X-Planes: Bell X-22

The Bell X-22A had four propellers, each inside a tilting duct, two forward and two aft. It first flew on 17 March 1966, one of the two aircraft was destroyed five months later, and the survivor went on flying into the 1980s, until October 1984 in the summary of the Wikipedia entry and until 1988 in the account of the Vertical Flight Society. Even the earlier date makes a research career of about eighteen years, twice the nine years and four months over which the X-15 flew. This article is the twenty-third 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, and the X-21.

It did not spend those years being an X-22. From 1968 it carried a variable-stability system that let it imitate the handling of other aircraft in flight, and what it produced was not data about four-ducted-propeller aeroplanes but data about how any vertical-takeoff aircraft ought to handle, a career that NASA TM-81156 and the Vertical Flight Society both describe. The most successful vertical-takeoff research aircraft of the period succeeded by ceasing to be a prototype and becoming an instrument.

The standard inventory entry is Jenkins Landis and Miller 2003 American X-Vehicles, An Inventory X-1 to X-50 and the vehicle compilation is Miller 2001 The X-Planes, X-1 to X-45. The programme’s retrospective is The Bell X-22A V/STOL, Variable Stability Research Airplane, Lessons Learned.

The Research Question

The series has now met four ways of getting an aeroplane off the ground vertically. The X-13 stood on its tail. The X-14 deflected jet thrust. The X-18 tilted its whole wing and the X-19 tilted four propellers mounted on two tandem wings. The X-22 tilts four propellers as well, but it puts each one inside a duct, as the Vertical Flight Society describes it, and almost everything that distinguishes this aeroplane follows from that decision.

A shroud around a propeller is not a fairing. It changes the momentum balance, it carries part of the thrust on its inner surface, and in forward flight it behaves like a short annular wing. Its period theory is in Kruger 1949, Lerbs 1953, Thwaites 1953, Van Niekerk 1958, Theodorsen 1960a, Ordway et al. 1960, Morgan 1961, and Greenberg and Ordway 1964, its static tests begin with Platt 1948, and the large-scale tests of the period are summarised in Mort 1966. The full literature appears below under ducted propellers, shrouds and lift fans.

The question this article asks is what the duct is worth and what it costs, because the answer turns out to be large in both directions and the two effects arrive at different points in the flight.

The period record behind that question is very large, and this article’s weight sits on it. Between the war and the end of the 1960s the vertical-takeoff problem was worked over by many laboratories with wind tunnels, across ducted and open propellers, tilting wings, deflected slipstreams and jet lift. Examples are the ducted-propeller assault transport studies in Zabinsky 1956, the static thrust of open propellers in Coward 1955, tilt-wing design in McCormick and Mallen 1957, the deflected slipstream in Kuhn and Grunwald 1960, jet lift in Smith 1961a, and the state of the art as the NASA conferences and the national survey of the period recorded it in NASA Conference on V/STOL 1960, and Campbell 1964. The period records are spread across the clusters below, with the largest shares in the clusters on ducted propellers and on vertical and short takeoff configurations. Every aircraft in this part of the series was designed on top of it.

Programme Origin

The Navy requested two prototypes powered by four ducted fans in 1962 and ordered the X-22A in 1964, to give insight into the tactical use of vertical-takeoff troop transports. Bell had already flown the X-14 and had extensive experience of vertical-takeoff aircraft, in the Wikipedia entry, and the four-duct tandem layout had been under investigation in wind tunnels for several years before the contract, with its tunnel literature, early and recent, in Larry A. Young, Ronald C Busan et al, Siena K S Whiteside and Beau P Pollard, Goodson and Yaggy 1960, Tapscott and Kelley 1960, Kelley 1962, McKinney and Newsom 1962, Clark et al. 1963, Newsom 1963, Curtiss 1965, Biggers et al. 1966, Freeman and Newsom 1966, Xiang et al. 2016, Geuther et al. 2020, Zhang et al. 2020b, Lee et al. 2021, Meng et al. 2026.

The X-22A was the Navy’s part of the Tri-Service Assault Transport Program, in the history kept by the Vertical Flight Society, and its layout was chosen by arithmetic about engines. A NASA design study of a modern tiltduct, Whiteside and Pollard, reports from the Bell design study that cross-shafted arrangements of two, three, four and five ducts were considered, and that four were chosen on engine weight and availability with the thrust-to-weight ratio needed for an engine-out hover in view. The variable-stability system was designed into the aircraft before it flew, as Beilman’s 1965 description of the X-22A variable stability system shows.

Two aircraft were built. The first was rolled out on 25 May 1965 and made its first hovering flight in March 1966, according to the Vertical Flight Society. It was written off in August of the same year after a hard landing, which the Wikipedia entry attributes to the failure of a propeller control and the Vertical Flight Society to a hydraulic failure after about three hours of flying. The two accounts are compatible if the hydraulic failure was in the propeller pitch actuation, but no primary account of the accident is available. The second aircraft carried the programme on, and the Wikipedia entry reports that technicians made it flight capable with components stripped from the first.

The Aircraft

Four ducts of 7 feet diameter, each containing a three-bladed propeller. The rear wing spans 39 feet 3 inches and the forward one 22 feet 11 inches over the ducts, the aircraft is 39 feet 7 inches long, and it weighs 10,478 pounds empty against a gross weight of 15,287 and a maximum takeoff weight of 17,644, in the specification of the Wikipedia entry.

The duct itself is documented at full scale. A full-scale duplicate of the X-22A ducted propeller was tested in the Ames 40 by 80 foot wind tunnel, in Gamse and Mort 1967, and their table of dimensions gives a duct chord of 49 inches, a propeller tip clearance of 0.4 inch, a net area of 37.84 square feet at the propeller, a net exit area of 44.08 square feet and an exit vane of 31.8 square feet.

Four General Electric YT58-GE-8D turboshaft engines of 1,250 shaft horsepower each drive all four propellers through a cross-shafted transmission, so that any engine can drive any duct, as both the Vertical Flight Society and NASA TM-81156 describe. The 1,250 horsepower is also the design power per duct at which Gamse and Mort 1967 evaluated the duct’s thrust.

\[A_{d} = \frac{\pi D^{2}}{4} = \frac{\pi \times 7^{2}}{4} = 38.48\ \text{ft}^{2} \tag{1}\]

Four of those give 153.9 square feet of disc, and at 14,600 pounds, the three-engine hover weight assumed here, which no primary document read for this article states,

\[\frac{W}{A} = \frac{14{,}600}{153.9} = 94.8\ \text{lbf/ft}^{2} \tag{2}\]

That is a very high disc loading. A transport helicopter sits roughly between five and ten, the CH-47D Chinook at 8.8 pounds per square foot in the table of disc loadings, although light helicopters sit lower and the heaviest higher. The X-19 used large propellers and sat far below it, at 25.7 pounds per square foot, but the X-18, at 82.1, was not far short of it. The X-22 is closer to a lift jet than to a rotorcraft, and the consequences run through everything that follows.

Sizing From First Principles

What the Shroud Buys

Take a propeller inside a duct whose exit area is $\sigma$ times the disc area. Continuity and momentum across the disc give the thrust and the ideal power in terms of the exit velocity,

\[T = \rho \sigma A V_{e}^{2} \qquad P = \tfrac{1}{2} \rho \sigma A V_{e}^{3} \tag{3}\]

Eliminating $V_e$,

\[P = \frac{1}{2} \frac{T^{3/2}}{\sqrt{\rho \sigma A}} \qquad \Rightarrow \qquad T \propto \sigma^{1/3} \tag{4}\]

An open propeller is the case $\sigma = 1/2$, because its wake contracts to half the disc area far downstream, and substituting that recovers the familiar $T^{3/2}/\sqrt{2\rho A}$. So a duct that merely prevents the contraction, with $\sigma = 1$, gives

\[\frac{T_{\text{duct}}}{T_{\text{open}}} = (2\sigma)^{1/3} = 2^{1/3} = 1.26 \tag{5}\]

Twenty-six percent more static thrust for the same power, from a ring of metal that does no work. A mildly diffusing duct does better still. The configuration exists for that gain, which makes a seven-foot propeller viable at ninety-five pounds per square foot.

The X-22A duct is one of those. Its measured area ratio is

\[\sigma_{d} = \frac{A_{e}}{A_{p}} = \frac{44.08}{37.84} = 1.165 \tag{6}\]

with $A_e$ the net exit area and $A_p$ the net area at the propeller, from the table in Gamse and Mort 1967, and the same ideal relation then gives

\[\frac{T_{\text{duct}}}{T_{\text{open}}} = (2\sigma_{d})^{1/3} = 2.330^{1/3} = 1.33 \tag{7}\]

The hover arithmetic below keeps $\sigma = 1$ and lets the figure of merit absorb the difference.

The tunnel measured the real thing. Gamse and Mort 1967 report a maximum figure of merit of 81 percent based on the net exit area and a maximum propulsive efficiency of 74 percent. For free-stream speeds up to about 100 knots the measured thrust at the design 1,250 horsepower follows ideal ducted momentum theory with a propeller efficiency of 90 percent. Above that speed it falls away from the ideal curve, and they attribute the shortfall to the drag of the duct, centre body and struts, most of which is not skin friction.

The ideal power to hover 14,600 pounds on 153.9 square feet is 3,750 horsepower for an open rotor and

\[P_{\text{ideal}} = \tfrac{1}{2} \frac{W^{3/2}}{\sqrt{\rho A}} = 2{,}651\ \text{hp} \tag{8}\]

for the ducted case, which is $1/\sqrt{2}$ of it.

What the Quoted Margin Means

The programme is described by the Vertical Flight Society as having 35 percent excess power so that it could hover with one engine out. The NASA survey of in-flight simulators, NASA TM-81156, states the same number as a vertical thrust-to-weight ratio of 1.35 that allows a single-engine-out hover. The two readings give very different margins, and the arithmetic shows how different.

Four engines give 5,000 shaft horsepower and three give 3,750. If the installed power exceeds what hovering requires by 35 percent, then what remains after losing an engine is

\[\frac{3}{4} \times 1.35 = 1.0125 \tag{9}\]

One and a quarter percent. On the power reading the number is the smallest that makes a three-engine hover arithmetically possible, with nothing to spare.

On the thrust reading, thrust at a fixed figure of merit scales as power to the two-thirds, so losing a quarter of the power leaves

\[\frac{T_{3}}{W} = 1.35 \left( \frac{3}{4} \right)^{2/3} = 1.35 \times 0.8255 = 1.114 \tag{10}\]

an eleven percent thrust margin with an engine out, the margin the NASA report’s sentence describes. The NASA wording is the primary statement, so the thrust reading is the documented one, and the power reading that follows tests the secondary figure without describing the aircraft.

The power reading is still checkable, because it fixes the figure of merit. If hovering at 14,600 pounds requires 5,000 divided by 1.35, then

\[\text{FM} = \frac{P_{\text{ideal}}}{P_{\text{required}}} = \frac{2{,}651}{3{,}704} = 0.716 \tag{11}\]

That is a thoroughly ordinary figure of merit for a ducted lift fan, so the reading passes the first check. The second is stronger. Feeding 0.716 back through momentum theory gives the weight that three engines can lift,

\[W_{3} = W \left( \frac{P_{3} \, \text{FM}}{P_{\text{ideal}}} \right)^{2/3} = 14{,}721\ \text{lbf} \tag{12}\]

against the 14,600 assumed here. Agreement to 0.83 percent shows that the 35 percent and the 14,600 pounds are consistent with each other on the power reading, but because no primary document read here states the 14,600 pounds, the agreement checks two secondary figures against each other and not against the aircraft.

The full-scale tunnel figure separates the readings only partly. A figure of merit referred to the net exit area converts to the disc-area basis used here through the ideal power, which varies as the inverse square root of the area,

\[\text{FM}_{\text{disc}} = \text{FM}_{\text{exit}} \sqrt{\frac{A_{e}}{A_{d}}} = 0.81 \sqrt{\frac{44.08}{38.48}} = 0.867 \tag{13}\]

On the power reading the installed figure of merit of 0.716 is 83 percent of the tunnel’s best, and the difference would have to be accounted for by transmission losses, download on the wing and fuselage, and duct interference. On the thrust reading, the tunnel’s best figure of merit and the rated 5,000 horsepower give a four-engine thrust of

\[T_{4} = \left( 2\,\text{FM}_{\text{disc}}\, P \sqrt{\rho A} \right)^{2/3} = 20{,}261\ \text{lbf} \tag{14}\]

and a thrust-to-weight ratio of 1.35 at 15,008 pounds, essentially the 15,000 pound design gross weight that Gamse and Mort 1967 use to set their trim conditions. Three engines would then hover 16,725 pounds. That agreement assumes no installation loss at all, so it is an upper bound, and the record read here does not settle which reading the programme intended. What it does settle is that the NASA survey gives the 35 percent as thrust.

On the power reading, with the figure of merit of 0.716, the same arithmetic is unkind about the rest of the weight range.

condition	weight, lbf	power required, shp	four engines	three engines
three-engine vertical takeoff	14,600	3,704	+35.0%	+1.3%
gross	15,287	3,968	+26.0%	−5.5%
maximum takeoff	17,644	4,920	+1.6%	−23.8%

On that reading, at maximum takeoff weight the X-22 could not hover on three engines and had 1.6 percent in hand on four. Vertical takeoff was available at the bottom of the weight range and nowhere near the top, the recurring fact about every vertical-takeoff aircraft in this series, here put in numbers.

The Price in Downwash

High disc loading is not free at the bottom of the aircraft either. The exit velocity follows from the thrust per duct,

\[V_{e} = \sqrt{\frac{T}{\rho \sigma A_{d}}} = \sqrt{\frac{3{,}650}{0.0023769 \times 38.48}} = 200\ \text{ft/s} \tag{15}\]

One hundred and thirty-six miles per hour, straight down, from four ducts at once.

Disc loading is the parameter that sets all of this, and the relations are short. The induced velocity and the power loading follow from it alone,

\[v_{e} = \sqrt{\frac{W/A}{\rho}} \qquad \frac{T}{P} = \frac{2\,\text{FM}}{v_{e}} \tag{16}\]

so that lifting a pound costs power in proportion to the square root of the disc loading.

$W/A$, lbf/ft²	$v_e$, ft/s	lbf per horsepower
5	45.9	17.2
10	64.9	12.1
40	129.7	6.1
94.8	199.7	3.9

A transport helicopter of the period sat between five and ten and lifted about three and a half times as much per horsepower. The measurement and prediction of hover performance across that range is in Dyke 1963, Shivers 1967, Kocurek and Tangler 1977, Felker 1993, Ramasamy et al. 2010, Overmeyer and Martin 2017, and Jimenez Garcia and Barakos 2018, with the rest under hover performance below, and that literature quantifies the penalty for choosing a small, heavily loaded disc. The penalty is the standing charge for choosing ducts, and it is paid in every second of hover. The dynamic pressure in that jet is 47 pounds per square foot. The ground erosion, the recirculation and the hazard to anyone nearby are all consequences of the same choice that made the duct worth having, and they are treated in Morse and Newhouse 1960, Obryan 1960, Morse and Newhouse 1961a, O’Bryan 1961, George et al. 1964, Kuhn 1965, Pruyn and Taylor 1971, and Ison 2024a, and in the downwash cluster below.

What the Shroud Charges

A duct held at an angle to the oncoming air captures a mass flow and turns it onto the duct axis. Turning momentum requires a force, and the reaction on the duct is a normal force,

\[N_{\text{mom}} = \dot{m} V_{\infty} \sin\alpha \qquad \dot{m} = \rho A_{d} \left( V_{\infty} \cos\alpha + v_{i} \right) \tag{17}\]

The rounded lip adds a suction force, taken here to be of the same order, so the total is assumed to be roughly twice the momentum term. The duct is behaving as an annular wing, and the theory and measurement of that are Goodson and Grunwald 1962, Mort 1965, Curtiss and Howard C. 1969, Mann 1974, Walker 1981, Lee and Kwok 1983, Gill and D’Andrea 2020.

This has to be evaluated along a conversion, not on a grid. A duct angle of forty-five degrees at two hundred feet per second is not a flight condition, and tabulating it produces a normal force larger than the aeroplane.

The Corridor Can Be Derived, Not Assumed

No wing area appears in the sources read for this article, which looks like a dead end and is not one. At the end of a conversion the ducts are horizontal and the wings carry the whole weight, so the conversion speed fixes the area,

\[S = \frac{2W}{\rho V_{\text{conv}}^2 C_{L,\max}} = \frac{2 \times 14{,}600}{0.0023769 \times 203^2 \times 1.4} = 213\ \text{ft}^2 \tag{18}\]

That number has to survive a geometric check and it does. Two thirds of it on the 39.25 foot rear span is a mean chord of 3.62 feet, and the remaining third on the 22.92 foot forward span is 3.10 feet. No chord appears in those sources either, so the check is one of plausibility rather than agreement.

With an area the corridor follows from the force balance. Writing $i$ for the duct angle above the horizontal,

\[T \sin i + L = W \qquad T \cos i = D \tag{19}\] \[\tan i = \frac{W - L}{D} \qquad T = \sqrt{(W-L)^2 + D^2} \tag{20}\]

with $L = q S C_L$ and $D = q (S C_{D_w} + f)$, where $f$ is the equivalent flat-plate area of the four ducts computed below and the wing drag coefficient $C_{D_w}$ is the 0.10 assumed here. The trim of a vertical-takeoff aircraft through its conversion has a period literature, in Seibel 1963, Englar and Kirkpatrick 1969, Cheng and Pei 2023, Lee et al. 2026b, and the quantity it turns on is how much lift the wing is developing at each speed, which for a propeller aircraft depends on more than the wing. The slipstream changes the lift over whatever part of the wing it washes, and that effect has been measured since the 1930s, in Stuper 1938, Franke and Weinig 1939, Brenckmann 1958, Kuhn and Grunwald 1960, Winston and Huston 1962, Goland et al. 1964, Butler et al. 1966, and Rizk 1980, with more under propeller slipstream and wing interaction below.

Thrust required falls monotonically through the conversion, because the wing takes the lift faster than the drag builds, so the corridor was never thrust-limited. Whatever made the X-22 hard to convert, it was not power.

$V$, ft/s	knots	duct angle	$\dot m$, slug/s	$N$, lbf	$N/T$
20	11.8	81.1	18.6	733	0.20
60	35.5	63.4	20.7	2,224	0.61
100	59.2	45.7	24.7	3,528	0.97
120	71.1	36.8	27.1	3,890	1.07
140	82.9	27.9	29.6	3,881	1.06
180	106.6	10.2	34.5	2,197	0.60
200	118.5	1.3	36.6	340	0.09

The normal force peaks at about the thrust of its duct, and it peaks in the middle of the conversion. The table samples the conversion at seven speeds and the true maximum lies between two of its rows, at 130 feet per second, where the normal force reaches 3,941 pounds against a duct thrust of 3,650, a ratio of 1.08.

The linear schedule is close to what was flown. The Calspan account of the third research programme, Lebacqz and Aiken 1975b, states that for the X-22A the centre of the allowable transition corridor is well approximated by a linear relationship between duct angle and flight velocity, and notes that tilt-duct aircraft have a fairly narrow corridor bounded by buzz and buffet.

The Corridor With the Wing at Full Lift

The linear schedule is not the only one a force balance permits. Evaluating the same normal force along the derived corridor, where the wing pulls its full lift coefficient at every speed and the ducts make up the difference, gives something much worse. The ducts stay at large angles far later than a linear ramp suggests, and the momentum estimate climbs to 8,266 pounds per duct at 180 feet per second, or 2.26 times the whole aircraft weight over four ducts.

That is not a credible force and saying so is the point. More than twice the weight, applied sideways in mid-conversion, would be unflyable and unmissable. So the model is wrong there, and the useful question is where it stops being right.

The momentum-turning argument assumes the duct captures its streamtube and turns all of it. That holds while the crossflow component is small compared with the velocity the duct itself induces, so the validity parameter is

\[\mu = \frac{V_{\infty} \sin i}{v_{i}} \tag{21}\]

$V$, ft/s	knots	duct angle	$\mu$	$N/T$	status
40	23.7	89.6	0.20	0.40	model holds
60	35.5	89.2	0.30	0.60	model holds
100	59.2	87.2	0.50	1.02	marginal
140	82.9	82.1	0.69	1.52	model invalid
180	106.6	60.7	0.79	2.26	model invalid
200	118.5	11.2	0.20	0.77	model holds

The parameter passes 0.5 at 100 feet per second and comes back below it at 195. The momentum model is therefore valid at both ends of the conversion and invalid in the middle, and the middle is exactly where a tilt aircraft is hard to fly.

Momentum does not cap the force in that band. The lip cannot hold the flow round it at that incidence and separates, and this known weakness of every ducted fan now has a computed boundary. The honest statement is that the normal force reaches about the duct’s thrust where the model can be trusted, and that beyond it the binding limit is lip stall. Over four ducts that is of the order of the aircraft weight, applied perpendicular to the duct axes, at the speed where the wings are not yet working and the ducts are no longer pointing at the ground.

The measured record places lip separation in descent rather than in level conversion. On the full-scale duct, Gamse and Mort 1967 found from pressure distributions that separation over the whole upstream lip, the kind that changes forces and power, occurs on a representative four-duct configuration only at low power and high duct angle, as in descending flight, while partial separation in level flight brings no large change in force. The large-scale tandem model of Biggers et al. 1966 showed duct stall only on the front ducts and limited the estimated descent rate of a 6,500 pound aeroplane of that layout to about 600 feet a minute at a duct incidence near 60 degrees. In flight, the initial Navy tests reported by Rhodes in 1969 and summarised in NASA CR-1901 identified lip separation as the cause of duct buzz, a high-frequency vibration through the airframe, and suggested a descent-angle limit of about 10 degrees at low speed. At 40 knots, or 67.5 feet per second, a 10 degree path is a sink rate of

\[\dot{h} = 60\, V \sin\gamma = 60 \times 67.5 \times \sin 10^{\circ} = 703\ \text{ft/min} \tag{22}\]

which is the same order as the tunnel estimate.

The measured pitching moment peaks earlier than the momentum normal force. Biggers and his colleagues found the untrimmed pitching moment largest at about 60 degrees of duct incidence, and Whiteside and Pollard summarise the earlier Ames semispan tests as placing the pitch-up maximum near 45 knots at a duct angle near 60 degrees. On the linear schedule, with the ducts vertical at rest and horizontal at 203 feet per second,

\[i = 90^{\circ} \left( 1 - \frac{V}{V_{\text{conv}}} \right) \qquad V_{60^{\circ}} = \frac{203}{3} = 67.7\ \text{ft/s} = 40\ \text{kt} \tag{23}\]

against 130 feet per second, or 77 knots, where the momentum estimate of the normal force peaks. The moment the controls must trim arrives in the first third of the conversion, and the momentum-turning model, which places the whole force at one point on the lip, does not locate it.

That is the charge for the twenty-six percent. The shroud that makes the hover affordable is an annular wing that has to be flown through the conversion, and the aeroplane which needs the shroud most in hover is the one that has the most trouble in between.

The Ducts Are Also the Drag

The maximum speed in the specification of the Wikipedia entry, 278 knots at 10,000 feet, provides a check on all of this from a direction the hover calculation does not touch, although the record disagrees about whether it was flown. The Vertical Flight Society gives a maximum of 315 miles an hour, or 274 knots, Wikipedia’s own text says that the required 283 knots was never reached, and NASA TM-81156 gives 150 knots as the maximum speed of the aircraft in its research configuration. Taking 278 knots, an installed 5,000 shaft horsepower and the propulsive efficiency of 0.80 assumed here,

\[D = \frac{\eta P}{V} = \frac{0.80 \times 5{,}000 \times 550}{469.2} = 4{,}689\ \text{lbf} \tag{24}\] \[f = \frac{D}{q} = \frac{4{,}689}{193.3} = 24.3\ \text{ft}^2 \tag{25}\]

The X-22 has 24.3 square feet, and the lift-to-drag ratio at that condition is 3.26.

Now the same number from geometry. Four ducts of seven-foot diameter present 153.9 square feet of frontal area, so the equivalent flat plate implies a duct drag coefficient of

\[C_{D,\text{duct}} = \frac{f}{4 A_{d}} = \frac{24.3}{153.9} = 0.158 \tag{26}\]

which is derived and cannot be checked, since the full-scale duct test gives no drag coefficient on frontal area in its text. Estimating the drag of external bodies on an aeroplane in this way is old, standardised work, in Bonner et al. 1975, Neal 1975, Smetana 1975, Corsiglia et al. 1979, Corsiglia et al. 1981, Malone and Peavey 1999.

The measured propulsive efficiency is lower than the one assumed. Gamse and Mort 1967 report a maximum of 74 percent for the full-scale duct, and with that value the same relations give

\[D = \frac{0.74 \times 5{,}000 \times 550}{469.2} = 4{,}337\ \text{lbf} \qquad f = \frac{4{,}337}{193.3} = 22.4\ \text{ft}^{2} \qquad C_{D,\text{duct}} = \frac{22.4}{153.9} = 0.146 \tag{27}\]

so the duct drag coefficient lies between 0.146 and 0.158 on the two efficiencies. Their tunnel result also shows where the drag comes from. The drag measured with the propeller removed was much larger than the estimated skin friction of the shroud, and they conclude that a duct designed for high speed could have had a significantly higher propulsive efficiency.

That is the third face of the same trade. The shroud buys twenty-six percent of thrust in the hover, charges an annular wing’s normal force in the conversion, and then charges again in cruise by presenting four times thirty-eight square feet of frontal area to the airstream for the rest of the flight.

Dependent Systems

The Elevons Are in the Jet

In hover there is no free-stream dynamic pressure at all, so a conventional control surface has nothing to work with. The duct exits have plenty.

\[q_{\text{jet}} = \tfrac{1}{2} \rho V_{e}^{2} = 47.4\ \text{lbf/ft}^{2} \tag{28}\]

The duct normal force acts near the lip rather than at the duct centre, because the lip is where the flow is turned, so each duct contributes a nose-up couple of about

\[M = \frac{N \ell}{2} \tag{29}\]

for a duct of length $\ell$. At the largest defensible normal force and the four-foot duct, whose chord is 49 inches in the table of Gamse and Mort 1967, that is 7,900 foot-pounds per duct and 31,500 foot-pounds over four, and the tandem layout does not cancel it, because both duct pairs tilt the same way and both couples act nose-up about their centres.

Something has to trim that, and the X-22A uses two effectors whose roles exchange through the conversion. The ducts carry spanwise elevons across their exits, immersed in the propeller slipstream, and the propellers have collective and differential blade pitch. In the hover, according to NASA TM-81156 and Freeman and Newsom 1966, pitch and roll come from differential blade pitch between front and rear and between left and right. Yaw comes from differential elevon deflection in Freeman and Newsom, because a vane in a vertical jet turns the jet sideways, while NASA TM-81156 assigns hover yaw to left and right differential blade pitch, and the documents read do not reconcile the two. A mechanical mixer proportions the pilot’s commands between propellers and elevons as a function of duct angle, and in forward flight pitch comes from differential deflection of the front and rear elevons. In the large-scale tunnel model of Biggers et al. 1966, longitudinal trim came from differential fore and aft exit-vane deflection between cruise and 40 degrees of duct incidence and from differential fore and aft thrust above 50 degrees.

The elevons are large. The exit vane of the full-scale duct is 31.8 square feet, and the elevons of the 0.18-scale model of Freeman and Newsom scale up by the square of the length ratio to

\[S_{e} = 0.82 \times 5.56^{2} = 25.3\ \text{ft}^{2} \qquad S_{e} = 1.06 \times 5.56^{2} = 32.8\ \text{ft}^{2} \tag{30}\]

for the front and rear ducts. At the lift coefficient of 0.9 assumed here, a vane of 31.8 square feet in the hover jet gives

\[F = q_{\text{jet}} S_{e} C_{L_{e}} = 47.4 \times 31.8 \times 0.9 = 1{,}357\ \text{lbf} \tag{31}\]

which is more than a third of the duct thrust, a ratio of 0.37, turned sideways. With that force, one vane per duct is enough for yaw in the hover.

The free stream does not reach that dynamic pressure until about 200 feet per second, which is the end of the conversion, so through the conversion the elevons depend on the propeller slipstream. The design provided control power beyond trim in a 35 knot wind of 0.60 radian per second squared in pitch, 1.00 in roll and 0.56 in yaw, in Freeman and Newsom, whose free-flight model pilots needed about 110, 80 and 30 percent of the scaled values for the manoeuvres they flew. By 1979 the variable-stability aircraft had nominal hover control powers of 3.20, 3.45 and 0.75 radians per second squared in pitch, roll and yaw, according to NASA TM-81156.

The Cross-Shaft

Four engines drive four propellers through a common transmission, treated in Leishman 1966, Overfield and Crawford 1967, Envia 2016b, Casadei et al. 2019, Yan and Chen 2019, Yu et al. 2020, Leelaburanathanakul et al. 2021, Hoogreef and Soikkeli 2022, Kang et al. 2023, Zhang et al. 2024a, Aroussi 2025, Hung and Dai 2025, Nabadova and Sabziev 2025, Jokar and Khoshnood 2026, Mokotoff and Cinar 2026.

Cross-shafting adds no power. What it changes is the failure mode. Without it, losing an engine loses a duct, and losing one of four ducts on a machine with a rear semi-span of 19.6 feet applies

\[M = T_{\text{duct}} \, y = 3{,}650 \times 19.62 = 71{,}600\ \text{ft}\cdot\text{lbf} \tag{32}\]

of rolling moment that has to be trimmed out by the remaining three. With cross-shafting the same failure removes a quarter of the power and none of the symmetry.

The shaft itself is undramatic in torque. At the 700 foot per second tip speed assumed here the propellers turn at about 1,910 revolutions per minute, inside the range of 1,200 to 2,590 at which Mort and Gamse ran the full-scale duct, so each absorbs

\[Q = \frac{P}{\omega} = \frac{1{,}250 \times 550}{200} = 3{,}440\ \text{ft}\cdot\text{lbf} \tag{33}\]

and with one engine out the three survivors deliver 938 horsepower to each of four propellers, so 312 horsepower has to cross the airframe, a quarter of one engine.

It was not undramatic in heat. By 1979 the engine and fan systems were limited operationally to hover at air temperatures below 80 degrees Fahrenheit by gearbox temperature limits, which NASA TM-81156 notes precluded significant amounts of hover in the summer, and allowance for an engine-out hover limited operation further according to atmospheric conditions.

Sizing a drive train of this kind is rotorcraft engineering rather than aeroplane engineering, treated in Doblhoff 1956, Ward 1970, Cormier 1979, Dean 1979, Mancini 1983, White 1983, Albrecht 1988, Tokarski et al. 1994.

The cost of cross-shafting is not the shaft. It is that every gearbox must accept power from either direction, and that the train becomes a single path whose failure takes everything. The first aircraft was lost to the failure of a part that the test pilot Stanley Kakol, in the account of the Wikipedia entry, called the only non-redundant component in the power chain, which is the same lesson from the other side.

This is the X-18’s fatal deficiency, answered. The X-18 had two engines with no interconnection, and its flight testing ended after an engine failure in one account and a propeller pitch control problem that put it into a spin in another, which is the asymmetry rather than the shortfall. The X-22 was designed so that the asymmetry cannot happen, and the price is a transmission that has to carry full power to any duct from any engine.

The Flight Test Record

First flight 17 March 1966. The first aircraft was lost on 8 August 1966 in a hard landing, the date given by the Wikipedia entry, after about three hours of flying in which it had been tested to transition angles of up to 30 degrees and speeds of up to 100 knots, according to the Vertical Flight Society. The aircraft was written off.

The second aircraft flew on, performing hundreds of complete transitions and, on 30 July 1968, a hover above 8,000 feet that the Vertical Flight Society records as a record. Its variable-stability and control system, from the Cornell Aeronautical Laboratory, later Calspan, in the Wikipedia entry, was demonstrated in early 1968, and from that point its purpose changed. It stopped being a prototype of a configuration and became a flying simulator of configurations that did not exist, in Harper and Robert P. 1955, Creer and McNeill 1956, Marchese 1963, Newell et al. 1963, Garren and Kelly 1965, Person and Robbins 1965, Determination of Flight Characteristics 1967, Rhoads 1967, Szalai 1967, Eney 1968, Klopfstein 1968, Malcom 1969, Bell Aerospace Co Buffalo Ny 1970, Rhoads 1970, Schuler et al. 1972, Beilman 1973, Smith et al. 1973, Lebacqz 1974, Smith 1974, Lebacqz and Aiken 1975b, Motyka 1975, Aiken et al. 1977, Corliss et al. 1977, Parker 1986, Henschel and Chetty 1989, Sato and Satoh 2011, Sato 2020, Scholten et al. 2020a, Chandrasekaran et al. 2021, Network Solution for Real-Time 2022, Yahui et al. 2024, Yi and Feng 2025.

How the Variable-Stability System Worked

The system was a response-feedback design, the most common mechanization of the period in Lebacqz 1974, in which sensed motion variables command control deflections in proportion, so that changing the gains changes the closed-loop aircraft. NASA TM-81156 describes it in detail. It is a four-axis system, in thrust, pitch, roll and yaw, primarily analogue with an on-board digital computer, with electrohydraulic servos driving the right-hand flight controls through the same linkages the right-hand pilot moves in normal flight. The evaluation pilot sits on the left, mechanically disconnected from the right-hand controls, and flies through artificial-feel servos whose force gradients run from 1.5 pounds per inch to a stiff stick in pitch and roll. The safety pilot on the right sets up each configuration in flight. Feedback gains are programmable with airspeed from 30 knots rearward to 150 knots forward, using an omnidirectional airspeed system with a second sensor on the nose boom for the vertical component in hover. A limited-authority feedforward system acts as a vernier on blade pitch and elevon angle, because a closed-loop variable-stability aircraft needs its actuators placed very precisely. The ducts rotate together between 0 and 95 degrees at no more than 5 degrees a second.

A response-feedback aircraft does not know exactly what it is simulating. The resulting dynamics are not known in advance, so each configuration has to be identified from its flight records, which is the subject of Lebacqz 1974. The Calspan team used a Kalman filter technique to estimate the derivatives the system had produced, among them the angle-of-attack stability and pitch rate damping varied in the first programme and every roll and yaw derivative varied in the second.

The limits are stated as plainly as the capabilities. The variable-stability system could not be used above about 125 knots, which excluded the upper end of the conversion. It had only limited uncoupled direct force in the longitudinal and vertical directions and none sideways. Hover was restricted by gearbox temperature as described above. And the airframe had an established service life of 500 flight hours, of which 80 were expected to remain at the end of 1980, in NASA TM-81156, so the aircraft would by then have flown about

\[500 - 80 = 420\ \text{h} \tag{34}\]

against the about 200 hours the Vertical Flight Society gives for its career. The two cannot both be right, and the NASA figure is the primary one.

The Research Programmes

NASA TM-81156 summarises the programmes flown through 1979, and the Calspan papers report them in detail. The first three were sponsored by an interagency steering group of the Navy, the Air Force, NASA Langley and the Federal Aviation Administration, and the later ones by the Navy alone.

The first programme measured short-term longitudinal dynamics for the steep approach of a short takeoff and landing, or STOL, aircraft. Two pilots made 50 evaluations of 18 combinations of short-period frequency and damping at 65 and 80 knots, on approach paths of 6 to 10 degrees, visual and on instruments, reported in Schuler et al. 1972 and Smith et al. 1973. The account in Lebacqz 1974 gives sixteen combinations at a 9 degree glide slope, and the two counts are not reconciled in the documents read. Essentially no data of this kind existed for STOL approaches before it, and supplying them for the V/STOL flying-qualities specification, MIL-F-83300, was a main purpose. It showed that steep instrument approaches could be flown satisfactorily with only instrument landing system information, given good short-term dynamics, and the results were applied in the development of the YC-14 and YC-15, in NASA TM-81156.

The second measured lateral-directional dynamics and roll control power. Three pilots flew 109 evaluations of 17 sets of dynamics at a 7.5 degree glide slope and 65 knots, varying the roll mode time constant, Dutch roll frequency, roll due to sideslip and yaw due to aileron, with roll authority limited electrically for some sets. Two findings bear directly on the specification. Satisfactory flying qualities needed about twice the roll damping that MIL-F-83300 specified, and about half its roll control power, in NASA TM-81156. Since the roll mode time constant is the inverse of the roll damping derivative,

\[\tau_{R} = -\frac{1}{L_{p}} \tag{35}\]

doubling the damping halves the time constant. The same programme expanded the system into the hover and made the first vertical landings performed with the X-22A’s own variable-stability system engaged, in NASA TM-81156.

The third flew instrument transitions to the hover, in Lebacqz and Aiken 1975b. The task was a hooded approach from 100 knots, capturing a 7.5 degree glide slope and decelerating at about 0.05 g to a hover at 100 feet. Decelerating uniformly from 100 knots, or 168.8 feet per second, at that rate takes

\[s = \frac{V^{2}}{2a} = \frac{168.8^{2}}{2 \times 0.05 \times 32.17} = 8{,}854\ \text{ft} \qquad t = \frac{V}{a} = 105\ \text{s} \tag{36}\]

which is consistent with the deceleration beginning about 8,000 feet out in still air, as the paper gives it, and continuing through the flare. On the glide slope at 100 knots the aircraft descends at

\[\dot{h} = 60\, V \sin\gamma = 60 \times 168.8 \times \sin 7.5^{\circ} = 1{,}322\ \text{ft/min} \tag{37}\]

Thirty-seven evaluations covered five display formats, from position information alone to four-axis control directors, against five levels of control augmentation, in a flight experiment of 45 hours, in NASA TM-81156. The central result is a trade between control and display, in which more augmentation needs less display and the reverse. Translational velocity had to be displayed for any acceptable system, and because the basic X-22A has low natural height damping near the hover, a thrust director was needed whenever the pilot also had to manage the duct angle. The programme also devised a duct-angle command, the Independent Thrust Vector Inclination Command, which follows the linear corridor described earlier, in Lebacqz and Aiken 1975b.

The fourth simulated the AV-8B for a decelerating instrument approach. Forty-three evaluations of 22 configurations, drawn from six flight control schemes and seven head-up display formats, showed that no display gave consistently satisfactory ratings with the proposed rate stability augmentation, while rate-command and attitude-command systems did with several displays, and the resulting display formats were being considered for the AV-8B. The fifth, begun in April 1978 and planned through 1980, addressed hover and low-speed criteria for visual and instrument flight and then transition criteria, in NASA TM-81156.

The four completed programmes add up to

\[50 + 109 + 37 + 43 = 239 \tag{38}\]

piloted evaluations in NASA TM-81156, each a configuration flown and rated.

The final flights are dated October 1984 in the summary of the Wikipedia entry and 1988 in its text and in the account of the Vertical Flight Society. No primary document read here records the end of flying.

Comparison With Ground Prediction

The four-duct tandem layout had been in wind tunnels since at least 1960, and the reports on it, from the period to the present, are Larry A. Young, Ronald C Busan et al, Siena K S Whiteside and Beau P Pollard, Goodson and Yaggy 1960, Tapscott and Kelley 1960, Kelley 1962, McKinney and Newsom 1962, Clark et al. 1963, Newsom 1963, Curtiss 1965, Biggers et al. 1966, Freeman and Newsom 1966, Xiang et al. 2016, Geuther et al. 2020, Zhang et al. 2020b, Lee et al. 2021, Meng et al. 2026. On the gross behaviour the tunnels were right. The thrust augmentation, the general shape of the conversion, and the pitching behaviour were all anticipated.

The full-scale duct test anticipated the duct’s performance well. Gamse and Mort 1967 measured a figure of merit and a propulsive efficiency that bracket the figures this article derives, found the thrust following ideal ducted theory to about 100 knots, and located the upstream lip separation that flight later reported as duct buzz in descent.

The free-flight model anticipated the handling problems. The 0.18-scale model of Freeman and Newsom 1966 had unstable control-fixed pitching and rolling oscillations in hover, with periods of 3.4 and 3.0 seconds that scale with the square root of the length ratio,

\[T_{\text{full}} = T_{\text{model}} \sqrt{5.56} \qquad 3.4 \times 2.358 = 8.0\ \text{s} \qquad 3.0 \times 2.358 = 7.1\ \text{s} \tag{39}\]

slow enough that the pilots found them easy to control. Near the ground the fan slipstreams met between the fore and aft ducts and formed an upward flow that went erratically into one fan or the other, the model gained 20 percent in lift from an upload on the fuselage, and the disturbances were severe enough that the authors concluded artificial stabilisation would be needed in ground effect. Through most of the conversion the model had an unstable Dutch roll and very low directional stability, and stall of the upper outside duct surfaces caused wing dropping on the approach, although the authors note that small ducts stall differently from full-scale ones.

The ground work was weakest where it usually is, in the interference between parts. The rear ducts operate in air the forward ducts have already worked on, and the wake of a duct is not the wake of an open propeller. The large-scale model of Biggers et al. 1966 measured some of it. The static thrust of the complete model matched that of four isolated ducts, so interference in the hover was negligible, but in the conversion duct stall appeared only on the front ducts, because their downwash delayed stall on the rear ones, and the interference lowered the configuration’s stall boundary below that of an isolated duct.

Flight added a characteristic the tunnels did not isolate. The Calspan pilots met a low natural height damping near the hover in the basic aircraft, with vertical damping that fell as the duct angle increased, and the guidance in Lebacqz and Aiken 1975b compensated with a gain that rose with duct angle.

What the Data Changed

The X-22 settled that the configuration flies. Nothing in eighteen years of operation suggested that a four-duct tandem vertical-takeoff aircraft was uncontrollable or unsafe, which is a stronger negative result than the X-18 or the X-19 produced.

What it did not settle is whether anyone wanted one. The arithmetic of the useful load is short and unkind,

\[\frac{W_{\text{payload}}}{W} = \frac{1{,}200}{14{,}600} = 0.082 \tag{40}\]

against an empty weight of 10,478 pounds and a useful load of 4,122, most of which is fuel. The 1,200 pound maximum payload is from the specification in the Wikipedia entry, and the Vertical Flight Society gives the same figure, with six passengers as the alternative. Weight estimation is the discipline that decides whether a configuration survives contact with a requirement, and its methods are set out in Torenbeek 1972, Ascani 1974, Hayase 1974f, Hayase 1974b, Hayase 1974d, Hayase 1974e, Hayase 1974a, Hayase 1974c, Hiyama 1974, Martindale et al. 1974, Wildermuth et al. 1974b, Wildermuth et al. 1974a, DeBilzan 1975, Onat and Tolle 1979, Hajela and Chen 1988. The disc loading that the duct makes affordable also produces a 136 mile per hour downwash, a severe weight sensitivity in the hover, and a payload of 1,200 pounds on an aircraft of 15,000. The configuration works and the mission arithmetic is unattractive, a different verdict from the one the earlier tilt aircraft received.

The largest thing it changed is not about ducts at all. The variable-stability system turned the aircraft into a source of handling-qualities data for vertical-takeoff aircraft generally. That literature runs from the proposed V/STOL criteria of Curry et al. 1965, and Anderson 1966 through the specification of Key 1971 and the simulator work that supported its further development in Vinje and Miller 1973 to the later Navy criteria of Clark 1982 and the retrospectives of Ashkenas 1984, and Harper and Cooper 1986, and the cluster below on handling and flying qualities criteria holds it, with the aircraft’s programme reports, such as Smith 1974, and Aiken et al. 1977, in the first cluster. Most of the titles in this survey that name the X-22A concern flying qualities, variable stability or simulation, and none names the duct, as the cluster on the aircraft below shows.

That influence is most direct in the specification work. MIL-F-83300, the military specification for the flying qualities of piloted V/STOL aircraft, was generated around 1970, in Key 1971, and the X-22A’s first programme was flown in large part to supply it with STOL approach data that did not otherwise exist. Its second programme then found the specification’s roll damping requirement too low by about a factor of two and its roll control power requirement about twice what satisfactory flying qualities needed, according to NASA TM-81156. Those are corrections in both directions, measured in flight, and they are what a variable-stability aircraft is for.

The Contemporary Literature

Cluster	Records
The X-22A and the ducted-propeller assault transport	26
Variable-stability aircraft and flight simulation	44
The duct at incidence and the lip	20
Engine inlets in crosswind and inlet distortion	26
Ducted fan, rotor and vertical-takeoff noise	185
Downwash, ground effect and recirculation	77
Transmissions, drive shafts and power transfer	12
Weight, sizing, performance and cost estimation	24
Drag of nacelles, ducts and external bodies	14
Electric, hybrid-electric and distributed propulsion	156
eVTOL aircraft, urban air mobility and certification	88
Ducted propellers, shrouds and lift fans	356
Transition and conversion	66
Handling and flying qualities criteria	204
Multirotor and unmanned vertical-takeoff vehicles	86
Flight control, displays and guidance for vertical takeoff	105
Propeller slipstream and wing interaction	26
Hover performance and hovering flight	57
Vertical and short takeoff configurations	81
Propellers, rotors and rotorcraft	38
Total	1,691

Ducted fans are in the middle of the largest revival they have ever had, which the cluster on ducted propellers, shrouds and lift fans below counts, in work such as Ohanian et al. 2012, Deng et al. 2020, Zhang and Barakos 2021, Jin et al. 2018, Akturk and Camci 2022, and Liu et al. 2025a. The broader vertical-takeoff field around them, from the control of multirotor vehicles to urban air mobility, is gathered in the clusters on multirotor and unmanned vehicles and on eVTOL aircraft, and is surveyed in Saied et al. 2024, Xu et al. 2025b, and Darvishpoor et al. 2025.

Almost nothing in that revival changes the aerodynamics. The momentum theory is the same, the thrust augmentation is the same, and the three charges the shroud levies are the same three this article computes. What changed is the machinery, and the machinery changed everything about how the configuration is used.

Electric Propulsion Dissolved the Cross-Shaft

The X-22’s most consequential single decision was the cross-shafted transmission, and it was forced. Four turboshafts driving four propellers cannot be allowed to fail independently, because losing one duct applies 71,600 foot-pounds of rolling moment, so every gearbox had to accept power from either direction and the whole train became one failure path.

An electric machine removes the requirement rather than solving it, in Distributed Electric Propulsion 2018, Weng et al. 2021, Li et al. 2022, Darmstad et al. 2024, Siddavatam et al. 2024, Chen et al. 2025a, Xiao et al. 2025, and Ma et al. 2025, and in the cluster below on electric, hybrid-electric and distributed propulsion. Motors can be sized with margin individually, they can be fed from separate buses, and a failure removes one rotor’s thrust without any mechanical coupling to the others. The redundancy moves from the shaft to the wiring.

And it changes how thrust is controlled. Every propeller on a shafted system turns at the same speed, so the X-22 changed one duct’s thrust by changing its blade pitch, and that differential blade pitch was its primary pitch and roll control in the hover, with the elevons in its duct exits providing yaw in Freeman and Newsom 1966. An electric rotor can instead change thrust by changing speed, and a fixed-pitch rotor controlled that way needs no variable-pitch hub. The control principle is the X-22’s, and the mechanism that delivered it is what has gone.

The Lip Still Stalls

A ducted fan is weak at the lip, which separates at large incidence or in a crosswind, in Jacocks and Kneile 1975, Mugridge 1975, Groeneweg 1977, Seidel and Matwey 1983, Motycka 1985, Sedlock 1985, Longley and Greitzer 1992, Xu et al. 2015, Minaker and Defoe 2019b, Minaker and Defoe 2019a, Akturk and Camci 2022, Chennuru et al. 2025.

This article computes where the momentum model stops describing the flow, and the X-22A record shows where the lip actually let go, in descent at low power and high duct angle, with a buzz felt through the whole aircraft, in Gamse and Mort 1967 and NASA CR-1901. Nothing about that has moved. A modern ducted electric vertical takeoff and landing aircraft, or eVTOL, hovering in a crosswind meets the same separation at the lip, and recent work such as Xu et al. 2015 and Akturk and Camci 2022 treats lip separation as a problem still to be controlled.

The Normal Force in Transition Is Still the Hard Part

The duct as an annular wing at incidence is Goodson and Grunwald 1962, Mort 1965, Milla and Blick 1966, Curtiss and Howard C. 1969, Mann 1974, Walker 1981, Lee and Kwok 1983, and Gill and D’Andrea 2020, and the conversion it complicates is Nardizzi et al. 1971, Huntley 1972, Hill 1983, Jiang and Zhang 2021, Pfeifle and Fichter 2023, Li et al. 2020, and Zhou et al. 2025, with the rest in the cluster on transition and conversion below.

What has changed is the tool rather than the answer. The article’s momentum estimate with a lip factor is what could be done with a slide rule, and it fails in the middle of the conversion for reasons the article states. Modern work computes the flow, and it still treats the pitching moment of a lift fan in transition as something to be reduced, in Jiang and Zhang 2021. The X-22 met that with elevons in its jets at low duct angles and differential blade pitch at high ones, in Freeman and Newsom 1966 and NASA TM-81156. A modern aircraft can meet it with rotor speed, and the transition control problem is now posed as an allocation problem, in Pfeifle and Fichter 2023, and no longer as a question about where to put a surface.

Hover Efficiency Has Not Improved and Cannot

The disc-loading relations in this article are momentum theory, so they are not going to be superseded, and the modern hover measurements are Helf et al. 1973, Velkoff 1981, Lee and Dassonville 2020, Son and Kim 2023.

A ducted lift fan at ninety-five pounds per square foot pays about three and a half times what a helicopter pays per pound lifted, and it always will. Electric propulsion changes the source of the power and not the amount of it.

Downwash Became a Public Problem

The 136 mile per hour downwash this article computes is now a matter for the safety standards of the places such aircraft land, in Ison 2024a, resting on measurements of downwash and outwash such as Chaderjian et al. 2002, Ramasamy and Yamauchi 2017, Tan et al. 2018, Mehrabi and Davari 2020, and Wu et al. 2026, and on the rest of the cluster on downwash, ground effect and recirculation below.

High disc loading near people is the constraint that the X-22 never had to answer to, because it was a research aircraft flown by test crews, away from the public. An aircraft expected to operate from a city rooftop has to account for what its jets do to anyone standing nearby, and the arithmetic that produces the jet velocity is the same arithmetic that produces the hover efficiency. The two cannot be traded against each other. They are the same number.

Noise Became a Requirement

Ducted fan acoustics, gathered in the cluster on ducted fan, rotor and vertical-takeoff noise below, run from the period analysis of ducted turbomachinery noise in Zorumski and Lester 1974 to the shape of the duct inlet in Shur et al. 2018, acoustic liners in Azimi et al. 2014, and Sato et al. 2024, ducted lift fans designed for low noise in Zhang et al. 2024b, and Zhao et al. 2025, and the community noise of urban air mobility in Rizzi and Rafaelof 2021, and Raza and Stansbury 2025.

The duct is helpful here, because it shields the blades and gives somewhere to put a liner, and that is a real reason to choose the configuration that did not weigh in 1962. It is also the clearest case in this survey of a modern advantage that the X-22 could not have collected, since nobody was choosing a military research aircraft’s configuration for its noise.

The Field Has Moved to Certification

The X-22 spent eighteen years measuring how vertical-takeoff aircraft ought to handle, and the modern version of that question is certification, in Cardoso et al. 2022, Lim et al. 2023, Norsetter and Smith 2024, Pleffken 2026, and Shubert et al. 2026. Beneath it lies handling-qualities work for eVTOL and multicopter aircraft such as Bahr et al. 2021, Li et al. 2024d, Favaro et al. 2025b, Wang et al. 2025c, and Jusko and Berger 2026, and the wider literature on handling and flying qualities criteria below.

This was the aircraft’s legacy, and it should be stated plainly. Its in-flight simulation work supplied data to the V/STOL flying-qualities specifications of its own period, in NASA TM-81156, and the certification work cited above addresses the same question for a new class of aircraft.

In-Flight Simulation Outlived the Configuration

Variable-stability aircraft are Harper and Robert P. 1955, Creer and McNeill 1956, Drinkwater and Rolls 1962, Marchese 1963, Newell et al. 1963, Garren and Kelly 1965, Person and Robbins 1965, Determination of Flight Characteristics 1967, Rhoads 1967, Szalai 1967, Eney 1968, Klopfstein 1968, Malcom 1969, Michaels 1969, Bell Aerospace Co Buffalo Ny 1970, Rhoads 1970, Schuler et al. 1972, Beilman 1973, Smith et al. 1973, Lebacqz 1974, Smith 1974, Lebacqz and Aiken 1975b, Motyka 1975, Aiken et al. 1977, Corliss et al. 1977, Corliss et al. 1978, Parker 1986, Henschel and Chetty 1989, Sato and Satoh 2011, Ko and Park 2014, Sato 2020, Scholten et al. 2020a, Chandrasekaran et al. 2021, Fang et al. 2022, Network Solution for Real-Time 2022, Yahui et al. 2024, Yi and Feng 2025.

The technique the X-22 was converted to use outlived the aircraft built for it. Ground-based simulation improved, and by 1979 the remaining in-flight simulation capability for vertical-takeoff work was two fixed-wing aircraft and a few helicopters, with no replacement for the X-22A yet identified, in NASA TM-81156. The X-22 was the last of a line as well as the best of it.

What the Survey Shows

The duct’s arithmetic was correct in 1962 and is correct now. Twenty-six percent more static thrust for a ring of metal, an annular wing’s normal force through the conversion, frontal area in cruise, and a hover bill set by disc loading. None of that has changed, and none of it is in dispute.

What came back is not the X-22’s aeroplane but the X-22’s component, attached to a machine that has no shafts, changes thrust by changing speed, and is being asked to fly near people. The three charges are unchanged and two of the answers are new.

And the thing the X-22 was actually for turned out to be the thing that lasted. The configuration was not adopted, and the programme was cancelled, in the Wikipedia entry. The handling-qualities data was, in the flying-qualities specifications of its period in NASA TM-81156, and the question it answered for eighteen years, by pretending to be other aeroplanes, is the one a modern ducted eVTOL must answer for certification.

The X-22A and the ducted-propeller assault transport

Reports and papers whose titles name the X-22A, together with the 1956 studies of a ducted-propeller assault transport from which the four-duct configuration descends.

Of the 16 titles that name the X-22A, 11 name flying qualities, variable stability, simulation, identification or displays, and none names the duct. They run from 1963 to 1990. The aircraft’s ducted propulsion is documented in tunnel reports whose titles do not name it, of which the full-scale duct test of Mort and Gamse is the most important, and that is the shape the Source Base describes.

26 records. [Aiken et al. 1977] [Beilman 1973] [Bell Aerospace Co Buffalo Ny 1956a] [Bell Aerospace Co Buffalo Ny 1956b] [Bell Aerospace Co Buffalo Ny 1956c] [Bell Aerospace Co Buffalo Ny 1970] [Henderson 1964] [Hiller Aircraft Corp Palo Alto Ca 1956] [Lebacqz 1974] [Lebacqz and Aiken 1975b] [Lebacqz and Aiken 1975a] [Lebacqz et al. 1974] [Macey 1956] [Marchese 1963] [Michaels 1969] [Pfeiff 1965] [Schuler et al. 1972] [Sing and Knauer 1956] [Smith 1974] [Smith et al. 1973] [Stearns et al. 1956] [The Bell X-22A V/STOL, Variable Stability Research Airplane, Lessons Learned] [Vollo and Brassaw 1956] [Walz 1978] [Zabinsky 1956] [Zabinsky and Laszewski 1956]

Variable-stability aircraft and flight simulation

Variable-stability aircraft, in-flight simulators and the ground simulators set beside them, including the other airborne V/STOL simulators of the X-22’s period.

The technique outlived the aircraft. Of the 44 records, 7 date from 1965 or earlier and 37 from 1966 or later, 12 of them from 2015 or later.

44 records. [Aláez et al. 2022] [Chandrasekaran et al. 2021] [Corliss et al. 1977] [Corliss et al. 1978] [Creer and McNeill 1956] [Davies 1975] [Determination of Flight Characteristics 1967] [Drinkwater and Rolls 1962] [Ellis 1971] [Ellis et al. 2002] [Eney 1968] [Fang et al. 2022] [Gallagher 1971] [Garren and Kelly 1965] [Hamel 2017] [Hamidani and Kunz 2018] [Harper and Robert P. 1955] [Henschel and Chetty 1989] [Kereliuk and Sinclair 1979] [Key et al. 1965] [Klopfstein 1968] [Ko and Park 2014] [Komoda et al. 1989] [Malcom 1969] [McGREGOR and Smith 1966] [Motyka 1975] [Network Solution for Real-Time 2022] [Newell et al. 1963] [Parker 1986] [Person and Robbins 1965] [Portapas 2025] [Rhoads 1967] [Rhoads 1970] [Sato 2020] [Sato and Satoh 2011] [Scamps and Gibbens 2003] [Scholten et al. 2020a] [Scholten et al. 2020b] [Sims and Kimberlin 1995] [Sinacori 1970] [Szalai 1967] [Vinje and Miller 1973] [Yahui et al. 2024] [Yi and Feng 2025]

The duct at incidence and the lip

The ducted propeller or fan at angle of attack, in non-axial inflow and in crosswind, and separation at the duct lip.

The subject the conversion depends on is small and recent. Of the 20 records, 10 date from 2015 or later and two from 1965 or earlier, the shrouded-propeller tunnel tests of the NACA and NASA that measured the loads on an isolated duct through the whole range of incidence.

20 records. [Aktürk and Camcı 2010] [Akturk and Camci 2022] [Akturk and Camcı 2014] [An et al. 2012] [Cantos et al. 2026] [Cao et al. 2024] [Cerny and Breitsamter 2020] [Chen et al. 2026b] [Goodson and Grunwald 1962] [Hall and Delaney 1991] [Hwang et al. 1994] [Lieblein et al. 1973] [Parlett 1955] [Pflimlin et al. 2006] [Pflimlin et al. 2007b] [Roh et al. 2018] [Roh et al. 2020] [Wang et al. 2024b] [Wang et al. 2026b] [Xu et al. 2015]

Engine inlets in crosswind and inlet distortion

The inlets of engine nacelles and turbomachines in crosswind and with distorted inflow, kept because their lip separates for the reason a duct lip does.

26 records. [Chen et al. 2021] [Chennuru et al. 2025] [Dickinson et al. 2024] [Longley and Greitzer 1992] [Jacocks and Kneile 1975] [Koch 2012] [Kokubo et al. 2024] [Kokubo et al. 2026] [Lavi and Headley 1967] [Li et al. 2027] [Lin et al. 2023] [Minaker and Defoe 2019b] [Minaker and Defoe 2019a] [Motycka 1985] [Nichols et al. 2019] [Nichols et al. 2020] [Nichols et al. 2021] [Nichols et al. 2022] [Nichols et al. 2024] [Nichols et al. 2026] [Sedlock 1985] [Seidel and Matwey 1983] [Song et al. 2025a] [Song et al. 2025b] [Ting et al. 1975] [Trapp and da Motta Girardi 2010]

Ducted fan, rotor and vertical-takeoff noise

Noise of ducted fans and shrouded propellers, of rotors and of vertical-takeoff aircraft, the community response to it, and the noise of fans in ducts outside aircraft, whose acoustics is the same.

The duct’s acoustic advantage is a modern subject. Of the 185 records, 109 date from 2015 or later and 5 from 1965 or earlier.

185 records. [Aalmoes et al. 2025] [Abdelhamid 1974a] [Abdelhamid 1974b] [Adámek et al. 2021] [Agarwal 1997] [Ahmed et al. 2025] [Aircraft Noise and Certification 2019] [Alexander A Svetgoff and Kevin Walczyk] [Araghizadeh et al. 2024] [Atassi and Grady 2003] [Azimi et al. 2014] [Bai et al. 2025b] [Balakrishnan and Srinivasan 2019] [Bauer and Redmann 2023] [Bauer et al. 2021] [Bekofske et al. 1977] [Bennett and Fitzpatrick 2007] [Bielak et al. 2002] [Boucher et al. 2023] [Boxwell et al. 1978] [Bu et al. 2026] [Bulaga 2005] [Buǧday and Saetti 2024] [Cantos et al. 2024] [Chen et al. 2015] [Chen et al. 2023] [Cho et al. 2024] [Cole and England 1967] [de Laborderie and Moreau 2016] [Deming 1940] [Dittmar 1978] [Dittmar 1988] [Dittmar et al. 1993] [Doherty and Butzel 1979] [Dunn 1997] [Dunn and Farassat 1998] [Envia 2016b] [Envia 2016a] [Eversman 1992] [Eversman and Roy 1993] [Falarski 1972] [Farazi and Zou 2024] [Kilcoyne and Huang 2025] [Merino-Martinez and Schade 2025] [Schoder et al. 2023] [Simon et al] [Fricke and Bissell 1968] [Glegg et al. 1997] [Go et al. 2022] [Go et al. 2023a] [Go et al. 2023b] [Goethert and Borchers 1974] [Goethert and Borchers 1975] [Goldschmidt and Ukeiley 2025] [Goudswaard et al. 2024] [Groeneweg 1977] [Hanson 2001] [Hargest 1966] [He et al. 2026a] [Henderson et al. 2005] [Henschel et al. 1974] [Hilton et al. 1960] [Hubbard 1950] [Hummel et al. 2026] [Huo et al. 2025] [Jdiobe et al. 2024] [Jia and Li 2025] [Jiang et al. 2019] [Johnson 1974] [Johnson-Groh 2024] [Jones et al. 1979, Evaluation of two inflow control] [Jung et al. 2025] [Li and Lee 2021] [Khorrami and Fares 2019] [Killeen et al. 2023] [Kobayashi 1978] [Koch 2010] [Koch et al. 2011] [Koch et al. 2012b, Tone Noise Predictions for a Spac] [Koppelberg et al. 2023] [Krishnamurthy and Rizzi 2022] [Koch et al. 2012a] [Koch et al] [Lee et al. 2025] [Lendvai and Benedek 2023] [Lendvai and Benedek 2024] [Lewy 2002] [Li et al. 2023a] [Liu et al. 2021] [Liu et al. 2024a] [Liu et al. 2026a] [Longhouse 1972] [Longhouse 1973] [Lowson 1972] [Dunn et al. 1996] [Ma] [Majić et al. 2016] [Margetts 1987] [Marques et al. 2026] [McArdle et al. 1981] [McLemore and Pegg 1980] [Meng et al. 2026] [Miller and Beranek 1958] [Miller and Papamoschou 2024] [Miller et al. 2023] [Modeling of Ducted Acoustic 2021] [Moreau et al. 2022] [Morhy Cavalcante et al. 2026] [Moulton and Brown 1992] [Mugridge 1975] [Musser et al. 2023] [Netjasov 2012] [Yao et al. 2026] [Zawodny et al. 2025] [Nt et al. 2024] [Nöding and Bertsch 2021] [Oh et al. 2026] [Ohtsuta and Akishita 1990] [Oleson and Patrick 1998] [Page et al. 2021] [Palleja-Cabre et al. 2024] [Palleja-Cabre et al. 2025] [Papamoschou 2023] [Park et al. 2017] [Park et al. 2022a] [Park et al. 2022b] [Pascioni et al. 2026] [Posey et al. 2004] [Qingyi et al. 2023] [Rao et al. 1974] [Raza and Stansbury 2025] [Richards 1955] [Rizzi and Rafaelof 2021] [Rizzi et al. 2026] [Sato et al. 2024] [Schade et al. 2024] [Schmidt et al. 2021] [Schmitz and Stepniewski 1973] [Schmähl et al. 2021] [Sharma et al. 1987] [Shur et al. 2016] [Shur et al. 2018] [Simon 2024] [Smith et al. 2000] [Sofrin and Cicon 1987a] [Sofrin and Cicon 1987b] [Son et al. 2025] [Sorenson et al. 2023] [Sow et al. 2025] [Spence and Spence 1997] [Sun et al. 2024] [Sun et al. 2026b] [Sutliff 2019] [Sutliff and Nagel 1993] [Tangler et al. 1973] [Thalheimer 2021] [Time Domain Sound Spectrum 2015] [Tinney and Valdez 2026] [Truong and Papamoschou 2014] [Truong and Papamoschou 2015] [Tweed 2000] [Wang 2017] [Wang and Li 2025] [Wang and Ma 2026] [Wang et al. 2005] [Wang et al. 2023c] [Wang et al. 2024a] [Wang et al. 2025b] [Wang et al. 2026e] [Woodward and Glaser 1981] [Woodward et al. 1984] [Woodward et al. 1992] [Wu et al. 2025] [Yadegari et al. 2024] [Yang et al. 2022c] [Yeow 1974] [Yusri et al. 2026] [Zhang and Barakos 2021] [Zhang et al. 2024b] [Zhao and Yang 2023] [Zhao and Yang 2026] [Zhao et al. 2025] [Zhao et al. 2026c] [Zhong et al. 2023] [Zorumski and Lester 1974]

Downwash, ground effect and recirculation

Downwash, outwash and ground erosion, ground effect and suckdown, recirculation and exhaust ingestion, and the agricultural spraying literature in which rotor downwash is the working medium.

The problem has two literatures with a gap between them. Of the 77 records, 15 date from 1965 or earlier, 15 from 1966 to 1989, 3 from 1990 to 2014 and 44 from 2015 or later.

77 records. [Adarkar and Hall 1969] [Ai et al. 2020a] [Arabshahi and Pankajakshan 1994] [Bai and Zhou 2023] [Bardera Mora and Matías García 2022] [Brinkman and Johnson 2021] [Brinkman et al. 2020] [Butler and Thomas 1964] [Chaderjian et al. 2002] [Chang et al. 2023] [Chen et al. 2025b] [Curtiss 1965] [Doğru et al. 2016] [Editor 2016] [George et al. 1964] [Georgiev 2025] [Hall 1967] [He and Leang 2025] [He et al. 2026b] [Higgins et al. 1966] [Hoad and Gentry 1975] [Hoad and Gentry 1977] [Hover over from Dover 1968] [Huang and Hu 2018] [Huston and Winston 1960] [Hwang and Kwon 2019] [Irmawan et al. 2023] [Ison 2024a] [Kalra and Baeder 2017] [Kato and Suzuki 2019] [Kemp 1969] [Kim and Yee 2020] [Kuhn 1965] [Kuhn 1979] [Kuhn and Grunwald 1960] [Kuhn and Grunwald 1961] [Lee et al. 2026a] [Levinsky et al. 1968] [Li et al. 2024c] [Louisse and Marshall 1976] [Mehrabi and Davari 2020] [Milluzzo and Kuerbitz 2017] [Milluzzo and Leishman 2017] [Minervino et al. 2016] [Morse and Newhouse 1960] [Morse and Newhouse 1961b] [Morse and Newhouse 1961a] [Neumann et al. 2020] [Newsom and Tosti 1962] [O’Bryan 1961] [Obryan 1960] [Otsuka et al. 2024] [Page and Aiken 1971] [Pasquali et al. 2020] [Pruyn and Taylor 1971] [Ramasamy and Yamauchi 2017] [Renselaer 1975] [Renselaer 1977] [Rogers et al. 1969] [Sagaga and Lee 2025] [Shouji et al. 2021] [Spray-on Landing Field Aids 1965] [STOL Operation Transition-in-Ground Effect 2007] [Su et al. 2024] [Tan et al. 2018] [Trivkovic et al. 2016] [White et al. 1960] [Wu et al. 2026] [Yang et al. 2022b] [Yang et al. 2022a] [Zhang et al. 2018] [Zhang et al. 2021b] [Zhao et al. 2022a] [Zhao et al. 2023b] [Zheng et al. 2018] [Zhou et al. 2026] [Zhu et al. 2024]

Transmissions, drive shafts and power transfer

Transmissions, gearboxes, drive shafts and their bearings, almost all of them for rotorcraft.

12 records. [Albrecht 1988] [Aroussi 2025] [Caldwell 1940] [Cormier 1979] [Dean 1979] [Deckert and Rolls 1974] [Leishman 1966] [Mancini 1983] [Overfield and Crawford 1967] [Tokarski et al. 1994] [Ward 1970] [White 1983]

Weight, sizing, performance and cost estimation

Weight estimation programmes and methods, sizing, performance estimates and operating cost.

24 records. [Ascani 1974] [Bonner et al. 1975] [Burnell and Fan 1957] [DeBilzan 1975] [Gallagher and Stoessel 1967] [Hajela and Chen 1988] [Hayase 1974f] [Hayase 1974b] [Hayase 1974d] [Hayase 1974e] [Hayase 1974a] [Hayase 1974c] [Hiyama 1974] [Irvin and Swan 1956] [Martindale et al. 1974] [Mokotoff and Cinar 2026] [Onat and Tolle 1979] [Otsuka et al. 2015] [Park 2025] [Saelman 1963] [Taflan et al. 2024] [Torenbeek 1972] [Wildermuth et al. 1974b] [Wildermuth et al. 1974a]

Drag of nacelles, ducts and external bodies

Drag of nacelles, ducted bodies and other external bodies, and its estimation.

14 records. [Callaghan et al. 1973] [Corsiglia et al. 1979] [Corsiglia et al. 1981] [Definitions of the Thrust 1955] [Gilman and Burdges 1967] [Jiang and Zhang 2021] [Kuhn 1959] [Levine 1957] [Malone and Peavey 1999] [Milla and Blick 1966] [Neal 1975] [Smetana 1975] [Takita et al. 2019] [Tinkler 1962]

Electric, hybrid-electric and distributed propulsion

Electric, hybrid-electric and distributed propulsion, electric ducted fans, motors, batteries and the power electronics that drive them.

This literature did not exist when the X-22 flew. Of the 156 records, 148 date from 2015 or later, and the one record from before 1966 is a 1952 whirl test of a propeller driven by an electric motor.

156 records. [Akash et al. 2021] [Alfares 2026] [Ali and Maqsood 2024] [Alvarez et al. 2023] [Ambroziak et al. 2023] [Arace et al. 2026] [Bacchini and Cestino 2019] [Chakraborty et al. 2023] [Chu et al. 2025b] [Jiang et al. 2025a] [Junaidin and Wicaksono 2022] [Li et al. 2025b] [Niță et al. 2026] [Sedunin et al. 2026] [Simmons and Murphy] [Brancaleoni et al. 2025] [Bravo et al. 2021] [Brucculeri et al. 2019] [Bustamante Alarcon et al. 2023] [Bustamante Alarcon et al. 2025] [Chakraborty and Mishra 2023] [Chen et al. 2025a] [Choi and Kim 2025] [Choi et al. 2014] [Choi et al. 2026] [Chu et al. 2025a] [Cole et al. 2021] [Comunian et al. 2026] [Cusati et al. 2023] [Darmstad et al. 2024] [Darrah et al. 2020] [Dayhoum et al. 2024a] [de Vries et al. 2019] [Distributed Electric Propulsion 2018] [Donateo and Çinar 2022] [Dorfling and Traub 2023] [Dzulfikar et al. 2025] [Ebus et al. 2022] [Ebus et al. 2024] [Eqbal et al. 2023] [Fan et al. 2023] [Fang and Callegaro 2021] [Farras et al. 2021] [Finger et al. 2018] [Finger et al. 2020] [Fredericks et al. 2013] [Friedrich and Robertson 2015] [Gao et al. 2025] [Gholamian and Beik 2026] [Goshtasbi et al. 2025] [He et al. 2020] [He et al. 2025] [Hossain and Bodson 2022] [Hu and Booker 2022] [Hu et al. 2026] [Huang et al. 2025] [Hui et al. 2025] [Ison 2024b] [Horton et al] [Jin et al. 2018] [Junaidin 2023] [Junaidin and Cahyono 2019] [Kamarudin 2020] [Kang et al. 2023] [Kang et al. 2025] [Kliza et al. 2025] [Kou et al. 2021] [Kozakiewicz and Grzegorczyk 2021] [Kruger and Uranga 2024] [Krznar et al. 2021a] [Krznar et al. 2021b] [Kubo et al. 2009] [Lee and Yee 2024] [Lee et al. 2022] [Legrand et al. 2025] [Lei and Zhao 2023] [Li et al. 2022] [Li et al. 2024a] [Li et al. 2024d] [Li et al. 2024b] [Li et al. 2025a] [Li et al. 2026b] [Litt 2024] [Liu et al. 2024b] [Liu et al. 2025b] [Ma et al. 2020] [Ma et al. 2022] [Ma et al. 2025] [DeVore et al. 2022] [Myasnikov and Ilyin 2023] [Nandy and Kim 2025] [Neogi et al] [Ng et al. 2020] [Odukoya and Jo 2026] [Park and Park 2026] [Pavel 2022] [Perry et al. 2023] [Pouryoussefi et al. 2023] [Qian et al. 2023] [Qiao and Zhou 2026] [Qin et al. 2023] [Busan et al] [Safieh and Rauleder 2024] [Safwat et al. 2026] [Saif et al. 2025] [Sajid et al. 2026] [Sarjito and Mulyadin 2024] [Sarup 2025] [Sarup 2026] [Serrano et al. 2021] [Serrano et al. 2022] [Shang et al. 2025] [Shi et al. 2024] [Showers 1952] [Siddavatam et al. 2024] [Su et al. 2026] [Suiçmez and Kutay 2023] [Sun et al. 2025a] [Sun et al. 2025b] [Takeyeldein 2026] [Teichert et al. 2026] [Tyan et al. 2017] [Van et al. 2019] [Vechtel and Buch 2022] [Vepa 2018] [Vieira et al. 2019] [Vratny and Hornung 2018] [Wachłaczenko 2025] [Wahid et al. 2025] [Walvekar and Chakravarthy 2023] [Wang et al. 2023b] [Wang et al. 2024c] [Watthewaduge and Bilgin 2023] [Wei et al. 2026] [Weinstein et al. 2026] [Weintraub et al. 2022] [Weng et al. 2021] [Wiston and Yan 2025] [Wu et al. 2023] [Xiao et al. 2024] [Xiao et al. 2025] [Xie et al. 2023] [Xin and Lee 2024] [Yan et al. 2019] [Yang et al. 2026b] [Yildiz 2022] [Yingtao et al. 2025] [Yoon and Jeong 2025] [Yuan et al. 2026] [Zhang et al. 2023a] [Zhao et al. 2022b] [Zhao et al. 2023c] [Zhong et al. 2026] [Zhu et al. 2022] [Zong et al. 2021] [Zong et al. 2022]

eVTOL aircraft, urban air mobility and certification

The eVTOL aircraft as a vehicle and as a transport system, covering configurations, operations, vertiports, public acceptance, safety and certification, with the earlier literature of VTOL transport.

It is almost entirely recent. Of the 88 records, 74 date from 2015 or later.

88 records. [Adeline et al. 2023] [Al-Rubaye et al. 2023] [Alkaabneh et al. 2026] [Alomar and Shafqat 2026] [Altouq et al. 2025] [Asher 1969] [Bahr et al. 2021] [Simmons and Hatke 2021] [Simmons] [Simmons 2023] [Simmons and Busan] [Bogdanović et al. 2024] [Brown and Harris 2020] [Franciscone and Fernandes 2023] [Campbell 1965] [Cardoso et al. 2022] [Chen et al. 2026a] [Choi and Suk 2026] [Ci̇zreli̇oğullari et al 2022] [Darvishpoor et al. 2025] [Caudle et al] [Favaro et al. 2025b] [Favaro et al. 2025a] [Fu et al. 2025a] [Fu et al. 2025b] [Goyal and Cohen 2022] [Guo et al. 2026] [Han and Pei 2026] [Hearn et al. 2023] [Jiang et al. 2025c] [Kim and Zhang 2025] [Kirste and Stumpf 2025] [Koumoutsidi et al. 2022] [국립한국교통대학교 경영학과 교수 and Kwak 2026] [Laarmann et al. 2023] [Lebacqz and Scott 1985] [Lee et al. 2021] [Li et al. 2026c] [Lim et al. 2023] [Liu et al. 2026b] [Mak et al. 2025] [Mall et al. 2026] [Marzouk 2025] [McKercher et al. 2024] [Radotich] [Min et al. 2026] [Mirković et al. 2026] [Ngcukayitobi 2026] [Norsetter and Smith 2024] [Oyama et al. 2024] [Pasupuleti 2025] [Pearlman 1968] [Pleffken 2026] [Pooladsanj et al. 2026] [Pradeep and Wei 2019] [Pukhova et al. 2021] [Qian et al. 2026] [Qiao and Zhou 2025] [Rao and Chimata 2024] [Ren and Wang 2025] [Rigas et al. 2024] [Rolls 1965] [Salvador 2022] [Savino and Zanotti 2025] [Schade 1968] [Schatrow et al. 2025] [Shao et al. 2021] [Shubert et al. 2026] [Whiteside and Pollard] [Simpson 1968] [Spühler et al. 2025] [Stapleford et al. 1974] [Sun et al. 2026a] [Takacs and Haidegger 2022] [Wang et al. 2023a] [Wang et al. 2025c] [Wang et al. 2025d] [Wang et al. 2026c] [Xu et al. 2025b] [Xue et al. 2026] [Yan et al. 2026] [Yang et al. 2026a] [Liu and Wang] [Yu et al. 2024] [Zhang et al. 2024a] [Zhang et al. 2024c] [Zhao and Cao 2026] [Zhou et al. 2024]

Ducted propellers, shrouds and lift fans

Ducted propellers, shrouded rotors, ducted fans and lift fans, covering their theory, tunnel tests and design, and the modelling and control of ducted-fan vehicles.

The revival is larger than the period literature, and the interval between them is thin. Of the 356 records, 59 date from 1965 or earlier, 38 from 1966 to 1989, 86 from 1990 to 2014 and 162 from 2015 or later.

356 records. [Luo et al. 2024d] [Aboelezz et al. 2022] [Abrego et al. 2002a] [Abrego et al. 2002b] [Acheson 2011] [Advanced Ducted Propulsor In-Flight] [Afjeh 1991] [Ahmadi et al. 2025] [Ahn and Lee 2004] [Ai et al. 2020b] [Ai et al. 2025] [Albachten 1956] [Ale Isaac Khoueini] [Alesin et al. 2020] [Applin et al. 1994] [Armutcuoglu et al. 2004] [Avanzini et al. 2001] [Avanzini et al. 2003] [Bai et al. 2025a] [Bangalee et al. 2025] [Beck et al] [Beeler 1965] [Betz 1966] [Bigarella 2025] [Biggers et al. 1966] [Black and Wainauski 1967] [Boldman et al. 1991] [Boldman et al. 1993] [Bontempo and Manna 2016] [Brabec and Helmich 2012] [Brizzolara et al. 2009] [Brogan et al. 1961] [Brown 1950] [Buba et al. 2024] [Bulat and Chernyshov 2026] [Bulat et al. 2023] [Cai et al. 2014] [Cai et al. 2019] [Cai et al. 2022] [Cao et al. 2005] [Cao et al. 2021] [Cao et al. 2022b] [Carmichael and McNay 1961] [Castles et al. 1960] [Chambers and Grafton 1968] [Chen et al. 1991] [Chen et al. 2017] [Chen et al. 2018] [Cheng and Pei 2020] [Cheng and Pei 2022a] [Cheng and Pei 2022b] [Cheng and Pei 2023] [Cheng and Pei 2024] [Cheng and Pei 2026] [Cheng et al. 2020] [Chiu et al. 2025] [Cho 2025] [Clark et al. 1963] [Colman et al. 2011] [Cook and Hickey 1967] [Cousins et al. 2026] [Cui et al. 2025] [Curtiss and Howard C. 1969] [Dallas and Irvin 1956] [Davis 1977] [Dayhoum et al. 2024b] [Dayhoum et al. 2025a] [Dayhoum et al. 2025b] [Deng et al. 2018] [Deng et al. 2020] [Denisenko et al. 2021] [Du et al. 2025] [Ducted fan] [Ducted Fan Model Ala 2026] [Echavarria and Poroseva 2015] [Effati and Banazadeh 2013] [Emami and Banazadeh 2015] [Eversman and Moehring 1987] [Falarski and Mort 1971] [Fan et al. 2017] [Fan et al. 2018a] [Fan et al. 2018b] [Fan et al. 2020] [Fan et al. 2022] [Fang et al. 2025] [Farassat et al. 2001] [Fazeli Asl and Moosapour 2017] [Flight Characteristics of Quad 2014] [Franz and Hauser] [Freeman and Newsom 1966] [Fu et al. 2023] [Gamse and Mort 1967] [Gao and Xu 2022] [Gentili et al. 2009] [Gill and D’Andrea 2020] [Gilmore and Grahame 1959] [Gong et al. 2021] [Goodson and Yaggy 1960] [Graf et al. 2008] [Grafton and Newsom 1971] [Grant et al. 2015] [Gray 1961] [Greenberg and Ordway 1964] [Griffith and Moller 1990] [Guerrero et al. 2003] [Guo and Zhou 2022b] [Guo and Zhou 2022a] [Guo and Zhou 2026] [Głowacki et al. 2015] [Hall and Delaney 1990] [Hall et al. 1991] [Ham and Moser 1958] [Han et al. 2014] [Han et al. 2019] [Han et al. 2024] [Harada 2018] [He et al. 2013] [Heyson 1974] [Hickling 1963] [Hoehne and Hoffman 1961] [Hook et al. 2011] [Hou et al. 2015] [Hough 1961] [Huo et al. 2015] [Huo et al. 2019] [Iek et al. 1992] [Iek et al. 1993a] [Iek et al. 1993b] [Jensen] [Jang et al. 2012] [Janus et al. 1992] [Jasudavisius 2021] [Jeong et al. 2019] [Jiang et al. 2015] [Jiang et al. 2018] [Jiang et al. 2025b] [Johnson 1958] [Kaji et al. 2017] [Kaji et al. 2018] [Kang et al. 2021] [Kantner et al] [Kaskel et al. 1963] [Keith and Srivastava 1997] [Keller and Holliger 1959] [Kelley 1962] [Kondor and Moore 2005] [Liu and Li 2024] [Liu et al. 2019b] [Lu et al. 2025] [Marconi and Naldi 2012] [Mort 1966] [Kim et al. 2018] [Kim et al. 2019] [Kim et al. 2020] [Kirby 1963, Flight-and Force-test Investigati] [Kondor et al. 2003] [Kriebel 1964] [Kriebel and Mendenhall 1966] [Kriebel et al. 1963] [Kruger 1949] [Kuantama and Tarca 2017] [Naldi et al. 2010] [Parlett 1961a] [Pflimlin et al. 2010] [Pütsep et al. 2023] [Rostami and Farajollahi 2021] [Wang et al. 2014] [Wang et al. 2018b] [Wang et al. 2026d] [Yilmaz et al. 2015] [Young] [Lawrence 1965] [Lee and Kwok 1983] [Lei et al. 2024] [Lerbs 1953] [Li 2008] [Li and Liu 2023] [Li et al. 2021] [Li et al. 2023b] [Li et al. 2024e] [Lin et al. 2019] [Liu 2023] [Liu and Mi 2025] [Liu et al. 2012] [Liu et al. 2013] [Liu et al. 2019a] [Liu et al. 2022a] [Liu et al. 2023] [Liu et al. 2025a] [Lovell 1955] [Lu] [Luo et al. 2023] [Luo et al. 2024a] [Luo et al. 2024b] [Luo et al. 2024c] [Mahakalkar et al. 2024] [Maldonado and Fernandes 2024] [Maldonado et al. 2024] [Mann 1974] [Manzoor et al. 2020] [Manzoor et al. 2022a] [Manzoor et al. 2022b] [Mao et al. 2024] [Martin 1964] [Martin and Tung 2004] [McCormick 1956a] [McCune 1993] [McKinney and Newsom 1962] [McKinney et al. 1966] [McNay 1958] [Meyerhoff and Zvengrowski 1962] [Mi 2020] [Miwa and Marubashi 2014] [Miwa et al. 2012] [Miwa et al. 2013] [Modelling and Controller Design 2021] [Mohammadi and Boroomand 2014] [Morgan 1961] [Morse 1956] [Mort 1965] [Moser 1959] [Mouille 1970] [Muehlebach and D’Andrea 2017] [Mumasha et al. 2026] [Murthy et al. 2002] [Myers et al. 2010] [Naldi et al. 2015] [Nardi et al. 1999] [Nelson 1956] [Nelson 1959] [Newsom 1963] [Nguyen and Ngo 2017] [Pettingill et al] [Niwa and Suzuki 1991] [Ohanian et al. 2009] [Ohanian et al. 2011] [Ohanian et al. 2012] [Okan et al. 2002] [Ordway and Greenberg 1961] [Ordway et al. 1960] [Otsuka et al. 1969] [Ozdemir and Horn 2009] [Pahonie et al. 2018] [Pangaribuan and Hartono 2024] [Park et al. 2013] [Park et al. 2015] [Parlett 1961b] [Pawłucki 2016] [Peddle et al. 2009] [Performance Validation 1999] [Pflimlin et al. 2007a] [Phanindra et al. 2020] [Platt 1948] [Przedpelski 1965] [Qing et al. 2019] [Raeisi 2021] [Rajagopalan and Zhang 1989] [Maki and Giulianetti 1966] [Regier et al. 1947] [Ritschl et al. 2003] [Roberts 1964] [Ruzicka et al. 2004] [Ryals et al. 2026] [Sargent and Anemaat 2018] [Savage et al. 2026] [Schaller] [Sellers et al. 1977] [Seo and Kim 2016] [Sheehy 1973] [Sheng and Sun 2015] [Sheng et al. 2015a] [Sheng et al. 2015b] [Shi et al. 2022] [Shiau et al. 2024] [Shuai and Xiao-hui 2011] [Simmonds 1967a] [Simmonds 1967b] [Simmonds 1967c] [Sinacori and Lange 1961] [Singh and Dinavahi 2011] [Smith 1960] [Srivastava 1992] [Srivastava et al. 1996] [Stiltner and Ohanian 2012] [Stockman 1970] [Szafran et al. 2014] [Taher et al. 2026] [Takallu 2009] [Takeda et al. 2020] [Tang et al. 2026] [Tapscott and Kelley 1960] [Taylor 1958] [Tekinalp et al. 2009] [Theodorsen 1960b] [Theodorsen 1960a] [Theodorsen and Nomicos 1961] [Thwaites 1951] [Thwaites 1953] [Tian et al. 2026a] [Tobias and Horn 2008] [Tran et al. 2021] [Tran Minh 2025] [Valarezo 1990] [Van Niekerk 1958] [Vu et al. 2026] [Wahl and Julian 1956] [Wainauski 1968] [Walker 1981] [Walters and Ashworth 1974] [Wang and Qi 2011] [Wang et al. 2007] [Wang et al. 2025a] [Weetman and Cromack 1973] [Weir 1988] [West 1969] [White and Phelan 1987] [Winter 1980] [Wonseok Lee and Hyochoong Bang 2007] [Worobel and Peracchio 1968] [Xiang et al. 2015] [Xiang et al. 2016] [Xu et al. 2026a] [Xu et al. 2026b] [Yaggy and Mort 1961] [Yang et al. 2004] [Yang et al. 2011] [Yauwenas et al. 2022] [Yilmaz et al. 2013] [Yin and Pei 2025] [Yin and Pei 2026] [Yoeli 2002] [Yoeli 2005] [Yoshikawa et al. 2019] [Yu 2023] [Yuska and Diedrich 1972] [Zakaria et al. 2019] [Omar 2011] [Zeng et al. 2025] [Zhang and Barakos 2020] [Zhang and Fan 2012] [Zhang et al. 2016] [Zhang et al. 2020b] [Zhang et al. 2020a] [Zhang et al. 2021a] [Zhang et al. 2022b] [Zhang et al. 2022a] [Zhang et al. 2023b] [Zhang et al. 2025b] [Zhang et al. 2025a] [Zhang et al. 2026] [Zhao and Bil 2008] [Zhao et al. 2013] [Zhao et al. 2026a] [Zhao et al. 2026b] [Zheng et al. 2026] [Zondervan et al. 2006]

Transition and conversion

Transition and conversion between hover and wingborne flight, from the period flight tests to the transition control of modern unmanned aircraft.

66 records. [Aroussi 2026] [Burton et al. 2026] [Chen 2023] [Cheng et al. 2026] [Clark et al. 1982] [Coles 1968] [Comer et al. 2026] [Cong et al. 2024] [Daud Filho and Belo 2023] [Di et al. 2025] [Englar and Kirkpatrick 1969] [Girard 1959] [Hill 1983] [Huntley 1972] [INAV-Based Adaptive Transition Control 2025] [Johnson and Craig 1974] [Kikumoto et al. 2022] [Kuhn 1981] [Laillatul and Darwito 2026] [Lee et al. 2026b] [Li et al. 2020] [Liu et al. 2018] [Lombaerts et al. 2022] [Lovell and Parlett 1956] [Ma and Wang 2018] [Magee and Taylor 1971a] [Magee and Taylor 1971b] [Marchini] [Margason and Hoad 1979] [May et al. 2024] [Mineck and Margason 1974] [Naldi and Marconi 2009] [Naldi and Marconi 2013] [Nardizzi et al. 1971] [Otis 1962] [Pfeifle and Fichter 2023] [Pirera 1983] [Pobikrowska and Goetzendorf-Grabowski 2025] [Rae 1972] [Ramnath 1970] [Rampy 1966] [Rehan et al. 2026] [Setiawarman and Sasongko 2026] [Shimizu and Miwa 2018] [Shimizu and Miwa 2019b] [Skelton 1968] [Smith 1958] [Smith 1961b] [Spreemann 1960] [Spreemann 1966] [Spreemann 1968] [Thirumaleshwar Hegde et al. 2020] [Trenka 1967] [Wang et al. 2019] [Wang et al. 2026a] [Winston 1970] [Xia et al. 2026] [Yan et al. 2023] [Yang et al. 2024] [YAV-8B Reaction Control System 1993] [Yue et al. 2026] [Yuksek and Inalhan 2022] [Zhao et al. 2023a] [Zhao et al. 2024] [Zhao et al. 2026d] [Zhou et al. 2025]

Handling and flying qualities criteria

Handling and flying qualities criteria and specifications for V/STOL aircraft, helicopters, rotorcraft and eVTOL aircraft, with the conventional-aircraft criteria and pilot rating methods they rest on.

The cluster is weighted to the X-22’s working life. Of the 204 records, 99 date from 1966 to 1989, and six titles name MIL-F-83300.

204 records. [Abdulrahim et al. 2017] [Adams and Hatch 1971] [Air Force Test Pilot School Edwards Afb Ca 1969] [Air Force Test Pilot School Edwards Afb Ca 1981] [Air Force Test Pilot School Edwards Afb Ca 1988c] [Air Force Test Pilot School Edwards Afb Ca 1988a] [Air Force Test Pilot School Edwards Afb Ca 1988b] [Air Force Test Pilot School Edwards Afb Ca 1989] [Air Force Test Pilot School Edwards Afb Ca 1990b] [Air Force Test Pilot School Edwards Afb Ca 1990a] [Air Force Test Pilot School Edwards Afb Ca 1990c] [Air Force Test Pilot School Edwards Afb Ca 1991a] [Air Force Test Pilot School Edwards Afb Ca 1991b] [Air Force Test Pilot School Edwards Afb Ca 1992] [Alexander 2025] [Alscher et al. 1966] [Anderson 1960a] [Anderson 1960b] [Anderson 1966] [Anderson 1970] [Anderson 1979] [Anderson 1985] [Anderson and Foster 1984] [Anderson and Schroers 1972] [Antonakis 2025a] [Antonakis 2025b] [Ashkenas 1965a] [Ashkenas 1965b] [Ashkenas 1984] [Bachelder et al. 2021] [Bailes et al. 1975] [Barbini et al. 1970] [Baughman and Longeauay 2015] [Berger et al. 2010] [Besco 1965] [Bivens 1985] [Bivens 1986] [Black and Moorhouse 1979] [Blanken et al. 2000] [Boeing Vertol Co Philadelphia Pa 1983] [Boothe et al. 1974] [Bowes and Miller 1976] [Brauser 1982] [Breul 1963] [Campos and Marques 2021] [Cao et al. 2022a] [Cappetta 1993] [Cappetta and Johns 1990] [Carlson 1958] [Cavallo et al. 1990] [Chalk and Key 1969] [Chalk and Saunders 1969] [Chalk et al. 1969] [Chalk et al. 1974] [Chance Vought Corp Dallas Tx 1979] [Cheatham and Hackler 1966] [Chowhan et al. 2019] [Blanken and Whalley 1993] [Citurs and Caton 1985] [Clark 1980] [Clark 1982] [Clarke and Griffin 2001] [Clarke et al. 2003] [Corless and Blanken 1983] [Corliss 1982] [Corliss 1983] [Craig et al. 1978] [Crim 1959] [Crombie and Moorhouse 1980] [Crother et al. 1973] [Curry et al. 1965] [Curtiss 1971] [Daughaday and Duwaldt 1955] [Difranco 1970] [DiFranco 1971] [Doman 1995] [Dooley 1977] [Drinkwater and Feistel 1965] [Dudgeon et al. 1998] [Dussart et al. 2019] [Ford 1989] [Franklin 2000] [Franklin 2002] [Garkushenko and Vinogradov 2016] [Garrard and Liebst 1990] [Garren 1962] [Gerdes and Hynes 1971] [Gerken 1979] [Goldstein 1982] [Gorham 1977] [Green 1972] [Griffin and Bellaire 1968] [Harper and Cooper 1986] [Harper and Sardanowsky 1969] [Harper et al. 1969] [Harper et al. 1970] [Hebbar and Pashilkar 2016] [Helicopter Handling Qualities 1982] [Henriquez Huecas et al. 2022] [Hess 2016] [Higgins and Shomber 1965] [Hoffman 1969b] [Hoffman 1969a] [Hoffman 1971] [Hoffman et al. 1970] [Hoh and Mitchell 1983] [Hoh et al. 1981] [Holladay 1966] [Holzhauser et al. 1965] [Huff 1949] [Hung and Dai 2025] [Ioannis and Ioannis 2026] [Jacobson and Joshi 1977] [Jacobson and Joshi 1978] [Ji et al. 2022] [Johnston and Friend 1965] [Johnston et al. 1965] [Johnston et al. 1974] [Jusko and Berger 2026] [Key 1971] [Key 1982] [Kidd and Bull 1963] [Kozhanov et al. 2022] [Kriechbaum and Lollar 1968] [Kriechbaum and Stineman 1972] [Kuhn et al. 1964] [Lacey 1977] [Lantzsch et al. 2014] [Lateral-Directional Flying Qualities 2002] [Lawrence et al. 2016] [Lawrence et al. 2018] [Lebacqz and Scott 1984] [Levison 1982] [Li et al. 2026a] [Liao et al. 2025] [Lollar and Kriechbaum 1968] [Lollar and Matous 1963] [Longitudinal Flying Qualities 2002] [Low and Garrard 1991] [Malpica and Lusardi 2013] [Malpica et al. 2011] [Malpica et al. 2012] [Martin 1963] [McCormick 1969] [Memon et al. 2021] [Miller 1970] [Miller and Clark 1965] [Mitchell and Hoh 1983] [Mitchell et al. 2003] [Miyajima 1969] [Momiyama 1977] [Moorhouse et al. 1989] [Nagata et al. 1973] [Nagy and Kirsten 1976] [Nettleton 1965] [Nonnenmacher and Jones 2016] [Place et al. 1974] [Pomfret and Clarke 2009] [Portapas and Cooke 2020] [Rauer 2019] [Reeder 1958] [Reschak 1970] [Reschak 1971] [Rich 1969] [Ritter et al. 1971] [Rotorcraft Handling Qualities Design 2011] [Rylko et al. 2025] [Saetti and Rogers 2024] [Safe Coordinated Maneuvering 2016] [Salem et al. 2014] [Shomber and Gertsen 1967] [Shubert and Jones 2025] [Slaughter 1958] [Smith 1966] [Smith 1977] [Smith 2023] [Smith and Geddes 1979] [Srinathkumar 2011] [Srinathkumar 2015] [Stapleford and Walton 1966] [Swaim 1970] [Swaim and Yen 1979] [Tapscott 1960] [Tapscott 1964] [Tischler and Hoh 1982] [Truong et al. 2016] [Vinje 1968] [Walter et al. 2020] [Walter et al. 2022] [Wang and Chen 2024] [Wei et al. 2023] [Welter 1966] [Wernecke 1958] [Westbrook 1964] [Whitbeck and Hofmann 1978] [Wilhelm and Schafranek 1986] [Willebeek-LeMair and Rhinehart 2023] [Wilson et al. 1993] [Wright and Lappos 1981] [Yan and Chen 2019] [Yu et al. 2020] [Yuan et al. 2022] [Zanoni et al. 2022] [Zhou et al. 2017]

Multirotor and unmanned vertical-takeoff vehicles

Multirotor and other unmanned vertical-takeoff vehicles, mostly their modelling and control.

All 86 records date from 2015 or later.

86 records. [Abdessameud and Janabi-Sharifi 2015] [Abdul Ghaffar et al. 2021] [Ahmadi Dastgerdi and Nabavi-Chashmi 2026] [Ahmed and Xiong 2024] [Akshat Deshpande and Shyamkant Limaye 2016] [Aláez et al. 2023] [Badea et al. 2026] [Bangura and Mahony 2017] [Barra et al. 2020] [Bezerra and Santos 2022] [Bouzid et al. 2017] [Chen and Pérez-Arancibia 2024] [Chen et al. 2019] [Choi et al. 2017] [Chung and Son 2020] [Chung and Son 2023] [Chung et al. 2019] [Czyba et al. 2018] [Dargham et al. 2015] [De Wagter and Meulenbeld 2019] [Derawi et al. 2015] [Ducard and Allenspach 2021] [Edmonds and Yi 2021] [Erasmus and Jordaan 2020] [Faizal et al. 2018] [Fernandez et al. 2023] [Gong et al. 2025] [Habibnia and Pascoa 2021] [Hafezi et al. 2022] [Halder and Benedict 2018] [Hashim 2022] [Hayama et al. 2021] [Hegde 2020] [Invernizzi et al. 2020] [Iriarte et al. 2021] [Islam et al. 2017] [Islam et al. 2020] [Ispiryan 2024] [Jabbari Asl 2019] [Jung et al. 2019] [Kulathunga and Klimchik 2023] [Lee and Son 2021] [Lei et al. 2020] [Lei et al. 2021] [Lei et al. 2023a] [Lei et al. 2023b] [Li et al. 2018] [Lin and Supsukbaworn 2017] [Lin et al. 2024] [Logan et al. 2017] [Lovas 2026] [Manzoni et al. 2024] [Mendes and Egbue 2018] [Milić et al. 2025] [Miyazaki et al. 2020] [Moeini et al. 2021] [Murata et al. 2025] [Nabadova and Sabziev 2025] [Noboni et al. 2025] [Nugroho et al. 2022] [Porter et al. 2016] [Reut and Tsukanov 2025] [Riboldi and Rolando 2023] [Ruggia 2025] [Runco and Benedict 2023] [Saied et al. 2019a] [Saied et al. 2019b] [Saied et al. 2024] [Slim et al. 2021] [Strampe and Klingauf 2026] [Takita and Kashitani 2016] [Takita et al. 2018] [Tolba and Shirinzadeh 2022] [Rohit 2024] [Wang 2019] [Wang and Zhang 2018] [Wang et al. 2017] [Whidborne and Cooke 2017] [Wijaya et al. 2023] [Wokanubun et al. 2023] [Yamaguchi et al. 2026] [Yu and Kwon 2017] [Zimmer and Gagnon 2023] [Öznalbant and Kavsaoğlu 2018] [聂 2017] [鲁 2020]

Flight control, displays and guidance for vertical takeoff

Flight control systems, stability augmentation, displays, guidance and instrument approach for vertical-takeoff aircraft and helicopters.

105 records. [A Piloted Simulator Investigation 1979] [Alford and Luoma 1960] [Anderson 1967] [Comer et al. 2025] [Arizaga et al. 2021] [Axten et al. 2024] [Bird 1970a] [Bird 1970b] [Bird and McLarty 1970] [Boothe and Ledder 1973] [Champine 1971] [Chu and Berman 2025] [Clark 1975] [Craig 1961] [Craig and Heffley 1972] [Demko and Boschma 1979] [Di Carlo et al. 1971] [Douglas Aircraft CO INC Santa Monica CA 1963] [Downing and Bryant 1979] [Drinkwater et al. 1963] [Drinkwater et al. 1965] [Duda et al. 2010] [Dukes 1970] [Ema 1992] [J. Victor Lebacqz; Edwin W. Aiken 1978] [Fay 1963] [Faye 1960] [Foster et al. 1987] [Franklin et al. 1986] [Frost et al. 2002] [Fry et al. 1966] [Gallagher and O’Donnell 1965] [Garren and Kelly 1966] [Garren et al. 1969] [Garren et al. 1970] [Gentry et al. 1966] [Gerdes 1964] [Gerdes 1977] [Guy 1976] [Hammond and Margason 1964] [Hegarty et al. 1965] [Hill 1966] [Hiller Aircraft Corp Palo Alto Ca 1965b] [Hoh and Ashkenas 1981] [Holzhauser et al. 1971] [Holzhauser et al. 1972] [Hoogreef and Soikkeli 2022] [Hua et al. 2015] [Cook and Gregory] [Johannsen and Govindaraj 1978] [Jokar and Khoshnood 2026] [Kaufman 1965] [Kelly et al. 1973] [Kelly et al. 1974] [Kelly et al. 1979] [Kirby and Newsom 1964] [Klinar and Craig 1961] [Laskowitz 1961] [Lazer and Kuatbayeva 2026] [Lebacqz 1979] [Lebacqz 1982] [Lebacqz 1983] [Lebacqz and Aiken 1977] [Lebacqz et al. 1981] [Leelaburanathanakul et al. 2021] [Liu et al. 2022b] [McGee 1977] [McGee et al. 1981] [McIntyre 1963] [Merrick 1984] [Merrick and Gerdes 1978] [Merrick et al. 1990] [Mitchell et al. 2014] [Miwa and Maruhashi 2016] [Morris et al. 1964] [Mueller 1965] [Ostheimer and Giguere 1963] [Patton 1972] [Pauli 1965] [Pauli 1969] [Pauli et al. 1970] [Renselaer 1974] [Ricardo and Santos 2023] [Roscoe et al. 1984] [Schwartz and Shearer 1964] [Seher-Weiß and Jones 2021] [Seibel 1963] [Selman 2023] [Shivers 1967] [Spreemann 1958] [Spreemann and Kuhn 1956] [Stendahl 1985] [Stortz and Franklin 1996] [Takahashi et al. 2017] [The Role of Human 1986] [Tosti 1962] [VTOL Control and Display 1988] [Wachtell 1970] [Wilson et al. 2012] [Winick 1968] [Ye et al. 2020] [Young 1969] [Yuan 1970] [Zhao and Liu 2018] [Çakan 2026]

Propeller slipstream and wing interaction

Propeller slipstream and its interaction with the wing, from deflected-slipstream V/STOL tests to the transonic wing in a slipstream.

None of the 26 records is later than 1989.

26 records. [Bencze et al. 1978] [Brenckmann 1958] [Butler et al. 1966] [Cummings 1968] [Fink 1963] [Franke and Weinig 1939] [Goland et al. 1964] [Hayes et al. 1958] [Howard and Miley 1989] [Howard et al. 1985] [Kirby 1956] [Kuhn 1957] [Lan 1975] [Mallen and Dancik 1959] [Winston and Huston 1962] [Miley et al. 1985] [Miley et al. 1986] [Newsom 1967] [Rizk 1980] [Rizk 1981] [Schouten 1982] [Stuper 1938] [Takagi and Inumaru 1967] [Turner and Drinkwater 1963] [Vidal et al. 1960] [Welge and Crowder 1978]

Hover performance and hovering flight

Hover performance of rotors, propellers and ducted rotors, and the stability of hovering flight.

57 records. [Arnold 2025] [Bramwell 1956] [Cameron and Sirohi 2019] [Cameron et al. 2016] [Chaderjian 2023] [Choi et al. 2022] [Coward 1955] [Dai et al. 2025] [Eilertson 1977] [Erickson et al. 1965] [Felker 1993] [Goland 1956] [Hammond 1966] [Han et al. 2021] [Helf et al. 1973] [Hohenemser 1956] [Hwang and Kwon 2015] [Jacobellis et al. 2021] [Jacobson and Smith 2018] [Jimenez Garcia and Barakos 2018] [Johnson and Sirohi 2024] [Kirk and Pitt 1969] [Kocurek and Tangler 1977] [Kozapalli and Warmbrodt 1997] [Lee and Dassonville 2020] [Lee and Kim 2020] [Lucassen and Sterk 1965] [Mihaila et al. 2026] [Mortimer et al. 2026] [Chaderjian] [Overmeyer and Martin 2017] [Park and Kwon 2021] [Payne 1955] [Pohly et al. 2021] [Ramanujam and Abhishek 2022] [Ramasamy et al. 2010] [Rand and Khromov 2017] [Shahmiri 2017] [Sheng 2018] [Shivers 1961] [Shrestha et al. 2016] [Son and Kim 2023] [Szolnoky Cunha and Ortiz 2024] [Tian et al. 2026b] [Velkoff 1981] [Wang et al. 2018a] [Webb and Willer 1952] [White and Crimi 1961] [Koning et al] [Koning et al] [Xu et al. 2025a] [Zhao 2018] [Zhao and Li 2018] [Zhao et al. 2014] [Zhao et al. 2019] [Zhou et al. 2022] [Zhu et al. 2023]

Vertical and short takeoff configurations

Vertical and short takeoff configurations other than the ducted propeller, covering tilt wings, deflected slipstreams, jet lift and lift engines, and programmes such as the XC-142A and XV-4.

81 records. [Adamson 1968] [American Helicopter Society INC Washington DC 1965] [Beppu and Curtiss 1966] [Boeing Co Morton Pa Vertol Div 1956] [Brown and Fisher 1968] [Campbell 1968] [Chambers and Grafton 1966] [Chambers and Grafton 1970] [Chance Vought Corp Dallas Tx 1963] [Conference on V/Stol Aircraft 1960] [Curtiss et al. 1961] [Curtiss et al. 1967] [DE Decker 1966] [Dyke 1963] [Edenborough 1968] [Egerton and Fitzpatrick 1967] [Garner 1967] [General Electric Co Cincinnati Oh 1964] [Giurca 2025] [Goodson 1966b] [Grima 2016] [Ground Tests of Piasecki 1958] [Hall 1965] [Hargraves 1961] [Heyson and Grunwald 1966] [Hebert and Joseph 1970] [Hebert et al. 1970] [Hesse 1965] [Hill and Waters 1974] [Huston and Winston 1969] [Irvine 1968] [Jacobson 1965] [Hassell and Kirby 1966] [Campbell 1964] [Kanishk Mahaveer Jain 2025] [Goodson 1966a] [Kirby 1960a] [Kirby 1961] [Kirby et al. 1963] [Lacey et al. 1979] [Laskowitz 1963] [Lavi 1967] [Liu 1962] [Lockheed-Georgia Co Marietta 1969] [Loewy and Yntema 1958] [Margason 1970] [Marsh 1967] [McCormick and Mallen 1957] [Mort and Yaggy 1963] [NASA Conference on V/STOL 1960] [Nicholson and lowry 1966] [O’Malley 1959] [Payne and Henry E. 1961] [PlCKERELL and Cresswell 1968] [Putman 1961] [Kuhn and McKinney 1965] [Kirby 1960b] [Roberts 1965] [Rolls 1960] [Schwaiger and Wills 2016] [Scientific and Technical Information Division 1966] [Shimizu and Miwa 2019a] [Shimizu and Miwa 2020] [Skifstad 1970] [Smith 1959] [Smith 1961a] [Snyder 2014] [Spillman 1967] [Stepniewski 1957] [Stepniewski and Schneider 1964] [Geuther et al. 2020] [Strand and Levinsky 1969] [Stuart 1957] [Swaim 1969] [Swaim and Connor 1968] [Trenka 1966] [Vertical Takeoff and Landing 2014] [VTOL 1969] [VTOL BOOSTER 1961] [Ward 1960] [Zosimovych 2022]

Propellers, rotors and rotorcraft

Propellers, rotors and rotorcraft design outside the hover-performance literature.

38 records. [Army Aviation Board Fort Rucker Al 1964] [Avant and Cunningham 1952] [Briardy and Head 1968] [Cardinale 1969] [Casadei et al. 2019] [Crist and Symes 1981] [Doblhoff 1956] [Doman 1957] [Drees 1963] [Dutton 1967] [Ekquist 1965] [Fay and Johnstone 1960] [Ham and Madden 1965] [Hiller Aircraft Corp Palo Alto Ca 1965a] [Hiller Aircraft Corp Palo Alto Ca 1965e] [Hiller Aircraft Corp Palo Alto Ca 1965f] [Hiller Aircraft Corp Palo Alto Ca 1965d] [Hiller Aircraft Corp Palo Alto Ca 1965c] [Kidwell and Wray 1964] [Kolesar et al. 1970] [Lerbs 1955] [Lieberman and Hoffman 1964] [McCormick 1956b] [McDonnell Aircraft Corp St Louis Mo 1950] [Morduchow et al. 1953] [Nelson 1965] [Peters et al] [Zawodny et al] [Roberts 1956] [Schroers and Antoniou 1966] [Sikorsky 1960] [Simpson 1967] [Sissingh 1941] [Smith 1968] [Snyder 1950] [Stange 1959] [Tung 1950] [Yamazaki 1965]

Where the Framing Breaks Down

The thrust augmentation figure assumes an ideal duct with no internal losses and an assumed exit area ratio. A real duct has friction, tip clearance and a diffuser that may separate, and the figure of merit derived here absorbs all of it into a single number.

The normal force calculation is the weakest part of the article. It is momentum turning multiplied by an assumed lip factor of two, and the sensitivity is large, giving a peak of anywhere between 0.54 and 1.35 times the aircraft weight over four ducts as that factor runs from one to two and a half. With $k$ the lip factor and $N_{\text{mom}}$ the momentum term at the peak, half of the 3,941 pounds computed with $k = 2$,

\[\frac{4 N_{\max}}{W} = \frac{4 k N_{\text{mom}}}{W} = \frac{4 k \times 1{,}971}{14{,}600} = 0.54\, k \tag{41}\]

The magnitude is not robust, and neither is the location, since the measured pitching moment peaks near 60 degrees of duct incidence in Biggers et al. 1966, well before the momentum estimate’s peak.

The conversion corridor is derived rather than assumed, from a wing area implied by the conversion speed, since no data sheet read here gives one. That derivation rests on an assumed maximum lift coefficient of 1.4 and on the assumption that the wings carry the whole weight at the conversion speed, and the resulting area is checked against the two spans, with no published figure to compare.

The article states the weakness of the normal force openly. The momentum model overestimates it badly wherever the crossflow parameter exceeds about one half, which is most of the middle of the conversion, and the article marks the number the model produces there as not credible and does not rely on it.

The tandem interference enters only through the tunnel and model results reported above, which show it protecting the rear ducts from stall and unsettling the hover near the ground. No relation in the article models it.

Several figures are assumptions with no source, and each is labelled where it is used. They are the 14,600 pound three-engine hover weight, the propulsive efficiency of 0.80 at maximum speed, the wing drag coefficient of 0.10 in the corridor calculation, the maximum lift coefficient of 1.4, the lip factor of two, the 700 foot per second tip speed and the elevon lift coefficient of 0.9.

The Source Base

The X-22 is well documented on the flying-qualities side and documented on the ducts mainly by tunnel tests, of which the full-scale test of its own duct is the most important. The programme’s own retrospective is The Bell X-22A V/STOL, Variable Stability Research Airplane, Lessons Learned, written twenty-four years after first flight, and the tri-service description of the aircraft is contemporary with the contract.

The primary documents behind the account of the vehicle are NASA reports. NASA TM-81156 describes the aircraft, its variable-stability system and its research programmes through 1979. Gamse and Mort 1967 report the full-scale duct, Biggers et al. 1966 and Freeman and Newsom 1966 the large-scale and free-flight models, Lebacqz 1974 and Lebacqz and Aiken 1975b two of the Calspan programmes, and NASA CR-1901 the initial military flight tests at second hand. The programme’s retrospective of 1990 and the 1969 report of the initial military tests are not freely available, the NASA records of Aiken et al. 1977 and Smith 1974 carry no full text, and the Defense Technical Information Center reports cited here, among them Bell Aerospace Co Buffalo Ny 1970, were not retrievable. The accident, the first flight of the second aircraft, the last flight and the maximum speed therefore rest on secondary accounts that disagree with each other.

The imbalance is a consequence of what the aircraft became. Eighteen years of variable-stability work generated a large literature about handling qualities in which the X-22 is the instrument rather than the subject, and comparatively little was published about the ducted propulsion after the configuration stopped being a candidate for production.

The research survey holds 1,691 research records drawn from the NASA Technical Reports Server, the Defense Technical Information Center and the journal literature indexed by Crossref, of which 499 are report primaries, being 29.5 percent, by the identifier rule set out under The Definition of Primary. The median publication year is 2013. Of the 1,666 dated records, 258 were published in 1965 or earlier, before the aircraft flew, being 15.5 percent, and 810 were published in 2015 or later, being 48.6 percent.

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 vehicle’s own record is primary under that rule only in part. Of the 16 titles that name the X-22A, 10 are report primaries. The papers presented to the American Helicopter Society and to the American Institute of Aeronautics and Astronautics, among them the programme’s 1990 retrospective, and a 1973 journal description of the aircraft as an in-flight simulator are not, so 29.5 percent is a lower bound on how much of the survey is first-hand. The NASA survey of in-flight simulators and the NASA contractor report on terminal guidance, on which much of the account of the aircraft rests, are curated references rather than survey records.

Thin Subjects

Seven subjects that this article’s derivations 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. Where a row joins two groups of terms with the word together, a title must carry a term from each group.

Subject	Title terms counted	Records
the normal force and pitching moment of a duct at incidence	normal force, pitching moment together with duct, ducted, shroud, shrouded, fan, propfan	1
thrust augmentation by a shroud	thrust augmentation, augmentation ratio, static thrust together with duct, ducted, shroud, shrouded	3
the cross-shafted transmission	cross shaft, cross shafting, cross shafted, interconnect, interconnected, shaft coupled	1
duct buzz	buzz	0
height damping and height control in the hover	height damping, vertical damping, height control, heave damping, vertical rate command	4
vanes and elevons in a duct exit	vane, vanes, elevon, elevons, deflector together with duct, ducted, shroud, shrouded	2
hover with an engine out	engine out, engine failure, engine inoperative, one engine together with hover, VTOL, V/STOL, vertical, tilt rotor, eVTOL, helicopter	7

The force the conversion turns on is rarely named. One title names a pitching moment, for an annular lift fan aircraft, and none names a normal force, although tunnel reports in the incidence cluster measure the loads on a duct at angle of attack, of which those are the components. The estimate of that force above therefore rests on the momentum relation and on the full-scale duct test.

The shroud’s thrust gain is measured but not named. Three titles name static thrust together with a duct or shroud, and none uses the phrase thrust augmentation, so the twenty-six percent rests on the momentum relation derived above.

The cross-shaft has almost no literature of its own. One title names a shaft-coupled drive, a 1977 analysis of control concepts for gas-coupled and shaft-coupled lift fan systems, and of the 12 records of the transmission cluster only a 1974 study of integrated propulsion and energy transfer control for lift-fan aircraft concerns the interconnection of separate lift units, while the rest concern drive trains, gearboxes and shafts.

Duct buzz has none. No title in the survey names buzz, and the account of it above rests on the initial Navy flight tests as summarised in NASA CR-1901.

Height damping is a helicopter subject in the literature. Four titles name height control or a vertical rate command. Three concern helicopters or rotorcraft, and the fourth is a 1964 piloted motion simulator study of height-control requirements for vertical-takeoff aircraft. The low natural height damping that the Calspan pilots met in the X-22A is documented in the programme’s own reports rather than in a literature of its own.

The exit vane appears twice. Two titles name vanes in a duct, a 1959 study of a ducted fan with turning vanes and a 2021 computation of a ducted fan and vane configuration in hover, and no title names an elevon.

Engine-out hover is a recent subject. Seven titles name an engine failure or an inoperative engine together with a vertical-flight vehicle, all of them published in 2019 or later, and none names a cross-shafted or interconnected drive, which is the arrangement that makes the X-22A’s engine-out case a loss of power rather than of symmetry.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject, which is the ducted propeller, the vertical-takeoff problem around it, and the handling-qualities work the X-22 served. Many words this subject depends on also name something else, and a record that shares only such a word is excluded.

A ducted propeller is a marine technology, an aeronautical one and a wind-energy one, and a title search on the phrase returns all three. The Kort nozzle is a duct around a ship’s propeller and its literature is large, old and entirely irrelevant here. Diffuser-augmented wind turbines and tidal turbines are ducted rotors whose momentum theory is the same and whose application is not. Marine, tidal and wind-turbine records are excluded from the reference base, and often only the venue separates them, because their titles are indistinguishable from the aeronautical ones.

Shared words also mislead in the other direction. A paper on the United States Marine Corps and vertical takeoff is not marine engineering and belongs here, and a paper on Building Credible Flight Models is not building aerodynamics. The phrase tandem propeller, by contrast, also describes a submarine.

Five more words are shared, and four of the five are shared inside engineering rather than outside it. Trim means the aircraft’s balance, the interior fittings, the engine setting and the attitude of a planing hull, so the word alone gathers door seals and engine test sets. Inlet belongs to propulsion and to coastal geomorphology, where a tidal inlet is the channel between barrier islands, so inlet flow is also a subject in the literature of sediment transport. Figure of merit is the hover efficiency of a rotor and also a performance metric in thermoelectric materials, electronic devices, optics and nuclear-radiation detectors. Electric propulsion means an aircraft motor here and an ion thruster in the spacecraft literature, where it covers subjects such as optimal low-thrust interplanetary trajectories. And transition is the conversion from hover to wingborne flight here and the change from a laminar to a turbulent boundary layer in aerodynamics generally, so a study of transition on a hovering rotor blade belongs to hover performance and a study of transition on a slender re-entry body does not belong at all. The ducted-fan engine of the 1940s and 1950s is the turbofan, and ducted propagation is a phenomenon of radio and ocean acoustics.

Excluded besides the homonym families are community noise studies that contain no aircraft, ducts that carry steam, radiation or fuel sprays, the disc loading of hummingbird wings and the aerodynamics of flapping wings, wing-in-ground-effect craft, supersonic and swept-wing aerodynamics and wave drag, jet mixing, pulsejets, ducted rockets and rocket nozzles in ducts, the handling qualities of road vehicles, room and duct silencing acoustics, signal-processing noise reduction, machines that use a ducted fan only as an actuator, such as a crane, a pipeline robot and a wall-climbing robot, and records that are not works, meaning figures, tables, supplementary files, peer-review reports, notices of erratum, correction, retraction or withdrawal, and journal front matter. A review of a book, a dictionary or short encyclopedia entry and a notice such as an editorial, an announcement or a news item are not research works either and are excluded. A document deposited twice under two identifiers is counted once. Doubtful records are kept where the problem is shared, such as the downwash load of an agricultural spraying aircraft, a cross-Channel hovercraft and an exterior noise test facility, because each bears on a consequence of high disc loading that the X-22 also produced. Engine nacelle inlets in crosswind are kept because their lip separates for the reason a duct lip does.

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. Three further doubtful classes are kept besides those just named. The aeroacoustics of axial fans in ducts outside aircraft, such as ventilation and server-rack fans, is kept because the fan and duct physics is the same. The handling qualities of spacecraft and lunar landers are kept because their criteria were developed by the same method as the vertical-takeoff criteria. Noise studies of aircraft in general, such as airport and landing-gear noise, are kept because they frame the community-noise problem that ducted fans are now asked to meet.

Epistemic State

Established and not in dispute. The aircraft first flew in 1966, one of two was lost in 1966, and the survivor operated as a variable-stability in-flight simulator from 1968 and was scheduled to fly research programmes through 1980 on a 500-hour service life.

Documented in primary reports. The full-scale duct’s area ratio of 1.165, figure of merit of 81 percent on exit area, propulsive efficiency of 74 percent and lip stall boundaries. The thrust-to-weight ratio of 1.35. The variable-stability system’s architecture and limits, and the results of the four research programmes completed by 1979.

Disputed among secondary accounts. The cause of the 1966 accident, the first flight of the second aircraft, the last flight in 1984 or 1988, the career hours, and whether the specified maximum speed was reached.

Computed here from quoted figures. The 26 percent thrust augmentation follows from momentum theory given the exit area ratio. The figure of merit of 0.716 follows from reading the quoted 35 percent as excess power, and reproduces the assumed three-engine hover weight to 0.83 percent. The documented reading, a thrust-to-weight ratio of 1.35, leaves an eleven percent thrust margin on three engines, and the tunnel’s best figure of merit makes it reachable at the 15,000 pound design weight only with no installation loss.

Not supported. That the 35 percent was chosen as the bare minimum for three-engine hover. That reading requires the figure to be excess power, and the primary statement gives it as thrust to weight.

Weakly supported. The magnitude of the duct normal force, which depends on an assumed lip factor, and the position of its peak, which falls later in the conversion than the measured pitching-moment peak.

Not addressed. A model of the tandem interference, and the structural and weight cost of the cross-shafted transmission.

Out of Scope

The detailed design of the transmission. The variable-stability system’s control laws, which are a subject in their own right. The tri-service requirement that produced the programme and the politics of its cancellation. Comparison with the tilt-rotor line that eventually succeeded, which belongs to a later article.

Conclusion

The duct is the aeroplane. It gains twenty-six percent more static thrust for nothing but a ring of metal, enough for a seven-foot propeller to carry ninety-five pounds per square foot, and it charges for that in the conversion by acting as an annular wing whose normal force peaks at about the duct thrust in the middle of the manoeuvre.

The margin depends on what the 35 percent measured. Read as excess power it leaves one and a quarter percent after an engine fails, and read as thrust to weight, which is how the NASA survey states it, it leaves eleven percent. The full-scale duct’s measured figure of merit makes the thrust reading at the 15,000 pound design weight possible only with almost no installation loss, so the design was at best tight, and how tight remains open on the record read here.

And the aeroplane outlived its question. It was built to find out whether four ducted propellers made a practical transport, and the answer was that they made a practical aircraft and an unattractive transport. What kept it flying for eighteen years was that somebody realised a machine which can hover and convert, and whose control system can be reprogrammed to feel like something else, is more valuable as a laboratory than as a prototype.

None of the four aircraft before it in this series was rescued that way. The X-18 is generally assumed to have been scrapped, the X-19 crashed, the X-20 was cancelled and the X-21 was left derelict and used as a photographic target, in the Wikipedia entry on the X-21. The X-22 was repurposed, and it is the only one of them still whole, stored at the Niagara Aerospace Museum according to the Wikipedia entry.

Equations

This section collects the 41 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 41, 19 are established and 22 are bespoke. Quantities are in United States customary units, with force in pounds, area in square feet, speed in feet per second unless knots are stated and power in horsepower converted at 550 foot-pounds per second, and the hover weight of 14,600 pounds that many lines use is a value the article assumes because no primary document read for it states one.

Equation 1, Disc Area of One Duct. The disc area of one duct follows from the seven-foot propeller diameter as the area of a circle.

\[A_{d} = \frac{\pi D^{2}}{4} = \frac{\pi \times 7^{2}}{4} = 38.48\ \text{ft}^{2} \tag{1}\]

Equation 2, Bespoke Disc Loading at the Assumed Hover Weight. Dividing the assumed three-engine hover weight of 14,600 pounds by the disc area of four ducts gives a disc loading near 95 pounds per square foot.

\[\frac{W}{A} = \frac{14{,}600}{153.9} = 94.8\ \text{lbf/ft}^{2} \tag{2}\]

Equation 3, Momentum Theory Thrust and Power of a Ducted Propeller. Continuity and momentum across a propeller in a duct whose exit area is $\sigma$ times the disc area give the thrust and the ideal power in terms of the exit velocity.

\[T = \rho \sigma A V_{e}^{2} \qquad P = \tfrac{1}{2} \rho \sigma A V_{e}^{3} \tag{3}\]

Equation 4, Ideal Power of a Ducted Propeller in Terms of Thrust. Eliminating the exit velocity expresses the ideal power through the thrust and shows that thrust at fixed power grows as the cube root of the exit area ratio.

\[P = \frac{1}{2} \frac{T^{3/2}}{\sqrt{\rho \sigma A}} \qquad \Rightarrow \qquad T \propto \sigma^{1/3} \tag{4}\]

Equation 5, Static Thrust Augmentation of a Non-Contracting Duct. A duct that only prevents the wake contraction of an open propeller, an area ratio of one against one half, gives about twenty-six percent more static thrust for the same power.

\[\frac{T_{\text{duct}}}{T_{\text{open}}} = (2\sigma)^{1/3} = 2^{1/3} = 1.26 \tag{5}\]

Equation 6, Measured Exit Area Ratio of the Duct. The ratio of the net exit area to the net area at the propeller, from the measured duct geometry, is about 1.17. Gamse and Mort 1967

\[\sigma_{d} = \frac{A_{e}}{A_{p}} = \frac{44.08}{37.84} = 1.165 \tag{6}\]

Equation 7, Ideal Thrust Augmentation at the Measured Area Ratio. The same ideal relation evaluated at the measured exit area ratio gives a thrust augmentation of about one third over an open propeller. Gamse and Mort 1967

\[\frac{T_{\text{duct}}}{T_{\text{open}}} = (2\sigma_{d})^{1/3} = 2.330^{1/3} = 1.33 \tag{7}\]

Equation 8, Bespoke Ideal Hover Power at the Assumed Weight. The ideal power of a non-contracting ducted rotor hovering the assumed 14,600 pounds on four discs at sea level is about 2,650 horsepower.

\[P_{\text{ideal}} = \tfrac{1}{2} \frac{W^{3/2}}{\sqrt{\rho A}} = 2{,}651\ \text{hp} \tag{8}\]

Equation 9, Bespoke Engine-Out Power Margin on the Power Reading. Reading the documented 35 percent margin as installed power in excess of hover power leaves three engines with a margin of one and a quarter percent.

\[\frac{3}{4} \times 1.35 = 1.0125 \tag{9}\]

Equation 10, Engine-Out Thrust Margin at Fixed Figure of Merit. Thrust at a fixed figure of merit scales as power to the two-thirds, so losing a quarter of the power from a thrust-to-weight ratio of 1.35 leaves an eleven percent thrust margin.

\[\frac{T_{3}}{W} = 1.35 \left( \frac{3}{4} \right)^{2/3} = 1.35 \times 0.8255 = 1.114 \tag{10}\]

Equation 11, Bespoke Installed Figure of Merit on the Power Reading. The figure of merit is the ideal power at the assumed 14,600 pounds over the required power that the power reading of the 35 percent margin implies.

\[\text{FM} = \frac{P_{\text{ideal}}}{P_{\text{required}}} = \frac{2{,}651}{3{,}704} = 0.716 \tag{11}\]

Equation 12, Bespoke Three-Engine Hover Weight on the Power Reading. Feeding the inferred figure of merit back through momentum theory with three engines gives a lifted weight within one percent of the assumed 14,600 pounds.

\[W_{3} = W \left( \frac{P_{3} \, \text{FM}}{P_{\text{ideal}}} \right)^{2/3} = 14{,}721\ \text{lbf} \tag{12}\]

Equation 13, Figure of Merit Referred to the Disc Area. Because ideal power varies as the inverse square root of area, a figure of merit measured on the net exit area converts to the disc-area basis through the square root of the area ratio.

\[\text{FM}_{\text{disc}} = \text{FM}_{\text{exit}} \sqrt{\frac{A_{e}}{A_{d}}} = 0.81 \sqrt{\frac{44.08}{38.48}} = 0.867 \tag{13}\]

Equation 14, Bespoke Four-Engine Thrust at the Tunnel Figure of Merit. Applying the best tunnel figure of merit to the rated 5,000 horsepower under the assumption of no installation loss gives an upper bound on the four-engine thrust.

\[T_{4} = \left( 2\,\text{FM}_{\text{disc}}\, P \sqrt{\rho A} \right)^{2/3} = 20{,}261\ \text{lbf} \tag{14}\]

Equation 15, Bespoke Duct Exit Velocity in the Hover. The exit velocity of one non-contracting duct carrying a quarter of the assumed 14,600 pounds at sea level is about 200 feet per second.

\[V_{e} = \sqrt{\frac{T}{\rho \sigma A_{d}}} = \sqrt{\frac{3{,}650}{0.0023769 \times 38.48}} = 200\ \text{ft/s} \tag{15}\]

Equation 16, Induced Velocity and Power Loading from Disc Loading. In momentum theory the induced velocity grows as the square root of disc loading and the thrust per unit power falls in inverse proportion to it.

\[v_{e} = \sqrt{\frac{W/A}{\rho}} \qquad \frac{T}{P} = \frac{2\,\text{FM}}{v_{e}} \tag{16}\]

Equation 17, Momentum Normal Force on a Duct at Incidence. A duct at an angle to the oncoming air captures a mass flow and turns it onto its axis, and the reaction is a normal force equal to the turned momentum flux.

\[N_{\text{mom}} = \dot{m} V_{\infty} \sin\alpha \qquad \dot{m} = \rho A_{d} \left( V_{\infty} \cos\alpha + v_{i} \right) \tag{17}\]

Equation 18, Bespoke Wing Area from the Conversion Speed. Requiring the wing to carry the assumed 14,600 pounds at the conversion speed of 203 feet per second with an assumed maximum lift coefficient of 1.4 gives a wing area of about 213 square feet.

\[S = \frac{2W}{\rho V_{\text{conv}}^2 C_{L,\max}} = \frac{2 \times 14{,}600}{0.0023769 \times 203^2 \times 1.4} = 213\ \text{ft}^2 \tag{18}\]

Equation 19, Force Balance Through the Conversion. With the duct thrust inclined at the duct angle, its vertical component and the wing lift balance the weight and its horizontal component balances the drag.

\[T \sin i + L = W \qquad T \cos i = D \tag{19}\]

Equation 20, Duct Angle and Thrust Required in Conversion. Solving the two force balance equations gives the duct angle from the ratio of unsupported weight to drag and the thrust as the resultant of the two.

\[\tan i = \frac{W - L}{D} \qquad T = \sqrt{(W-L)^2 + D^2} \tag{20}\]

Equation 21, Bespoke Validity Parameter of the Momentum-Turning Model. The article defines the ratio of the crossflow velocity component to the induced velocity as the parameter that must stay small for the duct to capture and turn its whole streamtube.

\[\mu = \frac{V_{\infty} \sin i}{v_{i}} \tag{21}\]

Equation 22, Bespoke Sink Rate at the Suggested Descent-Angle Limit. The suggested 10 degree descent-angle limit flown at a low speed of 40 knots, a speed the article takes as representative, gives a sink rate near 700 feet per minute.

\[\dot{h} = 60\, V \sin\gamma = 60 \times 67.5 \times \sin 10^{\circ} = 703\ \text{ft/min} \tag{22}\]

Equation 23, Bespoke Linear Duct Angle Schedule. The article assumes the duct angle falls linearly from vertical at rest to horizontal at the conversion speed, which places 60 degrees of incidence near 40 knots.

\[i = 90^{\circ} \left( 1 - \frac{V}{V_{\text{conv}}} \right) \qquad V_{60^{\circ}} = \frac{203}{3} = 67.7\ \text{ft/s} = 40\ \text{kt} \tag{23}\]

Equation 24, Bespoke Cruise Drag from Power and Propulsive Efficiency. Drag at 278 knots, a value between the conflicting 274 and 283 knot figures, follows from the installed 5,000 shaft horsepower at an assumed propulsive efficiency of 0.80.

\[D = \frac{\eta P}{V} = \frac{0.80 \times 5{,}000 \times 550}{469.2} = 4{,}689\ \text{lbf} \tag{24}\]

Equation 25, Bespoke Equivalent Flat-Plate Area. Dividing the inferred cruise drag by the dynamic pressure at 278 knots gives an equivalent flat-plate area of about 24 square feet.

\[f = \frac{D}{q} = \frac{4{,}689}{193.3} = 24.3\ \text{ft}^2 \tag{25}\]

Equation 26, Bespoke Duct Drag Coefficient on Frontal Area. Attributing the whole equivalent flat-plate area to the four ducts and dividing by their frontal area gives a drag coefficient near 0.16.

\[C_{D,\text{duct}} = \frac{f}{4 A_{d}} = \frac{24.3}{153.9} = 0.158 \tag{26}\]

Equation 27, Bespoke Drag Chain at the Measured Propulsive Efficiency. Repeating the drag, flat-plate area and duct drag coefficient chain with the measured efficiency of 0.74 still rests on the 278 knot speed and on attributing the whole drag to the ducts. Gamse and Mort 1967

\[D = \frac{0.74 \times 5{,}000 \times 550}{469.2} = 4{,}337\ \text{lbf} \qquad f = \frac{4{,}337}{193.3} = 22.4\ \text{ft}^{2} \qquad C_{D,\text{duct}} = \frac{22.4}{153.9} = 0.146 \tag{27}\]

Equation 28, Bespoke Dynamic Pressure of the Hover Jet. The dynamic pressure in the duct exit flow follows from the exit velocity inferred at the assumed hover weight.

\[q_{\text{jet}} = \tfrac{1}{2} \rho V_{e}^{2} = 47.4\ \text{lbf/ft}^{2} \tag{28}\]

Equation 29, Bespoke Lip Pitching Couple of a Duct. Placing the duct normal force at the lip, half a duct length from the duct centre, gives the nose-up couple each duct contributes.

\[M = \frac{N \ell}{2} \tag{29}\]

Equation 30, Elevon Area Scaled from the Free-Flight Model. Model elevon areas scale to full size with the square of the length ratio of 5.56. Freeman and Newsom 1966

\[S_{e} = 0.82 \times 5.56^{2} = 25.3\ \text{ft}^{2} \qquad S_{e} = 1.06 \times 5.56^{2} = 32.8\ \text{ft}^{2} \tag{30}\]

Equation 31, Bespoke Exit Vane Side Force in the Hover. The force on a 31.8 square foot vane in the hover jet at an assumed lift coefficient of 0.9 is more than a third of the duct thrust.

\[F = q_{\text{jet}} S_{e} C_{L_{e}} = 47.4 \times 31.8 \times 0.9 = 1{,}357\ \text{lbf} \tag{31}\]

Equation 32, Bespoke Rolling Moment from Losing One Duct. Without cross-shafting the loss of one duct leaves its quarter share of the assumed hover weight acting at the rear semi-span as an untrimmed rolling moment.

\[M = T_{\text{duct}} \, y = 3{,}650 \times 19.62 = 71{,}600\ \text{ft}\cdot\text{lbf} \tag{32}\]

Equation 33, Bespoke Shaft Torque per Propeller. The torque each propeller absorbs at 1,250 horsepower follows from the rotational speed implied by an assumed tip speed of 700 feet per second.

\[Q = \frac{P}{\omega} = \frac{1{,}250 \times 550}{200} = 3{,}440\ \text{ft}\cdot\text{lbf} \tag{33}\]

Equation 34, Airframe Hours Flown by 1980. The established service life of 500 flight hours less the 80 expected to remain gives the hours flown by the end of 1980. NASA TM-81156

\[500 - 80 = 420\ \text{h} \tag{34}\]

Equation 35, Roll Mode Time Constant. The roll mode time constant is the negative reciprocal of the roll damping derivative, so doubling the damping halves the time constant. NASA TM-81156

\[\tau_{R} = -\frac{1}{L_{p}} \tag{35}\]

Equation 36, Distance and Time of a Uniform Deceleration to the Hover. Decelerating uniformly from 100 knots at 0.05 times standard gravity takes about 8,900 feet and 105 seconds. Lebacqz and Aiken 1975b

\[s = \frac{V^{2}}{2a} = \frac{168.8^{2}}{2 \times 0.05 \times 32.17} = 8{,}854\ \text{ft} \qquad t = \frac{V}{a} = 105\ \text{s} \tag{36}\]

Equation 37, Sink Rate on a 7.5 Degree Glide Slope. The vertical component of 100 knots on the 7.5 degree glide slope is a descent of about 1,320 feet per minute. Lebacqz and Aiken 1975b

\[\dot{h} = 60\, V \sin\gamma = 60 \times 168.8 \times \sin 7.5^{\circ} = 1{,}322\ \text{ft/min} \tag{37}\]

Equation 38, Total Piloted Evaluations of the Completed Programmes. The evaluation counts of the four completed variable-stability programmes sum to 239.

\[50 + 109 + 37 + 43 = 239 \tag{38}\]

Equation 39, Froude Scaling of Oscillation Periods. Periods of a dynamically scaled free-flight model scale with the square root of the length ratio, so the model oscillations of 3.4 and 3.0 seconds become about 8.0 and 7.1 seconds at full scale. Freeman and Newsom 1966

\[T_{\text{full}} = T_{\text{model}} \sqrt{5.56} \qquad 3.4 \times 2.358 = 8.0\ \text{s} \qquad 3.0 \times 2.358 = 7.1\ \text{s} \tag{39}\]

Equation 40, Bespoke Payload Fraction. The documented 1,200 pound maximum payload over the assumed 14,600 pound hover weight is a payload fraction of about eight percent. Bell X-22A Vertical Flight Society

\[\frac{W_{\text{payload}}}{W} = \frac{1{,}200}{14{,}600} = 0.082 \tag{40}\]

Equation 41, Bespoke Peak Normal Force with a Lip Factor. Multiplying the momentum normal force by an unknown lip factor $k$ shows that the peak normal force over four ducts scales directly with a factor the article can only assume.

\[\frac{4 N_{\max}}{W} = \frac{4 k N_{\text{mom}}}{W} = \frac{4 k \times 1{,}971}{14{,}600} = 0.54\, k \tag{41}\]

Notation

• $A_{d}$, the disc area of one duct
• $D$, the propeller diameter in Equation 1 and the drag in Equations 19, 20 and 24
• $W$, the hover weight, taken as 14,600 pounds
• $\sigma$, the ratio of duct exit area to disc area, with $\sigma_d$ the measured ratio
• $V_{e}$, the exit velocity of the duct flow
• $T$, the thrust
• $P$, the power
• $\rho$, the air density, taken at sea level
• $\text{FM}$, the figure of merit, the ratio of ideal to required hover power
• $A_{e}$, the net exit area of a duct
• $A_{p}$, the net area of a duct at the propeller
• $\dot{m}$, the mass flow captured by a duct
• $N_{\text{mom}}$, the momentum normal force on a duct at incidence
• $v_{i}$, the induced velocity of a duct
• $V_{\infty}$, the free-stream speed
• $\alpha$, the angle of attack of the duct
• $i$, the duct angle above the horizontal
• $L$, the wing lift
• $V_{\text{conv}}$, the conversion speed at which the ducts reach horizontal
• $C_{L,\max}$, the maximum lift coefficient
• $\mu$, the ratio of crossflow speed to induced velocity that bounds the momentum-turning model
• $f$, the equivalent flat-plate drag area
• $\eta$, the propulsive efficiency
• $q_{\text{jet}}$, the dynamic pressure of the hover jet
• $S$, the wing area
• $S_{e}$, the area of an elevon or exit vane
• $\ell$, the length of a duct
• $L_{p}$, the roll damping derivative
• $\tau_{R}$, the roll mode time constant
• $k$, the lip factor that multiplies the momentum normal force

References

Primary Sources, Peer-Reviewed

• Abdessameud, Abdelkader, and Farrokh Janabi-Sharifi. 2015. “Image-Based Tracking Control of VTOL Unmanned Aerial Vehicles.” Automatica 53: 111–19. https://doi.org/10.1016/j.automatica.2014.12.032
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