The Boeing X-32 is the only aircraft in this series that was built to lose or win a competition rather than to answer a research question, and it lost. Every other X-plane so far existed to find something out. The X-31 flew adversarial engagements to learn whether post-stall manoeuvring wins. The X-30 was cancelled because its central quantity could not be established. The X-32 was a competitor, flown against the Lockheed Martin X-35 in a fly-off for the largest military aircraft procurement in history, and on 26 October 2001 the Department of Defense chose the other one. This is the thirty-third 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, and the X-31.

The easy misreading is that the X-32 lost because direct lift does not work. It works. It had been working since the Hawker Siddeley Harrier entered service in 1969, and the X-32B hovered and landed vertically. Nothing about the mechanism was in doubt.

What was being decided was something else, and it has two halves. The first is a question in propulsion physics with a clean answer that this article derives from published numbers, drawing on a research base that the National Aeronautics and Space Administration had been building since the 1970s. The second is a question about evidence, namely whether two demonstrators, neither of which was the aeroplane being bought, could settle a choice about an aircraft that did not yet exist.

The Research Question

The keystone is what a fly-off decides and on what evidence.

A research aircraft is dimensioned against an unknown. A competitor is dimensioned against a rival, and the two are not the same discipline. The X-32 had to be good enough at everything and better at something, against an opponent whose design it could not see, under a set of criteria written by a customer buying three different aircraft for three different services.

The binding question is therefore evidentiary rather than physical. Both companies could build an aeroplane that hovered. What neither could do was build the aeroplane it was proposing, because the demonstrators were concept demonstrators, funded to reduce risk and never meant as prototypes. A demonstrator that differs from the proposal in the feature under test is evidence about something other than the proposal, and this article’s central historical finding is that the X-32’s wing was such a feature.

The Physical Half Has a Clean Answer

Two ways exist to hold a fighter up on its engine. The direct-lift approach sends the engine’s own exhaust downward through vectoring nozzles, the Harrier’s method and Boeing’s. The lift-fan approach takes shaft power off the engine, drives a large fan mounted behind the cockpit, and adds a second cold stream, which was Lockheed Martin’s.

Those are not two arrangements of the same thing. They are two points on a curve, and the curve has a known shape. All of the propulsion argument in this article follows from one relation derived in the sizing section below, and the relation is undisputed. It has been in the textbooks since momentum theory was written down.

The Evidentiary Half Remains Open

The second half is harder, and this article spends its effort there. A fly-off produces one comparison. It is not a sample, it is not repeatable, and the thing compared is not the thing being bought. Asking what such an exercise establishes is a question about whether the quantity measured is the quantity that matters, rather than about sampling error.

The previous article in this series asked a related question and got a different kind of answer. The X-31’s combat evaluation flew a series of engagements and the difficulty was that a finite sample carries a wide interval. Here the sample size is one, and the difficulty is that the one trial was not a trial of the proposed aircraft.

The Contemporary Literature collects the acquisition studies of what competitive prototyping can establish in its cluster on defence acquisition, competition, prototyping and cost.

Programme Origin

Three Aircraft, One Airframe

The Joint Strike Fighter programme set out to build one aircraft for three services with three incompatible requirements. The Air Force wanted a conventional runway fighter to replace the F-16. The Navy wanted a carrier aircraft, which means a stronger structure, a bigger wing and an approach speed low enough to catch a wire. The Marine Corps and the Royal Navy wanted a short takeoff and vertical landing aircraft to replace the Harrier, which means carrying a lift system in an airframe the size of the Air Force variant at the cost of fuel volume.

The STOVL requirement drives the rest of the design, because it is the only one that cannot be met by scaling. A carrier aircraft is a heavier version of a land aircraft. A vertical-landing aircraft is a different aeroplane wearing the same skin.

Studies of commonality between variants form the cluster on commonality, product families and requirements, later in this article.

The Programme That Preceded It

The competition descends from two earlier efforts. The Common Affordable Lightweight Fighter work at the Defense Advanced Research Projects Agency explored whether a single design could serve several services, and the Joint Advanced Strike Technology programme consolidated a set of service-specific studies into one. The concept demonstration contracts were awarded to Boeing and Lockheed Martin in November 1996, and McDonnell Douglas, whose entry used a gas-coupled lift fan, was eliminated at that point.

That elimination means the fly-off was already the second round. The field had been narrowed from three to two before either surviving aircraft existed.

Writing on the programme, from the Joint Advanced Strike Technology studies onward, makes up the cluster on the Joint Strike Fighter programme and its demonstrators in the survey below.

What Each Company Brought

Boeing’s design used a single large delta wing with 55 degrees of leading-edge sweep, a chin inlet under the nose, and a direct-lift STOVL system in which a valve diverted the core exhaust to a pair of vectoring nozzles near the centre of gravity.

Lockheed Martin’s design used a conventional wing and tail, a shaft-driven lift fan behind the cockpit, a three-bearing swivel module at the tail, and roll posts in the wings [Lockheed Martin F-35B propulsion ground test release].

The chin inlet is a consequence rather than a choice. A direct-lift aircraft must put its lift nozzles at the centre of gravity, which puts the engine in the front portion of the fuselage, which puts the inlet forward and low [Jenkins, Landis and Miller, American X-Vehicles]. The configuration follows from the propulsion decision, a first sign that the two entries were not two styles of the same aeroplane.

For the lineages each company drew on, see the clusters on lift fans, lift engines, ejectors and remote lift and on the Harrier, the Pegasus engine and the vectored-thrust lineage in The Contemporary Literature.

Sizing From First Principles

This section derives the relation the competition turned on, checks three published numbers against each other, and computes the quantity that settled the decision.

The Relation

Static thrust is mass flow times jet velocity,

\[T = \dot{m} V_j \tag{1}\]

and the power added to the stream is the rate of increase of its kinetic energy,

\[P = \tfrac{1}{2} \dot{m} V_j^{2} \tag{2}\]

Eliminating the velocity between them gives the relation that governs the choice,

\[T = \sqrt{2 P \dot{m}} \tag{3}\]

For a fixed power, thrust rises as the square root of the mass flow. Equivalently, writing it the other way,

\[T = \frac{2P}{V_j} \tag{4}\]

halving the jet velocity doubles the thrust for the same power.

Mass flow ratio Thrust ratio at fixed power Power ratio at fixed thrust
1.00 1.000 1.000
2.00 1.414 0.500
2.24 1.497 0.446
4.00 2.000 0.250

That table is the entire case for the lift fan and it fits on four lines. A lift fan spends shaft power accelerating a large cold mass flow slowly. A direct-lift system spends the same power accelerating a smaller hot flow quickly. The first produces more thrust from the same core, and the other differences between the two aircraft follow from it.

Modern work on momentum theory appears below in the cluster on momentum theory, rotors, propellers and hover performance.

The Disc-Loading Form of the Same Statement

The relation is more useful expressed through the area the flow passes through, and the momentum theory that governs it has been the standard treatment of a static disc since the 1970s, as in Azuma and Kawachi 1975, with the actuator-disc optimum in hover worked out more recently. It is the disc loading, which momentum theory relates to the induced velocity. The relations used here are the standard ones set out in Leishman on helicopter aerodynamics and in Hill and Peterson on propulsion. For a disc of area $A$ producing thrust $T$ in still air, momentum theory gives the velocity induced at the disc,

\[V_i = \sqrt{\frac{T}{2 \rho A}} \tag{5}\]

and the flow reaches twice that velocity far downstream. The ideal power is the thrust times the induced velocity,

\[P_{\text{ideal}} = T V_i = T \sqrt{\frac{T}{2 \rho A}} \tag{6}\]

So the power required for a given lift rises as the square root of the disc loading. A system that pushes its air through a small hole pays for it in power, in exhaust velocity, in noise, in ground erosion and in temperature.

Three Published Numbers That Were Never Published Together

The lift fan’s diameter, its cold thrust and its shaft power appear in different places, and taken together they imply a figure of merit that has to be a number a real fan can achieve.

Quantity Value
Lift fan diameter 50 inches
Disc area 13.64 sq ft
Cold thrust 20,000 lbf
Shaft power delivered 29,000 hp

The disc loading is 1,467 pounds per square foot, the induced velocity is

\[V_i = \sqrt{\frac{20{,}000}{2 (0.0023769)(13.64)}} = 555.5 \ \text{ft/s} \tag{7}\]

with a far-field velocity of 1,110.9 feet per second, and the ideal power is

\[P_{\text{ideal}} = (20{,}000)(555.5) = 1.111 \times 10^{7} \ \text{ft lbf/s} = 20{,}199 \ \text{hp} \tag{8}\]

That is 20,199 horsepower of ideal power. Dividing by the delivered shaft power gives

\[\text{FM} = \frac{20{,}199}{29{,}000} = 0.697 \tag{9}\]

The same two relations fix the mass flow the fan moves, since the thrust is the mass flow times the far-field velocity,

\[\dot{m} = \frac{T}{2 V_i} = \frac{20{,}000}{2(555.5)} = 18.00 \ \text{slug/s} = 579 \ \text{lb/s} \tag{10}\]

and the power loading follows as 0.690 pounds of thrust per horsepower delivered.

A figure of merit near 0.7 is what a good rotor achieves in hover. The measure is the standard one used in rotor design optimisation. The three numbers are mutually consistent, a check to make before building an argument on them, and one that no printed source appears to have made.

The Nozzle the Direct-Lift System Would Have Needed

The X-32B’s nozzle size need not be assumed, because the question can be inverted. What nozzle area would the direct-lift system have needed for its jets to match the lift fan’s disc loading?

\[A = \frac{T}{T/A} = \frac{28{,}000}{1{,}467} = 19.09 \ \text{sq ft} \tag{11}\]

That is a single circular nozzle 4.93 feet across, or two nozzles each 3.49 feet across, on a fuselage 45.0 feet long and 17.3 feet tall.

The obstacle is geometric, and no engineering trade removes it. There is nowhere on a single-engine fighter to put two three-and-a-half-foot nozzles at the centre of gravity, and the exhaust passing through them would in any case be hot, where the fan’s is cold.

Taking plausible nozzle sizes instead shows how far from the fan the direct-lift system had to sit.

Two nozzles Total area Disc loading Induced velocity Loading against the fan
2.0 ft across 6.28 sq ft 4,456 lb/sq ft 968.2 ft/s 3.04
2.5 ft across 9.82 sq ft 2,852 lb/sq ft 774.6 ft/s 1.94
3.0 ft across 14.14 sq ft 1,981 lb/sq ft 645.5 ft/s 1.35

The Disc Loading Is Also the Pressure on the Ground

The table above says more than it appears to, because of an identity the article had already assembled without stating. Momentum theory gives the disc loading as

\[\frac{T}{A} = 2 \rho V_i^{2} \tag{12}\]

and the flow reaches twice the induced velocity far downstream, so the dynamic pressure in the fully developed jet is

\[q_{\infty} = \tfrac{1}{2} \rho (2 V_i)^{2} = 2 \rho V_i^{2} = \frac{T}{A} \tag{13}\]

The disc loading and the dynamic pressure in the jet are the same number. The jet impingement ground-effect literature measures that quantity directly, and its computational treatment reproduces it. A table of disc loadings is therefore also a table of the pressure each architecture imposes on whatever it is hovering over.

System Disc loading Dynamic pressure at the ground Against the fan
Lift fan 1,467 lb/sq ft 1,467 lb/sq ft 1.00
Two nozzles 3.0 ft across 1,981 lb/sq ft 1,981 lb/sq ft 1.35
Two nozzles 2.5 ft across 2,852 lb/sq ft 2,852 lb/sq ft 1.94
Two nozzles 2.0 ft across 4,456 lb/sq ft 4,456 lb/sq ft 3.04

Deck coatings, runway surfaces and the people standing near the aeroplane all feel that difference, and deriving it costs nothing extra, since the propulsion argument already needed the quantity.

The lift fan and the vectoring nozzle sit at different points on the curve, and the curve is steep.

What the Two Architectures Produced

The published totals make the consequence plain. The engine’s military rating is from the X-32’s published specification, and the lift system’s components and total are from the LiftSystem’s published component thrusts.

System Lift Source of lift
Rolls-Royce Pegasus, for reference 23,800 lbf Vectored fan and core
Direct lift, engine military rating 28,000 lbf Entirely hot core stream
Lift fan plus swivel module plus roll posts 41,900 lbf 47.7 percent cold

The lift system exceeds the Pegasus by a factor of 1.76 and the direct-lift core by 1.18. The lift fan alone contributes 20,000 pounds, the swivel module 18,000 and the roll posts 3,900.

The partition is exact,

\[L = T_{\text{fan}} + T_{\text{3BSM}} + T_{\text{posts}} = 20{,}000 + 18{,}000 + 3{,}900 = 41{,}900 \ \text{lbf} \tag{14}\]

with shares of 47.7, 43.0 and 9.3 percent. The published total equals the sum of its published parts, a small check worth making before relying on any of the four numbers.

Nearly half of the winning aircraft’s vertical lift came from air that never went through the engine. That is the square-root law made physical.

Engine cycles and thrust more broadly are the subject of the cluster on engine cycles, variable cycle engines and engine performance.

The Number the Competition Was About

A vertical landing is not a demonstration. It is an operational requirement with a weight attached, because an aircraft returning from a mission with unexpended weapons has to be able to land with them aboard. The quantity that matters is what can be brought back.

The landing weight is bounded by the lift divided by a control margin, and what is available for fuel and stores is whatever is left after the empty weight is paid,

\[W_{\text{land}} = \frac{L}{k} \qquad \text{and} \qquad W_{\text{allowance}} = \frac{L}{k} - W_{\text{empty}} \tag{15}\]

At an empty weight of 24,030 pounds and an assumed five percent control margin, so that $k = 1.05$,

Architecture Lift Maximum landing weight Allowance over empty
Direct lift, core only 28,000 lbf 26,667 lb 2,637 lb
Lift fan plus core plus posts 41,900 lbf 39,905 lb 15,875 lb

The difference is 13,238 pounds and the ratio is 6.02. The empty weight cancels from the difference, which depends only on the two lifts $L_{\text{fan}}$ and $L_{\text{direct}}$ and the margin,

\[\Delta W_{\text{allowance}} = \frac{L_{\text{fan}} - L_{\text{direct}}}{k} = \frac{41{,}900 - 28{,}000}{1.05} = 13{,}238 \ \text{lb} \qquad \text{and} \qquad \frac{15{,}875}{2{,}637} = 6.02 \tag{16}\]

That is the competition in one line. Both aircraft can hover. One of them can come home with two and a half thousand pounds of fuel and weapons and the other with nearly sixteen thousand.

Why the Allowance Is Badly Conditioned

The allowance is a small difference between two large numbers, and that makes it fragile in a way the raw thrust figures conceal. Differentiating,

\[\frac{\partial W_{\text{allowance}} / W_{\text{allowance}}}{\partial L / L} = \frac{L/k}{W_{\text{allowance}}} \tag{17}\]

or the landing weight divided by the allowance.

Architecture Amplification Meaning
Direct lift 10.11 One percent of thrust is ten percent of the allowance
Lift fan 2.51 One percent of thrust is two and a half percent

The same physical loss costs the direct-lift aircraft four times as much of what it can bring home.

Because the X-32B’s STOVL lift is not published, the conclusion is tested against the assumption rather than resting on it. The engine’s military rating is an upper bound, since a direct-lift arrangement loses thrust in the ducting and the vanes.

Assumed lift Allowance After a 50 degree inlet rise Amplification
24,000 lbf −1,173 lb −2,201 lb not meaningful
26,000 lbf 732 lb −382 lb 33.83
28,000 lbf 2,637 lb 1,437 lb 10.11
30,000 lbf 4,541 lb 3,256 lb 6.29
32,000 lbf 6,446 lb 5,076 lb 4.73

The allowance is a straight line in the lift, of slope one over the margin,

\[W_{\text{allowance}} = \frac{1}{k} L - W_{\text{empty}} = 0.9524 \, L - 24{,}030 \tag{18}\]

crossing zero at

\[L_{\text{break even}} = k \, W_{\text{empty}} = 1.05 (24{,}030) = 25{,}232 \ \text{lbf} \tag{19}\]

Below that lift the allowance is negative, meaning the aircraft could not land vertically at its empty weight, let alone with anything in it.

The amplification blows up as the allowance approaches zero, and no numerical artefact causes it. The shape of the problem does. A direct-lift fighter of this size operates near a singularity in its bring-back capability. A single figure of 10.11 understates the matter, because the quantity is badly conditioned across the plausible range, and no plausible assumption rescues it.

The Vehicle

The published table is thinner than for any flown aircraft in this series, and the sources disagree with one another on a basic dimension. Every figure in the table except the second span is from the X-32’s published specification, and the second span is the 9.15 metres that the same source gives in its description of the wing.

Quantity Value Metric
Length 45 ft 0.1 in 13.72 m
Wingspan, one published figure 36 ft 0 in 10.97 m
Wingspan, another published figure 30 ft 0 in 9.15 m
Height 17 ft 3.8 in 5.28 m
Wing area 590 sq ft 54.8 m²
Leading-edge sweep 55 degrees  
Empty weight 24,030 lb 10,900 kg
Maximum takeoff weight 38,000 lb 17,200 kg
Engine One Pratt and Whitney YF119-PW-614  
Military thrust 28,000 lbf 120 kN
Afterburning thrust 50,000 lbf 220 kN
Maximum speed Mach 1.2  

The Span Disagreement Is Not a Rounding Difference

Two published spans differ by 19.9 percent and they cannot both describe the same airframe. Thirty-six feet against thirty is not a conversion error and not a rounding, and the two imply materially different aeroplanes.

\[A = \frac{b^{2}}{S} = \frac{36.0^{2}}{590} = 2.197 \qquad \text{against} \qquad \frac{30.02^{2}}{590} = 1.527 \tag{20}\]

An aspect ratio of 2.20 and one of 1.53 are different wings. The article carries both figures without choosing between them, because no source available pairs either figure with a particular airframe, although the X-32B is recorded as having a narrower span than the X-32A, and a specification sheet transcribed through several publications acquires this kind of error. The dimensional record for these aircraft is collected in the inventory of X-vehicles, which is also on the reports server.

Where the record permits a check, it passes. The two ratios that a specification sheet has to satisfy are

\[\frac{W}{S} = \frac{38{,}000}{590} = 64.41 \ \text{lb/ft}^{2} \qquad \text{and} \qquad \frac{T}{W} = \frac{28{,}000}{38{,}000} = 0.737 \tag{21}\]

with 1.316 on afterburner, and all three are ordinary values for a fighter of this size.

Dependent Systems

The Direct-Lift Arrangement

A butterfly valve diverted the core stream to a pair of thrust-vectoring nozzles near the centre of gravity. The arrangement is a form of thrust vectoring. In conventional flight the exhaust went aft through the main nozzle. In STOVL mode it went down [Boeing X-32B first flight release]. The arrangement is the Harrier’s in principle, executed with a modern engine and a single core, where the Pegasus’s exhaust left through four rotating nozzles.

The consequence for the airframe is the chin inlet. Putting lift nozzles at the centre of gravity puts the engine in the front portion of the fuselage, which puts the intake forward and low, under the nose [Jenkins, Landis and Miller, American X-Vehicles]. That inlet is what most people remember about the aeroplane, and it follows downstream from the propulsion choice and is no styling decision, and the two entries were therefore different aircraft.

Inlets and vectoring nozzles each have a cluster in The Contemporary Literature, on supersonic inlets, intakes and airframe-propulsion integration and on nozzles, thrust vectoring and thrust reversers.

Hot Gas Ingestion Is Worse Than It Sounds

An aircraft hovering on its exhaust stands in a fountain of its own hot gas, and some of it reaches the inlet. The mechanism has two paths, and the aerodynamics of a jet close to a surface is the subject of ground effect. In the near field the jets impinge on the ground, spread outward, meet under the fuselage and rise as a fountain, which twin-jet impingement studies treat directly. In the far field the outward wall jet meets the free stream or the aircraft’s motion and rolls up into a ground vortex that carries hot gas forward and up into the intake.

The cost is thrust, and the relation is simple. A turbofan matched at a corrected operating point carries its mass flow and its thrust in the corrected forms

\[\dot{m}_{\text{corr}} = \frac{\dot{m} \sqrt{\theta}}{\delta} \qquad \text{and} \qquad T_{\text{corr}} = \frac{T}{\delta} \qquad \text{with} \qquad \theta = \frac{T_{t}}{T_{\text{ref}}}, \ \delta = \frac{p_{t}}{p_{\text{ref}}} \tag{22}\]

so at a fixed corrected point and a fixed inlet pressure the delivered thrust falls as the square root of inlet total temperature. This makes reingestion expensive rather than merely untidy, and the effect was being measured on lift engines by the end of the 1960s in model tests of concepts to reduce it and correlated against geometric scale and surface wind. A rise of $\Delta T$ therefore costs a fraction of thrust

\[\frac{\Delta T_{\text{thrust}}}{T} = 1 - \sqrt{\frac{T_{\text{ref}}}{T_{\text{ref}} + \Delta T}} \tag{23}\]

where $T_{\text{ref}}$ is the standard sea-level temperature of 59 degrees Fahrenheit, or 518.67 degrees Rankine, and $\Delta T$ is in Fahrenheit degrees.

Inlet temperature rise Thrust lost
10 degrees Fahrenheit 0.95 percent
25 degrees 2.33 percent
50 degrees 4.50 percent
100 degrees 8.44 percent
150 degrees 11.93 percent

The corrected-parameter treatment behind that relation is standard and is set out in Mattingly on engine design, with the configuration consequences in Raymer on conceptual design and the underlying aerodynamics in Kuethe and Chow.

Those look like small numbers and they are not. Apply the amplification derived above. A fifty degree rise costs 4.50 percent of lift, and the allowance that remains, written $W_{\text{allowance}}’$, is

\[W_{\text{allowance}}' = \frac{L \left(1 - \Delta T_{\text{thrust}}/T\right)}{k} - W_{\text{empty}} = \frac{28{,}000 (1 - 0.0450)}{1.05} - 24{,}030 = 1{,}437 \ \text{lb} \tag{24}\]

so the fraction of the allowance the rise consumes is the amplification times the thrust lost,

\[\frac{W_{\text{allowance}} - W_{\text{allowance}}'}{W_{\text{allowance}}} = \frac{L/k}{W_{\text{allowance}}} \, \frac{\Delta T_{\text{thrust}}}{T} = 10.11 \times 0.0450 = 0.455 \tag{25}\]

which is 45.5 percent of the entire bring-back allowance, taking it from 2,637 pounds to 1,437. The same relation applied to the 2.33 percent lost to a twenty-five degree rise gives 23.5 percent.

The ingestion penalty comes off the small number, not the large one, and that sentence states the difficulty in full.

The Feedback Makes It Dangerous

A thrust deficit at hover is not a performance shortfall. It is a descent. Lift below weight gives a downward acceleration of

\[a = g \, \frac{\Delta T_{\text{thrust}}}{T} \tag{26}\]

which for a fifty degree rise is 1.45 feet per second squared. Integrating twice gives the sink,

\[s = \tfrac{1}{2} a t^{2} = \tfrac{1}{2} (1.45)(2)^{2} = 2.89 \ \text{ft in two seconds} \tag{27}\]

against 1.50 feet for a twenty-five degree rise.

And a descent is proximity to the ground, and proximity is more ingestion. The loop closes on itself. The pilot’s response is more throttle, which produces more hot gas, which is fed back into the inlet.

The temperature rise alone therefore does not measure the difficulty. A system with margin absorbs it. A system operating where its allowance is badly conditioned does not.

Two clusters below hold the experimental and computational record of hot gas ingestion and of the jet-induced ground environment, those on hot gas ingestion, reingestion and inlet temperature distortion and on jet-induced ground effects, suckdown, fountains and ground vortices.

What the Lift Fan Does About the Same Problem

The lift fan attacks hot gas ingestion three times over, and none of the three was designed for that purpose. They are consequences of the square-root law.

The exhaust is cooler, and the mixing relation says by how much. The parameters that correlate ingestion were identified early, in Krishnamoorthy 1971. Two streams combine at the mass-weighted mean of their temperatures,

\[T_{\text{mix}} = \frac{\dot{m}_c T_c + \dot{m}_h T_h}{\dot{m}_c + \dot{m}_h} \tag{28}\]

and the mass flows follow from the thrusts and the velocities, since $\dot{m} = T / V$.

Here the square-root law appears from the other side. The cold stream is slower, so it carries more mass per unit of thrust than the hot one. At a 47.7 percent share of the lift it carries 60.9 percent of the mass.

Cold share of thrust Cold share of mass Mixed-mean exhaust
0 percent, all direct lift 0 percent 1,200 degrees Fahrenheit
30 percent 42.3 percent 718 degrees
47.7 percent, the lift system 60.9 percent 505 degrees
60 percent 72.0 percent 379 degrees

Roughly seven hundred degrees of exhaust temperature is bought by an architecture chosen for thrust per unit of power, and the temperatures above use a representative core exit value rather than a published one, so the column is indicative and the trend is not.

The exhaust is also slower, because the disc loading is lower, and the ground vortex is driven by the wall jet’s momentum. And the cold stream is in front, since the fan sits behind the cockpit and the hot core exhausts at the tail, so the cold jet stands between the hot one and the intake [Lockheed Martin F-35B propulsion ground test release].

A design chosen for thrust per unit power turns out to solve the ingestion problem as a side effect. In this sense the competition was decided by a relation rather than by a contest.

Hover Control and the Reaction Controls

An aircraft in the hover has no aerodynamic controls, because control surfaces need dynamic pressure and there is none. Attitude has to be held by differential thrust.

The lift-fan aircraft used roll posts in the wings, contributing 3,900 pounds of lift between them and providing roll control with engine bypass air, with pitch from varying the areas of the fan inlet and the exhaust nozzle and yaw from yawing the swivel module [Rolls-Royce LiftSystem] [Lockheed Martin F-35 Lightning II].

The moment available from a pair of posts is the differential thrust on the lateral arm,

\[M = \Delta T \, y \tag{29}\]

so posts carrying 3,900 pounds between them at an assumed station ten feet outboard command up to 39,000 foot-pounds of roll moment at full differential.

The direct-lift aircraft had a harder problem because all of its lift came from one place. Roll control requires either bleed-air reaction jets or differential nozzle modulation, and the first of those has a price that is paid before any moment is produced. Bleeding a fraction $b$ of the mass flow removes that fraction of the thrust,

\[L_{\text{after bleed}} = (1 - b) L \tag{30}\]

and the loss comes off the allowance with the amplification derived earlier.

Bleed fraction Lift lost Allowance remaining
0 percent 0 lb 2,637 lb
2 percent 560 lb 2,103 lb
4 percent 1,120 lb 1,570 lb
6 percent 1,680 lb 1,037 lb

A four percent bleed costs forty percent of the bring-back allowance, and the roll control it pays for has not yet been used to do anything. The lift-fan aircraft takes its roll control from posts that are already producing lift, so the same function costs it nothing it was not already spending.

Hover control and reaction controls fall within the cluster on handling qualities, flight control and hover control.

The Wing Boeing Did Not Propose

Boeing’s demonstrators flew a large single-piece composite delta with 55 degrees of leading-edge sweep and no horizontal tail. The production proposal did not use that wing. It used a conventional wing with a canted twin tail, and the change was made before the X-32 ever flew.

That fact is the most important one in this article and it is not a propulsion fact.

A concept demonstrator exists to reduce the risk of a proposal. If the demonstrator does not carry the proposal’s configuration in the feature under examination, then flying it establishes something about a different aeroplane. The X-32 demonstrated that a delta-winged direct-lift aircraft could hover and go supersonic. Boeing was offering a tailed aircraft.

The customer was therefore looking at an aeroplane Boeing did not intend to build, and had to reason from it to one that did not exist, while the competitor’s demonstrator was configurationally much closer to its own proposal.

The Flight Test Record

The two aircraft flew 144 times between them, with the X-32A opening on 18 September 2000 and the X-32B on 29 March 2001, and the flight programme ending before the decision in October 2001 [Jenkins, Landis and Miller, American X-Vehicles] [Boeing X-32B flight test release].

Event Date
Concept demonstration contracts awarded November 1996
X-32A first flight 18 September 2000
X-32B first flight 29 March 2001
X-35B first short takeoff, supersonic dash and vertical landing in one flight 20 July 2001
Decision announced 26 October 2001

The X-32A demonstrated conventional flight, supersonic performance and air refuelling. [Boeing X-32A flight test release] The X-32B demonstrated hover and vertical landing [Boeing X-32B flight test release]. What neither demonstrated was both at once, because the aircraft had to be physically reconfigured between the two roles [Boeing X-32].

The Reconfiguration, Stated Precisely

This is where the article has to be careful, because the popular account overstates it and the underlying fact is damaging enough without help.

The X-32 was a single-engine aircraft whose STOVL system diverted the core exhaust. Converting the demonstrator between the conventional and the STOVL configurations was a ground operation, not a cockpit switch. The aircraft could not take off short, accelerate through the sound barrier and land vertically on the same sortie, and it did not attempt to [Boeing X-32].

The X-35B did exactly that on 20 July 2001. A short takeoff, a level supersonic dash and a vertical landing, in one flight [Lockheed Martin X-35] [National Air and Space Museum X-35B].

The evidentiary difference is not that one aircraft is faster or lifts more. It is that one of them demonstrated the integration and the other demonstrated the components. A customer buying an aircraft that must do all three in an operational sortie has been shown the thing itself in one case and its parts in the other.

What the X-32B Did Not Do

The X-32B flew its STOVL tests with some parts removed [Boeing X-32], and no source available here establishes whether it ever performed a vertical landing at full weight. This article treats the question as open and marks it accordingly in the Epistemic State.

But the arithmetic above shows what a landing below full weight would mean, and it is not a qualitative shortcoming. At an assumed 28,000 pounds of lift, the bring-back relation displayed in the section headed The Number the Competition Was About gives an allowance over empty weight of 2,637 pounds before any ingestion penalty, and the break-even relation displayed in the section that follows it puts the lift at which the allowance vanishes entirely at 25,232 pounds. A demonstrator flying with instrumentation, ballast and test equipment aboard is not at its empty weight.

The jet screen fitted to hold hot gas away from the intake drew its air from the engine [Boeing X-32], and that air and the screen’s weight both come off the same small number.

Comparison With Ground Prediction

The Prediction That Mattered Was Not Aerodynamic

In most articles in this series this section compares a wind tunnel against flight. Here the comparison that decided the outcome was between a prediction about a production aircraft and the evidence a demonstrator could supply, and the two are not commensurable.

The ground prediction for hot gas ingestion was, and remains, difficult. The phenomenon involves an impinging jet, a wall jet, a fountain, a ground vortex and an inlet, at full-scale temperatures, in a flow field that depends on the height above the ground and on any wind. Scale models mispredict it because the temperature ratios and the Reynolds numbers do not scale together.

The NASA research base on this is substantial and predates the competition by two decades, and it explains why the physics was understood well enough that neither company was surprised in principle. What could not be settled on the ground was the margin. That research base is catalogued in the cluster on jet-induced ground effects, suckdown, fountains and ground vortices under The Contemporary Literature, where 85 of its 143 records date from 1970 to 1995.

Where the Two Demonstrators Sat Relative to Their Proposals

  Boeing Lockheed Martin
Demonstrator wing Large delta, no horizontal tail Conventional wing and tail
Proposed wing Conventional wing, canted twin tail Conventional wing and tail
STOVL and supersonic in one sortie No, reconfiguration required Yes, demonstrated 20 July 2001
Lift architecture demonstrated The proposed one The proposed one

Both companies demonstrated their propulsion architecture and only one demonstrated its airframe. That asymmetry answers what the fly-off decided, and it answers in terms of evidence rather than aeroplanes.

The cluster on defence acquisition, competition, prototyping and cost, cited above for competitive prototyping, also holds the acquisition studies of prototypes and proposals.

What the Data Changed

The Winner Acquired a Literature and the Loser Did Not

This article’s second finding concerns the literature itself, and it is measurable.

The reference set this article cites holds 3,528 research records from the NASA reports server, the Defense Technical Information Center and the Crossref registry. Counting the titles of those records that contain each term gives the following, and anyone can repeat the count on the cited set.

Term in the title Records
X-32 1
X-35 6
F-35 38
Joint Strike Fighter 72
Harrier or Pegasus 46

Exactly one of those 3,528 records carries the X-32 in its title, and it was written by the engine supplier rather than the airframer. It reports testing of the Rolls-Royce lift system for the X-32B, in 2002, after the competition was over [Roberts 2002].

The winner’s record runs from 2002 to 2026. The loser’s stops at one. Writing the asymmetry as a ratio,

\[R = \frac{N_{\text{winner}}}{N_{\text{loser}}} = \frac{38}{1} = 38 \tag{31}\]

against two aircraft that flew in the same years, under the same programme, for the same customer.

The count does not say that Boeing did no engineering. It measures what becomes public. An aircraft that enters production is written about for twenty years by the people who build it, operate it, modify it and study it. An aircraft that loses a competition is written about by almost nobody, because its proprietary data stays proprietary and there is no operating community to generate questions.

The consequence for this article is uncomfortable and is stated rather than hidden. The technical case made here depends on published numbers for the winning system and on an assumed upper bound for the losing one, because the losing one’s numbers were never published. The asymmetry in the evidence available to a historian is a direct inheritance of the asymmetry in the decision.

The X-32, X-35, F-35 and Joint Strike Fighter titles counted here are listed in the cluster on the Joint Strike Fighter programme and its demonstrators.

The Architecture Won and Kept Winning

The shaft-driven lift fan now powers the first operational supersonic STOVL fighter, and the arrangement demonstrated in 2001 is the arrangement flying on the F-35 today. Its designers received the Collier Trophy for 2001.

The direct-lift approach did not fail. It stopped being competitive, which is a different statement. The Harrier flew for decades on direct lift and did useful work, and the same square-root law, applied to a heavier aeroplane where the allowance runs out, explains why direct lift was not the answer for a supersonic aircraft.

What the Competition Format Itself Established

The concept demonstration phase is now a reference case in acquisition literature, a field whose institutional history is set out in Gansler on the defence industry and whose cost-growth folklore is collected in Augustine’s laws, cited both as evidence that competitive prototyping produces better decisions and as evidence that it produces expensive ones. The programme that followed acquired a reputation for cost growth that the fly-off did not prevent.

That point cuts against the natural reading of this article. The fly-off made a defensible technical choice, on the best evidence available, and the resulting programme still exceeded its estimates by a wide margin. A good decision procedure on the propulsion question did not produce a good outcome on cost, because the two questions were not the same question.

That literature is surveyed under defence acquisition, competition, prototyping and cost in The Contemporary Literature.

The Contemporary Literature

Cluster Records
The Joint Strike Fighter programme and its demonstrators 118
The Harrier, the Pegasus engine and the vectored-thrust lineage 85
Hot gas ingestion, reingestion and inlet temperature distortion 76
Jet-induced ground effects, suckdown, fountains and ground vortices 143
Jet impingement and jet flow physics 120
Ship decks, landing surfaces and shipboard operations 117
Lift fans, lift engines, ejectors and remote lift 220
Nozzles, thrust vectoring and thrust reversers 419
Momentum theory, rotors, propellers and hover performance 213
Ducted fans and ducted-fan vehicles 117
Distributed and electric propulsion and electric vertical flight 156
Supersonic inlets, intakes and airframe-propulsion integration 243
Engine cycles, variable cycle engines and engine performance 278
Defence acquisition, competition, prototyping and cost 280
Commonality, product families and requirements 88
Decision analysis, selection and cost-effectiveness 47
Digital engineering, model-based systems engineering and machine learning 87
Low observability and signatures 32
Automatic and autonomous landing and guidance 18
Handling qualities, flight control and hover control 235
V/STOL and STOVL aircraft concepts, programmes and design studies 267
Flight test, instrumentation and system identification 14
Fighter and supersonic aircraft design 104
High-lift and powered-lift aerodynamics 51
Total 3,528

The X-32 flew before three of the fields that now own its questions existed, and one of those fields exists because of the aircraft that beat it.

Powered lift became an electric problem

The square-root law is the reason the electric vertical-takeoff industry looks the way it does. Every configuration in that field spreads its lift over as much disc area as the airframe will carry, because the power required for a given lift rises as the square root of the disc loading and battery energy is the binding constraint. The design pressure that produced the lift fan produces distributed rotors when the power source is a battery, through the same relation. Distributed electric propulsion is reviewed in Kim et al. 2018, and Fulton and Gandhi 2026 treat the disc loading of multi-passenger rotors as a design variable.

Hot gas and jet impingement are computed now

The flow the competition could not settle on the ground is now simulated, and the modern literature on impinging jets, ground vortices and thermal fields around vertical-landing aircraft is substantial. The difficulty that remains is the one that was always there, namely that the temperature ratios and the Reynolds numbers do not scale together. Fountain formation between twin impinging jets is computed in Zhang and Agarwal 2020, and the heat transfer of an impinging round jet by large eddy simulation in Li et al. 2016b.

Deck and surface heating became an operational subject

A supersonic aircraft landing vertically puts a hot, fast jet onto a surface, and the surface has to survive it. The Harrier introduced that materials and operations subject, the production successor made it acute, and it descends directly from the disc-loading argument in this article.

The identity derived earlier makes the connection exact rather than rhetorical. The disc loading is the dynamic pressure in the jet, so an architecture at 2,852 pounds per square foot imposes almost twice the pressure of one at 1,467, on the same deck, at the same landing weight. Airfield concrete under the F-35B is studied in Autelitano et al. 2016 and Balaban and Erdem 2022, a flight deck heat spreader in Semenic et al. 2016, and exhaust gases and over-deck air temperatures on a ship in Scott et al. 2015.

The fly-off was partly replaced by simulation

The question this article asks is what evidence a competition can gather about an aircraft that does not yet exist, and the modern answer is that some of it need not be gathered by building two aeroplanes.

Digital engineering, model-based systems engineering and simulation-based acquisition are the literature of that shift. A model does not have the X-32’s difficulty, which was that the demonstrator differed from the proposal in the feature under examination, because a model can be made to be the proposal.

What a model does not have is the thing the X-35B’s single sortie demonstrated, namely that the integration works in the presence of everything nobody modelled. The trade is between an evidence source that matches the proposal exactly and one that matches reality exactly, and this competition shows why neither alone is sufficient. The digital thread in defence acquisition is examined in West and Pyster 2015, and the adoption of virtual prototyping across the defence research and acquisition communities in Post and Sundt 2017.

Acquisition analysis kept the case

The concept demonstration phase remains a case in the literature on competitive prototyping. Competition within the programme itself is examined in Assessing Competitive Strategies 2001 and Birkler 2001, and prototyping more widely in Cate 1997, Medlej et al. 2017 and Fast 2014.

Decision analysis under uncertainty

The question this article calls construct validity has a formal literature. Choosing between alternatives on evidence that does not directly measure the quantity of interest is the subject of decision analysis. Its literature includes Montibeller and von Winterfeldt 2015 on biases in multi-criteria analysis, French 2025 on scenario-focused decision analysis and Kahneman and Tversky 1977 on decisions under risk.

Propulsion, nozzles and integration since

The direct-lift arrangement made the propulsion system the centre of the competition, and its components are still being studied. The X-32B diverted its core stream through a butterfly valve to a pair of thrust-vectoring nozzles near the centre of gravity, and that arrangement forced the chin inlet of the Boeing X-32, and the winner added a lift fan, a three-bearing swivel module and roll posts. The modern work on those components and their neighbours, namely fluidic and mechanical thrust vectoring, swivel nozzles and thrust reversers, supersonic inlets and their bleed systems, and the coupling of engine and airframe performance, fills the clusters on nozzles, thrust vectoring and thrust reversers and on supersonic inlets, intakes and airframe-propulsion integration below. The three-bearing swivel duct is modelled and controlled in Wei et al. 2019 and designed in Shi et al. 2026, and a ventral diverterless inlet is analysed in Ge et al. 2021.

Autonomy arrived in the hover

The precision required for a vertical landing on a moving deck is now within reach of automatic systems, which changes what the pilot has to do and therefore what the control power has to cover. Autonomous ship-deck landing is treated in Grocholsky et al. 2016 and Lee et al. 2021b, and the precision hover control of the production aircraft in Denham and Paines 2008.

Machine learning and digital engineering

The fly-off was partly replaced by simulation, and the data-driven tools those simulations are now built from are the subject of the cluster on digital engineering, model-based systems engineering and machine learning below. The article argues that a model can be made to be the proposal but does not match reality exactly, which is why the X-35B’s single sortie still mattered. The records there apply digital threads and twins, model-based systems engineering, neural networks and reinforcement learning to aircraft, engines and their design, and they extend the subject of simulation-based acquisition rather than replace it. Massegur Sampietro and Da Ronch 2024 apply geometric deep learning to the aerodynamics of a future fighter demonstrator in dynamic manoeuvres.

Momentum theory, still

The relation behind this article’s sizing has been in the textbooks since momentum theory was written, and work on it continues. Momentum theory relates disc loading to induced velocity, and through it the power required for a given lift rises as the square root of the disc loading, the steep curve that separates the lift fan from a vectoring nozzle. The cluster on momentum theory, rotors, propellers and hover performance below holds the work that extends actuator-disc and blade-element momentum theory to open rotors, propellers and hovering rotors and, as neighbouring science, to tidal and wind turbines, among them Mahmuddin 2017 on blade element momentum theory and Shives and Crawford 2017 on a tuned actuator disc for tidal turbines.

Low observability

This literature is thin, with 32 records in the cluster on low observability and signatures below. The role of radar cross section in stealth design is set out in Lee 2024, the radar cross section of engine inlets including their fan blades is computed in Vogel 2016, and a low-observable intake is designed in Edefur and Tormalm 2018. Low-observable design shaped both entries decisively and is almost entirely absent from the open literature, as one should expect of the subject.

The Joint Strike Fighter programme and its demonstrators

Titles that name the X-32, the X-35, the F-35, the Joint Strike Fighter, its Joint Advanced Strike Technology predecessor or the ASTOVL studies that preceded both.

One of these titles names the X-32 and 6 name the X-35, against 38 that name the F-35, which is the asymmetry measured under What the Data Changed.

118 records. [Aaron et al. 2003] [Advanced Short Takeoff 1995] [Aksoy et al. 2006] [Andersen and Kimbel 2005] [Antill and Ito 2013] [Armstrong and Levine 1988] [Assessing Competitive Strategies 2001] [Atkinson et al. 2013] [Autelitano et al. 2016] [Balaban and Erdem 2022] [Ball et al. 2006] [Beisbier 2002] [Bevilaqua 2005] [Bevilaqua 2007] [Bevilaqua 2009b] [Bevilaqua 2009a] [Birckelbaw et al. 1995] [Birkler 2001] [Bishop et al. 2000] [Bogdan 2015] [Bordignon and Bessolo 2002] [Brown et al. 2009] [Browning and Jennewine 1996] [Buchholz 2002] [Burkhard and Deitrich 2003] [Calvello et al. 2007] [Campos 2001] [Canin 2019] [Chapman 2018c] [Chapman 2018b] [Chapman 2018f] [Chapman 2018g] [Chapman 2018d] [Chapman 2018e] [Chapman 2019] [Chung et al. 1995a] [Chung et al. 1995b] [Crowe et al. 2010] [Curtis and Penrose 1993] [Denham and Paines 2008] [Final Assembly and Checkout 2002] [Flight Tests of Distributed 2006] [Franklin 1997b] [Franklin 1997a] [Frey 2011] [Gallagher 2013] [Gerhold and Buchholz 2002] [Gero 2001] [Green and Zeckhauser 2019] [Gutterman 2007] [Hange and Wardwell 1993] [Hange et al. 1996b] [Hange et al. 1996a] [Haro 2003] [Hartnett and Mittlesteadt 2000] [Hess and Fila] [Hoggarth and Mange 2009] [Hollenbach 2001] [Horowitz and Harmon 2020] [Hoskin et al. 1991] [Hughes 2017] [Johns 1998] [Samuels 2005] [Jones 2014] [Kapstein 2004] [Karabag 2026] [Lam 1998] [Levin et al. 2018] [Levine and Inglis 1989] [Lewis 2000] [Maddock et al. 2011] [Mange et al. 2002] [Mathcad as a Standard 2004] [Mathews and Rothstein 1998] [McCarthy 1996] [McCarthy 2002] [McConnell 2006] [Menke et al. 2000] [Migone et al. 2023] [Moore 2007] [Naumowicz et al. 1996] [Norman et al. 2018] [Brauer and Dunne 2004] [Olson] [Owens et al. 2004] [Owens et al. 2006] [Philpot et al. 1993] [Powrie and Novis] [Roberts 2002] [Rudnick 1998] [Salisbury 2026] [Saripalli et al. 1991] [Scheuren et al. 1998] [Self 2026] [Skelley et al. 2007] [Smith 1996a] [Smith et al] [Smith et al. 1999] [Sokhey et al. 2002] [Stortz and O’Donoghue 1993] [Struth 1999] [Tauke and Bordignon 2002] [Taylor and Owens 2004] [Taylor et al. 2006] [Timothy et al. 2009] [Unlisted 1999] [Van de Vijver and Vos 2006] [Vucetic 2010] [Vucetic 2013] [Vucetic and Nossal 2013] [Walker and Allen 2002] [Wardwell and Hange 1993] [Warren and Floden 2001] [Winfree 1998] [Witek 2017] [Wurth 2018] [Wurth et al. 2002] [Zaffran and Erwes 2015]

The Harrier, the Pegasus engine and the vectored-thrust lineage

The direct-lift lineage the X-32B continued, being titles that name the Harrier, the P.1127, the Pegasus engine, the VAK 191B or the VAAC Harrier research aircraft.

The median publication year is 1986, because the lineage was studied while it was being built.

85 records. [Anderson and Foster 1984] [Anderson et al. 1983] [AV-8B Design for Maintainability 1986] [Banks et al] [Baron 1983] [Beale and Hess] [Bear et al. 1979] [Bedford 1962] [Bigler 1986] [Bode et al. 1978] [Bowles 1980] [Chaderjian et al. 2002c] [Chaderjian et al. 2002b] [Chow 1993] [Chung and Parikh] [Clark and Vasta 1984] [Cooper et al. 1985] [Cox and Kirby 1986] [Dorr et al. 1992] [Farley 1971] [Ford 1981] [Fozard 1978] [Franklin and Stortz 1993] [Frost 1962] [Gaston et al. 1984] [Gea et al. 1991] [George 1999] [Gingras 1999] [Gingras et al. 1986] [Hahn and Wilson 1985] [Hariharan et al. 2010b] [Hariharan et al. 2010a] [Hill 1970] [Hollingsworth et al. 1977] [Hooker 1981] [Huttrop 1980] [Klepper et al. 2017] [Lacey and Miller 1977] [Lacey et al. 1979] [Lake et al. 2000] [Lipera and Sandlin 1984] [Mathews 1987] [McNally 1986] [Merewether 1963] [Merrick et al. 1991] [Migbee et al. 1987] [Mihaloew et al. 1981] [Moss 1995] [Murman et al. 2001] [Mysko et al. 1993] [Naumowicz et al. 1998] [Newman 1984] [Ornelas 1985] [Pandya et al. 2002] [Postlethwaite 1998] [Pryce and Hirschberg 2003] [Pryce et al. 2005] [Rawnsley 1994] [Richardson et al. 2005] [Richardson et al. 2006] [Richardson et al. 2007] [Riley 1978] [Runyon et al. 2020] [Ryan 1986] [Scopes 2001] [Shanks et al. 1993] [Shanks et al. 2018] [Showers 1980] [Smith 1961] [Smiths Industries Ltd London (United Kingdom) 1998] [Soderman and Foster 1988] [Sotheran 1982] [Stanley and Hood 1981] [Stevenson et al. 1992] [The Hawker P1127 Vectored 1990] [Tinger 1987] [Veninger and Reed 1989] [VSTOL Systems Research Aircraft 1994] [Wall 1989] [Warakomski 1979] [Watson 1980] [Watson 1981] [Weinraub 1977] [Wilson and Liperra 1984] [Wilson and Wurts 1985]

Hot gas ingestion, reingestion and inlet temperature distortion

Hot gas ingestion and reingestion, exhaust recirculation and inlet temperature rise and distortion, with bird ingestion admitted because an inlet swallowing a bird and an inlet swallowing its own exhaust are the same fluid mechanics.

44 of these 76 records date from 1970 to 1995, which is the period base on which the article’s central failure mechanism rests.

76 records. [A Current Assessment of the Inlet/Engine Temperature Distortion Problem] [Adarkar and Hall 1969] [Amin and Richards 1983] [Amin and Richards 1984] [Amuedo et al. 1989] [Assessment of the Inlet/Engine Total Temperature Distortion Problem] [Bauer 1987] [Behrouzi and McGuirk 1999] [Behrouzi and McGuirk 2000b] [Behrouzi and McGuirk 2000a] [Biesiadny et al. 1984] [Binion 1970] [Blake and Laughrey 1987] [Braithwaite and Soeder 1979] [Braithwaite et al. 1973] [Castner 2005] [Cook et al. 2005] [Cosgrove and Ryan 1969] [Cosgrove et al. 1968] [Curtis 2002a] [Curtis et al. 2005] [Davis 2010] [Design Concepts for Minimizing 1981] [Dowler et al. 1989] [Sun et al. 2024a] [Fricker et al. 1992] [Gray and Kisielowski 1971] [Green and Zanine 1984] [Hall 1970] [Hammond and McLemore 1967] [Hange and Wardwell 1992] [Hemeter et al. 1970] [Hot Gas Ingestion 1984] [Hot-Gas Ingestion 2007] [Jackson and House 1981] [Johns et al. 1988] [Johns et al. 1990c] [Johns 1989] [Johns et al. 1987] [Johns et al. 1990b] [Johns et al. 1990a] [Joshi et al. 2021] [Kaemming and Smith 1984] [Kemp 1969] [Kirk and Barrack 1969] [Klann et al. 1984] [Koc¸er et al 2008] [Krishnamoorthy 1971] [Kuhn et al. 1993a] [Lewis and Hurd 1980] [Li et al. 2022a] [Limage 1978] [McLemore 1966] [McLemore and Smith 1968] [Mehalic 1988] [Min et al. 2021] [Penrose 1987] [Penrose and Smith 1996] [Ryan 1966] [Saripalli et al. 1997] [Sherman 1964] [Soeder and Bobula 1979] [Soeder et al. 1985] [Spong et al. 1979] [Sullivan and Murthy 1990] [Tafti and Vanka 1990] [Teng et al. 2024] [Tokarski et al. 1994] [Turczeniuk 1979] [Vanka 1998] [Vanoverbeke and Holdeman 1988] [VanOverbeke and Holdeman 1990] [Walter and Shaw 1979] [Wang 2003] [Weber and Gay 1975] [Wendt and Reichert 1996]

Jet-induced ground effects, suckdown, fountains and ground vortices

Suckdown, fountain lift, ground vortices, jet-induced loads and the ground environment of jet and fan lift in hover and transition.

85 of these 143 records date from 1970 to 1995, the decades of NASA and industry research that let both companies understand the physics before either aircraft flew.

143 records. [Allen 2004] [Arledge et al. 1996] [Asdurian 1967] [Batther et al. 2026] [Bellavia et al. 1991b] [Bellavia et al. 1991a] [Bevilaqua et al. 2007] [Bevilaqua et al. 2010] [Blake and Stewart 1993] [Cabrita et al. 2005] [Campbell et al. 1977] [Campbell et al. 1978] [Carlisle 1988] [Chilukuri 2019] [Christiansen et al. 1985] [Christiansen 1984] [Corsiglia et al. 1990] [Curtis 2002b] [Curtis et al. 2007] [Dent 1966] [Doğru et al. 2016] [Dudley et al. 1981] [Dudley et al. 1986] [Eshleman et al. 1986] [Eshlemen 1985] [Esker and Roddiger 1979] [Eyles et al. 2002] [Foley 1979] [Garner 1967] [George et al. 1964] [Gratzer and Mahal 1972] [Greco et al. 1997] [Hall 1967] [Hall 1968] [He et al. 2026b] [Hill and Jenkins 1979] [Hoad and Gentry 1975] [Hoad and Gentry 1977] [Holdeman and Vukits 2004] [Holder and Tritschler 2019] [Tadghighi and Rajagopalan 1999] [Huggett 1959] [Hwang 1990] [Hwang and Tsou 1981] [Ing and Zhang 1993] [Ing and Zhang 1994] [Ing et al. 2002] [Jakubowski et al. 1985] [Jenkins 1999] [Johns et al. 1989b] [Johns et al. 1989a] [Joshi 1985] [Joshi and Compton 1984] [Jung et al. 2024] [Kakka and Anupindi 2020] [Kamman and Hall 1978b] [Kamman et al. 1979] [Karemaa et al. 1979] [Kemmerly 1989] [Kotansky 1978] [Kotansky and Bower 1977] [Kotansky and Glaze 1980] [Kotansky 1982] [Kotansky and Glaze 1981] [Kristy 1995] [Kuhlman and Cavage 1994] [Kuhlman and Warcup 1977] [Kuhlman and Warcup 1978] [Kuhlman and Warcup 1980] [Kuhlman and Cavage 1992] [Kuhn 1987] [Kuhn 1998] [Kuhn et al. 1991a] [Kuhn et al. 1991b] [Kuhn et al. 1993b] [Kuhn 1986] [Kuhn 1997] [Lavi 1967b] [Levin and Wardwell 1997] [Li et al. 2020c] [Lift Loss in Hover 2007] [Lissaman 1967] [Lissaman 1969] [Lord 1985] [Louisse and Marshall 1974] [Maclean 1991] [Margason 2002b] [Margason et al. 1996] [McGuirk 2007] [Miller et al. 1991] [Mitchell 1987] [Morse and Newhouse 1961] [Mourtos et al. 1995] [Newman and Atassi 1980] [Pandya et al. 2003] [Paulson 1981] [Paulson 1980] [Polsky 2000] [Poppen et al. 1991] [Pruyn and Taylor 1970] [Renselaer 1977] [Rogers et al. 1969] [Saberi 1983] [Saddington 2000] [Saddington and Knowles 1999] [Saddington and Knowles 2001] [Saddington et al. 2002] [Saddington et al. 2005] [Sandlin and Howard 1991] [Saripalli 1987] [Schnell and Grossman 1978] [Sharma et al. 2021] [Siclari et al. 1975] [Siclari et al. 1976] [Siclari et al. 1977] [Smith et al. 1993b] [Smith et al. 1993a] [Smith et al. 1994] [Soderlund and Matveev 2010] [Solies 1992] [Stewart 1979b] [Stewart 1987] [Stewart and Walters 1983] [Stewart et al. 1995] [STOL Operation Transition-in-Ground Effect 2007] [Tritschler et al. 2019] [Van Dalsem et al. 1987] [Von Glahn and Groesbeck 1979] [Wachspress et al. 2026] [Wardwell et al. 1992] [Wardwell et al. 1993] [Watson et al. 1967] [Weber and Williams 1978] [Winston et al. 1975] [Wohllebe and Migdal 1979] [Worden et al. 2016] [Yang et al. 2017] [Yen 1980] [Zhang and Agarwal 2020] [Zhang and Ing 1993] [Zhang and Ing 1994] [Zhang et al. 2019b] [Zhao et al. 2022]

Jet impingement and jet flow physics

The physics of impinging jets, jets in crossflow and hot and supersonic jet flows, including the impingement cooling literature of industry, kept as the neighbouring physics of the deck heating problem.

102 of these 120 records date from 2015 or later, so the modern computation of impinging jets is almost wholly a literature written after the competition.

120 records. [Abdol-Hamid et al. 2003] [Almohammadi and Alsaiari 2024] [Alvi and Strykowski 1999] [Alzahrani et al. 2023] [Baker and Orzechowski 1982] [Barbosa et al. 2024] [Behrouzi 2000] [Bhansali and Ekkad 2021] [Bhansali et al. 2021] [Cali 2000] [Cao et al. 2022a] [Castner et al. 2017] [Celik 2019] [Chang et al. 2020] [Colombié et al. 2021] [Cornelius and Lucius 1993] [Corvera and Mahjoob 2023] [Da Soghe et al. 2018] [DeBonis 2017] [Devakottai et al. 2020] [Dhanasegaran and Pugazhendhi 2017] [Draksler et al. 2017] [Draksler et al. 2019] [Dutta et al. 2016] [El-Jummah et al. 2016] [Elavarasan et al. 1999] [Fogleman et al. 2026] [Ganatra et al. 2024] [Gao et al. 2018] [Gao et al. 2019] [Garcia et al. 2026a] [Grenson and Deniau 2017] [Gudi and Hindasageri 2021] [Gupte et al. 2015] [He and Liu 2018a] [He and Liu 2018b] [Hsu et al. 2025] [Hu and Onishi 2024] [Hu et al. 2023] [Jagajith et al. 2026] [Jalamani et al. 1990] [Jensen et al. 2017] [Joshi and Sahu 2022] [Joshi and Sahu 2024] [Joshi et al. 2023] [Junqueira-Junior et al. 2017] [Kaewbumrung and Plengsa-Ard 2023] [Kamrass and Swartzel 1955] [Karabulut 2019] [Keleş and Özmen 2025] [Khademi and Bazargan 2024] [Kim et al. 2026a] [Kim et al. 2026b] [Kitayama and Kubo 2021] [Kobayashi et al. 2022] [Koizumi et al. 2017] [Kopriva et al. 2019] [Krothapalli and Alvi 2002] [Kukutla and Prasad 2016] [Lagarza et al. 2016] [Lak et al. 2020] [LeBlanc et al. 2019] [Lemanov et al. 2018] [Li et al. 2016b] [Li et al. 2020b] [Li et al. 2024a] [Liu and Junkui 2015] [Liu et al. 2018] [Liu et al. 2020b] [Lyu et al. 2023] [Madhavan et al. 2019] [Manoharan and Mokhtar 2018] [Mezzacapo et al. 2025] [Morsbach et al. 2024] [Nakazawa et al. 2022] [Natarajan et al. 2016] [Nenni 1980] [Nguyen et al. 2019] [Nguyen et al. 2022a] [Nguyen et al. 2023b] [Noah et al. 2024] [Ou and Lai 2024] [Paez et al. 2022] [Page 2023] [Pawar et al. 2020] [Qin et al. 2023] [Rudenko et al. 2016] [Saini et al. 2022] [Salehian and Mankbadi 2020] [Saripalli and Kroutil 1985] [Seiner and Gilinsky 1995] [Seo and Mittal 2017] [Shahrin et al. 2026] [Shaikh et al. 2023] [Sharif 2016] [Sheng et al. 2025] [Shih et al. 2002] [Shukla and Dewan 2021] [Singh 2022] [Singh et al. 2019] [Singh et al. 2020] [Singh et al. 2023] [Smith 2015] [Soderman 1990] [Stewart and Blake 1992] [Tabassum et al. 2023] [Taghinia and Rahman 2018] [Torres et al. 2020] [Torres et al. 2022] [Tumuklu 2024] [Venkatakrishnan 2004] [Verrière 2022] [Wang et al. 2026b] [Wen et al. 2019] [Wilson and Knowles 1994] [Xing et al. 2024] [Yang et al. 2025b] [Zhao et al. 2021] [Zhong et al. 2016] [Zhong et al. 2022]

Ship decks, landing surfaces and shipboard operations

Deck landing, ship airwakes, carrier approach, flight deck heating and the landing surfaces on which jet and rotor downwash acts.

117 records. [Adiyasa and Sasongko 2025] [Ambroziak et al. 2022] [Bhatia et al. 2021a] [Bhatia et al. 2021b] [Bihrle 1969] [Blinkhorn 1948] [Bodson and Athans 1985] [Le Bris and Nguyen 2023a] [Britcher et al. 2023] [Britcher et al. 2024] [Britcher et al. 2025] [Calvano and Harney 1998] [Chang and Ai 2026] [Chen et al. 2026] [Chopra 2025] [Clark 1965] [Clarke et al. 1973] [Comandur et al. 2019] [Comandur et al. 2020] [Comeau et al. 2024] [Connelly 1982] [Daffer and Rogers 1973] [de Paula et al. 2025] [Deng et al. 2025] [Deveson and Deveson 1997] [Dong et al. 2021a] [Donley 1980] [Douglas Aircraft Co Long Beach Ca 1963] [Duehring et al. 2023] [Durand and Wasicko 1965] [Editor 2016] [Fang et al. 2021] [Farris et al. 1983] [Fenwick 1966] [Fenwick 1967] [Ferrier et al. 2015] [Fortenbaugh 1972] [Frost et al. 2021] [Furey 1983] [Gnanamanickam et al. 2020] [Grasso 1994] [Gribanov et al. 2022] [Grocholsky et al. 2016] [Hailiang 2026] [Han et al. 2019a] [He et al. 2023a] [Hendrick et al. 2023] [Huang et al. 2019] [Imhof and Schork 1999] [Jordan et al. 2002] [Kalra et al. 2022] [Kamman and Hall 1978a] [Kim and Costello 2016] [Kim et al. 2022] [Le Bris and Nguyen 2023b] [Lee et al. 2021b] [Lee et al. 2021a] [Lin et al. 2015] [Liting et al. 2023] [Lu et al. 2022] [Luan and Sun 2020] [Ma et al. 2018b] [Ma et al. 2018a] [McGee et al. 1978] [Miller 1970] [Minotra and Feigh 2018] [Ngo and Sultan 2024] [Nguyen et al. 2024] [Oldmixon 1963] [Patel et al. 2021] [Pavlov 2016] [Peer 2000] [Phelps et al. 2018] [Radford and Andrisani 1984] [Richez and Costello 2024] [Schock and Langlois 2023] [Scott et al. 2015] [Semakov 2021] [Semakov and Semakov 2022] [Semenic et al. 2016] [Setiawan et al. 2025] [Shafer et al. 2019] [Shipman and Bin 2021] [Stanisławski 2019] [Stanton et al. 2018] [Stevens and Roskam 1985] [Stevens et al. 1981] [Stewart 1979a] [Stewart 1980] [Sun et al. 2015] [Telford and Vasiloff 1968] [Thomas et al. 2023] [Topczewski and Bibik 2023] [Topczewski et al. 2021] [Tugolukov 2020] [Venkatesh 2025] [Vitale et al. 2023] [Waanders and Rauleder 2026] [Wang et al. 2020b] [Wang et al. 2022] [Warner et al. 1986] [Wilhelms et al. 2026] [Wilson 1992] [Wolkovitch and Brassell 1978] [Wu et al. 2026] [Wynn and McLain 2019] [Xu et al. 2022b] [Yackle 1992] [Yang et al. 2026a] [Yang et al. 2026b] [Ye et al. 2024] [Zhang and Fu 2024] [Zhao et al. 2018] [Zhou et al. 2026] [Zhu and Yang 2020] [Zilver et al. 2025] [Štrbac et al. 2022]

Lift fans, lift engines, ejectors and remote lift

Lift fans, lift and lift-cruise engines, ejectors, remote augmented lift and the shaft and tip-turbine drives that power them.

The median publication year is 1975. The lift fan the winner flew was a revival of a programme of the 1960s and 1970s, and its literature is mostly that programme’s.

220 records. [Abdullah and Husi 2026] [Additional Design Studies 1976] [Alscher et al. 1966] [Ames 1975] [Aoyagi 1979] [Arnulfo and Pilidis 2000] [Atencio 1973] [Atencio et al. 1973] [Barankiewicz 1991] [Barankiewicz et al. 1994] [Barankiewicz 1993] [Beattie 1975] [Beeler 1965] [Beeler and Russell 1964] [Beeler and Volk 1965] [Benzakein and Kazin 1971] [Benzakein and Volk 1970] [Bevilaqua 1996] [Biesiadny et al. 1993] [Biggers et al. 1964] [Blackhurst 1969] [Bland and Konsewicz 1976] [Bland et al. 1976] [Bowling et al. 1969] [Brogan et al. 1961] [Byrnes et al. 1974] [Campbell and Quinn 1974] [Cavage 1975] [Chen et al. 2021a] [Chu et al. 1983] [Cican et al. 2023] [Civinskas 1973] [Clark and Smith 1965] [Cole et al. 1980] [Conceptual Design 1973] [Conceptual Design Studies 1974a] [Conceptual Design Studies 1974b] [Cook and Hickey 1967] [Cook 1993] [Coplin 1965] [Corden and Everett 1963] [Corgiat et al. 1993] [Corsiglia et al. 1989] [Hickey et al. 1966] [Davis and Ela 1969] [Deckert 1993] [Deckert 1995] [Deckert and Rolls 1974] [Deng et al. 2017] [Design Definition Study 1975] [DeSmidt et al. 2001] [Diedrich 1971] [Diedrich 1975] [Dobek 1973] [Donateo and Çinar 2022] [Doonan and Kuchar 1992] [Drummond and Barankiewicz 1990] [Dudley 2016] [Dudley et al. 1990] [Duffy and Samaritano 2015] [Dugan et al. 1971] [Eccles 1983] [Eldridge et al. 1973] [Elliott 1976] [Fasching and Kutney 1964] [Fishbach and Franciscus 1982] [Fletcher 1962] [Fluctuating Pressures on Aircraft 1976] [Ford 1973] [Fry 1967] [Gambucci et al. 1976b] [Gambucci et al. 1976a] [Garland 1987] [Gates and Cochran 1961] [Gelhausen and Wilson 1986] [General Electric Co Cincinnati Oh 1962] [General Electric Co Cincinnati Oh 1963] [General Electric Co Cincinnati Oh 1964] [Gerdes 1993a] [Gerdes 1993b] [Gerdes and Hynes 1972] [Gleiter 1976] [Gotlieb 1977] [Gotlieb et al. 1976] [Grahame 1968] [Grahame 1969] [Green 1980] [Griffin 1983] [Haas et al. 1976] [Haas et al. 1978b] [Haas et al. 1978a] [Hall and Hodder 1971] [Hall et al. 1967] [Hall et al. 1970] [Harris 1968] [Hickey and Kirk 1993] [Hill and Waters 1974] [Hiraoka et al] [Hudson 1977] [Hudson and Gee 1977] [Huntley 1972] [Jacobson 1964] [Jaklitsch et al. 1971] [Jensen and Pera 1977] [Jiang and Zhang 2016a] [Jiang and Zhang 2016b] [Jiang and Zhang 2017] [Jiang and Zhang 2018] [Jiang and Zhang 2021] [Jiang et al. 2015] [Karemaa 1971] [Kazin and Volk 1971] [Keller 1969] [Kelly and Tolhurst 1966] [Kentfield 1967] [Kirk et al. 1972] [Knight et al. 1973] [Knox 1962] [Kochanski 1966] [Kutney 1963] [Kutney 1964a] [Lake 1990] [Lamb 1995] [Lebacqz and Radford 1979] [Lee et al. 2016] [Lieblein 1970b] [Lieblein and Stockman 1969] [Lieblein et al. 1973] [Lieblein 1970a] [Lockheed-Georgia Co Marietta 1969] [Lockwood 1963] [Lockwood 1964] [Love 1993] [Lowe and Sanger 1972] [Luidens et al. 1984] [Lummus et al. 1980] [Mazzei and Scott 2003] [Mazzei et al. 1999] [McNally and Brown 1985] [McNeill et al. 1995] [Myers et al. 2010] [Myers et al. 2019] [NASA/Navy Lift/cruise Fan Cost 1977] [NASA/Navy Lift/cruise Fan. Phase 1977] [Naumowicz and Smith 1992] [Nicholson and lowry 1966] [Nishimura 1980] [Novak 1975] [O’Keefe et al. 1973] [Obrien 1976a] [Obrien 1976b] [Oganyan and Loginov 2025] [Palmer and Holdo̸ 2002] [Peterson 1964] [Peterson 1965] [Petrov 1993a] [Petty 1980] [Posnett et al. 1987] [Posnett et al. 1986] [Prasad and Choi 2017] [Pratt et al. 1971] [Przedpelski 1965] [Przedpelski 1967] [Pyle 1971] [Quigley and Franklin 1977] [Rabone and Paulson 1973] [Rao et al. 1973] [Remote Lift Fan Study 1973] [Riccius 1984] [Roelke and Zigan 1972] [Rolls et al. 1976] [Rumsey et al. 1972] [Salter 1975] [Sayma et al. 2003] [Schaeffler et al. 1967] [Schlundt 1975] [Schlundt 1976] [Sellers 1973] [Sellers and Szuch 1973] [Sellers et al. 1977] [Sheridan 1985] [Sheridan 1986] [Smith 1966a] [Smith et al. 1992] [Sowers 1965] [Starkey and True 1963] [Stimpert 1973c] [Stimpert 1973a] [Stimpert 1973b] [Stimpert 1975] [Stockman et al. 1973] [Streiff and Henderson 1974] [Sully and Whittley 1987] [Szuch 1973] [Tape 1990] [Tauber et al. 1976] [The Jet Lift Controversy 1962] [Thomas 1972] [Tich 1991] [True 1967] [Turney and Allen 1980] [Volk 1969] [Weber 1960] [Weber 1961] [Webster 1973] [Williams 1960] [Willis 1980a] [Willis 1980b] [Willis 1981b] [Willis et al. 1982] [Wind Tunnel and Ground 1976] [Winston 1969] [Xu et al. 2022a] [Yuska 1972] [Yuska and Diedrich 1972] [Zabinsky et al. 1974] [Zabinsky et al. 1975] [Zhang et al. 2013] [Zimmerman 1958] [Zola et al. 1984]

Nozzles, thrust vectoring and thrust reversers

Exhaust nozzles, mechanical and fluidic thrust vectoring, swivel and ventral nozzles, and thrust reversers.

419 records. [Adamson 1980] [Adavbiele 2009a] [Adavbiele 2009b] [Adavbiele and Salami 2007] [Adkins and Sherwood 1996] [向 et al. 2023] [Afridi and Khan 2022] [Afridi et al. 2023a] [Afridi et al. 2023b] [Afridi et al. 2024] [Ahmed et al. 2023] [Ahuja and Spencer 1987] [Aikens et al. 2015] [Aircraft Engine Thrust Reverser 1998] [Al-Akam et al. 2019] [Ale Isaac Khoueini] [Amoozgar et al. 2024] [Anderson and Bradley 1987] [Application of Fluidic Thrust 2024] [Arbiter 1985] [Aroussi 2026] [Arshad et al. 2020] [Asbury and Yetter 1998] [Asbury et al. 1996] [Avanzini and Matteis 1995] [Bahamon Blanco 2023] [Banazadeh and Banazadeh 2014] [Baranwal 2026] [Barham 1994] [Barnes et al. 1984] [Barrett 1965] [Bauer 1980] [Beck et al] [Beilman 1983] [Berens 2019] [Bergman 1979] [Berrier 1983] [Berrier and Mason 1987] [Berrier and Re 1978] [Berry 1998] [Bhabar and Sharma 2025] [Bindu Mounica et al and Tjprc 2020] [Bloomer and Miller 1954] [Bowers 1979] [Bowers and Buchan 1978] [Brodsky 1970] [Brown 1987] [Bruce et al. 2016] [Burger 1983] [Burnes et al. 2001] [Bursey and Dickinson 1990] [Capello et al. 2019] [Capone 1974] [Carlson 1992] [Carr 1984] [Carter et al. 2015] [Casau et al. 2016] [Caton and Franke 1991] [Chakraborty and Comer 2024] [Chandra Sekar et al. 2017] [Chandra Sekar et al. 2021] [Cheatham et al. 1990] [Chen and Liao 2020] [Chen et al. 2022a] [Chen et al. 2022b] [Chen et al. 2025a] [Chen Xuyi and Xiaoying Zhang 2015] [Cheng et al. 2020a] [Chi et al. 2022] [Chouicha et al. 2019] [Chouicha et al. 2020] [Chpoun et al. 2017] [Cliff et al. 1982] [Cohn et al. 1985] [Coles 1968] [Collins 2005] [Comer 2024] [Compton and Bowers 1983] [Computational and Experimental Analysis 2024] [Salimi et al. 2022] [Corva et al. 2021] [Costes 1988] [Crandall et al. 1973] [Crowe and Martin 2019] [Crown 1950] [Culpepper et al. 2021] [Cunningham and Boytos 1981] [Cunningham and Boytos 1983] [Curry et al. 1983] [Dahl et al. 2015] [Das et al. 2024] [Das et al. 2025] [Davis and Hines 1976] [Davis and Spicer 1965] [de Matteis et al. 1998] [Deere 2003] [Deere et al. 2003] [Deere et al. 2005a] [Deere et al. 2007] [Deere et al. 2005b] [Demetriades 1977] [Deng et al. 2014] [Di et al. 2025] [Di Verniere et al. 2026] [Dong et al. 2025] [Doonan et al. 1983] [Dunbar et al. 2002] [Dunn and Emery 1966] [Eames 1993] [Eames and Mason 1988] [Enenakpogbe et al. 2024b] [Enenakpogbe et al. 2024a] [Enenakpogbe et al. 2025] [Erwin et al. 1964] [Esker and Debonis 1991] [Esker and McArdle 1990] [Esker and Sedrick 1972] [Esker and McArdle 1993] [Thillaikumar et al. 2020] [Fang et al. 2025] [Farras et al. 2021] [Fazeli Asl and Moosapour 2017] [Federspiel 1979] [Ferlauto 2018] [Ferlauto and Marsilio 2016a] [Ferlauto and Marsilio 2016b] [Ferlauto and Marsilio 2017] [Fernando et al. 2026] [Flamm 1998] [Flamm et al. 2005] [Flamm et al. 2006] [Flamm et al. 2007] [Flight Characteristics of Quad 2014] [Foley and Woodrey 1980] [Friddell and Franke 1990] [Friehmelt 1996] [Frost and Bishop 1963] [Fujii et al. 2020] [Gal-Or] [Gal-Or 1990] [Gal-Or 1995a] [Gal-Or 1995b] [Gehrke et al. 2017] [Gill 1973] [Giuliano et al. 1997] [Glezer et al. 1985] [Goetz et al. 1976] [Gogoi and Dhamalekar 2021] [Gogoi et al. 2021] [Goss et al. 2009] [Granasy 1995] [Gridley and Walker 1996] [Gu and Xu 2013] [Gupta 2025] [Gupta 2026] [Ha et al. 2025] [Kbab et al. 2020] [Hall 1965] [Hambly 1974] [Hamed et al. 1997b] [Hammond et al. 1995] [Hardy 1987] [Hauser and Jadbabaie] [Hawkes and Obye 1993] [Herrick 1989] [Herrick 1990] [Hienz and Vedova 1984] [Hiley and Bowers 1981] [Hoffmann and Joachimiak 2026] [Holder et al. 2018] [Hosseini et al. 2026] [Hou and Hong 2023] [Hou et al. 2024] [Hou et al. 2025] [Hou et al. 2026] [Hu et al. 2024a] [Hu et al. 2026] [Huang et al. 2022a] [Huang et al. 2023b] [Huang et al. 2025b] [Huang et al. 2026] [Hui-min et al. 2005a] [Hui-min et al. 2005b] [Hunter and Deere 1999] [Hunter 2004] [Idzorek 1988] [Imlay 1986] [In-Flight Thrust Determination for Aircraft with Thrust Vectoring] [Irfan and Shah 2016] [Islam et al. 2018a] [Islam et al. 2018b] [Isono et al. 2017] [Jadbabaie and Hauser 2002] [Jammalamadaka et al. 2020] [Jayakody and Katupitiya 2015] [Jegede and Crowther 2016] [Jiméneze and Icaza 2000] [Jinxin et al. 2026] [Johns 2000] [Jois et al. 2024] [Jyothy and John Wessley 2023] [Kantner et al] [Kara and Kurtuluş 2024] [Kedia et al. 2021] [Kelley et al. 1982] [Kim 2026] [Kim and Choi 2025] [King and Schnelker 1970] [King et al. 1991] [Klafin 1988] [Krenkel and Salzman 1968] [Kuang et al. 2017] [Kuchar and Tabakoff 1976] [Kuchar and Tabakoff 1977] [Kuchar and Wolf 1993] [Kumar and Ghosh 2018] [Kumon et al. 2010] [Kumon et al. 2011] [L’Ecuyer et al. 1971] [Lampard 1978] [Lander and Palcza 1974] [Lavrukhin et al. 2014] [Lecuyer 1970] [Lee et al] [Lee et al. 2018b] [Leovan 2019] [Lewis and Simpkin 1981] [Li et al. 2013] [Li et al. 2016a] [Li et al. 2020a] [Lichtsinder et al. 1998] [Lieu 1964] [Linderman et al. 1974] [Liu et al. 2013] [Liu et al. 2020a] [Liu et al. 2022a] [Liu et al. 2024a] [Liu et al. 2025c] [Liu et al. 2026c] [Liu et al. 2026d] [Long 2017] [Lu and Terrier 2003b] [Lu and Terrier 2003a] [Ma et al. 2024] [Maarouf et al. 2009] [Mace et al. 1989] [Madarasz et al. 2012] [Madeiras et al. 2026] [Makarchuk and Ponomarenko 2026] [Malaek and Parastari 2001] [Mangin et al. 2006] [Mansell 1987] [Mao et al. 2019] [Marconi et al. 1997] [Margetts et al. 2015] [Marubashi and Miwa 2015] [Marubashi and Miwa 2016] [Maruyama et al. 2019] [Mason and Crowther 2004] [Masters 2015] [Matesanz et al. 1995] [Matveev and Wheeler 2019] [McArdle and Smith 1990] [Meyer et al. 1991] [Milam et al. 2005] [Milford and Migdal 1967] [Miller 1983] [Miller and Protopapas 1985] [Miller et al. 1979] [Minin et al. 2016] [Mishra et al. 2025] [Mitchell 1979] [Miwa and Maruhashi 2016] [Miwa et al. 2012] [Mo et al. 2018] [Molyneux 1983] [Muir and Bradshaw 1996] [Nafi and Hasan 2019] [Naik and Chiarelli 1988] [Nair et al. 2020] [Nardi et al. 1999] [Naumova and Shmyglevskii 1967] [Nayebi and Taeibi Rahni 2024] [Nie et al. 2026] [Obye and Hakim 1984] [Orme et al. 1998] [Ornob et al. 2025] [Otani 2023] [Pang et al. 2024] [Papamoschou et al. 2016] [Park et al. 2025] [Pastorelli 2013] [Payne 1980] [Pennington and Meintel 1980] [Peters 1981] [Petit and Scholey 1973c] [Petit and Scholey 1973b] [Petit and Scholey 1973a] [Petrie 1982] [Pruitt and Bates 1992] [Qi et al. 2020] [Radhakrishnan et al. 2021] [Rajendran et al. 2020] [Rajput et al. 2021] [Rakesh and Varghese 2018] [Rao 1958] [Ravindranath 2025] [Re and Mason 1985] [Resta et al. 2021] [Resta et al. 2022] [Ritter 2016] [Robinson 1978] [Robinson and High 1974] [Rolls and Aoyagi 1977] [Romine and Johnson 1984] [Romine et al. 1989] [Rosenberg and Esker 1980] [Rosenberg and Christiansen 1981] [Rowe et al. 1984] [Ruetten 2018] [Russo et al. 2011] [Akshay et al. 2020] [Saghafi and Banazadeh 2007] [Salahudden et al. 2025] [Schirmer and Capone 1989] [Schneider and Watt 1988] [Schnell et al. 1977] [Sellam et al. 2012] [Semlitsch and Mihăescu 2021] [Shcherbakov 1983] [Shebl 2026] [Sheu 1999] [Shi 2014] [Shi et al. 2024a] [Shi et al. 2026] [Shigematsu et al. 2012] [Shin et al. 2010] [Shukla et al. 2026] [Siddiqui 2022] [Simmons 2022] [Singh and Kushari 2008] [Smith and McArdle 1990] [Smith and McArdle 1992] [Snyder and Thompson 1971] [Sobel and Lallman 1988] [Sobester and Keane 2006] [Soundararajan and Sridhar 2022] [Sparavalo 2019] [Sparavalo 2021] [Steer 2000] [Sundararaj et al. 2021] [Suresh et al. 2026] [Suñol et al. 2014] [Suñol et al. 2015] [Sørensen et al. 1996] [Tamrat and Antani 1988] [Tatom et al. 1972] [Taylor 1988] [Taylor 1990] [Terrier and Lu 2003] [Terrier and Lu 2005] [Test Bed for Vectored 1963] [Thompson and Epstein 1977] [Thrust Vectoring 2020] [Tsentis et al. 2023] [Tsentis et al. 2024] [Tudosie 2023] [Tudosie 2024] [Ulizar 1997] [Van Nieuwstadt and Murray 1998] [VAN Poppel et al. 1998] [Variable Mode Turbofan Jet 2002] [Varsegov 2010] [Varsegov and Saukhin 2025] [Vashistha et al. 2014] [Vectored Thrust 1992] [Visser 1999] [Waithe and Deere 2003] [Wallace and Bowers 1982] [Wang et al. 2014] [Wang et al. 2017] [Wang et al. 2019a] [Wang et al. 2020a] [Wang et al. 2020c] [Wang et al. 2027] [Ward and Lewis 1987] [Ward and Penrose 1983] [Wei et al. 2019] [Wei Yuan and Katupitiya 2013] [Werner and Wolter 2010] [Williams and Vittal 2002] [Wilson et al. 1999] [Wilson et al. 2001] [Wilson et al. 2003] [Wing and Asbury 1991] [Wing 1998] [Wing and Capone 1993] [Wing and Giuliano 1997] [Wooten et al. 1984] [Wu and Chow 1985] [Xiangyang et al. 2019] [Xu et al. 2024] [Yagle et al. 2000] [Yang et al. 2021b] [Yang et al. 2023] [Yetter et al. 1996] [Zawislak and Birk 2020] [Zhang et al. 2024] [Zhang et al. 2025a] [Zhang et al. 2025b] [Zhang et al. 2026c] [Zhang et al. 2026b] [Zhao-miao and Chuan 2013] [Zhijie et al. 2026] [Zhou et al. 2022b] [Zmijanovic] [Zmijanovic et al. 2012] [Zmijanovic et al. 2013] [Živković et al. 2014]

Momentum theory, rotors, propellers and hover performance

Momentum, actuator-disc and blade-element theory, rotor and propeller performance and hover efficiency, with tidal and wind turbines kept as neighbouring science of the same relation.

213 records. [Aa. Madsen 2024] [Aerodynamic Design of Low-Speed 1986] [Ahmed et al. 2025] [Allsop et al. 2017] [Alvarez et al. 2025] [Anantha et al. 2024] [Apkarian 2018] [Arents 1977] [Arif and Sasongko 2021] [Azuma and Kawachi 1975] [Bachelder et al. 2021] [Barakos and Jimenez Garcia 2016] [Barakos et al. 2020] [Belák and Hromčík 2023] [Benjamin 2023] [Berton et al. 2000] [Biggi et al. 2024] [Binion 1971] [Bohorquez et al. 2010] [Bontempo and Manna 2016] [Bowman et al. 2018] [Brown and Fischer 1967] [Bulten and van Esch 2005] [Burton et al. 2024] [Cai et al. 2019] [Cao et al. 2025] [Caracostas 1978] [Casablanca et al. 2025] [Chattot 2020] [Chen and Hubner 2020] [Chen and Hubner 2021] [Chen et al. 2019a] [Chen et al. 2023b] [Chen et al. 2025b] [Chiang et al. 2020] [Cousins et al. 2026] [Cox-Gross and Collins 2025] [Critchfield and Ning 2023] [Critchfield and Ning 2026] [Dai et al. 2025] [Davis et al. 1961] [Detore and Gaffey 1969] [Droandi and Gibertini 2015] [Duan et al. 2024] [Dyke 1963] [Edenborough 1968] [Edkins 1969] [Fan et al. 2020] [Fardin et al. 2026] [Farrar and Agarwal 2015] [Felker 1991] [Felker 1993] [Felker et al. 1988] [Firnhaber Beckers et al. 2023] [Fujiwara et al. 2026] [Fulton and Gandhi 2026] [Fulton et al. 2026] [Gahlot and Sankar 2024] [Gill and Lee 2025] [Goland et al. 1964] [Gress 2002] [Gur et al. 2021] [Hariharan et al. 2017] [Harned and Head 1965] [Hashem Dabaghian et al. 2025] [Hermes and Wood 1969] [Hiller Aircraft Corp Palo Alto Ca 1965a] [Hiller Aircraft Corp Palo Alto Ca 1965d] [Hiller Aircraft Corp Palo Alto Ca 1965c] [Hiller Aircraft Corp Palo Alto Ca 1965b] [Himmelberg and Benedict 2017] [Hirschberg and Müller 2007] [Hirschberg et al. 2005] [Ho et al. 2015] [Hu et al. 2025a] [Hua et al. 2025] [Huang et al. 2020b] [Hamlaoui et al. 2021] [Ishaque et al. 2026] [Jacobson and Smith 2018] [Jain 2017] [Jain 2018] [Jimenez Garcia and Barakos 2015] [Jimenez Garcia and Barakos 2018] [Jimenez-Garcia and Barakos 2017] [Jo et al. 2017] [Kandath et al. 2019] [Kang et al. 2025a] [Katzenberger 1967] [Keller 2023] [Keller 2025] [Kim 2021] [Kim et al. 2020a] [Kiran and Breuer 2023] [Klimchenko et al. 2023] [Kozapalli and Warmbrodt 1997] [Ku and Sankar 2026] [Kwon et al. 2015] [Lamar et al. 2003] [Lampl and Armanini 2023] [Landgrebe 1971] [Lee and Dassonville 2020] [Lee and Park 2022] [Lei et al. 2021] [Li and Da Ronch 2025] [Li et al. 2023b] [Liao et al. 2024] [Lichota 2023] [Lindner et al. 2023] [Liu and Zhang 2024] [Liu et al. 2025b] [Lucarini 2026] [Lyu and Yang 2025] [MacNeill and Verstraete 2017] [Mahmuddin 2017] [Maisel and Harris 1981] [Malick and Agarwal 2015] [Martin 2025] [McCormick 2002] [McDonald 2015] [Mihaila et al. 2026] [Min et al. 2026] [Modarres and Peters 2015] [Nagaraju et al. 2015] [Narducci 2015] [Nark et al. 2017] [Nguyen 2021] [Zawodny et al. 2025] [Oldeweme et al. 2024a] [On the Rotor Lifting 2016] [Oosedo et al. 2012] [Overmeyer and Martin 2017] [Ramesh and Jeyan 2022] [Pascioni et al. 2026] [Patterson et al. 2016] [Pereyra and Kung 2026] [Petroff and Wattson 1954] [Poggi et al. 2024] [Polak and George 1998] [Polonsky et al. 2023] [Pomin and Wagner 2002] [Powell 1959] [Prasad 2025] [Qing et al. 2023] [Quackenbush et al. 1989] [Quackenbush et al. 1991] [Quackenbush et al. 2019] [Rakshith et al. 2015] [Ramachandran et al. 1989] [Ramasamy et al. 2010] [Ritter et al. 1971] [Rotor Noise 1976] [Rubin and Zhao 2021] [Saberi et al. 2026] [Sadowski et al. 2023] [Sambell 1972] [Sankar et al. 2015] [Schaefer et al. 2026] [Schmaus and Chopra 2016] [Schrenk 1934] [Schwartz and Rogers 1992] [Scully 2018] [Serrano et al. 2021] [Shahmiri 2017] [Shaidakov and Brusov 2017] [Shankar et al. 2023] [Sharpe and Agarwal 2019] [Sheng et al. 2015] [Shi et al. 2024b] [Shinoda and Johnson 1993] [Shivananda et al. 1978] [Shives and Crawford 2017] [Simmons and Ackerman 2026] [Simmons et al. 2023] [Simpson 1967] [Sinnige et al. 2018] [Smith 1968] [Soemarwoto et al. 2022] [Son and Kim 2023] [Stanly et al. 2020] [Stepniewski and Keys 1984] [Stringer et al. 2020] [Szafran et al. 2014] [Tai and Vorwald 1993] [Takallu and Gentry 1992] [Thomason 1982] [Tinney and Valdez 2024] [Troldborg et al. 2015] [Tyler et al. 2026] [Van Riper and Wood 2003] [Veldhuis and Heyma 2000] [Venter et al. 2024] [Walsh 1991] [Walvekar and Chakravarthy 2023] [Wang et al. 2007] [Wang et al. 2021a] [Wernicke 1980] [Withrow-Maser et al. 2021] [Xu et al. 2016] [Xu et al. 2025] [Yan and Chen 2019] [Yang et al. 2024a] [Yang et al. 2025a] [Yassini and Syrovy 2002] [Yomchinda et al. 2009] [You et al. 2026] [Yuan 1970] [Yuan et al. 2020] [Yurt et al. 2026] [Zhang et al. 2018a] [Zhao and Sheng 2015] [Zhao et al. 2025a] [Zhou and Huang 2023]

Ducted fans and ducted-fan vehicles

Ducted fans and the vehicles built around them, from research testbeds to electric ducted-fan aircraft.

117 records. [Luo et al. 2024] [Aboelezz et al. 2022] [Ahn and Lee 2004] [Akturk and Camci 2022] [Akturk and Camcı 2014] [Alabdali et al. 2025] [Ali and Maqsood 2024] [Alvarez et al. 2023] [Avanzini et al. 2001] [Avanzini et al. 2003] [Boldman et al. 1991] [Bustamante Alarcon et al. 2025] [Casagrande Hirono et al. 2022] [Castegnaro 2019] [Chakraborty et al. 2022a] [Chakraborty et al. 2023] [Chen 2024] [Chen et al. 2018a] [Cheng and Pei 2020] [Cheng and Pei 2021] [Cheng et al. 2020b] [Chi 1991] [Choi et al. 2012] [Cui et al. 2025] [Darrah et al. 2020] [Deng et al. 2020] [Dorfling and Traub 2023] [Dos Santos et al. 2024] [Ebus et al. 2024] [Effati and Banazadeh 2013] [Engelbrecht et al. 2022] [Fan et al. 2017] [Fan et al. 2018] [Feng et al. 2026a] [Fleming et al. 2003] [Fu et al. 2023] [Gao and Xu 2022] [Graf et al. 2008] [Grant et al. 2015] [Guerrero et al. 2003] [Guo and Zhou 2022b] [Guo and Zhou 2022a] [Harada 2018] [Hess and Ussery 2004] [Huang et al. 2021] [Hui et al. 2025] [Jiang et al. 2025b] [Jiang et al. 2025a] [Jin et al. 2018] [Junaidin and Cahyono 2019] [Kang et al. 2021] [Keller and Holliger 1959] [Kondor et al. 2001] [Young] [Lei et al. 2024] [Li 2008] [Li and Liu 2023] [Liu 2023] [Liu and Mi 2025] [Liu et al. 2019] [Liu et al. 2022b] [Liu et al. 2025f] [Liu et al. 2025a] [Ma et al. 2017] [Ma et al. 2022] [Mao et al. 2024] [Mehr and Ning 2024] [Mi 2020] [Modelling and Controller Design 2021] [Moser 1959] [Muehlebach and D’Andrea 2017] [Mumasha et al. 2026] [Niwa and Suzuki 1991] [Niță et al. 2026] [Odukoya and Jo 2026] [Ozdemir and Horn 2009] [Pangaribuan and Hartono 2024] [Park et al. 2017] [Peddle et al. 2009] [Pflimlin et al. 2004] [Regan et al. 2025] [Ritschl et al. 2003] [Rybakov et al. 2020] [Safieh and Rauleder 2024] [Sargent and Anemaat 2018] [Sarjito and Mulyadin 2024] [Savage et al. 2026] [Sedunin et al. 2024] [Seo and Kim 2016] [Shao et al. 2022] [Sheng and Sun 2015] [Shiau et al. 2023] [Shiau et al. 2024] [Srivastava et al. 1996] [Srivastava et al. 1997] [Stiltner and Ohanian 2012] [Su et al. 2021] [Su et al. 2025a] [Su et al. 2026] [Sun et al. 2025a] [Van Niekerk 1958] [Van Weelden and Smith 1995] [Vasanthakumar et al. 2019] [Wahid et al. 2025] [Wahl and Julian 1956] [Wang and Li 2025] [Wang and Qi 2011] [White and Phelan 1987] [Wu et al. 2025b] [Xiang et al. 2015] [Yoeli 2002] [Yu 2023] [Zakaria et al. 2019] [Zhang and Fan 2012] [Zhang et al. 2004] [Zhang et al. 2016a] [Zhao and Bil 2008]

Distributed and electric propulsion and electric vertical flight

Electric vertical takeoff and landing aircraft, distributed propulsion for lift and control, and the electric and hybrid powertrains that drive them, the field in which the square-root law now decides configurations.

152 of these 156 records date from 2015 or later.

156 records. [Agustinho and Bento 2022] [Ayar et al. 2021] [Baculi et al. 2023] [Baculi et al. 2024] [Bahr et al. 2020] [Bai et al. 2022] [Barbosa Marques and Silva 2021] [Beals et al. 2026] [Benyamen and Keshmiri 2022] [Bills et al. 2023] [Brenner et al. 2022] [Brenner et al. 2023] [Cai et al. 2026] [Campagna et al. 2021] [Cao et al. 2024] [Casalino et al. 2024] [Chakraborty and Mishra 2023b] [Chakraborty et al. 2022b] [Chan 2019] [Chen et al. 2025c] [Cheng et al. 2025] [Comunian et al. 2026] [Courtin and Hansman 2019] [Cusati et al. 2023] [Nithya et al. 2025] [Darmstadt et al. 2021] [de Vries and Vos 2023] [Deere et al. 2017] [Demers Bouchard et al. 2015] [Distributed Electric Propulsion 2018] [Dožić et al. 2026] [Elahi Kahooker and Liu 2026] [Feroskhan et al. 2025] [Figueira et al. 2025] [Filippoli et al. 2026] [Fisler and Datta 2019] [Fossati et al. 2024] [Foy 1983] [Fredericks et al. 2013] [Freeman and Klunk 2018] [Gallani et al. 2020] [Gan et al. 2021] [Garcia et al. 2026b] [Gothow et al. 2023] [Gothow et al. 2024] [Govindarajan and Sridharan 2021] [Guo et al. 2024] [Ha et al. 2020] [Halder and Gandhi 2026] [He et al. 2020] [He et al. 2025] [He et al. 2026a] [Herzog et al. 2021] [Hu et al. 2024b] [Hu et al. 2025b] [Jeong et al. 2024] [Jia et al. 2025] [Jiao and Yang 2026] [Johnsen et al. 2022] [Johnson and Silva 2026] [Hansman et al. 2023] [Kaneshige et al. 2023] [Kang et al. 2025b] [Kim et al. 2018] [Klunk and Freeman 2018] [Kraenzler et al. 2019] [Krammer et al. 2022] [Kuzniar et al. 2020] [Lee and Yee 2024] [Lee et al. 2022] [Lee et al. 2026] [Lei and Zhao 2023] [Li et al. 2022b] [Li et al. 2024c] [Li et al. 2025] [Li et al. 2026b] [Li et al. 2026a] [Lian and Wu 2018] [Liang et al. 2025] [Liang et al. 2026] [Lim] [Litt 2026] [Liu and Tan 2024] [Liu and Wang 2024] [Liu et al. 2023b] [Love 2022] [Lympany and Page 2024] [Ma et al. 2020] [Ma et al. 2025] [Mahvelatishamsabadi and Emadi 2020] [Maroldt et al. 2023] [Mathur and Atkins 2026] [Moore and Ning 2019] [Müller et al. 2026] [Narjes et al. 2018] [Neogi et al. 2025] [Ng and Datta 2018] [Nguyen et al. 2022b] [Nguyen et al. 2023a] [Nguyen Van et al. 2020] [Niemiec et al. 2020] [Oldeweme et al. 2024b] [Orefice et al. 2019] [Panayotov and Zikyamov 2026] [Papathakis et al. 2017] [Park 2025] [Park and Park 2026] [Pavel 2022] [Paw and Ang 2023] [Performance Metrics Required of Next-Generation Batteries to Electrify Vertical Takeoff and Landing VTOL Aircraft] [Perry et al. 2023] [Pham et al. 2022] [Raush et al. 2016] [Rizzi et al. 2017] [Russo et al. 2023] [Sarikaya et al. 2026] [Schrage et al. 2018] [Scott 2025] [Seren and Hornung 2023] [Shang et al. 2025] [Shankar et al. 2022] [Shi et al. 2023] [Shihua et al. 2023] [Consulting et al. 2025] [Shubert et al. 2026] [Simmons 2023] [Snyder 2020] [Synodinos et al. 2018] [Thapa et al. 2025] [Theron et al. 2020] [Van et al. 2019] [Wang and Fang 2023] [Wang and Hu 2026] [Wang et al. 2023b] [Wang et al. 2023a] [Wang et al. 2024] [Wang et al. 2026a] [Wei et al. 2021] [Wei et al. 2024] [Wei et al. 2026] [Weng et al. 2021] [Wiston and Yan 2025] [Wu et al. 2023] [Xie et al. 2023] [Yan et al. 2025] [Yanev and Staack 2026] [Yang et al. 2021a] [Yang et al. 2026d] [Yang et al. 2026e] [Zhang et al. 2021b] [Zhang et al. 2023a] [Zhao et al. 2024a] [Zhao et al. 2024b] [Zhao et al. 2025b] [Zheng et al. 2025] [Zong et al. 2022]

Supersonic inlets, intakes and airframe-propulsion integration

Supersonic and subsonic inlets, inlet distortion and the integration of propulsion with the airframe.

243 records. [Abdel-Fattah 1997] [Abdul-Kaiyoom et al. 2025] [Abedi et al. 2020] [Afzal et al. 2021] [Amin and Hollweger 1983] [Anderson 1983a] [Andrew et al. 1991] [Arif et al. 2021] [Askari and Abedi 2026] [Askari and Soltani 2017] [Askari and Soltani 2020] [Bai et al. 2025] [Bangert et al. 1982] [Barr et al. 2018] [Barry 1971] [Beale et al. 2002] [Beale et al. 2006] [Beale et al. 2007] [Benjamin et al. 2023] [Benton et al. 2021] [Boles et al. 2021] [Bond and Key 2025] [Braun and Podleski 2019] [Brix et al. 2000] [Brown and Slaboch 2019] [Bucknell 1987] [Burrows et al. 2017] [Cai and Huang 2022] [Cai et al. 2022a] [Cai et al. 2022b] [Candon et al. 2016] [Cao et al. 2017] [Castner et al. 2018] [Chaudhari and Takahashi 2022] [Chen and Tan 2019] [Chen et al. 2019b] [Chen et al. 2023a] [Choe and Kim 2016] [Choe et al. 2018] [Choe et al. 2020] [Choi et al. 2025] [Chopde et al. 2025] [Chun and Burr 1969] [Chun and Swanson 1964] [Clark 1974] [Clingingsmith 1983] [Colbert et al. 2023] [Conners et al. 2005] [Control System Design Using 1976] [Davis et al. 2001] [Davoudzadeh et al. 1987] [Dickman and Takahashi 2016] [Du et al. 2012] [Edefur and Tormalm 2018] [Endo et al. 2016] [Ezrokhi and Khoreva 2018] [Ezzeldin and Wu 2025] [fang et al 2024] [Farahani and Mahdavi 2019] [Ferrero 2020] [Florea et al. 2015] [Flores et al. 1989] [Fuqun et al. 1985] [Gaglio et al. 2021] [Gas Turbine Engine Inlet Flow Distortion Guidelines] [Ge et al. 2021] [Gillen and Loth 2015] [Glasgow et al. 1983] [Godard et al. 2017] [Godard et al. 2019] [Godston and Reynolds 1983] [Gubanov 2019] [Guidelines for Characterization of Gas Turbine Engine Total-Pressure, Planar-Wave, and Total-Temperature Inlet-Flow Distortion] [Guimarães et al. 2017] [Halwas and Aggarwal 2019] [Hamed et al. 1997a] [Harjes et al. 2022] [Hawkins 1976] [He et al. 2023b] [Heberling 2020] [Herrick 1986] [Herrmann 1996] [Hinz and Miller 1979] [Huang et al. 2020a] [Hubble and Smith 1979] [Influence of Back Pressure 2017] [Inlet Total-Pressure-Distortion Considerations for Gas-Turbine Engines] [Jahnen et al. 1999] [Jin et al. 2023] [Jones et al. 2021] [Karaselvi and Nikbay 2021] [Kato et al. 2024] [Kawai 1973] [Kaya 1998] [Keller et al. 2018] [Khobragade et al. 2021] [Kim and Kwon 2015] [Kim and Park 2026] [Kitowski 1992] [Knoth and Breitsamter 2017] [Kong 2000] [Korn 1974] [Koval 2020] [Kursakov et al. 2022] [Kurzke 2006] [Ladd and Norby 1998] [Lauer and Ansell 2022] [Lavan Kumar et al. 2013] [Lavi 1967a] [Lee et al. 2007] [Lee et al. 2010] [Lei and Zha 2022] [Lepicovsky 2008] [Li and Geiselhart 2024] [Li and Geiselhart 2026] [Li et al. 2023e] [Lin et al. 2018] [Lind and Protopapas 1977] [Liou et al. 2016] [Liou et al. 2017] [Liou et al. 2019] [Little 1983] [Liu and Wu 2023] [Liu et al. 2024b] [Loss in Turbofan Thrust 1985] [Loth et al. 2016] [Lowe 2020] [Lucas et al. 2014] [Luidens 1976] [Harish et al. 2017] [Ma et al. 2026] [Mace and Nyberg 1992] [Malan and Brown 1994] [Marvin 1968] [Medina et al. 2021] [Menegozzo and Benini 2021] [Miao et al. 2026] [Moore 1985] [Mufti et al. 2019] [Naseri et al. 2012a] [Naseri et al. 2012b] [Nichols et al. 2015] [Nicolae Tudosie 2018] [O’brien and Lowe 2015] [O’Neill 2020] [Omar and Lampkin 1977] [Opalski and Sajben 2002] [Ordaz et al. 2017] [Otto et al. 2015] [Overall 1976] [Page et al. 2017] [Palumbo et al. 2022] [Patel and Chudoba 2026] [Pecinka et al. 2015] [Peters et al. 2001] [Pečinka et al. 2017] [Piovesan et al. 2025] [Powers and Robinson 1992] [Processing and Validating CFD Data for Estimating Inlet Dynamic Total-Pressure Distortion] [Qiu et al. 2018] [Quraishi et al. 2025] [Reyhner and Hickcox 1972] [Richey et al. 1983] [Rohacs et al. 2018] [Safoklov et al. 2025] [Saleem Yusoof et al. 2016] [Sanders and Palasics 1948] [Schierman and Lowell 1992] [Schmidt and Wild 2026] [Sedlock 1985] [Semmes and Weyer 1990] [Shimabukuro et al. 1979] [Shimabukuro et al. 1982] [Shmilovich and Yadlin 2026] [Shu et al. 2025] [Silva et al. 2024] [Slater 2016] [Slater 2019] [Smeltzer et al. 1981] [Smeltzer et al. 1982] [Smith 1997a] [Snyder 2003] [Soeder and Bobula 1982] [Sorensen and Bencze 1974] [Sorensen and Latham 1975] [Sorensen and Smeltzer 1972] [Sorensen et al. 1969] [Sorensen et al. 1973] [Soto and Hernandez 2004] [Spencer et al. 2016] [Stephens and Svetgoff 2024] [Stephens et al. 2023] [Stylianides et al. 2020] [Substantiation of Power Available and Inlet Distortion Compliance for Rotorcraft Engine Inlet Barrier Filter Installations] [Sun and Zhang 2016] [Sun et al. 2024b] [Sun et al. 2025b] [Surber and Robinson 1983] [Surber and Sedlock 1979] [Sussman 1968] [Sutrakar et al. 2026] [Syberg and Koncsek 1976] [T-4 Inlet/engine Compatibility Flight 1989] [Tekaslan et al. 2021] [Tindell and Flynn 1978] [Tongguang et al. 2015] [Tudosie 2017a] [Tudosie 2017b] [Tudosie 2018] [Tudosie 2022] [Tudosie and Prisacariu 2022] [Tudosie and PĂUnescu 2017] [Tudosie et al. 2019] [Türkkahraman et al. 2024] [Utomo and Bura 2019] [Vadyak et al. 1987] [Vinogradov et al. 2017] [Vnuchkov et al. 2018] [Vogel 2016] [Vogel and Junqueira 2017] [Vohra 2024] [Wang et al. 2013] [Wang et al. 2015] [Wang et al. 2023c] [Wang et al. 2025a] [Williams and Hunt 1980] [Wilson and Wright 1977] [Wilson and Zhang 2025] [Woollett 1983] [Wu et al. 2022] [Wu et al. 2024] [Xia and Zhou 2024] [Xie et al. 2015a] [Yan et al. 2023] [Yang et al. 2026c] [You et al. 2016] [Yuan et al. 2021] [Zhang et al. 2017a] [Zhang et al. 2020b] [Zhang et al. 2020a] [Zhang et al. 2026d] [Zhao et al. 2025c] [Zhu et al. 2020]

Engine cycles, variable cycle engines and engine performance

Engine cycles, variable and adaptive cycle engines, the performance of fighter and lift engines, and propulsion systems and their control.

278 records. [A Synopsis on Q/STOL 1971] [Adibhatla 1993] [Adibhatla 1994] [Airfoil Static-Pressure Thrust 1990] [Amundson and Holm 1989] [Andreev and Druzhinin 1991] [Antonakis et al. 2019] [Arar 2002] [Asri et al. 2019] [Atkinson and Raymond 1968] [Aygun and Turan 2020] [Bailey et al. 1979] [Balke 1970] [Barrack and Kirk 1968] [Barrett 1952] [Batterton and Blaha 1987] [Bayati and Williston 1977] [Beale 1986] [Beard and Foley 1982] [Berg et al. 1988] [Bhandari et al. 2024] [Biesiadny 1992] [Blaha and Batterton 1987] [Blaha and Batterton 1990] [Bloomfield 1959] [Bogdanovic et al. 1964] [Bolam et al. 2021] [Bolivar et al. 2003] [Boruff and Roch 1981] [Boschma 1998] [Boschma 2001] [Bougas et al. 2017] [Brandt 2018] [Brear et al. 2003] [Brines 1973] [Brooks 1990] [Brown 1981] [Bucknell et al. 1990] [Burcham 1971] [Butler and Thomas 1964] [Cao et al. 2022b] [Carlin et al. 1984] [Cartagena et al. 2000] [Chakraborty and Mishra 2022] [Chakraborty and Mishra 2023a] [Chapman et al. 2025] [Chen et al. 2021b] [Chen et al. 2024] [Chipperfield et al. 1999] [Clark et al. 2023b] [Clark et al. 2023a] [Clough 1990] [Colbert et al. 2020] [Collopy and Collopy 1997] [Compton and Burgess 2021] [Conners 1992] [Conners 1995] [Coons 1987] [Curran and Bergsten 1975] [Curry 1975] [Cyrus 1995] [Dannenhoffer 1981] [Davenport et al. 1974] [Denham 2002] [Denning and Mitchell 1986] [Design and Analysis 2023] [Digital Engine Control 1982] [Duvivier and McCallum 1960] [Elliott and Simmons 1987] [Engine Selection 2002a] [Engine Selection 2018] [Engine Selection 2002b] [Farokhi 1998] [Feddersen and Cea 1977] [Feng et al. 2026b] [Fetahi et al. 2022] [Flight-Test Evaluation of Engine 1985] [Franciscus 1983] [Franciscus and Luidens 1984] [Franklin 1993c] [Franklin 1996] [Franklin and Engelland 1991] [Franklin and Engelland 1993] [Franklin 1993a] [Franklin and Stortz 1989] [Franklin et al. 1990] [Frazzini 1970] [Gallops et al. 1990] [Garg 1993b] [Garg and Mattern 1991] [Garg and Mattern 1994] [Garg and Ouzts 1991] [Garg and Schmidt 1993] [Garg et al. 1990] [Garg 1993a] [Garvin et al. 2018] [Gerend 1971] [Gertsma and Zigan 1973] [Gielow 1971] [Gilyard et al. 1991] [Goldsmith and Hickey 1963] [Gologan et al. 2009] [Gou et al. 2019] [Gray et al. 2017] [Hao et al. 2018] [Hao et al. 2020a] [Harned and Nay 1963] [Harrell 2018] [Hatta and Matsuki 1964] [Havey and Kline 1989] [Hensley et al. 1950] [Herrmann and Biehl 1986] [Highly Noise-Suppressed Bypass 6 1975] [Hill 1971] [Hill and Schmitt 1964] [Hirsh 1965] [Hobson et al. 2004] [Hoskin 1993] [Huang et al. 2022b] [Huete and Singh 1997] [Hughes and Ray 1985] [Hughes Tool Co Culver City Ca 1963] [Tupitsyin 2023] [Imrak et al. 2021] [Integration and Simulated Flight 1977] [Franklin 1993b] [Ji et al. 2026] [Jia et al. 2023] [Jiang et al. 2023] [Jiang et al. 2025c] [Kamman and Perryman 1982] [Keller 1982] [Khalid 1989] [Khalid 1992] [Kim and You 2026] [Kimberlin 1987] [Kleckner 1973] [Kohn 1972] [Kozlaykov 1997] [Kress 1980] [Krishnakumar et al. 1996] [Kutney 1964b] [Kuzmin 2021] [Lawrence and Cerbone 1990] [Lee et al. 1988b] [Lewis 1989] [Lewis and Lewis 1981] [Lewis and Simpkin 1980] [Li and Livne 1997] [Li et al. 2018b] [Li et al. 2023c] [Li et al. 2024b] [Lin and Jules 1998] [Liu et al. 2022c] [Liu et al. 2024c] [Liu et al. 2026b] [Liu et al. 2026a] [Lu and Burken 1999] [Lu et al. 2019] [Luidens et al. 1981] [l’Anson 1969] [Ma et al. 2023] [Mahmoudi et al. 2022] [Maine et al. 1994] [Malloy et al. 2002] [Margason 1998] [Martin 1977] [Mattingly 1989] [Matuschek et al. 2023] [McGuigan 1970] [Mehrab et al. 2023] [Mello and Kotansky 1985] [Meng et al. 2017] [Meng et al. 2018] [Mihaloew 1988] [Mihaloew and Weiss 1989] [Mihaloew and Drummond 1989] [Miller and Hackney 1976] [Moller 1985] [Nelson and Current 2018] [Neville et al. 1992] [Nichols 1960] [Nie et al. 2020] [Nilchiani et al. 2025] [Ouyang et al. 2024] [Panella 1975] [Pang et al. 2025] [Papamoschou 2004] [Patel and Wilson 2018] [Perusek 1994] [Petrov 1993b] [Pilsch 1975] [Platzer and Margason 1976] [Plourde et al. 1983] [Pour Razzaghi et al. 2025] [Pulk and Stolarik 1977] [Qian et al. 2020] [Rauh and Anders 1986] [Ray 1983] [Rebeske and Rohlik 1953] [Reed 1980] [Reed 1984] [Reemsnyder and Sagerser 1979] [Ren et al. 2017] [Requirements for STOVL Integrated 1994] [Requirements of a Commercial 1967] [Richardson 1959] [Riggins 1996] [Robbins 1967] [Rodenbaugh and Veno 1965] [Rom and Koutz 1950] [Rose 1986] [Roth and Mavris 1999] [Ryan et al. 1977] [Saboe 1963] [Sabzehali et al. 2022] [Sallee 1973] [San Martin and Melnyk 2022] [Sanders 1964] [Sanghi 1999] [Seo et al. 2022] [Serovy and Kavanagh 1974] [Sheridan 1983] [Shovlin et al. 1980] [Simmons and Brant 1988] [Sininger 1976] [Spratt 1990] [Stewart 1992] [Strack 1973] [Su et al. 2025b] [Sulkoske et al. 1977] [Swavely 1974] [Tahsin et al. 2025] [Tam 2015] [Tao et al. 2022] [Tape and McIntyre 1990] [Tate and Gillard 1975] [Tindell 1966] [Toenskoetter 1984] [Treubig et al. 2015] [V/STOL Propulsion Control Analysis 1981] [Wagner 1977] [Wahler and Elham 2025] [Warwick 1983] [Watts et al. 1993] [West 1969] [Willis 1981a] [Wilson et al. 1981b] [Wilson et al. 1997] [Wright and Jones 1970] [Wright and Russell 1980] [Xiao-bo and Zhan-xue 2017] [Xu et al. 2026] [Yang et al. 2024b] [Ye et al. 2022] [Yi Fan et al. 2021] [Young 1961] [Yu et al. 2019] [Yuan et al. 2024] [Zabinsky 1964] [Zabinsky 1978] [Zabinsky 1979] [Zabinsky and Carter 1972] [Zein-Sabatto et al. 2017] [Zeng et al. 2020a] [Zeng et al. 2020b] [Zenkner et al. 2025] [Zhang et al. 2017b] [Zhang et al. 2018c] [Zhang et al. 2018b] [Zhang et al. 2020c] [Zhang et al. 2023b] [Zhao et al. 2017] [Zhou 2023] [Zhou et al. 2019] [Zhou et al. 2020] [Zhu et al. 2024] [Zou et al. 2025]

Defence acquisition, competition, prototyping and cost

Defence acquisition, competitive prototyping and fly-offs, source selection, cost estimation and cost growth, acquisition reform, and operational test and evaluation as part of acquisition.

140 of these 280 records are report primaries, the highest share of any cluster, because the literature of the decision is mostly written by the institutions that make such decisions.

280 records. [Abouamod and Awad 2017] [Achmadi and Priyatiningsih 2016] [Aggarwal et al. 2010] [AI-Based Framework for Forecasting 2025] [Air Force Flight Test Center Edwards AFB CA 1995] [Alberts 1995] [Alford 2004] [Aliyanto et al. 2017] [Amara and Franck 2026] [Andrastek et al. 1966] [Angell et al. 2020] [Apgar 2003] [Army Aviation Materiel Labs Fort Eustis VA 1966] [Army Materiel Command Alexandria VA 1987] [Ascani et al. 1980] [Aten and Dillard 2013] [Babione 1978] [Bacon 1988] [Bagan 1967] [Bahram 2022] [Bair 1994] [Balakrishnan and Lazar 2022] [Bangert et al. 2017] [Bastola et al. 2015] [Baylot et al. 2018] [Bell 1993] [Bell et al. 2018] [Bennett 1990] [Bergey and Wood 2002] [Berteau et al. 2011] [Biggs et al. 2014] [Bilardo 2026] [Bilodeau and Dallosta 1978] [Blank 2019] [Blumstein 1965] [Boger and Liao 1988] [Boger and Nussbaum 1990] [Boger et al. 1989] [Boyd and Mundt 1995] [Brauer 2001] [Brett et al. 1986] [Bridgeforth et al. 2015] [Brisacier‐Porchon and Hammami 2023] [Bronson 2020] [Brooks et al. 2012] [Brown 2010] [Brown and White 2017] [Buettner 2010] [Burton et al. 2004] [Calafut et al. 2021] [Campbell et al. 2011] [Carlyle 1976] [Castagne et al. 2004] [Cate 1997] [Cavolowsky et al. 2010] [Cherry 1975] [Chewning and Moretto 2000] [Christensen 2023] [Christensen et al. 1999] [Cisneros et al. 2024] [Cloos and Nelson 1990] [Coble et al. 2014] [Cox and Bohn 1982b] [Cox and Bohn 1982a] [Cronie and Thompson 1980] [Cubillos Chacon 2007] [Curran et al. 2002] [Curtis 1987] [D’Amico et al. 2018] [Daly et al. 1979] [Davis 1973] [Davis 2011] [Davis and Tate 2020] [Defense Acquisition Univ Ft Belvoir Va 2005] [Defense Acquisition Univ Ft Belvoir Va 2007a] [Defense Acquisition Univ Ft Belvoir Va 2007b] [Defense Science Board Washington Dc 1975] [Defense Science Board Washington Dc 1979] [Defense Science Board Washington Dc 1993a] [Defense Science Board Washington Dc 1993b] [DeLaurentis 2011] [Dement 1990] [Program Acquisition Costs 1993] [Program Acquisition Costs 1994] [Program Acquisition Costs 1995] [Department of Defense Budget 1996] [Program Acquisition Costs 1998] [Department of Defense Budget 1999] [Program Acquisition Costs 2000] [Test and Evaluation Guidelines. 1992] [Dietz and Bailey 1973] [Dillard 2005] [Dougherty 2018] [Drake 1977] [Dreier 2022] [Droegkamp et al. 1998] [Drozd and Procházka 2024] [Drury et al. 2015] [Duddy et al. 2020] [Dwyer et al. 2015] [Enthoven 2019] [Espinoza-Garcia et al. 2026] [Fast 2014] [Fellers and Patierno 1970] [Figge 1973] [Flores 2015] [Franck and Dillard 2006] [Franck et al. 2012] [Frerking and Beauchamp 2016] [Fuhrman 1999] [Gallagher 1999] [Gallagher et al. 1997] [Gansler and Lucyshyn 2006] [Gansler et al. 2010] [Gaver et al. 1997] [Gideon and Wasek 2015] [Gluckman and Celmins 1993] [Greer 2010] [Greer et al. 1984] [Grosse 1965] [Guajardo 2020] [Guinivan 2004] [Hale 2004] [Hall 2019] [Hamada 2021] [Hans et al. 2021] [Hantos 2008] [Hardy 1983] [Harris and Lewis 2012] [Harvey 2019] [Harvey and Ryan 2012] [Haug et al. 1993] [Hawkins et al. 2023] [Hawley et al. 1986] [Healy et al. 2014] [Herd and Moxley 1965] [Hermann 1999] [Heymont et al. 1965] [Hibbard and O’Brien 1993] [Hirsch 1998] [Hjorth et al. 2020] [Hoffman 1971] [Horowitz et al. 2014] [Hubbard and Caldwell 1989] [Huete and Nance 1994] [Hui et al. 2017] [Hwang 1971] [Insaurralde and Kaupisch 2016] [Jessup and Williams 2015] [Jimenez et al. 2016] [Jm and Dj 2017] [Jones 2024] [Jones and Wilbur D. 1989] [Jones et al. 2023] [Kasunic 2004] [Keaton 2015] [Kilicay‐Ergin and Dagli 2015] [Kim and Hur 2016] [Koster 2004] [Kozlak et al. 2017] [Kratz et al. 1984] [Kubricky 2007] [Kundu et al. 2002] [Labro 2004] [Lamoureux et al. 2015] [Landale et al. 2017] [Laughman 2010] [Lavelle 2017] [Lee 2022] [Leete et al. 2015] [Li et al. 2018a] [Lieberman 2000] [Lieberman 2002] [Lisy et al. 2023] [Logan 1974] [Logistics Management Inst Bethesda Md 1964] [Lorell 1989] [Loren and Beverly 2009] [Loren et al. 1992] [MacKenzie 2003] [MacKenzie and Addison 2001] [Mandell 1997] [Marchinski 1974] [Markman et al. 2021] [Marquiz et al. 2025] [Marx 1983] [Marx et al. 1995] [Marx et al. 1998] [Mayori et al. 2019] [McBride and Paret 2010] [McCown 2011] [McDaniel and Cooper 1999] [McDaniel et al. 1995] [McDaniel et al. 1998] [McGowin et al. 2018] [McNicol 2022] [McNicol and Wu 2014] [McNicol et al. 2015] [Medlej et al. 2017] [Metcalf and Eftekhari-Shahroudi 2026] [Moeller 1980] [Moody 1997] [Moorhouse 1994] [Morgenfeld 1992] [Mortlock 2020] [Mortlock 2024] [Muchow 2013] [Mun 2020] [Na et al. 2024] [Naval Sea Systems Command Washington DC 2010] [Noguchi 2019] [One Prototype Three Prototype 1986] [Palavenis 2024] [Park et al. 2024] [Parrish 1978] [Pavick et al. 2006] [Percival 1988] [Post and Sundt 2017] [Post et al. 2017] [Pottinger et al. 2017] [Preidis 1984] [Quinn and Choe 2012] [Rais-Rohani and Huo 1999] [Ramelli and Daniel S. 1976] [Rand 1999] [Regnier and Nussbaum 2011] [Rhoads 1992] [Robinson and Smith 1999] [Rosen et al. 2019] [Rosenthal and Brandeau 1983] [Ross 2022] [Rozum 1992] [Rubinstein 2014] [Ryan 2018] [Sai 2004] [Salado and Shadab 2023] [Sauser and Ramirez-Marquez 2009] [Sauser et al. 2009] [Schrage 1989] [Schrage 2015] [Schwartz 2019] [Shafer et al. 1990] [Shawler 1981] [Shroder 1999] [Simms and Wehrkamp 2024] [Simpleman et al. 1998] [Simpleman et al. 2003] [Simpson 2003] [Smith 1999] [Sobel 2013] [Stahl et al. 1984] [Stewart et al. 2011] [Stuckey et al. 2017] [Tan et al. 2024] [Tate 2015] [Templin and Noffsinger 1994] [Test and Evaluation 1994] [The Integrated Flight 1993] [Trepel and Bohmann 1973] [Trudelle et al. 2017a] [Trudelle et al. 2017b] [Turtle and Hermann 1998] [University of South Florida Tampa 2000] [Valerdi et al. 2015] [Vanderplaats 2001] [Vargo 2000] [Vascik et al. 2015] [Wang et al. 2021b] [Watkins 2019] [Weed 2002] [Wei and Shi 2022] [Weinig 2019] [West and Pyster 2015] [Wickert 1985] [Wilken 1991] [Winbush and James O. 2012] [Worm 1980] [Yasir 2025] [Yates 1964] [Yu et al. 2021]

Commonality, product families and requirements

Commonality across product families and variants, and the setting of requirements.

88 records. [Baker and Mavris 2001] [Bannova and Camba 2018] [Barber et al. 1978] [Bashkirov et al. 1997] [Baylis et al. 2018] [Bye 1993] [Chen et al. 2021c] [Cheng et al. 2018] [Chuprun 1984] [Cole and Jenkins 2015] [Crites and Tremblay 1988] [Cunningham 1981] [Dang and Nagarur 2000] [Dong et al. 2020] [Fujita et al. 2020] [Fusaro and Viola 2018] [Garmilla Manzano et al. 2026] [Gerken 1979] [Goldberger 1966] [Han et al. 2019b] [Hansen and Rosen 2018] [Hao et al. 2020b] [Hillier 1999] [Hou and Lai 2015] [Hummell and Hause 2015] [Jennings et al. 2025] [Jiang 2026] [Jung and Simpson 2015] [Kanon et al. 2023] [Kim et al. 2016a] [Kim et al. 2016b] [Kim et al. 2020b] [Krammer and Holzapfel 2023] [Kwapisz et al. 2019] [Lange and Mikolowsky 1979] [Lebacqz et al. 1986] [Lei et al. 2016] [Levine and Zalesch 1983] [Li et al. 2023d] [Lind and Tamplin 1981] [Mane et al. 2021] [Milford and Pena 2015] [Mirchandani and Mishra 2002] [Morandini et al. 2015] [Mullin 1986] [Nicolai 1978] [Nomaguchi et al. 2017] [Oakes 1970] [Oh and Hong 2024] [Okumoto and Elsanker 1973] [Ordaz et al. 2015] [Parker 1986] [Pinson and Ryan 1972] [Price 1964b] [Rajpaul and Yurczyk 1977] [Ransone 1972] [Salado and Nilchiani 2015] [Schrage 1983] [Schrage et al. 2001] [Schwartz and Shearer 1964] [Sepulveda Palacios and Smith 2019] [Siddique 2025] [Simpson 2017] [Smith 1966b] [Spinelli and Kipouros 2025] [Stepniewski and Schneider 1964] [Stern 1984] [Stojanovski and Selva 2017] [Subarna et al. 2020] [Takai 2018] [Takai 2019] [Takai and Sengupta 2016] [Takeda et al. 2018] [Total Control over Design 2001] [Van Dyke et al. 1990] [Visconti 2026] [Wilcox and Quigley 1978] [Wong et al. 2019] [Xu and Yang 2025] [Xu et al. 2020a] [Yang et al. 2019] [Yao et al. 2017] [Yongjie et al. 2021] [Young et al. 2017] [Zhang et al. 2015] [Zhang et al. 2019a] [Zhang et al. 2022b] [Zweber et al. 2017]

Decision analysis, selection and cost-effectiveness

Multi-criteria decision analysis, selection, tradespace exploration and cost-effectiveness.

47 records. [Arfer 2024] [Barbour 1996] [Bertoni et al. 2018] [Bhatra and Mishra 2023] [Braafladt et al. 2020] [Buchanan et al. 2019] [Chhabra and Warn 2017] [Cordeaux 1991] [Daniels et al. 2022] [de Moraes et al. 2025] [Egorov et al. 1997] [Englar and Kirkpatrick 1969] [Erwig and Kumar 2025] [Fralish 1998] [Franklin and Nicholas 1992] [French 2025] [Fujita et al. 2017] [Gillespie et al. 2017] [Goncalves and Kokkolaras 2015] [Gordon 1980] [Hakan Ayhan Dağıstanlı 2025] [Houten et al. 2024] [Howard 1974] [Huang et al. 2023a] [Jackson et al. 2017] [Jaini and Utyuzhnikov 2016] [Jamali and Lazarova-Molnar 2024] [Kahneman and Tversky 1977] [Kiratsoudis and Tsiantos 2025] [Kizielewicz et al. 2025] [Louw and Esterhuyse 2022] [Montibeller and von Winterfeldt 2015] [Phillips 2024] [Radojcic 2018] [Rosaria 2017] [Schneider 1989] [Shekhovtsov et al. 2025] [Shi and Chen 2022] [Shrivastava et al. 2016] [Specking et al. 2019] [Stach and Pizzolo 2025] [StojkoviĆ and DimiĆ 2024] [Sundararajan 2020] [Sutton et al. 2024a] [Sutton et al. 2024b] [Turner et al. 2022] [Zhang et al. 2016b]

Digital engineering, model-based systems engineering and machine learning

Model-based systems engineering, digital threads and twins, simulation-based acquisition and machine learning applied to aircraft and their design.

87 records. [Ahlbrecht et al. 2024] [Akundi and Mondragon 2021] [Assef and Geiger 2023] [Aydemir et al. 2020] [Babineau 2015] [Bachman 2016] [Bader et al. 2024] [Beery and Paulo 2019] [Bennett 1997] [Benyamen et al. 2024] [Bickford et al. 2020] [Bluff 2001] [Brusa 2021] [de Longueville et al. 2024] [Doff-Sotta et al. 2025] [Duverger et al. 2024] [Duverger et al. 2025] [French 2015] [Garriga et al. 2019] [Georgiades et al. 2019] [Gharbi et al. 2017] [Gracias and Gallegos 2024] [Gregory et al. 2024] [Gregory et al. 2026] [Pierce et al. 2024] [Huang et al. 2025a] [Huldt and Stenius 2018] [Iwata et al. 2015] [Jacobitz and Liu-Henke 2020] [Jia et al. 2021] [Kallou et al. 2022] [Kallou et al. 2024] [Kamberov and Ivanov 2024] [Kirz 2022] [Kraft 2018] [Liu et al. 2023a] [Lopez and Akundi 2022] [Lu et al. 2026] [Lukyanov et al. 2024] [Madni et al. 2019] [Martinez et al. 2025] [Massegur Sampietro and Da Ronch 2024] [Mavris et al. 2018] [McManus and Goodrich 1989] [Medinacelli et al. 2023] [Shi et al. 2025] [Muthukumar et al. 2026] [Noguchi 2026] [Nunes et al. 2023] [Oyama and Kato 2025] [Ponsard and Darimont 2023] [Popisal 2015] [Power et al. 2021] [Qiao et al. 2026a] [Engelbeck et al. 2025] [Rauzy and Haskins 2018] [Richardson 2023] [Ruan et al. 2025] [Rudolph 2024] [Sahebsara et al. 2026] [Schluse et al. 2017] [Schumacher et al. 2025] [Seddik 2026] [Soares 2007b] [Soares 2007a] [Specking et al. 2018] [Sundaram and Brownlow 2018] [Sungyeon et al. 2024] [System Entity Structure 2017] [Tadeja et al. 2019] [Kulkarni et al. 2016] [Thomas and Mesmer 2016] [Through the Virtual Barrier 2017] [Tsui et al. 2018] [Walter et al. 2019] [Wang 2020] [Williams 2004] [Wu et al. 2025a] [Xie et al. 2015b] [Yang and Yee 2022] [Yin et al. 2017] [Arias et al. 2025] [Zargariasl and Herglotz 2024] [Zech et al. 2026] [Zhang et al. 2021a] [Zhao et al. 2026] [Zhou et al. 2022a]

Low observability and signatures

Radar cross section, infrared and visual signatures, and low-observable design.

32 records. [Abdullah and Miao 2026] [Abdullah et al. 2025] [Aleisa et al. 2024] [Appendix 1998] [Baldwin 1973] [Chen et al. 2015] [Cheng et al. 2016] [Cho et al. 2015] [Colbacchini et al. 2016] [Design and Analysis 2020] [Jeong et al. 2018] [Jylha et al. 2019] [Kurdyla 1963] [Lee 2024] [Lee et al. 2018a] [Liu et al. 2025d] [Marcus 2019] [Narayan et al. 2022] [Ohio State Univ Columbus Electroscience Lab 1968] [Persson 2017] [Persson and Bull 2016] [Poe and Arthur C. 1974] [Ryan 1967] [Sai Teja et al. 2017] [Sharma et al. 2023] [Sreeja et al. 2019] [van Schalkwyk and Smit 2017] [Wang et al. 2025b] [Wright 1966] [Xu et al. 2020b] [Yu Zhou Zhong et al. 2018] [Zhang et al. 2026a]

Automatic and autonomous landing and guidance

Automatic, guided and autonomous landing of vertical, short takeoff and fighter aircraft, including vision-based landing on moving platforms.

18 records. [Ailon 2006] [Ailon 2009] [Chen 2018] [Franklin et al. 1996] [Guy 1976] [Hess 1977] [Hynes et al. 1989] [Lee et al. 2020] [Marconi et al. 2002] [McGee 1977] [Shah et al. 2019] [Seitz and Goodson 1973] [Silva et al. 2017] [Vaispacher et al. 2025] [Watson et al. 1986] [Weichelt et al. 1986] [Wen et al. 2021] [Zhang et al. 2022a]

Handling qualities, flight control and hover control

Handling and flying qualities, flight control laws and pilot workload of powered-lift, vertical and fighter aircraft, and hover and transition control.

235 records. [Aiken et al. 1977] [Akagi et al. 2024] [Albang and Roberts 1974] [Aliaga et al. 2026] [Anderson 1984] [Anderson 1996] [Anderson and Innis 1965] [Anderson et al. 1984] [Armutcuoglu et al. 2004] [Athani and Agarwal 1994] [Bachelder et al. 2019] [Balas et al. 1996] [Barker 1966] [Baron 1981] [Beard and Foley 1983] [Beaufrere 1988] [Bellaire and Bousman 1970] [Beppu and Curtiss 1966] [Bhardwaj and Holzapfel 2024] [Bodden and Virnig 1994] [Boothe et al. 1974] [Borchers et al. 1992] [Boskovic and Mehra 2000] [Bosworth and Cox 1989] [Bryson et al. 1970] [Buffington 1997] [Buffington 1999a] [Buffington 1999b] [Cabarbaye] [Calise and Kramer 1982] [Capen 1971] [Cappetta 1993] [Carpenter 1970] [Carpio-Alemán et al. 2016] [Chance Vought Corp Dallas Tx 1979] [Chen et al. 2018b] [Chetty and Raol 1992] [Blanken and Whalley 1993] [Chung et al. 1993] [Clark 1964] [Coder 2015] [Cook 1964] [Corliss et al. 1977] [Cornish 1965] [Cunningham 1976] [Curtiss 1969] [Curtiss 1971] [Czerwiec et al. 2000] [Dendy and Tribken 1968] [Design of the Circulation 1979] [Determination of the Energy 2018] [Do 2021] [Dobos-Bubno and Hartsook 1977] [Dong et al. 2021b] [Douglas et al. 1990] [Drake 1965] [Du 2025] [Dukes 1970] [Eilertson 1977] [Engelland 1991] [Engelland et al. 1992] [Englar 1975] [Englar 1987] [Englar and Huson 1984] [Englar et al. 1977] [Englar et al. 1999] [Equations of Motion 2002] [Erzberger and McLean 1979] [Ferrell et al. 1974] [Fialho et al. 1997] [Fielding and Lodge 2000] [Fielding and Southworth 2001] [Flight Control System 1977] [Foster et al. 1987] [Franklin 1994] [Franklin and Innis 1977] [Franklin et al. 1986] [Franklin et al. 1989] [Franklin et al. 1982] [Franklin et al. 1988] [Friedman et al. 2016] [Friend 1964] [Frost et al. 2002] [Gallagher and O’Donnell 1965] [Gao et al. 2020] [Garratt et al. 2013] [General Electric Co Schenectady Ny 1952] [H H Aerospace Design CO INC Bedford MA 1987] [Hall 1998] [Harper and Robert P. 1955] [Harper and Sardanowsky 1969] [Harschburger 1983] [Haugen 1966] [Haworth et al. 2024] [Hebbar et al. 1999a] [Hebbar et al. 1999b] [Hill 1966] [Hill 1981] [Hill 1987] [Hoffman et al. 1971] [Hoh and Mitchell 1983] [Hosseini et al. 2021] [Huang et al. 2003b] [Jackson and Coyle 1983] [Jarvis 1967] [Jenkins 1973] [Jewell et al. 1978] [Jewell et al. 1979] [Johnson and Craig 1974] [Johnston and Friend 1965] [Kai 2024] [Kalemaris 1983] [Kazan and Krause 1968] [Kazan and Krause 1967] [Key et al. 1965] [Kim et al. 2025] [Klingloff et al. 1965] [Kogler and Quam 1983] [Kok et al. 2017] [Konar et al. 1974] [Krosche and Heinze 2015] [Kubo and Suzuki 2007] [Lacey 1977] [Landy and Kim 1984] [Lateral-Directional Flying Qualities 2002] [Lee et al. 1988a] [Lei and Zha 2021] [Lei and Zha 2023] [Lei and Zhao 2024] [Li 2021] [Li et al. 2023a] [Li et al. 2024d] [Lin and Hsu 1984] [Lin et al. 1994] [Liu et al. 2025e] [Longitudinal Flying Qualities 2002] [Loranchet et al. 2025] [Lorenzetti et al. 1969a] [Lorenzetti et al. 1969b] [Loth and Boasson 1984] [Loth et al. 1976] [Makarov 2019] [Malicki et al. 2023] [Malik and Lin 2004] [Malpica et al. 2023] [Margason and Hoad 1979] [McCormick 1956] [Meckstroth and Blake 2015] [Merrick 1960] [Merrick 1981] [Mitchell and Hoh 1983] [Moens and Dandois 2016] [Moitra 2002b] [Moralez et al. 1987] [Morris et al. 1964] [Mueller 1964] [Nardi 1970] [Neal and Smith 1971] [Nichols and Englar 1980] [Osterman and Mulley 1977] [Ostheimer and Giguere 1963] [Panish et al. 2023] [Patierno and Asdurian 1965] [Pauli 1964] [Pinsker 1970] [Planeaux 1990] [Powers et al. 1992] [Prilliman and Slingerland 1966] [Putman 1961] [Qiao et al. 2026b] [Raab et al. 2018] [Ramachandran and Wells 1974] [Ramnath 1969] [Rampy 1966] [Reschak 1970] [Rigatos 2021] [Riley et al. 1989] [Rizzetta and Visbal 2016] [Roberts et al. 1966] [Roltgen and Byrnes 1991] [Sachs 1977] [Samuels and Hahn 1986] [Saraswathi 2000] [Saripalli 1995] [Schmidt 1987] [Schroeder and Merrick 1990] [Schütte and Hummel 2023] [Sellers et al. 2002] [Selman 2023] [Shannon and Wang 1973] [Shrivastava and Mohite 2015] [Shubert and Jones 2025] [Shunxiang and Rui 2017] [Silva-Martinez et al. 2015] [Skelton 1968] [Smith and Meyer 1981] [Smith et al. 1973] [Soudakov et al. 2018] [Sparks 1991] [Stauffer et al. 1990] [Steer 2003] [Steils 1965] [Stone 2002] [Stradtner et al. 2026] [Swaim 1970] [Swortzel and Barfield 1976] [Szabolcsi and Gáspár 1997] [Takahashi and Gaydusek 2026] [Tanaka et al. 1994] [Tao et al. 2021] [Tatum and Giles 1988] [Teel 1999b] [Teel 1999a] [Thames 1965] [The Role of Human 1986] [Theisen et al. 1973] [Tischler and Hoh 1982] [Vincent and Anex 1990] [Vogt et al. 1989] [VTOL Aircraft Control Design 2010] [Wang and Ma 2021] [Wang et al. 2019b] [Weber 1982] [Westbrook 1964] [Whatley et al. 1990] [Winick 1968] [Wise et al. 1999] [Wlezien and Ferraro 1990] [Wood and Roberts 1988] [Xili et al. 2008] [YAV-8B Reaction Control System 1993] [Zha and Ren 2023] [Zha et al. 2024] [Zhu et al. 2022] [Zipf 1989]

V/STOL and STOVL aircraft concepts, programmes and design studies

V/STOL, STOVL and STOL aircraft concepts, programmes and design studies whose titles name no particular propulsion component.

267 records. [Adelt 1983] [Airspeed vs Flight Path 2003] [Anderson 1983b] [Bay 1977] [Beebe 1968] [Bell Aerospace Co Buffalo Ny 1970] [Belluomini et al. 2023] [Bhandari and Chakraborty 2026] [Biesiadny 1991] [Biggers and Linden 1985] [Binkley 1986] [Birckelbaw and Nelson 1992] [Blackwell 1970] [Boeing Co Morton Pa Vertol Div 1956] [Bottorff 2004] [Bradfield 1981] [Brady and Gururajan 2025] [Briggs and Schwind 1983] [Brown 1965] [Brown 1989] [Brown and Fisher 1968] [Brown 1978] [Caldwell and Lafavor 1980] [Camacho 1991] [Campbell 1959] [Chaderjian et al. 2002a] [Chana 2002] [Chin 1988] [Chong and Simmons 2024] [Cole and England 1967] [Composite Power Plant System 1962] [Conlon and Bowles 1977] [Conlon and Bowles 1978] [Cornish 1964] [Coty and Kesling 1967] [Courtin et al. 2020] [Cox and Roskam 1990] [Crafa and Reed 1980] [Cui et al. 2019] [Czinczenheim 1977] [Davenport et al. 1972] [Day 1965] [Deckert and Franklin 1989] [Denning 1962] [Diekmann 2019] [Doerr 1987] [Doherty and Butzel 1979b] [Doherty and Butzel 1979a] [Driggers 1978] [Durbin and McGeer 1982] [Durston and Smith 1981] [Durston and Stonum 1987] [Durston and Stonum 1988] [Dymarchuk and Marynoshenko 2025] [Eckard and Poth 1983] [Egerton and Fitzpatrick 1967] [Englar and Campbell 2002] [Englar and Campbell 2005] [Falarski et al. 1981] [Ferry 1960] [Fielding 1982] [Fry and DeDecker 1971] [Galdieri et al. 1992] [Gamon 1988] [Gappa 1964] [Gerhardt and Chen 1978] [Giurca 2014] [Gorham 1977] [Gowanlock 2025] [Green and Andrews 1989] [Green and Bogle 1991] [Groen 1987] [Groen 1988] [Hall 2002] [Hamilton and Richardson 1988] [Harding n.d.] [Hardman et al. 1991] [Harradine 1977] [Harris 1956] [Hays and Schultz 2025] [Hazen 1963] [Hebert and Joseph 1970] [Hebert et al. 1970] [Hebert et al. 1973] [Heintzman 1965] [HELICOPTER AND V/STOL AIRCRAFT NOISE MEASUREMENT PROBLEMS] [Henderson 1964] [Hendrickson et al. 1984] [Henschel et al. 1974] [Hesse 1965] [Hirschberg 1997] [Hirschberg and Pryce 2008] [Hirschberg et al. 2002] [Hirschberg et al. 2003] [Hiscock 1981] [Hollister 1969] [Holloway et al. 1972] [Holzhauser et al. 1972] [Howze 1969] [Hsin 1974] [Hutchison et al. 1983] [Hynes and Scott 1976] [Irvin and Swan 1956] [Irvine 1968] [Jain and Mukkamala 2016] [Jenista and Sheridan 1987] [Johns 1986] [Johnston 1964] [Jones 1971] [Joppa 1969] [Kakavitsas et al. 2024] [Kalemaris and Cea 1977] [Kelley 1970] [Kelly et al. 1977] [Kidwell 1981] [Kidwell and Rapp 1985] [Kidwell and Lampkin 1983] [Kimberlin and Sinha 1983] [Kirby 1964] [Knapp 1980] [Knott 1977] [Koenig et al. 1977] [Kondo 1975] [Kondoleon 1968] [Krepski and Hudson 1981] [Kuhn 1979] [Kuhn 1980] [LaBiche 2003] [Landfield and Henderson 1984] [Levinsky and Ramsey 1972] [Lind and Beck 1991] [Linnell 1963] [Lo 1970] [Lombard and Heyworth 1963] [Maita et al. 1983] [Maita et al. 1990] [Manley and von Klein 2002] [Marchese 1963] [Margason 2002a] [May and Widdison 1971a] [May and Widdison 1971b] [McCarthy 1992] [McCarthy and Kelly 1993] [McCormack and Poteate 1965] [McCrea 1992] [McElreath 1972] [McIntyre 1963] [McIntyre et al. 1977] [McNally and Bach 1988] [McPherson 1977] [Meiklem 1969] [Melgaard 1986] [Mendela 1971] [Michaels 1969] [Mihalik and Keane 2022] [Minsk 1970] [Moller 1998] [Moorhouse 1990] [Morozov et al. 2006] [Mueller et al. 2009] [Musselwhite 1978] [Müller and Hirschberg 2007] [Nadel 2017] [Nakaguchi 1967] [Nelms 1984] [Nelms and Durston 1980] [Norton 2002] [O’Brien and Delgado 2024] [O’Mallei 1957] [Overfield and Crawford 1967] [Papadales and Basil S. 1979] [Peaslee 1971] [Petrolo et al. 2014] [Philhower et al. 1998] [Platt 1991] [PlCKERELL and Cresswell 1968] [Price 1964a] [Puvrez 1965] [Ramirez et al. 1980] [Ransone 1971] [Ransone 2002] [Ransone and Basquez 1967] [Rapp 1985] [Raymer 1988] [Reed and Avery 1966] [Reid 1982] [Reid et al. 1977] [Representative Operations of V/STOL 2002] [Rich 1969a] [Rich 1969b] [Riesenfeld 1968] [Riviere and Vignevic 1981] [Roberts and Deckert 1982] [Rocher et al. 2002] [Rosenthal et al. 1988] [Roth 1993] [Roth 1996] [Roth 1997] [Rudolph 1972] [Rusbarsky 1990] [Sabut et al. 1999] [Salkind 1973] [Samuels and Payne 1990] [Schade 1968] [Schaefer and Velten 1971] [Scherrer and Olson 1971] [Schmitz and Stepniewski 1973] [Scientific and Technical Information Division 1966] [Selegan 1983] [Sivan 1971] [Sivrioğlu 2023] [Skifstad 1970] [Smith 1996b] [Smith 1997b] [Song et al. 2021] [Spillman 1965] [Spivey 2002] [Spooner 1968] [Stark 2003] [Steele and Aurora 1978] [Sternfeld and Hinterkeuser 1970] [STOL VTOL and V/STOL 1971] [Strand 2010] [Stutz and Price 1964] [Swaim 1969] [Swaim and Connor 1968] [Szlenkier 1972] [Takeda 1985] [Tamplin et al. 1990] [Tuck 1970] [Turkmen and Altug 2020] [Turner 1969] [V/STOL R and D in France 1971] [V/STOL 1971] [Vagianos and Rooney 1964] [Van Dalsem et al. 1990] [Vandalsem et al. 1989] [Vertical Take-off Aircraft 2001] [VTOL 1969] [Nelms and Anderson 1984] [Wachtell 1970] [Waesche and Midgal 1975] [Wardwell and Sandlin 1988] [Wardwell et al. 1996] [Watson et al. 2019] [White et al. 1985] [Wiargason and Kuhn 1987] [Wigeland et al. 1977] [Willis and Genever-Watling 1977] [Wilson et al. 1981a] [Wilson et al. 1982] [Wilson and White 1993] [Wilson et al. 1985] [Winborn 1970] [Windolph 1969] [Wollner 1971] [Wood 1972] [Woods 1957] [Woolard 1974] [Wynosky et al. 1974] [Yang and Wang 2017] [Yoo and Strash 1990] [Yoon 2025] [Zabinsky and Burnham 1977] [Zafi and Chakraborty 2023] [Zhang 2017] [Zimmerman 1957]

Flight test, instrumentation and system identification

Flight test of fighters, demonstrators and research aircraft, with its instrumentation and the analysis of its data.

14 records. [Armstrong 1977] [Baier 1970] [Dungan and Clark 1994] [Hess 1986] [Jain et al. 2017] [Martínez Morán 2018] [Metz 1992] [Nagel and Thomas 1965] [Smith and Pellicano 1992] [Smith et al. 1979] [Thigpen and Whitmoyer 1976] [Veletas 2026] [Wages 1971] [Wulff and Zoellner 1991]

Fighter and supersonic aircraft design

Fighter and military aircraft design, from combat aircraft concepts to demonstrators and their structures.

104 records. [Adams et al. 2025] [Agrawal et al. 1992] [Aleisa et al. 2023] [Allen et al. 2000] [Apte and Athani 1979] [Bacci et al. 2026] [Badaliance and Dill 1981] [Banks 1988] [Behavior Patterns of Three 2022] [Beskar 2004] [Bischoff 1981] [Bischoff and Palmer 1983] [Bonner 1971] [Boppe 1985] [Bryson 1971] [Bykerk et al. 2022] [Caap and Elemeland 1986] [Casteel and Weyl 1970] [Cenko 1979] [Chapman 2018a] [Clark 1984] [Computational Analysis 1994] [Cummings et al. 2018] [Dacquino and Raffaele 1982] [Dement and Hartman 1986] [Donegan and Fox 1991] [Dudley 1986] [Enzinger 1988] [Erickson 1980] [Finger et al. 2023] [Fletcher and Burns 1979] [Foss 1978] [Fundamentals of Fighter Design 2001] [Gangl et al. 2013] [Geiger 2002] [Ghazi 1994] [Gibb 1976] [Glenn and Koch 1973] [Harrell 1986] [Harris 1989] [Hendrickson et al. 1978] [Hentges 1985] [Herbst and Ross 1970] [Hitzel 2022] [Horie and Conway 2000] [Howell 1987] [Huang et al. 2003a] [Huffman et al. 1987] [Hwang and Pi 1975] [Johnson 1985] [Karniadakis 2004] [Kisslinger and Vetsch 1965] [Kolodziejczyk 1984] [Lee and Boedicker 1985] [Lewis 2002] [Mann and Carlson 1994] [Mann and Mercer 1986] [Masud et al. 2017] [McClaskey and Evans 1996] [Meckstroth and Ordóñez 2020] [Miller and Schemensky 1979] [Miller and Wood 1986] [Murnane 1975] [Nangia et al. 2004] [Nastase 1998] [Norris and Lan 1991] [Olwi 1995] [Palusamy and Sivier 1993] [Parker and Ball 1974] [Rallabhandi and Mavris 2003] [Ray et al. 1988] [Raymer 1995] [Raymer 1998] [Reubush et al. 1985] [Reuther 2002] [Reymer et al. 2014] [Sutrisno et al. 2018] [Samuels 1992] [Schwartz 1988] [Sepulveda and Smith 2019] [Shane 1992] [Silverman 1978] [Spearman 1984] [Squires 2004] [Stanniland 1974] [Takovitskii 2023] [Tamrat 1983] [Tamrat 1988] [Tariq and Mazhar 2021] [Teng and Yu 2023] [Tikka 2008] [Triplett 1980] [Vázquez et al. 2004] [Wang et al. 2021c] [Ward 1989] [Weeks 1986] [Wells 1974] [Whitford 1991] [Whitford 1995] [Woelk 1989] [Xu 2023] [Xu and Yu 2025] [Yu 2025] [Zhang and Cheng 2024]

High-lift and powered-lift aerodynamics

High-lift and powered-lift systems and their computation, with the jet flow studies that fit no narrower cluster.

51 records. [Aliaga et al. 2025] [Beatty and Narramore 1976] [Bennie and Fossati 2024] [Bertram 2016] [Carrannanto et al. 1998] [Cohen 1984] [Colletti and Ansell 2023] [Thanigaiarasu et al. 2023] [Direct Lift in Theory 1936] [Dixon and Driskill 1985] [Eyi et al. 1996] [Galpin et al. 2002] [Gimmestad 1981] [Gong 2017] [Hendrickson and Agarwal 2021] [Hwang 2015] [Iannelli et al. 2017] [Jandaurek and Johst 2019] [Jie et al. 2017] [Kang Ning and Shi YouMin 2018] [Kim et al. 2004] [Kojima et al. 2026] [Kress 1983] [Kuhlman and Collins 2000] [Kuhlman and Scarberry 2002] [Lacy and Sclafani 2016] [Liebeck 1978] [Lindblad and de Cock 1999] [Liu et al. 2016] [Lu et al. 2025] [Moitra 2002a] [Morgan 1985] [Olson and Albertson 2016] [Pease et al. 2022] [Philipsen 2021] [Pratap Singh et al. 2023] [Probst and Melber-Wilkending 2021] [Rogers 1994] [Sarakinos et al. 2018] [Sau 2022] [Selig and Guglielmo 1997] [Snyder 1950] [Stewart et al. 2026] [Somashekar et al. 2024] [Valarezo and Chin 1994] [Valarezo and Mavriplis 1995] [van Dam et al. 2001] [van den Kieboom and Elham 2016] [Yan et al. 2021] [Yoon et al. 2016] [Łapka et al. 2019]

Where the Framing Breaks Down

Treating this aircraft through its keystone misleads in five places.

The Square-Root Law Is Not the Whole Trade

A lift fan costs weight, volume and complexity, and this article has priced none of them. The fan, its shaft, its clutch and its gearbox occupy the space immediately behind the cockpit in the STOVL variant, which trades fuel volume for them [Lockheed Martin X-35], and every pound of that hardware is carried on every sortie by every STOVL aircraft in the fleet.

The appeal of a direct-lift system is that it adds almost nothing. The engine is already there and the valve and the nozzles are comparatively light [Boeing X-32]. The correct comparison is not thrust against thrust but thrust against the weight and volume spent to obtain it, and this article has computed only one side of it.

The Bring-Back Number Uses an Assumed Lift

The X-32B’s STOVL lift is not published and the article assumes the engine’s military rating as an upper bound. Every allowance figure inherits that assumption. The sensitivity table shows that the conclusion holds across the plausible range and that no value inside it produces a comfortable allowance, but a published figure could move the numbers and the article would have to follow.

A Fly-Off Is Not the Only Evidence

The decision was not made by watching two aeroplanes fly. It rested also on each team’s Preferred Weapon System Concept, the production design that the concept demonstration contracts paid each team to define [Joint Strike Fighter programme], of which the flight demonstrations were one input. Treating the competition as a race is a simplification that this article has adopted for the sake of a clean argument, and a source selection weighs many factors of which demonstrated performance is one.

The Wing Change Cuts Both Ways

The article treats Boeing’s mid-competition wing change as damaging to its evidentiary position, and it can be read the opposite way. A company that identifies a configuration problem and fixes it before proposing has done what a risk-reduction phase is for. The customer could reasonably have credited the correction rather than penalising the mismatch, and the public record does not say which reading the source selection took.

The Aircraft Was Not Bad

It flew 144 times, went supersonic, refuelled in the air, hovered and landed vertically. [Boeing X-32A flight test release] [Boeing X-32B flight test release] The government lead pilot praised its flying qualities [Boeing X-32A flight test release]. An aeroplane that does everything asked of it and loses is not a failure of engineering, and an article organised around why it lost risks implying that it should not have been built.

The Source Base

The research survey holds 3,528 research records drawn from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center, of which 629 are report primaries, being 17.8 percent, by the identifier rule set out under The Definition of Primary. The median publication year is 2003. Of the 3,514 dated records, 1,747 were published through 2002 and 1,480 from 2015 onward, and the table gives each period as a share of the dated records. Every anchored record is cited.

Period Records Share
Before 1970 287 8.2 percent
1970 to 1984 663 18.9 percent
1985 to 1995 501 14.3 percent
1996 to 2002, the programme window 296 8.5 percent
2003 to 2014 273 7.8 percent
2015 onward 1,480 42.3 percent
of which 2022 onward 730 20.9 percent

The count and the fraction are reported together, because adding a contemporary survey holds the period count and lowers its fraction while adding period sources does the reverse. Neither movement is a fact about coverage.

The Equations That Carry No Citation

Some displayed relations carry no citation of their own and that is deliberate. They are the relations that construct the bring-back allowance and follow its consequences, the roll moment as differential thrust times a lateral arm, and the ratio between the winner’s and the loser’s record counts.

The bring-back relations and the record-count ratio are constructions original to this article, so attaching a citation would be false attribution. The weights and thrusts they take as inputs are cited where they are first given. The roll moment is elementary statics and citing it would be worse than leaving it bare.

Everything else carries its literature. Momentum theory, the figure of merit, the disc loading as a dynamic pressure, the corrected engine parameters, the ingestion correlations, the twin-jet fountain and the competitive-prototyping case all rest on published work and say whose.

This Article Has Two Primary Bases and They Sit in Different Decades

A primary source is one contemporary with the work, and for this article the work is two things that happened thirty years apart.

The decision is a 1996 to 2002 subject. Source selection, competitive prototyping, cost estimation and requirements commonality are primary in that window and nowhere else, and that band holds 296 records.

The physics is not. The short takeoff and vertical landing research the competition rested on was done in the 1970s and 1980s, largely by NASA, and a 1985 report on hot gas ingestion is a primary source for this article’s central failure mechanism in a way that a 2019 review is not. That base holds 1,164 records across 1970 to 1995 and is the healthier of the two.

Treating the whole of the pre-2003 material as one undifferentiated period band would hide that distinction, so the table above separates them.

Two Contemporary Headings Follow From the Argument

Two contemporary subjects follow from results this article derives rather than from being merely recent.

Shipboard thermal and deck interaction is the operational consequence of the disc-loading identity derived in the sizing section. An architecture at 2,852 pounds per square foot imposes almost twice the pressure of one at 1,467 on the same deck at the same landing weight, and a deck that receives such an aircraft must be built to bear that number.

Digital engineering and model-based acquisition is what partly replaced the fly-off. A model does not have the X-32’s difficulty, since a model can be made to be the proposal, but a model also does not have what the X-35B’s single sortie demonstrated. The trade is between an evidence source that matches the proposal exactly and one that matches reality exactly, and this competition is the case that shows why neither alone is sufficient.

A Homonym Inside the Discipline

Hot gas ingestion is also a turbomachinery subject, and it uses the identical phrase. Sealing flows between a turbine rotor disc and its stator are an active field whose papers are titled “hot-gas ingestion” exactly as the inlet problem is.

Forty-four cited research titles contain the words “hot gas”, and none concerns a turbine rim. Rim cavities, purge flows and sealing flows in turbines, and combustor dampers, are excluded. Dust, particle and salt ingestion are a different inlet problem and are excluded too, and no cited title names any of them.

That is the most dangerous class of homonym, because it is internal to the discipline. Bird ingestion is deliberately admitted, because an inlet swallowing a bird and an inlet swallowing its own exhaust are the same fluid mechanics.

The Hot Gas Ingestion Literature Is Thin

Sixty-one cited research records, each under its own title, concern the ingestion, reingestion, recirculation or environment of hot or exhaust gas. The open literature on inlet reingestion is genuinely small, because the measurements that matter are full-scale, expensive, and made by manufacturers rather than by research agencies. The article’s central failure mechanism rests on a thin public base and says so.

The Vehicle Cluster Is the Finding

One cited research record carries the X-32 in its title. It comes from the engine supplier and was published after the decision.

That is reported as a finding rather than as a gap, and the article’s own argument depends on saying so, because it is the reason the technical case here rests on the winner’s published numbers and the loser’s inferred bound.

The Literature of the Decision

The keystone of this article is not a physical quantity, so part of its literature is the literature of a decision. Source selection, competitive prototyping, cost growth and requirements commonality are that literature, and they have their own headings because a paper on acquisition strategy is not a paper on aerodynamics.

The keystone word is also the worst homonym. Competition between firms and competition between species are both enormous literatures, and both dwarf the procurement sense. So do dietary ingestion against inlet ingestion, and language acquisition against defence acquisition. Records in those other senses are excluded.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when 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. The NASA reports on powered lift of the 1970s and 1980s that carry this article’s physics are report primaries under that rule, and so are 140 of the 280 acquisition studies. The rule does not reach the conference and journal papers of the competition years, such as the engine supplier’s report on the X-32B lift system and the X-35B control papers of 2002, so 17.8 percent is a lower bound on how much of the survey is first-hand.

Thin Subjects

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

Subject Title terms counted Records
the bring-back allowance in vertical landing bring back, bringback, vertical landing weight, vertical landing thrust 1
disc loading as the variable of the square-root law disc loading, disk loading 13
the fountain between two lifting jets fountain 14
suckdown in hover suckdown, suck down 10
the three-bearing swivel nozzle swivel, three bearing, 3 bearing 10
source selection between competing designs source selection 10
construct validity of a demonstration construct validity 0

The bring-back allowance has one title. It concerns the vertical landing thrust requirements of a STOVL aircraft, so the allowance relations derived above are this article’s own construction, as the subsection on uncited equations says.

Disc loading is named in 13 titles, and 12 of them name a low or a high disc loading. Those titles compare configurations by their disc loading rather than derive the square-root law, which is textbook momentum theory.

The fountain has 14 titles, of which 8 date from before 1995, and suckdown has 10, so the two jet-induced effects the hover argument names are carried by a small and mostly older literature.

The three-bearing swivel nozzle that the winner flew has 10 titles, and 8 of them date from 2014 or later, after the nozzle had flown on the production aircraft.

Source selection has 10 titles and none of them names an aircraft. The account of how the competition was decided therefore rests on the programme’s public record rather than on a published analysis of this source selection.

No title names construct validity. The term is used here in its sense from measurement theory, as set out in construct validity.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. That subject is the short takeoff and vertical landing fighter and the decision between two of them. A title is therefore admitted when it concerns lift propulsion by direct lift, lift fans, lift engines or ejectors, momentum theory and hover performance, jet-induced and ground effects, hot gas ingestion and inlet temperature distortion, nozzles and thrust vectoring, impinging and hot jets, ship decks and landing surfaces, or the design, control and history of vertical and short takeoff aircraft. It is admitted too when it concerns fighter design, inlets and fighter engine cycles, low observability, carrier approach and landing, electric vertical flight and distributed propulsion for lift, or the acquisition, commonality, decision analysis and digital engineering of a competition between prototypes. A title that shares only general aeronautics with that subject is excluded. So are the classes of title that most often do so, namely turbomachinery components and engine health, conventional electric, hybrid, hydrogen and solar aircraft, the flight control and structures of helicopters, the flight control and handling of conventional fixed-wing aircraft, small unmanned aircraft and their autonomy, flight test of unrelated aircraft, generic aerodynamics and unrelated airframe subsystems, hypersonic vehicles, supersonic transports and air cushion vehicles, and decision and digital methods applied to systems other than aircraft. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Figure of merit also names measures in electronics, optics and thermoelectric materials. Lift also names gas lift in oil wells, heavy lift in shipping and the lift of hydrofoils, and thrust also names the thrust bearings of rotating machinery. Hot gas ingestion also names the sealing flows at turbine rims, inlet temperature distortion also names the hot streaks a combustor sends into a turbine, and reingestion also names a feeding behaviour of rabbits, hares and gophers. Landing pads are also built on the Moon and on Mars, and nozzles are also rocket nozzles, so aerospike, pintle, solid-motor and spacecraft nozzles and reaction controls are excluded. The designations F119 and F135 also number abstracts in medical conference programmes. Propulsion research on ships, underwater vehicles and spacecraft, and acquisition in its data, visual, seismic and corporate senses, share the vocabulary of this subject without its subject, and so does impingement by liquid jets. Correction, erratum, retraction and withdrawal notices, journal front matter and conference indexes are excluded as well, because a survey counts research works, and one document deposited twice is counted once.

Some records of neighbouring science are kept as doubtful. Momentum theory for tidal, wind and hydrokinetic turbines shares the sizing relation, industrial cooling by impinging air jets shares the physics of the hot jet on a deck, and product-family commonality and technology readiness assessment outside aircraft share the management side of the decision. Each is kept, and a reader may weigh it accordingly.

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.

The survey has no residual cluster. Every admitted title belongs to one of the named literatures above. Titles on test and evaluation belong to the acquisition literature, and analyses of takeoff, landing and flight performance belong to flight test, so a title whose only link to the subject is a test, evaluation or simulation vocabulary is excluded.

Epistemic State

Historical fact, from the published record.

  • Two X-32 demonstrators were built by Boeing under a concept demonstration contract awarded in November 1996. The X-32A first flew on 18 September 2000 and the X-32B on 29 March 2001.
  • The two aircraft flew 144 times between them.
  • The X-32B used direct lift, diverting the core exhaust to vectoring nozzles near the centre of gravity, and required ground reconfiguration between the conventional and STOVL arrangements.
  • The X-35B performed a short takeoff, a level supersonic dash and a vertical landing in a single flight on 20 July 2001.
  • The Department of Defense selected the Lockheed Martin entry on 26 October 2001.
  • The Rolls-Royce lift system produces 20,000 pounds from the lift fan, 18,000 from the swivel module and 3,900 from the roll posts, for a published total of 41,900 pounds, with 29,000 shaft horsepower delivered to a fan 50 inches in diameter.
  • Boeing’s production proposal used a conventional wing with a canted twin tail rather than the demonstrators’ delta, and the change was made before the X-32 flew.

Engineering analysis performed for this article and verified independently.

  • Thrust for a given power rises as the square root of mass flow. This is an identity, obtained by eliminating the jet velocity between the thrust and power relations.
  • The lift fan’s published diameter, thrust and shaft power imply a figure of merit of 0.697, a value a real ducted fan can achieve, so the three numbers are mutually consistent.
  • Matching that disc loading with 28,000 pounds of core thrust would need 19.09 square feet of nozzle, a single opening 4.93 feet across, which does not fit on the airframe.
  • A fifty degree Fahrenheit inlet temperature rise costs 4.50 percent of thrust.
  • At an empty weight of 24,030 pounds and a five percent margin, the direct-lift allowance over empty weight is 2,637 pounds against 15,875 for the lift system, a ratio of 6.02.
  • The allowance amplifies a fractional thrust change by 10.11 for direct lift and 2.51 for the lift system, so the same physical loss costs the direct-lift aircraft four times as much.
  • The direct-lift allowance vanishes entirely below 25,232 pounds of lift.
  • One record in the cited set of 3,528 carries the X-32 in its title, against 38 for the F-35.

Inference, where the record supports a conclusion without stating it.

  • The X-32B’s STOVL lift is not published, and this article uses the engine’s military rating as an upper bound. Every allowance figure inherits that assumption, and the sensitivity table is given so the reader can see how much rests on it.
  • The nozzle sizes in the disc-loading table are plausible values rather than published ones, used to bracket the comparison.
  • The attribution of the chin inlet to the propulsion choice is an inference from the geometry of where lift nozzles must sit, and the sources describe the arrangement without drawing that conclusion.

Claims the record does not settle.

  • Whether the X-32B ever landed vertically at full weight is not established. Its STOVL tests were flown with some parts removed, and no source available here states its landing weights.
  • The lift fan’s weight, volume and cost penalty is not computed here. The trade is therefore presented from one side only.
  • The source selection’s reasoning is not public in any detail. The weight it gave to the single-sortie demonstration, to the wing change, or to cost cannot be established.
  • Two published wingspans differ by 19.9 percent. The X-32B is recorded as narrower in span than the X-32A, but no source available here pairs either figure with an airframe.
  • Whether Boeing’s wing change should be read as a weakness in its evidentiary position or as evidence of a working risk-reduction process is a judgement the public record leaves open.

Out of Scope

  • The F-35 programme after 2001, including its cost history, its variants and its service entry.
  • The detailed design of the Rolls-Royce lift system beyond the published thrust and power figures.
  • Low-observable design beyond the thin cluster in The Contemporary Literature, since it shaped both entries decisively but is almost absent from the open literature.
  • The McDonnell Douglas entry eliminated in 1996, which used a gas-coupled lift fan and deserves separate treatment.
  • Carrier suitability and the Navy variant’s structural requirements.
  • The international partnership arrangements that funded part of the programme.

Conclusion

The X-32 lost a competition it was well built to enter, and the physics of why is a single relation that has been in the textbooks for a century.

Thrust for a given power rises as the square root of mass flow. A lift fan spends its power on a large cold stream and a direct-lift system spends the same power on a smaller hot one, so the first produces more lift from the same core. Everything that separated the two aircraft follows from that. The cooler exhaust, the slower wall jet, the cold stream standing between the hot one and the intake, and above all the weight that can be brought home.

That last quantity is the competition in one number. At an empty weight of 24,030 pounds and an assumed five percent control margin, direct lift permits an allowance over empty weight of 2,637 pounds and the lift system permits 15,875. And the small number is badly conditioned, amplifying a one percent thrust loss into a ten percent loss of everything the aircraft can carry home, so a fifty degree ingestion of its own exhaust takes nearly half of it.

But the article ends on the evidentiary argument, because it is sharper than the propulsion one. Boeing flew a delta wing it had already decided not to propose. The customer was therefore shown an aeroplane nobody intended to build and had to reason from it to one that did not exist, while the competitor’s demonstrator flew a short takeoff, a supersonic dash and a vertical landing in a single sortie in the configuration it was offering.

A fly-off decides between the things placed in front of it. When one of those things is not the thing being bought, the fly-off has answered a question adjacent to the one asked.

And the decision determined not only which aircraft was built but which one is known. Among the three thousand five hundred and twenty-eight research records this article cites, the winner appears in thirty-eight titles across two decades and the loser in one, written by its engine supplier, after the result was announced. An aeroplane that flew one hundred and forty-four times, went supersonic, refuelled in the air and landed vertically left almost no public technical trace, and that silence is the last thing the competition decided.

Equations

This section collects the 31 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 31, 19 are established and 12 are bespoke. Forces are in pounds, masses in slugs or pounds, speeds in feet per second, powers in horsepower and temperatures in degrees Fahrenheit or Rankine, and several letters are reused, so $T$ is a thrust except where a subscript marks it as a temperature, $A$ is a disc or nozzle area except in the aspect ratio relation, and $b$ is the wing span in the aspect ratio relation and a bleed fraction in the reaction control relation.

Equation 1, Static Thrust of a Jet. Static thrust is the mass flow times the jet velocity.

\[T = \dot{m} V_j \tag{1}\]

Equation 2, Kinetic Power Added to the Stream. The power added to the stream is the rate at which its kinetic energy increases.

\[P = \tfrac{1}{2} \dot{m} V_j^{2} \tag{2}\]

Equation 3, Thrust at Fixed Power as a Function of Mass Flow. Eliminating the jet velocity shows that at fixed power the thrust rises as the square root of the mass flow.

\[T = \sqrt{2 P \dot{m}} \tag{3}\]

Equation 4, Thrust at Fixed Power as a Function of Jet Velocity. Written in jet velocity, the same relation shows that halving the jet velocity doubles the thrust for the same power.

\[T = \frac{2P}{V_j} \tag{4}\]

Equation 5, Induced Velocity of an Actuator Disc in Hover. Momentum theory gives the velocity induced at a static disc as the square root of thrust over twice the density times the disc area. momentum theory Leishman on helicopter aerodynamics Hill and Peterson on propulsion

\[V_i = \sqrt{\frac{T}{2 \rho A}} \tag{5}\]

Equation 6, Ideal Hover Power From Momentum Theory. The ideal power is the thrust times the induced velocity, so for a given lift it rises as the square root of the disc loading. Leishman on helicopter aerodynamics Hill and Peterson on propulsion

\[P_{\text{ideal}} = T V_i = T \sqrt{\frac{T}{2 \rho A}} \tag{6}\]

Equation 7, Induced Velocity of the Lift Fan. The published cold thrust and the disc area of the fifty-inch fan at sea-level density give an induced velocity of about 556 feet per second.

\[V_i = \sqrt{\frac{20{,}000}{2 (0.0023769)(13.64)}} = 555.5 \ \text{ft/s} \tag{7}\]

Equation 8, Ideal Power of the Lift Fan. The thrust times the induced velocity gives an ideal power of about 20,200 horsepower.

\[P_{\text{ideal}} = (20{,}000)(555.5) = 1.111 \times 10^{7} \ \text{ft lbf/s} = 20{,}199 \ \text{hp} \tag{8}\]

Equation 9, Figure of Merit of the Lift Fan. The figure of merit is the ideal power divided by the published shaft power delivered, about 0.70, a value typical of a good rotor in hover. rotor design optimisation

\[\text{FM} = \frac{20{,}199}{29{,}000} = 0.697 \tag{9}\]

Equation 10, Mass Flow Through the Lift Fan. Thrust equals mass flow times the far-field velocity of twice the induced velocity, which fixes the mass flow at about 579 pounds per second.

\[\dot{m} = \frac{T}{2 V_i} = \frac{20{,}000}{2(555.5)} = 18.00 \ \text{slug/s} = 579 \ \text{lb/s} \tag{10}\]

Equation 11, Bespoke Nozzle Area for Direct Lift at the Fan’s Disc Loading. The article asks what nozzle area the direct-lift system would need for its jets to match the lift fan’s disc loading, and divides the military-rated thrust by that loading.

\[A = \frac{T}{T/A} = \frac{28{,}000}{1{,}467} = 19.09 \ \text{sq ft} \tag{11}\]

Equation 12, Disc Loading From Induced Velocity. Momentum theory gives the disc loading as twice the density times the square of the induced velocity.

\[\frac{T}{A} = 2 \rho V_i^{2} \tag{12}\]

Equation 13, Jet Dynamic Pressure Equals Disc Loading. Because the far-field jet moves at twice the induced velocity, its dynamic pressure equals the disc loading. jet impingement ground-effect

\[q_{\infty} = \tfrac{1}{2} \rho (2 V_i)^{2} = 2 \rho V_i^{2} = \frac{T}{A} \tag{13}\]

Equation 14, Partition of Lift-System Thrust. The published lift of 41,900 pounds equals the sum of the published fan, swivel module and roll-post thrusts. shaft-driven lift fan

\[L = T_{\text{fan}} + T_{\text{3BSM}} + T_{\text{posts}} = 20{,}000 + 18{,}000 + 3{,}900 = 41{,}900 \ \text{lbf} \tag{14}\]

Equation 15, Bespoke Landing Weight and Bring-Back Allowance. The article bounds the vertical landing weight by the lift divided by a control margin factor $k$ and takes the allowance as that weight less the empty weight.

\[W_{\text{land}} = \frac{L}{k} \qquad \text{and} \qquad W_{\text{allowance}} = \frac{L}{k} - W_{\text{empty}} \tag{15}\]

Equation 16, Bespoke Difference and Ratio of Allowances. With a control margin of five percent that the article assumes, the lift-fan architecture can bring back 13,238 pounds more than direct lift, a ratio of about six. Boeing X-32

\[\Delta W_{\text{allowance}} = \frac{L_{\text{fan}} - L_{\text{direct}}}{k} = \frac{41{,}900 - 28{,}000}{1.05} = 13{,}238 \ \text{lb} \qquad \text{and} \qquad \frac{15{,}875}{2{,}637} = 6.02 \tag{16}\]

Equation 17, Bespoke Amplification of a Lift Error in the Allowance. Differentiating the article’s allowance model shows that a relative error in lift reaches the allowance multiplied by the landing weight over the allowance.

\[\frac{\partial W_{\text{allowance}} / W_{\text{allowance}}}{\partial L / L} = \frac{L/k}{W_{\text{allowance}}} \tag{17}\]

Equation 18, Bespoke Allowance as a Linear Function of Lift. Under the assumed five percent control margin the allowance is a straight line in the lift with slope one over the margin factor.

\[W_{\text{allowance}} = \frac{1}{k} L - W_{\text{empty}} = 0.9524 \, L - 24{,}030 \tag{18}\]

Equation 19, Bespoke Break-Even Lift. The allowance crosses zero at the empty weight times the assumed margin factor of 1.05, about 25,200 pounds of lift.

\[L_{\text{break even}} = k \, W_{\text{empty}} = 1.05 (24{,}030) = 25{,}232 \ \text{lbf} \tag{19}\]

Equation 20, Aspect Ratios From the Two Published Spans. The two published spans of 36.0 and 30.02 feet with the published wing area give aspect ratios of 2.20 and 1.53.

\[A = \frac{b^{2}}{S} = \frac{36.0^{2}}{590} = 2.197 \qquad \text{against} \qquad \frac{30.02^{2}}{590} = 1.527 \tag{20}\]

Equation 21, Wing Loading and Thrust-to-Weight Ratio. The published gross weight, wing area and military thrust give a wing loading of 64.4 pounds per square foot and a thrust-to-weight ratio of 0.737. the inventory of X-vehicles

\[\frac{W}{S} = \frac{38{,}000}{590} = 64.41 \ \text{lb/ft}^{2} \qquad \text{and} \qquad \frac{T}{W} = \frac{28{,}000}{38{,}000} = 0.737 \tag{21}\]

Equation 22, Corrected Mass Flow and Corrected Thrust. Engine mass flow and thrust are corrected to reference inlet conditions with the total temperature ratio $\theta$ and the total pressure ratio $\delta$. Mattingly on engine design

\[\dot{m}_{\text{corr}} = \frac{\dot{m} \sqrt{\theta}}{\delta} \qquad \text{and} \qquad T_{\text{corr}} = \frac{T}{\delta} \qquad \text{with} \qquad \theta = \frac{T_{t}}{T_{\text{ref}}}, \ \delta = \frac{p_{t}}{p_{\text{ref}}} \tag{22}\]

Equation 23, Bespoke Thrust Loss From an Inlet Temperature Rise. Holding the engine at a fixed corrected operating point and a fixed inlet pressure, an assumption the article makes, the fraction of thrust lost to a rise in inlet temperature is one minus the inverse square root of the temperature ratio.

\[\frac{\Delta T_{\text{thrust}}}{T} = 1 - \sqrt{\frac{T_{\text{ref}}}{T_{\text{ref}} + \Delta T}} \tag{23}\]

Equation 24, Bespoke Allowance After a Fifty Degree Inlet Rise. Reducing the military-rated direct lift by the 4.50 percent loss modelled for a fifty degree rise and applying the assumed margin leaves 1,437 pounds of allowance.

\[W_{\text{allowance}}' = \frac{L \left(1 - \Delta T_{\text{thrust}}/T\right)}{k} - W_{\text{empty}} = \frac{28{,}000 (1 - 0.0450)}{1.05} - 24{,}030 = 1{,}437 \ \text{lb} \tag{24}\]

Equation 25, Bespoke Fraction of Allowance Consumed by Reingestion. The amplification of 10.11 times the modelled thrust loss gives 45.5 percent of the bring-back allowance consumed by a fifty degree rise.

\[\frac{W_{\text{allowance}} - W_{\text{allowance}}'}{W_{\text{allowance}}} = \frac{L/k}{W_{\text{allowance}}} \, \frac{\Delta T_{\text{thrust}}}{T} = 10.11 \times 0.0450 = 0.455 \tag{25}\]

Equation 26, Downward Acceleration From a Thrust Deficit in Hover. When lift falls below weight in the hover the aircraft accelerates downward at gravity times the fractional thrust deficit.

\[a = g \, \frac{\Delta T_{\text{thrust}}}{T} \tag{26}\]

Equation 27, Bespoke Sink in Two Seconds. Integrating the acceleration from the modelled fifty degree thrust loss over a two-second interval the article chooses gives a sink of 2.89 feet.

\[s = \tfrac{1}{2} a t^{2} = \tfrac{1}{2} (1.45)(2)^{2} = 2.89 \ \text{ft in two seconds} \tag{27}\]

Equation 28, Mixed Temperature of Two Streams. Two streams combine at the mass-weighted mean of their temperatures.

\[T_{\text{mix}} = \frac{\dot{m}_c T_c + \dot{m}_h T_h}{\dot{m}_c + \dot{m}_h} \tag{28}\]

Equation 29, Roll Moment From Differential Post Thrust. The roll moment from a pair of posts is the differential thrust times the lateral arm.

\[M = \Delta T \, y \tag{29}\]

Equation 30, Bespoke Lift After Bleeding for Reaction Control. The article takes thrust as proportional to mass flow, so bleeding a fraction $b$ of the flow for reaction jets removes the same fraction of lift.

\[L_{\text{after bleed}} = (1 - b) L \tag{30}\]

Equation 31, Bespoke Literature Asymmetry Ratio. The article measures the asymmetry of the record by the ratio of records naming the winner to records naming the loser in the title, counted on its own cited set.

\[R = \frac{N_{\text{winner}}}{N_{\text{loser}}} = \frac{38}{1} = 38 \tag{31}\]

Notation

  • $\dot{m}$, the mass flow, with $\dot{m}_c$ and $\dot{m}_h$ the cold and hot stream mass flows
  • $V_j$, the jet velocity
  • $P$, the power added to the stream, with $P_{\text{ideal}}$ the ideal hover power
  • $V_i$, the velocity induced at the disc
  • $\rho$, the air density
  • $\text{FM}$, the figure of merit
  • $L$, the vertical lift, with $L_{\text{fan}}$ and $L_{\text{direct}}$ the lifts of the two architectures
  • $k$, the control margin factor, taken as 1.05
  • $W_{\text{empty}}$, the empty weight
  • $W_{\text{allowance}}$, the bring-back allowance over the empty weight
  • $\theta$, the inlet total temperature ratio
  • $\delta$, the inlet total pressure ratio
  • $T_{\text{ref}}$, the standard sea-level temperature of 518.67 degrees Rankine
  • $\Delta T_{\text{thrust}}$, the thrust lost, distinct from the inlet temperature rise $\Delta T$
  • $T_{\text{mix}}$, the mixed exhaust temperature, with $T_c$ and $T_h$ the cold and hot stream temperatures
  • $y$, the lateral arm of the roll posts
  • $R$, the ratio of literature records naming the winner to those naming the loser

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