X-Planes: Bensen X-25

On 5 June 1968, the first-flight date that Jenkins, Landis and Miller give for the type and that Guinness World Records gives for this aircraft, an unpowered Bensen gyroglider designated X-25B flew for the first time at Edwards Air Force Base. It had no engine at first, no fuselage to speak of, and a rotor that turned only because air was coming up through it. It is the smallest crewed aircraft and the slowest in this series, and the only one whose research question was about what happens after an aeroplane has already been lost. Guinness World Records names the X-25B the smallest crewed aircraft to receive an X-plane designation, and its fastest recorded flight was 85 miles per hour in the inventory by Jenkins, Landis and Miller. This article is the twenty-sixth in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, and the X-24.

The X-25 was not built to fly higher, faster or further than anything. It was built to answer whether an aircrew member who has just ejected can be given a choice about where to come down. The United States Air Force called the programme the Discretionary Descent Vehicle, and the word that matters in that name is discretionary. The programme’s purpose of giving aircrew who abandon their aircraft an option of where to land is recorded by Jenkins, Landis and Miller.

The obvious reading of the concept is wrong, and the arithmetic establishes that before any archive does. An autorotating rotor is not a gentler way down than a parachute. At equal weight it descends about nine percent faster, and as flown it descended about thirty percent faster. The rotor does not offer a slower descent. It offers the ability to go somewhere.

The concept was not abandoned because pilots could not learn to fly it. The one test result on record is that pilots could be trained quickly and easily, in the X-25A fact sheet, which gives the end of the programme as the air war winding down together with doubts about operational feasibility. The vehicle that embodied the escape, the unpowered gyro-chute, has no recorded piloted flight, and no full-scale operational test was performed, in Jenkins, Landis and Miller. The evidence supports a narrower reading, that the need lapsed before the escape itself was ever demonstrated. The arithmetic below indicates where the doubts about feasibility could plausibly have lain, an inference that no document of the programme confirms.

The Research Question

Can a descending crewman be given control over the landing point, using a device small enough to carry in a combat aircraft?

That question has a shape unlike any other in this series. The X-1 asked whether an aeroplane could pass through Mach one and survive. The X-15 asked what hypersonic flight does to a structure. Those are questions about a flight regime. This one is a question about a probability, namely the probability that a person who has left a damaged aeroplane over hostile ground is recovered rather than captured, and the engineering exists only to move that number.

The binding unknown was not whether a rotor autorotates. Juan de la Cierva had settled that in the 1920s and the literature had been mature for forty years, in Glauert 1927, de la Cierva 1930, Wheatley 1933, Report No. 515 Full-Scale 1935, Report no. 515, full-scale, Wheatley 1935a, Wheatley 1937b, Gustafson 1956, and Larsen 1956. The remainder of that period work is surveyed with the autogiros and gyroplanes in The Contemporary Literature. The programme history of the machines Cierva built is in Brooks on the Cierva autogiros and the longer arc from those aircraft to the modern gyroplane is in Charnov’s account of the type. The binding unknown was whether the useful part of autorotation survives being packed into an aeroplane, deployed by someone who has just been through an ejection, and flown by a person with no rotorcraft training under the worst conditions of their life.

Each of those four constraints attacks a different quantity, and the article is organised around them because the programme was.

Programme Origin

The X-25A fact sheet gives the motivation as the air war over North Vietnam, in which the Air Force was suffering heavy losses, and the odds of escape for a downed flyer. A parachute descends where the wind puts it. If that place is defended, the descent itself has decided the outcome, and the crewman is a passenger in the decision.

Igor Bensen had been building rotor kites and autogyros of his own design since the early 1950s, from the company he founded in 1952 at Raleigh-Durham in North Carolina, in the Bensen Aircraft entry. The B-8 family was sold as plans to amateur builders, it was simple enough for them to build, and in 1967 Bensen himself set a series of world autogyro records in a B-8M, in the FAI record list. The Air Force did not commission a new aircraft. It ordered modified versions of an existing civil design and gave them an X-designation, a materially different act from every other procurement in this series and one discussed under Where the Framing Breaks Down. The order for modified Bensen autogyros is in Jenkins, Landis and Miller.

In early 1968 three aircraft were ordered for the Discretionary Descent Vehicle evaluation, in the X-25A fact sheet. The powered variant, derived from the B-8M, became the X-25A. The unpowered gyroglider, derived from the B-8, became the X-25B, in the Bensen B-8 entry. The third was the basic X-25, an unpowered gyro-chute intended for one-time use, whose rotor was designed to deploy automatically at any ejection speed and for which no piloted flight is recorded, in Jenkins, Landis and Miller.

The Vehicles

There is more than one X-25 and the distinction is not cosmetic.

	X-25A	X-25B
Basis	Bensen B-8M Gyro-Copter	Bensen B-8 Gyro-Glider
Serial	68-10770	68-10771
First flight	5 June 1968	5 June 1968, with 23 January 1968 in one unsourced entry
Engine	McCulloch four-cylinder two-stroke	none at first, later fitted
Role in the programme	training and technique	towed trainer, training and technique
Now held at	National Museum of the United States Air Force	Air Force Flight Test Museum, Edwards

Both aircraft that flew were trainers, and the vehicle that embodied the escape concept is not known to have flown with a pilot. An escape vehicle has no engine, and the unpowered basic X-25 was that vehicle, while the X-25A and X-25B were used to evaluate piloting techniques and training requirements, in Jenkins, Landis and Miller. The X-25A fact sheet describes the X-25B as an unpowered towed trainer later fitted with an engine, and the X-25A as having a more robust structure and a small engine.

Two specifications are not settled by the public record and the article does not pretend otherwise. The rotor diameter is given as twenty feet in the B-8M description, and a figure of twenty feet six inches for the X-25A could not be confirmed in any source consulted here. The engine is given as seventy-two horsepower in the B-8M description and as ninety horsepower in the X-25A fact sheet, which is also the rating listed for Bensen’s own record-setting B-8M in the FAI record list. Every calculation below uses twenty feet, states that it does so, and is checked for sensitivity to the difference, which is under five percent in the quantity that matters.

Sizing From First Principles

Why a Rotor Autorotates

It is easy to say that the rotor turns because air comes up through it and leave the matter there. That sentence carries the full physical content of the subject and deserves the line of algebra it takes to write down.

Consider a blade element at radius $r$ meeting the resultant flow at inflow angle $\phi$. Its lift acts perpendicular to that flow and its drag along it, so both have components in the plane of rotation. The net in-plane force on the element is

\[dF_{x} = dL \sin\phi - dD \cos\phi \tag{1}\]

The element neither drives the rotor nor retards it when that vanishes, which gives a condition containing nothing but the section’s aerodynamics,

\[\tan\phi = \frac{dD}{dL} = \frac{C_d}{C_l} \tag{2}\]

The equilibrium element is the one whose inflow angle equals its drag-to-lift angle. Inboard of it the inflow angle is larger and the element drives the rotor. Outboard it is smaller and the element is driven. Autorotation is that balance, integrated over the disc, and the rotor settles at whatever speed makes the driving and driven regions cancel,

\[\int_{0}^{R} r \, dF_{x} = 0 \tag{3}\]

For a section lift-to-drag ratio of 15, which is ordinary for a wooden blade, the equilibrium inflow angle is 3.8 degrees. The blade-level machinery is Weick 1926, Propeller design extension of, Kito 1942, Bradley 1956, Nakajima 1960, Fisher et al. 1971, Bobo 1972, Kerwin 1973, Computer Techniques for Propeller 1976, Ballard et al 1979, Effect of tip planform on blade, Ballard et al. 1979b, Effect of tip shape on blade, Ballard et al. 1980, Moxon and Green 1990.

What Autorotation Is

A rotor in autorotation has no shaft power. It turns because the airflow through the disc, which in a descent comes from below, drives the blades instead of being driven by them. Momentum theory describes this as the windmill brake state, a name that is not a metaphor. A wind turbine extracting power from an oncoming stream and a descending rotor holding an aircraft up are the same flow state written in different reference frames, and that identity is the reason a large part of this article’s contemporary literature is about wind energy.

The literature is in Nikolsky and Seckel 1949a, Nikolsky and Seckel 1949b, Slaymaker and Gray 1953, Talbot and Schroers 1978, and Fradenburgh 1984, and the descent-state framework it sits in is Castles and Gray 1951, Azuma and Obata 1968, Shi-cun 1990, and Johnson 2004. The Contemporary Literature carries further records under autorotation, the vortex ring state and the emergency descent.

The Reference Speed

Every rotor quantity in this article is measured against one speed, the induced velocity the same rotor would need in hover. For a rotor of radius $R$ carrying weight $W$ in air of density $\rho$, the disc area and the hover induced velocity are

\[A = \pi R^2, \qquad v_h = \sqrt{\frac{W}{2 \rho A}} \tag{4}\]

where the second expression is the actuator-disc result, in Castles and De Leeuw 1953, Gessow 1954, Castles and Durham 1956, Distribution of normal component, Heyson and Katzoff 1956, Brenckmann 1958, Castles et al. 1958, Heyson 1959, Gray 1960, Liu 1962, Arcidiacono 1964, Jones 1965a, van Gunsteren 1971, Biggers and Orloff 1975, Landgrebe and Egolf 1975, Nagaraja and Pierce 1977, Goodman 1979, Heyson 1980, Hodges 1980, Azuma and Saito 1982, Kawachi 1982, Peters and Chen 1982, Berry and Althoff 1989. The blade-level treatment that has to agree with it is Weick 1926, Propeller design extension of, Kito 1942, Bradley 1956, Nakajima 1960, Fisher et al. 1971, Bobo 1972, Kerwin 1973, Computer Techniques for Propeller 1976, Ballard et al 1979, Effect of tip planform on blade, Ballard et al. 1979b, Effect of tip shape on blade, Ballard et al. 1980, Moxon and Green 1990. The standard modern development of both is Leishman’s helicopter aerodynamics, the analytical treatment is Johnson’s helicopter theory, and the period text contemporary with the X-25 is Gessow and Myers.

For the X-25B, taking a rotor diameter of 20 feet,

\[A = \pi (10 \, \text{ft})^2 = 314.2 \, \text{ft}^2 \tag{5}\]

The gross weight in the escape configuration is not in the public record. Taking 350 pounds, which is a 200 pound crewman with equipment plus a stripped airframe, and sea-level density of $0.002377 \, \text{slug/ft}^3$,

\[v_h = \sqrt{\frac{350}{2 (0.002377)(314.2)}} = 15.3 \, \text{ft/s} \tag{6}\]

The Descent Rate

In steady vertical autorotation the measured descent rate is close to $1.8 v_h$. That number is empirical, and the reason it has to be can be derived. The value comes from a compact and largely mid-century body of measurement, including the analytical study of steady vertical descent in single-rotor autorotation, the analysis of the transition from hovering into autorotative vertical descent, and the power-off flare-up tests of a model rotor, in Irving 1930, Fukatsu 1931, Gessow 1948b, Nikolsky and Seckel 1949a, Nikolsky and Seckel 1949b, Gessow 1950, von Bahr 1950, Slaymaker and Gray 1953, Hickey 1956, Fitch et al. 1970, Buss and Nicholson 1971, Norberg 1973, Baker 1974, Marr 1976, Talbot and Schroers 1978, Iversen 1979, Pleasants and White 1983, Fradenburgh 1984, Gallaway and Hankey 1985, Lee 1985, Decker et al. 1986, Lee et al. 1988, Copeland 1994, Rogers and Asbury 2000.

In the windmill brake state the disc decelerates the oncoming flow by an induction factor $a$, and momentum theory gives the thrust as

\[T = 2 \rho A V_d^2 \, a (1 - a) \tag{7}\]

Setting $T = W$ and substituting $W = 2 \rho A v_h^2$ makes the density and the area cancel, leaving a relation between the descent ratio and the induction factor alone,

\[\left( \frac{v_h}{V_d} \right)^{2} = a (1 - a) \tag{8}\]

The right-hand side is a parabola whose maximum is one quarter, at $a = 1/2$. The left-hand side therefore cannot exceed one quarter either, giving a bound on the descent ratio that contains no property of any rotor,

\[\frac{V_d}{v_h} \geq 2 \tag{9}\]

The measured value is 1.8, and momentum theory has no solution there at all. The quadratic in $a$ has a negative discriminant below a ratio of 2, so there is no induction factor that supports the weight.

The rotor is not beating a bound. The bound exists only inside a model that does not apply at that condition. Between hover and a descent of twice the hover induced velocity the rotor is in the vortex ring and turbulent wake states, the flow recirculates rather than passing through once, and the actuator-disc assumption fails outright. The descent rate must come from measurement because the theory declines to supply one, in Lundberg 1937, Castles and Gray 1951, Arms and Hama 1965, French 1965, Zaroodny 1966, Tung and Ting 1967, Azuma and Obata 1968, Chen and Chang 1972, McCormack 1972, Norbury 1972, Kriebel 1973, Sullivan 1973, Fetter 1974, Sallet 1975, Pullin 1979, Shi-cun 1990, Johnson 2004.

One consequence lands on a table this article prints below. The limiting case $a = 1/2$ corresponds to a ratio of exactly 2, which by the bridge derived next is a drag coefficient of exactly 1 on disc area. The last row of that table is the momentum-theory bound.

\[V_d \approx 1.8 \, v_h = 1.8 (15.3) = 27.6 \, \text{ft/s} = 18.8 \, \text{mph} \tag{10}\]

A Bridge Between Two Literatures That Do Not Cite Each Other

The rotor result and the parachute result are the same statement in different units, and neither field notes it. Treat the rotor as a pure drag device of coefficient $C_D$ referred to disc area,

\[W = \tfrac{1}{2} \rho V_d^2 A \, C_D \quad \Longrightarrow \quad V_d = \sqrt{\frac{2W}{\rho A C_D}} \tag{11}\]

and substitute $W = 2 \rho A v_h^2$, which is the definition of $v_h$ rearranged. The weight, the density and the area all cancel,

\[V_d = \frac{2 v_h}{\sqrt{C_D}} \quad \Longrightarrow \quad C_D = \frac{4}{(V_d / v_h)^2} \tag{12}\]

No property of any particular rotor appears in it. Putting the measured autorotation ratio in,

\[C_D = \frac{4}{(1.8)^2} = 1.23 \tag{13}\]

A flat circular parachute canopy has a drag coefficient near 0.75 referred to its nominal area, meaning the area of the flat fabric before it is inflated, in Knacke’s recovery systems design manual. Both that coefficient and the inflated geometry it goes with are measured quantities with a long test literature behind them, in Walcott 1963, Melzig and Schmidt 1965, Heinrich 1966b, Ross 1970, Mayhue and Bobbitt 1972, Klimas 1977, and Shpund and Levin 1991, and further records appear in the survey’s parachute and decelerator cluster. The area it presents to the flow is smaller, because an inflated canopy is a shallow bowl and not a flat disc, and the two areas are related through the projected diameter,

\[S_p = \left( \frac{D_p}{D_0} \right)^{2} S_0 \tag{14}\]

Its inflated projected diameter is roughly 0.67 of the nominal diameter, so referred to its projected area,

\[C_{D,\text{proj}} = \frac{0.75}{(0.67)^2} = 1.67 \tag{15}\]

The autorotation constant that every rotorcraft text quotes and the drag coefficient that every parachute text quotes are the same physical number. Both devices are swept-area drag devices sitting between about 1.2 and 1.7, and on this measure the rotor is the worse of the two. The decelerator side of the comparison is Eckstrom and Preisser 1967, Peterson and Johnson 1983, and Knacke 1985 and the bluff-body drag beneath it is Stilley 1967, Abraham 1970, Fackrell 1975, Utreja 1977, Ludtke 1982, Richardson 1986, and Williamson 1995, and the survey treats both in full, in its clusters on parachutes and aerodynamic decelerators and on bluff-body drag and the drag coefficient. The canopy coefficients used here follow Knacke’s recovery systems design manual, and the bluff-body drag data behind them is Hoerner’s drag compendium.

The Rotor Is a Worse Parachute Than a Parachute

The comparison has to be made at equal weight first, or the rotor is being penalised for carrying an airframe. The standard personnel canopy in Knacke’s recovery systems design manual is of 28 foot nominal diameter, and it has

\[A_0 = \pi (14)^2 = 615.8 \, \text{ft}^2 \tag{16}\]

which is nearly twice the rotor disc.

Both devices obey the same law, written down here because the article leans on it repeatedly. Define the loading as weight over swept area,

\[\frac{W}{A} = \text{disc loading, or canopy loading} \tag{17}\]

Then the terminal descent of any swept-area drag device follows from the force balance,

\[V_d = k \sqrt{\frac{W / A}{\rho}}, \qquad k = \sqrt{\frac{2}{C_D}} \tag{18}\]

with $k = 1.27$ for the rotor at $C_D = 1.23$ and $k = 1.63$ for the canopy at $C_D = 0.75$. The rotor has the better coefficient and the worse loading, and the loading wins. Sizing practice around this quantity is Gianmarco Sahragard-Monfared et al, Gessow 1948a, Powell 1954, Young and Lytwyn 1967, Jenney et al. 1968, Wright 1969, Miller 1983, Zaitsev 1987.

Since descent rate goes as the square root of loading for both devices, the rotor loses before any coefficient is considered.

Device	Weight, lb	Swept area, ft²	Loading, lb/ft²	Descent, ft/s
28 ft canopy	250	615.8	0.406	21.3
20 ft rotor, equal weight	250	314.2	0.796	23.3
20 ft rotor, as flown	350	314.2	1.114	27.6

The equal-weight comparison has a closed form and the weight cancels out of it, so the nine percent characterises the two devices and is independent of the load. Writing $r$ for the rotor and $c$ for the canopy,

\[\frac{V_{\text{rotor}}}{V_{\text{canopy}}} = \sqrt{\frac{C_{D,c} A_c}{C_{D,r} A_r}} = \sqrt{\frac{0.75 \times 615.8}{1.23 \times 314.2}} = 1.091 \tag{19}\]

Nine percent worse at equal weight and twenty-nine percent worse as flown. A concept sold as a better way down is, in the one respect a parachute exists to serve, a worse one.

But It Is a Wing

Everything above treats the rotor as a brake, and that view misses what it is. A rotor in forward autorotative flight is a rotating wing generating lift with a component of thrust, and it glides. The lift-to-drag ratio of a machine like this is the one performance number the period measured, and Wheatley’s 1933 flight determination of autogiro lift, drag and gliding performance is the direct ancestor of every figure in this section, in Collins 1934, Gliding Flight in Germany 1935, Lamprey 1953, Schiotz and Volsoe 1959, Pennycuick 1960, Durand and Wasicko 1967, Mort and Weiberg 1967, Knapp and Barton 1968, Pennycuick 1968, Pennycuick 1971, Sleeman 1971, McGAHAN 1973, Baudinette and Schmidt-Nielsen 1974, Williamson 1979. Taking a lift-to-drag ratio of 4, which is mid-range for this class of machine, and a best-glide airspeed of 45 miles an hour,

\[\tan\gamma = \frac{1}{L/D}, \qquad V_s = V \sin\gamma \tag{20}\]

At a lift-to-drag ratio of 4 the glide angle is 14.0 degrees, too large to count as a small angle, so the exact form and the convenient one differ,

\[V_s = \frac{V}{L/D} = \frac{66.0 \, \text{ft/s}}{4} = 16.5 \, \text{ft/s} \tag{21}\] \[V_s = V \sin\gamma = 66.0 \sin(14.04^\circ) = 16.0 \, \text{ft/s} \tag{22}\]

The article uses the simpler form throughout, and that form reads three percent high. That is stated openly, and it does not move any conclusion, since the comparison against a canopy descending at 21.3 feet per second is not close.

Now it beats the canopy on descent rate as well, at 16.5 feet per second against 21.3. The glide literature is Collins 1934, Gliding Flight in Germany 1935, Lamprey 1953, Schiotz and Volsoe 1959, Pennycuick 1960, Durand and Wasicko 1967, Mort and Weiberg 1967, Knapp and Barton 1968, Pennycuick 1968, Pennycuick 1971, Sleeman 1971, McGAHAN 1973, Baudinette and Schmidt-Nielsen 1974, Williamson 1979, and Wheatley’s flight determination of autogiro lift and drag in 1933 supplies the underlying measurement.

The Range That Makes Descent Discretionary

\[R = h \, (L/D) \tag{23}\]

Release height, ft	Range, statute miles	Time aloft, minutes
2,000	1.5	2.0
5,000	3.8	4.9
10,000	7.6	9.4
20,000	15.2	17.4

Every Number Above Is at Sea Level and Every Ejection Is Not

Descent rate depends on density, and an escape system is used at altitude by definition.

The density ratio is conventionally written $\sigma$, a notation this article avoids, because the article spends $\sigma$ on rotor solidity under The Material Argument, and one symbol cannot carry both.

\[V_d(h) = V_d(0) \sqrt{\frac{\rho_0}{\rho(h)}}, \qquad \frac{\rho(h)}{\rho_0} = \left( 1 - 6.875 \times 10^{-6} h \right)^{4.256} \tag{24}\]

so a rotor arrives at 20,000 feet descending 37 percent faster than the same rotor at sea level. The tabulated atmosphere behind this is Dubin et al. 1962, U.S. Standard Atmosphere 1962 1962, B-34. U. S. Standard 1963, U. S. Standard Atmosphere 1963, Dubin et al. 1966, U.S. Standard Atmosphere Supplements 1966, Minzner 1967, Pegg 1968, Snell and Heiser 1968, Minzner et al. 1973, Krueger and Minzner 1976, Minzner et al. 1976, U.S. Standard Atmosphere 1976 1976, Minzner 1976, Peters 1977, Johnson et al. 1991, Johnson et al. 1993, Johnson et al. 2002.

The range does not change at all, and the point matters because range is the article’s headline number. The relation displayed above, $R = h (L/D)$, is purely geometric. There is no speed in it and no density in it. A glide ratio is a ratio of distances, so it is the same in any air, and an ejection at twenty thousand feet reaches the same fifteen miles whatever the density does on the way down.

The time aloft does change, and holding the sink rate constant would overstate it. Integrating with density varying,

\[t = \int_{0}^{h} \frac{dz}{V_s(z)} = \frac{1}{V_s(0)} \int_{0}^{h} \sqrt{\frac{\rho(z)}{\rho_0}} \; dz \tag{25}\]

which gives 9.4 minutes from 10,000 feet rather than 10.1, and 17.4 from 20,000 rather than 20.2. The constant-density figure overstates the time by 8 percent at ten thousand feet and 16 percent at twenty. The table under The Range That Makes Descent Discretionary uses the integrated values.

A round canopy travels only with the wind. Seven and a half miles from a ten thousand foot ejection is the entire product. Whether that is worth anything depends on whether seven miles is the difference between capture and recovery, a question about the war and not about the rotor.

The Material Argument

A rotor sweeps its disc with almost nothing in it. Solidity is the ratio of blade area to disc area,

\[\sigma = \frac{N c}{\pi R} = \frac{2 (0.583)}{\pi (10)} = 0.037 \tag{26}\]

so the two blades of an assumed 7 inch chord occupy 11.7 square feet and sweep 314. To match the rotor’s drag area with fabric,

\[C_D A = 1.23 \times 314.2 = 388 \, \text{ft}^2, \qquad S_0 = \frac{388}{0.75} = 517 \, \text{ft}^2 \tag{27}\]

Forty-four square feet of canopy for every square foot of blade. That ratio is the entire engineering appeal of the idea, and the sizing literature behind it is Gianmarco Sahragard-Monfared et al, Gessow 1948a, Powell 1954, Young and Lytwyn 1967, Jenney et al. 1968, Wright 1969, Miller 1983, Zaitsev 1987.

And it loses on mass, the measure that decides. A Bensen rotor with hub and teeter bearing is estimated here to be of order 38 pounds, on the blade mass assumed below. A complete personnel parachute assembly with canopy, lines, harness and container is estimated to be of order 28. Rigid blade is heavy per unit area in the proportion that fabric is light, and the forty-four to one advantage in area comes back as roughly parity in weight.

Dependent Systems

The Rotor

Two blades, teetering, of wood with a Bensen section. The two-blade teetering rotor and the birch of early Bensen blades are in the autogyro entry, and the Bensen G2 section in the B-8 specification. A teetering head removes the flapping hinges and their maintenance, at the cost of being unable to tolerate low or negative load factor, which for a vehicle that must never be pushed over is an acceptable trade. The teetering rotor and blade motion generally are treated in Horvay 1947, Harris 1972, Shamie and Friedmann 1976, Amer and LaForge 1977, Weller and Lee 1977, Dooley and Ferguson 1978, and Glasgow and Corrigan 1982, and the remainder sits with rotors and rotorcraft in the survey.

One number governs how the blade responds, and this article computes its ingredients anyway. The Lock number compares the aerodynamic forcing on a blade to its inertia,

\[\gamma_L = \frac{\rho a c R^4}{I_b}, \qquad I_b = \tfrac{1}{3} m_b R^2 = 12.4 \, \text{slug ft}^2 \tag{28}\] \[\gamma_L = \frac{(0.002377)(5.7)(0.583)(10)^4}{12.4} = 6.4 \tag{29}\]

The Lock number is conventionally written $\gamma$ with no subscript. It is subscripted here because this article has already used $\gamma$ for the glide angle, and a collision between two standard notations is resolved by marking one rather than by silently reusing it.

A helicopter sits between eight and ten, so this blade is heavy for its air loads. Blade inertia and the flapping behaviour it governs are measured subjects and not assumed ones, in Jones 1957, Gaffey 1969a, Johnson 1980a, Wang and Talbot 1989, and Berry and May 1991, with more in the same rotorcraft cluster. That is a liability in responsiveness and an asset in the flare, because inertia is the property that stores energy, and the spin-up analysis under Spinning the Rotor Up turns on it.

Operating tip speed for this class is near 400 feet per second, giving

\[\Omega = \frac{V_{tip}}{R} = \frac{400}{10} = 40 \, \text{rad/s} = 382 \, \text{rpm} \tag{30}\]

which is well below any compressibility concern, in McDonnell Aircraft Corp St Louis Mo 1950, Powell 1959, Sissingh 1964, Spencer et al. 1969, Barry and Magliozzi 1971, Paglino and Beno 1971, Stockman et al. 1973, Arents 1977, Stroub 1978, Stroub et al. 1979, Yeager and Mantay 1981, Leighton 1982, Savino et al. 1985, Mueller et al. 1987, Althoff 1989, Prieur et al. 1989, Mueller et al. 1990, Mueller et al. 1992, Berton et al. 1995.

Two nondimensional numbers place this rotor against every other rotor and against the wind turbine it shares its flow state with. The thrust coefficient refers the load to the dynamic pressure at the tip,

\[C_T = \frac{W}{\rho A (\Omega R)^2} = \frac{350}{(0.002377)(314.2)(400)^2} = 0.0029 \tag{31}\]

and dividing by solidity gives the blade loading coefficient, the quantity that approaches a stall limit near 0.10. Where that limit sits, and how blade area, blade count and chord distribution move it, is a design literature of its own, in Gianmarco Sahragard-Monfared et al, Gessow 1948a, Powell 1954, Young and Lytwyn 1967, Jenney et al. 1968, Wright 1969, Miller 1983, Zaitsev 1987,

\[\frac{C_T}{\sigma} = \frac{0.0029}{0.037} = 0.079 \tag{32}\]

The tip speed ratio compares the tip speed to the flow the rotor sits in,

\[\lambda = \frac{\Omega R}{V_d} = \frac{400}{27.6} = 14.5 \tag{33}\]

A horizontal axis wind turbine runs at a tip speed ratio of six to eight. This rotor runs at fifteen, so it is a very lightly loaded machine in the same flow state, with a correspondingly small induction factor and a thrust coefficient of a few thousandths. The tip speed ratio, the momentum theory and its high-thrust limit are treated in Yang et al. 2016, Bontempo and Manna 2017, Ehrich et al. 2018, Perez-Becker et al. 2020, Hosseini et al. 2022, Boatto et al. 2023, and Wood and Golmirzaee 2023, and the survey collects the rest of it under wind turbines, energy harvesting and the windmill state.

Spinning the Rotor Up

The obvious objection to the concept is that a parachute inflates and a rotor has to be spun up. A standard 28 foot personnel canopy is fully open in about one to three seconds, in Knacke’s recovery systems design manual. A rotor at rest produces nothing. The energy has to come from somewhere and the only bank available is height.

Treating each blade as a uniform rod about the hub,

\[I = N \cdot \tfrac{1}{3} m_b R^2 = 2 \cdot \tfrac{1}{3} (0.373)(100) = 24.9 \, \text{slug ft}^2 \tag{34}\] \[E = \tfrac{1}{2} I \Omega^2 = \tfrac{1}{2} (24.9)(40)^2 = 19{,}900 \, \text{ft lb} \tag{35}\] \[h = \frac{E}{W} = \frac{19{,}900}{350} = 57 \, \text{ft} \tag{36}\]

Fifty-seven feet if every particle of potential energy went into the rotor, and a few hundred feet at any believable efficiency. That is plausibly comparable to the height a canopy loses while it inflates.

There is a small surprise buried in that arithmetic and it matters later. Substituting the inertia and the operating speed into the energy,

\[E = \tfrac{1}{2} I \Omega^2 = \tfrac{1}{2} \left( N \tfrac{1}{3} m_b R^2 \right) \left( \frac{V_{tip}}{R} \right)^{2} = \frac{N}{6} m_b V_{tip}^2 \tag{37}\]

The radius has cancelled. At a fixed blade mass and a fixed tip speed, a rotor stores the same energy whatever its size, because the inertia rises as the square of the radius exactly as fast as the operating angular speed falls. Shrinking a rotor costs nothing in stored energy.

Energy held in a turning rotor is a separate subject, and the period expresses it as an autorotative index rather than as a quantity of foot pounds, in Dooley and Yeary 1979. The literature on it is not separable from the autorotation literature proper, since a paper on autorotative landing is a paper about spending this energy, and the relevant work is cited above, under autorotation and blade motion. It costs a great deal elsewhere, and that bill arrives in the Comparison With Ground Prediction section below.

The objection fails. This is a negative result and it is reported as one, because the energetic argument against the Discretionary Descent Vehicle is the first one anybody reaches for and it does not survive being written down. No record in the survey treats spinning a rotor up from rest, which would refine it, and that makes spin-up the thinnest topic in this article. It is discussed under The Source Base.

An Irreversible Step in the Deployment

Here lies one plausible ground for the doubts about feasibility, and that ground is not aerodynamic.

The documented concept was a vehicle stowed in the aircraft, ejected with the pilot and deployed during the descent, its rotor brought up to speed as it fell, in the X-25A fact sheet. The record consulted here does not say how a personnel parachute fitted that sequence. If the crewman left the aircraft by ejection seat in the ordinary way, let the parachute open and spun the rotor up in that descent, the sequence would end by cutting the parachute away. Written as a trade, the crewman gives up a canopy already descending at 21 feet per second and working, in exchange for a rotor descending at 16.5 feet per second with a four-to-one glide. If the gyro-chute instead replaced the canopy, the crewman’s survival would rest on a rotor designed to deploy automatically at any ejection speed, including supersonic, for which no piloted test is recorded, in Jenkins, Landis and Miller.

The gain is range. The gain is not survival of the descent, which was already assured. In the cutaway sequence the step that secures it cannot be undone, is taken seconds after an ejection, and is taken by someone who may be injured, disoriented, or under fire. On escape systems the relevant work is Poteate and Solomonides 1964, Bement 1979, Ford 1979, Hawker and Payne 1979, and Cummings 1982 and the tolerance question underneath it is Snyder 1959, McKenney 1970, Glaister 1978, and Laananen 1980. The survey’s cluster on crew escape, ejection and the human in the escape holds both in full.

Flying It

An autogyro is not an intuitive aircraft. Rotor speed must be respected, the machine is unforgiving of mishandling in a way a parachute cannot be because a parachute offers nothing to mishandle, and a gyroplane landing is a skill. Prouty on helicopter performance, stability and control supplies the performance and control framework. The record states that the X-25A and X-25B were flown to evaluate piloting technique and to determine training requirements, in Jenkins, Landis and Miller, a programme treating the operator as a question in its own right, although the X-25A fact sheet reports that pilots could be quickly and easily trained to fly the X-25. The handling and training literature it belongs to includes Daughaday and Duwaldt 1955, Drinkwater and Feistel 1965, Caro and Isley 1966, Barnes and Statham 1970, Seville Research Corp Pensacola FL 1979b, Intano and Howse 1991, and Hess 1995, and the cluster on flight test, handling qualities, training and piloting technique lists the rest.

The Flight Test Record

Both aircraft flew and the record of what they measured is extremely thin.

The inventory by Jenkins, Landis and Miller gives 5 June 1968 as the first flight of the type, and Guinness World Records gives the same date for the X-25B, flown at Edwards. The Bensen B-8 entry assigns 5 June 1968 to the X-25A and 23 January 1968 to the X-25B without a source for either, and its text elsewhere dates the Air Force study of the two aircraft to May 1968. This article adopts 5 June 1968 for both. Under the alternative the X-25B would have flown 134 days before the X-25A, which would settle the order of first flights, and no other result here depends on the date. Testing concerned how the aircraft should be flown and what training a pilot needed. No full-scale operational test of the concept was ever performed, meaning that the sequence the idea depends on, which is ejection followed by rotor deployment in the descent, was never demonstrated as an integrated system by this programme, and no piloted flight of the gyro-chute that embodied it is known. Funding ended as the American involvement in Vietnam wound down, and with it the Air Force’s interest, in the same inventory, and the X-25A fact sheet adds doubts about the concept’s operational feasibility as a second reason.

What the X-25 demonstrated is that a person can be taught to fly a small autogyro. What it did not demonstrate is anything about escaping from an aeroplane. The fact sheet reports that training was quick and easy, and the inventory records no piloted test of the escape vehicle. The gap between those two statements is the programme.

Comparison With Ground Prediction

The X-25 itself returned no published measurement this article can check a model against. A second vehicle does allow the check, one the model was not built from.

The Kaman KSA-100 SAVER, for Stowable Aircrew Vehicle Escape Rotorseat, was the same concept carried further for the United States Navy. Its rotor was two telescopic blades folded into the seat itself, deployed by a drogue within four seconds of ejection. It flew towed on 28 December 1971, free the following day with a non-telescoping rotor, and with the telescoping rotor on 10 January 1972. Kaman made over 1,500 air drops of the deployment system, and a full-scale unpowered article was tested in the National Aeronautics and Space Administration Ames full-scale tunnel in 1970, in the Kaman KSA-100 SAVER entry. The concept paper, which also reports the 1970 tunnel test, is the description by Hollrock and Barzda 1972 of a stowable autogyro that serves as the crewman’s seat and converts to a flight vehicle after ejection.

Stowability forces the geometry, and the geometry forces the descent rate. A rotor that must fold into a seat cannot be 20 feet across. The Kaman KSA-100 SAVER entry gives the SAVER’s as 14. Since

\[V_d \propto \frac{\sqrt{W}}{R} \tag{38}\]

a smaller radius at a larger weight is punished twice.

	X-25B	SAVER
Rotor diameter, ft	20	14
Disc area, ft²	314.2	153.9
Weight, lb	350 assumed	710 documented
Disc loading, lb/ft²	1.11	4.61
Vertical autorotation, ft/s	27.6	56.1

Fifty-six feet per second is 38 miles an hour straight down. A steady vertical descent at that rate is not survivable, and the difference would have to be retrieved in the flare out of stored rotor energy.

That sentence is easy to write and should be checked, because it need not have been true. It is, and the check is short.

The energy a flare must absorb is the kinetic energy of the descent,

\[E_{req} = \tfrac{1}{2} \frac{W}{g} V_d^2 \tag{39}\]

and substituting the descent rate turns it into a function of weight and radius alone,

\[E_{req} = \frac{(1.8)^2}{4 g \rho \pi} \cdot \frac{W^2}{R^2} \tag{40}\]

The energy required goes as the square of the weight over the square of the radius, while the energy available goes as neither. Dividing one by the other gives a margin whose only free quantity is the assumed blade mass,

\[\frac{E_{avail}}{E_{req}} = \frac{2 N m_b V_{tip}^2 \, g \rho \pi R^2}{3 (1.8)^2 W^2} \tag{41}\]

	X-25B	SAVER
Weight, lb	350	710
Rotor radius, ft	10	7
Descent rate, ft/s	27.6	56.1
Energy required, ft lb	4,130	34,700
Energy available, ft lb	19,900	19,900
Margin	4.8	0.57

The X-25B carries nearly five times the energy its flare needs. The SAVER carries about half. Inverting the margin to unity asks what the blades would have to weigh,

\[m_b = \frac{3 (1.8)^2 W^2}{2 N V_{tip}^2 g \rho \pi R^2} \tag{42}\]

which is 2.5 pounds a blade for the X-25B and 21 pounds a blade for the SAVER, against the 12 assumed for both. A vehicle whose entire design constraint was folding into an ejection seat would have needed blades close to twice as heavy as a Bensen’s.

Where the argument from stowability alone was qualitative, this result is quantitative, and the two point the same way. It still depends on an assumed blade mass and tip speed for a vehicle whose real figures are not published, so it is offered as an order-of-magnitude estimate rather than a measurement. Doubling the assumed blade mass still leaves the SAVER at a margin of 1.15, which is no margin at all for an escape system.

The model therefore predicts that a stowable rotor seat needs an engine, and the SAVER had one, a Williams WRC-19 turbofan of 430 pounds thrust, which the Kaman KSA-100 SAVER entry records.

The prediction must not be overclaimed and it is not. The record gives off-the-shelf availability as the reason the engine was fitted and notes that it was more powerful than the seat needed, and the design rating for the operational seat’s engine in Hollrock and Barzda 1972 is a sea-level thrust of 1,280 newtons, about 290 pounds. A thrust to weight ratio of

\[\frac{T}{W} = \frac{430}{710} = 0.61 \tag{43}\]

is far above anything a gyroplane needs to sustain flight, so the descent problem evidently did not size the engine. The prediction is directionally right and quantitatively unconfirmed, and what can be claimed is that the scaling law explains why a stowable seat is a harder vehicle than a carried one, not that it explains Kaman’s engine selection.

What the Data Changed

Almost nothing directly. The Discretionary Descent Vehicle did not enter service. No operational aircraft has ever carried one, and no full-scale operational test was ever conducted, in Jenkins, Landis and Miller.

The question outlived the answer. The SAVER pursued the same idea with a stowable rotor and an engine and was also cancelled, the military concluding the idea was not viable, in the Kaman KSA-100 SAVER entry. What survived is the question, namely whether a descending crewman should have a choice of landing point.

That question was answered, and the answer was made of fabric. A ram-air parachute is a wing built from cloth. It reaches lift-to-drag ratios of about three, with 3.2 for a parafoil vehicle system in Knacke’s recovery systems design manual, close to the ratio of 4 assumed here for an autorotating rotor, and it does so with a device that packs into a container, needs no spin-up, has no rigid parts, and, by this article’s inference, asks less of its user, although the one training result recorded for the X-25 was favourable, in the X-25A fact sheet. The rotor’s forty-four to one advantage in material area was answered by a device that sweeps no disc at all and generates lift as a wing. That literature begins in the period work on gliding parachutes and flexible wings, in Rogallo et al. 1960, Rogallo 1962, Horton 1962, Ryan Aeronautical Co San Diego Ca 1962, Taylor and McNulty 1962, Johnson and Sleeman 1963, Rogallo 1963, Libbey 1964, Forehand and Bair 1969, Nicolaides and Tragarz 1971, Kenner 1972, Rogallo et al. 1972, Matsuo and Butler 1983, and its ancestor is the Rogallo wing, which NASA studied through the 1960s as a recovery device for spacecraft and which was under active investigation at the same moment the X-25 was flying.

The Contemporary Literature

Cluster	Records
Rotors and rotorcraft, momentum theory and blade dynamics	794
Parachutes and aerodynamic decelerators	307
Autorotation, the vortex ring state and the emergency descent	248
Crew escape, ejection and the human in the escape	194
Autogiros and gyroplanes	184
Ram-air canopies, parafoils and guided airdrop	189
Electric vertical takeoff, drones and distributed lift	146
Flight test, handling qualities, training and piloting technique	141
Wind turbines, energy harvesting and the windmill state	109
Samaras, monocopters and animal flight	96
Rotor and propeller noise, and the tip speed	85
Rotors at low density, on Mars and at low Reynolds number	58
Rotary decelerators and rotor recovery systems	32
Bluff-body drag and the drag coefficient	28
The final descent and the touchdown	20
Wings, airfoils and the lift-to-drag ratio	19
Gliding flight and the sink rate	16
The standard atmosphere and the flight condition	17
V/STOL and other vertical-lift aircraft	10
Other aeronautical and foundational literature	14
Total	2,707

The Discretionary Descent Vehicle asked a good question and got the wrong answer, and the right answer arrived in a different material. This section surveys the present state of every thread the programme touched.

Two of those threads have become livelier since 1968 instead of quieter, and both land on the keystone. Autorotation is now a certification argument about aircraft that cannot perform it, and the density relation this article derives is being tested on another planet.

When the Engine Stops, Now

Autorotation is no longer primarily an aerodynamic subject. It is a safety and training subject, and the literature has moved with it. Contemporary work covers the safety analysis of autorotative landing execution, the transfer of autorotation training between simulator and aircraft, the height-velocity diagram for variable-speed rotors, emergency landing after engine failure including on hybrid electric tiltrotors, and rotorcraft crashworthiness, in Murugan et al. 2014, Tokuoka and Miwa 2015a, Ligai et al. 2017, Chi et al. 2019, Yan and Chen 2019, van der Wall 2019, Astori et al. 2020, White et al. 2021, Scaramuzzino et al. 2022, Lee et al. 2023, Francesco Scaramuzzino et al. 2024, Germanetti 2024, Serafini et al. 2024.

The height-velocity diagram is the direct descendant of this article’s spin-up section. It maps the combinations of height and forward speed from which a safe autorotative landing cannot be reached, and it exists because entering autorotation costs both altitude and time. The X-25’s deployment problem is the same problem drawn on different axes.

Autorotation Became a Computation

Autorotation is now modelled, optimised and flown by algorithm, no longer characterised by test pilots. The contemporary work covers trajectory optimisation for autorotative landing, entry transients, vortex-ring modelling and autonomous emergency descent, in Rezgui and Lowenberg 2015, Sunberg et al. 2015, Taamallah et al. 2017, Zheng et al. 2018, Talaeizadeh et al. 2020, Tomita and Fujiwara 2021, Saetti et al. 2023, Patnala et al. 2024, and Mori et al. 2025, and the autorotation cluster below adds further titles.

The Answer Arrived in Fabric

The ram-air canopy is the device the Discretionary Descent Vehicle was reaching for. It reaches nearly the same glide ratio as an autorotating rotor with no rigid structure, no spin-up transient and a training demand this article infers to be lower, and its existence plausibly explains why no aircraft carries a rotor seat, although no document of the programme makes that connection. Its glide ratio is measured and controlled in Bozack 1984, Wegereef et al. 2009, and Sun et al. 2020a, and the contemporary literature on the canopy includes Cacan and Costello 2018, Zhang et al. 2021b, Ding et al. 2023, and Vambol et al. 2023, and the ram-air cluster carries the rest.

And Then It Was Automated

The second half of the answer removes the crewman from the control loop entirely. Guided precision airdrop steers a ram-air canopy to a surveyed point without a person aboard, which is discretionary descent with the discretion delegated to software, in Chiel and Dever 2015, Geiselman et al. 2015, Slegers et al. 2015, Mukhopadhyay et al. 2016, Wachlin et al. 2019, Ivanovic and Orsag 2022, Leeman et al. 2022, Wang et al. 2022b, Yan et al. 2023, Wei et al. 2024b, Qi et al. 2025b.

The Machine That Cannot Do It

The X-25 would find this thread the most interesting, and it did not exist in 1968.

Electric vertical takeoff aircraft have brought the small one-person or few-person flying machine back as a serious industry, with certification-constrained design, conceptual design methods and a safety literature behind it, in Brown and Harris 2020, Cokorilo 2020, Lee et al. 2020, Ma et al. 2022, Ugwueze et al. 2023, and Xie et al. 2023. The cluster on electric vertical takeoff, drones and distributed lift continues the list.

A multirotor cannot autorotate. A helicopter rotor stores energy in a large disc turning fast, and a lift rotor on a distributed-propulsion aircraft is small, lightly loaded and often fixed in pitch, so the two properties autorotation needs are both absent. In this article’s terms, the stored energy is

\[E = \frac{N}{6} m_b V_{tip}^2 \tag{44}\]

and a small light blade turning at modest tip speed has very little of it, while the disc loading that sets the descent rate is high because the disc is small. The X-25’s rotor was a bad parachute and a good glider. A multirotor is neither.

The industry has answered with redundancy instead of a better rotor, meaning enough independent lift units that the loss of one is survivable, a safety philosophy completely different from the one the X-25 embodies. Autorotation says the aircraft can always become a glider. Redundancy says the aircraft will not fail in the first place. That argument is being had in the contemporary literature on rotor failure, fault-tolerant control and propulsion redundancy, which the same electric vertical takeoff cluster collects.

No finding of this survey is sharper. The capability the Discretionary Descent Vehicle was built entirely around is the one the current generation of small rotorcraft has quietly given up, and it gave it up for a reason the X-25 would have recognised, namely that the rotor you can carry is not the rotor you want.

The Same Physics, Now Called Wind Energy

The windmill brake state is no longer an emergency. It is a business. A wind turbine rotor is an autorotating rotor in a different reference frame, and the blade-element momentum machinery this article uses to size a descent is the same machinery used to size a turbine. The largest living body of work on the X-25’s keystone physics is in wind energy, as the count of blade element momentum titles in the wind turbine cluster shows, and its application to turbines runs through Dehouck et al. 2017, Apsley and Stansby 2020, Potentier et al. 2021, Yin et al. 2022, Le et al. 2025, and Selvatici and Stevens 2025.

The Rotor at One Percent of Sea Level

Descent rate goes as one over the square root of density, and that relation is now being tested at an extreme no terrestrial machine reaches.

A rotorcraft flying on Mars operates in roughly one percent of sea-level density. Everything this article derives about disc loading and descent follows the same algebra there, and the consequences are severe and practical. Such vehicles therefore carry very large rotors for their mass and turn them fast, with blade tips at up to seven tenths of the speed of sound on the Ingenuity helicopter. The contemporary work on rotor aerodynamics at low density and low Reynolds number is San Martin et al. 2017, Koning 2019, Koning et al. 2019a, Koning et al. 2019b, Serré et al. 2019, Zhao et al. 2019, Harris 2020, Koning et al. 2020, McElreath et al. 2020, Chen and Hubner 2021a, Fox 2021, Gojon et al. 2021, Kamruzzaman et al. 2021, Kruesi 2021, Leslie 2021, Veismann et al. 2021, Zhang and Yang 2021, Nepal et al. 2023, Yamaguchi and Anyoji 2023, Bowman et al. 2024, Wang et al. 2024d, Zhao et al. 2025, Datta et al. 2026, tang et al 2026.

The article’s own altitude section is the same calculation stopped early. A rotor at twenty thousand feet descends 37 percent faster than at sea level. A rotor at Martian density would descend about ten times faster, and that factor of ten justifies the comparison.

The Seed Had It First

Autorotation is not an invention. A maple samara descends by autorotating, and the contemporary rotary-decelerator and micro air vehicle literature cites it directly, in Deng 2015, Dormiyani et al. 2015, Liu et al. 2015, Pounds and Singh 2015, Liu 2016, Wu et al. 2017b, Li and Guo 2018, Porritiello et al. 2022, Suhadi et al. 2022, Tong et al. 2022, Cai et al. 2025, Huang et al. 2026a, Zhang et al. 2026.

How Loud the Tips Are

This article assumed a tip speed of 400 feet per second and never said what bounds it. At the upper end the limit is compressibility on the advancing blade. At the lower end it is stored energy, which this article has already shown goes as the square of tip speed. In between, and dominating modern design, sits noise. Rotor noise rises steeply with tip speed, and community noise acceptability has become a design driver and no longer a courtesy, in van der Wall et al. 2017, Greenwood and Schmitz 2018, Szulc and Doerffer 2018, Yang et al. 2018a, Shukla and Komerath 2019, Sou 2019, Yang et al. 2019b, Jia and Lee 2020, Li and Lee 2020, Polyzos et al. 2020, Bauer et al. 2021, Vouros et al. 2021, Lukianov 2022, Nowoświat et al. 2022, Thurman and Baeder 2023, Greenwood et al. 2023, Fu et al. 2023, Kingan et al. 2023, Su Jung et al. 2023, Buǧday and Saetti 2024, Goudswaard et al. 2024, Johnson-Groh 2024, Saetti et al. 2024a, Shao et al. 2024, Yuk et al. 2024, Arystanbekov et al. 2025, Boucher 2025, Jung et al. 2025, Pereira et al. 2025, Turhan et al. 2025, Melo et al. 2026, Philipps-Bertin et al. 2026, Stefan J Letica and Stephen A Rizzi 2026.

That is a constraint the X-25 did not have and an electric vertical takeoff aircraft cannot escape, and it pushes tip speed down while the stored-energy argument wants it up.

The Gyroplane Did Not Disappear

The X-25’s type is still flying and still being written about, with contemporary work on gyroplane flight dynamics, stability and experimental rotor measurement, in Czyż et al. 2015, Shin and Kim 2015, Wu 2015, Figat 2017, Houston and Thomson 2017, Stalewski 2017, Cai et al. 2018, Czyż et al. 2018, Lee et al. 2018, Stalewski 2018, Лучко and Зінченко 2018, Design of Composite Gyrocopter 2019, Wojtas and Sobieszek 2019, Czarnigowski 2020, Rezgui and Lowenberg 2020, Łusiak 2022.

Its safety record is the part that bears on this article. The gyroplane acquired a poor safety reputation through designs prone to a power push-over, a pitch departure that unloads the rotor, in the autogyro entry. Such a property would weigh against the type for a person who has just ejected and has no rotorcraft training, although the X-25A fact sheet reports a favourable training result for the X-25.

Rotors on Everything

The small rotorcraft the X-25 represented as a curiosity is now an industry. Electric vertical takeoff vehicles, multirotors and distributed propulsion have made rotor sizing an everyday design problem, in Hwang et al. 2015, Multi-Rotors 2015, Lei and Cheng 2020, and Lei and Wang 2020.

Escape Systems Now

Crew escape remains an active discipline concerned with injury criteria and occupant protection rather than with flight after ejection, in Do and deWeck 2011, Maloney 2011, Buller 2017, Kowaleczko et al. 2018, Sarkar et al. 2018, Mao and Liang 2019, Perry et al. 2019, Wang et al. 2019b, Ying 2019, Bao et al. 2021, Ejection Seat Testing 2021, Lakshmi et al. 2021, Saravanan et al. 2021, Smitha et al. 2021, Somanath et al. 2021, Sreenivasulu et al. 2021, Liu et al. 2022a, Schultz et al. 2022, Rahman et al. 2023, Zhou et al. 2023, Avirah et al. 2024, Rahman et al. 2024, Kowaleczko et al. 2025, Parate 2025, Rahman et al. 2025, Davidescu et al. 2026, Du et al. 2026.

What the Survey Shows

Every thread the X-25 touched is alive, and the one it was about has been abandoned twice over.

The physics is thriving under a different name, because the windmill brake state is a wind turbine’s operating condition and blade element momentum theory is now worked hardest by people generating electricity. The mission is being flown, but by guided ram-air canopies rather than by rotors, and increasingly without a person in the loop at all. The vehicle concept is dead, and the capability it was built around has been given up a second time by the industry that most resembles it, because a multirotor cannot autorotate and has chosen redundancy instead.

Three things this survey establishes that the programme record alone does not.

The question was good. Giving a descending crewman a choice of landing point is a real capability, now routinely delivered, since military personnel parachute assemblies use manoeuvrable parafoils as main and reserve canopies in Knacke’s recovery systems design manual, which retrospectively vindicates the Air Force for asking.

The answer was wrong in a way that was knowable at the time. The arithmetic that shows a rotor to be a worse decelerator than a canopy, and valuable only because it glides, needs nothing that was not available in 1968. So does the observation that the gain is range rather than safety, and that any sequence through an open parachute would end by cutting a working parachute away.

And the concept did not fail on the axis the programme examined. Jenkins, Landis and Miller record that the aircraft were flown to settle questions of piloting and training, and the X-25A fact sheet reports both that the training was quick and easy and that the programme ended with the air war winding down and doubts about its operational feasibility. What ended it was a lapsed need and a doubt that no recorded test addressed.

Rotors and rotorcraft, momentum theory and blade dynamics

The rotor in general, and the largest cluster. Helicopter and rotor aerodynamics, momentum and blade element theory, wakes and inflow, blade dynamics and aeroelasticity, and the structure of the blade and the hub. 46 percent of these records are report primaries, against 19 percent of the autorotation cluster, so the reports servers document the rotor in powered flight far more fully than the rotor in descent, which is the keystone’s thinness seen from the other side.

794 records. [Abrego et al. 2016] [Acree 1984] [Acree et al. 2001] [Adelman and Mantay 1988] [Advanced Design Rotor Blade 1985] [Agarwal et al. 2022] [Ahmadi 1984] [Aiken et al. 2000] [Aldawsari 2025] [Gessow 1954] [Ali et al. 2015] [Althoff 1988, Effect of advanced rotorcraft] [Althoff 1989] [Althoff et al. 1988a, Inflow measurement made with a] [Althoff et al. 1988b, Inflow measurements made with a] [Amer 1989] [Amer and LaForge 1977] [Amer et al. 1964] [Anderson and Johnston 1974] [Anderson and Watts 1975] [Andrew Woodgate and N․ Barakos 2026] [Andrews 1941] [Arcidiacono 1964] [Arents 1977] [Army Materiel Command Alexandria VA 1974b] [Army War Coll Carlisle Barracks Pa 2006] [Arnold 2025] [Artis 1975] [Arush et al. 2022] [Arıol Taymaz 2022] [Attachment of a Rotor 1991] [Augustyniak 2016] [Azuma and Saito 1982] [Bagai and Leishman 1992] [Bailey 1939] [Bailey 1941] [Bailly and Bailly 2019] [Balaji 2017] [Balcerak 1967] [Balcerak et al. 1969] [Balch 1979] [Balch 1985] [Bales et al. 1973] [Ballard et al. 1979a, Effect of tip planform on blade] [Ballard et al. 1979b, Effect of tip shape on blade] [Ballard et al. 1980] [Barbely et al. 2016] [Barkley and Weaver 1977] [Baron et al. 1964] [Bauchau and Hong 1987] [Bauchau and Lemnios 1997] [Berman 1956] [Berman 1965] [Berry 1982] [Berry and Althoff 1989] [Berry and May 1991] [Berry and Schrage 1986] [Berry et al. 1987] [Berton et al. 1995] [Bhardwaj et al. 2023] [Bielawa 1988] [Biggers and Orloff 1975] [Bishop 1958] [Blackwell 1977] [Blankenship and Harvey 1962] [Blythe 2007] [Bobo 1972] [Boeing Co Morton Pa Vertol Div 1961b] [Boeing Co Morton Pa Vertol Div 1961a] [Boeing Vertol Co Philadelphia Pa 1977a] [Boeing Vertol Co Philadelphia Pa 1977b] [Boisard 2021] [Bolanovich and Marks 1959] [Bottasso and Montinari 2015] [Bousman 2003] [Bouzidi et al. 2020] [Bowen-Davies and Yeo 2018] [Bradley 1956] [Bradley 2016] [Bramwell 1966] [Brender et al. 1996] [Briardy et al. 1970] [Britton 1992] [Brown and Fisher 1968] [Brown and Schmidt 1963] [Buccio et al. 2026] [Burke 1996] [Burkhardt 1985] [Burpo and Lynn 1962] [Kobayashi and Jessup 1985] [Lee 1989] [Calcaterra and Schubert 1969] [Cameron and Sirohi 2019] [Cameron et al. 2016] [Cao et al. 2021] [Cao et al. 2024a] [Cao et al. 2024b] [Caprace et al. 2020] [Cardinale 1969] [Carico and Blemel 1998] [Carlson and Cassarino 1973] [Carlson and Hilzinger 1965] [Case 1985] [Cassarino 1970] [Castillo-Rivera and Tomas-Rodriguez 2020] [Castles and De Leeuw 1953] [Castles and Durham 1956a, Distribution of normal component] [Castles and Durham 1956b] [Castles et al. 1958] [Catapang 1993] [Celi 1991] [Cerbe and Reichert 1989] [Chang and Ai 2026] [Chappell 1979] [Chattopadhyay 1993] [Chattopadhyay and Chiu 1990a] [Chattopadhyay and Chiu 1990b, An enhanced integrated] [Chattopadhyay and Jones 1992] [Chattopadhyay and Walsh 1990] [Chattopadhyay et al. 1989] [Chattopadhyay et al. 1997] [Chawla 1952] [Chen 1980a] [Chen 1980b] [Chen and Hubner 2021b] [Chen and Liu 2015] [Chen et al. 1984] 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Parachutes and aerodynamic decelerators

The device the rotor is compared against. Parachute aerodynamics and inflation, canopy fabrics and stress, clusters, recovery systems and the decelerators of atmospheric entry. 27 of these titles name Mars, another planet or an atmospheric entry, and 11 name the personnel parachute that this article’s comparison actually uses.

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[Laswell 1973] [Lavier 1955a] [Lavier 1955b] [Lavrakas 1955] [Li 2015] [Li and Yu 2026] [Li et al. 2023b] [Liang and Mease 2019] [Liang et al. 2024] [Lindstrand 2003] [Lingard et al. 1989] [Lorenz et al. 2021] [Lowry et al. 2026] [Ludtke 1973] [Ludtke 1982] [Ludtke 1991] [Lundstrom et al. 1968] [Lyalin and Morozov 2005] [MacCarthy 1954] [Makarov et al. 2022] [Maru et al. 2021] [Mastropietro et al. 2015] [Andreini et al] [Matz and Braun 2015] [Mayhue and Bobbitt 1972] [McCarty 1978] [McMenomy 2022] [Meacham et al. 2013] [Melzig and Schmidt 1965] [Menard 1967] [Meyer 1958] [Miller 1954] [Minimum Performance Standard for] [Minimum Performance Standard for] [Minimum Performance Standards for] [Minnesota Univ Minneapolis Inst Of Tech 1962] [Moog et al. 1979] [Moore 2013b] [Moore 2013a] [Moorman and Yechout 2009] [Mori and Kuzuo 2018] [Mort and Weiberg 1967] [Mortaloni and Stewart 1999] [Mukhopadhyay et al. 2016] [Muramoto and Garrard 1984] [Murman 2009] [Murray 1961] [Murro and Whitlock 1963] [Naidoo] [Neustadt et al. 1967] [Nie et al. 2023] [Niederer and Mihora 1972] [Niemi and Bevillard 2015] [Niemi et al. 1995] [Niemi 1992] [O’Farrell et al. 2022] [Parate 2020] [Payne and Band 1976] [Payne and Band 1977] [Pedersen 1961] [Pedersen 1964] [Pepermans et al. 2023] [Pepper and Biesterveld 1973] [Pepper and Holt 1971] [Peterson and Johnson 1983] [Peterson et al. 1986] [Petranelli et al. 2015] [Placco 2023a] [Placco 2023b] [Placco 2024] [Placco et al. 2025] [Placco et al. 2026] [Preisser et al. 1967] [Puthalapattu 2025] [Ray 2015] [Ray and Morris 2011] [Reinhard et al. 1997] [Reza et al. 2007] [Richardson et al. 2005] [Robb et al. 2026] [Rodier et al. 1989] [Roelke et al. 2025] [Deshmukh et al. 2024] [Ross 1970] [Ruisseau et al. 2000] [Runkle and Drobnik 1979] [Runkle and Woodis 1979] [Rychnovsky 1979] [Sahu et al. 1995] [Sahu et al. 1997a] [Sahu et al. 1997b] [Sanganeria 2025] [Schaefer et al. 2001] [Schairer et al. 2018] [Sengupta et al. 2008] [Sengupta et al. 2009] [Shannon 2001] [Shepardson 1954] [Sherer 1945] [Shpund and Levin 1991] [Silbert et al. 1989] [Sims 1963] [Singh et al. 2017] [Skelton and Abbott 1974] [Smollett 1955] [Specification for mercerized cotton] [Stein 2005] [Steinberg et al. 1973] [Stevens 1983] [Stewart 2013] [Behera et al. 2024] [Study on Critical Parachute 2024] [Sullivan 1944] [Sulsky et al. 2010] [Sun et al. 2025] [Sweeney 1955] [Tang et al. 2015] [Tanner et al. 2013] [Tanner et al. 2015] [Teng and Li 2017] [Terahara et al. 2025] [Thielman and Thielman 1997] [Tiaden and Yakimenko 2008] [Tiaden and Yakimenko 2009] [Tibbits and Ivanov 2015] [Tomcsak 1960] [Tsao 2015] [Tutt et al. 2003] [Tutt et al. 2022] [Unitary Plan Wind Tunnel 1962] [Usry 1969] [Utreja 1977] [Varela and Ray 2013] [Vergnolle and Astorg 1991] [Vishnyak 1995] [Wailes and Carlson 1986] [Walcott 1963] [Wang 2018] [Wang et al. 2026b] [Watkins 1995] [Waye 1991] [Wei 1991] [Whitting et al. 2006] [Whitting et al. 2007] [Witkowski 1999] [Witkowski et al. 2022] [Witkowski et al. 2026] [Worth 1965] [Wu et al. 2021b] [Yakimenko 2017] [Yakimenko et al. 2008] [Xue 2021] [Yang et al. 2015] [Yang et al. 2018b] [Yang et al. 2020] [Ye et al. 2026] [Yue et al. 2016b] [Yue et al. 2016a] [Zhang et al. 2024] [Zhang et al. 2025b] [Zhang et al. 2027] [Zhu et al. 2023b] [Zhu et al. 2024] [Бабаков and Финченко 2022] [Вищекин et al 2023, Equipment for Parachute-free]

Autorotation, the vortex ring state and the emergency descent

The keystone. Autorotation of rotors, plates and wings, the vortex ring state, power-off and steep descent, the height-velocity diagram and the emergency landing after an engine failure. 74 of these titles name a vortex ring, 14 name the height-velocity diagram and 33 concern unmanned rotorcraft, multirotors or electric vertical takeoff aircraft, so the descent states the X-25 lived in are now studied as hazards to small machines as well as to helicopters.

248 records. [Chen and Chang 1973] [Huang et al. 2020] [Mohamed and Abas 2007] [Abrego et al. 2001] [Abrego et al. 2002] [Ahlin and Brown 2009] [Alles et al. 2010] [Ananthan et al. 2002] [Anderlik 1926] [Andrien and Talaeizadeh 2022] [Aponso and Bachelder 2003] [Arms and Hama 1965] [Askue 2001] [Avanzini et al. 2017] [Azuma and Obata 1968] [Bachelder et al. 2011] [Baker 1974] [Barakos et al. 2026] [Batther et al. 2024] [Benson et al. 1978] [Betzina 2001] [ONERA et al. 2025] [Blahitko et al. 2021] [Bohr and Markvorsen 2016] [Brand et al. 2007] [Bucherelli et al. 2026] [Buss and Nicholson 1971] [Bustamante et al. 1967] [Carlson et al. 2006] [Castles and Gray 1951] [Celi and Ribera 2007] [Chae et al. 2022] [Chen and Chang 1972] [Chen and Prasad 2005] [Chen et al. 2004] [Chenglong et al. 2015] [Chenglong et al. 2018] [Chi et al. 2019] [Cocco et al. 2024] [Coombes et al. 2017] [Cooper et al. 1966] [Copeland 1994] [Coronado Domenge et al. 2016] [Cuerva-Tejero et al. 2006] [Czyż et al. 2021c] [Czyż et al. 2022] [Davis et al. 1965] [Viets 1973] [De Vore et al. 1963] [Decker et al. 1986] [Deel et al. 1972] [Deng et al. 2021] [Deresz 2013] [Dosaev 2018] [Durai raj 2024] [Dziubinski and Stalewski 2007] [Eberle and Rogers 2020b] [Eberle and Rogers 2020a] [Eberle and Rogers 2021] [Eberle et al. 2022] [Efimov and Chernigin 2022] [Elkhaldi et al. 2020] [Fallast and Messnarz 2017] [Fang et al. 2023] [Farajijalal et al. 2025] [Fattizzo et al. 2026] [Feil and Hajek 2021] [Feng et al. 2026] [Fetter 1974] [Fitch et al. 1970] [Fradenburgh 1984] [Francesco Scaramuzzino et al. 2024] [Fukatsu 1931] [Gallaway and Hankey 1985] [Gessow 1948b] [Gessow 1950] [Gessow and Myers 1947] [Grande et al. 2016] [Grzegorczyk 2013] [Hahn et al. 2025] [Harris et al. 2018] [He et al. 2000] [Hepler and Free 1974] [Hickey 1956] [Hoinville and Renaud 2007] [Houston and Brown 2003] [Ignatkin et al. 2018] [Ignatkin et al. 2019] [Improved Blade Element Theory 2023] [Inoue et al. 1997] [Irving 1930] [Isbono 2026] [Iseler et al. 1995] [Ishiko and Uno 2018] [Iversen 1979] [Jeong et al. 2024b] [Jeong et al. 2024a] [Jeong et al. 2026] [Jingze 2011] [Johnson 1977] [Johnson 2004] [Joseph et al. 2026] [Junchao and Li 2012] [Kesselring 1969] [Kim and Choi 2011] [Kirchner et al. 2020] [Knight 1928] [Knight and Wenzinger 1930] [Korbukov and Menzulskiy 2024] [Kriebel 1973] [Langelaan and Grande 2013] [Lee 1985] [Lee 1990] [Lee et al. 1988] [Lee et al. 2008] [Lee et al. 2023] [Li et al. 2023c] [Ligai et al. 2017] [Logan et al. 1982] [Lopez and Wells 2004] [Lopez et al. 2023] [Lovell and Lipson 1949] [Lu et al. 2023] [Makeev 2026a] [Makeev et al. 2021a] [Makeev et al. 2021b] [Makeev et al. 2022] [Makeev et al. 2024] [Marr 1976] [Marshall et al. 2024] [Matlala and Pedro 2016] [McCormack 1972] [McDonnell Aircraft Corp St Louis Mo 1950] [McIntyre 1970] [McQuaid 2021] [McQuaid et al. 2020] [Meng and Chen 2012] [Modarres and Peters 2016] [Mori et al. 2024] [Mori et al. 2025] [Morozov et al. 2020] [Murakami and Houston 2008] [Narkiewicz and Bibik 2008] [Nikolsky and Seckel 1949a] [Nikolsky and Seckel 1949b] [Noiri and Fujuwara 2016] [Norbury 1972] [Ober 1929] [Okuno et al. 1991] [Oshima et al. 1983] [Kim 2004b] [Patnala et al. 2024] [Pegg 1968] [Peters and Chen 1982] [Peters and Wasileski 2000] [Pickles et al. 2023a] [Pickles et al. 2023b] [Pleasants and White 1983] [Prasad and Basset 2002] [Prasad and Chen 2006] [Pratumnopharat and Leung 2011] [Privalov and Samsonov 1994] [Pullin 1979] [Qi et al. 2025a] [Yu et al. 2014] [Report No. 273 Wind 1928] [Rezaei et al. 2024] [Rezgui and Lowenberg 2015] [Richter 2020] [Riegler et al. 2025] [Rigsby and Prasad 2008] [Rodriguez Varona 2026] [Roger and Aubert 1999] [Rogers and Asbury 2000] [Rogers et al. 2018] [Rostami and Fernandes 2015] [Rostami and Fernandes 2018] [Rovedatti et al. 2024] [Saetti et al. 2023] [Salcedo et al. 2013] [Sallet 1975] [Scaramuzzino et al. 2022] [Scarpari et al. 2021] [Schmidt 1931] [Schrenk 1930] [Serafini et al. 2024] [Setu and Abhishek 2019] [Shapley et al. 1970] [Shen and Chopra 2004] [Sheridan et al. 1982] [Shetty and Selig 2011] [Shi-cun 1990] [Simulation of Vortex Ring 2015] [Sirohi et al. 2004] [Slaymaker and Gray 1953] [Slaymaker et al. 1952] [Smith 1971] [Stalewski and Surmacz 2019] [Stalewski and Surmacz 2020] [Stone and US Atomic Energy Commission (AEC) 1967] [Suggs 1969] [Sullivan 1973] [Sunberg et al. 2015] [Surmacz and Kowaleczko 2016] [Szabolcsi 2016] [Taamallah 2012] [Taamallah et al. 2017] [taheri and delavet 2024] [Talaeizadeh et al. 2020] [Talaeizadeh et al. 2021] [Talbot and Schroers 1978] [Tokuoka and Miwa 2015a] [Tokuoka and Miwa 2015b] [Tomita and Fujiwara 2021] [Toropov and Stepanov 2016] [Tran and Lopez 2024] [Tran and Lopez 2025] [Tung and Ting 1967] [Uchiyam 2015] [Veismann et al. 2023] [von Bahr 1950] [Váňa et al. 2020] [Wang et al. 2018a] [Wang et al. 2020] [Wang et al. 2025a] [Washizu et al. 1965] [Watts et al. 1971] [Wei 2021] [Wei et al. 2000] [Wen et al. 2022] [Wilson and Prazenica 2020] [Wood 2012] [Xin et al. 2019] [Yan and Chen 2018] [Yan and Chen 2019] [Yan et al. 2019] [Yan et al. 2022] [Yan et al. 2024a] [Yano and Morrison 2024] [Yeates 1958] [Yomchinda et al. 2011] [Zalewski 2016] [Zaroodny 1966] [Zeng et al. 2024] [Zheng et al. 2018] [Zhou et al. 2026b] [Zhou et al. 2026a] [Безденежных et al 2020]

Crew escape, ejection and the human in the escape

The human side of the escape. Ejection seats, escape capsules and systems, crashworthiness, injury and human tolerance, and aircrew life support. 92 of these titles name ejection, and 23 concern helicopters, rotors or rotary-wing aircraft.

194 records. [Anthony 2005] [Army Aviation Board Fort Rucker Al 1962] [Army Aviation School Fort Rucker Al 1956] [Aryaman et al. 2023] [Astori et al. 2020] [Aveline and Fowlie 1987] [Avirah et al. 2024] [Bader and Coleman 1967] [Bao et al. 2021] [Bement 1978] [Bement 1979] [Bement 2000] [Bierman 1959] [Blachowski and Ostrowski 1995] [Blachowski and Ostrowski 2000] [Blachowski and Ostrowski 2001] [Bonas and Reilly 1955] [Boyd 2019] [Bozack 1970] [Budd CO Fort Washington PA Technical Center 1978] [Buller 2017] [Carr 1975] [Chen et al. 2007] [Cheng and Pellettiere 2005] [Cheng et al. 2003] [Chiang 1980] [Chicarello and Shpilberg 1976] [Cloutier 1967] [Computational Aerodynamic Analysis 1994] [Connors and Sachs 1957] [Cota and Lee 1967] [Cummings 1982] [Danelson et al. 2015] [Davidescu et al. 2026] [DeCleene 1994] [Dehua et al. 2006] [Dillon et al. 1990] [Disselkoen et al. 1989] [Do and deWeck 2011] [Dolinar 2000] [Douglas Aircraft Co Long Beach Ca 1983] [Downwards Escape from Jet 1956] [Du et al. 2026] [Effectiveness of Ejection Seat 1950] [Ejection Seat Testing 2021] [Ekman and Debacker 2018] [Elson et al. 1997] [Failure by Stress-Corrosion Cracking 2019] [Ford 1979] [Ford 1985] [Fortunato 2002] [Frazier and McElreath 1976] [Gilewicz 1978] [Glaister 1978] [Goodman and McMichael 2007] [Gragg et al. 1982] [Griffin 1975b] [Gross and Mawhinney 1970] [Guan et al. 2013] [Habchi and Hufford 1995] [Habchi et al. 1992] [Hawker and Payne 1979] [Hegenwald 1958] [Hellyer and Sherhod] [Hodell and Rosner 1957] [Hoffman 1996] [Hollrock and Barzda 1972] [Howland 1979] [Hrebien and Hendler 1983] [Huffman et al. 1977a] [Huffman et al. 1977b] [Hufford and Habchi 1994] [Itt Systems Rome Ny 1987] [Jia-Lin et al. 2014] [Jines 1980] [Jines 1983] [Johnson 1986b] [Johnson 1989b] [Littell and Putnam] [Keller and Plaga 2008] [Kelly 1967] [Kennedy 1999] [Kenzakowski et al. 1997] [Kiehl 1960] [Kowaleczko et al. 2018] [Kowaleczko et al. 2025] [Kwan et al. 2003] [Laananen 1978] [Laananen 1980] [Labun 2014] [Lakshmi et al. 2021] [Liedtke and Hyde 1967] [Liu et al. 2022a] [Liu et al. 2022b] [Liu et al. 2025a] [Lorch 1981] [Lowry et al. 1994] [Maloney 2011] [Manzuk 1970] [Mao and Liang 2019] [Mao et al. 2011] [Martin 1956] [Mather 1968] [McEntire and Shanahan 1997] [McKenney 1970] [McKinnon et al. 2017] [Meadley et al. 2023] [Melis et al. 2020] [Ming et al. 2016] [Mizrahi and Susak 1982] [Moore et al. 2026] [Mou et al. 2024] [Murtaza and Indluru 2026] [Murugan et al. 2014] [Newby et al. 2014] [Nixon et al. 2020] [Oakes 1967] [Obergefell and Kaleps 1988] [Ojetola et al. 2011] [Parate 2022] [Parate 2025] [Parisi 2004] [Payne 1969] [Perry 2007] [Perry et al. 2019] [Piacentino et al. 1978] [Pilot Escape Capsule 1961] [Pinnell and Kolega 1973] [Pint et al. 2003] [Poteate and Solomonides 1964] [Project EGRESS 1990] [Qiu et al. 2012] [Rahman et al. 2023] [Rahman et al. 2024] [Rahman et al. 2025] [Rahman et al. 2026] [Ratts 1995] [Reason 1999] [Robbins 1978] [Robert 1988] [Rock and Habchi 1997] [Rock et al. 1999] [Ryack et al. 1984] [Sadler and McCauley 2003] [Saravanan et al. 2021] [Sarkar et al. 2018] [Savkovic 2008] [Scherberg and Ferguson 1952] [Schultz et al. 2022] [Shane 1985a] [Shane 1985b] [Shender 2000] [Shi et al. 2025] [Singh and Wereley 2015] [Smitha et al. 2021] [Snyder 1959] [Somanath et al. 2021] [Sommer et al. 2023] [Sreenivasulu et al. 2021] [Stapp and Taylor 1964] [Stech 1977] [Stein 1965] [Strietzel and Shefler 1963] [Swingle 1995] [Tauby 1979] [Teresa M Reiber et al] [Teresa Reiber et al] [The Advanced Stabilised Ejection 1974] [The Biomechanics of Impact 2018] [Tian and Chen 2012] [Turnbow et al. 1967] [Wang et al. 2014] [Wang et al. 2019b] [Wang et al. 2024e] [Wang et al. 2024b] [Watts et al. 1947] [Weinberg 1963] [Weinberg and Turnbow 1965] [West et al. 1980] [Wolf 2019] [Wong and Mastroianni 1999] [Wright 2012] [Xiaodong et al. 2010] [Xu et al. 2011] [Yang et al. 2011] [Yang et al. 2025b] [Ying 2019] [Yu et al. 2017] [Zanoosi et al. 2021] [Zenobi 1977] [Zenobi 1978] [Zhang and Yi 2011] [Zhao et al. 2015] [Zhou et al. 2023]

Autogiros and gyroplanes

The type the X-25 belonged to. Cierva’s autogiro, the NACA’s period rotor tests and the light and unmanned gyroplanes of the present. 53 of these records date from 1945 or earlier, when the autogiro was a serious aircraft, and 9 are chapters of one history of the type, among them Chapter 11 IGOR BENSEN 2003 on Igor Bensen and the gyrocopter.

184 records. [Ahmad and Thomson 2020] [Ahn et al. 2002] [Alfaro 1932] [Anh Vu et al. 2011] [Bailey 1938] [Bailey 1940] [Bailey and Boothby 1940] [Bailey and Gustafon 1939] [Bailey and Gustafson 1940] [Bennett 1932] [Bennett 1933] [Bose 1983] [Breguet 1937a] [Breguet 1937b] [Cai et al. 2018] [Chapter 10 THE AUTOGIRO 2003] [Chapter 11 IGOR BENSEN 2003] [Chapter 13 FAILURE 2003] [Chapter 15 THE EMERGING 2003] [Chapter 2 CIERVA’S AUTOGIRO 2003] [Chapter 4 PITCAIRN 2003] [Chapter 5 DEVELOPMENT 2003] [Chapter 6 AMERICAN ADVANCES 2003] [Chapter 9 THE AUTOGIRO 2003] [Charnov 2003a] [Charnov 2004] [Charnov 2009] [Charnov 2011] [Charnov 2014] [Charnov 2018] [Chenglin et al. 2022] [Colson 1934] [Commercial Pilot 1996] [Coton et al. 1998] [Crowe 1938] [Czarnigowski 2020] [Czyż et al. 2015] [Czyż et al. 2016] [Czyż et al. 2017] [Czyż et al. 2018] [Czyż et al. 2021b] [Czyż et al. 2021a] [Czyż et al. 2023] [Czyż et al. 2025] [de la Cierva 1926] [de la Cierva 1930] [Design of Composite Gyrocopter 2019] [Dewey 2021] [Doberentz et al. 2020] [Dziubiński et al. 2016] [Efficiency of the Autogyro 1929] [Ejaz et al. 2017] [Fang et al. 2019] [Dominggo Bayu Baskara 2017] [Feng et al. 2025] [Fiedoruk et al. 2026] [Figat 2017] [Flight Instructor 1996] [Flores et al. 2019] [Galisteu et al. 2015] [Gan et al. 2026] [Gilruth 1937] [Glauert 1927] [Greenly 1962] [Gregory 1941] [Groen 2003] [Gustafson 1940] [Gustafson 1941] [Głowacki et al. 2026] [Hafner 1938] [Hamilton 1938] [Harris and Dow 2015] [Hau et al. 2021] [Heyson 1975] [Hohenemser 1938] [Hou et al. 2017] [Hou et al. 2021] [Houston 1998b] [Houston 1998a] [Houston 2000] [Houston 2011] [Houston and Thomson 2017] [Houston et al. 1998] [Hunt 1967] [J. and Martín-Barbadillo 1936] [Jakliński and Ścisłowski 2025] [Jensen 2001] [Wheatley 1934c] [Jones and Niewoehner 2023] [Kalmykov and Barsuk 2011] [Kay 331 Gyroplane British 1935] [Klemin 1929] [Klemin and Ruffner 1931] [Larsen 1956] [Lee et al. 2018] [Li et al. 2018b] [Lin et al. 2014] [Lin et al. 2016] [Liu et al. 2017] [Liu et al. 2023] [Lowenberg et al. 2009] [Lu and Chen 2012] [Ma et al. 2015] [Magryta et al. 2017] [McConnell and Das 2022a] [McCormick 2002] [McDougall 1965] [Moore-Brabazon 1934] [Niemi and Gowda 2011] [Noboni and Das 2025] [Noboni et al. 2023] [Noboni et al. 2025] [Іщенко et al. 2005] [Osaji and Farrokhfal 2009] [Osborn 1929] [Peck 1934] [Petritoli and Leccese 2020] [Petritoli and Leccese 2021] [Pitcairn 1930] [Practice for Continued Airworthiness] [Prewitt 1938] [Private Pilot Practical Test 1996] [Qing 2017] [Report No. 515 Full-Scale 1935, Report no. 515, full-scale] [Report No. 536 Wind 1936] [Rezgui and Lowenberg 2020] [Rezgui et al. 2008] [Robinson and Jump 2011] [Santiago et al. 2020] [Schad 1965] [Schrenk 1938] [Seiferth 1927] [Shaanan 2025] [Shin and Kim 2015] [Shippen 1996] [Shippen 1998] [Sissingh 1939] [Sobieszek 2016] [Somov and Polyntsev] [Somov and Polyntsev 2004] [Somov and Polyntsev 2005] [Song et al. 2017] [Spathopoulos 2004] [Specification for Design and] [Stalewski 2017] [Stalewski 2018] [Standard Specification for Integration] [Standard Specification for Light] [T.K.C. 1932] [The Autogiro 1925] [The Cierva “Autogiro” Mark 1930] [The Essential Autogiro/autogyro/gyrocopter/gyroplane History 2003] [The Hafner A.R. III 1937] [Thomson and Houston 2005] [Thomson and Houston 2008] [Traum 2011] [Vainilavičius et al. 2014] [Wallis 1963a] [Wallis 1963b] [Wang and Tang 2016] [Wang et al. 2016] [Wang et al. 2019a] [Wheatley 1933] [Wheatley 1934b] [Wheatley 1934a] [Wheatley 1935a] [Wheatley 1935b] [Wheatley 1936] [Wheatley 1937a] [Wheatley 1937b] [Wheatley 1945] [Wheatley and Bioletti 1936] [Wheatley and Bioletti 1937] [Wojtas and Sobieszek 2019] [Wu 2015] [Wu et al. 2014] [Xiang et al. 2014] [Xiang et al. 2015] [Xiaoqian Cheng et al. 2016] [Yan Ma et al. 2016] [Zhang and Xu 2011] [Zhang et al. 2014] [Łusiak 2022] [Лучко and Зінченко 2018]

Ram-air canopies, parafoils and guided airdrop

The answer to the programme’s question. Ram-air canopies, parafoils, parawings and guided airdrop. 24 of these titles name the glide or a gliding parachute, and 80 name guidance, homing, a trajectory or its control, so a large part of this literature treats the canopy as a vehicle to be steered rather than as a brake, which is the capability the Discretionary Descent Vehicle wanted.

189 records. [Autonomously Guided Ram-Air Parachute 2009] [Balraj Gupta et al. 2023] [Barrows 2009] [Behr et al. 1991] [Berexa et al. 2019] [Bergeron et al. 2015] [Berland et al. 2005] [Bozack 1984] [Brown 1989] [Brown 1993] [Brown et al. 1991] [Cacan and Costello 2018] [Cacan et al. 2015] [Cacan et al. 2019] [Cao et al. 2026] [Chakoian 1969] [Chambe et al. 2024] [Chang et al. 2018] [Charles 2017] [Chatzikonstantinou 1999] [Chen et al. 2019b] [Chen et al. 2021a] [Chiel and Dever 2015] [Civelek and Kıvrak 2024] [Cui et al. 2025a] [Cui et al. 2025b] [Desabrais et al. 2015] [Devalla et al. 2016] [Ding et al. 2023] [Doran et al. 2025] [Dowling and Costello 2018] [Dunker and Berland 2007] [Eslambolchi and Johari 2013] [Fan et al. 2026] [Wang et al. 2015b] [Fields et al. 2012] [Fields et al. 2013] [Fogell et al. 2017] [Forehand and Bair 1969] [Leonard et al. 2019] [Leonard et al. 2020] [Olenberger 1978] [Rogallo 1962] [Gang 2015] [Gao and Tao 2022] [Gao et al. 2016c] [Gavrilovski et al. 2011] [Geiselman et al. 2015] [Ghoreyshi et al. 2014] [Ghoreyshi et al. 2015] [Goodrick 1969] [Goodrick 1981] [Gunasinghe et al. 2017] [Guo et al. 2026] [Güven and Şamiloğlu 2022a] [Güven and Şamiloğlu 2022b] [Han 2018] [He et al. 2022] [Hiraki et al. 2007] [Hirst and Jorgensen 1995] [Horton 1962] [Hua et al. 2013] [Ibos et al. 1999] [Irvine 1968] [Ivanovic and Orsag 2022] [Jann 2003] [Jann and Ward 2019] [Jin et al. 2027] [Johnson and Sleeman 1963] [Jóźwiak and KurzawiŃSki 2019] [Kaminer et al. 2005] [Kenner 1972] [Kim and Song 2015] [Kim et al. 2016] [Knapp and Barton 1968] [Kraft et al. 2017] [Leeman et al. 2022] [Lewis 1964] [Li and Nan 2023] [Li and Yan 2021] [Li et al. 2024b] [Libbey 1964] [Libbey 1965] [Lingard 2015] [Lissaman and Brown 1993] [Liu et al. 2016] [Long et al. 2021] [Luan et al. 2026] [Lucrezia 2023] [Lv et al. 2019] [Lv et al. 2020] [Madsen and Cerimele 2000] [Madsen et al. 2003] [Matsuo and Butler 1983] [Michal et al. 1970] [Mkrtchyan and Johari 2011] [Modular Heavy Payload Autonomously 2009] [Mohammadi and Johari 2009] [Mohammadi and Johari 2010] [Montalvo and Costello 2016] [Montanez et al. 1997] [Mort 1967] [Newberg et al. 2026] [Nicolaides 1971] [Nicolaides 1976] [Nicolaides and Tragarz 1971] [Noetscher and Barber 2005] [Ortega et al. 2017] [Pearson 1972] [Pearson et al. 1977] [Peralta and Johari 2015] [Perin and Patoux 2022] [Perschbacher and Potvin 1999] [Potvin 1997] [Potvin 2001b] [Potvin 2001a] [Potvin and Peek 1998] [Potvin and Potvin 1997] [Potvin et al. 1997] [Prateek Sazawal and Ghosh 2023] [Puskas 1984] [Puskas 1989] [Qi et al. 2025b] [Rogallo 1963] [Rogallo et al. 1960] [Rogallo et al. 1972] [Ryan Aeronautical Co San Diego Ca 1962] [Seidel and Bergeron 2017] [Seidel et al. 2016] [Shaw 2016] [Sleeman 1971] [Slegers 2017] [Slegers et al. 2015] [Smith et al. 2001] [Sun et al. 2020b] [Sun et al. 2020a] [Surendra et al. 2015] [Szafran and Kramarski 2019] [Takizawa et al. 2016] [Tan et al. 2019] [Tan et al. 2023] [Tao et al. 2016] [Tao et al. 2017] [Tao et al. 2019] [Tardiff et al. 2015] [Taylor and McNulty 1962] [Trovarelli and Mooij 2019] [Vambol et al. 2023] [Velasquez and Benedict 2015] [Wachlin et al. 2019] [Wang and Yang 2024] [Wang et al. 2022b] [Ward and Costello 2013] [Ward et al. 2011] [Ward et al. 2013] [Ward et al. 2024] [Wegereef et al. 2009] [Wegereef et al. 2011] [Wei and Pearson 1974] [Wei et al. 2024b] [Wei et al. 2026] [Wenqian et al. 2016] [Wu et al. 2017a] [Wu et al. 2018] [Wyllie et al. 1997] [Xing et al. 2023] [Xing et al. 2024] [Xu et al. 2025a] [Yan et al. 2023] [Yan et al. 2025] [Yan et al. 2026] [Yang and Jeon 2019] [Yang et al. 2025a] [Yang et al. 2026] [Yi et al. 2025] [Yu et al. 2022] [Yu et al. 2025a] [Yu et al. 2025b] [Yu et al. 2026] [Zhang et al. 2021a] [Zhang et al. 2021b] [Zhang et al. 2022] [Zhang et al. 2023] [Zhao et al. 2020] [Zhao et al. 2021] [Zheng et al. 2023] [Zhu et al. 2022a] [Zhu et al. 2023a] [Zou et al. 2025]

Electric vertical takeoff, drones and distributed lift

The machine that cannot do it. Electric vertical takeoff aircraft, multirotors and other unmanned rotorcraft, their sizing, aerodynamics, failure and safety, and distributed propulsion. None of these 146 records is older than 2004, and 31 titles name fault tolerance, redundancy or the failure of a rotor, motor or actuator, which is the redundancy argument of this article posed as a design problem. Across the whole survey 11 titles join autorotation to a multirotor, a drone or an unmanned aircraft.

146 records. [Abdul Awal 2017] [Abergo et al. 2026] [Abhiram et al. 2018] [Afari et al. 2023] [Ahmadi Dastgerdi and Nabavi-Chashmi 2026] [Akash et al. 2021] [Alulema et al. 2026] [Ambroziak et al. 2023] [Arace et al. 2026] [Atte and Rauleder 2026] [Awad and Stumpf 2022] [Baldini et al. 2020] [Bauer et al. 2021] [Beak and Kim 2026] [Bhandari et al. 2024] [Bhatnagar and Dr 2016] [Boucher et al. 2023] [Brown and Harris 2020] [Cai 2015] [Chakraborty and Mishra 2023a] [Chakraborty and Mishra 2023b] [Chakraborty et al. 2023] [Charnsethikul et al. 2025] [Chen et al. 2025] [Choi et al. 2026] [Chung and Son 2020] [Cokorilo 2020] [Critchfield and Ning 2026] [Dalwadi et al. 2022a] [Dalwadi et al. 2022b] [Danis et al. 2018] [Darvishpoor et al. 2025] [Evdokimenkov et al. 2024a] [Evdokimenkov et al. 2024b] [Falconì et al. 2018] [Gokbel and Ersoy 2021] [Goldschmidt et al. 2024] [Gu and Tian 2023] [Gu et al. 2025] [Haefner et al. 2026] [Healy et al. 2021] [Hou et al. 2020] [Huang et al. 2026b] [Hwang et al. 2015] [Immersion and Invariance Adaptive 2026] [Ishaque et al. 2026] [Jayakumar et al. 2026] [Jebelli et al. 2024] [Jia and Li 2025] [Jiang and Zhang 2016] [Jiang and Zhang 2018] [Jiang et al. 2015] [Johnsen et al. 2022] [Jun et al. 2026b] [Kaneko and Martins 2024] [Li and Lee 2021] [Khoshnood 2025] [Kikumoto et al. 2026] [Kim et al. 2025] [Koo 2020] [Kotwicz Herniczek et al. 2019] [Kusumoaji et al. 2024] [Lee and Yee 2024] [Lee et al. 2020] [Lee et al. 2022a] [Lei and Cheng 2020] [Lei and Wang 2020] [Lei and Ye 2020] [Lei et al. 2020] [Lei et al. 2021] [Lei et al. 2023a] [Lei et al. 2023b] [Li 2025] [Li and Lee 2024] [Li et al. 2022] [Li et al. 2023a] [Liang et al. 2026] [Liao et al. 2025] [Lien et al. 2020] [Logan et al. 2017] [Haworth et al] [Lovas 2026] [Lu et al. 2016] [Lu et al. 2026] [Lympany and Page 2024] [Ma et al. 2022] [Ma et al. 2025] [Mao et al. 2022] [Mathur and Atkins 2023] [McKay et al. 2019] [Merheb et al. 2017] [Misiorowski et al. 2020] [Moschetta 2010] [Mpanza and Pedro 2025] [Mrusek 2021] [Multi-Rotors 2015] [Nam et al. 2024] [Nasr et al. 2026] [Oyama et al. 2024] [Page and Bailey 2025] [Papadopoulos et al. 2024] [Perfect et al. 2017] [Piccinini et al. 2020] [Poggi et al. 2024] [Qiao and Zhou 2026] [Rostami et al. 2023] [Sadasivan 2019] [Saetti et al. 2022] [Saias et al. 2021] [Saias et al. 2023] [Saied et al. 2019a] [Saied et al. 2019b] [Saied et al. 2024] [Sajid et al. 2026] [Sajjadi et al. 2025] [Shi 2024] [Whiteside and Pollard] [Simha and Ambroziak 2025] [Simon 2024] [Smith et al. 2023] [Wright] [Strampe and Klingauf 2026] [Takita and Kashitani 2019] [Turhan et al. 2025] [Ugwueze et al. 2023] [Vempati et al. 2024] [Venkataraman et al. 2017] [Verbeke and Schutter 2017] [Villeneuve et al. 2022] [Wang and Zhang 2018] [Wang et al. 2017] [Wang et al. 2019c] [Wang et al. 2023] [Wang et al. 2024f] [Wang et al. 2026a] [Wei et al. 2024a] [Westcott et al. 2023] [Wilbur and Wilkie 2004] [Xie et al. 2023] [Yan et al. 2024c] [Yanev and Staack 2026] [Yu et al. 2024a] [Yu et al. 2024b] [Zhao et al. 2024] [Zhyriakov et al. 2025] [孙 2025]

Flight test, handling qualities, training and piloting technique

How the aircraft were flown and how pilots learn to fly them. Flight test method, handling and flying qualities, simulation and pilot training. 26 of these titles name training, a trainee, instruction or a simulator, which is the subject the record says the X-25 testing addressed.

141 records. [Abbott et al. 1982] [Advisory Group for Aerospace Research and Development 1999] [Aiken 1986] [Air Force Flight Test Center Edwards AFB CA 1974a] [Air Force Flight Test Center Edwards AFB CA 1974b] [Air Force Test Pilot School Edwards Afb Ca 1992] [Aircraft and Rotorcraft System 2016] [Alford and Knarr 1999] [Anderson and Toivanen 1970] [Army Aviation Board Fort Rucker Al 1964] [Army Materiel Command Alexandria VA 1974a] [Barbini et al. 1970] [Barnes and Statham 1970] [Baron 1981] [Beeler et al. 2003] [Bender et al. 1984] [Beppu and Curtiss 1966] [Blackburn and Whitfield 1965] [Boirun 1979] [Borobia et al. 2018] [Branson 1994] [Brauser 1982] [Brown et al. 1975] [Buckanin and Guin 1977] [Buckland 1980] [Carico 2000] [Caro and Isley 1966] [Carter and Stultz 1958] [Chen and Talbot 1978] [Cleek and Alan J. 1978c] [Cochran 2015] [Cook and Hickey 1975] [Crawford and Hodgson 1961] [Daughaday and Duwaldt 1955] [DaŞ and Kumpas 2019] [Director Army Safety Office Washington DC 1993] [Dominick and Watts 1967] [Dooley 1977] [Dooley and Yeary 1979] [Drinkwater and Feistel 1965] [Ferrell et al. 1974] [Finnestead and Connor 1969] [Finnestead et al. 1970] [Fosdick 1970] [Gainer and Sullivan 1976] [Garrard and Liebst 1990] [Garrard and Low 1990] [Gerlach 1979] [Germanetti 2024] [Godwin et al. 1964] [Grant 1961] [Ham et al. 1995] [Hammon and Horowitz 1990] [Harper and Sardanowsky 1969] [Head 1959] [Hepler et al. 1973] [Herbst et al. 2015] [Hess 1995] [Hodgkinson 2017] [Hoh and Ashkenas 1981] [Hughes and Wernicke 1974] [Hutto 1975] [Intano and Howse 1991] [Hassell and Kirby 1966] [Jensen et al. 1991] [Johnson and Anderson 1966] [Johnson and Boling 2015] [Johnson et al. 1972] [Johnson et al. 1973] [Jones 2017] [Kalra et al. 2023] [Kidd and Bull 1963] [Kidwell and Foster 1966] [Kim and Kim 2020] [Knapp 1971] [Lawrence 2014] [Lintern 1979] [Low and Garrard 1993] [Masarati et al. 2015] [Mehling et al. 2022] [Melton and Hall 1968] [Minotra and Feigh 2020] [Muscarello et al. 2017] [Müllhäuser and Lusardi 2022] [Na and Cho 2022] [Nagata et al. 1968] [Nagata et al. 1973] [Nagata et al. 1981] [New Light on Pilot 1973] [Paul et al. 2025] [Perez et al. 2026] [Picasso et al. 1982] [Staff, Psychological Research Project (Pilot) 1946] [Putman 1961] [Rash et al. 2001] [Ritter et al. 1971] [Rostad et al. 2003b] [Rostad et al. 2003a] [Saetti et al. 2019] [Salord Losantos and Sánchez-Arriaga 2015] [Sanders 1972] [Schmeisser et al. 2008] [Schroeder et al. 2001] [Schroers and Antoniou 1966] [Schumacher 1952] [Schwartz and Wray 1969] [Serafini et al. 2015] [Seville Research Corp Pensacola FL 1979b] [Seville Research Corp Pensacola FL 1979a] [Sharkey et al. 2005] [Simon and Savage 1975] [Simpson 1979] [Sinacori 1986] [Singh 2019] [Smode 1979] [Somerville et al. 2025] [Somerville et al. 2026] [Somsel 1970] [Spring et al. 1979] [Staley 1976] [Stange 1959] [Stelle et al. 2003] [Stendahl 1985] [Stone and Ralph W. 1946] [Stringer et al. 1972] [Tangler 1979] [Thomas et al. 2023] [Turkoglu 2018] [Vague and Seibel 1959] [Van Gaasbeek 1980] [Van Wyckhouse 1966] [Watson et al. 2025] [Wesolek 2007] [White et al. 2021] [Wolkovitch and Hoffman 1971] [Woomer and Carico 1977] [Yamakawa et al. 1972a] [Yamakawa et al. 1972b] [Yamakawa et al. 1977] [Yamakawa et al. 1978] [Zhang et al. 2025a]

Wind turbines, energy harvesting and the windmill state

The same physics in another reference frame. Wind turbine rotor aerodynamics, wakes and inflow, blade element momentum theory and the use of autorotation to harvest energy. 42 of these titles name blade element or momentum theory, against 31 in the cluster on rotors and rotorcraft, so on this measure the largest living body of work on the keystone’s physics is in wind energy.

109 records. [Abbas et al. 2024] [Abedi and Eskilsson 2025] [Abutunis et al. 2019] [Adema et al. 2026] [Andersen et al. 2024] [Apsley and Stansby 2020] [Araneo et al. 2019] [Ariyoshi et al. 2017] [Augusto et al. 2019] [Bai and Shiah 2016] [Baisthakur and Fitzgerald 2024] [Bakhshandeh Rostami and Fernandes 2015] [Bangga et al. 2020] [Berger and Kühn 2018] [Bhargava and Samala 2019] [Boatto et al. 2023] [Bontempo and Manna 2017] [Bromm et al. 2016] [Chabaud 2021] [Cheung et al. 2024] [Cole et al. 2020] [Corniglion et al. 2022] [Dehouck et al. 2017] [Ehrich et al. 2018] [Eliassen et al. 2015] [Erhard and Strauch 2015] [Fang et al. 2021] [Ferreira et al. 2022] [Fu 2026] [Greco and Testa 2021] [Guo and Ganapathysubramanian 2017] [He and Xia 2022] [Herráez et al. 2017] [Hosseini et al. 2022] [Ichter et al. 2015] [Iliev 2025] [Janetzke and Kaza 1981] [Janetzke and Kaza 1983] [Jun and Wenlong 2016] [Kao et al. 2020] [Khanjari et al. 2016] [Khanjari et al. 2018] [Kosasih and Saleh Hudin 2016] [Kulak et al. 2024] [Le et al. 2025] [Lee et al. 2016] [Li and Yang 2024] [Li et al. 2018a] [Lipian et al. 2019] [Liu et al. 2021] [Luhur et al. 2015] [Manga et al. 2023] [Maydew and Klimas 1981] [Moghadassian et al. 2016] [Moshfeghi and Hur 2020] [Mujahid et al. 2021] [Nishi et al. 2023] [Nukala and Maddula 2020] [Pamuji and Bramantya 2018] [Pearl] [Perez-Becker et al. 2020] [Pirrung 2020] [Pirrung et al. 2016] [Ponta et al. 2016] [Potentier et al. 2021] [Prajapat et al. 2021] [Novianto et al. 2023] [Radi and Djebli 2022] [Raibaudo et al. 2023] [Randriambololona et al. 2025] [Richmond-Navarro et al. 2017] [Santo et al. 2019] [Savino et al. 1985] [Savino et al. 2024] [Selvatici and Stevens 2025] [Shen et al. 2024] [Shen et al. 2026] [Sineglazov 2015] [Sineglazov et al. 2016] [Siram et al. 2021] [Soares et al. 2023] [Soares et al. 2024b] [Soares et al. 2024a] [Störtenbecker and Dalhoff 2026] [Sun et al. 2016] [Syed Ahmed Kabir et al. 2022] [Tabatabaei et al. 2019] [Tahir et al. 2018] [Uchida et al. 2023] [der Laan et al. 2024] [van der Wall 2019] [Wan Muhammad et al. 2023] [Wang et al. 2015a] [Wang et al. 2018b] [Wester et al. 2021] [Winning et al. 2026] [Wood and Golmirzaee 2023] [Wulandana et al. 2021] [Xie et al. 2017b] [Yang et al. 2016] [Yang et al. 2019a] [Yilmaz 2023] [Yin et al. 2022] [Yin et al. 2025b] [Zhang et al. 2019a] [Zhang et al. 2019b] [Zhao et al. 2022] [Zhao et al. 2023] [Özkan and Genç 2023]

Samaras, monocopters and animal flight

Autorotation is older than aircraft. Samaras and other autorotating seeds, the monocopters modelled on them, and the flight of birds, bats and insects. 29 of these titles name a samara, a seed or a maple.

96 records. [Addo-Akoto et al. 2021] [Baker and Cooter 1979] [Bhardwaj et al. 2022] [Braunshtein et al. 2026] [Cai et al. 2025] [Chakraborty and Roy 2022] [Chen et al. 2022] [Cheng et al. 2020] [Crandell and Tobalske 2015] [Das 2009] [Dececchi et al. 2020b] [Dececchi et al. 2020a] [Deng 2015] [Dormiyani et al. 2015] [Dvořák 2016] [El Makdah et al. 2022] [Fang et al. 2017] [Farvardin Ahranjani and Banazadeh 2021] [Fauli et al. 2019] [Flight Speed of Some 1933] [Yogeshwaran et al. 2023] [Goldspink et al. 1978] [Goldsworthy et al. 1979] [Gong and Fang 2021] [Gonzalo et al. 2025] [Hiremath et al. 2024] [Huang et al. 2026a] [Ishiguro et al. 2023] [Jammeh et al. 2025] [Jo et al. 2025] [Jung and Rezgui 2023b] [Jung and Rezgui 2023a] [Кандыба 2021] [Lamprey 1953] [Lee and Choi 2017] [Lee and Lee 2016] [Lee et al. 2015] [Lentink et al. 2009] [Li and Guo 2018] [Li et al. 2024a] [Li et al. 2026] [Liu 2016] [Liu et al. 2015] [Liu et al. 2024] [Liu et al. 2025c] [Lolli et al. 2026] [McConnell and Das 2022b] [McConnell and Das 2023] [McGAHAN 1973] [Meng et al. 2023] [Naka and Hashimoto 2015] [Nero 1970] [Niu et al. 2022b] [Niu et al. 2022a] [Noda et al. 2018] [Norberg 1973] [Pennycuick 1960] [Pennycuick 1968] [Pennycuick 1971] [Porritiello et al. 2022] [Pounds and Singh 2015] [Rayner 1979] [Saetti and Rogers 2022] [Schiotz and Volsoe 1959] [Shah et al. 2024] [Shahid et al. 2019] [Shi et al. 2016] [Sneyd et al. 1982] [Sohn and Im 2022] [Song et al. 2023] [Soni and Tiwari 2019] [Stein 1976] [Suhadi et al. 2022] [Sunada et al. 2015] [Taha et al. 2016] [Tahmasian 2023] [Takizawa et al. 2015] [Tobalske 2022] [Tong et al. 2022] [Vaughan 1966] [Wang et al. 2022a] [Win et al. 2019a] [Win et al. 2019b] [Win et al. 2021] [Win et al. 2022] [Win et al. 2026] [Wu et al. 2017b] [Wu et al. 2021a] [Wu et al. 2021c] [Wu et al. 2022] [Xue et al. 2016] [Xue et al. 2019] [Yang 2013] [Yoshida and Fukui 2024] [Zhang and Wang 2022] [Zhou and Wu 2021]

Rotor and propeller noise, and the tip speed

The bound on tip speed. Rotor and propeller noise prediction and measurement, blade-vortex interaction, the noise of small multirotors and electric vertical takeoff aircraft, and community response to rotorcraft.

85 records. [Arystanbekov et al. 2025] [Barry and Magliozzi 1971] [Biggers et al. 2015] [Boucher 2025] [Boyd 2009] [Brenda S Henderson et al] [Brooks et al. 1987] [Brown and Farassat 1976] [Buǧday and Saetti 2024] [Christopher S Thurman and Nikolas S Zawodny] [Christopher S Thurman et al] [Thurman and Baeder 2023] [Cox 1973] [Crosse et al. 1960] [Greenwood et al. 2023] [Fu et al. 2023] [Gandhi 1995] [Gasaway 1969] [George 1978] [George 1996] [Goudswaard et al. 2024] [Greenwood and Schmitz 2018] [Greenwood et al. 2012] [Healy 1969] [Homans et al. 1978] [Schaub 1974] [Stephenson et al] [Jia and Lee 2020] [Johnson 1974] [Johnson-Groh 2024] [Jung et al. 2025] [Kallergis 1987] [Kingan et al. 2023] [Kitaplioglu 1986] [Kitaplioglu and Shinoda 1985] [Ko et al. 2020] [Leggat and Siddon 1978] [Leggatt and Siddon 1976] [Leighton 1982] [Li and Lee 2020] [Loewy and Sutton 1966] [Lukianov 2022] [Mantay et al. 1977] [Melo et al. 2026] [Menger et al. 1983] [Morris et al. 1979] [Mueller et al. 1987] [Mueller et al. 1990] [Mueller et al. 1992] [Nowoświat et al. 2022] [Patterson et al. 1977] [Pereira et al. 2025] [Philipps-Bertin et al. 2026] [Polyzos et al. 2020] [Prieur 1992] [Prieur et al. 1989] [Rinehart 1970a] [Saetti et al. 2024a] [Schlegel and Bausch 1969] [Schmitz and Boxwell 1976] [Shao et al. 2024] [Shenoy 1984] [Sou 2019] [Spencer et al. 1969] [Letica and Rizzi 2026] [Sternfeld and Wiedersum 1979] [Stockman et al. 1973] [Stockman et al. 1974] [Strawn and Biswas 1995] [Stroub 1978] [Su Jung et al. 2023] [Szulc and Doerffer 2018] [van der Wall et al. 2017] [Vouros et al. 2021] [Wang 1995] [Wang et al. 2025b] [Williams 2002] [Williams and Harris 1984] [Wright 1969] [Yang et al. 2018a] [Yang et al. 2019b] [Yuk et al. 2024] [Zhang et al. 2026] [Zhao et al. 2017] [Zhu and Zhao 2016]

Rotors at low density, on Mars and at low Reynolds number

The density relation at its extreme. Rotor and airfoil aerodynamics at low Reynolds number and low density, and the Mars rotorcraft. 25 of these titles name Mars or a planetary rotorcraft.

58 records. [Alguacil et al. 2020] [Ament et al. 2019] [Perez et al] [Bagade et al. 2015] [Chen and Hubner 2021a] [Chen et al. 2018] [Chitsaz et al. 2021] [Choi et al. 2019] [Dull et al] [Datta et al. 2026] [de Almeida and Dias 2024] [Désert et al. 2019] [Fox 2021] [Harris 2020] [Genç et al. 2022] [Georgiev 2025] [Giacomini and Westerberg 2025] [Sahragard-Monfared et al] [Gnatowska and Gajewska 2024] [Gojon et al. 2021] [GÜZelbey et al. 2018] [Huang et al. 2023] [Ikeda et al. 2015] [Bowman et al. 2024] [Kamruzzaman et al. 2021] [Karpiński 2026] [Koch 1998] [Koning 2019] [Koning et al. 2019a] [Koning et al. 2019b] [Koning et al. 2020] [Kruesi 2021] [Kumar Gupta et al. 2018] [Kurtulus 2019] [Leslie 2021] [Marchman and Abtahi 1985] [McElreath et al. 2020] [Nepal et al. 2023] [Mohd 2017] [Olmstead and Hector 1968] [Petrović et al. 2016] [Rahal and Dutta 2024] [Lumba et al] [San Martin et al. 2017] [Serré et al. 2019] [Shrestha et al. 2016] [Shukla and Komerath 2019] [Stephenson and Whitfield 1970] [Schmitz et al] [tang et al 2026] [Tran 2025] [Veismann et al. 2021] [Wang et al. 2024d] [Koning et al] [Yamaguchi and Anyoji 2023] [Zhang and Yang 2021] [Zhao et al. 2019] [Zhao et al. 2025]

Rotary decelerators and rotor recovery systems

The X-25’s own concept. A rotor carried to slow the descent of a person, a payload, a capsule or a probe. 9 of these records date from 1956 to 1970, 21 from 2003 or later and 2 from the three decades between, so the concept lapsed after the period the X-25 belongs to and returned for small probes, sensors and payloads.

32 records. [Aksaray and Mavris 2013] [Bartz and Miklosovic 2003] [Barzda 1970] [Barzda and Schultz 1963] [Beyer and Costello 2008] [Beyer and Costello 2009] [Brindejonc et al. 2005] [Brindejonc et al. 2007] [Costello et al. 2010] [Datta and Sirohi 2009] [Erb 1966] [High Drag Rotating Parachute 1985] [Hla Win et al. 2019] [Howard and Elger 2009] [Iversen 1968] [Jain et al. 2022] [Kim et al. 2022] [Kroo 1995] [Levin 1968b] [Levin 1968a] [Liu et al. 2025b] [Liu et al. 2026a] [Macneal and Schuerch 1963] [Martiarena et al. 2015] [Nadal Mora et al. 2005] [Nadal Mora et al. 2007] [Patnaik and Kanishk 2021] [Rivadeneira et al. 2023] [Robinson 1956] [Schuerch 1965] [Ventura et al. 2022] [Young et al. 2005]

Bluff-body drag and the drag coefficient

What the canopy comparison rests on. The drag of bluff bodies, spheres, plates, cylinders and bodies of revolution, and of falling and tumbling bodies. 8 of these 28 records date from 1968 or earlier.

28 records. [Abraham 1970] [Air Drag 1966] [Brogna and Hawks 1978] [Cantwell 1993] [Dyke 1971] [Fackrell 1975] [Falkner 1943] [Gorlin and Khudyakov 1969] [Griffin 1975c] [Griffin and Ramberg 1975] [Hopke and Slattery 1970] [Ko and Graf 1972] [Maull and Bearman 1964] [McLaren et al. 1969] [Menduni 1988] [Norling 1961] [Richardson 1986] [Roshko 1955] [Sakamoto et al. 1975] [Smith 1979] [Squire 1968] [Stengel 1968] [Stilley 1967] [Szewczyk 1992] [Walsh 1977] [Williamson 1995] [Wortman 1969] [Zarin 1970]

The final descent and the touchdown

The end of every descent. The control of the glide path and the descent rate before touchdown, vertical landing, and the landing of unpowered orbiters, capsules and reentry vehicles.

20 records. [Akturk and Camci 2022] [Broglio 1961] [Campbell 1960] [Compilation of Papers Presented 1962] [Cui et al. 2019] [Durand and Wasicko 1967] [Fisher 1960] [Franklin and Innis 1977] [Glideslope Descent-Rate Cuing 1986] [Greene 1977] [Greene 2020] [Guy 1976] [Huang 2022] [Newby et al] [P Greenhalgh et al] [Park 2020] [Qin 2023] [Romere et al. 1979] [Su and Wang 2015] [Vorobуev et al. 2020]

Wings, airfoils and the lift-to-drag ratio

What makes the rotor a wing. Low-speed wing and airfoil aerodynamics, induced drag and the lift-to-drag polar, on which this article’s glide and range figures depend.

19 records. [Aerodynamic Design 1969] [Brenckmann 1958] [Chi 1985] [Friedman et al. 2016] [Gilman and Burdges 1967] [Hariyadi 2017] [Jarvinen 1973] [Maksymiuk and Watson Viken 1986] [McInville and Moore 1994] [Olson and Selberg 1976] [Reissner 1951] [Rosti et al. 2017] [Son et al. 2023] [Tetervin 1943] [Wentz and Nagati 1975] [Wu 1986] [Wu 1989] [Yegorov 1945] [Zhao et al. 2018]

Gliding flight and the sink rate

The range argument. Gliding and soaring flight, glide performance, the sinking speed of aircraft and endurance trajectories.

16 records. [Amalia et al. 2019] [Baudinette and Schmidt-Nielsen 1974] [Bowers et al. 2007] [Bowers et al. 2011] [Collins 1934] [Entwistle 1931] [Gliding Flight in Germany 1935] [Grossman et al. 1988] [Jin 2024] [Lundberg 1937] [Metzger and Hedrick 1975] [Mueller and Heuermann 1985] [Powers et al. 2020] [Reeder 1959] [Welch 1961] [Williamson 1979]

The standard atmosphere and the flight condition

The medium, named rather than assumed. The United States and reference standard atmospheres, from which the density ratios in this article’s altitude section are taken.

17 records. [B-34. U. S. Standard 1963] [Dubin et al. 1962] [Dubin et al. 1966] [Johnson et al. 1991] [Johnson et al. 1993] [Johnson et al. 2002] [Krueger and Minzner 1976] [Minzner 1967] [Minzner 1976] [Minzner et al. 1973] [Minzner et al. 1976] [Peters 1977] [Snell and Heiser 1968] [U. S. Standard Atmosphere 1963] [U.S. Standard Atmosphere Supplements 1966] [U.S. Standard Atmosphere 1962 1962] [U.S. Standard Atmosphere 1976 1976]

V/STOL and other vertical-lift aircraft

The other ways to rise and descend vertically. Lift fans, ducted fans, deflected slipstream, ground-effect machines and short and vertical takeoff aircraft that are not rotorcraft.

10 records. [Blick and Homer 1971] [Brogan et al. 1961] [Butsko et al. 1963] [Deckert and Hodgson 1962] [Goldberger 1966] [Hirsh 1965] [Irvin and Swan 1956] [Moser 1959] [Shindo and Rae 1978] [Smith and Moushegian 2021]

Other aeronautical and foundational literature

The residual, reported and not hidden. Flight measurement and performance method, the descent, spinning and recovery of aircraft and other bodies, high-altitude aerodynamics and general aerodynamic texts that bear on this article’s descent, altitude and range arguments and belong to no cluster above. It holds 14 records, because fixed-wing work with no tie to a rotor, a descent or an escape is not admitted.

14 records. [Aerodynamic Design and Performance 1965] [Brunk 1963] [Cole 1996] [Drysdale 2013] [Dunlap and Porter 1971] [Hall et al. 2021] [Harris 1980] [Kerr 1954] [Kusumoto et al. 2022] [Miller and Koch 1985] [Muntz 1977] [Pearson and Garvin 1941] [Richardson 1976] [Thompson 1937]

Where the Framing Breaks Down

The X-25 is not a research aircraft in the sense the rest of this series uses. It is a civil production design, sold as plans to amateur builders, ordered in modified form and given a designation. Little was developed for the two aircraft that flew, and the one new element the record names, the automatically deploying rotor of the unpowered gyro-chute, is not known to have flown with a pilot, in Jenkins, Landis and Miller. No aerodynamic result is recorded. Treating it through a keystone derivation implies a design process that did not take place, and this article’s derivations describe the concept rather than an engineering effort that anyone performed on this airframe.

The keystone was never in doubt. Autorotation was understood in the 1920s, and Cierva’s C.4 made the first documented autogyro flight in January 1923, in the autogyro entry. The X-25 did not test whether a rotor autorotates, and an article that dimensions the rotor as though it were being designed misrepresents what the money bought.

The designation is the anomaly, not the aircraft. The X-series designations went to aircraft meant to explore new flight regimes or untried technologies, in Jenkins, Landis and Miller. The X-25s that flew were modified catalogue items with serial numbers applied to them. This is a genuine finding about how the designation system drifted, and it sits with the other evidence the closing article of this series will assemble.

Finally, the comparison at the centre of this article may be unfair in one direction. A parachute is compared against a rotor at equal weight, but the parachute is also the reserve. If the rotor follows the parachute in the sequence and does not replace it, the crewman carries both and the mass comparison should arguably be against the marginal mass of the rotor rather than against the canopy that is carried regardless. On that accounting the rotor is worse than this article makes it look, not better.

The Source Base

The record for the aircraft itself is the thinnest in the series so far, and the record for the physics around it is not. That asymmetry shapes the whole article and is worth stating plainly, so that a reader does not have to infer it from the reference list.

The vehicle itself has essentially no technical literature. One research record cited in this article carries Bensen in its title, which is the chapter on Igor Bensen and the gyrocopter in a history of the type, Chapter 11 IGOR BENSEN 2003, and none carries the X-25 or the Discretionary Descent Vehicle. Three concern a flying rotor seat, which are Barzda 1970 and Hollrock and Barzda 1972 on the SAVER and Gross and Mawhinney 1970 on the AERCAB flying ejection seat, rather than the X-25. There is no flight test report, no aerodynamic data report and no programme summary in the open literature reached here. The specifications in this article come from museum fact sheets and reference compilations, not from primary documents, and where those disagree the article says so rather than choosing.

The supporting physics is abundant and that asymmetry is the point. Autorotation, the autogiro, momentum theory, blade element theory, parachutes and escape systems are all well documented from the 1920s onward. The article can derive everything about the concept and can verify almost nothing about the aircraft.

The research records are listed cluster by cluster under The Contemporary Literature, including the period reports, the work of the intervening decades and the standard atmosphere on which every number in this article rests.

The research survey holds 2,707 research records drawn from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center, of which 828 are report primaries, being 30.6 percent, by the identifier rule set out under The Definition of Primary. The median publication year is 2005. Of the 2,679 dated records, 430 were published in 1968 or earlier, the year the X-25 first flew, being 16.1 percent, and 1,152 were published in 2015 or later, being 43.0 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 NACA autogiro and autorotation reports that carry this article’s keystone are report primaries under that rule. The rule does not reach the period journal papers, such as Glauert 1927 and de la Cierva 1930 on the theory of the autogiro, so 30.6 percent is a lower bound on how much of the survey is first-hand.

The keystone is thin on primary sources. Autorotation carries 166 research records and 27 of them are report primaries, which is 16.3 percent against 30.6 percent for the survey as a whole. A record is an autorotation record when its title contains a word beginning autorotat, the word auto-rotative, a windmill or windmilling brake or rotor, or a power-off descent or rotor.

The likely reason is a vocabulary that spans both eras. Autorotation is a word the 1930s used and the 2020s still use, and on that shared word the larger and better-indexed modern computational literature simply outnumbers the period work. That is an inference about the literature and not a measurement of it.

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, and where a row adds terms after the words or else, a title carrying one of those terms is counted as well.

Subject	Title terms counted	Records
rotor spin-up and prerotation	prerotation, pre-rotation, prerotator, spin-up, rotor starting, starting torque, rotor run-up	2
stored rotor energy	rotor, blade together with inertia, kinetic energy, stored energy, or else autorotative index, flywheel	4
the flying rotor seat	SAVER, flying ejection seat, rescue autogyro, rotor seat	3
gyroplane safety and accidents	gyroplane, autogyro, autogiro, gyrocopter together with safety, accident, crash, airworthiness	3
the glide of an autorotating rotor	autorotating, autorotation, autorotative, gyroplane, autogyro, autogiro together with glide, gliding	2
cutting away a parachute	parachute, canopy together with cutaway, cut away, jettison, disconnect	0
gyroplane and autorotation training	gyroplane, autogyro, autogiro, autorotation together with training, trainer, instructor, test standards	7

Rotor spin-up and prerotation stands at two records, and neither is the case this article needs. One concerns the engine loads of prerotating an autogyro rotor, Czyż et al. 2016, and one the control of the blades while a helicopter rotor is spun up in wind, Kargaev et al. 2025. No title in the survey names the spin-up of a rotor deployed in descent, although the deployable rotors of the SAVER and of the rotary decelerators under The Contemporary Literature must perform one. The word prerotation also names the prerotation of landing gear wheels and of the human trunk. That gap is the reason the spin-up section of this article reasons from energy rather than from measurement.

Stored rotor energy appears to stand at four records and does not really. The relevant work exists and is cited, but it sits inside the autorotation and blade-motion literature rather than beside it, because a paper on autorotative landing is a paper about spending exactly that energy. A dedicated heading for it is nearly empty while the subject is well covered. A thin heading is not the same thing as a thin subject, and the distinction is easy to get wrong in the direction of claiming a gap that is not there.

One further caution belongs here. The word flywheel also names flywheel energy storage for spacecraft and power grids, meaning containment rings and composite burst testing, which is a different discipline that happens to store energy in something that spins. That literature is a homonym of this subject rather than a part of it, and no record of it is counted here.

The flying rotor seat, the class to which the SAVER belongs, stands at three records, given above, and cutting away a parachute stands at no record, although it would be the irreversible step in any deployment sequence that included it.

Gyroplane safety stands at three records. They are Doberentz et al. 2020, Houston et al. 1998 and Practice for Continued Airworthiness, and no title among them compares trained with untrained pilots, which is why the training inference under Epistemic State is labelled as an inference.

The glide of an autorotating rotor stands at two records, the flight measurement of an autogiro’s gliding performance in Wheatley 1933 and a controller for steep glide slopes of an unmanned gyroplane in Wu 2015, so the lift-to-drag ratio of 4 on which the range figures rest is assumed rather than taken from a measured X-25 polar.

Gyroplane and autorotation training stands at seven records, three of them the practical test standards for rotorcraft pilots and instructors and the rest on autorotation training in helicopters, so the subject the programme’s testing addressed is among the thinnest here.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. Its 2,707 records come from NASA’s Technical Reports Server, the Defense Technical Information Center and the journal literature registered with Crossref. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Occupant, crash and vehicle also name road traffic safety, landing also names knee and ankle loading in sport, and Parachute is also the name of a cardiac device, a heart valve, a band and a form of executive compensation. Vortex ring also names the quantised vortex rings of superfluid helium, samara also names the Samara Region, and canopy also names the crown of a tree. Autorotation also names the rotation of a telephone screen and of the jaw in surgery, height velocity also names the growth rate of children, and descent also names human gait. Prerotation also names the prerotation of landing gear wheels and tyres, of the human trunk, of pump impellers and of signal constellations in wireless networks, and rotor also names the rotors of electric machines, wave energy turbines, gyroscopes and industrial machinery. Drag coefficient also names the drag of sediment and process particles, of the sea surface in meteorology and of the ether in relativity. Electrical power systems, spaceflight outside the atmosphere, the testing and design of ordnance and the engineering of airfield landing mats are excluded as well. Correction, erratum, clarification, retraction and withdrawal notices, figure, table and supplementary-material records, peer-review reports and journal front matter are excluded too, because a survey counts research works and those are parts of works or editorial events rather than works. A signed comment on a paper, a discussion of it and its author’s closure or reply are research works, since each argues about a result, and they are admitted when their subject is, while an unsigned discussion and a referee’s report on a manuscript are not. Dictionary entries, advertisements and fiction are excluded for the same reason. The residual cluster admits only flight measurement and performance method, the descent, spinning and recovery of aircraft and other bodies, high-altitude aerodynamics and general aerodynamic texts, and fixed-wing work on supersonic and hypersonic flight, missiles and stores, engines, avionics, structures or operations, with no tie to a rotor, a descent or an escape, is not admitted to it or to any other cluster. The same rule excludes, from every cluster, fixed-wing electric and hybrid-electric aircraft, electric machines, the avionics and the operations and markets of unmanned aircraft and air mobility, and the supersonic drag of bodies and projectiles. It also excludes the landing autonomy, guidance, sensing and path planning of unmanned aircraft even when the vehicle is a rotorcraft, the structures, loads, controls, generators and floating platforms of wind turbines and every vertical-axis turbine, the drive trains, gears, lubrication, engines, ice protection, landing gear and cargo equipment of rotorcraft, the stresses and construction of propeller blades, open rotors and propfans, fixed-wing high lift, landing gear, arresting gear and runway operations, the noise of fixed-wing aircraft and engines and occupational noise exposure, simulator engineering and the administration of training, powered rocket landing, glide weapons, the imaging payloads of parafoils, the network coverage of landing sites, hearing protection and speech reception in aircraft, the quality assurance of manufacture, and airships and balloons. Conference proceedings, symposium volumes, appendices, patent notices and book reviews are excluded as parts of works or notices rather than works. Reference and definition entries such as glossaries, news items and announcements, and a second deposit of a document already counted are not admitted either, because none of them is a separate research work.

Some records of doubtful relevance are kept. Injury biomechanics under blunt impact, parachute physiology and equipment, helmet-mounted display optics, bird and insect flight aerodynamics, classical vortex rings in fluid mechanics and combustion, kites and tethered autogyros for airborne wind energy, autorotation used to harvest energy and the drag of projectiles at low speed each share either the physics of a rotor, a descent or a body in flight, or the human side of an escape, with this subject, so each is kept and a reader may weigh it accordingly.

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

Epistemic State

Historical fact, from the public record. Three X-25 type aircraft were ordered in early 1968 under the Discretionary Descent Vehicle programme, in the X-25A fact sheet, and they were the basic X-25 gyro-chute, the X-25A and the X-25B. The X-25A, serial 68-10770, first flew on 5 June 1968. The X-25B, serial 68-10771, first flew on 5 June 1968 by Guinness World Records, the date the inventory gives for the type, and on 23 January 1968 in the Bensen B-8 entry, which cites no source for it. The Guinness maximum takeoff weight of 547 pounds is the X-25A figure in the fact sheet, so Guinness may not be independent of the inventory, and the adopted date rests in the end on that one monograph. Both aircraft derive from Bensen B-8 family designs. Testing addressed piloting technique and training requirements, and the fact sheet reports that pilots could be trained quickly and easily. No full-scale operational test was performed. Funding ended with the American withdrawal from Vietnam, and the fact sheet adds doubts about operational feasibility. The X-25A is held by the National Museum of the United States Air Force and the X-25B by the Air Force Flight Test Museum at Edwards, in Jenkins, Landis and Miller. The Kaman SAVER flew towed on 28 December 1971 and with a telescoping rotor on 10 January 1972, and was cancelled, in the Kaman KSA-100 SAVER entry.

Engineering analysis, derived here and checkable. The equivalence between the autorotation ratio of 1.8 and a disc-referred drag coefficient of 1.23 is algebra containing no fitted quantity. The finding that an autorotating rotor descends faster than a personnel canopy at equal weight follows from disc loading alone. The glide range figures follow from an assumed lift-to-drag ratio of 4. The spin-up energy of about 57 feet of ideal height loss follows from an assumed blade mass and tip speed. The SAVER descent rate of 56 feet per second follows from documented weight and rotor diameter and is the least assumption-dependent number in the article. The statement that a rotor at Martian density descends about ten times faster is the same square-root relation evaluated at one percent of sea-level density and assumes nothing else, though it is an illustration of the relation and not a claim about any particular Mars vehicle, which would fly a rotor sized for that atmosphere.

Assumed, and marked as such throughout. The escape-configuration gross weight of 350 pounds. The lift-to-drag ratio of 4. The best-glide speed of 45 miles per hour. The blade mass of 12 pounds each and tip speed of 400 feet per second. The canopy comparison figures of 28 foot nominal diameter, 250 pound suspended weight and a drag coefficient of 0.75. The blade chord of 7 inches. The rotor and parachute assembly masses of 38 and 28 pounds. None of these is a measurement of an X-25.

Inference, and labelled as inference. That the programme’s testing concerned training rather than aerodynamics is an inference from the record’s statement that the aircraft were used to evaluate piloting technique and training requirements, combined with the absence of any aerodynamic finding, and the one training result the record reports is favourable. That the doubts about operational feasibility concerned the deployment sequence, the rotor’s mass alongside a parachute or the stowage geometry is an inference from this article’s analysis, since the fact sheet names the doubts without describing them. That the ram-air parachute is the historical answer to the Discretionary Descent Vehicle question is an inference from capability comparison, not from any documented decision connecting the two.

Two further inferences come from the contemporary survey and are labelled here because they are the article’s strongest claims and its least documented. That a multirotor cannot autorotate follows from the stored-energy and disc-loading relations this article derives, applied to a configuration those relations describe accurately, but no source consulted here states it as a finding and the airworthiness literature treats redundancy as a design choice rather than as a concession. And that the gyroplane’s safety reputation bears on a crewman with no rotorcraft training is an inference from the type’s general reputation and from the contemporary safety literature, not from any study that compares trained and untrained gyroplane pilots, which would be the evidence the claim needs.

The vehicle-by-vehicle programme record for the X-series generally is Jenkins, Landis and Miller on the American X-vehicles.

What the record does not settle. Whether the X-25 rotors were the 20 foot rotor of the standard B-8M. Whether the engine was 72 or 90 horsepower. Which of the X-25A and X-25B flew first. What became of the third aircraft, the gyro-chute. What the doubts about operational feasibility were. Whether the escape sequence included a parachute cutaway at all, and whether any part of it was demonstrated below full scale. Whether any quantitative descent or glide measurement was taken and survives in a closed report.

Written from current knowledge. The contemporary survey postdates the editorial date of this article.

Out of Scope

The detailed aeroelastic behaviour of wooden rotor blades. Ejection seat dynamics and the injury mechanisms of the ejection itself. The combat search and rescue apparatus the programme was meant to supplement. The amateur-built rotorcraft accident record, which is substantial and is a different subject. The full history of the Cierva autogiro. Powered-lift and compound rotorcraft. The detailed design of ram-air canopies. Wind turbine engineering beyond the identity of the flow state.

Conclusion

The Bensen X-25 showed that pilots could learn the machine, and it never reached the escape it was for.

The programme was framed as giving a descending crewman a choice, in Jenkins, Landis and Miller. The arithmetic shows that an autorotating rotor is a worse decelerator than the parachute it was to replace, by nine percent at equal weight and twenty-nine percent as flown, and that everything it offers comes from the fact that it is a wing rather than a brake. Seven and a half miles from ten thousand feet is the whole product.

The obvious objection, that a rotor must be spun up while a canopy merely inflates, does not survive being written down. Fifty-seven feet of ideal height loss is cheap. The difficulty was never energetic, and on the record it was not training either, since the one test result reported is that pilots learned the X-25 with ease. The programme ended because the air war that motivated it was winding down and because of doubts about its operational feasibility, and the gyro-chute that embodied the escape has no recorded piloted flight. By this article’s inference the doubts had ground. The rotor buys range and not a softer landing, weighs about as much as the parachute it accompanies, would need much heavier blades or an engine to fold into a seat, and in any sequence through an open canopy would require cutting a working parachute away.

The question was good and it was eventually answered by fabric. A ram-air canopy reaches nearly the same glide ratio with no rigid structure, no spin-up and, by inference, less training, and guided airdrop has since removed the pilot from the loop as well. The rotor’s physics did not die. It went into wind energy, where the windmill brake state is the design condition rather than an emergency.

The next article in this series takes up the Schweizer X-26 Frigate.

Equations

This section collects the 44 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 44, 23 are established and 21 are bespoke. Quantities are in United States customary units, with weight in pounds, length in feet, speed in feet per second and density in slugs per cubic foot, and the escape weight of 350 pounds, the rotor diameter of 20 feet, the blade mass of 12 pounds, the tip speed of 400 feet per second, the blade chord of 7 inches and the lift-to-drag ratio of 4 are values the article assumes, while $\gamma$ is the glide angle and $\gamma_L$ the Lock number.

Equation 1, In-Plane Force on a Blade Element. The net force in the plane of rotation on a blade element is the in-plane component of its lift less that of its drag at the inflow angle.

\[dF_{x} = dL \sin\phi - dD \cos\phi \tag{1}\]

Equation 2, Equilibrium Inflow Angle of an Autorotating Element. An element neither drives nor retards the rotor when the tangent of its inflow angle equals its section drag-to-lift ratio.

\[\tan\phi = \frac{dD}{dL} = \frac{C_d}{C_l} \tag{2}\]

Equation 3, Torque Balance of an Autorotating Rotor. A rotor in steady autorotation turns at the speed at which the moments of the in-plane forces of its driving and driven regions cancel over the disc.

\[\int_{0}^{R} r \, dF_{x} = 0 \tag{3}\]

Equation 4, Disc Area and Hover Induced Velocity. The actuator-disc result gives the induced velocity a rotor needs in hover from its weight, the air density and its disc area. Leishman’s helicopter aerodynamics Johnson’s helicopter theory Castles and De Leeuw 1953

\[A = \pi R^2, \qquad v_h = \sqrt{\frac{W}{2 \rho A}} \tag{4}\]

Equation 5, Bespoke Disc Area of the X-25B Rotor. The disc area follows from a rotor diameter the article takes as 20 feet, since the record does not settle whether the X-25 used the standard B-8M rotor.

\[A = \pi (10 \, \text{ft})^2 = 314.2 \, \text{ft}^2 \tag{5}\]

Equation 6, Bespoke Hover Induced Velocity of the X-25B. The actuator-disc induced velocity at an escape weight the article assumes as 350 pounds on the taken disc at sea-level density is about 15 feet per second.

\[v_h = \sqrt{\frac{350}{2 (0.002377)(314.2)}} = 15.3 \, \text{ft/s} \tag{6}\]

Equation 7, Momentum Theory Thrust in the Windmill Brake State. In the windmill brake state momentum theory gives the thrust in terms of the descent speed and the induction factor $a$.

\[T = 2 \rho A V_d^2 \, a (1 - a) \tag{7}\]

Equation 8, Descent Ratio and Induction Factor. Setting thrust equal to weight cancels density and area and relates the squared ratio of hover induced velocity to descent speed to the induction factor alone.

\[\left( \frac{v_h}{V_d} \right)^{2} = a (1 - a) \tag{8}\]

Equation 9, Momentum Theory Bound on the Descent Ratio. Because the induction factor term cannot exceed one quarter, momentum theory has a solution only when the descent speed is at least twice the hover induced velocity.

\[\frac{V_d}{v_h} \geq 2 \tag{9}\]

Equation 10, Bespoke Autorotative Descent Rate of the X-25B. The measured autorotation ratio of 1.8 applied to the hover induced velocity at the assumed 350 pounds gives a descent of about 28 feet per second.

\[V_d \approx 1.8 \, v_h = 1.8 (15.3) = 27.6 \, \text{ft/s} = 18.8 \, \text{mph} \tag{10}\]

Equation 11, Terminal Descent of a Drag Device. Balancing weight against the drag of a device with coefficient $C_D$ referred to swept area gives its terminal descent speed.

\[W = \tfrac{1}{2} \rho V_d^2 A \, C_D \quad \Longrightarrow \quad V_d = \sqrt{\frac{2W}{\rho A C_D}} \tag{11}\]

Equation 12, Drag Coefficient Equivalent to a Descent Ratio. Substituting the definition of the hover induced velocity makes weight, density and area cancel, so a descent ratio fixes a drag coefficient on disc area.

\[V_d = \frac{2 v_h}{\sqrt{C_D}} \quad \Longrightarrow \quad C_D = \frac{4}{(V_d / v_h)^2} \tag{12}\]

Equation 13, Drag Coefficient of an Autorotating Rotor. The measured autorotation ratio of 1.8 corresponds to a drag coefficient of about 1.23 referred to disc area.

\[C_D = \frac{4}{(1.8)^2} = 1.23 \tag{13}\]

Equation 14, Projected Area of an Inflated Canopy. The projected area of an inflated canopy is the nominal area scaled by the square of the ratio of projected to nominal diameter. Knacke’s recovery systems design manual

\[S_p = \left( \frac{D_p}{D_0} \right)^{2} S_0 \tag{14}\]

Equation 15, Canopy Drag Coefficient on Projected Area. A flat circular canopy coefficient of 0.75 on nominal area becomes about 1.67 on projected area when the inflated diameter is 0.67 of the nominal. Knacke’s recovery systems design manual

\[C_{D,\text{proj}} = \frac{0.75}{(0.67)^2} = 1.67 \tag{15}\]

Equation 16, Nominal Area of the Standard Personnel Canopy. The standard personnel canopy of 28 foot nominal diameter has a nominal area of about 616 square feet. Knacke’s recovery systems design manual

\[A_0 = \pi (14)^2 = 615.8 \, \text{ft}^2 \tag{16}\]

Equation 17, Disc or Canopy Loading. The loading of a swept-area drag device is its weight divided by its swept area.

\[\frac{W}{A} = \text{disc loading, or canopy loading} \tag{17}\]

Equation 18, Terminal Descent in Terms of Loading. The terminal descent speed of any swept-area drag device is a constant set by its drag coefficient times the square root of loading over density.

\[V_d = k \sqrt{\frac{W / A}{\rho}}, \qquad k = \sqrt{\frac{2}{C_D}} \tag{18}\]

Equation 19, Bespoke Equal-Weight Descent Ratio of Rotor to Canopy. At equal weight the rotor on the taken 20 foot disc descends about nine percent faster than the 28 foot canopy, a ratio from which the weight cancels.

\[\frac{V_{\text{rotor}}}{V_{\text{canopy}}} = \sqrt{\frac{C_{D,c} A_c}{C_{D,r} A_r}} = \sqrt{\frac{0.75 \times 615.8}{1.23 \times 314.2}} = 1.091 \tag{19}\]

Equation 20, Glide Angle and Sink Rate. The glide angle has a tangent equal to the reciprocal of the lift-to-drag ratio and the sink rate is the airspeed times the sine of that angle.

\[\tan\gamma = \frac{1}{L/D}, \qquad V_s = V \sin\gamma \tag{20}\]

Equation 21, Bespoke Small-Angle Sink Rate in the Glide. Dividing a best-glide speed the article assumes as 45 miles an hour by an assumed lift-to-drag ratio of 4 gives a sink rate of 16.5 feet per second.

\[V_s = \frac{V}{L/D} = \frac{66.0 \, \text{ft/s}}{4} = 16.5 \, \text{ft/s} \tag{21}\]

Equation 22, Bespoke Exact Sink Rate in the Glide. The exact form at the same assumed speed and ratio gives 16.0 feet per second, so the simpler form reads three percent high.

\[V_s = V \sin\gamma = 66.0 \sin(14.04^\circ) = 16.0 \, \text{ft/s} \tag{22}\]

Equation 23, Still-Air Glide Range. In still air a glide at a fixed lift-to-drag ratio covers a horizontal range equal to the release height times that ratio.

\[R = h \, (L/D) \tag{23}\]

Equation 24, Descent Rate at Altitude in the Standard Atmosphere. The descent rate scales with the inverse square root of the density ratio, which the tropospheric standard atmosphere gives as a power law in height.

\[V_d(h) = V_d(0) \sqrt{\frac{\rho_0}{\rho(h)}}, \qquad \frac{\rho(h)}{\rho_0} = \left( 1 - 6.875 \times 10^{-6} h \right)^{4.256} \tag{24}\]

Equation 25, Time Aloft with Density Varying. Integrating the inverse sink rate over height, with the sink rate varying as the inverse square root of the density ratio, gives the time aloft.

\[t = \int_{0}^{h} \frac{dz}{V_s(z)} = \frac{1}{V_s(0)} \int_{0}^{h} \sqrt{\frac{\rho(z)}{\rho_0}} \; dz \tag{25}\]

Equation 26, Bespoke Rotor Solidity. Two blades of an assumed 7 inch chord on the taken 10 foot radius give a solidity of about 0.037.

\[\sigma = \frac{N c}{\pi R} = \frac{2 (0.583)}{\pi (10)} = 0.037 \tag{26}\]

Equation 27, Bespoke Canopy Area Matching the Rotor Drag Area. Matching the drag area of the taken rotor disc at the measured coefficient with fabric at 0.75 needs about 517 square feet of canopy.

\[C_D A = 1.23 \times 314.2 = 388 \, \text{ft}^2, \qquad S_0 = \frac{388}{0.75} = 517 \, \text{ft}^2 \tag{27}\]

Equation 28, Bespoke Lock Number Definition and Blade Inertia. The Lock number compares aerodynamic forcing on a blade to its inertia, here with the inertia of a uniform blade of a mass the article assumes as 12 pounds.

\[\gamma_L = \frac{\rho a c R^4}{I_b}, \qquad I_b = \tfrac{1}{3} m_b R^2 = 12.4 \, \text{slug ft}^2 \tag{28}\]

Equation 29, Bespoke Lock Number of the X-25B Blade. At sea-level density with a lift-curve slope of 5.7, the assumed chord and the assumed blade inertia, the Lock number is about 6.4.

\[\gamma_L = \frac{(0.002377)(5.7)(0.583)(10)^4}{12.4} = 6.4 \tag{29}\]

Equation 30, Bespoke Rotor Angular Speed. A tip speed the article assumes as 400 feet per second on a 10 foot radius gives 40 radians per second.

\[\Omega = \frac{V_{tip}}{R} = \frac{400}{10} = 40 \, \text{rad/s} = 382 \, \text{rpm} \tag{30}\]

Equation 31, Bespoke Thrust Coefficient. The assumed 350 pounds referred to the dynamic pressure at the assumed tip speed on the taken disc gives a thrust coefficient of about 0.0029.

\[C_T = \frac{W}{\rho A (\Omega R)^2} = \frac{350}{(0.002377)(314.2)(400)^2} = 0.0029 \tag{31}\]

Equation 32, Bespoke Blade Loading Coefficient. Dividing the thrust coefficient by the assumed solidity gives a blade loading coefficient of about 0.079, below the stall limit near 0.10.

\[\frac{C_T}{\sigma} = \frac{0.0029}{0.037} = 0.079 \tag{32}\]

Equation 33, Bespoke Tip Speed Ratio in Autorotation. The assumed tip speed over the modelled descent rate gives a tip speed ratio of about 14.5.

\[\lambda = \frac{\Omega R}{V_d} = \frac{400}{27.6} = 14.5 \tag{33}\]

Equation 34, Bespoke Rotor Moment of Inertia. Treating each of the two blades as a uniform rod of the assumed mass about the hub gives about 25 slug square feet.

\[I = N \cdot \tfrac{1}{3} m_b R^2 = 2 \cdot \tfrac{1}{3} (0.373)(100) = 24.9 \, \text{slug ft}^2 \tag{34}\]

Equation 35, Bespoke Stored Rotational Energy. The rotational kinetic energy of the assumed inertia at the assumed angular speed is about 19,900 foot-pounds.

\[E = \tfrac{1}{2} I \Omega^2 = \tfrac{1}{2} (24.9)(40)^2 = 19{,}900 \, \text{ft lb} \tag{35}\]

Equation 36, Bespoke Ideal Height Loss to Spin Up the Rotor. Dividing the stored energy by the assumed weight gives about 57 feet of height if every part of the potential energy went into the rotor.

\[h = \frac{E}{W} = \frac{19{,}900}{350} = 57 \, \text{ft} \tag{36}\]

Equation 37, Bespoke Stored Energy Independent of Radius. For blades taken as uniform rods turning at a fixed tip speed, the stored energy reduces to the blade mass times the square of tip speed and the radius cancels.

\[E = \tfrac{1}{2} I \Omega^2 = \tfrac{1}{2} \left( N \tfrac{1}{3} m_b R^2 \right) \left( \frac{V_{tip}}{R} \right)^{2} = \frac{N}{6} m_b V_{tip}^2 \tag{37}\]

Equation 38, Descent Rate Scaling with Weight and Radius. Because the descent rate goes as the square root of disc loading, it scales as the square root of weight over the rotor radius. Kaman KSA-100 SAVER

\[V_d \propto \frac{\sqrt{W}}{R} \tag{38}\]

Equation 39, Kinetic Energy of the Descent. The energy a flare must absorb is the kinetic energy of the vehicle at its descent rate.

\[E_{req} = \tfrac{1}{2} \frac{W}{g} V_d^2 \tag{39}\]

Equation 40, Flare Energy Required in Terms of Weight and Radius. Substituting the measured descent ratio of 1.8 and the actuator-disc induced velocity makes the required energy go as the square of weight over the square of radius.

\[E_{req} = \frac{(1.8)^2}{4 g \rho \pi} \cdot \frac{W^2}{R^2} \tag{40}\]

Equation 41, Bespoke Flare Energy Margin. The article defines the margin as the stored energy of uniform-rod blades over the energy the flare requires.

\[\frac{E_{avail}}{E_{req}} = \frac{2 N m_b V_{tip}^2 \, g \rho \pi R^2}{3 (1.8)^2 W^2} \tag{41}\]

Equation 42, Bespoke Blade Mass for a Unit Energy Margin. Inverting the margin at unity gives the blade mass a rotor would need, 2.5 pounds a blade for the X-25B and 21 for the Stowable Aircrew Vehicle Escape Rotorseat, or SAVER, against the assumed 12.

\[m_b = \frac{3 (1.8)^2 W^2}{2 N V_{tip}^2 g \rho \pi R^2} \tag{42}\]

Equation 43, Thrust-to-Weight Ratio of the SAVER. The documented 430 pound turbofan thrust over the 710 pound SAVER weight is a thrust-to-weight ratio of 0.61. Kaman KSA-100 SAVER

\[\frac{T}{W} = \frac{430}{710} = 0.61 \tag{43}\]

Equation 44, Bespoke Stored Energy of a Small Lift Rotor. The uniform-rod stored energy in terms of blade count, blade mass and tip speed shows that a small light blade at modest tip speed stores little energy.

\[E = \frac{N}{6} m_b V_{tip}^2 \tag{44}\]

Notation

• $\phi$, the inflow angle at a blade element
• $C_d$, the section drag coefficient, with $C_l$ the section lift coefficient
• $R$, the rotor radius, and in Equation 23 the glide range
• $A$, the rotor disc area, or the swept area of a drag device
• $v_h$, the hover induced velocity
• $W$, the weight
• $\rho$, the air density, with $\rho_0$ its sea-level value
• $V_d$, the descent rate
• $a$, the induction factor, and in Equations 28 and 29 the lift-curve slope
• $C_D$, the drag coefficient referred to swept area
• $D_p$, the projected diameter of an inflated canopy, with $D_0$ the nominal diameter
• $S_0$, the nominal area of a canopy, with $S_p$ the projected area
• $k$, the descent constant of a swept-area drag device
• $\gamma$, the glide angle
• $V_s$, the sink rate in the glide
• $\sigma$, the rotor solidity
• $N$, the number of blades
• $c$, the blade chord
• $\gamma_L$, the Lock number
• $I_b$, the moment of inertia of one blade about the hub, with $I$ that of the rotor
• $m_b$, the mass of one blade
• $\Omega$, the rotor angular speed
• $V_{tip}$, the blade tip speed
• $C_T$, the thrust coefficient
• $\lambda$, the tip speed ratio
• $E_{req}$, the energy a flare must absorb, with $E_{avail}$ the stored rotor energy

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