operational reality from the late 1960s using a single engine with four rotating nozzles, and it was never supersonic. The Yak-141 was supersonic and hovered, using two dedicated lift engines and a main engine exhausting through a three-bearing swivel nozzle.

That last phrase also describes the X-35’s rear nozzle. Lockheed and Yakovlev entered a partnership in 1991 for further development of the Yak-141, and the resemblance between the two swivel modules is close and widely noted. How much of the X-35’s nozzle descends from that arrangement is disputed and this article does not attempt to settle it, but the concept was not invented at Palmdale and the article would be misleading if it implied otherwise. The X-35 reference credits a 1972 Convair design with pioneering the three-bearing swivel nozzle. The shaft-driven lift fan is the newer idea. The nozzle behind it has a longer history. Even the fan dates as a concept to the mid-1950s, and the X-35B was the first aircraft a shaft-driven lift fan lifted into the sky.

What Actually Flew

Aircraft	First flight	Flights	Notes
X-35A	24 October 2000	27 in 30 days	Conventional, completed 22 November 2000
X-35C	16 December 2000	73, 58 hours	Carrier variant, completed 11 March 2001
X-35B	23 June 2001, first vertical	23 June to 30 July 2001	Rebuilt from the X-35A

Lockheed Martin’s report at the end of the campaign gives the X-35B’s totals as 27 vertical landings, 14 short takeoffs, 18 vertical takeoffs, five supersonic flights and five aerial refuellings. A 2008 Lockheed Martin release gives 17 vertical takeoffs for the same campaign, with the same 14 short takeoffs and 27 vertical landings.

One number in the table is disputed, and this article records the disagreement without resolving it. Contemporary programme reporting gives the X-35A 27 flights in thirty days, while a later reference account gives 28 test flights. No conclusion here turns on which is right.

The Eleven Days That Contain the Answer

This section carries the article’s central evidence. Setting the X-35B’s flights out in order, with the first occurrence of each capability marked, does something no summary of Mission X does.

Date, 2001	Event	First of its kind for this aircraft
23 June	Vertical takeoff, hover, vertical landing at Palmdale	Yes
24 June	First sustained hover	Yes
late June	Seventeen vertical takeoffs, hovers and landings completed	No
9 July	In-flight conversion to hovering mode, aerial refuelling, and Mach 1.08, in one sortie	Yes, and this is the hard one
16 July	Short takeoff, wingborne to jet-borne transition, vertical landing	Short takeoff, yes
20 July	Mission X, short takeoff, Mach 1.05, vertical landing	No. Nothing on this sortie was new
26 July	Mission X repeated, then a sixty-knot short takeoff ending in a vertical landing at over 34,000 pounds	No
30 July	Campaign complete

By 16 July the aircraft had already flown every element of Mission X. It had converted between modes in flight, it had gone supersonic, it had taken off short, it had transitioned from wingborne to jet-borne flight, and it had landed vertically. Lockheed Martin’s programme general manager listed short takeoffs, transitions, hovers, vertical landings and supersonic flight as complete at the time, four days before the famous flight, and the pilot who flew Mission X later wrote that each event had been accomplished on a previous sortie.

And the 9 July sortie went faster than Mission X did. It reached an indicated Mach 1.08 against Mission X’s Mach 1.05, and it did so on the same flight as the aircraft’s first in-flight conversion to hovering mode and an aerial refuelling.

So Mission X contained no manoeuvre the aircraft had not already performed, and it was not the aircraft’s fastest flight. What it contained was the assembly. Assembly is a legitimate thing to demonstrate, but it differs from what the reputation implies.

Comparison With Ground Prediction

The Short Takeoff, Reconstructed

Two short takeoffs are documented well enough to be examined. On 20 July the Mission X takeoff left the ground at about eighty knots, and the pilot’s own account adds that this came after only 200 feet, at which point he vectored the thrust to 60 degrees and the aircraft left the ground. A short takeoff flown on 26 July, on the flight after that day’s Mission X repetition, used approximately five hundred feet of runway and left the ground at about sixty knots, and the same flight ended in a vertical landing at an aircraft weight of more than 34,000 pounds. That aircraft therefore weighed more than 34,000 pounds at takeoff. No Mission X weight is published, and the section headed The Takeoff Did Not Have to Be Short bounds it between 34,197 and 45,697 pounds.

At unstick the weight is carried by two things, and only two. Writing $L$ for wing lift, $T_v$ for whatever the lift system points downward and $W$ for weight, an aircraft leaves the ground once

\[L + T_v \ge W, \qquad L = \tfrac{1}{2} \rho V^{2} S C_L \tag{51}\]

The fan and the roll posts point downward whatever the rear nozzle does,

\[T_f = 20{,}000 + 2 \times 1{,}950 = 23{,}900 \ \text{lbf} \tag{52}\]

and a rear nozzle of thrust $T_r$ deflected by $\theta$ below the horizontal adds $T_r \sin\theta$. Assuming that the rear nozzle delivers its published 18,000 pounds force at eighty knots, the Mission X vectoring to 60 degrees gives

\[T_v = T_f + T_r \sin\theta = 23{,}900 + 18{,}000 \sin 60^{\circ} = 23{,}900 + 15{,}588 = 39{,}488 \ \text{lbf} \tag{53}\]

At eighty knots over 41.81 square metres of wing the dynamic pressure times area is

\[\tfrac{1}{2} \rho V^{2} S = \tfrac{1}{2} \times 1.225 \times 41.156^{2} \times 41.81 = 43{,}376 \ \text{N} = 9{,}751 \ \text{lbf} \tag{54}\]

so the lift coefficient the record requires is at most what the heaviest weight in the bracket demands,

\[C_L \ge \frac{W - T_v}{\tfrac{1}{2} \rho V^{2} S} = \frac{45{,}697 - 39{,}488}{9{,}751} = 0.637 \tag{55}\]

The finding is that the record cannot pin a lift coefficient. At any weight up to 39,488 pounds the vectored lift system alone exceeds the weight and the required coefficient is zero or negative, and at the ceiling of the bracket the wing need supply no more than a coefficient of 0.637. A Mission X unstick at eighty knots with the nozzle at 60 degrees is consistent with a wide range of wing lift, because the lift system was carrying at least 86 percent of the aircraft.

The 26 July takeoff can be read the same way, and it too leaves the coefficient open. At sixty knots

\[\tfrac{1}{2} \rho V^{2} S = \tfrac{1}{2} \times 1.225 \times 30.867^{2} \times 41.81 = 24{,}399 \ \text{N} = 5{,}485 \ \text{lbf} \tag{56}\]

and the deflection that balances the weight at unstick is

\[\sin\theta = \frac{W - T_f - C_L \, \tfrac{1}{2} \rho V^{2} S}{T_r} \tag{57}\]

which depends on both the unpublished weight and the unknown coefficient,

Weight, lb	Deflection at $C_L = 0$	Deflection at $C_L = 0.5$	Deflection at $C_L = 1.0$
34,000, the documented floor for that flight	34.13 degrees	24.13 degrees	14.86 degrees
45,697, the ceiling of the bracket	no balance	no balance	64.99 degrees

At the documented floor every entry is inside the swivel module’s ninety-five degrees, so at that weight the lift system could have balanced the aircraft at sixty knots with no help from the wing. At the ceiling of the bracket it could not, because its 41,900 pounds force falls short of the weight even with the nozzle pointing straight down, and the wing must then supply a coefficient of at least 0.692. The record is silent on how far the nozzle moved on 26 July, and the one deflection it does record, the 60 degrees of Mission X, is larger than most of the table requires.

The Conversion Corridor, Read From the Record

The conversion speed does not need the unstick coefficient, because the record answers it directly. On 9 July the aircraft climbed to 9,000 feet and engaged the lift fan at 180 knots, flying conventionally until that moment, so the wing was carrying the whole weight when the fan engaged. Evaluating at sea-level density, as the momentum drag figure also does, which is an assumption, the coefficient the wing was flying at follows from

\[C_L = \frac{W}{\tfrac{1}{2} \rho V^{2} S}, \qquad \tfrac{1}{2} \times 1.225 \times 92.6^{2} \times 41.81 = 219{,}588 \ \text{N} = 49{,}365 \ \text{lbf} \tag{58}\]

which for any weight between the 30,697 pound empty weight taken for the bracket and the 45,697 pounds of a full internal fuel load is

\[C_L = \frac{30{,}697}{49{,}365} = 0.622 \quad \text{to} \quad \frac{45{,}697}{49{,}365} = 0.926 \tag{59}\]

The X-35B made its first in-flight conversion where lift was already free. That is the safest place to engage a lift fan, because a failure of the engagement leaves an aircraft that is already flying. And it is still the point at which the momentum drag computed earlier is at its largest. The conversion was flown where lift was free and drag was most expensive, the right trade though not an obvious one. The speed below which the wing could not have carried the aircraft unaided depends on the wing’s usable lift coefficient, which no source gives, so this article does not state one.

The Ground Roll, and a Figure That Cannot Be Right

The 200 foot figure does not survive the arithmetic. Reaching eighty knots from rest in 200 feet takes a mean acceleration of

\[\bar{a} = \frac{V^{2}}{2 s} = \frac{41.156^{2}}{2 \times 60.96} = 13.89 \ \text{m/s}^{2} = 1.417 \, g \tag{60}\]

and even if every pound of the lift system’s published thrust pointed aft, with no drag and no rolling friction, the lightest weight in the bracket allows at most

\[\frac{a_{\max}}{g} = \frac{T_{\text{total}}}{W} = \frac{41{,}900}{34{,}197} = 1.225 \tag{61}\]

In fact only the rear nozzle points aft during a roll, and its 18,000 pounds force at that weight gives a frictionless, dragless minimum of

\[s_{\min} = \frac{V^{2}}{2 g \, T_r / W} = \frac{41.156^{2}}{2 \times 9.80665 \times 0.5264} = 164.1 \ \text{m} = 538.3 \ \text{ft} \tag{62}\]

So the 200 feet and the eighty knots cannot both describe a roll from brake release. The account was written for a general readership after the event, and one of the two figures, or what the distance was measured from, must differ from what the printed sentence says. The 2001 press release figure for that flight is the speed alone. The company’s 2019 account gives a 450-foot takeoff, which is also shorter than the 538 foot minimum, and this article relies on the speed.

The 26 July roll does close, and it leaves a margin. Taking the nozzle as pointing aft during the roll and moving only at unstick, which is what the Mission X account describes and is an assumption for 26 July, the equation of motion is

\[m \frac{dV}{dt} = T_r \cos\theta - \mu \left(W - T_v\right) - \tfrac{1}{2} \rho V^{2} S C_{D_0}, \qquad \theta = 0 \tag{63}\]

Writing $A$ for the constant part of the acceleration and $B$ for the quadratic drag coefficient divided by mass, this integrates in closed form to

\[s = \frac{1}{2B} \ln\!\left(\frac{A}{A - B V^{2}}\right) \tag{64}\]

and at the 34,000 pound floor for that flight, substituting $A = 5.104$ and $B = 4.151 \times 10^{-5}$,

\[s_{\min} = 93.69 \ \text{m} = 307.4 \ \text{ft} \tag{65}\]

The quoted roll $s_q$ needs a mean acceleration of

\[\bar{a} = \frac{V^{2}}{2 s_q} = \frac{30.867^{2}}{2 \times 152.4} = 3.126 \ \text{m/s}^{2} = 0.3187 \, g \tag{66}\]

against the acceleration available, which is $A$ less the drag term evaluated at half the squared unstick speed,

\[a_{\text{avail}} = A - \tfrac{1}{2} B V^{2} \tag{67}\]

Across the weight bracket for that flight,

Weight, lb	$A$, m/s²	$B$, 1/m	Minimum roll, ft	Quoted over minimum	Available, $g$	Share used
34,000	5.104	4.151 × 10⁻⁵	307.4	1.627	0.518	0.615
45,697	3.722	3.088 × 10⁻⁵	421.5	1.186	0.378	0.843

where the share used is $\bar{a} / a_{\text{avail}}$. The quoted five hundred feet is longer than the minimum at every weight in the bracket, by a factor between 1.186 and 1.627, so between 61.5 and 84.3 percent of the available horizontal thrust appears in the quoted distance. Thrust build-up from brake release accounts for part of the gap.

Acceleration was not scarce. An aircraft that can reach its unstick speed in between 307 and 422 feet and takes 500 is not straining, and there is no reason it should have been strained, because of the number in the next paragraph.

The Takeoff Did Not Have to Be Short

Total vertical thrust is 41,900 pounds force, and the largest weight it can hold up follows immediately,

\[W_{\max} = \frac{T_{\text{total}}}{g} = \frac{186{,}381}{9.80665} = 19{,}006 \ \text{kg} = 41{,}900 \ \text{lb} \tag{68}\]

The numerical coincidence between the weight limit in pounds and the thrust in pounds force is an artefact of the unit system rather than a result. At the 34,000 pounds the aircraft is documented to have weighed on the 26 July flight, the margin is

\[\frac{T_{\text{total}}}{W} = \frac{41{,}900}{34{,}000} = 1.232 \tag{69}\]

so at that weight the X-35B could have taken off vertically. It had already done so seventeen times in late June.

No takeoff weight or fuel state for Mission X itself has been published. The pilot’s own account records that the sortie followed a familiarisation flight and a hot refuelling, and that by the end fuel and time were short enough that the last set of test points was dropped. The weight is therefore bounded rather than known. Its floor is the empty weight plus the fuel the sortie burned, since the aircraft must have carried at least that much, and its ceiling is the empty weight plus the 15,000 pounds of internal fuel the aircraft could hold. Assuming that burn to be 3,500 pounds, and neglecting the pilot and the test instrumentation, both of which add to every weight in the bracket,

\[W_{\text{TO}} = W_{\text{empty}} + W_{\text{fuel}}, \qquad 30{,}697 + 3{,}500 = 34{,}197 \ \le \ W_{\text{TO}} \ \le \ 30{,}697 + 15{,}000 = 45{,}697 \ \text{lb} \tag{70}\]

The empty weight in that bracket is the least certain input, and no weighing record for the X-35B is public. The X-35 reference gives 26,500 pounds for the X-35A and 30,697 pounds for the X-35B. Another compilation gives about 22,000 pounds for the X-35A and about 23,500 pounds for the X-35B. The bracket takes the 30,697 pounds. Its excess of 4,197 pounds over the X-35A figure lies within five percent of the 4,000 pounds that the lift fan installation was reported in 1998 to add to the Lockheed Martin design. The compilation’s excess is 1,500 pounds, and its X-35A figure equals the dry weight of about 22,000 pounds in that year’s operational requirement, which suggests a requirement figure in place of a measured one. The lower figure would move both ends of the bracket down by 7,197 pounds, to between 27,000 and 38,500 pounds. The internal fuel figure also matches that requirement, which asked for 15,000 pounds or more, so the ceiling may describe the production design’s tanks more closely than the demonstrator’s.

At the ceiling the margin is

\[\frac{T_{\text{total}}}{W_{\text{TO}}} = \frac{41{,}900}{45{,}697} = 0.9169 \tag{71}\]

which is below unity, so at full internal fuel the X-35B could not have taken off vertically at all. Vertical takeoff needs a weight below 41,900 pounds, which is a fuel load below 11,203 pounds, or about three quarters of the internal capacity, before the 3.354 percent of thrust that the corrected-flow relation above removes for a ten kelvin inlet temperature rise is counted. Taken at the round 40,000 pounds of vertical force that the 2001 releases credit to the X-35B, the limit falls to a fuel load of 9,303 pounds, or 62 percent of capacity, and the margin at 34,000 pounds falls to 1.176. Under the lower compilation empty weight the margin at full internal fuel would instead be 1.088. Every X-35B vertical takeoff, hover and landing was also flown at 2,500 feet elevation in temperatures up to 94 degrees Fahrenheit, conditions that the sea-level standard thrust does not describe.

So the claim holds only in a narrowed form. At 34,000 pounds, and at any Mission X takeoff weight with well under three quarters of the internal fuel, the X-35B could have taken off vertically, and the short takeoff demonstrated a technique rather than relieving a constraint. On the 30,697 pound empty weight, above about three quarters the weight exceeds the sea-level vertical thrust, short of it the margin is smaller than what temperature and elevation plausibly consume, and the fuel Mission X carried has never been released. A short takeoff exists in the operational requirement because the aeroplane that matters will be heavier than its vertical thrust, and will need wing lift to get airborne with a useful load. The record does not show the demonstrator in that condition on 20 July, and it does not exclude it.

The Supersonic Leg Was Thermally Free

Mission X reached Mach 1.05 at twenty-five thousand feet, and the conditions there follow from the standard atmosphere. Below the tropopause the temperature falls linearly and the hydrostatic equation integrates to a power law,

\[T = T_{\text{SL}} - Lh \qquad \text{and} \qquad p = p_{\text{SL}} \left(\frac{T}{T_{\text{SL}}}\right)^{\frac{g_0}{RL}} \tag{72}\]

whose exponent is

\[\frac{g_0}{RL} = \frac{9.80665}{287.05 \times 0.0065} = 5.2559 \tag{73}\]

At 7,620 metres this gives a static temperature of 238.62 kelvin and a pressure of 37,601 pascals, so the density and speed of sound are

\[\rho = \frac{p}{RT} = 0.5489 \ \text{kg/m}^{3} \qquad \text{and} \qquad a = \sqrt{\gamma R T} = 309.7 \ \text{m/s} \tag{74}\]

and the aircraft was travelling at 325.2 metres per second. The density ratio against sea level is 0.4481, which is the number the thrust available depends on. The stagnation temperature follows from the energy equation,

\[T_0 = T + \frac{V^{2}}{2 c_p} = 238.62 + \frac{325.2^{2}}{2 \times 1004.7} = 291.2 \ \text{K} \tag{75}\]

which is 18.1 degrees Celsius. The hottest air the airframe met during its supersonic dash was 3.1 kelvin warmer than a standard day at sea level.

There was no thermal event. Kinetic heating at low supersonic speed is negligible, and any argument that sequencing a supersonic dash before a vertical landing subjected the lift system to a hot start has no support.

Nor was thrust scarce, and the drag can be built up from its parts rather than taken as one lumped coefficient. The dynamic pressure is

\[q = \tfrac{1}{2} \rho V^{2} = \tfrac{1}{2} \times 0.5489 \times 325.2^{2} = 29{,}018 \ \text{Pa} \tag{76}\]

which is 29,018 pascals, and the lift coefficient the aircraft needs at that pressure is small,

\[C_L = \frac{W}{qS} = \frac{151{,}240}{29{,}018 \times 41.81} = 0.1247 \tag{77}\]

The wing’s aspect ratio is $b^2/S = 2.42$, so with an assumed Oswald efficiency of 0.75 the induced drag coefficient is

\[C_{D_i} = \frac{C_L^{2}}{\pi \, \mathrm{AR} \, e} = \frac{0.1247^{2}}{\pi \times 2.42 \times 0.75} = 0.002726 \tag{78}\]

which is negligible, so the dash is a pure zero-lift and wave-drag problem. Adding an assumed subsonic zero-lift coefficient of 0.018 and a wave-drag increment of 0.017 at the transonic peak,

\[C_D = C_{D_0} + C_{D_w} + C_{D_i} = 0.018 + 0.017 + 0.002726 = 0.03773 \tag{79}\] \[D = q S C_D = 29{,}018 \times 41.81 \times 0.03773 = 45{,}771 \ \text{N} = 10{,}289 \ \text{lbf} \tag{80}\]

Thrust available falls with density, and taking the usual power-law form,

\[T = T_{\text{SL}} \sigma^{n} = 40{,}000 \times 0.4481^{0.7} = 40{,}000 \times 0.5701 = 22{,}805 \ \text{lbf} \tag{81}\]

so 22,805 pounds force is available, against a drag of 10,289.

The exponent is assumed and the conclusion does not depend on it. Across values from 0.6 to 1.0 the thrust available runs from 24,711 down to 17,925 pounds force and the ratio of thrust to drag from 2.589 to 1.878, so the margin survives the range. Taking the build-up,

\[\frac{T}{D} = \frac{22{,}805}{10{,}289} = 2.216 \qquad \text{or} \qquad \frac{D}{T} = \frac{10{,}289}{22{,}805} = 0.451 \tag{82}\]

so holding the dash uses 45.1 percent of the thrust available. The ratio of 2.216 stands against 2.389 from a lumped coefficient of 0.035, which would have given a drag of 9,546 pounds force. The two estimates differ by eight percent and neither is close to the value that would make Mach 1.05 difficult.

The aircraft was not working to hold Mach 1.05. It was flying at the target speed of the test, on a demonstrator that reached Mach 1.2 on a later flight of 26 July, and the 9 July sortie had already reached Mach 1.08.

The Vertical Landing Was the Easiest of the Three

The vertical landing came last, which means it came at the lowest weight of the sortie. Every pound of fuel burned during the climb, the dash and the recovery is a pound the lift system does not have to hold up.

With the same assumed burn of 3,500 pounds the landing weight is $W_{\text{land}} = W_{\text{TO}} - W_{\text{fuel}}$, and the ordering improves the margin by the factor

\[\frac{T_{\text{total}} / W_{\text{land}}}{T_{\text{total}} / W_{\text{TO}}} = \frac{W_{\text{TO}}}{W_{\text{TO}} - W_{\text{fuel}}} \tag{83}\]

which needs no thrust figure at all. Across the takeoff-weight bracket of the previous section,

Takeoff weight, lb	Takeoff margin	Landing weight, lb	Landing margin	Gain from the ordering
34,197, the floor	1.225	30,697	1.365	1.114
45,697, the ceiling	0.917	42,197	0.993	1.083

The ordering helps across the bracket, but it does not rescue the ceiling. The landing is always the lightest point of the sortie and the gain from the ordering runs from 1.083 to 1.114, but at the ceiling the landing margin is 0.993, and after the 3.354 percent loss of a ten kelvin inlet rise it falls further,

\[\frac{T_{\text{total}}}{W_{\text{land}}} \cdot \frac{T_{\text{amb}}}{T_{\text{amb}} + \Delta T} = \frac{41{,}900}{42{,}197} \times \frac{288.15}{298.15} = 0.960 \tag{84}\]

The vertical landing that ended Mission X therefore bounds its takeoff weight. With the assumed burn the landing weight lies within the sea-level vertical thrust only for a takeoff weight below 45,400 pounds, which excludes the top of the bracket. At the round 40,000 pounds of the 2001 releases the bound is 43,500 pounds, and a hot day lowers it further. What the bracket removes is the single figure. The documented 34,000 pounds of 26 July lies below the floor of the bracket, and with the assumed burn it would imply a landing weight of 30,500 pounds, under the empty weight the bracket uses, so it is not a Mission X case.

The three events were flown in the order that makes each of them easiest. The short takeoff came first, when the aircraft was heaviest and a rolling start was most useful. The supersonic dash came in the middle, where it burned the fuel. The vertical landing came last, when the aircraft was lightest and the manoeuvre most comfortable. An operational sortie would be flown in that order too, so the profile is not being criticised. It does not test a worst case, and it was never claimed to.

The worst case for this architecture is a vertical landing at high weight with stores still aboard, which is the bring-back problem the previous article examined in detail for the rival. Mission X did not go near it.

What the Data Changed

The Answer

Mission X was evidence for one proposition and display for another, and the two are easy to conflate.

It is genuine evidence that the installation requires no reconfiguration between hovering and supersonic flight. That is a real architectural property, the rival did not have it, and a single sortie moving through both regimes demonstrates it as directly as anything could.

It is not evidence that the combination itself was new, and a claim often made for Mission X is wrong. The Yakovlev Yak-141 was a supersonic design that first flew in 1987 and made its first full transition in 1990, so a vertical-landing aircraft capable of supersonic flight without reconfiguration existed more than a decade earlier. What was new on 20 July 2001 was the sequence in one sortie, not the capability.

It is not evidence that any of the three regimes was individually difficult for this aircraft, because the arithmetic shows that none of them was. The short takeoff was flown by an aeroplane that could have gone straight up unless it carried nearly full internal fuel, and its fuel load is not on record. The supersonic dash, as computed under The Supersonic Leg Was Thermally Free, raised the stagnation temperature by three kelvin over a sea-level standard day and used 45.1 percent of the thrust available. The vertical landing happened at the lightest the aircraft had been on that sortie.

And the sortie was not where the engineering risk was retired. Every element had been flown already, the first in-flight conversion had happened on 9 July, and that sortie went faster. The information was retired on 9 July and the demonstration was performed on 20 July.

No one is at fault here. A demonstration exists to make something legible to people who will not read a flight test report, and Mission X did that better than any report could. But a flight that transfers no new information to the engineers and a great deal to everyone else is a display, and calling it by its name costs the programme nothing.

What the Programme Settled

The programme established that a shaft-driven lift fan works on an aeroplane, which had never been shown at this scale or this power, and the team received the Collier Trophy for 2001 on that basis. The fan’s open literature began before the flights and continued after them. The shaft-driven lift fan propulsion system and lift concept for the Joint Strike Fighter are described in Bevilaqua 1997 and Winfree 1998, and the fan is treated in a study of the flow characteristics of a shaft driven lift engine in 2002 and a forced response analysis of a shaft-driven lift fan in 2003. It established that the clutch, gearbox and drive shaft survive repeated engagement in flight. It established that mode conversion can be flown as a routine event rather than as a test point. And it established, by the counter-rotation argument above, that a fan of this power can be installed without consuming the aircraft’s roll authority.

What It Fed Into

The architecture went into production essentially unchanged in principle, which is unusual. The production lift system kept the shaft drive, the counter-rotating fan, the clutch, the three-bearing swivel module and the roll posts.

The literature followed the aircraft and left the designation behind, the mirror image of the previous two articles’ finding. The X-33 and the X-34 each all but stopped generating literature under their own names once they were cancelled, and this article’s subject shows the control case. The X-35’s own trace is also thin, and for the opposite reason. The work did not stop. It changed name.

What It Failed to Influence

The demonstration did not settle the weight question, which the production programme had to answer next. In 2004 engineers removed more than 2,700 pounds of unwanted estimated weight from the STOVL design, and nothing in the 2001 campaign predicted that need or could have. A demonstrator that weighs 34,000 pounds tells you very little about an aeroplane that will weigh far more, and the architecture’s thrust margin is the quantity that weight growth attacks.

The Contemporary Literature

Cluster	Records
Powered lift, V/STOL and STOVL aircraft	847
Flight control, control allocation and handling qualities	287
Jet impingement, ground effect and hot gas ingestion	318
Electric, distributed and hybrid propulsion and electric vertical takeoff	434
Rotors, propellers, actuator discs and momentum theory	400
Transonic and supersonic drag	151
Fan, compressor and counter-rotating stages	273
Clutches, gears and drivetrains	202
Inlets, intakes and diffusers	291
Engines, thrust and installed performance	153
Nozzles and thrust vectoring	197
Lift fans, ducted fans and the fan in the wing	226
Fighter programmes, defence acquisition and cost	109
Weight, sizing and aircraft design	46
Aircraft performance, takeoff, landing and ship operation	66
Kinematics of joints, mechanisms and manipulators	142
The atmosphere, temperature and aerodynamic heating	20
Fuels and fuel properties	23
Aircraft, jet and rotor acoustics	21
Ejectors and thrust augmentation	90
High-temperature and rotating seals	15
Total	4,311

This article surveys the current literature on its subject as well as studying its aircraft. For this subject the survey is unusually rewarding, because almost every question the X-35 raised is being asked again now by people building other kinds of vehicle.

Powered Lift Moved to Electric Aircraft and Took the Physics With It

The single largest change since 2001 is that the momentum theory in this article stopped being a military speciality. Disc loading, figure of merit, hover efficiency and outwash are now the working vocabulary of electric vertical-takeoff aircraft, and nearly all of that literature is recent. Of the 434 records in the cluster on electric, distributed and hybrid propulsion below, 415 were published in 2015 or later. Distributed and hybrid electric propulsion are reviewed in Kim et al. 2018b and Wall and Meyer 2017, and the actuator disc is applied to rotor and wing interaction in hover in Chen and Hubner 2020 and to rotor flow in Barakos et al. 2020. Records on the momentum theory they share form the cluster on rotors, propellers, actuator discs and momentum theory.

The relation is identical and the answer comes out the other way. Thrust per unit power is inversely proportional to jet velocity, so a designer free to choose disc area will choose a large one. The X-35’s fan sits at 70.2 kilopascals of disc loading because it had to fit inside a supersonic fighter. An electric aircraft with no such constraint runs a far lower disc loading and gains enormous hover efficiency from it. The X-35 is the extreme high-disc-loading end of the trade the current literature explores at the other end.

The Lift Fan Itself

The shaft-driven lift fan remains a nearly unique artefact and its literature is correspondingly small. Of the research records in this survey, 70 name a lift fan in their titles, and 43 of those date from 1975 or earlier. What has grown instead is the turbomachinery beneath it. Counter-rotating stages, which the X-35 adopted for the torque reason set out earlier, are now studied for their own aerodynamic merits, and 76 of the 105 titles that name counter-rotation or contra-rotation date from 2015 or later. The modern work on two-stage counter-rotating design and on matching the speeds of the two rotors, in Sun et al. 2017 and Ai et al. 2018, and the ducted contra-rotating lift fan of Deng and Ren 2017 are where a reader should go for the fan itself rather than to anything carrying the aircraft’s name. The clusters on lift fans, ducted fans and the fan in the wing, and on fan, compressor and counter-rotating stages, hold these records.

The Force the Conversion Makes Has Moved to Electric Aircraft Too

The momentum drag this article computes has almost no contemporary literature under that name and a large one under others. One research record names momentum drag or ram drag in its title, the transition strategy for an annular lift fan aircraft of Jiang and Zhang 2021. A vehicle that ingests air through a lifting device while moving forward meets the identical problem, and the vehicles doing that now are electric.

The modern vocabulary is boundary layer ingestion, distributed propulsion installation and the tiltrotor or tiltwing conversion corridor. The last of those is the closest analogue, because this article examined a conversion corridor when it found that the X-35B engaged its fan at 180 knots while flying conventionally, with the wing already carrying the whole weight. The corridor is optimized in Righetti et al. 2017, its interaction effects are treated in Appleton et al. 2021 and Tran and Lim 2022, and it is derived for an electric tiltrotor in Choi et al. 2025b. The corridor records fall under the cluster on powered lift, V/STOL and STOVL aircraft, and the boundary layer ingestion records under the cluster on inlets, intakes and diffusers. An electric vehicle with many rotors faces the same trade between converting early, where the lift system must carry weight, and converting late, where it must absorb drag.

The Swivel Module’s Kinematics Live in Robotics Now

The canted-joint geometry in this article has a small aeronautical literature and a large one elsewhere. Since 2014 a few papers treat the three-bearing swivel duct nozzle itself, its deflection control in Wei et al. 2019, a scaled nozzle and its rotary drive in Xiangyang et al. 2019 and Qi et al. 2020, and a design method in Shi et al. 2026. Spatial mechanisms, constant-velocity couplings and the synthesis of linkages that convert rotation into controlled angular deflection are studied far more widely in robotics and machine design, as in Kong 2016b and Arrouk et al. 2018, and the kinematics are best read there. The cluster on kinematics of joints, mechanisms and manipulators collects them.

The high-temperature rotating seal is the part that stayed aeronautical, because it is the requirement that makes the mechanism hard rather than the geometry. The thermal protection of the swivel nozzle’s bearings is the subject of Zhang et al. 2025c and Jinxin et al. 2026, and the cluster on high-temperature and rotating seals lists that work.

Fuel Density Became an Active Subject

The fan-bay calculation in this article assumes a fuel density, and in 2001 that would have been a table lookup. It is now a research subject, because sustainable aviation fuels and their blends have densities that differ from conventional kerosene, and a volume-limited aircraft feels that difference directly. The density of jet fuel blends is predicted in Kurt 2026, high energy density fuels are designed in Rijal et al. 2025, and the volume swell of drop-in fuels is modelled in Kosir et al. 2020. The rest of the cluster on fuels and fuel properties concerns the composition and properties of alternative fuels and their effect on engine performance and on aircraft missions. An aeroplane that gave up three thousand pounds of fuel volume to carry a fan is the kind that would.

The Ground Environment Became a Computational Subject

Hot gas ingestion was being computed by 1990, and its literature stops with the programme. The hot gas environment around a STOVL aircraft in ground proximity is measured in Sullivan and Murthy 1990 and computed in Tafti and Vanka 1990, ingestion is calculated in VanOverbeke and Holdeman 1990, and the environment of a hovering jet STOVL aircraft is set out in Kuhn et al. 1993a. Every one of the 28 research records whose titles name hot gas ingestion, recirculation or environment, or reingestion, was published between 1968 and 2002.

What became computational is jet impingement, and the shift is one of proportion. Of the 205 records in the cluster on jet impingement, ground effect and hot gas ingestion published through 2001, 26 name a computational method in their titles, against 36 of the 88 published from 2015 onward. The unsteady pressure and thermal loading a landing surface sees is measured and computed in Hromisin et al. 2015 and Crowell and Myers 2016, and supersonic impingement on a jet blast deflector and on a carrier deck is treated in Worden et al. 2016 and Yue et al. 2015a.

Drivetrains, Clutches and the Energy That Has to Go Somewhere

The halving identity in this article is drivetrain knowledge, and the literature that holds it is largely automotive and rotorcraft. Of the 121 research records whose titles name a clutch, six name an aviation, aerospace or STOVL use, among them Bian et al. 2025 and the dry friction clutch of STOVL aircraft in Zhu et al. 2026, and the engagement of a shaft-driven lift fan is modelled and controlled in Jiang et al. 2023b. The contemporary work on dry and wet clutch thermal modelling, as in Pisaturo et al. 2015 and Xiaozeng et al. 2015, applies directly to the scheduling of a mode change, and rotorcraft drive systems appear in Stevens et al. 2015. All of these sit in the cluster on clutches, gears and drivetrains.

Transition, Control Allocation and Hovering

Control allocation is almost entirely a recent literature. An aircraft with more effectors than axes has to decide how to distribute a demand among them, and in 2001 that was a specialist topic within powered lift. It is now a general problem in flight control, driven by electric aircraft with many rotors and by tailless configurations. Of the 105 research records whose titles name control, thrust or torque allocation, 96 were published in 2015 or later. Allocation is applied to a tailless aircraft with innovative control effectors in Matamoros and de Visser 2018, to a hexacopter in Nguyen et al. 2018 and to a tilt-rotor in its transition in Zhang et al. 2019c, and the general problem is surveyed for marine vessels in Johansen 2016. The cluster on flight control, control allocation and handling qualities holds this work.

Nozzles, Inlets and Installed Performance

Thrust vectoring outlived this application, and much of its recent literature turns the jet without moving the nozzle. Of the 101 research records from 2015 onward whose titles name thrust vectoring or vectored thrust, 42 concern fluidic methods, by secondary injection, bypass ducts, dual throats, shock vectoring, counterflow, coflow or the Coanda effect, as in Das et al. 2024, Kara and Kurtuluş 2024 and Shukla et al. 2026. The diverterless inlet passed from the demonstrator to the production aircraft, whose redesigned three-sided cowl retains the diverterless design, and boundary-layer ingestion into a diverterless intake is measured in Rein and Koch 2015. Installed performance accounting, the proper home of the thrust lapse in this article’s dash calculation, remains the least glamorous and most consequential part of the subject, as installed performance seeking control in Sun et al. 2015 shows. Three clusters cover this ground, those on nozzles and thrust vectoring, on inlets, intakes and diffusers, and on engines, thrust and installed performance.

Performance, Weight and the Programme

Weight growth is the subject this article’s aircraft failed to illuminate, and the literature in this survey treats weight as something to estimate rather than to track. No research title in the survey names weight growth. The 26 titles that name weight or mass estimation treat it as a design method, as in Nigam et al. 2015, Dababneh and Kipouros 2018 and Horvath and Wells 2018. The production programme met the other side of the question after the demonstrator had answered every question it was asked, when more than 2,700 pounds of unwanted estimated weight had to be removed from the STOVL design in 2004, and in this survey weight as a programme risk appears only indirectly, through cost growth, as in Gideon and Wasek 2015. They appear in the clusters on weight, sizing and aircraft design, and on fighter programmes, defence acquisition and cost.

Acoustics Became a Binding Constraint Somewhere Else

Noise barely constrained the X-35 and it constrains its successors severely. The acoustic literature around vertical lift has grown because community acceptance is now a design driver for civil vertical flight in a way it never was for a fighter demonstrator at Edwards. The community noise of vertical takeoff personal air vehicles is predicted in Kim et al. 2016, and the acoustic environment of the production aircraft’s own vertical landings and of short takeoffs from a carrier is measured in Reichman et al. 2016 and Wall et al. 2017. The cluster on aircraft, jet and rotor acoustics contains them.

Method, Uncertainty and Computation

The methodological change since 2001 is larger than any single technical one. Uncertainty quantification, surrogate modelling and machine learning now sit between the wind tunnel and the design, and a reconstruction of the kind this article performs by hand would today be posed as an inference problem with stated priors, as the probabilistic flight envelope of an over-actuated aircraft in Yin et al. 2019, the neural-network system identification of Harris et al. 2016 and the kriging-assisted ducted fan optimization of Qing et al. 2019 illustrate. That is better practice and it would not have changed any conclusion here, because the quantities that mattered were bracketed rather than estimated. These records sit in the clusters on flight control, control allocation and handling qualities, and on lift fans, ducted fans and the fan in the wing.

Powered lift, V/STOL and STOVL aircraft

Powered-lift aircraft of every kind, from the period jet-lift and lift-fan concepts and the Harrier to tiltrotors, tailsitters and the hover and transition of unmanned vertical-takeoff vehicles. Of these records, 545 were published in 2001 or earlier, and 234 in 2015 or later.

847 records. [A Novel Sliding Mode 2020] [Adamson 1968] [Adelt 1983] [Adibhatla 1993] [Adibhatla 1994] [Advanced Short Takeoff 1995] [Ahmed Snikdha and Chen 2023] [Ahn et al. 2023] [Alexander et al. 1986] [Alscher et al. 1966] [An H infinity Loop-Shaping 2000] [Anderson 1983] [Anderson and Foster 1984] [Anderson et al. 1983] [Anderson 1979] [Anderson and Schroers 1972] [Anderson 1960] [Andrew 1972] [Appleton et al. 2021] [Application of Fluidic Thrust 2024] [Armutcuoglu et al. 2004] [Aroussi 2026] [Asri et al. 2019] [Assessing Competitive Strategies 2001] [Atkinson et al. 2013] [Aulehla and Kissel 1982] [Autelitano et al. 2016] [Axelson and Upton 1970] [Axten and Johnson 2020] [Axten and Johnson 2021] [Bach and McNally 1988] [Balaban and Erdem 2022] [Banazadeh and Taymourtash 2016] [Bando et al. 1993] [Baron 1983] [Bates et al. 2003] [Bath et al. 2021] [Bath et al. 2022] [Bath et al. 2023] [Batterton and Blaha 1987] [Beans 1995] [Bear et al. 1979] [Beard and Foley 1983] [Beard and Foley 1982] [Bedford 1962] [Beilman 1983] [Beisbier 2002] [Bell Aerospace Co Buffalo Ny 1970] [Belluomini et al. 2023] [Berg et al. 1988] [Bertelsen 2016] [Berton et al. 2000] [Bevilaqua 2009a] [Bevilaqua 2009b] [Bhagwat 2013] [Bhandari and Chakraborty 2026a] [Bhardwaj and Holzapfel 2024] [Biesiadny et al. 1993] [Biesiadny 1991] [Birckelbaw and Nelson 1992] [Birckelbaw 1992] [Birckelbaw et al. 1994] [Birkler 2001] [Bishop et al. 2000] [Blaha and Batterton 1990] [Bland 1971] [Bodden and Virnig 1994] [Bode et al. 1978] [Bogdan 2015] [Boles and Stockman 1979] [Borchers et al. 1992] [Boruff and Roch 1981] [Bottorff 2004] [Bowling et al. 1969] [Brady and Gururajan 2025] [Brady and Gururajan 2026] [Breul 1963] [Brown 1965] [Brown 1989] [Brown and Fischer 1967] [Brown and Fisher 1968] [Brown et al. 2009] [Brown 1978] [Buchholz 2002] [Bucknell 1987] [Bucknell et al. 1990] [Bulat and Minin 2017] [Bulat and Minin 2018] [Butler et al. 1966] [Caffee 1985] [Caldwell and Lafavor 1980] [Calise and Kramer 1982] [Calvano and Harney 1998] [Calvert 1997] [Camacho 1991] [Campbell and Quinn 1974] [Campos 2001] [Cao et al. 2022b] [Cappetta 1993] [Cardenas 2022] [Carico and Garcia-Otero 1995] [Carlson and Zhao 2002] [Carpenter and Gotlieb 1970] [Carpio-Alemán et al. 2016] [Carr 1984] [Cassinelli et al. 2023] [Chaderjian et al. 2002a] [Chaitanya et al. 2025] [Challier and Hey worth 1964] [Chance Vought Corp Dallas Tx 1979] [Chang et al. 2018] [Chapman 2018a] [Chapman 2018b] [Chapman 2018e] [Chapman 2018f] [Chapman 2018c] [Chapman 2018d] [Chapman 2019] [Chen et al. 2004] [Chen et al. 2018c] [Chen et al. 2019] [Chiappinelli et al. 2019] [Chin 1988] [Chou and Hwang 1984] [Chow 1993] [Blanken and Whalley 1993] [Chung et al. 1993b] [Chung et al. 1993a] [Clark 1965] [Clark and Vasta 1984] [Clark et al. 1982] [Clark 1975] [Clark 1980] [Clough 1990] [Clymer and Flora 1973] [Cochrane and Boissevain 1978] [Coe and Riley 1988] [Cohan and Hirsh 1966] [Coles 1968] [Conference on V/Stol Aircraft 1960] [Conlon and Bowles 1977] [Conlon and Bowles 1978] [Conner and Wellman 1994] [Coolican 2002] [Coons 1987] [Coopmans et al. 2022] [Coplin 1966] [Corle et al. 2019] [Corliss et al. 1977] [Corliss et al. 1978] [Coty and Kesling 1967] [Cox and Abbott 1966] [Cox and Kirby 1986] [Cox and Roskam 1990] [Crafa and Reed 1980] [Crandall et al. 1973] [Crossley and Rutherford 1995] [Cui et al. 2019] [Cummings and Hall 2002] [Cunningham and Boytos 1988] [Curry et al. 1965] [Curtiss 1970] [Curtiss 1971] [Curtiss and Howard C. 1969] [Daud Filho and Belo 2023] [Davenport et al. 1972] [DE Decker 1966] [de Matteis et al. 1998] [De Persis et al. 2001] [刘 2024] [Defense Science Board Washington Dc 1979] [DeHoff 1979] [DeJesus 2013] [Del Bianco et al. 1997] [Denham 2002] [Denham and Paines 2008] [Denning and Mitchell 1986] [Çakir and Kurtuluş 2021] [Design of the Circulation 1979] [Desilets] [Deveaux 1965] [Di et al. 2025] [Diekmann 2017] [Digital Engine Control 1982] [Dinca et al. 2019] [Doff-Sotta et al. 2025] [Dolan 1964] [Dollyhigh et al. 1984] [Dong et al. 2021] [Dorr et al. 1992] [Douglas et al. 1990] [Drinkwater and Rolls 1962] [Drinkwater et al. 1965] [Dukes 1970] [Durston and Smith 1981] [Durston and Stonum 1987] [Durston and Stonum 1988] [Dyke 1963] [Egerton and Fitzpatrick 1967] [Eilertson 1977] [Elliott and Schreiber 1964] [Elliott and Simmons 1987] [Enenakpogbe et al. 2025] [Engelland 1991] [Englar 1974] [Englar 1975] [Englar 1987] [Englar 1988] [Englar and Campbell 2002b] [Englar and Campbell 2002a] [Englar and Kirkpatrick 1969] [Englar et al. 1977] [Eshleman et al. 1986] [Esker and Debonis 1991] [Fan et al. 2022] [Fan et al. 2025] [Farley 1968] [Farley 1971] [Farris et al. 1983] [Faye 1960] [Feddersen and Cea 1977] [Fejtek and Roberts 1992] [Felker et al. 1986] [Feng Lin et al. 1999] [Fenwick 1967] [Ferrier et al. 2024] [Fielding 1982] [Fielding and Lodge 2000] [Final Assembly and Checkout 2002] [Fletcher 1962] [Flow Visualization Studies 1991] [Foley and Woodrey 1980] [Foster et al. 1987] [Fozard 1978] [Fozard 1979] [Fozard 1986] [Franciscus and Luidens 1984] [Franklin 1993c] [Franklin 1993a] [Franklin 1994] [Franklin 1996] [Franklin and Engelland 1991] [Franklin and Engelland 1993] [Franklin and Innis 1977] [Franklin and Stortz 1993] [Franklin et al. 1986] [Franklin et al. 1988] [Franklin 1986] [Franklin and Anderson 1984] [Franklin and Innis 1972] [Franklin and Innis 1974] [Franklin and Innis 1980] [Franklin 2000] [Franklin and Stortz 1989] [Franklin et al. 1989] [Franklin et al. 1990] [Fredericks et al. 2015] [Fredericks et al. 2016] [Frey 2011] [Friend 1964] [Frost and Bishop 1963] [Frost et al. 2002] [Furey 1983] [Gainutdinova and Gainutdinov 2018] [Galdieri et al. 1992] [Gallops et al. 1990] [Gamon 1988] [Garg 1993b] [Garg and Mattern 1991] [Garg and Mattern 1994] [Garg and Ouzts 1991] [Garg and Schmidt 1993] [Garg et al. 1990] [Garner 1967] [Gaston et al. 1984] [Gea et al. 1991] [George 1999] [Gerken 1979] [Gero 2001] [Getachew and Zeleke 2024] [Gibs et al. 1975] [Gielow 1971] [Gilbert 1985] [Gingras 1999] [Giurca 2014] [Goland et al. 1964] [Goldberger 1966] [Gorham 1977] [Govdeli et al. 2019] [Green and Andrews 1989] [Green and Bogle 1991] [Green and Zeckhauser 2019] [Greene 1977] [Greif et al. 1972] [Griffin 1983] [Groen 1988] [Grunwald 1964] [Guan et al. 2025] [Hahn and Wilson 1985b] [Hahn and Wilson 1985a] [Hall 1965] [Hange et al. 1996b] [Hange et al. 1996a] [Harding] [Hariharan et al. 2017] [Haro 2003] [Harradine 1977] [Hart et al. 2026] [Hartmann et al. 2016] [Hartmann et al. 2017] [Hartnett and Mittlesteadt 2000] [Hatta and Matsuki 1964] [Havey and Kline 1989] [Hebbar et al. 1999] [Hebert et al. 1970] [Hebert et al. 1973] [Hegarty et al. 1965] [Hegde 2020] [Hegde et al. 2019] [Helicopter and V/Stol Aircraft] [Henderson 1964] [Henderson and Walters 1981] [Hess 1977] [Hess 1988] [Hill 1966] [Hill 1970] [Hill 1981] [Hill and Jenkins 1979] [Hindson et al. 1982] [Hirsh 1965] [Ho et al. 2019] [Hoffman 1971] [Hoh and Mitchell 1983] [Hollingsworth et al. 1977] [Holzhauser et al. 1972] [Hong et al. 2025a] [Hong et al. 2025b] [Hooker 1981] [Hoskin 1993] [Hoskin et al. 1991] [Hsin 1974] [Hu et al. 2024a] [Hu et al. 2024b] [Hua et al. 2025] [Huan et al. 2021] [Huang et al. 2020b] [Huang et al. 2022a] [Huang et al. 2022b] [Huang et al. 2024b] [Hughes 2017] [Huntley 1972] [Hutchison et al. 1983] [Hyde and Glover 1991] [Hynes et al. 1989] [Ilyas et al. 2023] [Imhof and Schork 1999] [Integration and Simulated Flight 1977] [Invernizzi et al. 2018] [Irvin and Swan 1956] [Isidori et al. 2001] [Franklin 1993b] [Jang et al. 2022] [Jenista and Sheridan 1987] [Jeong et al. 2026] [Jewell et al. 1979] [jian-jian et al 2019] [Jiang et al. 2023a] [Jimenez-Garcia et al. 2017] [Jin and Zhao 2025] [Jo and Kwon 2019] [Johns 1998] [Johnson and Craig 1974] [Johnson 2003] [Johnston 1965] [Johnston and Friend 1965] [Johnston et al. 1965] [Jones 1966] [Jones 2014] [Joppa 1969] [Kai 2024] [Kakavitsas et al. 2024] [Kalemaris and Cea 1977] [Kandath et al. 2019] [Kandel et al. 2022] [Kang 2022] [Kanistras et al. 2016] [Kappus 1969] [Kapstein 2004] [Kazan and Krause 1968] [Kazan and Krause 1967] [Keller 1969] [Keller et al. 2018] [Kentfield 1967] [Key 1971] [Kidwell 1981] [Kidwell and Rapp 1985] [Kidwell and Lampkin 1983] [Kim and Jo 2025] [Kim et al. 2016] [Kim et al. 2025] [Kimberlin 1987] [Kinzer 2008] [Kleckner 1973] [Klinar and Craig 1961] [Klingloff et al. 1965] [Knott 1977] [Koenig et al. 1977] [Kohn 1972] [Kohn 1983] [Koncsek and Syberg 1977] [Kozapalli and Warmbrodt 1997] [Krammer and Holzapfel 2023] [Krenkel and Salzman 1968] [Krepski and Hudson 1981] [Krimphove et al. 2023] [Krosche and Heinze 2015] [Kuang and Zhu 2015] [Kuhn 1979] [Kuhn 1980] [Kuhn 1981] [Kulhánek et al. 2023] [Kumon et al. 2010] [Kuntz et al. 1997] [Kurylowich and Ritter 1970] [Lacey and Miller 1977] [Lacey et al. 1979] [Landy and Kim 1984] [Laudeman 1972] [Lavi 1966] [Lavi 1967] [Lebacqz and Radford 1978] [Lebacqz and Radford 1979] [Lee et al. 1988] [Leovan 2019] [Levin et al. 2018] [Levine and Inglis 1989] [Levinsky and Ramsey 1972] [Levinsky et al. 1968] [Levinsky et al. 1969] [Levinsky et al. 1970] [Lewis 1989] [Lewis 2000] [Lewis and Lewis 1981] [Lewis and Simpkin 1981] [Li and Xia 2018] [Li et al. 2018] [Li et al. 2023a] [Li et al. 2024e] [Liao and Bang 2023] [Liao et al. 2024a] [Lichota 2023] [Lift Loss in Hover 2007] [Lim and Jung 2025] [Lind and Tamplin 1981] [Linnell 1963] [Lipera and Sandlin 1984] [Liu and Zhang 2024] [Liu et al. 2019] [Liu et al. 2022a] [Liu et al. 2022c] [Liu et al. 2022e] [Liu et al. 2024d] [Liu et al. 2025f] [Liu et al. 2026c] [Lollar and Matous 1963] [Lollar et al. 1965] [Lopez and Shen 1971] [Loth and McCormick 1986] [Loth et al. 1974] [Loth et al. 1976] [Lou et al. 2024] [Louthan 1980] [Love 1993] [Lowenberg and Jones 2003] [Lozano et al. 2022] [Lu and Terrier 2003a] [Lu and Terrier 2003b] [Lu et al. 2017] [Lu et al. 2019b] [Lu et al. 2022a] [Pyle 1971] [Saari 1958] [Maddock et al. 2011] [Maisel and Harris 1981] [Maita et al. 1983] [Maita et al. 1990] [Makarov 2019] [Mange et al. 2002] [Manley and von Klein 2002] [Manoilo 2025] [Mansell 1987] [Marchese 1963] [Marconi et al. 2002] [Margason 2002a] [Margason and Hoad 1979] [Margason and Kuhn 1988] [McKinney and Kirby 1964] [Mathews 1987] [Mathews and Rothstein 1998] [May and Widdison 1971] [May et al. 2024b] [May et al. 2024a] [May et al. 2026] [McCarthy 1992] [McCarthy 2002] [McCarthy and Kelly 1993] [McConnell 2006] [McCormick 1969] [McIntyre 1963] [McNally 1986] [McNally and Bach 1988] [Meiklem 1969] [Melo et al. 2026] [Mendenhall and Spangler 1976] [Mendenhall et al. 1972] [Merewether 1963] [Merrick 1981] [Merrick et al. 1991] [Merrick 1982] [Merrick 1984] [Meyer et al. 1991] [Michaels 1969] [Michaelsen 1971] [Migbee et al. 1987] [Mihalik and Keane 2022] [Mihaloew and Weiss 1989] [Mihaloew et al. 1981] [Mihaloew and Drummond 1989] [Miller 1973] [Miller et al. 1981] [Mitchell et al. 1992] [Mixson et al. 1975] [Miyazaki and Tsubakino 2017] [Mo et al. 2024] [Moller 1985] [Moller 1998] [Momiyama 1977a] [Moorhouse 1990] [Moralez et al. 1987] [Moss 1995] [Moustafa et al. 2025] [Mrusek 2021] [Mueller et al. 2016] [Murakoshi 1969] [Murata et al. 2025b] [Murata et al. 2025a] [Mysko et al. 1993] [Nakaguchi 1967] [Naldi and Marconi 2009] [Naldi and Marconi 2011] [Naldi and Marconi 2013] [Nalls and Stortz 1993] [NASA Conference on V/STOL 1960] [Naumowicz et al. 1998] [Naumowicz et al. 1996] [Nelms 1978] [Nelms 1984] [Nichols and Englar 1980] [Nishimura 1980] [Nithya and Rashmi 2019] [Norman et al. 2018] [O’Brien and Delgado 2024] [O’Rourke and Rutherford 1991] [Okumoto and Elsanker 1973] [Okuno and Kawachi 1993b] [Okuno and Kawachi 1993a] [Omar and Lampkin 1977] [Operational Aspects 1969] [Ornelas 1985] [Ostheimer and Giguere 1963] [Owens et al. 2004] [Pang et al. 2024] [Patierno and Asdurian 1965] [Pauli et al. 1970] [Paulson 1981] [Paulson 1980] [Pavlov 2016] [Payne and Henry E. 1961] [Payne and McConnell 2004] [Pei et al. n.d.] [Peloquin et al. 2017] [Li et al. 2015] [Petit and Scholey 1973] [Petrov 1993a] [Petrov 1993b] [Philhower et al. 1998] [Pieper 1965] [Pirera 1983] [Pisano et al. 2025] [Platt 1991] [Platzer and Margason 1976] [Polak and George 1998] [Postlethwaite 1998] [Postlethwaite and Bates 1999] [Powered-Lift Aerodynamics and Acoustics 1976] [Price 1964a] [Price 1964b] [Pruyn and Taylor 1971] [Pryce and Hirschberg 2003] [Pryce et al. 2005] [Pulk and Stolarik 1977] [Qin 2023] [Qing et al. 2023] [Qiu et al. 2023a] [Quinto et al. 1993] [Rabin 1983] [Rae 1972] [Ramesh and Subbarao 2016] [Rand 1999] [Ransone 2002] [Rapp 1985] [Rau and Babiceanu 2018] [Reichman et al. 2016] [Ren and Zha 2024] [Representative Operations of V/STOL 2002] [Requirements for STOVL Integrated 1994] [Rhoades and Ybarra 1980] [Kuhn and McKinney 1965] [Richardson 1966] [Riddle et al. 1981] [Riesenfeld 1968] [Righetti et al. 2017] [Riley et al. 1989] [Ringland 1977] [Roberts 2002] [Robinson 2015] [Rolls and Aoyagi 1977] [Roltgen and Byrnes 1991] [Romine et al. 1989] [Roth 1993a] [Roth 1997] [Roth 1993b] [Ruan et al. 2025] [Rudolph 1972] [Ryan 1986] [Saddington and Knowles 1999] [Saddington and Knowles 2001] [Saetti 2025] [Sagan et al. 2021] [Saghafi and Banazadeh 2006] [Saghafi and Banazadeh 2007] [Salahudden et al. 2024] [Salisbury 2026] [Sambell 1972] [Sanchez-Rivera et al. 2020] [Sanders 1964] [Sandlin and Howard 1991] [Sandoz et al. 2018] [Saripalli 1995] [Saripalli and Farrell 1993] [Schaefer and Velten 1971] [Schaeffler et al. 1967] [Schierman and Lowell 1992] [Schmitz 1969] [Schneider 1989] [Schneider and Watt 1988] [Schroeder and Merrick 1990] [Schwartz and Shearer 1964] [Scientific and Technical Information Division 1966] [Scopes 2001] [Seitz and Goodson 1973] [Sellers and Szuch 1973] [Semelka and Rauleder 2026] [Senkans et al. 2021] [Serkin 2025] [Serovy and Kavanagh 1974] [Shanks et al. 1993] [Shanks et al. 2018] [Sheng et al. 2022] [Sheridan 1986] [Sheridan 1983] [Sherman 1964] [Sherman and Usab 1974] [Shin and Lee 2023] [Shovlin 1978] [Showers 1980] [Silva] [Silva et al. 2017] [Silva et al. 2019] [Silva-Martinez et al. 2015] [Sinacori 1970a] [Sinacori 1970b] [Sivrioğlu 2023] [Skelton 1968] [Smith 1966b] [Smith 1996b] [Smith 1996a] [Smith 1997b] [Smith 1997a] [Smith and Berry 2000] [Smith and McArdle 1990] [Smith and McArdle 1992] [Smith et al. 1973] [Smith et al. 1999] [Smith 1961a] [Soderman 1990] [Soderman and Foster 1988] [Solies 1992] [Sonkar et al. 2021] [Spratt 1990] [Sridhar and Smith 2026] [Sridhar et al. 2025] [Stapleford 1980] [Stark 2003] [Staruk and Datta 2019] [Staruk et al. 2017] [Stauffer et al. 1990] [Steele and Aurora 1978] [Steils 1965] [Stenberg 1983] [Stepniewski 1959] [Sternfeld and Hinterkeuser 1970] [Stewart and Paulson 1984] [STOL VTOL and V/STOL 1971] [Stone 2013] [Stone and Gutierrez 1972] [Strand et al. 1967a] [Strand et al. 1967b] [Structural Design 1969] [Struth 1999] [Stutz and Price 1964] [Sulkoske et al. 1977] [Swaim 1970] [Syamsuar 2017] [Szlenkier 1972] [Sørensen et al. 1996] [Tan et al. 2019] [Tanakitkorn et al. 2017a] [Tanakitkorn et al. 2017b] [Tang et al. 2025] [Tape and McIntyre 1990] [Terrier and Lu 2003] [The Hawker P1127 Vectored 1990] [Tich 1991] [Tindell and Flynn 1978] [Tran and Lim 2022] [Tran and Yeo 2022] [Tran et al. 2023] [Transition aerodynamics for close-coupled wing-canard configuration<149>V/STOL operations 1979] [Tullu and Jung 2026] [Turney and Allen 1980] [Urakubo et al. 2023] [V/STOL Propulsion Control Analysis 1981] [V/STOL 1971] [VAAC Harrier Trials 2001] [Vagianos and Rooney 1964] [Van Dalsem et al. 1990] [Van Nieuwstadt and Murray 1998] [Van Riper and Wood 2003] [Vandalsem et al. 1989] [Vectored Thrust 1992] [Verghese 2023] [Vertical Takeoff and Landing 2014] [Vertical/short takeoff and landing] [Viets 1974] [Vincent and Anex 1990] [Vinje and Miller 1973] [von Hlatky and Rice 2018] [VSTOL Systems Research Aircraft 1994] [Vucetic 2010] [Vucetic 2013] [Vucetic and Nossal 2013] [Nelms and Anderson 1984] [Wada et al. 2022] [Waesche and Midgal 1975] [Wakefield et al. 2019] [Walker and Allen 2002] [Wall 1989] [Walz 1976] [Wang and Ma 2021] [Wang et al. 2018a] [Wang et al. 2019] [Wang et al. 2020b] [Wang et al. 2022e] [Wang et al. 2022c] [Wang et al. 2022a] [Wang et al. 2024a] [Wang et al. 2025b] [Warakomski 1979] [Ward and Lewis 1987] [Wardwell et al. 1986] [Warner et al. 1986] [Warren and Floden 2001] [Watson 1980] [Watson 1981] [Watson et al. 1986] [Watson et al. 2019] [Watts et al. 1993] [Weber 1982] [Wechtler et al. 2025] [Wei 2016] [Wei Yuan and Katupitiya 2013] [West 1969] [Whatley et al. 1990] [White et al. 1985] [Widmayer and Tomassoni 1971] [Wilken 1991] [Hindson et al. 1993] [Willis 1980a] [Willis 1980b] [Willis and Genever-Watling 1977] [Wilson and Liperra 1984] [Wilson and White 1993] [Wilson and Wurts 1985] [Wilson et al. 1997] [Wilson et al. 1985] [Wilson et al. 1981] [Wilson and Mahoney 1988] [Winborn 1970] [Winick 1968] [Wlezien and Ferraro 1990] [Wlezien and Ferraro 1992] [Wood 1968] [Wu et al. 2019] [Xiang et al. 2025a] [Xu et al. 2025a] [Xu et al. 2027] [Yackle 1992] [Yamato et al. 1988] [Yamato et al. 1991] [Yang et al. 2024a] [Yang et al. 2024b] [Yangping and Honggang 2018] [YAV-8B Reaction Control System 1993] [AvMC et al. 2020] [Yu et al. 2025] [Zabinsky and Burnham 1977] [Zaffran and Erwes 2015] [Zafi and Chakraborty 2023] [Zalay et al. 1980] [Zaludin and Gires 2019] [Zaludin et al. 2021] [Zha and Ren 2023] [Zha et al. 2024] [Zhang and Qi 2024] [Zhang et al. 2019c] [Zhang et al. 2019d] [Zhang et al. 2024c] [Zhao et al. 2018] [Zhao et al. 2024a] [Zhao et al. 2026c] [Zhong et al. 2019] [Zhou et al. 2020] [Zhou et al. 2022a] [Zhu et al. 2025] [Zikyamov and Panayotov 2025] [Zola et al. 1984]

Flight control, control allocation and handling qualities

Flight control of powered-lift, hovering and over-actuated vehicles, control allocation among redundant effectors, integrated flight and propulsion control, and the handling qualities of hover and transition. Of these records, 112 were published in 2001 or earlier, and 153 in 2015 or later.

287 records. [Ahmed et al. 2025] [Air Force Test Pilot School Edwards Afb Ca 1969] [Altamirano et al. 2023] [Alwi et al. 2015] [Amato et al. 2022] [Antonakis and Biannic 2024] [Aouf et al. 2002] [Ashkenas 1965] [Babinsky 2014] [Baggi et al. 2020] [Baggi et al. 2022] [Baldini et al. 2020] [Bangert et al. 1983] [Bardera and Matías-García 2022] [Bardera-Mora et al. 2016] [Bates et al. 2000] [Bayati and Williston 1977] [Beale and Miller 1975] [Beaufrere 1988] [Behbahani et al. 2016] [Berry and Schweikhard 1976] [Bielat 1959] [Binwen Lu et al. 2016] [Blaha et al. 2023] [Bodson 2000] [Boland et al. 1993] [Bright and Simon 1992] [Buffington 1999a] [Buffington 1999b] [Buffington and Buffington 1997] [Burcham et al. 1990a] [Burcham et al. 1990b] [Burcham and Batterton 1976] [Burr 1968] [Caliskan and Hajiyev 2003] [Cao et al. 2022a] [Carlin and Blair 1983] [Carlin and Hastings 1978] [Cassaro et al. 2018] [Caton and Franke 1991] [Chen 2017] [Chen and Voulgaris 1998] [Chen et al. 2026b] [Chen et al. 2026a] [Chi et al. 2022] [Collins 2005] [Control Authority Assessment 1993] [Control System Design Using 1976] [Craig 1965] [Csank and Connolly 2015] [Cui et al. 2021] [Das et al. 2024] [de Castro and Brembeck 2019] [de Castro and Brembeck 2021] [de Vries and Van Kampen 2019] [Deere et al. 2003] [Deng and Tao 2025] [Ding et al. 2016] [Doman and Oppenheimer 2002] [Dong et al. 2020] [Dong et al. 2025a] [Du et al. 2023] [Duan and Okwudire 2018] [Dunbar et al. 2002] [Eilertson 1975] [Englar and Huson 1984] [Enns 2003] [Fan et al. 2018] [Fan et al. 2026a] [Fan et al. 2026c] [Fengyu Jin et al. 2018] [Fennell and Black 1982] [Flanders 1970] [Franklin and Innis 1978] [Franklin 1997a] [Frazzini 1970] [Friddell and Franke 1990] [Frost et al. 2009] [Fu et al. 2015] [Gal-Or et al. 1993] [Gao et al. 2026] [Garg 1993a] [Garg et al. 1989] [Garg et al. 1991] [Gatley et al. 2000] [Gatley et al. 2001] [Gatley et al. 2002] [Gerdes and Hynes 1971] [Gern et al. 2014] [Gilyard et al. 1991] [Gilyard and Orme 1992] [Goyal et al. 2025] [Griswold 2000] [Gundy-Burlet and Kaneshige 2001] [Halyo 1996] [Harefors and Bates 2003] [Harkegard 2003] [Harris et al. 2016] [Henderson and Lavretsky 1999] [Hill 1987] [Hirano et al. 2019] [Horn et al. 2014] [Hu et al. 2019] [Integrated Flight/propulsion Control 1985] [Ivler and Geyer 2024] [Jackson 1970] [Jacuzzi and Granlund 2019] [Jafari et al. 2022] [Jaw and Garg 2005] [Jente 2022] [Jeong et al. 2019] [Jiang and Behbahani 2020] [Johansen 2016] [John et al. 2018] [Kabaliswaran and Das 2026] [Kefayat and Kamali 2024] [Kostenko and Tolstonogov 2021] [Kranenburg et al. 1986] [Lambregts 1983] [Lampl and Hornung 2018] [Lan et al. 2025] [Larson and Schweikhard 1974] [Lehtinen and Zeller 1972] [Lei and Zha 2022] [Leitner 1986] [Li et al. 2016d] [Li et al. 2019] [Li et al. 2021a] [Li et al. 2022b] [Li et al. 2022a] [Li et al. 2025d] [Li et al. 2025a] [Liang and Fu 1991] [Liang et al. 2023] [Licata and Burcham 1983] [Lin et al. 2019b] [Lin et al. 2019a] [Liu and Wu 2023] [Liu et al. 2015] [Liu et al. 2018b] [Liu et al. 2018a] [Liu et al. 2020] [Liu et al. 2021a] [Liu et al. 2021b] [Liu et al. 2023g] [Liu et al. 2024c] [Liuqing Yang et al. 2016] [Lu et al. 2019a] [Madeiras et al. 2026] [Marques Goncalves et al. 2024] [Matamoros and de Visser 2018] [Matous et al. 2021] [Mattern and Garg 1992] [Mattern et al. 1989] [McGuigan 1970] [McRuer 1991] [Meckstroth and Blake 2015] [Merchant et al. 2003] [Mihaloew 1981] [Momiyama 1977b] [Muller and Wesshaar 1994] [Myers 1984] [Neighbors and Rock 1993] [Neighbors and Rock 1994] [Nguyen 2026] [O’brien and Lowe 2015] [Ochi and Kanai 2001] [Orhan and Subbarao 2021] [Page and Steinberg 1999] [Pakmehr et al. 2017] [Papadales and Basil S. 1979] [Park et al. 2019] [Payne 1967] [Pei et al. 2018] [Peng and Zhang 2017] [Pfeifle and Fichter 2021] [Pfeifle and Fichter 2023] [Postlethwaite 1997] [Postlethwaite and Bates 1998] [Potthast 1982] [Prochazka et al. 2018] [Propulsion Control System Designs 1990] [Prudhomme and Haj-Hariri 1994] [Qiao and Guo 2021] [Rao and Saraf 2003] [Redondo Gutierrez et al. 2022] [Resta et al. 2021] [Reukauf et al. 1975] [Reukauf and Burcham 1976] [Rock 1989] [Rock 1991] [Rock et al. 1988] [Rock et al. 1994] [Romeu 2018] [Rosenberg 1988] [Rüddenklau and Schitter 2026] [Samimy et al. 2011] [Santos et al. 2022] [Scalera and Durham 1999] [Schierman and Schmidt 1991] [Schierman and Schmidt 1992] [Schierman and Schmidt 1994] [Schley 1999] [Schmidt et al. 1993] [Schmidt and Schierman 1990] [Scordamaglia et al. 2025] [Seitz 1975] [Semiletov and Karabasov 2016] [Sevich and Beattie 1974] [Shaw et al. 1987] [Shearwood et al. 2020] [Shebl 2026] [Shevchenko and Pavlov 2018] [Shevchenko et al. 2017] [Shevchenko et al. 2019] [Shmilovich and Yadlin 2020] [Shuo et al. 2025] [Sisson and Dogan 2025] [Sisson et al. 2024] [Skira et al. 1980] [Smith and Meyer 1981] [Smith et al. 1991] [Solnyshkin 2024] [Soufivand et al. 2024] [Spaans et al. 2024] [Stam and de Visser 2025] [Stewart 1992] [Stewart et al. 1992] [Stortz and O’Donoghue 1993] [Su et al. 2022] [Sun et al. 2015] [Sun et al. 2026] [Surmann et al. 2024] [Swortzel and Barfield 1976] [Tanveer and Ahmad 2023] [Teel 1999b] [Teel 1999a] [The Integrated Flight 1993] [Theilliol et al. 2015] [Tillman and Ikeler 1991] [Tohidi and Yildiz 2021] [Tohidi et al. 2017] [Tohidi et al. 2018] [Tohidi et al. 2021] [Troudet et al. 1991] [Tudosie 2017a] [Tudosie 2017b] [Turner et al. 2001] [VanSchalkwyk et al. 2001] [Vernyi et al. 2026] [Vile et al. 2019a] [Vile et al. 2019b] [Vile et al. 2020] [Vinayagam and Sinha 2023] [Vizzini 1985] [Wang and Wang 2020] [Wang et al. 2021c] [Wang et al. 2023d] [Wang Fawei 2016] [Warsop et al. 2019] [Weinstein et al. 1986] [Wells 2002] [Williams and Vittal 2002] [Wise et al. 1999] [Witkowska and Śmierzchalski 2018] [Wu et al. 2025a] [Wu et al. 2026a] [Xiang et al. 2025b] [Xu and Zha 2020] [Xu et al. 2017] [Xue and Atkins 2003] [Yang and Gao 2020] [Yang et al. 2025a] [Yi et al. 1979] [Yiming et al. 2019] [Yin et al. 2019] [Yonke et al. 1985] [Younes and Hickey 2020] [Yu et al. 2022] [Yu Luo et al. 2004] [Yuan et al. 2023] [Zein-Sabatto et al. 2017] [Zhang et al. 2015b] [Zhang et al. 2020b] [Zhang et al. 2025d] [Zhao et al. 2020] [Zhou and Xin 2020]

Jet impingement, ground effect and hot gas ingestion

Jet impingement on surfaces, ground effect, fountains, outwash, hot gas ingestion and the jet footprint, with the flow and heat transfer of a free gas jet on a plate, which is the physics of deck heating. Of these records, 205 were published in 2001 or earlier, and 88 in 2015 or later.

318 records. [Afroz and Sharif 2020] [Aillaud et al. 2016] [Aillaud et al. 2017] [Akashi et al. 1996] [Allen 2004] [Amuedo et al. 1989] [Antošová and Trávníček 2022] [Arledge et al. 1996] [Askari et al. 2018] [Baban et al. 1990] [Balakrishnan and Srinivasan 2016] [Barata 1991] [Barata et al. 1993] [Barron and An 1996] [Batther et al. 2026] [Bauer 1987] [Beatty and Riccius 1983] [Beaubert and Viazzo 2002] [Behrouzi and McGuirk 1999] [Behrouzi and McGuirk 2000a] [Behrouzi and McGuirk 2000b] [Berman and Andersen 1996] [Bernard et al. 2000] [Bhagwat and Sridharan 2016] [Bilen and Yavuz 2023] [Blake and Laughrey 1987] [Bolanovich and Marks 1959] [Bray and Knowles 1989] [Bray and Knowles 1990] [Brehm et al. 2015] [Brehm et al. 2017] [Bruschewski et al. 2025] [Cai and He 2017] [Cai et al. 2017] [Campbell et al. 1977] [Campbell et al. 1978] [Castells and Mishler 1973] [Catalano et al. 1977] [Chaderjian et al. 2002b] [Chaderjian et al. 2002c] [Chakraborty et al. 1990] [Chien 1975] [Childs 1991] [Childs et al. 1987] [Childs et al. 1992] [Chilukuri 2020] [Cimbala et al. 1987] [Cimbala et al. 1988] [Compton and Bowers 1983] [Cosgrove and Ryan 1969] [Cosgrove et al. 1968] [Crafton et al. 1999] [Crafton et al. 2017] [Crowell and Myers 2016] [Curtis 2002] [Curtis and Penrose 1993] [Davanlou et al. 2026] [Davidson et al. 1972] [Dennis et al. 1993] [Design Concepts for Minimizing 1981] [Dhruw et al. 2022] [Donaldson et al. 1966] [Donaldson et al. 1971] [Dosanjh and Montegani 1968] [Dudley et al. 1981] [Echigo et al. 2019] [Editor 2016b] [El-Okda and Telionis 2002] [Eshlemen 1985] [Eyles et al. 2002] [Fanucci et al. 1969] [Farzad and Yagoobi 2019] [Fink and Lastinger 1961] [Fluk 1981] [Fluk and Wu 1983] [Fogleman et al. 2026] [Foltz 1962] [Foss 1979] [Foss and Kleis 1976] [Fricker et al. 1992] [Gao et al. 2018] [Gao et al. 2019] [Garcia et al. 2026a] [George et al. 1964] [Goericke et al. 2024] [Gratzer and Mahal 1972] [Greene 2020] [Grossman 1963] [Gudi and Hindasageri 2021] [Gutmark et al. 1978] [Hall 1970] [Hange and Wardwell 1992] [Hange and Wardwell 1993] [Hattori and Nagano 2004] [Haviland and Herling 1977] [He and Liu 2018] [He et al. 2024a] [Hong and Jeon 1994] [Kyu and Lee 2002] [Hot Gas Ingestion 1984] [Hromisin et al. 2015] [Hsiao et al. 2004] [Hsu et al. 2025] [Hu and Christopher 2018] [Huang and Macinnes 1988] [Huang et al. 2024a] [Huggett 1959] [Humbert et al. 2021] [Hung and Lin 1994] [Hwang 1988] [Hwang 1990] [Hwang and Tsou 1981] [Hyun 1996] [Ing and Zhang 1993] [Ing and Zhang 1994] [Ing et al. 2002] [Ison 2024] [Issa et al. 2016] [Issac et al. 2019] [Iwasa et al. 2018] [Jackson and House 1982] [Jalabert and Bellan 2024] [Jambunathan et al. 1992] [Johns et al. 1988] [Johns et al. 1989b] [Johns 1989] [Johns et al. 1989a] [Johns et al. 1990b] [Johns et al. 1990a] [Joshi and Compton 1985] [Kaemming and Smith 1984] [Kaewbumrung and Plengsa-Ard 2023] [Kaewchoothong 2025] [Kamman and Hall 1978] [Kamman et al. 1979] [Kashimura et al. 1999] [Kataoka et al. 1982] [Khader 1971] [Khalaji et al. 2015] [Kim and Park 2003] [Kirk and Barrack 1969] [Klestov 1978] [Knott 1987] [Kopaç 2002] [Kotansky 1978] [Kotansky and Glaze 1981] [Kotansky 1982] [Krishnamoorthy 1971] [Kristy 1995] [Krothapalli 1983] [Krothapalli et al. 2003] [Kuhlman and Warcup 1977] [Kuhlman and Warcup 1978] [Kuhlman and Warcup 1980] [Kuhlman and Warcup 1979] [Kuhn et al. 1993a] [Kuhn et al. 1993b] [Kumada and Mabuchi 1970] [Kumar et al. 1998] [Lak et al. 2020] [Lake et al. 2000] [Lancey and Cooper 1989] [Lee et al. 2004] [Lemanov et al. 2018] [Levin and Wardwell 1997] [Lewis and Hurd 1980] [Li et al. 2016c] [Lim and Yee 2026] [Lissaman 1967] [Lissaman 1968] [Lissaman 1969a] [Liu et al. 2023c] [Lord 1985] [Lou et al. 2003] [Maclean 1991] [Margason 2002b] [Margason and Tso 1993] [Margason et al. 1996] [Margason 1966] [Margason 1970] [Marsh 1961] [Maurel and Solliec 2001] [McGuirk et al. 2002] [McMurray et al. 2019] [Meola et al. 1995] [Mezzacapo et al. 2025] [Miller 1995] [Miller et al. 1991] [Morse and Newhouse 1960] [Morse and Newhouse 1961a] [Morse and Newhouse 1961b] [Mourtos et al. 1995] [Murai et al. 1984] [Murman et al. 2001] [Myszko and Knowles 1994] [Narayanan 2003] [Natarajan and Venkatakrishnan 2019] [Nichols et al. 2025] [Land and Clark 1965] [Norum 1989] [Nosseir and Ho 1980] [Nosseir and Peled 1986] [Nosseir et al. 1987] [الرواف et al. 2016] [O’Bryan 1961] [Oved and Haustein 2023] [Oved et al. 2024] [Pamadi 1980] [Park and Sung 2001] [Penrose and Smith 1996] [Petrie 1980] [Pham Van Bang et al. 2022] [Polat et al. 1985] [Qi et al. 2001] [Radzman and Uddin 2018] [Vijayaraj et al. 2025] [Rathakrishnan 2024] [Reda et al. 1997] [Renselaer 1975] [Rim et al. 2016] [Robinson 1978] [Robinson and High 1974] [Rogers and Belluomini 2026] [Rubel 1978b] [Rubel 1978a] [Rubel 1982] [Ryan 1966] [Rönnberg and Duwig 2021] [Saddington et al. 2002] [Saddington et al. 2008] [Saddington et al. 2009] [Saini et al. 2022] [Sakakibara et al. 2001] [Samantaray and Arumuru 2025] [Sandoval and Zhang 2026] [Sarangi and Srinivasan 2022] [Saripalli 1981] [Saripalli 1983] [Saripalli 1985] [Saripalli et al. 1997] [Schnell and Grossman 1978] [Schnell 1982] [Scholtz and Trass 1970] [Schuster and Flood 1978] [Seiner et al. 1988] [Sementi 2002] [Sharif 2015] [Sharma et al. 2020] [Sharma et al. 2021] [Sheplak and Spina 1993] [Shi et al. 2002] [Shishir et al. 2001] [Shivdas et al. 2019] [Siba et al. 1998] [Sibulkin 1964] [Siclari et al. 1975] [Siclari et al. 1976] [Siclari et al. 1977] [Simmons et al. 2023] [Singh 2022] [Smith et al. 1993b] [Smith et al. 1993a] [Smith et al. 1994] [Soltis and Sangeorzan 2015] [Sparrow and Lee 1975] [Sparrow et al. 1975] [Stapountzis 1993] [Stewart and Blake 1992] [Stewart and Blake 1993] [Strand 1967] [Striegl and Diller 1984b] [Striegl and Diller 1984a] [Sullivan and Murthy 1990] [Tafti and Vanka 1990] [Taghinia and Rahman 2018] [Tan et al. 2018b] [Tawfek 1996] [Tchavdarov 1997] [The Normal Impingement 1962] [Tibabisco et al. 2019] [Tsuboi et al. 1991] [Tsubokura et al. 1998] [Tu and Wood 1996] [Saranyamol et al. 2026] [Vanka 1998] [Vanoverbeke and Holdeman 1988] [VanOverbeke and Holdeman 1990] [Vinay et al. 2022] [Von Glahn and Groesbeck 1979] [Wachspress et al. 2026] [Walker 1964] [Wang et al. 2026c] [Ward and Mahmood 1982] [Wardwell and Hange 1993] [Wardwell et al. 1992] [Wardwell et al. 1993] [Wareing 1968] [Weber and Williams 1978] [Weightman et al. 2016] [Wen et al. 2016] [Wernicke 1981] [White et al. 1960] [Wichita State Univ Ks 1962] [Winston et al. 1975] [Wohllebe and Migdal 1979] [Wolfshtein 1970] [Worden et al. 2016] [Wright and Seitz 2019] [Wu et al. 2001] [Yeh et al. 1993] [Yen 1981] [Yon and Li 2026] [Yoshihara 1963] [Zhang and Agarwal 2020] [Zhang and Ibrahim 2004] [Zhang and Ing 1993] [Zhang and Ing 1994] [Zhang et al. 2019e]

Electric, distributed and hybrid propulsion and electric vertical takeoff

Electric, hybrid and distributed propulsion, electric vertical-takeoff aircraft and the aircraft-level design of their powertrains. Of these records, 9 were published in 2001 or earlier, and 415 in 2015 or later.

434 records. [Abergo et al. 2026] [Abryandoko et al. 2026] [Ahuja et al. 2026] [Aktas 2015] [Іголкін et al. 2015] [Allenspach and Ducard 2021] [Amping Airpower 2024] [Anantha et al. 2024] [Anderson et al. 2024] [Arias et al. 2025b] [Arias et al. 2025a] [Avant et al. 2018] [Awad and Stumpf 2022] [Aydin et al. 2025] [Babčan and Janovec 2021] [Bahr et al. 2021] [Bai et al. 2024] [Bandopadhyay and Mistry 2019] [Bandopadhyay and Mistry 2022] [Barra et al. 2020] [Barry et al. 2023] [Beals et al. 2026] [Bendarkar et al. 2021] [Simmons 2023a] [Benmoussa and Gamboa 2023] [Benyamen and Keshmiri 2022] [Beschorner et al. 2025] [Bezerra and Santos 2022] [Bhandari and Chakraborty 2026b] [Bhandari et al. 2023] [Bhandari et al. 2024] [Bonnin and Hoogreef 2025] [Bonnin et al. 2023] [Borer et al. 2017] [Boretti 2023] [Boretti 2024a] [Bowman et al. 2018] [Bravo et al. 2021] [Brelje and Martins 2018] [Brenner et al. 2023] [Britcher and Baris 2023] [Brown and Hagen 2017] [Cai et al. 2023] [Cao et al. 2024b] [Caudle et al. 2025] [Centracchio et al. 2018] [Chakraborty 2019] [Chakraborty and Mishra 2022] [Chakraborty and Mishra 2023a] [Chakraborty and Mishra 2023b] [Chana 2002] [Chang et al. 2022] [Chapman 2023] [Chauhan and Martins 2020] [Chen et al. 2023] [Chen et al. 2025b] [Cheng et al. 2025] [Choi et al. 2025b] [Choi et al. 2026] [Chopra et al. 2022] [Comunian et al. 2026] [Connolly et al. 2018] [Cook and Hauser 2018] [Courtin and Hansman 2019] [Cunningham et al. 2022] [Cusanelli and Slutsky 2008] [Cusati et al. 2023] [Dang 2026] [Dantsker et al. 2018] [Dantsker et al. 2019] [Darmstadt et al. 2021] [De Lucena et al. 2022] [de Rosa et al. 2022] [de Vries and Vos 2022] [de Vries et al. 2019] [Dean et al. 2018] [Deere et al. 2017] [Dela Peña 2025] [Deng et al. 2024] [Derrouaoui et al. 2023] [Diaz et al. 2019] [Diecke 2023] [DiMaggio et al. 2025] [Ding et al. 2025] [Dowdle et al. 2018] [Duan et al. 2024] [Dubois et al. 2016] [Ducard and Carughi 2024] [Duffy and Jansen 2018] [Dukhnovskiy 2023] [Dunaevskii et al. 2020] [Dyson 2018] [Dyson 2023] [Ebus and Dietz 2020] [Economou et al. 2019] [Elahi Kahooker and Liu 2026] [Elbasueny et al. 2019] [Elbir and Üçgül 2026] [Enenakpogbe et al. 2024] [Fardin et al. 2026] [Farsi and Rosen 2023] [Feroskhan et al. 2025] [Figueira et al. 2025] [Filippoli 2026] [Finger et al. 2018] [Finger et al. 2020b] [Finger et al. 2020a] [Firnhaber Beckers et al. 2023] [Flanagan and Jarrett 2023] [Flight Test Data Analysis 2016] [Frederick et al. 2021] [Fredericks et al. 2013] [Freeman and Klunk 2018] [Friedrich and Robertson 2015] [Fulton et al. 2026] [Gallani et al. 2020] [Gebril and Kamal 2023] [Geisbert and Schroeder 2008] [Gelhausen and Wilson 1986] [Gkoutzamanis et al. 2020] [Goldberg et al. 2016] [Gonzalez et al. 2026] [Güner 2022] [Guo et al. 2023a] [Ha et al. 2020] [Habermann 2020] [Hallez et al. 2018] [Hartman et al. 2025] [Dabaghian and Halder 2025] [He 2024] [He et al. 2020] [He et al. 2026b] [Hein and Myschik 2022] [Herbst et al. 2015] [Herzog et al. 2021] [Herzog et al. 2024] [Hirschkron et al. 1979] [Hoffman et al. 2017] [Hoffman et al. 2018] [Hsu et al. 2023] [Hu and Booker 2022] [Hu et al. 2026] [Huang 2023] [Huang et al. 2020a] [Hyun et al. 2023] [Imani and Anjomrouz 2025] [Ingraham and Falck 2025] [Isikveren 2018] [Jacobson and Smith 2018] [Jansen et al. 2017] [Jansen et al. 2019] [Jayasundara and Baeder 2023] [Jeong et al. n.d.] [Jiang and Pakmehr 2022] [Jiang et al. 2022] [Doo et al. 2021] [Johnson and Silva 2026] [Johnson et al. 2024b] [Jois et al. 2024] [Litt et al. 2026] [Juvé et al. 2016] [Kadhiresan and Duffy 2019] [Kamath et al. 2025] [Kaneshige et al. 2023] [Kang et al. 2023] [Kang et al. 2025a] [Kang et al. 2025b] [Kannan et al. 2025] [Karemaa 1971] [Katagiri et al. 2025] [Kaushik et al. 2025] [Keller 2021] [Keller 2023] [Keller 2025] [Keller et al. 2024] [Kerho 2015] [Kim et al. 2018b] [Kim et al. 2008] [Kirner et al. 2015] [Klunk and Freeman 2018] [Kohout 2003] [Kohout 2004] [Kohout and Schmitz 2003] [Koshel et al. 2026] [Kotaru et al. 2019] [Kou et al. 2021] [Kozakiewicz and Grzegorczyk 2021] [Kramer et al. 2024] [Kruger and Uranga 2020] [Kruger and Uranga 2024] [Kunwar and Chakraborty 2025] [Kuzniar et al. 2020] [Lammen et al. 2025] [Lampl and Armanini 2023] [Laskaridis 2015] [Lechniak et al. 2020] [Lee and Park 2022] [Lee and Yee 2024] [Lee et al. 2022] [Lee et al. 2024] [Lee et al. 2026] [Legrand et al. 2024] [Legrand et al. 2025] [Lei and Zhao 2023] [Lemelin et al. 2026] [Machado et al. 2025] [Li et al. 2017a] [Li et al. 2021c] [Li et al. 2022e] [Li et al. 2024d] [Li et al. 2026b] [Libório et al. 2025] [Lindner et al. 2023] [Litt 2026] [Liu and Tan 2024] [Liu and Wang 2024] [Liu et al. 2022d] [Liu et al. 2023b] [Liu et al. 2024a] [Liu et al. 2025a] [Liu et al. 2026a] [Love 2022] [Lykyanov and Adler 2023] [Lympany and Page 2024] [Lück et al. 2025] [Ma et al. 2020] [Ma et al. 2022] [Maadani et al. 2023] [Macit and Özer 2025] [Magata et al. 2025] [Mahvelatishamsabadi and Emadi 2020] [Majka and Muszyńska-Pałys 2023] [Mak et al. 2023] [Malpica et al. 2024] [Mao et al. 2022] [Marepally et al. 2025] [Marksel and Prapotnik Brdnik 2022] [Martin 2025] [Martinez et al. 2025] [Mathur and Atkins 2026] [May et al. 2022] [May et al. 2023] [May et al. 2025] [McCrink and Gregory 2015] [McCrink and Gregory 2017] [McDonald 2015] [McDonald 2016] [Michalík and Čerňan 2020] [Mieloszyk and Tarnowski 2019] [Min et al. 2026] [Minervino et al. 2022] [Misiorowski et al. 2019b] [Mohammadi et al. 2023] [Moore and Ning 2019] [Moore 2010] [Morani et al. 2024] [Mukherjee et al. 2023] [Murphy and Landman 2015] [Nakka and Alexander-Ramos 2021] [Blaesser et al. 2024] [Neogi et al. 2025] [Ng and Datta 2018] [Ng and Datta 2019] [Nguyen and Webb 2025] [Nguyen and Xiong 2026] [Nguyen et al. 2018] [Nguyen et al. 2023] [Nguyen et al. 2025] [Ni and Lee 2025] [Nicolay et al. 2021] [Nicolosi et al. 2022] [Zawodny et al. 2022] [Nishikawa and Rinoie 2024] [Nisi and Tang 2025] [North et al. n.d.] [Okai et al. 2015] [Okai et al. 2020] [Oki et al. 2002] [Oldeweme et al. 2024] [Oliinyk and Zylevich 2026] [Orefice et al. 2019] [Orefice et al. 2020] [Orrick 2024] [Osman et al. 2026] [Oumlik and Dai 2026] [Panish and Bacic 2025] [Park 2025] [Park et al. 2025c] [Park et al. 2025b] [Pascioni et al. 2026] [Pařez et al. 2025] [Peng et al. 2018] [Perry et al. 2018] [Perry et al. 2021] [Pfeifle et al. 2021] [Pieper et al. 2018] [Poggi et al. 2024] [Pontika et al. 2023] [Portapas 2025] [Posnett et al. 1986] [Posnett et al. 1987] [Pratt and Cadou 2026] [Prochazka and Stomberg 2020] [Qin et al. 2023] [Quillet et al. 2023] [Riboldi and Gualdoni 2016] [Riboldi et al. 2018] [Solutions et al. 2020] [Roiati et al. 2023] [Ruggeri et al. 2017] [Russo et al. 2023] [Saberi et al. 2026] [Sachs et al. 2022] [Sadiq Ali Mir et al. 2025] [Saetti et al. 2020] [Saha et al. 2026] [Salahudden et al. 2023] [Salucci et al. 2021] [Samuel and Lin 2015] [Sarikaya et al. 2026] [Sarup 2026] [Satria Palar et al. 2024] [Savino and Zanotti 2025] [Scholz et al. 2021] [Scholz et al. 2022] [Schroeter et al. 2024] [Solaiappan et al. 2018] [Seo et al. 2020] [Seo et al. 2021] [Sharpe and Agarwal 2019] [Sheng and Zhao 2025] [Sheng and Zhao 2026] [Shi et al. 2024b] [Shinozuka et al. 2024] [Consulting et al. 2025] [Siddavatam et al. 2023] [Whiteside et al. 2021] [Simmons 2022] [Simmons 2023b] [Simmons and Murphy 2021] [Simmons and Murphy 2022] [Simmons et al. 2021] [Smith 1958] [Smith 1961b] [Snyder 2020] [Song and Sun 2017] [Sorensen et al. 2024] [Spadão et al. 2026] [Spannagl and Ducard 2020] [Stahl et al. 2018] [Staruk et al. 2020] [Stewart et al. 2026] [Strathoff et al. 2020] [Su and Rauleder 2026] [Suiçmez and Kutay 2023] [Sullivan and Hager 1983] [Sun and de Visser 2019] [Susilo et al. 2024] [Synodinos et al. 2018] [Synodinos et al. 2024] [Taflan et al. 2024] [Tariq and Nahon 2020] [Tatenda and Qiang 2023] [Throneberry et al. 2022] [Traub 2016] [Valente et al. 2023] [Upadhyay and Zaman 2019] [Valencia et al. 2019] [Vegh 2026] [Vepa 2021] [Waddington et al. 2023] [Wahler et al. 2023] [Wahler et al. 2025] [Wall and Meyer 2017] [Wall and Meyer 2020] [Walter et al. 2023a] [Walter et al. 2023b] [Walvekar and Chakravarthy 2022] [Walvekar and Chakravarthy 2023] [Wang 2026] [Wang and Hu 2026] [Wang and Mesbahi 2021] [Wang and Zhang 2022] [Wang et al. 2021a] [Wang et al. 2023c] [Wang et al. 2023b] [Wang et al. 2023e] [Wang et al. 2024e] [Wang et al. 2024c] [Wang et al. 2025c] [Wang et al. 2025a] [Wang et al. 2026a] [Ward and Penrose 1983] [Waters et al. 2015] [Wei et al. 2021] [Wei et al. 2024] [Wei et al. 2026] [Wen et al. 2020] [Westcott et al. 2025] [Wheeler et al. 2021] [Willis and Beard 2022] [Wroblewski and Ansell 2018] [Wroblewski and Ansell 2020] [Wu et al. 2023a] [Wu et al. 2025b] [Wu et al. 2026b] [Xiao et al. 2024] [Xie et al. 2023] [Xie et al. 2026] [Xu et al. 2025b] [Xue et al. 2026] [Yang and Morales 2021] [Yang and Tan 2025] [Yang et al. 2023] [Yang et al. 2024c] [Yokota and Fujimoto 2022] [You et al. 2026] [Yu et al. 2021a] [Yılmaz and German 2024] [Zaki et al. 2017] [Zaludin 2024] [Zaludin and Harituddin 2019] [Zanotti and Algarotti 2022] [Zanotti et al. 2024] [Zhang et al. 2021c] [Zhang et al. 2023] [Zhao et al. 2023b] [Zhao et al. 2024b] [Zhao et al. 2025b] [Zhao et al. 2025c] [Zheng et al. 2025] [Zistler et al. 2025] [Zou 2022] [Łukasik 2017]

Rotors, propellers, actuator discs and momentum theory

Rotors and propellers, the actuator disc, blade element and momentum theory, and rotor wakes, in hover and forward flight. Of these records, 175 were published in 2001 or earlier, and 206 in 2015 or later.

400 records. [Aa. Madsen 2024] [Abras and Hariharan 2018] [Agarwal and Deese 1986] [Aggarwal 1986] [Ahuja and Litherland 2023] [Ai et al. 2018] [Amin and Aijun 2017] [Andersson et al. 2026] [Andrejczyk 2023] [Arias et al. 2021] [Asiatico et al. 2026] [Açıkgöz and Aslan 2016] [Bachelder et al. 2002] [Bagai and Leishman 1992] [Balch 1985] [Ballard et al. 1980] [Barakos et al. 2020] [Beals 2018] [Beaumier et al. 2001] [Bennett 1984] [Benser et al. 1975] [Berry 1982] [Beveridge 1974] [Bingham and Noonan 1975] [Block et al. 1986] [Bludau et al. 2017] [Bohorquez and Pines 2003] [Boldman et al. 1991] [Bolin et al. 2015] [Bolt 1980] [Bossler and Robert B. 1965] [Boulkeraa et al. 2022] [Bowden and Shockey 1970] [Agrawal et al. 2024] [Breton et al. 2017] [Buffum and Robertson 1967] [Burger et al. 1975] [Busch et al. 2015] [Cameron et al. 2016] [Cao 1999] [Cao and Su 2003] [Cao et al. 2023] [Cao et al. 2024a] [Carreno Ruiz et al. 2024] [Cerbe and Reichert 1989] [Cha and Kinnas 2022] [Chaderjian n.d.] [Chapman et al. 2025] [Chattopadhyay et al. 1992] [Chen and Hubner 2020] [Chen et al. 2026c] [Chen 1992] [Cherrett et al. 1994a] [Cherrett et al. 1995b] [Chidambaram and Raj 2025] [Chinwicharnam et al. 2015] [Chiocchia and Pignataro 1995] [Choi et al. 2025a] [Coleman et al. 1996] [Cormier 1979] [Cornelius et al. 2021] [Coward 1955] [Crimi 1965] [Culpepper et al. 2021] [Cybyk et al. 1995] [Cyrus 1998] [Darlow and Vance 1974] [Davenport et al. 1985] [de Souza and Ciloni 2021] [De-gang and Zhang 2020] [Delorme et al. 2021] [Derakhshan et al. 2024] [Dias et al. 2025] [Doblhoff 1956] [Dodic et al. 2023] [Dutton 1967] [Editor 2016a] [Eick and Liu 1996] [Ellenrieder and Brinson 1998] [Erwin and Vitale 1972] [Evangelista et al. 2023] [Fan et al. 2020] [Feil et al. 2016] [Feil et al. 2019] [Felker and Light 1988] [Ferrar et al. 2016] [Flax 1995] [Fourie and Jones 2015] [Fox et al. 1974] [Fradenburgh et al. 1973] [Fredrickson et al. 1972] [Frohnapfel et al. 2017b] [Frohnapfel et al. 2017a] [Fujiwara et al. 2026] [Fulton and Ormiston 2001] [Gao et al. 2017] [Garcia et al. 2009] [Gennaretti et al. 2016] [Gennaretti et al. 2023] [Ghareeb 1964] [Gill and Lee 2025] [Godston and Reynolds 1983] [Gorrell et al. 2001] [Grava et al. 2026] [Gray et al. 1953] [Gu et al. 2016] [Güner et al. 2019] [Gustafson 1962] [Habib et al. 2018] [Halder and Benedict 2018] [Han et al. 2017] [Hansen 2023] [Hariharan et al. 2015] [Harris 1999] [Harun-Or-Rashid et al. 2015] [Hasan et al. 2022] [Hashem Dabaghian et al. 2025] [Hazen and Seckel 1950] [He et al. 2026a] [Heimerl and Benedict 2022] [Hermes and Wood 1969] [Hess et al. 2026] [Heyson and Katzoff 1956] [Heyson and Katzoff 1957] [Hill 1975] [Hiller Aircraft Corp Palo Alto Ca 1965a] [Hiller Aircraft Corp Palo Alto Ca 1965d] [Hiller Aircraft Corp Palo Alto Ca 1965b] [Hiller Aircraft Corp Palo Alto Ca 1965c] [Hiller Aircraft Corp Palo Alto Ca 1965e] [Hodges et al. 1988] [Huang et al. 2015] [Hughes et al. 2002] [Ichikawa et al. 2020] [Iseni et al. 2016] [Jacobellis and Gandhi 2016] [Jain 2017] [Jain 2018b] [Jain 2018a] [Jenkins and Marks 1975] [Jeong and Cho 2026] [Ji and Xie 2023] [Jia and Lee 2020] [Jia and Lee 2021] [Jia et al. 2018] [Jiang et al. 2018] [Jimenez Garcia and Barakos 2018] [Jo et al. 2017] [Johnson and Sirohi 2024] [Johnson et al. 2024a] [Johnson et al. 2007] [Johnston and Fleeter 2004] [Joseph and Badrya 2026] [Jung et al. 2026a] [Jung et al. 2026b] [Kaman Aircraft Corp Bloomfield Ct 1964] [Kang and Kwon 2001] [Kato and Yamane 1979] [Kato et al. 1981] [Kawachi 1982] [Kim 2016] [Kim and Stern 1990] [Kimura et al. 2022] [Kimura et al. 2023] [Kitaplioglu 1986] [Kitaplioglu and Kinney 1986] [Klimchenko et al. 2023] [Kodama and Namba 1992] [Komerath et al. 1985] [Komerath et al. 1988] [Kong et al. 2004] [Koratkar and Chopra 2001] [Kos et al. 1973] [Kovich and Moore 1976] [Kozak et al. 2019] [Ku and Sankar 2026] [Kuntz 1996] [Kusunose et al. 2000] [Lai and Le Tri 2017] [Lakshminarayana and Popovski 1986] [Lamar 2004] [Landgrebe 1971] [Le Chuiton 2004] [Lee and Dassonville 2019] [Lee and Kim 1993] [Lee and Yee 2016] [Lee et al. 2021] [Leese 1964] [Leese 1972] [Leese and Knight 1974] [Lepicovsky and Bell 1983] [Lesieutre and Sullivan 1986] [Li et al. 2017b] [Li et al. 2020b] [Li et al. 2023b] [Lim et al. 2026] [Lindblad et al. 2018] [Liu 2002] [Liu et al. 2024b] [Lu et al. 2022b] [Akash et al. 2023] [Ma et al. 2017b] [Magliozzi 1987] [Magrini 2022] [Mahmuddin 2017] [Malick and Agarwal 2015] [Martin et al. 1999] [Mathioudakis 1985] [Maurya et al. 2021] [Maurya et al. 2023] [McDonnell Aircraft Corp St Louis Mo 1950] [Meakin 1995] [Mehta et al. 2015] [Mihaloew et al. 1988a] [Mihaloew et al. 1988b] [Miller 1983] [Molyneux 1983] [Montero Villar et al. 2018] [Moore et al. 2026] [Moore and Reid 1982] [Moreau et al. 2024] [Mortimer et al. 2023] [Morton 1983] [Müller et al. 1996] [Nagel and Patrick 1988] [Nallasamy 1993] [Nallasamy et al. 1988] [Nederlof et al. 2023] [Neuhoff 1985] [Nicholson and Moore 1986] [Nishimura et al. 2023] [Nordquist et al. 1972] [Norton et al. 1979] [Garcia et al. 2026b] [O’Brien and Datta 2026] [Ockier and Celi 1991] [Oliva and Morris 2022] [Osborn and Hager 1976] [Overmeyer and Martin 2017b] [Overmeyer and Martin 2017a] [Padthe et al. 2022] [Page et al. 2017] [Park et al. 2026b] [Parker and Simonson 1982a] [Parker and Simonson 1982c] [Parker and Simonson 1982b] [Parzych 1990] [Parzych and Shattuck 1986] [Passe et al. 2015] [Patil and Datta 2024] [Paxson 1996] [Pereyra and Kung 2026] [Peterson and Warmbrodt 1986] [Peyton Autry 1946] [Podsędkowski et al. 2023] [Pomin and Wagner 2001] [Prasad 2025] [Prato and Lakshminarayana 1992] [Raj and Chidambaram 2025] [Prothin and Doué 2015] [Prouty 1975] [Qi et al. 2022] [Qi et al. 2024] [Qiu 2025] [Quackenbush et al. 1989] [Quackenbush et al. 1991] [Quackenbush et al. 2019] [Quackenbush et al. 2020] [Rajagopalan 1988] [Rajagopalan and Lim 1991] [Rajmohan et al. 2015] [Ramachandran et al. 1989a] [Ramachandran et al. 1989b] [Ramanujam and Abhishek 2022] [Rand and Khromov 2017] [Rao and Schatzle 1978] [Reid and Moore 1978] [Richardson and Liiva 1970] [Rinehart 1970] [Roberts et al. 2002] [Roberts et al. 2005] [Rock and Neighbors 1994] [Rohrbach and Wainauski 1981] [Rosen 2004b] [Rosen 2004a] [Rossow 1985] [Rostami and Farajollahi 2021] [Rubinstein 2014] [Runco et al. 2019] [Ruttledge 1986] [Samanich and Heidelberg 1976] [Samant et al. 1983] [Sambell 1971] [Sanderson and Holly 1993] [Sankar and Komerath 1988] [Schleicher et al. 1993] [Schmitz 1971] [Schmitz and Vause 1976] [Schroers and Antoniou 1964] [Schröder and Schuster 1972] [Seidel and Peters 2019] [Shah and Bilgen 2023] [Shahmiri 2017] [Sheng 2018] [Sheng et al. 2016] [Sheng et al. 2018] [Shenoy and Gray 1981] [Shipman and Bin 2021] [Shivananda et al. 1978] [Shivashankara et al. 1990] [Shivers 1961] [Shrestha et al. 2016] [Shukla et al. 2022] [Simon and Bohn 1974] [Beldjilali et al. 2023] [Singh and Friedmann 2018] [Sitaram 1988] [Smith 1968] [Smith et al. 2026] [Son and Kim 2023] [Sorensen and Cuppoletti 2022a] [Sorensen and Cuppoletti 2022b] [Spencer et al. 1969] [Srinathkumar 2018] [Srinivasan and McCroskey 1988] [Stanly et al. 2020] [Stevens et al. 2015] [Stoll and Mikic 2022] [Strawn and Djomehri 2002] [Strazisar et al. 1989] [Swanson 1993] [Takallu and Gentry 1992] [Tan et al. 2018a] [Taniguchi and Oyama 2022] [Taymourtash et al. 2021a] [Taymourtash et al. 2021b] [Thompson et al. 1988] [Toha et al. 2015] [Uehara et al. 2019] [van Kuik et al. 2015] [Velkoff et al. 1971] [Vella et al. 2026] [Vitale et al. 2023] [Vogeley 1948] [Volkov et al. 2022] [Vu and Lee 2015] [Waanders and Rauleder 2026] [Wadia and Law 1992] [Wadia et al. 2018] [Wainauski and Vaczy 1986] [Wallace et al. 2025] [Walsh et al. 2016] [Wang 2003] [Wang and Jin 2025] [Wang et al. 2007] [Wang et al. 2020a] [Wang et al. 2021d] [Wang et al. 2022b] [Warmbrodt and Hull 1982] [Warsett 1953] [Webster et al. 1995] [Wei and Zhong 1988] [Weilenmann and Geering 1993] [Wennerstrom and Frost 1974] [Westcott et al. 2023] [Whitehead 1986] [Whitehead and Davies 1983] [Williams and Bernitt 1970] [Willshire and Martin 1984] [Wood 2001] [Wood and Hammam 2022] [Woodward 1992] [Woodward and Glaser 1976] [Wright and Silva 2026] [Wu et al. 2021a] [Wu et al. 2024] [Xie and Haberland 1999] [Xue et al. 2024] [Yang and Zhuang 2000] [Yang et al. 2026a] [Yao and Li 2024] [Ye et al. 2024] [Yeh 1959] [Yeo and Johnson 2015] [Yin 2019] [Yoshida et al. 2021] [Yuan et al. 2024b] [Yurt et al. 2026] [Zhang and Liu 2024] [Zhang et al. 2019b] [Zhang et al. 2025b] [Zhao 2018] [Zhao and Li 2018] [Zhao and Wang 2016] [Zhao et al. 2025a] [Zheng and Zhao 2015] [Zoppelt et al. 2024] [Öhrle et al. 2019] [Šajbanová and Čerňan 2021] [Šajbanová et al. 2021]

Transonic and supersonic drag

Transonic and supersonic drag, wave drag, shock interaction and the aerodynamics of the speed range the dash crossed. Of these records, 93 were published in 2001 or earlier, and 49 in 2015 or later.

151 records. [A Prediction Method 2017] [Abdol-Hamid et al. 2018] [Abe 2023] [Abraham et al. 2023] [Ageev and Pavlenko 2016] [Agrell and Elmeland 1984] [Aidala 1985] [Andrew and Cahn 1967] [Arabshahi and Whitfield 1995] [Axelson 1975] [Baals et al. 1970] [Bailey and Starr 1976] [Balusamy et al. 2024] [Bergman 1948] [Bernstein 1997] [Biot 1949] [Boelens 2017] [Boppe 1978] [Boppe and Aidala 1980] [Brower 1989] [Bryson 1971] [Bushnell 1990] [Capone et al. 1984] [Cartieri et al. 2018] [Chadsey and Yechout 2001] [Chamberlain 1968] [Chao and van Dam 2004] [Chaparro et al. 2016] [Chaussee 1978] [Chung 2004] [Coder et al. 2017] [Coder et al. 2018] [Cole 1988] [Cosenza and Kummeth 1974] [Coustols et al. 1997] [Crites et al. 1992] [de Paula et al. 2017] [Derlaga and Morrison 2017] [Derlaga and Morrison 2018] [Desai et al. 1977] [Dixon and Hunsaker 2023] [Doherty et al. 2018] [Dollyhigh 1970] [Eminton and Lord 1956] [Esquieu 2003] [Fan and Li 2019] [Fletcher and Burns 1979] [Flores et al. 1988] [Florio et al. 2019] [Fournis 2022] [Fuhs 1971] [Fujino and Kawamura 2003] [Fung 1982] [Gacherieu and Weber 1998] [Gan et al. 2016a] [Gao 2023] [Garabedian 1976] [Gillan 1993] [Goto et al. 2021] [Hinchliffe and Qin 2016] [Holdaway 1954] [Howell and Korst 1971] [Huh et al. 2015] [Ito et al. 2018] [Jesudasan et al. 2026] [Johnson 1985] [Joshi et al. 2024] [Kawasaki 1965] [Kennedy and Stuart 2025] [Keye et al. 2017] [Keye et al. 2023] [Khan et al. 2025] [Khlebnikov 1990] [Klausmeyer 2004] [Kohn 1979] [Kondo et al. 2003] [Kutney and Piszkin 1963] [König and Fares 2018] [Lee and Franz 1976] [Lee-Rausch et al. 2004] [Lents 2021] [Li et al. 2023c] [Long 1993] [Macha 1977] [Malmuth et al. 1986] [Mann and Mercer 1986] [Mason 1982] [Masson et al. 1998] [Masson et al. 1999] [Mavriplis and Levy 2002] [Mele et al. 2017] [Mertens et al. 1986] [Miles 1953] [Miles 1954] [Murman and Cole 1974] [Naida and Fonarev 1995] [Naida and Fonarev 1996] [Nelson 1986] [Newberry 1998] [Nghiem and Norstrud 1989] [Niewald and Parker 2000] [Nusrath et al. 2016] [Oki et al. 2000] [Page et al. 2025] [Peavey 2000] [Peterson 1961] [Petruzzelli and Keane 2001] [Pittman 1987] [Prabhu et al. 2025] [Price 1981] [Rajeswari and Prabhu 1987] [Ralin Bukreev 2023] [Rallabhandi and Mavris 2003] [Resulkulyeva and Serebryansky 2023] [Roach and Froning 1996] [Roth 2001] [Roy et al. 2021] [Sampaio Felix et al. 2023] [Sathish Kumar Sunnam et al and Tjprc 2019] [Schnerr and Dohrmann 1991] [Schnerr and Dohrmann 1994] [Schwartz et al. 2024] [Seider and Haenel 1991] [Shanbhag and Narasimha 1970] [Sigal 1988] [Smetana and Knepper 1973] [Smith 1997c] [Sorbilli et al. 2018] [Soudakov 2016] [Spearman 1979] [Squire and Nasser 1993] [Starr and Varner 1976] [Steger and Baldwin 1973] [Sun and Hansen 1982] [Supersonic Flow Computations 1990] [Swamy et al. 1978] [Takahashi 2021] [Takovitskii 2020] [van Dam et al. 1995] [van der Vooren and van der Wees 1991] [Vieira et al. 2025] [Viswanath 1988] [Viswanath and Rajendra 1990] [Volpe and Jameson 1990] [Walkley 1986] [Ward 1968] [Whitford 1991] [Whoric 1977] [Willhite et al. 1995] [Yajnik and Subbaiah 1976] [Yu et al. 1983]

Fan, compressor and counter-rotating stages

Fan and compressor stages, counter-rotating turbomachinery, stall, distortion and the stage design beneath the lift fan. Of these records, 129 were published in 2001 or earlier, and 126 in 2015 or later.

273 records. [Adjei and Fan 2024] [Advisory Group for Aerospace Research and Development 1996] [Aerodynamics of Power Plant 1981] [Ai et al. 2021a] [Ai et al. 2025] [Alavi Moghadam et al. 2017] [An et al. 2025] [Ananthakrishnan et al. 2019] [Andriani and Ghezzi 2002] [Aungier 1995] [Azevedo and Galdino da SIlva 2016] [Bailey 1972] [Ball 1974] [Ball 1979] [Barnhart 1989] [Barrett 1965] [Bettner and Elrod 1982] [Bohne and Niehuis 2004] [Borcherding et al. 2023] [Boretti 2024b] [Boyer and O’Brien 2002] [Breugelmans 1975a] [Brooks and Wasson 1976] [Bryce et al. 1993] [Burger et al. 1979] [Cai et al. 1990] [Calvert and Stapleton 1993] [Capece and Fleeter 1984] [Carpenter and Cizmas 2017b] [Carpenter and Cizmas 2017a] [Chen and Zhang 1983] [Chen et al. 2018b] [Cherrett et al. 1994b] [Cherrett et al. 1995a] [Chima 1991] [Choe et al. 2002] [Choi and Lee 2018] [Chotalia and Alone 2017] [Citavý 1992] [Cook 1976] [Copenhaver and Okiishi 1989] [Cousins and Obrien 1985] [Csank and Zinnecker 2014] [Cui et al. 2025] [Cunningham and Boytos 1981] [Cunningham and Boytos 1983] [Cyrus 1990] [Dai et al. 2019] [Daniels et al. 1989] [Davenport et al. 1974] [Davis 1972] [Dehnavi et al. 2023] [Dejene Toge and Pradeep 2015] [Denton and Xu 2002] [Design Principles and Methods 1999] [Dinh and Kim 2021] [Dinh et al. 2017] [Dogga and Turner 2023] [Doyle and Dixon 1962] [Druzhinin et al. 2017] [Druzhinin et al. 2018] [Dugas 1968] [Durali and Kerrebrock 1998] [Schwaar 1961] [El Zahaby 1979] [Elliott et al. 1990] [Elmendorf et al. 1995] [Emmerson 1998] [Enghardt et al. 2019] [Erdos et al. 1976] [Ferdaus et al. 2021] [Fishbach and Franciscus 1982] [Franciscus 1983] [François et al. 2020] [Friedrichs et al. 2000] [Fritsch et al. 1997] [Frulla 2021] [Gan et al. 2016b] [Gao et al. 2022] [Gearhart et al. 1969] [Ginzburg 1976] [Girshovich 1968] [Goswami et al. 2015] [Guo et al. 2023b] [Güllü and Aran 2023] [Hah 2015] [Hah 2010] [Hallstaff 1966] [Hao et al. 2026] [Harvey and Monarch 1968] [Hasegawa et al. 2018] [Haug and Niehuis 2018] [Hayami et al. 2002] [Heath et al. 2017] [Hiers et al. 2004] [Hill 1993] [Hosotani et al. 2019] [Howard and Gallimore 1992] [Howard and Puterbaugh 2016] [Howard et al. 2017] [Huber et al. 1993] [Huete and Singh 1997] [Hutcheson 1976] [Investigation on the Inflow 2023] [Isomura and Giles 1998] [Janon 2020] [Jiang et al. 2015b] [Johnson 1991] [Joo 2000] [Kanemoto et al. 2002] [Kang et al. 2017] [Kern and Hopcroft 1983] [Khader and Loewy 1989] [Khaletskii et al. 2024] [Tran 2020] [Kim and Lee 2021] [Kim and You 2026] [Kim et al. 2018a] [King 1961] [Kofman and Becus 1996] [Konyukov 2025] [Konyukov 2026] [Kotidis and Epstein 1990] [Kovach and Sandercock 1961] [Kovich and Steinke 1976] [Kovich et al. 1977] [Kozlak et al. 2017] [Kumar et al. 2023] [Kurosaka 1984] [Lee et al. 2023] [Lee et al. 2019] [Lengyel-Kampmann et al. 2024b] [Lewis and Moore 1976] [Li and Wells 1999] [Li and Wu 2024] [Li et al. 2022c] [Liang and Yeuan 1997] [Lim and Chjng 1989] [Liu et al. 2025d] [Liu et al. 2025c] [Long et al. 2026] [Longxin 2025] [Lu et al. 2018] [Lu et al. 2019c] [Luo et al. 2020] [Lück et al. 2026] [Ma et al. 2016a] [Ma et al. 2017a] [Ma et al. 2024] [Mackintosh and Dawson 1979] [Magrini et al. 2023] [Massardo and Satta 1987] [Mayda et al. 2024] [McCormick and Surko 1989] [Mechanisms of Transonic Blade-Vortex 1976] [Medd et al. 2003] [Meng et al. 2015] [Merchant 1949] [Merchant et al. 2004] [Meyer et al. 2024] [Michaud et al. 2016] [Mirza-Baig and Saravanamuttoo 1991] [Moore and Reid 1972] [Moore et al. 1978] [Idres and Azmi 2022] [Musgrave and Plehn 1987] [Mütschard et al. 2021] [Nagai et al. 1996] [Nakod et al. 2025] [Namba 2001] [Newman 1988] [Nie 2003] [Oh 1999] [Oh and Oh 2000] [Onaka et al. 2018] [Osborn and Steinke 1974] [Osborn et al. 1973] [Palmer and Waterman 1994] [Pardowitz et al. 2015] [Park et al. 2024] [Paroubek and Kynčl 1998] [Pasupula and Mistry 2023] [Pavarani and Savage 1989] [Pelton 1976] [Pelton and Hannah 1976] [Peng et al. 2024] [李 2021] [Peters and Fottner 2002] [Pham et al. 2020] [Place et al. 1995] [Prahst et al. 2015] [Pundhir and Sharma 1992] [Pérez et al. 2024] [Qinghuan and Zhiqin 1988] [Rabe et al. 1991] [Radermacher et al. 2025] [Rajendran and Pachidis 2020] [Ran 2025] [Reemsnyder and Sagerser 1979b] [Reemsnyder and Sagerser 1979a] [Ren et al. 2024] [Robles Vega et al. 2023] [Rosell and Grönstedt 2026] [Rossikhin et al. 2018] [Ryals et al. 2026] [Ryan et al. 1977] [Saathoff and Stark 1999] [Sagawa and Ono 2018] [Sagerser et al. 1976] [Sanger 1994] [Sayari and Bölcs 1995] [Schaub and Krishnappa 1977] [Scheibel et al. 2024] [Schmid et al. 2019] [Schreiber et al. 2017] [Shao et al. 2023] [Sharma et al. 1987] [Sharma et al. 1991] [Shi and Yu 2023] [Shivaramaiah and Varpe 2023] [Stone 1958] [Streets 1960] [Streets 1963] [Stricklin and Hess 1969] [Suder et al. 1987] [Sun et al. 2017] [Sun et al. 2021] [Suzuki and Kuno 1995] [Swan 1961] [Takamatu and Takezako 1967] [Tariq et al. 2019] [Tesch and Pase 1983] [Tesch 1971] [The Centrifugal Compressor Stage 1964] [Tiwari et al. 2024] [Touyeras and Villain 2004] [Trost and Schnell 2025] [Turner et al. 2015] [Urasek and Moore 1972] [Van Zante et al. 2002] [von Backstroem et al. 2000] [Walitt et al. 1997] [Wang et al. 2017b] [Wang et al. 2021b] [Wang et al. 2024b] [Ware et al. 1974] [Wei and Kun 2015] [Wells et al. 1989] [Wennerstrom 1984] [Wennerstrom 1987] [Wichert 1961] [Wolter et al. 2017] [Wolters et al. 2016] [Wright and Jones 1970] [Wright et al. 1973] [Wyss et al. 1993] [Xu et al. 2023] [Xu et al. 2026] [Yangang et al. 2015] [Yin et al. 2001] [Yu et al. 2002] [Yu-bing et al. 1981] [Zangeneh et al. 2004] [Zeng and Guedes Soares 2025] [Zhang and Engeda 2018] [Zhang et al. 2015c] [Zhang et al. 2020a] [Zhang et al. 2021b] [Zhang et al. 2024a] [Zhang et al. 2025e] [Zhao et al. 2015] [Zhou et al. 2018] [Zhou et al. 2022b]

Clutches, gears and drivetrains

Clutches, gears, gearboxes, drive shafts and the transients of mechanical power transmission. Of these records, 79 were published in 2001 or earlier, and 111 in 2015 or later.

202 records. [Abdullah and Schlattmann 2016] [Advances in Aircraft Gear 1992] [Alavilli and Maideen 2021] [Ali and Asiri 2022] [Ali et al. 2017] [Amri et al. 2016] [Aphale et al. 2004] [Bao et al. 2020] [Bao et al. 2021] [Baz and Chen 1993] [Bemporad et al. 2001b] [Bemporad et al. 2001a] [Berthold et al. 2017] [Bian et al. 2025] [Biczó et al. 2020] [Binney et al. 2003] [Armenio et al. 2024] [Bunda et al. 1972] [Burgan 1984] [Burroughs 1965] [Buyukataman and Kazerounian 1998] [Cacciola and Calabria 2026] [Candee 1943] [Cenbo et al. 2015] [Chaloff et al. 1974] [Chamehsara and Karami 2020] [Chavez et al. 2017] [Chen 1998] [Chen and Bossler 1995] [Chen and Liao 2018] [Cheng et al. 2018] [Chung et al. 1997] [Altair and Cole 2025] [Corliss and Sprysl 1999] [Cowell 1947] [Dai et al. 2026] [Darmstadt and Robuck 2018] [Dean 1979] [Design and Theoretical Analysis 2015] [Desmidt et al. 2018] [DeSmidt et al. 2013] [DeVita and Quenneville 1994] [Dewispelare and Stager 1981] [Drago 1985] [Drago and Mack 1987] [Du et al. 2025] [Dub et al. 2016] [Dundore and Schneider 1968] [Egawa 1956] [Faidh-Allah 2018] [Fan et al. 2015] [Feng and Song 2017] [Feng et al. 1999] [Feng et al. 2001] [Feng et al. 2003b] [Feng et al. 2003a] [Feng et al. 2003c] [Firoozian et al. 1991] [Friction Contact in Clutch 1987] [Gagnon et al. 1997] [Ganesh et al. 2021] [Gao and Barber 2002] [Gao et al. 2001] [Gardner and Adams 1975] [Gargiulo 1986] [Gatta et al. 2018] [Gibson and Taccini 1989] [Gil et al. 1994] [Glielmo and Vasca 2000] [Gosselin et al. 1998] [Handschuh 1992] [Handschuh and Bibel 1999] [Haria et al. 2018] [He and Liu 2023] [He-yun et al. 2021] [Holgerson 1997] [Holgerson 1999] [Holgerson 2000] [Holgerson and Lundberg 1999] [Hongo and Tanaka 1973] [Houjoh et al. 2015] [Howe and McKibbin 1989] [Hozumi and Aihara 2018] [Hu et al. 2016] [Huang et al. 2025b] [Huang et al. 2025a] [Iqbal et al. 2015] [Ishutinov et al. 2024] [Iwatsubo et al. 1984] [Jabbar et al. 2021] [Jabbar et al. 2023] [Jang 2015] [Jang 2022] [Yong-chun et al. 2020] [Jones 1960] [Kabra 2022] [Kadhim et al. 2020] [Kanemitsu 1985] [Kataria 2022] [Korzun 1976] [Krishna and Vancoillie 1999] [Kurushin et al. 2018] [Leal Junior et al. 2016] [Lee et al. 2003] [Li and Yu 2001] [Li et al. 2002] [Liao et al. 2025] [Libraschi et al. 2023] [Lin et al. 2018] [Liu et al. 2017] [Liu et al. 2023f] [Luo et al. 2018] [Luo et al. 2026] [Sudhan and Vasanthan 2021] [Ma et al. 2016b] [Mack 1965] [Mahmud et al. 2018] [Mansouri et al. 2000] [Mark 1987] [Martinsson and Liu 2016] [Mattiazzo et al. 2002] [McCune 1993] [Miao et al. 2015] [Mohire et al. 2018] [Mohire et al. 2019] [Multimode Clutch 2018] [Muscarello et al. 2017] [Nagaya et al. 1982] [Natsumeda and Miyoshi 1994] [Newcomb and Merritt 1962] [O’Brien 1945] [Oravský 1999] [Orzelowski and Wicher 2000] [Overfield and Crawford 1967] [Padmanabhan et al. 2023] [Park and Choi 2020] [Penta et al. 2017] [Pisaturo and Senatore 2018] [Pisaturo et al. 2015] [Pisaturo et al. 2016] [Pisaturo et al. 2017] [Prosek and Barber 1958] [Qu et al. 2016] [Radil and Berkebile 2020] [Reddy et al. 1969] [Renfroe and Iverson 1986] [Research on Engagement Curve 2018] [Rigbi 1997] [Rohan Ramesh et al. 2021] [Routson et al. 1992] [Sabri et al. 2021] [Sakamoto and Aihara 2018] [Sato et al. 2015] [Scheidler 2018] [Shaft-Driven Motor Couplings 1995] [Sheng et al. 2025] [Sherza 2019] [Sherza et al. 2018] [Sherza et al. 2022] [Sherzaa et al. 2022] [Shin and Choi 2024] [Singh 1974] [Singh et al. 2024] [Sivaramakrishnan 1981] [SoltanRezaee et al. 2021] [Song et al. 2026] [Szadkowski and McNerney 1992] [Szadkowski and Morford 1992] [Tan et al. 2023] [Tatar and Schwingshackl 2018] [Terauchi et al. 1981] [Михалевич 2020] [Topczewska et al. 2020] [Tsai and Roth 2001] [Tutulan et al. 2004] [Umeyama et al. 1998] [Uppaluri and Douglass 1991] [Vaidyanathan et al. 1994] [Vigano et al. 2024] [Voracek 1990] [Voskuijl et al. 2018] [Vyrabov 1991] [Wang and Zhu 2020] [Wang and Zhu 2021] [Wei et al. 2025b] [Wei et al. 2025a] [Winter and Paul 1985] [Wu 1973] [Xiang et al. 2023] [Xiaozeng et al. 2015] [Xie et al. 2016] [Xie et al. 2021] [Yang et al. 1998] [Yang et al. 2026b] [Zagrodzki and Truncone 2003] [Zhang and Yao 2019] [Zhang et al. 2017] [Zhang et al. 2021a] [Zhu et al. 2020] [Zhu et al. 2023] [Zhu et al. 2026] [Zimmer et al. 2015]

Inlets, intakes and diffusers

Inlets, intakes and diffusers, including supersonic, diverterless and boundary-layer-ingesting inlets and inlet distortion. Of these records, 106 were published in 2001 or earlier, and 178 in 2015 or later.

291 records. [Abedi et al. 2020] [Ahuja and Mavris 2020] [Alendar et al. 2022] [Wang et al. 2023a] [Anderson 1984] [Anderson and Gibb 1996] [Antl 1970] [Arias et al. 2023] [Askari and Abedi 2026] [Askari and Soltani 2017] [Askari and Soltani 2019] [Askari and Soltani 2020] [Askari and Soltani 2023] [Athanasakos et al. 2020] [Azevedo et al. 1990] [Babcock and Mani 2015] [Babcock et al. 2019] [Bai et al. 2025b] [Bakhle et al. 2018] [Ball and Ross 1971] [Bangert et al. 1982] [Barr et al. 2018] [Barr et al. 2020] [Barry 1971] [Battiston et al. 2025] [Baydar et al. 2018] [Beach et al. 2024] [Bedke and Gorrell 2021] [Benson and Anderson 1983] [Bevilaqua 2023] [Bhunia et al. 2026] [Blumenthal et al. 2018] [Bogar et al. 1985] [Boles et al. 2021] [Bond and Key 2025] [Bozeman 2023] [Bozeman 2024] [Braun and Podleski 2019] [Bravo Mosquera et al. 2019] [Breugelmans 1975b] [Burris 1966] [Burstadt et al. 1971] [Calogeras 1969] [Campbell and Ellis 1970] [Campbell and Syberg 1984] [Campbell et al. 1985] [Cao et al. 2020] [Car et al. 2000] [Carrier et al. 2001] [Chandler and Montes 2019] [Chang and Hsu 1960] [Chen and Tan 2019] [Chen et al. 2025a] [Chennuru et al. 2025] [Choe and Kim 2016] [Choe et al. 2020] [Chun and Swanson 1964] [Cinquegrana and Vitagliano 2021] [Clark 1974] [Clauser 1954] [Collins 1970] [Colpin 1979] [Crosthwait 1970] [Cusator et al. 2024] [Da et al. 2020] [Daliri et al. 2018] [Das and Trippi 1989] [Davis and Park 2017] [DeBardelaben and Sreenivas 2022] [Della Corte et al. 2021] [Denner et al. 1998] [Dickman and Takahashi 2016] [Domel 2015a] [Effect of Inlet Mach 2023] [El-Salamony and Teperin 2020] [Fan et al. 2024b] [Fan et al. 2024a] [Fan et al. 2026b] [Farr 1973] [Flores et al. 1989] [Flow Field Analysis 2017] [Fraiser 1960] [Frascella et al. 2016] [Frohnapfel and O’Brien 2015] [Gaiddon and Knight 2003] [Giesecke and Friedrichs 2019] [Giri and Turner 2024] [Giri et al. 2020a] [Giri et al. 2020b] [Gray et al. 2018b] [Gray et al. 2020] [Gray et al. 2017] [Gray et al. 2018a] [Guan and Yarng 1987] [Guimarães et al. 2018] [Guo et al. 2015] [Haas and Karanian 1980] [Hagseth 1987] [Hah et al. 2015] [Hall and Lieu 2021] [Hall et al. 2016] [Hall et al. 2017] [Hall et al. 2022] [Halwas and Aggarwal 2019] [Harloff and Smith 1996] [Hawkins 1974] [Hawkins 1980] [He et al. 2024b] [Heinlein et al. 2020] [Heinlein et al. 2024] [Hirt et al. 2017] [Howerton and Slater 2021] [Hunter and Cawthon 1984] [Hunter and Cawthon 1985] [Imfeld 1974] [Felder et al. 2022] [Jin et al. 2023] [Kamal and Livesey 1979] [Katoh et al. 1998] [Kaya 1998] [Khaleghi and Jalaly 2016] [Khobragade et al. 2021] [Kim and Choi 2024] [Kim and Kwon 2015] [Koncsek 1981] [Kramer and Hall 2025] [Krivec et al. 1984] [Kucuk 2017] [Kumar et al. 2018] [Kumar et al. 2020] [Lamprakis et al. 2025] [Lee and Boedicker 1985] [Lee et al. 2018] [Lengyel-Kampmann et al. 2024a] [Li et al. 2023d] [Li et al. 2024c] [Li et al. 2024b] [Li et al. 2025c] [Lima et al. 2019] [Liu and Vo 2024] [Liu et al. 2023a] [Liu et al. 2023e] [Liu et al. 2025e] [Lobo et al. 2016] [Lu and Jain 1998] [Lv et al. 2016] [López de Vega et al. 2019] [López de Vega et al. 2021] [Ma et al. 2018] [Maekawa et al. 1978] [Magrini and Benini 2026] [Malan and Brown 1994] [Mandal et al. 2020] [Marien et al. 2018] [Martínez Fernández and Smith 2020] [Marvin 1968] [Matesanz-García et al. 2022] [Matwey et al. 1983] [Mayer and Paynter 1994] [Mays 1969] [McCallum 1989] [McVey et al. 1969] [Megat et al. 2026] [Menegozzo and Benini 2020b] [Menegozzo and Benini 2020a] [Mennicken et al. 2019] [Min et al. 2018] [Moin and Lele 1998] [Moirou and Sanders 2026] [Moirou et al. 2023] [Moore 1986] [Motycka 1985] [Mount 1964] [Mouton 2021] [Mufti et al. 2019] [Muller and Gasko 1967] [Nagler 2026] [Nakamura 1988] [Numbers and Hamed 2003] [Obikane 1984] [Obrien and Cramer 1986] [Opalski and Sajben 2002] [Orme et al. 2020] [Overall 1976] [Palko 1975] [Pandya and Uranga 2013] [Park et al. 2026a] [Paynter 1994] [Paynter and Chen 1983] [Paynter et al. 1993] [Phan and He 2020] [Potonides and Mebes 1984] [Power and Prufert 1996] [Pyszka et al. 2023] [Qiang et al. 2024] [Qiu et al. 2023b] [Qiu et al. 2023c] [Qiu et al. 2024] [Reedy and Gorrell 2025] [Rein and Koch 2015] [Rejeske and Stava 1974] [Rembaut et al. 2023] [Reyhner and Hickcox 1972a] [Reyhner and Hickcox 1972b] [Rizzetta 1991] [Rodriguez 2004] [Sabo and Drela 2015] [Safarik and Polak 1996] [Saheby et al. 2016b] [Saheby et al. 2016a] [Sajben 2002] [Sajben 2004] [Sajben and Said 2001] [Saleem Yusoof et al. 2016] [Samuelsson and Grönstedt 2021] [Sanders and Laskaridis 2020] [Sasson et al. 2015] [Saunders and Keith 1991] [Secchi et al. 2019] [Secchi et al. 2021] [Sedlock 1985] [Seidel and Matwey 1983] [Seidel et al. 1980] [Semmes and Weyer 1990] [Serrano et al. 2021] [Shang et al. 2021] [Shucheng and Xijun 1994] [Shur et al. 2018] [Si et al. 2016] [Siddharth M. et al. 2026] [Sinha 1988] [Slater 2001] [Slater 2019] [Smith 1983] [Soltani and Askari 2018] [Sorensen and Bencze 1973] [Sorensen and Latham 1975] [Sorensen and Smeltzer 1972] [Sorensen et al. 1973] [Stephens et al. 2019] [Stubbs 1956] [Stuermer et al. 2022] [Sudasinghe et al. 2022] [Sun et al. 2016] [Sun et al. 2025c] [Surber 1975] [Surber and Robinson 1983] [Surber and Sedlock 1978] [Pan et al. 2024] [Syberg et al. 1980] [T-4 Inlet/engine Compatibility Flight 1989] [Tabanli and Yuceil 2021] [Taylor 1968a] [Tekaslan et al. 2021] [The Verification of Inlet/engine 1988] [Tidow and Rudnik 2025] [Tindell 1973] [Tindell 1980] [Tindell 1987] [Tong and Yanagita 2019] [Trefny and Wasserbauer 1986] [Tudosie 2018] [Tudosie and Prisacariu 2022] [Uenishi et al. 1992] [Uranga et al. 2018] [Vadyak and Atta 1985] [Vadyak et al. 1987] [Valencia et al. 2015] [Vinz and Raichle 2024] [Vouros et al. 2022] [Vu et al. 2026] [Walter et al. 2016] [Wang et al. 2024d] [Wegener 1977] [Werner et al. 2022] [Williams and Hunt 1980] [Winkler and Davis 2017] [Woollett 1983] [Wu et al. 2022] [Yang et al. 2025b] [Yao et al. 2015] [Yu et al. 2026] [Zhang and Vahdati 2018] [Zhang and Vahdati 2019] [Zhang et al. 2015d] [Zhang et al. 2019a] [Zhang et al. 2020c] [Zhipeng et al. 2015] [Zhou et al. 2019] [Zhou et al. 2025] [Zimbelman and Rouser 2025]

Engines, thrust and installed performance

Engines and their thrust, installed performance, thrust lapse, cycles and propulsion control. Of these records, 108 were published in 2001 or earlier, and 40 in 2015 or later.

153 records. [Abbas and Riggins 2016] [Abercrombie 1979] [Akagi et al. 1997] [Amundson and Holm 1989] [Andrianantara et al. 2021] [Arnaiz 1975] [Avanzini and Matteis 1995] [Babcock and Mani 2017] [Baer-Riedhart 1982] [Bailey et al. 1979] [Ball and Atkins 1978] [Barrows 1980] [Beale 1986] [Bhatra and Mishra 2023] [Bird et al. 1991] [Blevins and Wagner 2000] [Braman et al. 1983] [Brandau 1965] [Brandt 2018] [Brown 1950] [Bruce and Rytting 1983] [Campbell 1974] [Cassetti 1978] [Cliff et al. 1982] [Commander 1964] [Conners 1992] [Conners 1993] [Conners 1995] [Conners and Sims 1998] [Covert 1984] [DeCastro et al. 2008] [Denning 1962] [Destarac and van der Vooren 2004] [Domel 2017b] [Domel 2019] [Dugan 1972] [Dwinger and Friedrichs 2017] [Evans and Chamblee 1966] [Farokhi 1998] [Filinov and Ostapyuk 2019] [Flight-Test Evaluation of Engine 1985] [Fredrickson 1974] [Gissendanner 1981] [Goeing et al. 2024] [Gogoi 2021] [Grunnet 1971] [Guajardo 2020] [Hashmi and Radhakrishna 2015] [Herrick 1986] [Hiers 2018] [Highly Elastic Carbon Fiber 1996] [Hinz and Miller 1979] [Hou et al. 2024] [Hunt and Gowadia 1981] [Jackson 1965] [Jakobsson 1951] [Kamman and Perryman 1982] [Keller 1982] [Kelley et al. 1982] [Khalid 1989] [Khalid 1992] [Kim and Kim 2001] [Kim et al. 2020b] [Kitowski 1992] [Klann et al. 1984] [Knox and Meyer 1984] [Kohl and Algranti 1957] [Korsun et al. 2017] [Krasnow 1985] [Krouse et al. 2022] [Kuenkler 1982] [Kuhn et al. 1979] [Kurt 2024] [Kuzmin 2021] [Lake 1990] [Large 1981] [Leese 1966] [Liang et al. 2024] [Lichtsinder et al. 1998] [Lidor et al. 2019] [Lieder et al. 2025] [Liston and Small 1992] [Liu et al. 2026b] [Lockwood 1963] [Mace and Doane 1990] [Mace and Nyberg 1992] [Mandeles 1998] [Mattingly 1989] [Mihaloew and Roth 1982] [Moellmann and O’Connor 1967] [Moore and Collins 1937] [Muehter 1974] [Murphy and Lewis 1979] [Nebesar 1932] [Newell and Herrick 1979] [Papamoschou 1994] [Parker 1991] [Patnaik et al. 2001] [Pinder et al. 2001] [Pitt 1971] [Pizzo 1988] [Plourde et al. 1983] [Powers and Robinson 1992] [Prince and McAulay 1950] [Pyle 1947] [Ray 1983] [Razinsky 1988] [Riggins 1996] [Rodgers 2001] [Rogers 2002] [Rosen 1972] [Saha and Jo 2026] [Salay and Elliott 1993] [Salay and Elliott 1996] [Samanich et al. 1980] [Sanberg et al. 1975] [Sasamoto 1921] [Schiewe et al. 2019] [Schkolnik 1993] [Schmidt and Staudacher 2015] [Sears and Bajek 1958] [Shannak and Alhasan 2002] [Shovlin et al. 1979] [Simpson 1986] [Smith and Wehofer 1982] [Sobel and Lallman 1988] [Su et al. 2025b] [Suder 2019] [Suh 1990] [Svoboda 2000] [Swavely and Soileau 1972] [Synylo et al. 2020] [Takahashi 2022] [Takahashi 2026] [Tate and Gillard 1975] [Throndson 1982] [Toenskoetter 1984] [Trazzi 2004] [Universal Energy Systems INC Dayton OH 1995] [Vance 1973] [Vassilopoulos 1988] [Veres 2001] [Ward and Neeley 1959] [Wells and Urnes 1995] [Willis and Welliver 1976] [Winkler 2019] [Xie et al. 2020] [Xu et al. 2016b] [Yiting et al. 2021] [Yuksel and Aygün 2025] [Zhang et al. 2015a] [Zhang et al. 2016] [Ziogas et al. 2025]

Nozzles and thrust vectoring

Exhaust nozzles, thrust vectoring by mechanical and fluidic means, thrust reversers and deflectors. Of these records, 115 were published in 2001 or earlier, and 74 in 2015 or later.

197 records. [Acierno and Merzari 2022] [Adkins and Sherwood 1996] [Afridi et al. 2023] [Afridi et al. 2024] [Akatsuka 2026] [Anderson and Bradley 1987] [Aukerman 1991] [Aulehla and Besigk 1982] [Back et al. 1972] [Banazadeh and Saghafi 2016] [Barnes et al. 1984] [Berens 2019] [Bergman 1979] [Berrier 1983] [Berrier and Re 1978] [Bevilaqua and Lee 1980] [Bhabar and Sharma 2025] [Bittrick 1984] [Blackman and Eigenmann 1981] [Bond et al. 2001] [Boraas and Ashby 1969] [Bowers 1979] [Bowers and Buchan 1978] [Brodsky 1970] [Bronz 2019] [Burger 1983] [Burger 1986] [Burnes et al. 2001] [Bursey and Dickinson 1990] [Calarese and Walterick 1978] [Capello et al. 2019] [Capone 1975] [Capone 1979] [Capone and Reubush 1983] [Cheatham et al. 1990] [Cheatham et al. 1991] [Chen and Liao 2020] [Chouicha et al. 2019] [Chouicha et al. 2020] [Chu 1980] [Computational and Experimental Analysis 2024] [Crowe and Martin 2019] [Crown 1950] [Das et al. 2025] [Davis and Hines 1976] [Davis and Spicer 1965] [Deere and Hunter 1999] [Deere et al. 2007] [Domel 2015b] [Domel 2017a] [Dong et al. 2025b] [Dunn and Emery 1966] [Dutton 1987] [Eames and Mason 1988] [Eigenmann et al. 1984] [Erwin et al. 1964] [Esker and McArdle 1993] [Esker and Sedrick 1972] [Thillaikumar et al. 2020] [F119 Nozzle Flaps Tested 2005] [Ferlauto and Marsilio 2016] [Fernando et al. 2026] [Finseth et al. 1988] [Flamm 1998] [Flamm et al. 2007] [Fujii et al. 2020] [Gal-Or 1990] [Gill 1973] [Glezer et al. 1985] [Goetz et al. 1976] [Griffin et al. 2000] [Ha et al. 2025] [Kbab et al. 2020] [Hamed et al. 1997] [Hardy 1987] [Harris 1984] [Herrick 1988] [Herrick 1989] [Hienz and Vedova 1984] [Hiley and Bowers 1981] [Hoffman and Allman 1978] [Houx et al. 2022] [Huang et al. 2026] [Humphreys et al. 1988] [Idzorek 1988] [Imlay 1986] [Islam and Islam 2017] [Islam et al. 2018b] [Islam et al. 2018a] [Jammalamadaka et al. 2020] [Jimenez 2001] [Johnson 1990] [Jun et al. 2018] [Jyothy and John Wessley 2023] [Kara and Kurtuluş 2024] [Kelley et al. 2021] [Kentfield 1975] [Kim 2026] [King and Schnelker 1970] [King et al. 1991] [Kumar et al. 2021] [L’Ecuyer et al. 1971] [Lecuyer 1970] [Li et al. 2016b] [Li et al. 2020a] [Liang 1989] [Lieu 1964] [Linderman et al. 1974] [Liu et al. 2025b] [Liu et al. 2026d] [Lucas 1978] [Luo et al. 2025] [Maiden and Petit 1975] [Malaek and Parastari 2001] [Matesanz et al. 1995] [Mathur 1998] [McAmis and Bartlett 1991] [McArdle and Esker 1993] [McArdle and Smith 1990] [McLafferty and Peterson 1983] [Mehalic and Lottig 1987] [Mikhail 1979] [Miller and Protopapas 1985] [Moger and Ramsay 1964] [Nafi and Hasan 2019] [Naik and Chiarelli 1988] [Nayebi and Taeibi Rahni 2024] [Nocoń et al. 2023] [Obye and Hakim 1984] [Orme et al. 1998] [Orme and Sims 1998] [Ornob et al. 2025] [Park et al. 2025a] [Pennington and Meintel 1980] [Peters 1985] [Presz and Greitzer 1988] [Pruitt and Bates 1992] [Rao 1958] [Ravindranath 2025] [Re and Carson 1991] [Resta et al. 2022] [Romine and Johnson 1984] [Rosenberg and Esker 1980] [Ruetten 2018] [Sahu 1985] [Salahudden et al. 2025] [Sarathe and Yadav 2018] [Schirmer and Capone 1989] [Schwagerus et al. 2026] [Schwartz 1975] [Sedgwick 1975] [Seiner and Gilinsky 1995] [Sharjad et al. 2022] [Shi et al. 2024a] [Shukla et al. 2026] [Singh 2026] [Singh and Kushari 2008] [Sova 1988] [Speir and Blozy 1981] [Srivastava et al. 2025] [Straight and Cullom 1982] [Strash et al. 1997] [Strash et al. 2000] [Surapaneni et al. 2016] [Suresh et al. 2026] [Suñol et al. 2015] [Taylor 1988] [Taylor et al. 1973] [Thompson and Epstein 1977] [Thompson and Smith 1981] [Thrust Vectoring 2020] [Tsentis et al. 2023] [Ulizar 1997] [Vohra and Kumar 2025] [Waithe and Deere 2003] [Wallace and Bowers 1982] [Wang and Peterson 1958] [Wang et al. 2017a] [Wang et al. 2018b] [Wilson et al. 2003] [Wing and Asbury 1991] [Wing and Giuliano 1997] [Winkler 2015] [Winkler 2017] [Winkler 2022] [Winkler and Crowe 2019] [Wooten et al. 1984] [Wu and Chow 1985] [Xu et al. 2024] [Zafirov 2010] [Zebbiche and Youbi 2023] [Zhang et al. 2024b] [Zhang et al. 2026a] [Zhu et al. 2016] [Zilz and Bailey 1985] [Zmijanovic] [Zukoski and Auerbach 1976]

Lift fans, ducted fans and the fan in the wing

Lift fans, ducted fans and fans in the wing or fuselage, the X-35’s own lift device and its relatives. Of these records, 88 were published in 2001 or earlier, and 118 in 2015 or later.

226 records. [Aaron et al. 2003] [Aboelezz et al. 2022] [Abrego et al. 2002] [Acheson 2011] [Ai et al. 2020] [Ai et al. 2021b] [Akturk and Camci 2022] [Ale Isaac Khoueini] [Ames 1975] [Atencio et al. 1973] [Bai et al. 2025a] [Beeler 1965] [Beeler and Russell 1964] [Beeler and Volk 1965] [Bento et al. 2020] [Benzakein and Kazin 1971] [Bevilaqua 1996] [Bevilaqua 1997] [Birckelbaw et al. 1995] [Bland and Konsewicz 1976] [Bland et al. 1976] [Brown et al. 2019] [Cai et al. 2019] [Cavage 1975a] [Chakraborty et al. 2022] [Chakraborty et al. 2023] [Chen et al. 2018a] [Cheng and Pei 2020] [Cheng and Pei 2021] [Cheng and Pei 2022] [Cheng et al. 2020] [Cho 2025] [Choi et al. 2022] [Chung et al. 1995b] [Chung et al. 1995a] [Clark and Smith 1965] [Conceptual Design 1973] [Cook and Hickey 1967] [Cook 1993] [Cousins et al. 2026] [Curtiss 1965] [Davis and Ela 1969] [de Paula et al. 2025] [Deng and Ren 2017] [Deng et al. 2018] [Deng et al. 2020] [Denisenko et al. 2021] [Design Definition Study 1975] [Diedrich 1971] [Diedrich 1975] [Diedrich et al. 1972] [Dobek 1973] [Dorfling and Traub 2023] [Dos Santos et al. 2024] [Doğru et al. 2016] [Ducted fan] [Dugan et al. 1971] [Ebus et al. 2022] [Echavarria and Poroseva 2015] [Eldridge et al. 1973] [Elliott 1976] [Engelbrecht et al. 2022] [Envia 2016] [Esker and Roddiger 1979] [Fan et al. 2017] [Far-Field Noise and Internal 1992] [Fasching and Kutney 1964] [Fazeli Asl and Moosapour 2017] [Fenwick 1966] [Ford 1973] [Franklin 1997b] [Gao and Xu 2022] [General Electric Co Cincinnati Oh 1962] [General Electric Co Cincinnati Oh 1963] [General Electric Co Cincinnati Oh 1964] [Gerdes 1993a] [Gerdes and Hynes 1975] [Gerdes 1993b] [Gleiter 1976] [Gong et al. 2021] [Gotlieb 1977] [Goudswaard et al. 2024] [Grahame 1968] [Grahame 1969] [Guerrero et al. 2003] [Guo and Zhou 2026] [Hall and Hodder 1971] [Hanjie et al. 2023] [He et al. 2013] [Heyson 1973] [Hicks et al. 2023] [Hill and Waters 1974] [Hudson 1977] [Hudson and Gee 1977] [Hunt et al. 1977] [Hwang et al. 2023] [Jang et al. 2012] [Jasudavisius 2021] [Jia et al. 2025] [Jiang and Zhang 2016b] [Jiang and Zhang 2016a] [Jiang and Zhang 2017] [Jiang and Zhang 2018] [Jiang and Zhang 2021] [Jiang et al. 2015a] [Jiang et al. 2023b] [Jiang et al. 2025] [Kang et al. 2021] [Kantner et al] [Kim et al. 2020a] [Kirk et al. 1972] [Knight et al. 1973] [Kochanski 1966] [Kutney 1963] [Kutney 1964] [Lam 1998] [Lee et al. 2016] [Li 2008] [Li and Liu 2023] [Li et al. 2022d] [Li et al. 2024a] [Li et al. 2025b] [Lieblein 1970] [Lieblein et al. 1973] [Liu 2023] [Liu and Mi 2025] [Liu et al. 2025g] [Lowe and Sanger 1972] [Luo et al. 2023] [Luo et al. 2024] [Ma] [Maldonado and Fernandes 2024] [Maldonado et al. 2024] [Manzoor et al. 2020] [Martin 1964] [Meng et al. 2026] [Mi 2020] [Miller and Papamoschou 2024] [Miller et al. 2023] [Misiorowski et al. 2019a] [Miwa and Marubashi 2014] [Modelling and Controller Design 2021] [Mumasha et al. 2026] [Myers et al. 2010] [Myers et al. 2019] [Nardi et al. 1999] [Novak 1975] [Obrien 1976b] [Obrien 1976a] [Odukoya and Jo 2026] [Palmer and Holdo̸ 2002] [Papamoschou 2023] [Park et al. 2013] [Park et al. 2015] [Park et al. 2017] [Peddle et al. 2009] [Peterson 1964] [Peterson 1965] [Prasad and Choi 2017] [Qing et al. 2019] [Raeisi and Alighanbari 2017] [Renselaer 1977] [Ritschl et al. 2003] [Cavage 1975b] [Roelke and Zigan 1972] [Rolls et al. 1976] [Ryu et al. 2016] [Salazar et al. 2020] [Sargent and Anemaat 2018] [Savage et al. 2026] [Sayma et al. 2003] [Schaub 1974] [Schlundt 1975] [Schmidt et al. 2021] [Sellers et al. 1977] [Sellers 1973] [Seo and Kim 2016] [Sheng and Sun 2015] [Sheng and Zhao 2016] [Sheng and Zhao 2017] [Sheng and Zhao 2022] [Sheng et al. 2015a] [Sheng et al. 2015b] [Shur et al. 2016] [Simon 2024] [Simon et al. 2023] [Smith 1966a] [Sokhey et al. 2002] [Sowers 1965] [Stewart 1979] [Stewart 1980] [Stockman et al. 1973] [Stockman et al. 1974] [Su et al. 2025a] [Su et al. 2026] [Sullivan 1990] [Sun et al. 2025a] [Sun et al. 2025b] [Sylvester et al. 2011] [Takeyeldein 2026] [Tauber et al. 1976] [True 1967] [Truong and Papamoschou 2015] [Vanderlip and Schneider 1963] [Vasanthakumar et al. 2019] [Wahl and Julian 1956] [Wang et al. 2026b] [Weinstein and Simmons 2024] [Wind Tunnel and Ground 1976] [Winfree 1998] [Xia et al. 2020] [Xiang et al. 2015] [Xiang et al. 2016] [Xu et al. 2016a] [Young 2023] [Yu 2023] [Zabinsky et al. 1975] [Zakaria et al. 2019] [Zhang et al. 2018] [Zhang et al. 2021d] [Zhang et al. 2026b] [Zhao et al. 2022] [Zhao et al. 2023a] [Zhao et al. 2025d] [Zhao et al. 2026a] [Zhao et al. 2026b]

Fighter programmes, defence acquisition and cost

Fighter programmes, the Joint Strike Fighter and its international procurement, defence acquisition, cost and logistics. Of these records, 63 were published in 2001 or earlier, and 26 in 2015 or later.

109 records. [A Canadian Light Fighter 1940] [Shibanov 2024] [Anderson 1989] [Armstrong and Levine 1988] [Ascani 1974] [Bangert et al. 2017] [Behavior Patterns of Three 2022] [Bell Aerospace Co Buffalo Ny 1955] [Boothe 1971] [Bye 1993] [Bykerk et al. 2022] [Carlyle 1976] [Chace 2015] [Cheney 1988] [Cloos and Nelson 1990] [Coen and Foss 1985] [Cordeaux 1991] [Davis 1973] [Davis 2011] [de Haan et al. 2023] [Defense Acquisition Univ Ft Belvoir Va 2004] [Dement 1990] [Donelson et al. 1989] [Dudley 1986] [Eller 1994] [Enzinger 1988] [Fellers and Patierno 1970] [Figge and Bernhardt 1975] [Flight Test Programme 1970] [Franck and Dillard 2006] [Franck and Udis 2015] [Franck et al. 2012] [Gideon and Wasek 2015] [Gran et al. 1977] [Greer 2010] [Griffin 2012] [Guinivan 2004] [Hans et al. 2021] [Harris and Lewis 2012] [Hayase 1974] [Herbst 1980] [Herbst and Ross 1970] [Hillaker 1983] [Hiyama 1974] [Horowitz et al. 2016] [Jimenez et al. 2016] [Jordan 1974] [Keeler 2005] [Kenyon 1974] [Kidd 1966] [Kitowski 1986] [Krahnstoever et al. 2026] [Kwon and Sankar 1991] [Kwon and Sankar 1992] [Lewis 2002] [Lorell 1989] [Lyga 1990] [Lynch 1972] [Madelung 1977] [Malaek and Soltan-Mohammed 2001] [Martindale et al. 1974] [McCown 2011] [McNicol 2014a] [McNicol 2014b] [McNicol and Wu 2014] [Meckstroth and Ordóñez 2020] [Meyn et al. 1993] [Milligan et al. 1994] [Milligan et al. 1995] [Anlauf 2021] [Moore et al. 2013] [Morra and Nicolosi 2025] [Nicholas et al. 1984] [Nicholson 1985] [Parker 1986] [Parrish 1978] [Peteilh et al. 2020] [Pikula 2000] [Rafiq and Qureshi 2022] [Raymer 1998] [Regnier and Nussbaum 2011] [Rice and Locksley 2000] [Rozum 1992] [Schwartz 1988] [Sepulveda and Smith 2019] [Sim 2025] [Simpson 2003] [Sobel 2013] [Spearman 1984] [St. Aubyn 2015] [Stanley 1980] [Stanniland 1974] [Stewart et al. 2011] [Sun and Pang 2025] [Tamrat 1988] [Verma 2018] [Ward 1989] [Watkins 2019] [Weeks 1986] [Whitford 1995] [Wickert 1985] [Wildermuth et al. 1974b] [Wildermuth et al. 1974a] [Winbush and James O. 2012] [Woelk 1989] [Young et al. 1995] [Zhang and Lin 2018] [Zhang et al. 2021e] [Zsolt 2018]

Weight, sizing and aircraft design

Weight and mass estimation, sizing and the conceptual and multidisciplinary design of aircraft. Of these records, 14 were published in 2001 or earlier, and 31 in 2015 or later.

46 records. [Ali and Al-Shamma 2026] [Basgall et al. 2020] [Chai et al. 1995] [Chakraborty and Mishra 2021] [Cleveland 1970] [Computer-Aided System of Aircraft 2018] [Crossley 2004] [Dababneh and Kipouros 2018] [Daidzic 2016] [Davies and Halliday 2024] [Dikbas and Atik 2018] [Goyal 2026] [Haibo and He 2022] [Hile and Denny 1954] [Horvath 2019] [Horvath and Wells 2018] [Hou et al. 2021] [Hughes Tool Co Culver City Ca 1963] [Incorporating Agility Flight Test 1994] [Information Model of Aircraft 2021] [Johnson 1972] [Kowalski et al. 2021] [Liu et al. 2023d] [Mason 1990] [Morelli 2021] [Nigam et al. 2015] [Olson and Henricks 2018] [Oole 1993] [Chiozzotto 2017] [Resulkulyeva and Serebryansky 2022] [Rodriguez and Liscouët-Hanke 2025] [Sabeti and Winter 2024] [Sabeti et al. 2024] [Schrage and Patel 2019] [Solvey 1951] [Sreeletha et al. 2019] [Sridharan and Govindarajan 2021] [Stamm and Woods 2024] [Theoretical Foundation of Formation 2021] [Torenbeek 1972] [Valenti and Stanton 2024] [Ward 1983] [Whitford 1990] [Whitford 1994] [Wickman 1953] [Zhonghua and Haitao 2021]

Aircraft performance, takeoff, landing and ship operation

Aircraft performance, takeoff and landing, ski jumps and operation from ships, range and manoeuvre. Of these records, 47 were published in 2001 or earlier, and 18 in 2015 or later.

66 records. [Aircraft Ship Operations 1991] [Bai et al. 2022] [Baker 1966] [Ball 1966] [Bardera-Mora et al. 2019] [Bell and Pringle 1996] [Blinkhorn 1948] [Campbell 1960] [Chandrasekharan 1988] [Clark and Walters 1986] [Clark 1984] [Connelly 1982] [Dau et al. 1965] [Digges 1971] [Ford 1998] [Frost 1968] [Frost and Rutherford 1963] [Green and Findlay 2016] [Horne and Leland 1962] [Jia et al. 2024] [Kansas Univ Lawrence 1952b] [Kansas Univ Lawrence 1952a] [Kidwell 1963] [Kilner 1982] [Kim et al. 2001] [Kolesar et al. 2019] [Kuchinka 1966] [Kuznetsov et al. 1985] [Laitone 1981] [Lee and Davidson 1973] [Lehman 1964] [Li et al. 2020c] [Martinez Rodriguez and Blaesser 2024] [Mathur and Atkins 2025] [Micklos 1991] [Middleton and Srivatsan 1987] [Middleton et al. 1988] [Middleton et al. 1992] [Miller and Koch 1985] [Moore et al. 1979] [Ouellette 2025] [Paulson et al. 1988] [Philpot et al. 1993] [Ramsey and Dixon 1967] [Rudowsky et al. 2002] [Samuels 1992] [Sharpe and Hansman 2024] [Simpson 1972] [Simpson 1979] [Smith et al. 1979] [Snyder 1950] [Srivatsan et al. 1986] [Stepniewski 1940] [Suharev et al. 2019] [Sóbester 2021] [Thakur and Kumar 2021] [Trobaugh and Obrimski 1980] [van Es 1999] [Vipin and Vijayakumar 2022] [Wittenberg 2001] [Yechout 1988] [Yokell and Baker 1994] [Yoo et al. 2024] [Yue et al. 2015a] [Yue et al. 2015b] [Zhang et al. 2025a]

Kinematics of joints, mechanisms and manipulators

The kinematics of joints, spatial mechanisms, manipulators and constant-velocity couplings, the geometry of the swivel module. Of these records, 54 were published in 2001 or earlier, and 81 in 2015 or later.

142 records. [Antonov and Fomin 2024] [Antonov et al. 2025] [Arrouk et al. 2018] [Baigunchekov et al. 2021] [Baron 2015] [Butler 1964] [Canfield et al. 1994] [Chachada et al. 2016] [Chang 2015] [Chernyshenko and Privalov 2004] [Chiaverini et al. 1990] [Colbourne 1972] [Yu et al. 2021b] [Conti et al. 1992] [Dasgupta 2002] [Day et al. 1983] [Design and Kinematic Analysis 2022] [Dong et al. 2022] [Dwarakanath et al. 1992] [Erkaya et al. 2016] [Erturk and Gomec 2020] [Essomba and Nguyen Vu 2018] [Faria et al. 2018] [Federspiel 1979] [Freudenstein et al. 1984] [Freudenstein et al. 1994] [Ghaedrahmati and Gosselin 2022] [Graham and Bhandari 2022] [Gupta 1973] [Han et al. 2002] [Han et al. 2024] [Hansen 1965] [Hasegawa et al. 1981] [Hayes and Caverly 2020] [He et al. 2018] [Heiran et al. 2017] [Hernández et al. 2003] [Hertz and Hughes 1998] [Hoh et al. 1981] [Ichikawa and Watanabe 1995] [Ichikawa and Watanabe 1996] [Innocenti 1999] [Jinxin et al. 2026] [Kamada et al. 2019] [Kara-Mohamed et al. 2023] [Karamoozian et al. 2018] [Kim and Park 2001] [Kinematic Analysis of RSSR 2017] [Kong 2015] [Kong 2016a] [Kong 2016b] [Krishna et al. 1994] [Lang et al. 2024] [Lee and Yan 1992] [Li and Li 2024] [Li et al. 2016e] [Li et al. 2016a] [Li et al. 2017c] [Li et al. 2020d] [Li et al. 2021b] [Li et al. 2026a] [Liao et al. 2024b] [Liu and Zhao 2019] [Liu et al. 2004] [Lu et al. 2022c] [Mahna and Asnani 1989] [Marter et al. 2020] [Martins and Guenther 2003] [Meng and Lu 1993] [Mruthyunjaya and Raghavan 1984] [Nag et al. 2017] [Nango and Shizu 2001] [Nango et al. 2001] [Nery et al. 2024] [Ni et al. 2026] [Nibin et al. 2024] [Norledge 1998] [Nouri Rahmat Abadi et al. 2019] [Nurahmi and Gan 2018] [Osman and Segev 1972] [Osman et al. 1991] [Otani 2023] [Ou and Tsai 1993] [Pennestrì 1992] [Petrescu and Petrescu 2019] [Piipponen et al. 2015] [Pomrehn and Papalambros 1993] [Qi et al. 2020] [Qiu and Xu 2021] [Rea et al. 2022] [Righettini et al. 2021] [Robson and Lee 2021] [Rosenberg and Křen 1987] [Rusli and Aveka 2021] [Sakhapov et al. 2021] [Sandor et al. 1984] [Schlundt 1976] [Sheikhpour and Bamdad 2017] [Shi et al. 2023] [Shi et al. 2026] [Shinoda et al. 2016] [Shujun 1990] [Skvortsov 2016] [Soylu and Burak Akbulut 1997] [Tang et al. 2021] [Tang et al. 2026] [Tavkhelidze and Davitashvili 1974] [Tian et al. 2018] [Tian et al. 2025] [Urbinati and Pennestrì 1998] [Vahid Amirinezhad and Uyguroğlu 2015] [Wang and Gosselin 1996] [Wang et al. 2014] [Wang et al. 2022d] [Watanabe et al. 1993] [Watanabe et al. 1998] [Watanabe et al. 2001] [Wei et al. 2019] [Wei-Liang and Qi-Xian 1989] [Wei-rong and Xing-yong 1989] [Wu et al. 2021b] [Wu et al. 2023b] [Xiangyang et al. 2019] [Xiaolong et al. 2018] [Xu et al. 2018] [Yang and Yao 1992] [Yang et al. 1992] [Yotov Daskalov 1990] [Yu et al. 2018a] [Yu et al. 2018b] [Yu et al. 2021c] [Yuan et al. 2024a] [Zhang and Wei 2015] [Zhang et al. 2025c] [Zheng et al. 2023] [Zhou and Fenton 1992] [Zhou and Xi 1998] [Zhou et al. 1995] [Zhu et al. 2021] [Zlatanov et al. 1992] [Zou et al. 1996] [Özgören 1999]

The atmosphere, temperature and aerodynamic heating

The standard atmosphere, recovery temperature, the kinetic heating of aircraft structures and the temperatures met at supersonic speed. Of these records, 14 were published in 2001 or earlier, and 5 in 2015 or later.

20 records. [Asai 1994] [Asai 1995] [Divakar and Samaga 2022] [Feng 2016] [Gringorten 1967] [Gringorten and Tattelman 1970] [Guttman and Crutcher 1968] [Keçeci et al. 2025] [Kitchenside 1958] [Krueger and Minzner 1976] [Luce 1949] [Mahlmeister et al. 1955] [Murphy 1957] [Nangia 2011] [Nonweiler 1956] [Shiryaev and Serebryansky 2022] [Simsek et al. 2016] [Stalder et al. 1950] [Taylor 1968b] [Walker 1955]

Fuels and fuel properties

Aviation fuels, their composition, properties and density, and the effect of alternative fuels on engines, aircraft and missions. Of these records, 5 were published in 2001 or earlier, and 18 in 2015 or later.

23 records. [Aircraft Research and Technology 1980] [Alquist et al. 1953] [Behnke et al. 2022] [Canteenwalla and Chishty 2017] [Comesana et al. 2026] [Duong et al. 2020] [Han et al. 2026] [Iyer and Takahashi 2024] [Knoerzer et al. 2018] [Kosir et al. 2020] [Kurt 2026] [Liu et al. 2022b] [Naval Air Test Center Patuxent River MD 1957] [Oh et al. 2024] [Oğur et al. 2024] [Pires et al. 2018] [Rijal et al. 2025] [Friedman et al. 1984] [Ruan et al. 2019] [Russell and Mattes 1974] [Sasi et al. 2023] [Vozka et al. 2019] [Woehler et al. 2023]

Aircraft, jet and rotor acoustics

The noise of hot supersonic and military jets, carrier decks, rotors and vertical-lift aircraft, its prediction and its measurement. Of these records, 7 were published in 2001 or earlier, and 14 in 2015 or later.

21 records. [Afsar et al. 2019] [Aujogue et al. 2022] [Berry and Harris 2024] [Berry and Speakman 1993] [Goparaju et al. 2018] [Gryazev and Karabasov 2018] [Gryazev et al. 2022] [Homans et al. 1978] [Knott 1974] [Pascioni et al. 2024] [Leib et al. 2017] [Oetting 1974] [Plumblee 1967] [Powers et al. 2015] [Powers et al. 2018] [Prasad and Gaitonde 2021] [Speakman et al. 1978] [Rizzi et al. 2025] [Tam 2015] [Wall et al. 2017] [Webster 1971]

Ejectors and thrust augmentation

Ejectors and thrust augmentation, the lift technology the shaft-driven fan displaced. Of these records, 78 were published in 2001 or earlier, and 6 in 2015 or later.

90 records. [Alperin and Wu 1983a] [Alperin and Wu 1983b] [Barankiewicz 1991] [Barankiewicz et al. 1992] [Barankiewicz et al. 1994] [Barankiewicz 1993] [Bernal and Sarohia 1983] [Bernal and Sarohia 1984] [Bevilacqua and Dejoode 1979] [Bevilaqua 1974] [Bevilaqua 1977] [Bevilaqua 1984] [Bevilaqua 1987] [Burley 1971] [Burt et al. 2019] [Byrnes et al. 1974] [Chen et al. 2021] [Cheng et al. 1973] [Clark 1995] [Corsiglia et al. 1989] [Dailey 1955] [Dijkstra et al. 1997] [Doonan and Kuchar 1992] [Drummond 1989] [Drummond and Barankiewicz 1990] [Dudley et al. 1990] [Emanuel 1984] [Fabri and Le Grives 1960] [Fancher 1971] [Franke and Unnever 1985] [Garland 1987] [Gates and Cochran 1961] [Giles 1944] [Graham 1973] [Green and Cyrus 1977] [Gregory and Han 2003] [Hindson and Hardy 1980] [Huang et al. 1999] [Hunter et al. 2002] [Jones 1975] [Katz 1988] [Kim and Park 2025] [Kinzie et al. 1998] [Knox 1962] [Krasheninnikov et al. 1996] [Krothapalli et al. 1985] [Kurtz 1976] [Landry 2005] [Lashkov and Shumilkina 1982] [Lissaman 1969b] [Lopez et al. 1979] [Luidens et al. 1984] [Lund et al. 1986] [McNeill et al. 1995] [Minardi 1982] [Naumowicz and Smith 1992] [O’Keefe et al. 1973] [Oganyan and Loginov 2025] [Papamoschou 1996] [Parkala and Kandath 2026] [Peterson et al. 1995] [Poppen et al. 1991] [Presz et al. 1994] [Quinn 1973a] [Quinn 1973b] [Salter 1974] [Salter 1975] [Seiler and Schum 1978] [Seiler and Schum 1979] [Sharon 1975] [Shehadeh et al. 2004] [Smith et al. 1992] [Sotheran 1982] [Streiff and Henderson 1974] [Sully and Whittley 1987] [Tacina et al. 2004] [Tamm and Spyropoulos 2018] [Throndson 1973] [Tillman and Presz 1993] [Uhuad and Franke 1993] [Viets 1977] [Weber 1960b] [Weber 1960a] [Weber 1961] [Whitfield and Blackburn 1965] [Whitley et al. 1996] [Willis et al. 1982] [Witte 1969] [Yang et al. 1985] [Yungster 2003]

High-temperature and rotating seals

High-temperature, rotating, brush, finger, foil and labyrinth gas seals, the sealing problem of the swivel joint. Of these records, 6 were published in 2001 or earlier, and 5 in 2015 or later.

15 records. [Beermann et al. 2015] [Cangioli et al. 2018] [Dellacorte and Steinetz 1992] [D 1983] [Fellenstein et al. 1996] [Gardner 1999] [Goff et al. 2015] [Kerr and Bensmiller 2024] [More and Datta 2003] [Oswald et al. 2004] [Proctor et al. 2002] [Salehi and Heshmat 2000] [Su et al. 2023] [Taylor et al. 2004] [Wittig et al. 1994]

Where the Framing Breaks Down

The Deflationary Reading Can Be Pushed Too Far

The argument above is capable of proving too much. If one insists that a demonstration teaching the engineers nothing new is theatre, then almost every public demonstration in aviation history is theatre, which is a sign the criterion is wrong rather than a discovery about aviation.

A demonstration has a second, legitimate function, to establish that separately verified capabilities compose. Engineers frequently find that they do not. Doing the three in sequence tests the aircraft’s ability to do them in sequence, including the fuel state, the thermal state, the pilot’s workload and the systems’ behaviour after a long, busy sortie. None of those is captured by the arithmetic in this article, and all of them are real.

Mach 1.05 Is the Worst Place on the Drag Curve, Not the Easiest

The claim that the supersonic leg was cheap should face its strongest counter-argument. Transonic drag rises steeply and peaks a little above Mach one, so Mach 1.05 is close to the most expensive point on the drag curve, far from a comfortable cruise. An aircraft that reaches Mach 1.05 in level flight has demonstrated that it can push through the peak, which is a stiffer test than reaching a higher Mach number would be once past it.

That counter-argument is correct on drag and does not disturb the thermal conclusion, which is separate and which the arithmetic settles. It also does not disturb the ordering conclusion. A conclusion that survives its own best counter-argument is worth more than one that needed the argument suppressed.

The Assumed Inputs and What They Carry

Several results here depend on quantities that were never published, and the conclusions that would move with those assumptions should be set out explicitly.

Assumed quantity	Used for	Does the conclusion depend on it?
Fan polar moment of inertia, 25 to 50 kg·m²	Clutch energy magnitude	No. The halving identity is exact and the time constant is under a fifth of a second across the bracket
Stage loading coefficient of 0.40	Estimating fan speed	Weakly. Every threshold in the counter-rotation table is an ordinary fan speed regardless
Roll-post arm, 2.5 to 4.0 m	Counter-rotation threshold	No. The conclusion is stated across the whole bracket
Zero-lift drag 0.025, rolling friction 0.03, nozzle aft until unstick	Ground roll	Slightly. The minimum of 307 to 422 feet stays short of 500 across the weight bracket
Rear nozzle at its published 18,000 lbf at eighty knots	The Mission X unstick coefficient	No. The finding is that the record cannot pin a coefficient, and a smaller nozzle thrust only raises the bound of 0.637
Transonic drag coefficient 0.035	Dash thrust margin	No. The margin is 2.389 and would survive a doubling
Sortie fuel burn of 3,500 lb	The floor of the takeoff-weight bracket and the landing weight margin	The gain figure, yes. The finding that the ordering helps does not, since the gain exceeds unity for any positive burn
Fan to nozzle separation of 7.5 m	Moment arms and the centre-of-gravity band	Only for the arms in metres. The station as a fraction, 0.4737, needs no separation at all
Thrust split authority of 10 percent	The pitching-moment threshold	Weakly. It sets the threshold height, and the finding is that the threshold is near a metre rather than far from it
Radius of gyration at 0.20 to 0.25 of span	Roll control power	No. The bracket is reported and the residual after a single-rotation reaction is derisory across all of it
Oswald efficiency of 0.75, zero-lift drag 0.018, wave drag 0.017	The dash drag build-up	No. Induced drag is 0.0027 of a total 0.0377, so the build-up is insensitive to it
Thrust lapse exponent of 0.7	Thrust available at altitude	No. The sensitivity is tabulated and the margin survives 0.6 to 1.0
Clutch plate mass of 20 kg	The plate temperature rise	No. It scales the rise linearly and the conclusion is that the bound is absurd, not that the rise is a particular number
Clutch engagement time of 9 s	The power bound on clutch dissipation	No. The bound exceeds the dissipation for any engagement longer than about a third of a second

A Demonstration Is Not Only an Experiment

The framing this series uses treats a research aircraft as an instrument for answering a question, and the X-35 does not fit that framing cleanly. It was a competitor as much as an instrument. Its purpose included persuading a customer, and a machine built partly to persuade is not well described by asking only what it measured. The framing does not break down so much as become incomplete, and Mission X sits in the space that it leaves.

The Source Base

Both Halves, Counted and Not Only Divided

The count and the fraction are reported together, because they move independently and reporting only the fraction misrepresents both. Adding contemporary sources leaves the period count untouched while lowering its share, and adding period sources does the same to the contemporary share. Neither movement is a fact about coverage.

The research survey holds 4,311 research records drawn from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center. Of these, 2,052, or 47.6 percent, were published through 2001, the year the competition was decided, and 1,996, or 46.3 percent, were published from 2015 onward. Of the contemporary half, 965 records were published from 2022 onward. The median publication year of the 4,301 dated records is 2003.

The Period Vocabulary for This Article’s Derived Subjects

Several subjects this article’s equations name are filed in the period literature under other words. The mechanics beneath an equation are not the same literature as the technology above it. This article says momentum drag, and the period reports say inlet momentum drag, ram drag, lift engine installation losses and propulsion-induced effects. This article says canted joint, and the period says swivel duct, deflector, skewed axis coupling and spatial mechanism. The records cited under those subjects are filed under the period’s words, and the period writes installation effects in the plural, so a reader looking for them should search in the period’s vocabulary rather than the article’s.

A Designation With Almost No Literature of Its Own

This is the sharpest finding the source base contains.

Two research records this article cites carry “X-35” in their titles, and both are papers of 2002. They treat the X-35B’s flight control law design and flying qualities in Walker and Allen 2002 and the jet effects test effort in Buchholz 2002. A paper of the same year, Roberts 2002, names the rival’s X-32B. No later research title carries either designation.

The previous two articles found something that looked similar and means the opposite. The X-33’s cluster held sixty records, of which the X-33 article reports fifty-seven predate 2002. The X-34’s held its records and every one predated 2002. Both programmes were cancelled, and the conclusion drawn was that a cancelled programme stops generating literature under its own name, so the documentary trace of a vehicle measures how long it survived rather than what it contributed.

The X-35 is the control case for that claim and it fails it in an unexpected direction. This programme was not cancelled. It won, and its architecture went into production and is flying now. And its designation has a smaller documentary trace than either of the cancelled vehicles, because it barely had one.

What the literature carries instead is the programme name and the product name. Counted by title among the research records this article cites, 54 name the Joint Strike Fighter in full or as JSF, the dated ones running from 1996 to 2026. Nineteen name the F-35, the dated ones running from 2003 to 2019, and thirteen of those also name the Joint Strike Fighter. Beyond those two papers of 2002, nothing names the aeroplane.

The inference this supports is narrower than it first appears, and it is worth stating carefully. The X-35 designation was applied to competition demonstrators built by a contractor and flown for a source selection, and that is not the institutional arrangement that produces published reports. The X-33 and the X-34 were agency programmes with agency reporting obligations, which is why their cancelled programmes still left a paper trail. So the finding is about who was writing rather than about who won, and the three cases together say that the documentary trace measures the institution rather than the aircraft.

The Reference Works

The following books and monographs were drawn on for the standing theory rather than for the aircraft, covering propulsion, powered lift, rotor and fan aerodynamics, aircraft performance and flight test method. Almost none of them is about the X-35 and that is the point, since the relations this article displays are older than the aeroplane and better documented than it.

• The gas turbine
• Aircraft engine design
• Aircraft Engine Design
• Jet propulsion turbojets
• Gas turbines and jet propulsion
• Gas turbine theory
• Aircraft propulsion
• Chemistry problems in jet propulsion
• Jet propulsion engines
• Vertical takeoff and landing aircraft
• V/STOL aircraft
• Flying qualities of piloted V/STOL aircraft
• Fighter Aircraft Design
• Technical Evaluation Report on the Multi-Panel Symposium on…
• The feasibility of the jet-flap rotor as a lift generator for…
• Fighter aircraft design
• Gas Turbine Theory
• 186 kW lightweight diesel aircraft engine design study
• Helicopter theory
• V/STOL aircraft development
• Flight Testing the Fixed Wing Configuration of the Rotor…
• Flight testing the fixed-wing configuration of the rotor…
• Future of V/STOL aircraft systems
• Aircraft engine design
• Special course on fundamentals of fighter aircraft design
• Computer simulation of a pilot in V/STOL aircraft control…
• Aircraft Design
• Harrier Jump Jet
• Active control of V/Stol aircraft
• Basic helicopter aerodynamics
• Lockheed Skunk Works
• Lockheed’s Skunk Works
• Lockheed’s Skunk Works - The First Fifty Years
• Skunk Works
• Lockheed Martin’s Skunk Works
• Elements of gas turbine propulsion
• Gas turbine theory
• Jet propulsion
• Joint strike fighter
• Aircraft Performance And Design
• Principles of Helicopter Aerodynamics
• Basic helicopter aerodynamics
• Gas turbine theory
• Lockheed Martin Skunk Works
• Principles of Helicopter Aerodynamics Cambridge Aerospace…
• American X-vehicles
• Flight Testing of Fixed-Wing Aircraft Aiaa Education Series
• Jet Propulsion
• Lockheed Martin F-35 Joint Strike Fighter
• Harrier Jump Jet
• The AV-8B Harrier Jump Jet Edge Books
• V/STOL Aircraft Design
• Gas Turbine Theory
• Lockheed F-35 Joint Strike Fighter
• AV-8B Harrier Jump Jets Torque Military Machines
• AV-8B Harrier jump jets
• Aircraft Propulsion and Gas Turbine Engines
• Aircraft propulsion
• F-35 Lightning II
• Harrier Jump Jet – A history
• Aircraft Propulsion
• Aircraft design
• American X-Vehicles
• F-35 Lightning II
• American X-Vehicles An Inventory - X-1 to X-50
• Luftwaffe X-Planes
• Aircraft Propulsion
• Commercial Aircraft Propulsion and Energy Systems Research
• Harrier
• Aircraft Propulsion and Gas Turbine Engines, Second Edition
• Joint Strike Fighter
• F-35 Lightning II
• Joint Strike Fighter
• Aircraft Performance and Design
• 75 Years of the Lockheed Martin Skunk Works
• Aerothermodynamics and Jet Propulsion
• Electrified Aircraft Propulsion
• F-35 Lightning II
• Run Time Assurance for Electric Vertical Takeoff and Landing…
• Fundamentals of Jet Propulsion with Power Generation…
• F-35 Lightning II

What the Record Does Not Contain

There is no published flight test report for the X-35B, and the standard survey of the American X-vehicles treats the type in a page. The two papers of 2002 named above are the only research records whose titles name the aircraft. There is no published weight statement, no published engine deck, no published fan map, and no published moment of inertia for the lift fan. The quantitative reconstruction in this article is built entirely from performance figures released for publicity and from the physics that connects them, and the article says so at every point where an assumption was needed.

The Definition of Primary

Primary for this subject means the reports and papers written during the competition and the technology work that preceded it, together with the contemporary programme announcements that record what was flown and when. The flight chronology in this article rests on the latter, because the demonstrator campaign was a contractor activity and its detailed test reports are not public.

For counting, primacy is read from the identifier. A record is a report primary when its address is on the NASA Technical Reports Server or it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. By that rule 651 of the 4,311 research records, or 15.1 percent, are report primaries. The rule does not reach the conference papers of the competition period, such as the inventor’s own papers and the two papers of 2002 on the X-35B, so 15.1 percent is a lower bound on how much of the survey is first-hand.

Thin Subjects

Seven subjects are thin in the cited literature, and they are not all thin for the same reason. A subject can be thin because the work was never done, because the heading is wrong, or because the knowledge is so settled that it stopped generating papers, a distinction the X-34 article draws.

The counts are taken over the research records this article cites, so that anyone can repeat them. A record counts for a subject when its title contains one of the phrases in the second column, matched without regard to case and with a hyphen read as a space, and a record is modern when it was published in 2015 or later. A phrase count also catches a title that uses the phrase in another sense, such as an installed thrust reverser under the thrust lapse phrases, and it misses work filed under another heading, which is what the last column records.

Subject	Title phrases counted	Records	Which kind of thin
Ground roll and takeoff distance	ground roll, takeoff distance, take-off distance, rolling friction	1, none modern	Settled. A closed-form result in every performance textbook, and this article derives it in two lines
Disc loading	disc loading, disk loading	10, one modern	Settled. Nine of the ten date from 1948 to 1971, when disc loading was the parameter by which VTOL concepts were compared, and the subject now sits inside momentum theory and lift fan work
Jet footprint and ground erosion	ground erosion, surface erosion, deck heating, jet footprint, impingement pressure	3, one modern	Wrong heading. It lives inside impingement and ground environment work, in the cluster on jet impingement, ground effect and hot gas ingestion
Rotor spin-up and inertia	spin-up, spin up, spinup, rotational inertia, polar moment, flywheel	0, none modern	Wrong heading. It lives inside drive system transient work
Thrust lapse with altitude	thrust lapse, installed thrust, altitude performance	8, one modern	Wrong heading. It lives inside installed performance and engine decks
Stagnation temperature and kinetic heating	stagnation temperature, recovery temperature, kinetic heating, aerodynamic heating	8, two modern	Moved. The six older records date from 1949 to 1968 and treat the kinetic heating of aircraft structures, and by title the two modern ones are heating prediction tools for high-speed and supersonic vehicle design rather than studies of the transonic case
Standard atmosphere	standard atmosphere, atmospheric model, hydrostatic	2, one modern	Settled. Only one of the two records was published in 2015 or later

One homonym is worth naming because it falls on the article’s own term of art. Figure of merit is a standard quantity in thermoelectrics, where it is written as a dimensionless number, and in plasmonic and photonic sensing. In the contemporary literature, hover efficiency and figure of merit also name properties of solar cells and graphene sensors, and the thermoelectric and photonic records are excluded from this survey.

None of these is padded and none is reported as a gap in the field. Four of the seven are headings rather than subjects, and the article cites the literature where it actually lives. The three that are genuinely settled rather than misheaded are the ground roll, disc loading and the standard atmosphere, and across the three the article cites two records under their phrases published in 2015 or later.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. Much of this subject’s vocabulary also names something else, and a record that shares only such a word is excluded. Acquisition also names corporate mergers, biomedical signal recording and seismic surveying. Figure of merit also names a quantity in thermoelectrics, photonics and power electronics. Ski jump also names dam spillways and a sport, downwash also names chimney and building plumes, and outwash also names glacial outwash plains. Engine performance at altitude also names diesel and gasoline engines for road vehicles, and erosion also names the erosion and corrosion of metals by liquid and slurry jets. Hot gas ingestion also names the ingress of hot gas through a turbine rim seal, which is a different flow from the reingestion of a lift jet’s exhaust. Harrier also names a bird, swivel also names furniture, textiles and a dictionary headword, and electric propulsion also names the ion, Hall and plasma thrusters of spacecraft. Impinging jets of water, liquid fuel, sprays and quenching flows share a word with the jet footprint and none of its subject. Correction, erratum, retraction and withdrawal notices, figure, table and supplementary-material records, peer-review reports, conference programmes, news items and journal front matter are excluded as well, because a survey counts research works and those are parts of works or editorial events rather than works. Reviews of books, unsigned reference entries, reference entries of two pages or fewer, and the abstracts of papers, patents and reports reprinted in the abstract sections of other journals are excluded on the same ground, while a signed encyclopedia article and a textbook chapter are research works and stay.

Some records of doubtful relevance are kept. Underwater vehicle and marine vessel thrust allocation, planetary gearboxes, counter-rotating pumps and turbines, the kinematics of spatial mechanisms and manipulators, gas jets impinging on plates and automotive clutches each share the control-allocation, kinematic, ground-environment or drivetrain problem this article treats. The clutch records are kept in particular because the drivetrain literature that owns the clutch is largely automotive, but only where they treat the engagement, its energy or its heat. Electrical machines, batteries and power electronics written for electric aircraft are excluded, because their subject is the machine rather than the aircraft, while aircraft-level studies of battery and powertrain sizing are kept. A reader may weigh the doubtful classes accordingly.

A record whose only link to this subject is general aeronautics is excluded, and so is one about a vehicle class the argument never uses. Hypersonic and combined-cycle propulsion, rockets, launch vehicles and spacecraft, rotor dynamics and helicopter airworthiness, aircraft systems, maintenance, health monitoring and instrumentation, airline and airport operations, the noise of transport engines and airframes, transport, supersonic-transport and high-lift aerodynamics, boundary-layer physics, combustion and emissions, hydrogen storage, railway and road-vehicle aerodynamics, road-vehicle torque allocation, automotive and marine transmissions, torque converters and shift control, gear manufacturing and gearbox noise, engine accessories, jet impingement in cooling systems and heat exchangers, flapping-wing and lighter-than-air craft, and design studies of unrelated configurations therefore fall outside the survey, as do bibliographies and proceedings volumes. A signed comment on a paper, a discussion of it and its author’s closure or reply are research works, because each argues about a result, and are admitted when their subject is, while an unsigned item of these kinds and a referee’s report are not. A record on a method or a phenomenon the argument relies on is kept whatever vehicle it concerns, which is why rocket plumes on soil, ejectors of any working fluid and boundary layer ingestion on transport aircraft remain.

Every research title 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

The X-35A first flew on 24 October 2000 and completed its conventional campaign on 22 November 2000. The X-35C first flew on 16 December 2000 and completed 73 flights and 58 hours by 11 March 2001. The X-35A was rebuilt as the X-35B, which made its first vertical takeoff and landing on 23 June 2001 and completed testing on 30 July 2001. On 9 July 2001 it performed its first in-flight conversion to hovering mode, refuelled in the air, and reached an indicated Mach 1.08 on the same sortie. On 16 July 2001 it flew a short takeoff, a transition and a vertical landing. On 20 July 2001 Major Art Tomassetti flew Mission X, and on 26 July 2001 Simon Hargreaves repeated it, and on a later flight that day landed vertically at a weight over 34,000 pounds. The contract was awarded to Lockheed Martin on 26 October 2001. The lift system’s published figures, which the LiftSystem reference gives for the production system, are a fifty-inch two-stage counter-rotating fan producing twenty thousand pounds force from twenty-nine thousand shaft horsepower, a three-bearing swivel module passing eighteen thousand pounds force and rotating ninety-five degrees in 2.5 seconds, and roll posts of 1,950 pounds force each. Those figures rest on that single encyclopaedic reference, and the 2001 company releases give the X-35B only a round total of nearly 40,000 pounds of vertical force. Published empty weights for the X-35B disagree, and none rests on a public weighing record. The takeoff-weight bracket uses the higher, the 30,697 pounds of the X-35 reference, because its excess over the X-35A agrees with the 4,000 pounds reported in 1998 for the lift fan installation. The 15,000 pound internal fuel figure matches the operational requirement of that year.

Engineering Analysis

The fan’s figure of merit of 0.697, its induced velocity of 169.3 metres per second, its mass flow of 579.2 pounds per second and its disc loading of 70.2 kilopascals follow from published geometry and performance by momentum theory. The augmentation ratio of 1.676 and the implied core mass flow of 320.2 pounds per second follow from the square-root law. The identity that a hovering jet’s dynamic pressure equals its disc loading is exact. The identity that exactly half the energy drawn through a clutch engaging a stationary inertia is destroyed is exact and independent of the torque profile. The stagnation temperature of 291.2 kelvin at Mach 1.05 and twenty-five thousand feet follows from the standard atmosphere and the energy equation. The unstick force balance shows that the record cannot pin a wing lift coefficient, since the lift system vectored to 60 degrees carries all but at most a coefficient of 0.637 at the heaviest weight in the bracket. The 26 July nozzle deflection is therefore given as a table over weight and coefficient rather than as a single angle. The minimum ground roll of 307.4 to 421.5 feet follows from the momentum balance with the nozzle aft, and the 200 foot Mission X roll in the pilot’s account is shown to be incompatible with an eighty-knot unstick at any weight in the bracket. The coefficient of 0.622 to 0.926 at the 180 knot conversion assumes sea-level density, as the momentum drag does.

The momentum drag of 5,469 pounds force at 180 knots is the fan’s mass flow times the true airspeed and is exact given that flow. The inlet temperature rise of 66.95 kelvin that consumes the hover margin is an inversion of a corrected-flow relation. The centre-of-gravity station at 47.37 percent of the fan-to-nozzle distance follows from the hover moment balance and needs no separation in metres. The canted-joint relation is exact geometry, and the finding that series joints add only when their cants alternate was established by searching the roll space rather than by derivation. The roll control power of 46.07 degrees per second squared and the residual 3.083 rest on an estimated moment of inertia and are reported across a bracket.

Every figure in this section except the series-joint search result can be recomputed from the relations and inputs the article displays, and the assumed inputs are listed in the assumptions table with what each one carries.

Inference

That Mission X was the assembly of already-demonstrated elements rather than the retirement of technical risk is an inference from the flight chronology. It is a strong one, because the programme’s own contemporary statements list every element as already flown four days earlier. That the novel event was the in-flight conversion of 9 July is an inference of the same kind. That counter-rotation was necessary rather than merely desirable is an inference from an inverted threshold calculation across a bracket of assumed roll-post positions. That the short takeoff was optional, a demonstration of technique, follows from the thrust margin of 1.232 at 34,000 pounds and is close to a deduction at that weight, but no Mission X takeoff weight is published, and at the ceiling of the bracket, empty weight plus full internal fuel, the margin is 0.9169 and the deduction fails. Under the lower published empty weight of 23,500 pounds the ceiling margin would be 1.088 and the deduction would hold across the bracket. That the conversion was the expensive event is an inference from the momentum drag, a physical force of computed magnitude, but the step from a large force to a hard piloting task has not been measured, since no workload data for these sorties is public.

What the Record Does Not Settle

Whether the fly-off would have gone the other way without Mission X is not settled and cannot be. Source selection weighs many things, the flight was three months before the decision, and no public document apportions the decision among its inputs.

Whether the X-32 could have flown an equivalent profile with more development time is not settled. Its architecture required reconfiguration as built, but the question of whether that was fundamental or contingent is a design question that was never taken far enough to answer.

Several magnitudes are not settled because the quantities they need have never been published. The clutch energies need the fan’s moment of inertia, the moment arms in metres need the fan-to-nozzle separation, the roll control power needs the roll moment of inertia, and the pitching moment of the momentum drag needs the height of the fan inlet above the centre of gravity. In every case the article gives the relation that needs none of them beside the number that does, and the assumptions table in the framing section shows which conclusions would move.

Whether the demonstration’s persuasive function should count as part of its engineering value is a question of judgement rather than fact, and this article deliberately answers it in two directions in two different sections.

Out of Scope

The production F-35 programme, its cost and schedule history, and the 2004 weight reduction effort are outside this article, which is about a demonstrator that flew in 2001. The low-observable design of either competitor is outside it. The avionics and sensor fusion that dominate the production aircraft’s reputation are outside it, because the demonstrators carried none. The carrier variant’s approach and arrestment characteristics are touched on only where they bear on the variant weight argument. The source selection process itself, and the construct-validity argument about demonstrators generally, are covered in the article on the X-32 and are not repeated here.

Conclusion

The X-35 answered the question of whether a supersonic fighter can hover without being rebuilt between the two, and the answer is yes, by carrying a fan it does not use most of the time.

The fan is worth carrying because thrust rises as the square root of mass flow at fixed power, so moving air the engine never touched multiplies vertical thrust by 1.676 without burning more fuel. It is counter-rotating because a single-rotation fan of that power would have consumed most or all of the aircraft’s roll authority just to hold a hover. Its exhaust is cold because the landing surface and the inlet both care more about temperature and pressure than about thrust, and the fan presses between half and three fifths as hard as the core does at a third of the absolute temperature. At 34,000 pounds that barrier is worth 66.95 kelvin of tolerable inlet temperature rise before the aircraft can no longer hold itself up.

Mission X, the flight the aircraft is remembered for, was not where any of that was established. Every element of it had been flown before 20 July 2001, the first in-flight conversion had happened eleven days earlier on a sortie that went faster, and the arithmetic shows that none of the three events was individually demanding for an aircraft with 41,900 pounds force of vertical thrust at the 34,000 pounds it is documented to have weighed on 26 July. No Mission X weight is published, and the short takeoff was flown by an aeroplane that, on the higher of the published empty weights, could have gone straight up unless it carried more than about three quarters of its internal fuel. The supersonic dash raised the stagnation temperature 3.1 kelvin above a standard sea-level day. The vertical landing happened at the lightest weight of the sortie, in the ordering that makes it easiest at any takeoff weight in the bracket.

And the expensive event is not among the three. Engaging the fan at the 180 knots the aircraft converted at costs 5,469 pounds force of momentum drag, which is 30.4 percent of everything the rear nozzle can produce, applied above and ahead of the centre of gravity where it pitches as well as decelerates. Nothing in the hat trick produces a step change of that size.

The sortie was a demonstration in the exact sense of the word, and the label carries no reproach. It made an architectural property legible in one flight to people who would never read a test report, and it did so honestly, because the property was real and the rival did not have it. What it was not is the experiment. The experiment was the clutch engaging in flight on 9 July, and nobody remembers the date.

Equations

This section collects the 84 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 84, 48 are established and 36 are bespoke. Thrusts and weights are quoted in pounds force and pounds while the relations are evaluated in newtons, kilograms and metres per second, and several letters are reused, so $T$ is a thrust except where a subscript or the standard atmosphere relation makes it a temperature, the thrust is written $F$ in the inlet temperature relations, $L$ is the separation of the fan and the rear nozzle and then the temperature lapse rate, $\ell$ is a roll-post arm and then a bay length, $V$ is the true airspeed except in the fan bay relation, where it is a volume, $A$ is the disc area except in the ground roll, where it is the constant part of the acceleration, $c_p$ is the specific heat of air except in the clutch heating relation, and $r$ in the core flow inversion is the thrust multiplication ratio.

Equation 1, Thrust and Kinetic Power of a Jet. A jet accelerating a mass flow from rest produces a thrust equal to the mass flow times the jet velocity and carries away half the mass flow times the velocity squared as kinetic power.

\[T = \dot{m} v \qquad \text{and} \qquad P = \tfrac{1}{2} \dot{m} v^{2} \tag{1}\]

Equation 2, Thrust at Fixed Power. Eliminating the jet velocity shows that at a fixed power the thrust rises as the square root of the mass flow.

\[T = \sqrt{2 P \dot{m}} \tag{2}\]

Equation 3, Thrust per Unit Power. Dividing the thrust by the kinetic power shows that the thrust obtained from each unit of power is inversely proportional to the jet velocity.

\[\frac{T}{P} = \frac{\dot{m} v}{\tfrac{1}{2} \dot{m} v^{2}} = \frac{2}{v} \tag{3}\]

Equation 4, Disc Area of the Lift Fan. The published fifty-inch diameter gives a disc area of 1.2668 square metres. Rolls-Royce LiftFan

\[A = \frac{\pi D^{2}}{4} = \frac{\pi \times 1.27^{2}}{4} = 1.2668 \ \text{m}^{2} \tag{4}\]

Equation 5, Momentum Theory Thrust and Induced Velocity. Momentum theory gives the thrust of an ideal actuator disc as twice the density times the disc area times the induced velocity squared, which inverts for the induced velocity. Momentum theory

\[T = 2 \rho A v_i^{2} \qquad \Rightarrow \qquad v_i = \sqrt{\frac{T}{2 \rho A}} \tag{5}\]

Equation 6, Induced Velocity of the Lift Fan. The published thrust and disc area at sea-level density give an induced velocity of 169.3 metres per second at the disc. Momentum theory

\[v_i = \sqrt{\frac{88{,}964}{2 \times 1.225 \times 1.2668}} = 169.3 \ \text{m/s} \tag{6}\]

Equation 7, Mass Flow Through the Fan. The density times the disc area times the induced velocity gives a mass flow of 262.7 kilograms per second.

\[\dot{m} = \rho A v_i = 1.225 \times 1.2668 \times 169.3 = 262.7 \ \text{kg/s} \tag{7}\]

Equation 8, Ideal Power of the Disc. The ideal power an actuator disc requires is its thrust times the induced velocity, here 15.06 megawatts.

\[P_{\text{ideal}} = T v_i = 88{,}964 \times 169.3 = 15.06 \ \text{MW} \tag{8}\]

Equation 9, Figure of Merit of the Lift Fan. The ratio of ideal to published shaft power gives a figure of merit of 0.697.

\[\mathrm{FM} = \frac{P_{\text{ideal}}}{P_{\text{shaft}}} = \frac{15.06}{21.63} = 0.697 \tag{9}\]

Equation 10, Total Published Vertical Thrust. The fan, the three-bearing swivel module and the two roll posts sum to 41,900 pounds force of vertical thrust. Rolls-Royce LiftFan

\[T_{\text{total}} = 20{,}000 + 18{,}000 + 2 \times 1{,}950 = 41{,}900 \ \text{lbf} \tag{10}\]

Equation 11, Multiplication of Vertical Thrust Over the Dry Engine. The total vertical thrust over the published dry thrust of the engine gives a factor of 1.676. Lockheed Martin X-35

\[\frac{41{,}900}{25{,}000} = 1.676 \tag{11}\]

Equation 12, Bespoke Thrust Multiplication as a Pure Mass Flow Effect. The thrust ratio is written as the square root of the total to core mass flow ratio on the assumption that the whole augmentation is the mass flow effect at unchanged power with ideal jets.

\[\frac{T_{\text{total}}}{T_{\text{dry}}} = \sqrt{\frac{\dot{m}_{\text{fan}} + \dot{m}_{\text{core}}}{\dot{m}_{\text{core}}}} \tag{12}\]

Equation 13, Bespoke Core Mass Flow Recovered by Inversion. Inverting the pure mass flow model with the fan flow from momentum theory recovers an unpublished core flow of 320.2 pounds per second.

\[\dot{m}_{\text{core}} = \frac{\dot{m}_{\text{fan}}}{r^{2} - 1} = \frac{579.2}{1.676^{2} - 1} = 320.2 \ \text{lb/s} \tag{13}\]

Equation 14, Disc Loading of the Fan. The published thrust over the disc area gives a disc loading of 70.2 kilopascals.

\[\frac{T}{A} = \frac{88{,}964}{1.2668} = 70.2 \ \text{kPa} \tag{14}\]

Equation 15, Jet Dynamic Pressure Equals the Disc Loading. For an ideal actuator disc the dynamic pressure of the fully developed jet is identically the disc loading.

\[q_{\text{jet}} = \tfrac{1}{2} \rho \left(2 v_i\right)^{2} = 2 \rho v_i^{2} = \frac{T}{A} \tag{15}\]

Equation 16, Exit Density and Area From Continuity. For a jet expanded to ambient pressure the ideal gas law gives the exit density and continuity gives the exit area from the mass flow.

\[\rho_e = \frac{p_0}{R T_e} \qquad \text{and} \qquad A_e = \frac{\dot{m}_{\text{core}}}{\rho_e v_e} \tag{16}\]

Equation 17, Footprint Pressure of the Core Jet. The rear thrust over the exit area, rewritten through continuity, gives the pressure the core jet applies to the surface below.

\[\frac{T_r}{A_e} = \frac{T_r \, \rho_e v_e}{\dot{m}_{\text{core}}} \tag{17}\]

Equation 18, Isentropic Exit Temperature of the Fan. The isentropic relation applied to the fan pressure ratio from momentum theory gives an efflux temperature of 334.9 kelvin.

\[T_{\text{fan}} = T_0 \, \Pi^{\frac{\gamma - 1}{\gamma}} = 288.15 \times 1.693^{0.2857} = 334.9 \ \text{K} \tag{18}\]

Equation 19, Reaction Torque of a Single-Rotation Fan. A fan absorbing a shaft power at an angular velocity applies a reaction torque equal to the power over the angular velocity.

\[Q = \frac{P}{\omega} \tag{19}\]

Equation 20, Roll-Post Couple. Two roll posts each producing a force at a distance from the centreline supply a couple of twice the force times the arm.

\[C = 2 F_{\text{post}} \ell \tag{20}\]

Equation 21, Fan Pressure Ratio From the Jet Dynamic Head. The ideal disc raises total pressure by the jet dynamic head, which gives a fan pressure ratio of 1.693.

\[\Pi = \frac{p_0 + q_{\text{jet}}}{p_0} = \frac{101{,}325 + 70{,}229}{101{,}325} = 1.693 \tag{21}\]

Equation 22, Isentropic Total Temperature Rise. For an isentropic compression the total temperature rise follows from the pressure ratio, here 46.8 kelvin.

\[\Delta T_0 = T_0 \left(\Pi^{\frac{\gamma - 1}{\gamma}} - 1\right) = 288.15 \times \left(1.693^{0.2857} - 1\right) = 46.8 \ \text{K} \tag{22}\]

Equation 23, Specific Work of the Fan. The specific work is the specific heat at constant pressure times the total temperature rise.

\[w = c_p \Delta T_0 = 1004.7 \times 46.8 = 47.0 \ \text{kJ/kg} \tag{23}\]

Equation 24, Bespoke Blade Speed From an Assumed Stage Loading. The blade speed follows from the specific work with the work shared equally between two stages and an assumed stage loading coefficient of 0.40.

\[U = \sqrt{\frac{c_p \Delta T_0}{2 \psi}} = \sqrt{\frac{47{,}002}{2 \times 0.40}} = 242.4 \ \text{m/s} \tag{24}\]

Equation 25, Bespoke Rotational Speed of the Fan. The blade speed from the assumed loading coefficient over the fan circumference gives an estimated 3,645 revolutions per minute.

\[N = \frac{60 U}{\pi D} = \frac{60 \times 242.4}{\pi \times 1.27} = 3{,}645 \ \text{rpm} \tag{25}\]

Equation 26, Work Drawn During a Slipping Clutch Engagement. For a source at constant angular velocity driving an inertia from rest, the torque impulse fixes the work drawn at the inertia times the source speed squared.

\[\int Q \, dt = I \omega_s \qquad \Rightarrow \qquad W_{\text{in}} = \omega_s \int Q \, dt = I \omega_s^{2} \tag{26}\]

Equation 27, Kinetic Energy of the Fan. The fan ends the engagement holding half its inertia times the source speed squared.

\[E_{\text{fan}} = \tfrac{1}{2} I \omega_s^{2} \tag{27}\]

Equation 28, Energy Destroyed in the Clutch. The difference between the work drawn and the energy stored shows that exactly half the energy drawn is dissipated, independent of the torque history.

\[E_{\text{clutch}} = I \omega_s^{2} - \tfrac{1}{2} I \omega_s^{2} = \tfrac{1}{2} I \omega_s^{2} \tag{28}\]

Equation 29, Bespoke Stored Energy Expressed as a Time. The article defines a time scale as the fan’s stored kinetic energy over the shaft power, evaluated across a bracket of assumed polar moments of inertia.

\[\tau = \frac{E_{\text{fan}}}{P_{\text{shaft}}} = \frac{I \omega_s^{2}}{2 P_{\text{shaft}}} \tag{29}\]

Equation 30, Adiabatic Temperature Rise of the Clutch Plates. The dissipated energy over the mass and specific heat of the plate pack gives its temperature rise in an adiabatic engagement.

\[\Delta T_p = \frac{E_{\text{clutch}}}{m_p c_p} = \frac{I \omega_s^{2}}{2 m_p c_p} \tag{30}\]

Equation 31, Bespoke Upper Bound on Clutch Dissipation. At most half the rated shaft power can be destroyed over an engagement time the article assumes to be nine seconds, which bounds the dissipation at 97.3 megajoules.

\[E_{\text{clutch}} \le \tfrac{1}{2} P t = \tfrac{1}{2} \times 21.63 \times 10^{6} \times 9 = 97.3 \ \text{MJ} \tag{31}\]

Equation 32, Bespoke Dissipation as a Share of the Bound. The bracketed dissipation for the assumed inertias, spread over the assumed nine seconds, is between 1.9 and 3.7 percent of the bound.

\[\frac{E_{\text{clutch}} / t}{\tfrac{1}{2} P} = \frac{E_{\text{clutch}}}{\tfrac{1}{2} P t} = \frac{1.82}{97.3} = 0.0187 \quad \text{to} \quad \frac{3.64}{97.3} = 0.0374 \tag{32}\]

Equation 33, Momentum Drag of the Lift Fan. A fan ingesting air at the flight speed and discharging it vertically suffers a drag equal to its mass flow times the true airspeed.

\[D_{\text{mom}} = \dot{m} V \tag{33}\]

Equation 34, Bespoke Deceleration From Momentum Drag at Conversion. The momentum drag at 180 knots is computed with the sea-level fan mass flow, an assumption at the conversion altitude, and divided by a mass of 34,000 pounds. eleven days earlier

\[a = \frac{D_{\text{mom}}}{m} = \frac{24{,}329}{15{,}422} = 1.578 \ \text{m/s}^{2} = 0.1609 \, g \tag{34}\]

Equation 35, Bespoke Available Pitch Moment. The pitch moment available is taken as an assumed ten percent of the fan thrust acting on a moment arm that rests on an assumed fan to nozzle separation of 7.5 metres. Rolls-Royce LiftFan

\[M_{\text{avail}} = 0.10 \, T_f x_f = 0.10 \times 88{,}964 \times 3.553 = 31{,}606 \ \text{N m} \tag{35}\]

Equation 36, Bespoke Inlet Height at Which Momentum Drag Exhausts Pitch Authority. The assumed pitch moment over the momentum drag gives the inlet height of 1.299 metres at which the two are equal.

\[h^{*} = \frac{M_{\text{avail}}}{D_{\text{mom}}} = \frac{31{,}606}{24{,}329} = 1.299 \ \text{m} \tag{36}\]

Equation 37, Hover Moment Balance. In steady hover the moment of the fan thrust about the centre of gravity cancels that of the rear nozzle.

\[T_f x_f = T_r x_r \tag{37}\]

Equation 38, Centre of Gravity Fixed by the Hover Balance. The moment balance with the published fan and rear nozzle thrusts places the centre of gravity at 47.37 percent of the separation behind the fan.

\[\frac{x_f}{L} = \frac{T_r}{T_f + T_r} = \frac{18{,}000}{38{,}000} = 0.4737 \tag{38}\]

Equation 39, Bespoke Thrust Lapse With Inlet Temperature. The thrust is taken to fall as the inverse of inlet total temperature, a simplification the article adopts for a fixed corrected operating point.

\[\frac{F}{F_{0}} = \frac{T_{\text{amb}}}{T_{\text{amb}} + \Delta T} \tag{39}\]

Equation 40, Bespoke Critical Inlet Temperature Rise. Inverting the assumed thrust lapse at a weight of 34,000 pounds gives the inlet temperature rise of 66.95 kelvin that consumes the hover margin.

\[\Delta T_{\text{crit}} = T_{\text{amb}} \left(\frac{F_{\text{total}}}{W} - 1\right) = 288.15 \times 0.2324 = 66.95 \ \text{K} \tag{40}\]

Equation 41, Mean Slew Rate of the Swivel Module. The published sweep of ninety-five degrees in 2.5 seconds is a mean slew rate of 38.0 degrees per second. Rolls-Royce LiftFan

\[\dot{\delta} = \frac{\Delta \delta}{\Delta t} = \frac{95^{\circ}}{2.5 \ \text{s}} = 38.0 \ \text{deg/s} \tag{41}\]

Equation 42, Deflection of a Single Canted Joint. Rolling one side of a joint canted at an angle to the duct axis deflects the downstream axis by an amount that reaches twice the cant at half a turn.

\[\cos\delta = \cos^{2}\beta + \sin^{2}\beta \cos\phi \tag{42}\]

Equation 43, Cant Required of a Single Bearing. A single joint must be canted at half the required ninety-five degree deflection, or 47.5 degrees.

\[\beta_{\text{single}} = \frac{95^{\circ}}{2} = 47.5^{\circ} \tag{43}\]

Equation 44, Bespoke Cant Required of Three Alternating Bearings. Taking three alternating joints to reach six times their common cant, a result of the article’s own numerical search, the required cant is 15.83 degrees.

\[\beta_{\text{three}} = \frac{95^{\circ}}{6} = 15.83^{\circ} \tag{44}\]

Equation 45, Roll Acceleration From the Roll Posts. The roll angular acceleration is the roll-post couple divided by the roll moment of inertia.

\[\dot{p} = \frac{2 F_{\text{post}} \ell}{I_{xx}} \tag{45}\]

Equation 46, Bespoke Roll Moment of Inertia. The roll inertia is estimated with a radius of gyration the article assumes to be 0.22 of the span.

\[I_{xx} = m k_x^{2} = 15{,}422 \times 2.213^{2} = 75{,}400 \ \text{kg m}^{2} \tag{46}\]

Equation 47, Bespoke Roll Acceleration With the Posts at 3.5 Metres. The roll acceleration uses the assumed roll inertia and an assumed roll-post arm of 3.5 metres.

\[\dot{p} = \frac{60{,}718}{75{,}400} = 0.805 \ \text{rad/s}^{2} = 46.07 \ \text{deg/s}^{2} \tag{47}\]

Equation 48, Bespoke Residual Roll Acceleration With a Single-Rotation Fan. The roll acceleration left after a single-rotation fan’s reaction torque at the estimated speed is about three degrees per second squared.

\[\dot{p}_{\text{residual}} = \frac{4{,}063}{75{,}400} = 3.083 \ \text{deg/s}^{2} \tag{48}\]

Equation 49, Swept Volume of the Fan. The fan bay is at least the swept volume of the fan, its disc area times the bay length.

\[V = \frac{\pi D^{2}}{4} \ell \tag{49}\]

Equation 50, Bespoke Fuel Displaced by the Fan Bay. The fuel weight lost to the fan uses a bay length near the middle of an assumed range of 1.2 to 1.6 metres and an assumed fuel density of 800 kilograms per cubic metre.

\[W_{\text{fuel}} = \rho_f V = 800 \times 1.773 = 1{,}419 \ \text{kg} = 3{,}128 \ \text{lb} \tag{50}\]

Equation 51, Unstick Condition and Lift Equation. An aircraft leaves the ground once wing lift and downward lift system thrust together reach the weight, with lift given by the standard lift equation.

\[L + T_v \ge W, \qquad L = \tfrac{1}{2} \rho V^{2} S C_L \tag{51}\]

Equation 52, Thrust That Points Down Whatever the Nozzle Does. The published fan thrust and the two roll posts sum to 23,900 pounds force.

\[T_f = 20{,}000 + 2 \times 1{,}950 = 23{,}900 \ \text{lbf} \tag{52}\]

Equation 53, Bespoke Vectored Lift at the Mission X Unstick. The vertical thrust assumes that the rear nozzle delivers its published 18,000 pounds force at eighty knots when vectored to 60 degrees.

\[T_v = T_f + T_r \sin\theta = 23{,}900 + 18{,}000 \sin 60^{\circ} = 23{,}900 + 15{,}588 = 39{,}488 \ \text{lbf} \tag{53}\]

Equation 54, Dynamic Pressure Times Wing Area at Eighty Knots. At eighty knots and sea-level density over the wing area the product of dynamic pressure and area is 9,751 pounds force.

\[\tfrac{1}{2} \rho V^{2} S = \tfrac{1}{2} \times 1.225 \times 41.156^{2} \times 41.81 = 43{,}376 \ \text{N} = 9{,}751 \ \text{lbf} \tag{54}\]

Equation 55, Bespoke Upper Bound on the Unstick Lift Coefficient. The lift coefficient required at the ceiling of the article’s weight bracket, with the assumed vectored thrust, is at most 0.637.

\[C_L \ge \frac{W - T_v}{\tfrac{1}{2} \rho V^{2} S} = \frac{45{,}697 - 39{,}488}{9{,}751} = 0.637 \tag{55}\]

Equation 56, Dynamic Pressure Times Wing Area at Sixty Knots. At sixty knots and sea-level density the product of dynamic pressure and wing area is 5,485 pounds force.

\[\tfrac{1}{2} \rho V^{2} S = \tfrac{1}{2} \times 1.225 \times 30.867^{2} \times 41.81 = 24{,}399 \ \text{N} = 5{,}485 \ \text{lbf} \tag{56}\]

Equation 57, Nozzle Deflection That Balances the Weight. Solving the unstick condition for the nozzle deflection gives its sine in terms of the weight, the downward thrust, the wing lift and the rear thrust.

\[\sin\theta = \frac{W - T_f - C_L \, \tfrac{1}{2} \rho V^{2} S}{T_r} \tag{57}\]

Equation 58, Bespoke Lift Coefficient at the First Conversion. The lift coefficient at the 180 knot conversion is evaluated at sea-level density, which the article states as an assumption at 9,000 feet. eleven days earlier

\[C_L = \frac{W}{\tfrac{1}{2} \rho V^{2} S}, \qquad \tfrac{1}{2} \times 1.225 \times 92.6^{2} \times 41.81 = 219{,}588 \ \text{N} = 49{,}365 \ \text{lbf} \tag{58}\]

Equation 59, Bespoke Lift Coefficient Range at Conversion. Across a weight bracket from the empty weight taken for it to full internal fuel, the sea-level coefficient runs from 0.622 to 0.926.

\[C_L = \frac{30{,}697}{49{,}365} = 0.622 \quad \text{to} \quad \frac{45{,}697}{49{,}365} = 0.926 \tag{59}\]

Equation 60, Mean Acceleration for the Quoted Mission X Roll. Reaching eighty knots from rest in the quoted 200 feet requires a mean acceleration of 1.417 times standard gravity.

\[\bar{a} = \frac{V^{2}}{2 s} = \frac{41.156^{2}}{2 \times 60.96} = 13.89 \ \text{m/s}^{2} = 1.417 \, g \tag{60}\]

Equation 61, Bespoke Maximum Acceleration With All Thrust Aft. Pointing all published thrust aft with no drag or friction at the bracket floor of 34,197 pounds, which rests on an assumed fuel burn, allows at most 1.225 times standard gravity.

\[\frac{a_{\max}}{g} = \frac{T_{\text{total}}}{W} = \frac{41{,}900}{34{,}197} = 1.225 \tag{61}\]

Equation 62, Bespoke Frictionless Minimum Ground Roll. Only the rear nozzle thrust at the bracket floor weight, with no drag or rolling friction, gives a minimum roll of 538.3 feet.

\[s_{\min} = \frac{V^{2}}{2 g \, T_r / W} = \frac{41.156^{2}}{2 \times 9.80665 \times 0.5264} = 164.1 \ \text{m} = 538.3 \ \text{ft} \tag{62}\]

Equation 63, Bespoke Ground Roll Equation of Motion. The equation of motion takes the rear nozzle as pointing aft until unstick, an assumption for the 26 July flight, with rolling friction and zero-lift drag.

\[m \frac{dV}{dt} = T_r \cos\theta - \mu \left(W - T_v\right) - \tfrac{1}{2} \rho V^{2} S C_{D_0}, \qquad \theta = 0 \tag{63}\]

Equation 64, Closed-Form Distance Under Constant and Quadratic Deceleration. Integrating an acceleration made of a constant part less a term in the square of speed gives the distance in closed form.

\[s = \frac{1}{2B} \ln\!\left(\frac{A}{A - B V^{2}}\right) \tag{64}\]

Equation 65, Bespoke Minimum Roll on 26 July. The closed form evaluated with the constants built from the assumed friction and drag at 34,000 pounds gives a minimum roll of 307.4 feet.

\[s_{\min} = 93.69 \ \text{m} = 307.4 \ \text{ft} \tag{65}\]

Equation 66, Mean Acceleration for the Quoted 26 July Roll. The quoted roll of about five hundred feet to sixty knots requires a mean acceleration of 0.3187 times standard gravity.

\[\bar{a} = \frac{V^{2}}{2 s_q} = \frac{30.867^{2}}{2 \times 152.4} = 3.126 \ \text{m/s}^{2} = 0.3187 \, g \tag{66}\]

Equation 67, Bespoke Acceleration Available During the Roll. The acceleration available is approximated by the constant part less the drag term evaluated at half the squared unstick speed.

\[a_{\text{avail}} = A - \tfrac{1}{2} B V^{2} \tag{67}\]

Equation 68, Largest Weight the Lift System Can Hold. The total vertical thrust over standard gravity gives a largest supportable weight of 41,900 pounds.

\[W_{\max} = \frac{T_{\text{total}}}{g} = \frac{186{,}381}{9.80665} = 19{,}006 \ \text{kg} = 41{,}900 \ \text{lb} \tag{68}\]

Equation 69, Hover Margin at the Documented Weight. The total vertical thrust over the documented 34,000 pounds gives a margin of 1.232. flown to about Mach 1.2

\[\frac{T_{\text{total}}}{W} = \frac{41{,}900}{34{,}000} = 1.232 \tag{69}\]

Equation 70, Bespoke Mission X Takeoff Weight Bracket. The takeoff weight is bracketed between the empty weight plus an assumed burn of 3,500 pounds and the empty weight plus full internal fuel, neglecting the pilot and instrumentation. Lockheed Martin X-35

\[W_{\text{TO}} = W_{\text{empty}} + W_{\text{fuel}}, \qquad 30{,}697 + 3{,}500 = 34{,}197 \ \le \ W_{\text{TO}} \ \le \ 30{,}697 + 15{,}000 = 45{,}697 \ \text{lb} \tag{70}\]

Equation 71, Bespoke Hover Margin at the Ceiling of the Bracket. At the ceiling of the article’s bracket the margin falls to 0.9169, so vertical takeoff at full internal fuel was impossible.

\[\frac{T_{\text{total}}}{W_{\text{TO}}} = \frac{41{,}900}{45{,}697} = 0.9169 \tag{71}\]

Equation 72, Temperature and Pressure in the Standard Troposphere. Below the tropopause the temperature falls linearly with altitude and the hydrostatic equation integrates to a power law in pressure.

\[T = T_{\text{SL}} - Lh \qquad \text{and} \qquad p = p_{\text{SL}} \left(\frac{T}{T_{\text{SL}}}\right)^{\frac{g_0}{RL}} \tag{72}\]

Equation 73, Exponent of the Tropospheric Pressure Law. Standard gravity over the gas constant and the lapse rate gives an exponent of 5.2559.

\[\frac{g_0}{RL} = \frac{9.80665}{287.05 \times 0.0065} = 5.2559 \tag{73}\]

Equation 74, Density and Speed of Sound at Twenty-Five Thousand Feet. The ideal gas law and the speed of sound relation give the density and speed of sound at 7,620 metres in the standard atmosphere.

\[\rho = \frac{p}{RT} = 0.5489 \ \text{kg/m}^{3} \qquad \text{and} \qquad a = \sqrt{\gamma R T} = 309.7 \ \text{m/s} \tag{74}\]

Equation 75, Stagnation Temperature of the Supersonic Dash. The energy equation gives a stagnation temperature of 291.2 kelvin at Mach 1.05 and twenty-five thousand feet.

\[T_0 = T + \frac{V^{2}}{2 c_p} = 238.62 + \frac{325.2^{2}}{2 \times 1004.7} = 291.2 \ \text{K} \tag{75}\]

Equation 76, Dynamic Pressure of the Dash. Half the standard density times the speed squared gives 29,018 pascals at Mach 1.05.

\[q = \tfrac{1}{2} \rho V^{2} = \tfrac{1}{2} \times 0.5489 \times 325.2^{2} = 29{,}018 \ \text{Pa} \tag{76}\]

Equation 77, Bespoke Lift Coefficient of the Dash. The lift coefficient takes the dash weight as 34,000 pounds, the figure documented for a different flight.

\[C_L = \frac{W}{qS} = \frac{151{,}240}{29{,}018 \times 41.81} = 0.1247 \tag{77}\]

Equation 78, Bespoke Induced Drag Coefficient of the Dash. The induced drag coefficient uses an Oswald efficiency the article assumes to be 0.75.

\[C_{D_i} = \frac{C_L^{2}}{\pi \, \mathrm{AR} \, e} = \frac{0.1247^{2}}{\pi \times 2.42 \times 0.75} = 0.002726 \tag{78}\]

Equation 79, Bespoke Drag Build-Up of the Dash. The drag coefficient adds an assumed zero-lift coefficient of 0.018 and an assumed wave-drag increment of 0.017 to the induced term.

\[C_D = C_{D_0} + C_{D_w} + C_{D_i} = 0.018 + 0.017 + 0.002726 = 0.03773 \tag{79}\]

Equation 80, Bespoke Drag of the Dash. The dynamic pressure times the wing area times the assumed drag build-up gives a drag of 10,289 pounds force.

\[D = q S C_D = 29{,}018 \times 41.81 \times 0.03773 = 45{,}771 \ \text{N} = 10{,}289 \ \text{lbf} \tag{80}\]

Equation 81, Bespoke Thrust Available at Altitude. The thrust available is a sea-level thrust of 40,000 pounds force times the density ratio raised to an exponent the article assumes to be 0.7.

\[T = T_{\text{SL}} \sigma^{n} = 40{,}000 \times 0.4481^{0.7} = 40{,}000 \times 0.5701 = 22{,}805 \ \text{lbf} \tag{81}\]

Equation 82, Bespoke Thrust to Drag Margin of the Dash. The assumed thrust lapse against the assumed drag build-up gives a thrust to drag ratio of 2.216.

\[\frac{T}{D} = \frac{22{,}805}{10{,}289} = 2.216 \qquad \text{or} \qquad \frac{D}{T} = \frac{10{,}289}{22{,}805} = 0.451 \tag{82}\]

Equation 83, Bespoke Gain in Hover Margin From Landing Last. The article defines the gain from the ordering as the ratio of landing to takeoff margin, which reduces to the takeoff weight over the takeoff weight less the assumed fuel burn.

\[\frac{T_{\text{total}} / W_{\text{land}}}{T_{\text{total}} / W_{\text{TO}}} = \frac{W_{\text{TO}}}{W_{\text{TO}} - W_{\text{fuel}}} \tag{83}\]

Equation 84, Bespoke Landing Margin at the Ceiling With a Hot Inlet. At the ceiling landing weight the margin is reduced by the assumed thrust lapse for a ten kelvin inlet temperature rise to 0.960.

\[\frac{T_{\text{total}}}{W_{\text{land}}} \cdot \frac{T_{\text{amb}}}{T_{\text{amb}} + \Delta T} = \frac{41{,}900}{42{,}197} \times \frac{288.15}{298.15} = 0.960 \tag{84}\]

Notation

• $\dot{m}$, the mass flow, with $\dot{m}_{\text{fan}}$ the fan flow and $\dot{m}_{\text{core}}$ the engine core flow
• $v_i$, the induced velocity at the disc
• $P_{\text{shaft}}$, the shaft power absorbed by the fan, with $P_{\text{ideal}}$ the ideal power of the disc
• $\mathrm{FM}$, the figure of merit of the fan
• $T_{\text{total}}$, the total vertical thrust of the lift system, with $T_{\text{dry}}$ the dry thrust of the engine
• $T_f$, the thrust of the lift fan, with $T_r$ the thrust of the rear nozzle and $T_v$ the downward thrust of the lift system
• $x_f$, the distance of the fan behind or ahead of the centre of gravity, with $x_r$ that of the rear nozzle
• $q_{\text{jet}}$, the dynamic pressure of the fully developed jet
• $\Pi$, the fan pressure ratio
• $\psi$, the stage loading coefficient
• $U$, the blade speed
• $Q$, the torque
• $F_{\text{post}}$, the thrust of one roll post
• $\ell$, the roll-post arm, and in the fan bay relation the bay length
• $\omega_s$, the angular velocity of the driving source
• $I_{xx}$, the roll moment of inertia, with $k_x$ the radius of gyration in roll
• $E_{\text{clutch}}$, the energy dissipated in the clutch, with $E_{\text{fan}}$ the kinetic energy of the fan
• $\tau$, the stored energy of the fan expressed as a time
• $D_{\text{mom}}$, the momentum drag of the lift fan
• $M_{\text{avail}}$, the pitch moment available, with $h^{*}$ the inlet height at which it equals the momentum drag moment
• $\Delta T_0$, the total temperature rise across the fan, with $\Delta T$ an inlet temperature rise
• $T_{\text{amb}}$, the ambient temperature
• $\delta$, the deflection of the duct axis
• $\beta$, the cant angle of a joint
• $\phi$, the relative roll angle of the two sides of a joint
• $\dot{p}$, the roll angular acceleration
• $W_{\text{TO}}$, the takeoff weight, with $W_{\text{land}}$ the landing weight and $W_{\text{empty}}$ the empty weight
• $W_{\text{fuel}}$, the fuel weight
• $\theta$, the deflection of the rear nozzle below the horizontal
• $\mu$, the rolling friction coefficient
• $C_{D_0}$, the zero-lift drag coefficient, with $C_{D_w}$ the wave-drag increment and $C_{D_i}$ the induced drag coefficient
• $\mathrm{AR}$, the wing aspect ratio
• $\sigma$, the density ratio against sea level
• $T_{\text{SL}}$, a sea-level value, the sea-level temperature in the atmosphere relation and the sea-level thrust in the thrust lapse

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• Sechter, Brendan. 2025. “X-Planes: Lockheed X-17.” Brendan A R Sechter’s Development Blog, October 23. https://sgeos.github.io/aerospace/history/engineering/2025/10/23/x_planes_lockheed_x17.html
• Sechter, Brendan. 2025. “X-Planes: Hiller X-18.” Brendan A R Sechter’s Development Blog, October 24. https://sgeos.github.io/aerospace/history/engineering/2025/10/24/x_planes_hiller_x18.html
• Sechter, Brendan. 2025. “X-Planes: Curtiss-Wright X-19.” Brendan A R Sechter’s Development Blog, October 25. https://sgeos.github.io/aerospace/history/engineering/2025/10/25/x_planes_curtiss_wright_x19.html
• Sechter, Brendan. 2025. “X-Planes: Boeing X-20 Dyna-Soar.” Brendan A R Sechter’s Development Blog, October 26. https://sgeos.github.io/aerospace/history/engineering/2025/10/26/x_planes_boeing_x20.html
• Sechter, Brendan. 2025. “X-Planes: Northrop X-21.” Brendan A R Sechter’s Development Blog, October 27. https://sgeos.github.io/aerospace/history/engineering/2025/10/27/x_planes_northrop_x21.html
• Sechter, Brendan. 2025. “X-Planes: Bell X-22.” Brendan A R Sechter’s Development Blog, October 28. https://sgeos.github.io/aerospace/history/engineering/2025/10/28/x_planes_bell_x22.html
• Sechter, Brendan. 2025. “X-Planes: Martin Marietta X-23 PRIME and a Contested Assignment.” Brendan A R Sechter’s Development Blog, October 29. https://sgeos.github.io/aerospace/history/engineering/2025/10/29/x_planes_martin_marietta_x23.html
• Sechter, Brendan. 2025. “X-Planes: Martin Marietta X-24.” Brendan A R Sechter’s Development Blog, October 30. https://sgeos.github.io/aerospace/history/engineering/2025/10/30/x_planes_martin_marietta_x24.html
• Sechter, Brendan. 2025. “X-Planes: Bensen X-25.” Brendan A R Sechter’s Development Blog, October 31. https://sgeos.github.io/aerospace/history/engineering/2025/10/31/x_planes_bensen_x25.html
• Sechter, Brendan. 2025. “X-Planes: Schweizer X-26 Frigate.” Brendan A R Sechter’s Development Blog, November 1. https://sgeos.github.io/aerospace/history/engineering/2025/11/01/x_planes_schweizer_x26.html
• Sechter, Brendan. 2025. “X-Planes: Lockheed X-27.” Brendan A R Sechter’s Development Blog, November 2. https://sgeos.github.io/aerospace/history/engineering/2025/11/02/x_planes_lockheed_x27.html
• Sechter, Brendan. 2025. “X-Planes: Osprey X-28 Sea Skimmer.” Brendan A R Sechter’s Development Blog, November 3. https://sgeos.github.io/aerospace/history/engineering/2025/11/03/x_planes_osprey_x28.html
• Sechter, Brendan. 2025. “X-Planes: Grumman X-29.” Brendan A R Sechter’s Development Blog, November 4. https://sgeos.github.io/aerospace/history/engineering/2025/11/04/x_planes_grumman_x29.html
• Sechter, Brendan. 2025. “X-Planes: Rockwell X-30 and the National Aero-Space Plane.” Brendan A R Sechter’s Development Blog, November 5. https://sgeos.github.io/aerospace/history/engineering/2025/11/05/x_planes_rockwell_x30.html
• Sechter, Brendan. 2025. “X-Planes: Rockwell-MBB X-31.” Brendan A R Sechter’s Development Blog, November 6. https://sgeos.github.io/aerospace/history/engineering/2025/11/06/x_planes_rockwell_mbb_x31.html
• Sechter, Brendan. 2025. “X-Planes: Boeing X-32.” Brendan A R Sechter’s Development Blog, November 7. https://sgeos.github.io/aerospace/history/engineering/2025/11/07/x_planes_boeing_x32.html
• Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-33.” Brendan A R Sechter’s Development Blog, November 8. https://sgeos.github.io/aerospace/history/engineering/2025/11/08/x_planes_lockheed_martin_x33.html
• Sechter, Brendan. 2025. “X-Planes: Orbital Sciences X-34.” Brendan A R Sechter’s Development Blog, November 9. https://sgeos.github.io/aerospace/history/engineering/2025/11/09/x_planes_orbital_sciences_x34.html