No specifications for this vehicle have ever been released, and it is not certain that the designation in the title belongs to it. What is public is a mission requirement, and a mission requirement is a physics problem. This article derives what the vehicle had to be from what it had to do, and then checks the derivation against the one thing that did fly. This is the forty-second article in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, the X-24, the X-25, the X-26, the X-27, the X-28, the X-29, the X-30, the X-31, the X-32, the X-33, the X-34, the X-35, the X-36, the X-37, the X-38, the X-39, and the X-40.

The public record of this vehicle is a mission requirement and a few published performance figures. With no specification released, the statement of what is unknown carries the weight that a specification table would otherwise carry.

The finding is that classification hides the design and not the physics. A published range, a published mass and a published lift to drag ratio bound the problem tightly enough to show where it becomes impossible, and the place it becomes impossible is the leading edge. When the vehicle finally flew, twice, both flights were lost, and the official failure report on the second attributes its loss to degradation of the aeroshell.

The Research Question

The binding unknown was whether a body could glide most of the way around the world and still be pointed at something when it arrived.

The Common Aero Vehicle was defined as a manoeuvrable hypersonic reentry vehicle able to dispense a variety of payloads inside the atmosphere [X-41 CAV]. The word Aero stood for aeroshell rather than aerospace, because the vehicle was conceived as a common thermal shell that different payloads could sit inside [X-41 CAV]. That naming is the clearest statement of the design intent available, and it identifies the shell as the product.

The requirement that sets everything else is range. The programme’s ultimate vehicle, a reusable Hypersonic Cruise Vehicle, was to strike targets 9,000 nautical miles distant in two hours [DARPA Falcon Project]. The glider’s own requirement, as the Congressional Research Service summarises the programme’s study, was to deliver a payload from the continental United States to anywhere on Earth in less than two hours, carrying approximately 1,000 pounds of munitions or other payload and able to manoeuvre 3,000 nautical miles across range [Woolf 2011]. The farthest point on Earth from any launch site is half a great circle away, so for Earth radius $R_{e}$ the global requirement is bounded by

\[\pi R_{e} = \pi \times 6{,}371 \ \text{km} = 20{,}015 \ \text{km} = 10{,}807 \ \text{nautical miles} \tag{1}\]

A published trajectory analysis of the vehicle that flew gives its planned range as 17,000 kilometres [Acton 2015a], matching the cruise vehicle’s figure to within two percent.

\[\frac{17{,}000 \ \text{km}}{9{,}000 \times 1.852 \ \text{km}} = \frac{17{,}000}{16{,}668} = 1.020 \tag{2}\]

This article therefore takes 9,000 nautical miles as the glider’s range requirement, and the discussion of where the framing breaks down examines what follows if that attribution is wrong.

Those two numbers plus the laws of motion are enough to bound the design, and the sizing section does it. The chain runs from range to the required lift to drag ratio, from there to the speed the vehicle must be boosted to, from there to the air density it must fly in to hold itself up, and from there to the temperature of its leading edge. The last number in that chain decides whether the vehicle exists, and it does not depend on anything classified.

Programme Origin

The vehicle began as an Air Force programme, was merged into a joint one, lost its weapon, and changed its name.

In December 2002 the Air Force’s Common Aero Vehicle work was merged with a Defense Advanced Research Projects Agency effort into a joint programme named Force Application and Launch from the Continental United States, which carried two tasks, being a small launch vehicle and the aero vehicle itself [X-41 CAV]. The launch vehicle task was for a cheap booster, a quick-response launcher at a planned cost of about 5 million US dollars per launch, for the aero vehicle and for other small suborbital and orbital payloads [X-41 CAV].

By 2004 the offensive strike element had been cancelled, and the vehicle was then renamed. The Common Aero Vehicle became the Hypersonic Technology Vehicle, and research on weaponisation ended [X-41 CAV]. The designation directory places the change of name in 2004, whereas the Congressional Research Service dates the redesignation to 2006 [Woolf 2011]. Congress increased the vehicle’s funding for fiscal years 2004 and 2005 while questioning its strike mission [Woolf 2011], and that concern is the proximate reason a vehicle designed to deliver munitions anywhere on Earth [DARPA Falcon Project] [Prompt Global Strike] became a vehicle designed to demonstrate that the glide was possible. The restriction was explicit. The conference report on the defence appropriations act for fiscal year 2005, passed in July 2004, allowed the vehicle’s funds to be used only for research that was not related to weapons, and barred their use to “develop, integrate, or test a CAV variant that includes any nuclear or conventional weapons” or to “develop, integrate, or test a CAV for launch on any ICBM or SLBM”, meaning an intercontinental or submarine-launched ballistic missile. The administration answered by restructuring the programme and renaming the vehicle the Hypersonic Technology Vehicle [Woolf 2011].

The first design did not fly either, for a reason that anticipates the rest of this article. The initial Hypersonic Technology Vehicle was to reach Mach 19 at 30 to 45 kilometres, but construction of both vehicles was cancelled in May 2006 because the subcontractor could not stop the curved leading edges of the aeroshell from delaminating, and the programme went directly to the second design [X-41 CAV].

The designation is the least certain thing in this section. The X-41A was allocated in late 1997 or early 1998, years before the joint Falcon programme existed, and the authoritative survey of these designations records that it was never used again in any official announcement and that it is not clear the designation was ever actually applicable to the vehicle discussed here [X-41 CAV].

The article immediately before last concerned a number reserved and never assigned. This one concerns a number that was assigned, went unused, and was later attached by the public record to a vehicle it may have nothing to do with. Both are failures of the same register, and the X-39 article describes the mechanism.

Sizing From First Principles

The Range Requirement Fixes the Lift to Drag Ratio

A hypersonic glider is held up by lift and by the curvature of its path, and the second term is not small. Let $V$ be the vehicle’s speed, $R_{e}$ the radius of the Earth and $g$ the acceleration due to gravity. The speed at which a body would orbit at the surface is

\[V_{c} = \sqrt{g R_{e}} = \sqrt{(9.80665)(6.371 \times 10^{6})} = 7{,}904 \ \text{m/s} \tag{3}\]

At a fraction of that speed the vehicle is partly in orbit already. The lift a steady glide requires is the weight less the centrifugal relief. That balance is the equilibrium glide condition.

\[L = W \left( 1 - \frac{V^{2}}{V_{c}^{2}} \right) \tag{4}\]

Integrating the resulting equation of motion over a glide that decelerates from an initial speed $V$ gives the classical equilibrium glide range, in which the entire vehicle enters only through its lift to drag ratio. The relation is not new and the article does not claim it. It is the comparative analysis of long-range hypervelocity vehicles that Eggers and his colleagues published in 1955 and refined through 1958 [Eggers et al. 1955] [Eggers et al. 1958], written before any such vehicle existed, and its framing of the choice between ballistic, skip and glide trajectories frames the analysis that follows.

\[R = \left(\frac{L}{D}\right) \frac{R_{e}}{2} \ln \left( \frac{1}{1 - V^{2}/V_{c}^{2}} \right) \tag{5}\]

That relation carries the argument of this article. By it, range is bought with two things only, being the aerodynamic efficiency of the shape and the speed it is launched at, and that neither can be classified away.

Range is strictly linear in the ratio and strongly non-linear in speed, which sets where the design effort goes.

\[\frac{\partial R}{R} = \frac{\partial (L/D)}{L/D} \tag{6}\]

A ten percent loss of aerodynamic efficiency is a ten percent loss of range, so anything that blunts the shape is paid for directly, and the sizing below ends by blunting the shape.

Inverting it for the stated requirement gives the design space. Solving the range relation for the ratio gives the demand placed on the shape by a fixed distance.

\[\frac{L}{D} = \frac{R}{\dfrac{R_{e}}{2} \ln\left(\dfrac{1}{1 - V^{2}/V_{c}^{2}}\right)} \tag{7}\]

Entry speeds are quoted here as Mach numbers on a fixed speed scale of 295 metres per second. That is the speed of sound the 1976 standard atmosphere tabulates, 295.07 metres per second, through its isothermal layer from about 11 to about 20 kilometres, and it lies close to the scale behind the agency’s statement of Mach 20 for more than 13,000 miles per hour, which the comparison with ground prediction below works out as 290.6 metres per second for each Mach number. At 40 kilometres the same standard gives 317.19 metres per second [U.S. Standard Atmosphere 1976 1976]. The Mach numbers quoted here are a speed scale and not local Mach numbers, and the conversion is

\[V = M a \qquad a \approx 295 \ \text{m/s} \tag{8}\]

For a range of 9,000 nautical miles, being 16,668 kilometres, the required ratio at each entry speed is

entry Mach at 295 m/s $V$ (m/s) $V/V_{c}$ required $L/D$
15 4,425 0.560 13.92
20 5,900 0.746 6.42
22 6,490 0.821 4.67
24 7,080 0.896 3.23
26 7,670 0.970 1.84

The Hypersonic Barrier Says Most of That Table Is Impossible

Hypersonic aerodynamic efficiency has an empirical ceiling, and a low one. Küchemann correlated the attainable maximum for a hypersonic configuration as a function of Mach number [Küchemann 1965], and the general shape of the difficulty was stated even earlier [Allen 1958] [Allen 1962].

\[\left(\frac{L}{D}\right)_{\max} \approx \frac{4(M + 3)}{M} = 4 + \frac{12}{M} \tag{9}\]

The published analysis of the flight tests uses the same correlation in its second form, and the same range relation as the next section, and it concludes that the vehicle’s ratio sits well below the ceiling because heat management rather than aerodynamics limited it [Acton 2015a].

At Mach 20 that ceiling is 4.60 and the table demands 6.42, so a 9,000 nautical mile glide entered at Mach 20 is not merely hard but unavailable to any shape. The mission becomes available at the Mach number where demand and ceiling meet, which is the root of

\[\frac{R}{\dfrac{R_{e}}{2} \ln\left(\dfrac{1}{1 - (M a / V_{c})^{2}}\right)} = \frac{4(M + 3)}{M} \tag{10}\]

and solving it numerically gives

\[M_{\min} = 22.2 \qquad V_{\min} = 6{,}537 \ \text{m/s} = 0.83 \ V_{c} \tag{11}\]

The vehicle must therefore be boosted to at least 83 percent of orbital speed. That demand falls on the launch vehicle and not on the glider, and it explains why the programme carried a launch vehicle task at all.

The correlation takes the local Mach number, but the figures here use the 295 metres per second scale. At 40 kilometres a given speed is a local Mach number smaller by the factor 295/317.19, which raises the ceiling by about 1 percent. Solved with the local value, the minimum speed is 6,521 metres per second, still 83 percent of orbital speed, so the conclusion does not depend on the convention.

\[\frac{4 + 12 \times 317.19/5{,}900}{4 + 12/20} = \frac{4.645}{4.600} = 1.010 \tag{12}\]

The ceiling is a correlation, and measurements on hypersonic shapes can be set beside it. Wind tunnel and free-flight characterisations of hypersonic glider and all-body configurations [Seiff and Wilkins 1961] [Nelms 1972] [Clark 1973] [Penland et al. 1978], and of the lifting bodies that followed [Ware et al. 1991], span Mach 0.2 to 10.6, and all but the first postdate the correlation. None of them was made near Mach 20, so they test the shapes and leave the ceiling untested at the speed this mission needs, and the one hypersonic lifting body among them trims at a ratio of 1.4 [Ware et al. 1991], far below the 6.42 the table demands.

Optimal manoeuvring for a vehicle of this class has been treated separately, and it does not rescue the range [Vinh and Chern 1979].

The Real Vehicle Confirms the Model

One figure of merit for the vehicle that flew has been published, and it lets the model be checked. Fitting a trajectory model to Department of Defense data on the first flight gives the lift to drag ratio of the Hypersonic Technology Vehicle 2 as 2.6 [Acton 2015a].

The check has to compare like with like. The agency’s flight plan was a launch from Vandenberg Air Force Base to the ocean north of Kwajalein Atoll, about 4,100 nautical miles in less than thirty minutes [Falcon HTV-2 fact sheet 2010], and that distance and time run from launch, through the rocket’s climb and the pull-up out of the dive into the atmosphere, to impact. The glide is only part of it. Reading the agency’s published trajectory map, the same analysis places the start of the glide at $t_{4} = 620$ seconds after launch and its end at $t_{5} = 1{,}798$ seconds, when the vehicle was to be $x_{5} - x_{2} = 5{,}900$ kilometres downrange of the point $x_{2}$ where it re-entered the atmosphere. Its fitted trajectory puts the start of the glide at $x_{4} - x_{2} = 1{,}100$ kilometres, at a speed of about 5,500 metres per second, and the end of the glide between 2,000 and 2,500 metres per second [Acton 2015a]. The planned glide therefore lasted and covered

\[t_{5} - t_{4} = 1{,}798 - 620 = 1{,}178 \ \text{s} \qquad x_{5} - x_{4} = 5{,}900 - 1{,}100 = 4{,}800 \ \text{km} \tag{13}\]

The range relation applies between any two speeds, being the difference of two ranges to rest.

\[R = \left(\frac{L}{D}\right) \frac{R_{e}}{2} \ln \left( \frac{1 - V_{f}^{2}/V_{c}^{2}}{1 - V_{i}^{2}/V_{c}^{2}} \right) \tag{14}\]

Taking the initial speed $V_{i}$ as 5,500 metres per second and the final speed $V_{f}$ as the middle of the reconstructed range, 2,250 metres per second, gives

\[R = 2.6 \times 3{,}185.5 \ \text{km} \times \ln\left(\frac{1 - 0.2847^{2}}{1 - 0.6958^{2}}\right) = 2.6 \times 3{,}185.5 \times \ln(1.7815) = 4{,}783 \ \text{km} \tag{15}\]

against the planned 4,800 kilometres. The agreement is close, but it does not validate the model independently. The speeds are the analysis’s own fitted estimates, obtained with this ratio in a model of the same family, so the agreement shows that the relations used here reproduce the published reconstruction of the plan. The model is close enough to trust for the argument that follows and not close enough to trust for design.

Asking what the demonstrated ratio would need for the original mission closes the loop.

\[\frac{V}{V_{c}} = \sqrt{1 - \exp\left(-\frac{16{,}668}{2.6 \times 3{,}185.5}\right)} = 0.931 \tag{16}\] \[V = 7{,}357 \ \text{m/s} = \text{Mach } 24.9 \ \text{at } 295 \ \text{m/s} \tag{17}\]

The Hypersonic Technology Vehicle 2 would have needed boosting to 93 percent of orbital speed to make the nine thousand mile requirement by gliding alone. Acton, who also credits the distance covered before the glide, puts the speed at which the glide would have had to begin at 6,900 metres per second [Acton 2015a], which is 87 percent of orbital speed. Either figure is very nearly a launch to orbit, which puts a number on the observation that boost-glide weapons and space launch are the same problem wearing different labels.

\[\frac{6{,}900}{7{,}904} = 0.873 \tag{18}\]

The same model predicts how long the glide should take. The deceleration along the path is the drag divided by the mass, and drag is the lift divided by the ratio.

\[\frac{dV}{dt} = -\frac{g\left(1 - V^{2}/V_{c}^{2}\right)}{L/D} \tag{19}\]

The deceleration is gentle, and it explains the flight time. At Mach 20 it is 1.67 metres per second squared, or 0.17 of a gravity, rising to 0.36 of a gravity by 2,000 metres per second as the vehicle slows and the centrifugal relief disappears. Separating and integrating gives the time to decelerate from an initial speed to a final one.

\[t = \left(\frac{L}{D}\right) \frac{V_{c}}{g} \left[ \operatorname{artanh}\left(\frac{V_{i}}{V_{c}}\right) - \operatorname{artanh}\left(\frac{V_{f}}{V_{c}}\right) \right] \tag{20}\]

Evaluating it between the same two speeds recovers the planned glide duration.

\[t = 2.6 \times \frac{7{,}904}{9.80665} \left[ \operatorname{artanh}(0.6958) - \operatorname{artanh}(0.2847) \right] = 2.6 \times 806.0 \times 0.5664 = 1{,}187 \ \text{s} \tag{21}\]

against the planned 1,178 seconds. The ratio and the reconstructed speeds reproduce both the distance and the duration of the planned glide to within one percent, with the caveat above applying to both.

The Corridor Between Lift and Heat

A glider at this speed is squeezed between two conditions. It must fly low enough for the air to hold it up and high enough for the air not to destroy it, and the gap between those is the corridor.

The lift condition fixes the density. Let $S$ be the reference area, $C_{L}$ the lift coefficient and $W$ the weight, taking the published mass of about 900 kilograms [X-41 CAV].

\[\rho = \frac{2 W \left(1 - V^{2}/V_{c}^{2}\right)}{V^{2} S C_{L}} \tag{22}\]

The weight follows from the published mass.

\[W = m g = (900)(9.80665) = 8{,}826 \ \text{N} \tag{23}\]

At 7,000 metres per second and an assumed $S C_{L}$ of 0.45 square metres this gives

\[\rho = \frac{2 (8{,}826)(0.2157)}{(7{,}000)^{2}(0.45)} = 1.73 \times 10^{-4} \ \text{kg/m}^{3} \tag{24}\]

Converting a density to an altitude needs a model of the atmosphere, and a single exponential fit from the standard sea-level density $\rho_{0}$ of 1.225 kilograms per cubic metre, with a scale height $H$ of 6.9 kilometres, is used here as a rough conversion. It is rough because the standard atmosphere tabulates a pressure scale height of 7,421 metres at about 40 kilometres and 7,241 metres at about 61.6 kilometres [U.S. Standard Atmosphere 1976 1976].

\[\rho = \rho_{0} \exp\left(-\frac{h}{H}\right) \qquad h = -H \ln\left(\frac{\rho}{\rho_{0}}\right) \tag{25}\] \[h = -6{,}900 \ln\left(\frac{1.73 \times 10^{-4}}{1.225}\right) = 61.2 \ \text{km} \tag{26}\]

which is the corridor altitude used below, as an approximate figure. The standard atmosphere places this density between 63.6 and 64.1 kilometres [U.S. Standard Atmosphere 1976 1976], so the fit puts the corridor about 3 kilometres low. The temperatures that follow depend on the density and not on the altitude, so they do not change. The lift coefficient implied is small, as it must be at this speed, and depends on an unpublished reference area.

\[C_{L} = \frac{2 W \left(1 - V^{2}/V_{c}^{2}\right)}{\rho V^{2} S} = 0.225 \ \text{at} \ S = 2 \ \text{m}^{2} \tag{27}\]

The heating condition then follows from the stagnation-point correlation, in which $R_{n}$ is the leading-edge radius and $k$ is $1.7415 \times 10^{-4}$ in SI units, so that $\dot{q}$ is in watts per square metre. Sutton and Graves give a heat-transfer coefficient for air of 0.1113 kilograms per second per metre to the three halves per atmosphere to the half, defined with the stagnation pressure and the enthalpy difference [Sutton and Graves 1971]. Taking the stagnation pressure as $\rho V^{2}$ in atmospheres and the enthalpy difference as $V^{2}/2$, which are the usual hypersonic approximations, converts it to

\[k \approx \frac{0.1113}{2 \sqrt{101{,}325}} = \frac{0.1113}{636.6} = 1.748 \times 10^{-4} \tag{28}\]

which the value used here matches to within 0.4 percent. The correlation form descends from a long line of stagnation-point work, running from the theory of heat transfer in dissociated and partially ionised air [Fay and Kemp 1963] through free-flight measurement at Mach 14.6 [Rumsey and Lee 1958] [Murphy and Rubesin 1965] and the review of entry-vehicle heating [Allen 1966], to modern prediction procedures for blunt bodies [Bouslog et al. 1993] and the radiative companion relations [Tauber and Sutton 1991]. The convective form used here is the simplest member of that family, adequate for a bound and no more.

\[\dot{q} = k \sqrt{\frac{\rho}{R_{n}}} \, V^{3} \tag{29}\]

A surface that rejects that heat by radiation alone reaches an equilibrium temperature, where $\varepsilon$ is the emissivity, taken here as 0.85, and $\sigma$ the Stefan-Boltzmann constant of $5.67 \times 10^{-8}$ watts per square metre per kelvin to the fourth power.

\[T = \left(\frac{\dot{q}}{\varepsilon \sigma}\right)^{1/4} \tag{30}\]

For a sharp edge of 50 millimetres radius at the corridor point that gives

\[\dot{q} = 3.51 \ \text{MW/m}^{2} \qquad T = 2{,}921 \ \text{K} \tag{31}\]

against the surface temperature the vehicle was expected to reach, published as more than 3,500 degrees Fahrenheit [Pentagon releases results of 13,000-mph test flight over Pacific] [Hypersonic Technology Vehicle 2], which converts as

\[T_{d} = \frac{5}{9}\left(3{,}500 - 32\right) + 273.15 = 1{,}926.7 + 273.15 = 2{,}200 \ \text{K} \tag{32}\]

and which this article calls the design temperature $T_{d}$. The radiating surface can reject only

\[\dot{q}_{d} = \varepsilon \sigma T_{d}^{4} = (0.85)(5.67 \times 10^{-8})(2{,}200)^{4} = 1.13 \ \text{MW/m}^{2} \tag{33}\]

which is less than a third of the 3.51 megawatts per square metre arriving at the sharp edge.

The Two Requirements Contradict Each Other

Holding the design temperature at the corridor point requires a leading-edge radius of

\[R_{n} = \rho \left(\frac{k V^{3}}{\varepsilon \sigma T_{d}^{4}}\right)^{2} = 0.484 \ \text{m} \tag{34}\]

on a vehicle 3.5 to 4.5 metres long [X-41 CAV]. A nose radius of nearly half a metre is more than a tenth of the vehicle’s length. Thin wings with sharp leading edges are what a high lift to drag ratio needs [Acton 2015a], so blunting a hypersonic shape that much would cost much of the ratio that the range depends on. Acton’s analysis of the flight tests reads the vehicle’s ratio as this compromise, between the long range that a high ratio buys and the low rate of heat absorption that a blunter, lower-ratio shape allows [Acton 2015a].

The design wants a sharp edge for range and a blunt edge for survival, and cannot have both. That trade has been analysed directly. An aerothermal performance constraint analysis of sharp nosecaps and leading edges works the same problem from the materials side [Rizk and Gee 2004], and a flight experiment programme was built to attack it, producing both a sharp leading-edge flight article [Rasky et al. 1998] and its successor [Rasky 1998]. The materials that would have to close the gap are the ultra-high temperature ceramics [Johnson et al. 2007b] [Levine et al. 2004a], alongside lighter thermal protection approaches [Stewart and Leiser 2007]. Thermal protection remained a problem for the Hypersonic Technology Vehicle 2, whose 2011 test was ended prematurely as a direct result of damage to its aeroshell caused by heating [Acton 2015a]. Sweeping the two unpublished quantities, being the effective $S C_{L}$ and the leading-edge radius, shows how narrow the escape is.

$S C_{L}$ (m²) $R_{n}$ = 0.05 m $R_{n}$ = 0.20 m $R_{n}$ = 0.49 m
0.45 2,921 K 2,457 K 2,196 K
0.90 2,679 K 2,253 K 2,014 K
1.80 2,457 K 2,066 K 1,847 K

Each cell is the radiative equilibrium temperature above with the density set by that $S C_{L}$ through the lift condition. Five of those nine combinations exceed the design temperature, and every combination that does not requires an edge blunt enough to cost the range. That is the vehicle’s central problem, and it was derived here without a single classified number.

Dependent Systems

The Aeroshell

The aeroshell is the vehicle, as the programme’s name said. The flight article was built by Lockheed Martin from carbon composite in an arrowhead planform [Hypersonic Technology Vehicle 2], with internal electronics and avionics only a few inches from the surface [Pentagon releases results of 13,000-mph test flight over Pacific]. A carbon composite skin is a choice about mass rather than about temperature, and the corridor calculation shows why that choice was under pressure. The cancelled first design had already failed at the aeroshell’s curved leading edges, which delaminated in manufacture [X-41 CAV].

Guidance and Control

A glider with a lift to drag ratio near 2.6 has real manoeuvre authority and very little margin. The programme study asked for a cross-range of 3,000 nautical miles [Woolf 2011], and manoeuvring away from a straight path costs down-range [Acton 2015a], so the manoeuvrability that made the concept attractive is bought from the same account as the range. No guidance architecture has been published, and this article does not infer one. What it does give is the control finding of the first flight, in which the most probable cause of the loss was “higher-than-predicted yaw, which coupled into roll thus exceeding the available control capability”, and the remedy, which was to move the centre of gravity, fly a lower angle of attack and use the reaction control system to augment the flaps [DARPA concludes review of Falcon HTV-2 flight anomaly].

The Launch Vehicle

The boost requirement derived above is severe and the programme’s launch task reflects it. Flight articles were launched on a Minotaur IV Lite from Vandenberg Air Force Base [Falcon HTV-2 fact sheet 2010], the three-stage suborbital configuration of a rocket built from the stages of the retired Peacekeeper intercontinental ballistic missile [Minotaur IV]. The rocket flew at angles of attack up to 89 degrees to meet the glider’s release requirements [DARPA concludes review of Falcon HTV-2 flight anomaly] and spent its entire flight inside the atmosphere [Hypersonic vehicle test showcases significant feats]. The published reconstruction of the first flight puts the glider’s return into the atmosphere at about 100 kilometres, 435 seconds after launch, at 6,010 metres per second [Acton 2015a]. A vehicle that must reach 83 to 93 percent of orbital speed needs most of a space launcher, and the phrase can be made exact. Specific kinetic energy goes as the square of speed, so the fraction of orbital energy required is

\[\frac{E/m}{(E/m)_{\text{orbital}}} = \frac{V^{2}}{V_{c}^{2}} \tag{35}\] \[\left(0.83\right)^{2} = 0.69 \qquad \left(0.931\right)^{2} = 0.87 \tag{36}\]

Between 69 and 87 percent of the energy of reaching orbit, spent on a vehicle that then throws all of it away in the atmosphere.

The mass consequence follows from the rocket equation, where $I_{sp}$ is the specific impulse of the booster and $m_{0}/m_{f}$ the ratio of stack mass to delivered mass.

\[\frac{m_{0}}{m_{f}} = \exp\left(\frac{\Delta V}{g I_{sp}}\right) \tag{37}\]

At an assumed solid-propellant specific impulse of 280 seconds and the lower of the two speeds this gives

\[\frac{m_{0}}{m_{f}} = \exp\left(\frac{6{,}537}{(9.80665)(280)}\right) = 10.8 \tag{38}\]

so a 900 kilogram glider needs something near ten tonnes of stack before losses, and the vehicle actually used was far larger. The four-stage Minotaur IV has a launch mass of 86,300 kilograms [Minotaur IV], and the Lite configuration omits only the small fourth stage, so against the glider’s mass the ratio is of order

\[\frac{86{,}300}{900} = 96 \tag{39}\]

The cheap alternative to an intercontinental ballistic missile turns out to need most of one.

Payload Dispensing

The one system that would have distinguished a weapon from a demonstrator was removed before flight. The Common Aero Vehicle was to dispense payloads inside the atmosphere [X-41 CAV], and that function ended with the 2004 restriction, which barred any variant that included weapons [Woolf 2011]. None of it was ever flown, so there is nothing to dimension.

The Flight Test Record

Two vehicles flew, both were lost at about the ninth minute, and the two failures were not the same.

Flight one was on 22 April 2010. The vehicle was launched from Vandenberg toward the ocean north of Kwajalein on a plan of about 4,100 nautical miles in less than thirty minutes [Falcon HTV-2 fact sheet 2010]. It returned nine minutes of flight data, including 139 seconds of Mach 22 to Mach 17 aerodynamic data [Falcon HTV-2]. The review board found that the vehicle could not hold the angle of attack it had been programmed to fly for that speed and altitude, that yaw higher than predicted coupled into roll beyond the available control, and that the loss took the form of “a slow divergence about the longitudinal axis”, in roll, until the roll rate reached the threshold at which the autonomous flight safety system commanded termination. It also found that knowledge of several key aerodynamic parameters in that flight regime was limited [DARPA concludes review of Falcon HTV-2 flight anomaly].

The first flight never reached its glide. Reading the 139 seconds as running from the return to the atmosphere, as the published reconstruction does, places Mach 17 at

\[t_{2} + 139 = 435 + 139 = 574 \ \text{s} < t_{4} = 620 \ \text{s} \tag{40}\]

so the data end before the planned start of the glide [Acton 2015a]. The deceleration confirms it. Converting Mach 17 on the 295 metres per second scale gives 5,015 metres per second, and the average deceleration from the 6,010 metres per second of re-entry is

\[\bar{a} = \frac{6{,}010 - 5{,}015}{139} = 7.16 \ \text{m/s}^{2} = 0.73 \ g \tag{41}\]

against the glide relation’s

\[\frac{g\left(1 - 0.760^{2}\right)}{2.6} = 1.59 \ \text{m/s}^{2} = 0.16 \ g \tag{42}\]

at the same entry speed. Four and a half times the glide’s deceleration is the signature of the pull-up out of the dive, and Acton concludes that equilibrium gliding was not achieved on that flight [Acton 2015a]. The figure is approximate, because the speed of sound varies with altitude through the pull-up.

Flight two was on 11 August 2011. The vehicle separated cleanly and demonstrated stable, aerodynamically controlled flight at Mach 20 for nearly three minutes [Hypersonic vehicle test showcases significant feats]. The anomaly came “post perigee and into the vehicle’s climb”, and the autonomous flight safety system then used the vehicle’s aerodynamic controls to make a controlled descent into the ocean. The agency’s initial assessment was that the anomaly was unrelated to the first flight’s, and that the changes made after the first flight had been effective [DARPA hypersonic vehicle splash down confirmed]. Approximately nine minutes into the flight the vehicle met a series of shocks that culminated in the anomaly [Engineering review board concludes review of the second test flight].

Neither flight lasted a third of its planned mission. Taking the planned end of the glide 1,798 seconds after launch [Acton 2015a] as the length of the mission,

\[\frac{9 \times 60}{1{,}798} = 0.30 \tag{43}\]

There was no third flight. An originally planned third test was cancelled [X-41 CAV], and no further test of the vehicle has taken place [Acton 2015a].

Comparison With Ground Prediction

The ground predictions the record preserves are few, and flight missed the aerodynamic ones on the first flight and the thermal ones on the second. What is public is the flight plan, about 4,100 nautical miles in less than thirty minutes at more than 13,000 miles per hour [Falcon HTV-2 fact sheet 2010], together with an expected surface temperature of more than 3,500 degrees Fahrenheit [Pentagon releases results of 13,000-mph test flight over Pacific]. No specification for the Common Aero Vehicle has been released [X-41 Common Aero Vehicle], and no wind tunnel data or contractor estimate for it is public, so there is nothing earlier than that plan to set against flight. The same fact sheet gives the speed as Mach 20 [Falcon HTV-2 fact sheet 2010], and the two statements together imply the speed scale the agency used, which is close to this article’s convention of 295 metres per second.

\[13{,}000 \ \text{mph} \times \frac{1{,}609.344 \ \text{m}}{3{,}600 \ \text{s}} = 5{,}812 \ \text{m/s} \qquad \frac{5{,}812}{20} = 290.6 \ \text{m/s} \qquad 20 \times 295 = 5{,}900 \ \text{m/s} \tag{44}\]

Speed arrived as planned and temperature is not on the record. Both flights reached the Mach 20 regime, the first returning data from Mach 22 [Falcon HTV-2] and the second flying under control at Mach 20 for nearly three minutes [Hypersonic vehicle test showcases significant feats]. The public temperature figure records an expected value for the surface, and an expectation cannot be compared with flight.

One aerothermal prediction is reported as met. The agency’s initial assessment of the second flight was that the pre-flight models predicted the transition from laminar to turbulent flow to within ten seconds of the actual transition point, a preliminary finding it qualified as subject to further analysis [Hypersonic vehicle test showcases significant feats].

Duration did not arrive. Both flights ended at about nine minutes, which is 30 percent of the planned mission by the ratio displayed in the flight test record. The record gives no distance flown on either attempt, so the range half of the plan cannot be compared at all.

The first flight missed the aerodynamic prediction. Yaw was higher than predicted and knowledge of several key aerodynamic parameters in the regime was limited [DARPA concludes review of Falcon HTV-2 flight anomaly], and the board on the second flight later summarised that aerodynamic assumptions and extrapolations from known flight regimes had proved inadequate when preparing for the first [Engineering review board concludes review of the second test flight].

On the second flight, thermal prediction and flight parted. A gradual wearing away of the skin had been expected, but larger portions than anticipated peeled from the aerostructure, and the initial shockwave disturbances exceeded by more than 100 times what the vehicle was designed to withstand [Engineering review board concludes review of the second test flight]. The same board found the aerodynamic design validated and concluded that thermal modelling and ground testing alone could not predict Mach 20 atmospheric flight [Engineering review board concludes review of the second test flight]. The next section argues what that finding means.

The sizing model is a check on the plan, not a ground prediction of the flight. At the estimated lift to drag ratio of 2.6 it reproduces the planned glide’s 4,800 kilometres and 1,178 seconds to within one percent. Those figures were computed for this article from published numbers and agree with what the programme intended rather than with what flight returned. Its corridor calculation places the difficulty at the leading edge, which is consistent with the second board’s finding, but it is a bound derived here. The programme is not recorded as having made such a prediction.

What the Data Changed

The failure report is the programme’s most valuable output, and it confirms the sizing argument.

An independent engineering review board spent seven months on the second flight and concluded that the most probable cause was unexpected aeroshell degradation, which created a series of upsets of increasing severity until the flight safety system activated [Engineering review board concludes review of the second test flight]. Some wearing of the skin had been expected. Larger portions than anticipated peeled away from the structure, and the gaps created strong, impulsive shock waves that rolled the vehicle abruptly. The vehicle righted itself after several of those rolls, and the initial disturbances it recovered from exceeded by more than 100 times what it was designed to withstand, until the severity of the continued disturbances exceeded its ability to recover [Engineering review board concludes review of the second test flight].

The derivation above predicts the board’s first two conclusions. It found that the aerodynamic design was validated and that what the flight taught concerned the thermal material properties [Engineering review board concludes review of the second test flight]. The shape worked. The edge did not.

The board’s third conclusion is general, and the most important. It found that extrapolating from known flight regimes, relying on thermal modelling and ground testing alone, could not predict the realities of Mach 20 atmospheric flight [Engineering review board concludes review of the second test flight].

The finding concerns the limits of ground test at the top of the speed range, and this series has recorded the same finding for the X-15 at a third of the speed and for the X-43, whose fastest flight at about Mach 9.6 was half of it. It had also been stated in advance, repeatedly. A survey of hypersonic flight experimentation published in 1997 was subtitled status and shortfalls and argued precisely that the ground facilities do not reach the regime [Bushnell 1997], the structures community had said the same about flight test requirements two decades earlier [Stone and Koch 1979], and a later review of critical technologies repeated it [Research and Technology Organisation 2005]. The board did not discover that ground test runs out. It confirmed it with two vehicles. The programme’s answer was a remediation phase of further analysis and ground testing that used the flight data to validate new tools for thermal uncertainty and heat-stress allowances in the outer shell [Engineering review board concludes review of the second test flight]. The corridor derived above lies where ground facilities run out, and the programme paid two vehicles to establish it.

The Contemporary Literature

Cluster Records
Thermal protection, leading edges and ultra-high temperature materials 833
Hypersonic aerodynamics, configurations and lift to drag 826
Entry aerothermodynamics, stagnation-point heating and the hypersonic boundary layer 818
Boost-glide and entry trajectories, range and the corridor 785
Flight dynamics and control of hypersonic and entry vehicles 733
Entry guidance 520
Flight experiments, ground test facilities and their limits 367
Detection, tracking and interception of glide and reentry vehicles 195
Launch vehicles, boost and stage separation 173
Structures, aerothermoelasticity and loads 129
Hypersonic weapons, prompt global strike and policy 38
Total 5,417

The survey holds 5,417 research records in 11 clusters, and every one of them appears in exactly one cluster below. The clusters cover the chain of the sizing argument, from the heat the leading edge must survive and the ceiling on aerodynamic efficiency, through the trajectory, its guidance and its control, to the flight tests, the boost, the detection of such a vehicle and the policy that removed its weapon.

Thermal protection, leading edges and ultra-high temperature materials

The binding constraint has its own field. Thermal protection systems, ablators, reusable insulation, leading edges, nose tips and the materials meant to survive them. 182 of these titles name ultra-high temperature ceramics or their zirconium and hafnium diborides, and 114 name a leading edge, nose cap or nose tip, which is the literature of the technologies that would have to advance for the sizing section’s contradiction to be resolved. The second flight’s review board attributes that flight’s loss to aeroshell degradation.

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Hypersonic aerodynamics, configurations and lift to drag

The ceiling this article uses as a bound is the subject of a literature that tries to exceed it. Hypersonic configurations, lifting bodies, waveriders, minimum-drag bodies and the measurement of lift and drag. 252 of the 827 titles name the waverider, a shape designed to ride on its own attached shock in pursuit of a high hypersonic lift to drag ratio.

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2025a] [Weidner 1980] [Weil and Matranga 1960] [Weilmuenster et al. 1991] [Weilmuenster et al. 1993] [Weilmuenster et al. 1994] [Weilmuenster et al. 1995] [Weilmuenster et al. 1996a] [Wercinski et al] [White 1971] [White 1993] [Whitfield and Griffith 1963a] [Whitfield and Griffith 1963b] [Whitfield and Griffith 1964] [Winged Cargo Return Vehicle 1990] [Winn 1993] [Witzeman 2003] [Wright et al. 2019] [Wu 2018] [Wu et al. 2015b] [Wu et al. 2018e] [Wu et al. 2018b] [Wu and Xiao 2009] [Xianhong et al. 2017] [Xiao 2009] [Xiao et al. 2006] [Xiao-Qing et al. 2011] [Xie et al. 2024a] [Xiong et al. 2021] [Xu et al. 2013b] [Xu et al. 2021b] [Xu et al. 2022b] [Xuzhao et al. 2012] [Yan et al. 2008] [Yang 2025] [Yankui et al. 2005] [Yankui et al. 2007] [Yao et al. 2017] [Yatsukhno 2017] [Ye et al. 2016] [Yin et al. 2025] [Yoon and Rasmussen 1996] [Yoon and Suzuki 2024] [Yost et al. 2019] [You et al. 2009] [Young 1966] [Zadonsky et al. 2013] [Zhang et al. 2015a] [Zhang et al. 2016b] [Zhang et al. 2016a] [Zhang et al. 2019d] [Zhang et al. 2019e] [Zhang et al. 2019f] [Zhang and Tang 2015] [Zhao et al. 2018a] [Zhao et al. 2020b] [Zhao et al. 2024] [Zhao et al. 2025b] [Zheleznyakova and Surzhikov 2014] [Zheng 2021] [Zheng et al. 2020b] [Zheng et al. 2020c] [Zhivotov and Nikolaev 2011] [Zhou et al. 2023e] [Zou et al. 2023] [Zou et al. 2024] [Zuber and Bertin 1998] [Zubin et al. 1997] [Zweber et al. 2002] [안미치코 2013]

Entry aerothermodynamics, stagnation-point heating and the hypersonic boundary layer

The heating correlation used in the sizing section comes from this literature. Stagnation-point and convective heating, shock-layer radiation, nonequilibrium and rarefied flow, the plasma sheath and boundary-layer transition at hypersonic speed. 94 titles name the stagnation point and 99 name radiation, and 129 of these records date from before 1970, more than in any other cluster.

818 records. [Aero-Heating Prediction Model 2025] [Aerodynamic Heating 1979] [Aerodynamic Heating for Gaps 1981] [Aerothermodynamic Base Heating 1978] [Aerothermodynamic Design 1993] [Aerothermodynamic Design Feasibility 1982] [Aerothermodynamic Entry Environment 1983] [Aerothermodynamic Heating Analysis 1985] [Aerothermodynamic Predictions for Hypersonic 2004] [Aerothermodynamic Testing and Hypersonic 2023] [Agarwal 2011] [Ahmed and Qin 2010] [Ahmed and Qin 2011] [Ahmed and Qin 2012] [Al-Damook et al. 2026] [Allen 1966] [Allen et al. 2018] [Allouche et al. 2011] [Allouche et al. 2020] [Alpert et al] [Alpert and Tobin] [Amirkabirian et al. 1986] [Analysis of Aerothermodynamic Environment 1982] [Analytical Characterization of AOTV 1985] [Anderson 1968c] [Anderson 1968b] [Anderson 1968d] [Anderson 1968a] [Anderson 1973] [Appar et al. 2022] [Appartaim et al. 2001] [Application of Hypersonic Vehicle 2025] [Approximate Analysis 1986] [Arabshahi 2021] [Archer 1963] [Armstrong et al. 1960] [Arnold et al. 1979] [Aso et al. 1992] [Avallone et al. 2013] [Fujino and Ishikawa 2013] [Andrey 2011] [Babineaux 1966] [Bade 1962] [Bade 1975] [Bahrami 2012] [Bajpai and Jagadeesh 2023] [Balakrishnan and Chaussee 1988] [Balakrishnan et al. 1985] [Balakrishnan et al. 1986] [Balla 2013] [Bansal et al. 2012] [Barnhardt et al] [Barnhardt et al. 2019a] [Barnhardt et al. 2019b] [Barnhardt et al. 2021] [Bathel et al. 2019] [Bauer 1990] [Becker et al. 1973] [Beierholm et al. 2008] [Belov et al. 1999] [Benay 2003] [Bendor 1963] [Berger 2009] [Berry 1967] [Berry and Berger 2015] [Berry and Scott 2023] [Berry et al] [Berry et al. 2001] [Berry et al. 2002] [Berry et al. 2006] [Berry et al. 2009] [Berry et al. 2010] [Bertin and Cummings 2006] [Bettis and Hosder 2010] [Bhagwandin and Martin 2023] [Bhat and Lind 2009] [Bilchenko and Bilchenko 2017] [Bird 1966] [Blackwell et al. 1986] [Blackwell et al. 1989] [Blanchard and Nicholson 1995] [Blanchard et al. 1996] [Bogdonoff 1968] [Bond et al. 1958] [Bonin et al. 2017] [Borovoj and Kubyshina 1993] [Bortner 1964] [Bouslog et al. 1993] [Bouslog et al. 1997] [Boyd and Haas 1994] [Boyd and Padilla 2003] [Boyd and Whiting 1992] [Brandis 2012] [Brandis and Johnston 2014] [Brandis et al. 2018] [Brazhko et al. 2020] [Brewer et al. 1968] [Buchanan et al. 1978] [Burchfield and Bontrager 1966] [Burnett 1993] [Burns et al] [Busing 1964] [Cabrera and West 2026] [Caillaud et al] [Caledonia and Krech 1994] [Cambier and Edwards 1994] [Campbell et al. 1996] [Campbell et al. 2006] [Candler et al. 2015] [Cardone 2007] [Carleton and Marinelli 1991] [Carlson 1994] [Carlson 1999] [Carroll and Brandis] [Carroll and Brandis 2023] [Carter et al. 2005] [Cary 1970] [Cassell et al. 2016] [Chapman 1967] [Chapter 13 2013] [Chen and Fan 2025] [Chen and He 2025] [Chen, ine, W D et al. 1995] [Chen et al. 2015c] [Chen et al. 2015a] [Chen et al. 2016c] [Chen et al. 2016b] [Chen et al. 2021a] [Chen et al. 2026c] [Cheng et al. 2021b] [Cheng et al. 2024a] [Chernyi 1961b] [Chetverushkin et al. 2006] [Ching et al. 2024] [Chisnell et al. 1965] [Chou 1973] [Chou and Marineau 2024] [Chou et al] [Choudhari et al. 2020] [Chow 1966] [Chow 1967] [Chow and El-Assar 1970] [Chpoun 1990] [Chun 1991] [Chung and Liu 1962] [Cinquegrana et al. 2015] [Collins and Horton 1964] [Compton and Cooper 1965] [Computation of Skin Friction 1988] [Conti 1961] [Cooper 1966] [Copeland et al. 2014] [Craig et al. 1994b] [Creel 1974] [Cruden 2016] [Cruden and Brandis 2016] [Cruden et al. 2014] [Cruden et al. 2015] [Cruden et al. 2019] [Culler et al. 2007] [Cutrone 2023] [Cutrone and Schettino 2024] [D’Oriano et al. 2018] [da Costa et al. 2016] [Davami et al] [Davies et al. 1984] [Davis 1964] [De Filippis et al. 2005] [De Geyter 1973] [De Geyter et al. 1974] [DeChant and Wagnild 2020] [Deep and Jagadeesh 2018] [DeJarnette 1992] [DeJarnette et al. 2008] [Demele 1963] [Demetriades 1977] [Derienzo and Pallone 1967] [Desai et al. 2019] [Deyang and Kun 2016] [Di Clemente et al. 2006] [Di Clemente et al. 2009] [Di Giorgio et al. 2019] [Dilley and Nerem 1969] [Direct Numerical Simulations 2023] [Dirling et al. 1970] [Dix et al. 1967] [Dobrov et al. 2023] [Drag of Bodies 1986] [Dreyer et al. 2021] [Duan et al. 2026] [Dudin and Ledovskiy 2013] [Dudin and Ledovskiy 2020] [Dudin and Neiland 1980] [Dunavant and Edwards 1966] [Effects of Surface Discontinuities 1986] [Eilertson and Wing 1966] [Ellison 1969] [Engel 1979] [Engel and Spradley 1968] [Evans et al. 1973a] [Evans et al. 1973b] [Ewenz Rocher et al. 2022] [External Flows 1977b] [External Tank Laminar 1980] [Eyi 2013] [Eyi et al. 2018] [Eyi et al. 2019] [Eyi and Yumuşak 2014] [Falanga and Olstad 1974] [Fannelop 1968] [Fante et al. 1970] [Fay and Kemp 1963] [Faye-Petersen et al. 1972] [Fedioun and Orlik 2012] [Fehrman and Masek 1972] [Feng et al. 2014] [Ferrier et al. 2006] [Ferrier et al. 2008] [Filipkovskyi 2026] [Finkbeiner] [Finke 1990] [Finson 1975] [Finson et al. 1980] [Florence 1981a] [Florence 1981b] [Florence 1985] [Forsythe et al. 1961] [Franze and Barz 2025] [Gai et al. 1985] [Gaillard et al. 1999] [Gally and Campbell 2002] [Gao and Jiang 2015] [Gao et al. 2024a] [Gao et al. 2026a] [Garrett 1971] [Garrett et al. 1972] [Garvine 1964] [Garvine 1966] [Glass 1989] [Glass and Moss 2001] [Glass et al. 1989] [Gnoffo et al. 1997] [Gnoffo et al. 1999] [Goates et al. 2026] [Goldberg and Scala 1965] [Goldburg et al. 1965] [Golden 1969] [Golomazov and Ivankov 2013] [Gong Weijie and Tang Shuo 2010] [Goodrich et al. 1983a] [Goodrich et al. 1983b] [Gottmann 1996] [Goulard 1961] [Grant 1961] [Greendyke and Hartung 1990] [Greene and Hamilton 2006] [Griffin et al. 2022] [Gros 1963] [Grose and Nealy 1975] [Gruszczynski and Thomas 1966] [Gruszczynski and Warren 1966] [Gruszczynski and Warren 1967] [Gu 2026] [Gu et al. 2016] [Gui 2019] [Guo and Chen 2022] [Guo et al. 2024d] [Gupta et al. 1992] [Gupta et al. 1993] [Gupta et al. 1994] [Gusev 1990] [Gülhan et al. 2001] [Haas 1993] [Hackett 1993] [Hamed and Kumar 1992] [Hamilton 1982] [Hamilton et al. 1991] [Hamilton et al. 1993] [Hamilton et al. 1994] [Hammitt 1959] [Hammitt and Bogdonoff 1956] [Han and Su 2025] [Haney 1983] [Hankey and Hooks 1963] [Harloff and Petrie 1987] [Hartung et al. 1990] [Hartung et al. 1991] [Hartung et al. 1992] [Hartunian and Thompson 1963] [Harvey 2011] [Haskins et al] [Hassan et al. 1991] [Hassan et al. 2001] [He et al. 2023b] [He et al. 2025a] [Heat Transfer 1986] [Heffner et al. 1991] [Heliodyne Corp Los Angeles Ca 1964] [Helms 1973] [Higdon et al. 2016] [Hirschel 1991] [Hirschel 1992] [Hirschel 2015a] [Hirschel 2015b] [Hirschel et al. 2025a] [Hirschel and Weiland 2009e] [Hirschel and Weiland 2009b] [Hirschel and Weiland 2009c] [Hirschel and Weiland 2009a] [Hirschel and Weiland 2009f] [Hirschel and Weiland 2009d] [Holden 1978] [Holden 1986] [Holifield and Tufts 2024] [Hollis 2019] [Hollis and Hollingsworth 2012] [Hollis and Hollingsworth 2013] [Hollis and Hollingsworth 2014] [Hollis and Hollingsworth 2023b] [Hollis and Hollingsworth 2023a] [Hollis and Hollingsworth 2025] [Hollis et al. 2024] [Hollis and Perkins 1995] [Hollis and Prabhu 2011] [Hollis and Prabhu 2013] [Holloway and Sterrett 1953] [Hong and Neuenschwander 1991] [Horing et al. 2025b] [Horing et al. 2025a] [Hornung 2002] [Horton and Babineaux 1967] [Horton and Zeh 1966] [Horton and Zeh 1967] [Horvath et al. 1999] [Horvath et al. 2001] [Horvath et al. 2002] [Horvath et al. 2012] [Hoskin et al. 2024] [Hossein et al. 2025] [Hoult et al. 2003] [Hove and Shih 1977] [Hu et al. 1997] [Hu et al. 2026c] [Huang and Hwang 1970] [Huang et al. 1973] [Huang et al. 2025b] [Hung and Barnett 1973] [Huo and Yang 2015] [Hyatt and Johnson 2025] [Hypersonic Thin Viscous Shock 2018] [Influence of Corrugation-Roughness Shape 1980] [Inger 1991] [Inger 1995b] [Inger 1995a] [Inglesse and Cruden] [Inman et al. 2008] [Inoue and Page 1977] [Ito et al. 1999] [Ivanov et al. 2007] [Ivanov et al. 2011] [Jedlicka and Parker 1970] [Jewell et al. 2013a] [Jewell et al. 2013b] [Jie 2017] [Jo 2026] [Jo et al. 2019] [Jo et al. 2020] [John and Kulkarni 2014] [Johnston] [Johnston et al. 2011] [Johnston et al. 2012] [Jones 1962] [Jones 2013] [Jones and Berry 2013] [Jones and Cross 1972] [Jones et al. 1993] [Juang 1989] [Kaattari 1962] [Kaattari 1978] [Kanderpalli et al. 2014] [Kang et al. 2026] [Karlgaard et al. 2022a] [Karthick and Sriram 2019] [Kashkovsky 2014] [Katzin et al. 1960] [Kaufman 1963] [Kaufman and Louis G. 1964] [Kemp 1960] [Ketcham and Velkoff 1967] [Keyes 1977] [Khlopkov et al. 2014] [khraibut et al 2015] [Khraibut et al. 2017] [Khraibut et al. 2019a] [Khraibut et al. 2019b] [Kianvashrad and Knight 2018] [Kianvashrad and Knight 2019] [Kienappel et al. 1974] [King et al. 2008] [Kivel 1961] [Kleb and Johnston 2008] [Kline et al. 2019] [Klothakis and Nikolos 2024] [Klothakis et al. 2026] [Knight 2015] [Knight and Kianvashrad 2023] [Knisely et al. 2019] [Ko et al. 1981] [Ko et al. 1986] [Koike et al. 2018] [Kojima et al. 2012] [Kumar and De 2021] [Kumar et al. 1978] [Kumar et al. 2020] [Kunc and Soon 1988] [Kutkan and Eyi 2018] [Lago et al. 2012] [Lakin et al. 2025] [Lakshman et al. 2017] [Lau 2008] [Laurmann 1964] [Laux et al. 1992] [Lee et al. 2003] [Lee et al. 2026] [Lees 1956a] [Lees 1956b] [Lennon and Poirter 1974] [Letkemann et al. 2024] [Letkemann et al. 2026] [Li and Gao 2014] [Li et al. 2018c] [Li et al. 2020h] [Li et al. 2022a] [Li and Zhang 2021] [Liechty et al. 2002] [Liechty et al. 2011] [Liu 1967] [Liu et al. 2016a] [Liu and Qiang 2012] [Livingston and Williard 1969] [Livingston and Williard 1971] [Lovelace 1961] [Mahulikar 2005] [Maione et al. 2026] [Maise 1971] [Manned Mars Entry Vehicle 1994] [Maples 1979] [Marichalar et al. 2006] [Marichalar et al. 2012] [Marini 2001] [Masaki and Yakura 1968] [Masek 1970] [Mason 2020] [Mason and Berry 2015] [Matheny and Smith 2026] [Matsuda et al. 2013] [Matsunaga et al. 2017] [Matthews et al. 1972] [Mazaheri 2013] [McAnally and Engel 1979] [McConnell 1961] [McGinley et al. 2006] [McQuaid and Brehm 2024] [Meckler 1964] [Mehta 2023] [Menard and Thomas 1966] [Menard and Thomas 1967] [Menees et al. 1985] [Menees et al. 1987a] [Meng 1973] [Menssen 2026] [Mesalles Ripoll et al. 2021] [Meyer et al. 1999] [Micol 1991] [Micol 1995a] [Mifsud et al. 2012] [Miller 1984] [Miller 2005] [Mitcheltree 1991] [Mitcheltree et al. 1998] [Mitcheltree and Shebalin 1992] [Molina et al. 1996] [Moosavi et al. 2009] [Moreira et al. 2021] [Moreira et al. 2022b] [Moreira et al. 2022a] [Morimoto and Kinefuchi 2025] [Morreale and Wagnild 2021] [Moss 1974] [Moss 1977] [Moss and Kumar 1981] [Moss et al. 1978] [Moss et al. 1996] [Munipalli et al. 2005] [Murayama et al. 1992] [Musal 1962] [Nagamatsu and Li 1960] [Nagamatsu and Sheer 1960] [Nagel and Hanks 1960] [Najafiyazdi 2005] [Nardo and Sadler 1962] [Naughton et al] [Naughton et al] [Nealy and Haggard 1973] [Needham 1965] [Neely and Morgan 1994] [Neumann 1989] [Newell and Zakharov 2007] [Nicolet 1974] [Nie and Liu 2013] [Nomura 1983] [Nomura and Yamamoto 1996] [Nonequilibrium Stagnation Region Aerodynamic 1975] [Nowak et al. 1984] [Numerical Analysis of Aerothermodynamic 1994] [Okuno and Park 1968] [Okuno and Park 1969] [Oliveira Júnior et al. 2021] [Olivier 1995] [Olstad 1965] [Olstad 1969] [Ortloff 1968] [Otsu et al. 2015] [Palmer 1989] [Palmer et al. 1997b] [Pan et al. 2014] [Panagiotopoulos et al. 2005] [Panagiotopoulos et al. 2006] [Pang et al. 2021] [Papadopoulos and Subrahmanyam 2006] [Paredes et al] [Paredes et al. 2021] [Paredes et al. 2022] [Park 1971] [Park 1976b] [Park 1979a] [Park 1979b] [Park 1979c] [Park 1982] [Park 1985] [Park 2005] [Park 2007] [Park 2011] [Park and Ahn 1998] [Park and Bershader 1992] [Park et al. 1991] [Pate and Brillhart 1963] [Pearce 1970] [Pereira Lara et al. 2018] [Perini 1975] [Pezzella 2011] [Pezzella 2013] [Pezzella 2015] [Pionessa and Kinzel 2024] [Pollin 1963] [Pollock et al. 2023] [Polutchko 1974] [Polyanskii 1967] [Pope 1968] [Pope 1969] [Poplavskaya 2002] [Prabhu et al. 1991] [Prakash and Zhong 2008] [Prakash and Zhong 2009] [Probstein 1961] [Proceedings of the NASA 1964] [Qiu et al. 2017] [Qu et al. 2017] [Qu et al. 2018] [Qu et al. 2023b] [Quan et al. 2026] [DiviaHarshaVardini et al. 2023] [Radiative Flux Penetration through 1979] [Radiative Heat Transfer 2018] [Radiative Transport in Inviscid 1969] [Ragnoli et al. 2024] [Rao et al. 2026] [Rarefied Hypersonic Flow over 1994] [Rault 1992b] [Ravi et al. 2025] [Ray and De 2022] [Ray and De 2025] [Reda 2001] [Reda et al. 1970] [Reddish et al] [Reddy and Nagaraja 2024] [Reddy and Sinha 2009] [Reddy and Sinha 2012] [Reed 2005] [Reed 2006] [Reilly 1964] [Reller and Seegmiller 1960] [Reshotko 1961] [Reubush and Omar 1990] [Rhudy 1970] [Riabov 2026] [Richards et al. 1971] [Riedelbauch and Hirschel 1993] [Riggins and Camberos 2020] [Riggins et al. 2003] [Rijbin and Lin 1972] [Riley and DeJarnette 1992] [Rodriguez and Anderson 2010] [Rodriguez et al] [Rogers et al. 2022] [Rose and Stankevics 1963] [Rosner and Cibrian 1974] [Ru-ren Chow 1963] [Rubin 1968] [Rumsey and Lee 1958] [Running et al. 2019] [Sabapathy 2026] [Sabol 1958] [Sahai and Johnston] [Santos 1993] [Santos 2004] [Santos 2006] [Santos 2007b] [Santos 2012a] [Santos et al] [Santos et al. 2020] [Santos et al. 2021] [Sarma 1996] [Sarosh 2021] [Sasoh and Fujiwara 1990] [Sawada and Dendou 2001] [Scala 1961] [Scala 1962a] [Scala 1962b] [Schadt 1968] [Schmidt 1966] [Schouler et al. 2021] [Schouler et al. 2023] [Scott 1989] [Scott 2000] [Scott and Derry 1982] [Scott et al] [Seager and Agarwal 2015] [Seegmiller 1968] [Seiff 1967] [Sforza 2026] [Shang and Surzhikov 2011] [Sharma and Gillespie 1990] [Sharma et al. 2019] [Shebalin 1990] [Sheetz 1969] [Sheldon 1967] [Shevelev 2018] [Shevyrin et al. 2016] [Shi et al. 2019] [Shinn 1980] [Shirai and Park 1979] [Shivank et al. 2023] [Shock Layer Structure 1962] [Shock-Wave Relations and Aerothermodynamic 2023] [Shorenstein 1972] [Shrestha et al] [Simeonides 2003] [Simeonides 2006] 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al. 2023d] [Zhang et al. 2025e] [Zhang et al. 2026a] [Zhao 2011] [Zhao 2021a] [Zhao 2021b] [Zhi et al. 2015a] [Zhou et al. 2023a] [Zimmerman et al. 2002] [Zishka and Agarwal 2015] [Zoby and Moss 1980] [Zoby et al. 1993] [Zoby and Rumsey 1971] [Zuo and Hu 2021] [Zuppardi et al. 2006] [Ösün et al. 2026]

Boost-glide and entry trajectories, range and the corridor

This is the article’s keystone and it is an old subject. The equilibrium glide, the skip, range, cross-range, the footprint and the corridor, and the optimisation of entry and boost-glide trajectories. The earliest record is the comparative analysis of long-range hypervelocity vehicles of 1955 that the sizing section cites, and 74 records date from before 1970. 378 date from 2015 or later, and 138 titles concern lunar return, aerocapture or entry into another planet’s atmosphere.

785 records. [Alber 2012] [Albert and Braun 2020] [An et al. 2020] [Anderson and Kinzel 2023] [Anderson et al. 1963] [Andrus and Suchomel 1975] [Anhtuan D. 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Flight dynamics and control of hypersonic and entry vehicles

A glider that cannot be steered is a ballistic reentry vehicle, and steering starts with stability. Flight dynamics, attitude control, reaction control, fault tolerance and navigation of hypersonic and entry vehicles. 122 of the 733 titles name an air-breathing, scramjet or cruise vehicle, and 447 date from 2015 or later.

733 records. [212 Problems in Control 1994] [Adami and Zhu 2007] [Adami and Zhu 2008] [Adamov et al. 2014] [Agustin et al. 1998] [Agustin et al. 1999] [Almeida 2021] [Alunni et al. 2020a] [Alunni et al. 2020b] [Amrutha and Hari Kumar 2018] [An et al. 2017b] [An et al. 2017a] [An et al. 2021a] [An et al. 2025a] [An et al. 2025b] [Appleby and Adams 1991] [Austin and Jacobs 2003] [Autenrieb 2023] [Autenrieb and Fezans 2024] [Autenrieb and Gruhn 2025] [Autenrieb and Gruhn 2026] [Autenrieb et al. 2025] [Bai et al. 2013] [Bai et al. 2014] [Bai Weijie et al. 2019] [Bailey and Brownson 1979] [Banerjee 2019] [Bao et al. 2023b] [Bao et al. 2023a] [Bao et al. 2024] [Bassett et al. 2017] [Bebyakov 2013] [Becker et al. 1962] [Bedrov et al. 1965] [Bedrov et al. 1966] [Bhatta and Leonard 2004] [Bihari et al. 2011] [Bilimoria and Mueller 2010] [Bin and Hongxin 2006] [Blanchard and Hoffman 1961] [Blevins and Hohmann 1975] [Bolender and Doman 2005b] [Bolender and Doman 2005a] [Bolender et al. 2009] [Breeza Paulose et al. 2016] [Brugarolas et al. 2008] [Bu and Jiang 2023] [Bu and Ma 2023] [Bu et al. 2015] [Bu et al. 2019] [Bu et al. 2022a] [Bu et al. 2022b] [Bu et al. 2022c] [Bu et al. 2023a] [Bu et al. 2023c] [Bu et al. 2023d] [Bu et al. 2023b] [Buschek and Calise 1997] [Butt 2013] [Butt et al. 2010] [Butt et al. 2011a] [Butt et al. 2011b] [Butt et al. 2013] [Bykerk et al. 2020a] [Bykerk et al. 2020c] [Bykerk et al. 2020d] [Bykerk et al. 2020b] [Cai et al. 2010] [Cai et al. 2013a] [Cai et al. 2013b] [Cai et al. 2014] [Cai and Wu 2011] [Calhoun 2000] [Calhoun and Queen 2002] [Cavallo et al. 1996] [Cayse 1987] [Cefola and Shen 1968] [Cefola and Shen 1969a] [Chang et al. 1972] [Chao et al. 2014] [Chao et al. 2015] [Chao et al. 2022a] [Chao et al. 2022b] [Chen 2017b] [Chen 2017a] [Chen 2021] [Chen et al. 2016d] [Chen et al. 2016e] [Chen et al. 2016a] [Chen et al. 2017a] [Chen et al. 2017b] [Chen et al. 2018a] [Chen et al. 2018b] [Chen et al. 2018e] [Chen et al. 2018c] [Chen et al. 2019a] [Chen et al. 2019b] [Chen et al. 2020e] [Chen et al. 2020m] [Chen et al. 2020k] [Chen et al. 2020j] [Chen et al. 2020f] [Chen et al. 2021e] [Chen et al. 2022c] [Chen et al. 2022b] [Chen et al. 2022a] [Chen et al. 2023a] [Chen et al. 2024] [Cheng et al. 2016] [Cheng et al. 2019b] [Cheng et al. 2020] [Chengbin Lian et al. 2012] [Chi et al. 2021] [Chou et al. 1996] [Chu et al. 2023] [Clark and Evans 1960] [Cole et al. 1970] [Colgren et al. 2009] [Colwell 1963] [Cong and Kunfeng 2017] [Coupled Dynamic Model 2018] [Cruz] [Cruz and Guecha-Ahumada] [Cruz et al. 2009] [Cui et al. 2013b] [Cui et al. 2026b] [Dai and Xia 2016a] [Dai and Xia 2016b] [Dalle et al. 2010] [Dalle et al. 2011a] [David O. Sigthorsson 2006] [Davidson et al. 1999] [de Moura and Ribeiro 2026c] [de Moura and Ribeiro 2026a] [de Moura and Ribeiro 2026b] [Deshmukh et al. 2019] [Dickeson et al. 2009] [Dillman et al. 2013] [Ding et al. 2019] [Ding et al. 2023a] [Ding et al. 2025] [Djanal-Mann and Murugan 2025] [Dobies 1957] [Dodge et al. 2026] [Dong et al. 2014] [Dong et al. 2020] [Dong et al. 2023c] [Dong et al. 2023a] [Dong et al. 2024a] [Dong et al. 2025a] [Dong et al. 2025c] [Dou et al. 2013] [Dou et al. 2017] [Du et al. 2023] [Duan and Li 2012] [Duan and Zhang 2016] [Duan and Zhong 2010] [Dyakonov et al. 2007] [El-Kebir and Ornik 2020] [Elsey and Carlson 1968] [Engel et al] [Engel et al. 2024] [Falkiewicz et al. 2011a] [Famularo et al. 2016] [Fan et al. 2017a] [Fan et al. 2019] [Fan et al. 2021a] [Fan et al. 2022] [Fan et al. 2023] [Fan et al. 2024a] [Fan et al. 2024b] [Fang et al. 2024a] [Fedele et al. 2014] [Fenfen et al. 2020] [Feng 2011] [Feng 2022] [Feng et al. 2019] [Feng et al. 2022] [Feng et al. 2026] [Feng Li et al. 2016] [Fine 1967] [Finley and Cockrell 1995] [Finzi et al. 2003] [Fiorentini et al. 2007] [Fiorentini et al. 2009] [Fiorentini and Serrani 2012] [Forbes-Spyratos et al. 2014] [Foss and Whitcomb 1960] [Frayssinet 2019] [Friedman and Kuchta 1972] [Fusaro et al. 2022a] [Gao et al. 1997] [Gao et al. 2012] [Gao et al. 2013b] [Gao et al. 2013a] [Gao et al. 2014b] [Gao et al. 2014a] [Gao et al. 2018b] [Gao et al. 2020a] [Gao et al. 2024b] [Gao et al. 2026b] [Gao and Wang 2013a] [Gao and Wang 2013b] [Gaohua et al. 2014] [Garcia 1974] [Garrett et al. 1988] [Gockel 1993] [Goz and Theodoulis 2025] [Gregory 1960] [Groves et al. 2005a] [Groves et al. 2005b] [Groves et al. 2006] [Guan et al. 2013] [Guan Ping et al. 2012] [Guangren et al. 2015] [Guo and Liu 2024] [Guo and Lu 2021] [Guo et al. 2017c] [Guo et al. 2018a] [Guo et al. 2018b] [Guo et al. 2018c] [Guo et al. 2019a] [Guo et al. 2020b] [Guo et al. 2021a] [Guo et al. 2023a] [Guo et al. 2023b] [Guo et al. 2024b] [Guo et al. 2025a] [Guo et al. 2026b] [Guo and Xu 2022] [Hahne 1997] [Hall et al. 1998] [Han et al. 2024a] [Han et al. 2024b] [Han et al. 2025b] [Hassell 1960] [Hattis and Malchow 1992] [Hattis et al. 1991] [Hayes et al. 2020] [He et al. 2017c] [Heller et al. 1998] [Herrlin and Gelderloos 1988] [Hiruma et al. 2020] [Holleman et al. 1967] [Holm-Hansen et al. 2010] [Hong et al. 2014] [Hong Qian. Lu et al. 2011] [Hongbo Chen and Di Yang] [Hou et al. 2015] [Hu and Liu 2013] [Hu and Meng 2017] [Hu et al. 2012b] [Hu et al. 2012a] [Hu et al. 2015a] [Hu et al. 2015c] [Hu et al. 2016] [Hu et al. 2018] [Hu et al. 2021a] [Hu et al. 2021b] [Hu et al. 2022d] [Hu et al. 2022e] [Hu et al. 2022f] [Hu et al. 2022a] [Hu et al. 2022b] [Hu et al. 2024a] [Hu et al. 2025a] [Hu et al. 2026a] [Huang et al. 2013] [Huang et al. 2018a] [Huang et al. 2025a] [Huang and Zhang 2014] [Hughes and Wu 2010] [Hughes and Wu 2012] [Huo et al. 2006] [Jaffe 1970] [Janardanan and Jayakumar 2006] [Ji et al. 2017] [Ji et al. 2018] [Ji et al. 2019] [Ji et al. 2023] [Ji and Zhou 2017] [Ji and Zhou 2018] [Jianan et al. 2025] [Jiang and Bu 2022] [Jiang et al. 2018a] [Jiang et al. 2020] [Jiang et al. 2024a] [Jiang et al. 2024b] [Jianguo et al. 2018] [Jiayuan et al. 2018] [Jing-guang and Shen-min 2017] [Jingang et al. 2026] [Johnson et al. 2018b] [Johnston and Witcofski 1968] [Kempel 1971] [Keshmiri 2008] [Keshmiri et al. 2007] [Kilgore and Davenport 1975a] [Kilgore and Davenport 1975b] [Klimin and Yaroshevski 1970] [Kuchta and Friedman 1972] [Kuipers et al. 2008] [Kuipers et al. 2009] [Kulkarni et al. 2024] [Lan et al. 2014] [Lazur et al. 1999] [Le et al. 2023] [Lee and Mason 1960] [Lee et al. 2007] [Li 2021a] [Li and Fu 2010] [Li and Jia 2017] [Li and Lv 2016] [Li et al. 2010a] [Li et al. 2011d] [Li et al. 2011b] [Li et al. 2011c] [Li et al. 2011a] [Li et al. 2014b] [Li et al. 2016c] [Li et al. 2017b] [Li et al. 2019a] [Li et al. 2020b] [Li et al. 2022b] [Li et al. 2023b] [Li et al. 2023d] [Li et al. 2024j] [Li et al. 2025g] [Li et al. 2026a] [Li et al. 2026e] [Lian et al. 2012] [Lian et al. 2013b] [Lian et al. 2013a] [Liang and Liu 2009] [Liang et al. 2015a] [Liang et al. 2016b] [Liang et al. 2021] [Liang et al. 2023a] [Liang et al. 2025b] [Liang et al. 2025a] [Liaoni Wu et al. 2008] [Lin and Shen 1997] [Lind et al. 1999] [Linqi et al. 2015] [Liu and Duan 2018] [Liu and Lu 2011] [Liu and Lu 2015] [Liu et al. 2013] [Liu et al. 2014b] [Liu et al. 2016c] [Liu et al. 2019c] [Liu et al. 2020b] [Liu et al. 2020e] [Liu et al. 2021b] [Liu et al. 2021a] [Liu et al. 2022d] [Liu et al. 2023a] [Liu et al. 2024a] [Liu et al. 2025h] [Liu et al. 2026a] [Lohsoonthorn et al. 2001] [Long et al. 2020] [Longitudinal Range Control 1962] [Lu 2021] [Lu et al. 2016a] [Lubing et al. 2020] [Luo and Li 2011] [Luo et al. 2022a] [Luo et al. 2025b] [Neal 1963b] [Lv et al. 2023] [Lv et al. 2026] [Lv and Zhou 2023] [Ma et al. 2019] [Ma et al. 2023a] [Ma et al. 2024a] [Ma and She 2011] [Mao and Yang 2024] [Margolis et al. 2019] [Margolis et al. 2020] [Marrison and Stengel 1998] [McClary and Putnam 2021] [Meng et al. 2016] [Meng et al. 2019] [Meng et al. 2023] [Mi et al. 2022] [Ming et al. 2017b] [Minott et al. 1976] [Mirmirani et al. 2005] [Mirmirani et al. 2009] [Mishra and Sushnigdha 2025a] [Mo et al. 2022b] [Mo et al. 2023] [Moen 2011] [Mooij 2023] [Moul et al. 1961] [Ferreira de Moura and Borges Ribeiro 2025b] [Ferreira de Moura and Borges Ribeiro 2025a] [Ferreira de Moura and Borges Ribeiro 2025c] [Ferreira de Moura and Borges Ribeiro 2025d] [Moura and Ribeiro 2024] [Neuhaus 2018] [Nie et al. 2017] [Nie et al. 2023] [Niu et al. 2018] [Ohashi et al. 2018] [Okolo et al. 2020a] [Okolo et al. 2020b] [Olstad et al. 1961] [Otsu et al. 2011] [Owens and Giles] [Owens et al] [Owotunse et al. 2023] [Parker et al. 2006] [Parker et al. 2007] [Paulson 1958] [Peng et al. 2014a] [Peng et al. 2014b] [Peng et al. 2019a] [Peng et al. 2020] [Peng and Qi 2019] [Pengxin et al. 2015] [Piao et al. 2018] [Ping et al. 2017] [Poulain et al. 2009] [Powell 1975] [Powell 1977] [Prakash and Singh 2021] [Pu et al. 2012] [Pu et al. 2013b] [Pu et al. 2013a] [Pu et al. 2014] [Pu et al. 2016] [Qi and Jianliang 2017] [Qian and Xinguo 2011] [Qiang et al. 2017] [Qiao et al. 2019] [Qin Changmao et al. 2010] [Qu et al. 2023a] [Rainey and Close 1960] [Rathod and Sushnigdha 2025] [Rehman et al. 2009] [Ren et al. 2017] [Ren et al. 2022] [Ren and Yang 2017] [Rollins et al. 2013] [Rong et al. 2017] [Rong and Yang 2024] [Rosello 1995] [Rowell et al. 1980] [Ruimin and Jianguo 2018] [Rush and Schmidt 1965] [Sachan and Padhi 2018] [Sachan and Padhi 2020] [Sachs and Dinkelmann 1996b] [Sachs et al. 1996] [Sagliano et al. 2017] [Saranya et al. 2018] [Scallion 1999] [Schermerhorn and Demeritte 1960] [Schmidt 1993] [Schroenenberger et al. 2009] [Scott et al. 1997] [Seeny et al. 1971] [Serrani 2010] [Shafner et al] [Shakiba and Serrani 2011] [Shao et al. 2014a] [Shao et al. 2025b] [Shao and Wang 2015] [Shao and Wang 2016] [Shekhawat and Sinha 2025] [Shekhawat and Sinha 2026] [Shen et al. 2014] [Shen et al. 2023] [Shi et al. 2014] [Shi et al. 2017] [Shi et al. 2020b] [Shou and Han 2024] [Shou et al. 2021] [Shou et al. 2022] [Shou et al. 2025] [Shuai et al. 2022] [Shuping Tan and Zhibin Li 2010] [Si-Yuan et al. 2018] [Sigthorsson et al. 2006] [Sigthorsson et al. 2008] [Singh et al. 2022a] [Singh et al. 2022b] [Singh et al. 2022c] [Smiley and Camberos 2024] [Smith et al. 2018] [Song and Bian 2019] [Song et al. 2018] [Song et al. 2019] [Sridharan and Rodriguez 2013] [Steketee 1967] [Stokes and Lombaerts 2023] [Strahan et al. 2007] [Stubbs 1966] [Su et al. 2013a] [Su et al. 2013b] [Sun et al. 2013] [Sun et al. 2014] [Sun et al. 2017a] [Sun et al. 2017c] [Sun et al. 2017b] [Sun et al. 2026d] [Sun and Xin 2014] [Sun and Xin 2017] [Swaim 1966] [Takahashi and Griffin 2023] [Tan and Yan 2012] [Tang et al. 2018] [Tang et al. 2020a] [Tang et al. 2021b] [Tang et al. 2022a] [Tang et al. 2022b] [Tang et al. 2023b] [Tang et al. 2025c] [Tao et al. 2016] [Tao et al. 2017] [Tarpley and Lewis 1995c] [Tarpley et al. 1996] [Teng et al. 2016] [Tian et al. 2013a] [Tieshan et al. 2021] [Tigges et al. 2011] [Tillier 1998] [Tournes and Johnson 1999] [Vaknin and Idan 2026] [van Oort et al. 2007] [Vinh and Lin 1982] [Vogel et al. 2009] [vonEgger and Pines 1999] [Vu and Biezad 1994] [Wan and Chen 2022] [Wan et al. 2012] [Wang 2022] [Wang 2023] [Wang and Liu 2016] [Wang and Meng 2014] [Wang and Ning 2011] [Wang et al. 2012b] [Wang et al. 2012c] [Wang et al. 2012a] [Wang et al. 2013f] [Wang et al. 2013b] [Wang et al. 2014d] [Wang et al. 2014f] [Wang et al. 2014e] [Wang et al. 2014a] [Wang et al. 2014b] [Wang et al. 2015d] [Wang et al. 2017c] [Wang et al. 2017d] [Wang et al. 2018b] [Wang et al. 2018e] [Wang et al. 2019j] [Wang et al. 2020b] [Wang et al. 2020a] [Wang et al. 2021a] [Wang et al. 2021b] [Wang et al. 2022d] [Wang et al. 2023f] [Wang et al. 2024f] [Wang et al. 2024b] [Wang et al. 2024c] [Wang et al. 2025f] [Wang et al. 2025g] [Wang et al. 2025a] [Wang et al. 2025i] [Wang et al. 2026b] [Wang et al. 2026h] [Wang and Wu 2017] [Wang and Xia 2022] [Wang and Xu 2023] [Ware 1961] [Watts 2005] [Way and Brugarolas 2021] [Weaver and Hunsaker 2025] [Wei et al. 2012] [Wei et al. 2016] [Wei et al. 2019] [Wei et al. 2025b] [Weijie et al. 2016] [Wen et al. 2014] [Wen et al. 2017] [Wenbiao et al. 2014] [Wenfeng et al. 2017] [Wercinski and Edwards 1994] [Wexler and Idan 2026] [Wiese et al. 2013] [Wiese et al. 2016] [Wingrove 1966a] [Wingrove and Coate 1962] [Wiseman and Lopez 2026] [Wu and Guo 2018] [Wu and Meng 2016] [Wu et al. 2012b] [Wu et al. 2014] [Wu et al. 2018d] [Wu et al. 2023b] [Wu et al. 2025] [Wu and Wang 2015] [Wu and Yu 2018] [Xi and Meng 2019] [Xia et al. 2023] [Xiang and Deng 2023] [Xiaoqing et al. 2010] [Xie et al. 2017] [Xin Wang et al. 2008] [Xin Wang and Shijie Sun 2010] [Xingling and Honglun 2014] [Xiong Luo et al. 2008] [Xu 2015] [Xu 2023] [Xu and Huang 2018] [Xu et al. 2004] [Xu et al. 2012a] [Xu et al. 2012b] [Xu et al. 2013c] [Xu et al. 2013a] [Xu et al. 2017a] [Xu et al. 2017b] [Xu et al. 2019] [Xu et al. 2022c] [Xu et al. 2023c] [Xu et al. 2026a] [Xu and Zhang 2015] [Xue and Haibin 2017] [Xuebao et al. 2023] [Yan 2014] [Yan et al. 2017a] [Yan and Zhang 2023] [Yan Binbin et al. 2009] [Yang and Li 2023] [Yang et al. 2013] [Yang et al. 2014c] [Yang et al. 2014b] [Yang et al. 2017a] [Yang et al. 2019] [Yang et al. 2022a] [Yang et al. 2022b] [Yang and Wang 2012] [Yang and Wang 2021] [Yanli et al. 2016] [Yanli Du et al. 2008] [Yao et al. 2013] [Yao et al. 2023b] [Yao et al. 2025] [Yao and Wang 2013] [Yaosheng 2018] [Ye and Jiang 2020] [Ye et al. 2017a] [Ying et al. 2018] [Yiyin Wei et al. 2016] [Yizhen Meng et al. 2016] [Youssef et al. 2008] [Youssef et al. 2009] [Yu et al. 2014c] [Yu et al. 2015] [Yu et al. 2017] [Yu et al. 2019a] [Yu et al. 2020] [Yu et al. 2021] [Yuan et al. 2026] [Yujie and Yanhua 2025] [Yulian and Bin 2014] [Zhai et al. 2016] [Zhai et al. 2018] [Zhai et al. 2019] [Zhai et al. 2026] [Zhang and Cao 2019] [Zhang and Ding 2023] [Zhang and Du 2017] [Zhang and Han 2024] [Zhang and Han 2025] [Zhang et al. 2010] [Zhang et al. 2012a] [Zhang et al. 2013a] [Zhang et al. 2013b] [Zhang et al. 2013c] [Zhang et al. 2014a] [Zhang et al. 2017a] [Zhang et al. 2017c] [Zhang et al. 2018c] [Zhang et al. 2019g] [Zhang et al. 2021c] [Zhang et al. 2021a] [Zhang et al. 2022d] [Zhang et al. 2022h] [Zhang et al. 2022b] [Zhang et al. 2023f] [Zhang et al. 2023c] [Zhang et al. 2023e] [Zhang et al. 2023a] [Zhang et al. 2024a] [Zhang et al. 2025h] [Zhang et al. 2025g] [Zhang et al. 2025c] [Zhang et al. 2026c] [Zhang et al. 2026d] [Zhang and Tang 2012] [Zhang Zhikai et al. 2015] [Zhao and Chen 2021] [Zhao and Li 2019b] [Zhao et al. 2018d] [Zhao et al. 2018b] [Zhao et al. 2021a] [zhao et al 2021] [Zhao et al. 2022c] [Zhao and Tang 2015] [Zhao and Yang 2021] [Zhen and Fei 2012] [Zheng and Selezneva 2022] [Zhengdong et al. 2013] [Zhijian et al. 2018] [Zhou 2023] [Zhou and Fei 2013] [Zhou and Qi 2024] [Zhu 2013] [Zhu and Liu 2015a] [Zhu and Liu 2015b] [Zhu et al. 2016a] [Zhu et al. 2016c] [Zhu et al. 2017] [Zhu and Shen 2015] [Ziyang et al. 2025] [Zong et al. 2012] [Zong et al. 2013a] [Zong et al. 2013b] [Zou et al. 2015]

Entry guidance

Guidance is the capability that distinguished the concept from the missile it was meant to replace. Entry guidance, predictor-corrector and analytical guidance, skip-entry guidance, aerocapture guidance and the guidance of manoeuvring reentry vehicles. 79 of the 520 titles concern Mars, the Moon’s return or another planet.

520 records. [188 Nonlinear Control Approach 1994] [264 Guidance and Trajectory 1994] [266 on Ascent Guidance 1994] [A New Guidance Method 2014] [A Simple Re-Entry Guidance 1964] [Abbasi and Mortazavi 2013] [Adami and Nosratolahi 2009] [Afzal et al. 2009] [Alexander 1978] [An et al. 2023] [An et al. 2026] [Anderson et al. 1967] [Application of Numerical Methods 1972] [Arai and Matsumoto 2026] [Archer and Sworder 1977] [Archer and Sworder 1979] [Automatic Re-Entry Guidance 1962] [Bae et al. 2024] [Bahambari and Khankalantary 2023] [Bahm et al. 2005] [Bai et al. 2015] [Bairstow and Barton 2007] [Bao et al. 2021] [Bayard and Lu 1999] [Beall et al. 2017] [Bikdash et al. 1999] [Bin Jiang and Qi 2017] [Block et al. 1990] [Bollino et al. 2006a] [Bollino et al. 2006b] [Bollino and Ross 2007] [Brand et al. 1989] [Brandenburg et al] [Brandon 1985] [Brinda et al. 2006] [Broglio 1961] [Broglio 1962] [Brugarolas 2017] [Brugarolas 2021] [Brunner and Lu 2007] [Brunner and Lu 2008] [Brunner and Lu 2010] [Bryson and Denham 1962] [Bryson et al. 1968] [Bulirsch and Chudej 1992] [Bulirsch and Chudej 1993] [Bump 1977] [Byrne et al. 1996] [Calise and Bae 1988] [Carson et al. 2006] [Carter 1965] [Casoliva et al. 2021] [Causey and Sohoni 1973] [Cefola 1968] [Chadalavada et al. 2026] [Chander and Krishna 2013a] [Chander and Krishna 2013b] [Changsheng et al. 2006] [Chao et al. 2010] [Chapman 1959] [Chapman 1960a] [Chawla et al. 2010] [Chen et al. 2014b] [Chen et al. 2016f] [Chen et al. 2020b] [Chen et al. 2020l] [Chen et al. 2020i] [Chen et al. 2020g] [Chen et al. 2020a] [Chen et al. 2021b] [Chen et al. 2021d] [Chen et al. 2023b] [Chen et al. 2025d] [Cheng et al. 2017] [Cheng et al. 2019a] [Cheng et al. 2024b] [Cheng et al. 2025a] [Chirayath and Bindu 2014] [Chu et al. 2017] [Cliff et al. 1992] [Clutter Suppression for Hypersonic 2017] [Coate and Lessing 1965] [Coate and Lessing 1966] [Coate and Wingrove 1961] [Cramer et al. 1988] [Cruz and Skerbetz 1969] [Cui et al. 2022b] [Cui et al. 2024] [Cui et al. 2025] [Cui et al. 2026a] [D’Souza 2015] [D’Souza et al. 2008] [D’Souza et al. 2014] [D’Souza et al. 2019b] [D’Souza et al. 2019a] [D’Souza and Sarigul-Klijn 2008] [D’Souza and Sarigul-Klijn 2012] [Da-wei 2011] [Dai and Xia 2015] [Davis et al. 2010] [De Virgilio et al. 1973] [De Zaiacomo et al. 2009] [De-qing et al. 2019] [Derollez et al. 2021] [Deyst et al. 1971] [Deyst et al. 1972] [Diao et al. 2022] [Dieriam 1990] [Ding et al. 2022] [Dong et al. 2022] [Dongdong et al. 2026] [Dukeman and Fogle 2002] [Duncan 1968] [Dwyer Cianciolo and Powell 2017] [Eggleston 1960] [Eisler and Hull 1993] [Eisler and Hull 1994] [Elias 1973] [Elias 1974] [Engel et al] [Engel et al] [Enmi et al. 2018] [Evans and Dukeman 1993] [Evans and Dukeman 1995] [Fawley and Putnam 2020] [Foale 1984] [Foudriat 1961] [Foudriat and Wingrove 1961] [Friedlander and Harry 1960] [Fu et al. 2017] [Fuhry 1999] [Furfaro and Wibben 2012] [Gao et al. 2019b] [Gao et al. 2020b] [Garcia-Llama 2007] [Garcia-Llama et al. 2011] [Gay 2024] [Getzandanner et al] [Giraldo-Grueso et al. 2025] [Girerd and Barton 2000] [Gong et al. 2020] [Gracey et al. 1981] [Gracey et al. 1982] [Grail et al. 1993] [Grasso et al. 2010] [Grimm 1992] [Grimm 1993] [Grimm and Rotärmel] [Gräßlin et al. 2004] [Gu et al. 2018] [Guidance and Navigation 1968] [Gunckel 1966] [Guo et al. 2017b] [Guo et al. 2020a] [Guo et al. 2021c] [Guo et al. 2023d] [Guo et al. 2024c] [Guo et al. 2026a] [Halbe et al. 2010] [Halbe et al. 2014] [Han et al. 2025a] [Hanson and Jones 2003] [Hanson and Jones 2004] [Hanson et al. 1998] [Haoliang et al. 2015] [Harl 2008] [Harl and Balakrishnan 2010] [Harpold 1980] [Harpold and Gavert 1982] [Harpold and Gavert 1983] [Harpold and Graves 1978] [Harpold and Hill 1980a] [Harpold and Hill 1980b] [Harry and Friedlander 1960] [Hattis 1990] [Havill et al. 1966] [Haw 2003] [He et al. 2024] [Horneman et al. 2010] [Hu et al. 2023] [Hu et al. 2024b] [Hu and Zhou 2010] [Huang and Li 2016] [Hui et al. 2021] [Hull and Seguin 1994] 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Well 1996] [Perkins and Tannas 1967] [Powell 1993] [Powell 1998] [Powell and Cruz 1991] [Powell et al. 1976] [Putnam et al. 2006] [Putnam et al. 2008] [Putnam et al. 2013] [Qi et al. 2021] [Qian et al. 2014] [Qiao and Chen 2011] [Rahman et al. 2013] [Ran et al. 2023] [Rea and Putnam 2007a] [Rea and Putnam 2007b] [Reina and Patterson 1975] [Ren et al. 2019] [Ren et al. 2025a] [Roenneke and Well 1996] [Roeser et al. 2010] [Rui Teng et al. 2016] [Saito et al. 2025] [Samotokhin 2021] [San Martin et al. 2013] [Sana and Hu 2020] [Sarkar et al. 2021] [Schierman et al. 2001] [Schmidt and Velapoldi 1996] [Shao et al. 2015] [Shen and Li 2015] [Shen and Lu 2004] [Shi et al. 2020a] [Shou et al. 2023] [Smith 2016] [Sonandres et al. 2025] [Sonandres et al. 2026] [Song et al. 2022a] [Song et al. 2022b] [Song and Tong 2026] [Sostaric et al. 2011] [South 1974] [Space Shuttle Guidance Navigation 1973] [Speyer and Crues 1988] [Spratlin 1987] [Stengel 1972] [Stengel 1974] [Stiles 1970] [Stone and Powell 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Flight experiments, ground test facilities and their limits

The conclusion that ground test runs out at the top of the speed range rests on this literature. Flight experiments, flight data, arc-jet, shock-tunnel and ballistic-range facilities, and the comparison of ground prediction with flight. 25 titles name the X-43 or Hyper-X and 23 name the Space Shuttle or its orbiter, and one names the vehicle of this article, so the flight test literature of hypersonic gliding is the literature of other vehicles.

367 records. 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al. 2012] [Carbonaro 1993] [Carlomagno et al. 1993] [Carr 1966] [Cassanto 1966] [Cassanto et al. 1977] [Celenligil et al. 1991] [Chadwick 2000] [Characteristics of the HIEST 2002] [Chauvin and Speegle 1957] [Cheah et al. 2025] [Chen and Berry 2010] [Choudhari et al. 2009] [Chue et al. 2009] [Cockrell et al. 2000] [Cockrell et al. 2005] [Compton et al. 1979] [Compton et al. 1981] [Cox 1999] [Craig 1994] [Craig et al. 1994a] [Czysz et al. 1997] [D’Amico et al. 2004] [Danehy et al. 2010] [Dang et al. 2021] [Davis and White 2006] [Davis and White 2008] [Deangelis and Anderson 1992] [Deepak et al. 2006] [Deepak et al. 2008] [Defense Science Board Washington Dc 1992] [DelPapa et al. 2011] [Delpino et al. 1967] [Bushnell 1997] [Derbidge and Dahm 1976] [Deshmukh et al] [Deshmukh et al] [Deshmukh et al. 2024] [Lee 2008] [Deveikis et al. 1974] [Di Clemente and Marini 2011] [Dicristina 1979] [Dillman et al. 2014] [DiNonno and Cheatwood] [DiNonno and Cheatwood] [Dinonno et al. 2016] [Dogra et al. 1987] [Donohue and Fletcher 1996] [Draper et al. 1977] [Driver et al. 2018] [Edquist 2006] [Eggers et al. 2009] [Fedele et al. 2020] [Feie and Kretz 2008] [Freeman et al. 1997] [Frohme 1975] [Fuchs et al. 1971] [Fujii and Inoue 1998a] [Fujii and Inoue 1998b] [Fujii et al. 2000] [Fujii et al. 2001] [Garrard 2015] [Gasch et al. 2014] [General Technologies Corp Springfield Va 1963] [Gentry et al. 1966] [Gibson et al. 2002] [Glawe et al. 1963] [Gnoffo 1989] [Gnoffo and Greene 1987] [Goecke 1971] [Gokcen and Alunni 2016] [Goldie 1960] [Gong et al. 2014a] [Grantz et al. 1993] [Gregorek and Lee 1962] [Grindle 2011] [Grindle and Bahm 2006] [Hall 2002] [Hancock et al] [Hancock et al] [Hanumpatla and Knight 2026] [Harvey 2008] [Hass et al. 2005] [Haw] [Haw and Colom] [Heller and Widnall 1968] [Hellman 2014] [Hemanth et al. 2009] [Henning and Lundstrom 1972] [Hirose et al. 2015] [Hodge et al. 1981] [Holden et al. 2008] [Holland et al. 2000] [Holleman 1965] [Holleman 1966] [Holloway and Throckmorton 1995] [Horvath et al. 2007] [Huber 1966] [Hughes et al] [Hughes et al] [Hutt 1987] [Huynh and Kriz 2009] [Ishimoto et al. 1996] [Itoh et al. 1999] [Itoh et al. 2002] [Janovsky et al. 1999] [Jenkins 2007] [Jia-Ming et al. 2024] [Jiang and Luo 2019] [Jiang et al. 2017] [Jiang and Yu 2019] [Johnson et al. 1972] [Johnson and Robinson 2005] [Joseph et al. 2026b] [Joshi and Lu 2015] [Judd and Woodbury 1961] [Kalaiarassan et al. 2018] [Kaminsky and Klopfenstein 1960] [Karlgaard et al] [Karlgaard et al] [Karlgaard et al. 2018] [Karlgaard et al. 2022b] [Kempel et al. 1994] [Kennell et al. 2015] [Khatuntseva 2011] [Kim et al. 2015] [Kimmel et al. 2010] [Kimmel et al. 2011] [Kimmel et al. 2015] [Korte 1992b] [Korte et al. 1992] [Korzun et al] [Kraft and Chapman 1993] [Krane and Dybbs 1987] [Kushner et al. 2013] [Chethanrama et al. 2025] [Laster et al. 2006] [Layton and McTigue 1969] [Lecerf et al. 2014] [Li et al. 2012d] [Li et al. 2014a] [Li et al. 2015a] [Lichodziejewski et al. 2013] [Liechty et al. 2006] [Lin et al. 2025a] [Little et al. 2013] [Liu et al. 2019b] [Liu et al. 2022e] [Lockman 1967] [London and Sumrall 1999] [Long and Hanus 1989] [Longo 2008] [Lux and Burkes 2008] [Lux-Baumann and Burkes 2005] [Lux-Baumann and Burkes 2006] [Mackall et al. 1998] [Mansour and Lachaud 2013] [Marek 2011] [Marshall et al. 2005] [Martinez et al. 2011] [Matthews 1993] [Mazaheri et al. 2013] [McClinton et al. 2001] [McDanels 2005] [McGary and Li 1989] [McKee 1966] [McQuellin and Buttsworth 2024] [McTigue 1970] [McTigue and Ryan 1968] [Merlin 2014] [Metzger 1997] [Micol 1995b] [Miller 1985] [Miller 1990] [Miller 1992] [Miller 1993] [Minami and Tsukamoto 2006] [Minier and Suit 1988] [Mirels and Mullen 1965] [Mohring et al. 2021] [Moore 1960] [Moran et al. 2023] [Morelli 2008] [Morelli 2009] [Morelli et al. 2005] [Morgan et al] [Mori et al. 2002] [Morth 1970] [Moses 2003] [Moss et al. 1988] [Murphy and Rubesin 1964] [Murphy and Rubesin 1965] [Murty 1987] [Muylaert et al. 1998] [Nagai et al. 2011] [Nagamatsu et al. 1961] [Ochi 2004] [Ohlhorst et al. 2005] [Olds et al. 2013] [Palmer et al. 2015] [Park et al. 1983] [Parker et al] [Pate 1980] [Paul 2004] [Paul 2006] [Peebles 2007] [Penty Geraets and McGilvray 2019] [Piet-Lahanier and Serre 2017] [Potter 1985] [Prabhu et al. 2015] [Purpura et al. 2012] [Raiche 2009] [Ramsay et al. 1990] [Rana and Chudoba 2016] [Raper et al. 1973] [Rasky et al. 1998] [Ravichandran et al. 2023b] [Reddy 1968] [Redifer et al. 2007] [Reed et al. 1997] [Reimer et al. 2023] [Research and Technology Organisation 2005] [Riabov 2020] [Riabov and Fedoseyev 2015] [Rob 1996] [Rochefort et al. 1974] [Rochelle et al. 1989] [Rodrigues 2026] [Rollstin 1973] [Romere and Young 1982] [Rona and Zavalan 2022] [Rucker and Grandle 1973] [Sabin 1973] [Sacher 1993] [Sacher and Zellner 1995] [Sakurai et al. 1997] [Santos 2022] [Saravanan et al. 2009] [Saulman and Wagner] [Schettino and Borrelli 1998] [Schmidt et al. 2022] [Schoenenberger et al. 2005] [Schott et al. 2010] [Shams et al. 2020] [Sharma et al. 1995] [Shea 1968] [Shoemaker et al. 2012] [Silvester et al. 2007] [Sivells 1963] [Sivells 1969] [Sivells 1970] [Skalandunas 1963] [Song and Choi 2022] [Sostaric et al. 2019] [Spanos 2009] [Splinter et al. 2008] [Spravka and Jorris 2015b] [Spravka and Jorris 2015a] [Stainback et al. 1972] [Stainback et al. 1975] [Starshak and Laurence 2021] [Stoll et al. 1975] [Stone 1968] [Stone and Koch 1979] [Strawa et al. 1990] [Strawa et al. 1991] [Strawa et al. 1992] [Strike 1982] [Sullivan 1991] [Suzuki et al. 1997] [Swanson et al] [Swanson et al. 2018] [Taguchi et al. 2009] [Takahashi et al. 2025] [Takahashi et al. 2026] [Tang et al. 2010] [Tate 1964] [Tatsuta et al. 2025] [Thoemel et al. 2009] [Thompson 1966] [Thompson 1967] [Tirres et al. 2002] [Tobin and Brune] [Trivedi and Menezes 2012] [Tsuchiya et al. 2007b] [Turner 1965] [Turner et al. 2006] [Tuttle et al. 1994] [Ueda et al. 2011] [Vaughn et al. 2012] [Venkatapathy et al. 2005] [Vennik et al. 2017] [Veraar 2009] [Voland et al. 2006] [Wagner and Dale 1985] [Walberg 1984] [Walker et al. 2008] [Wang and Lin 2016] [Ward and Smart 2026] [Watanabe et al. 1996] [Watanabe et al. 1997] [Watson 1970] [Weilmuenster and Hamilton 1986] [Wells 1987] [Wells 1989] [Wercinski 2017] [Wittliff 1983] [Wittliff et al. 1992] [Xiao et al. 2020] [Yamada 2022] [Yang et al. 1987] [Yang et al. 1991] [Yang et al. 2024b] [Yao et al. 2023a] [Yi 1985] [Yin et al. 2017] [Zalameda et al. 2012] [Zhao 2021c] [Zhao et al. 2013] [Zhao et al. 2022a]

Detection, tracking and interception of glide and reentry vehicles

Whether such a vehicle can be seen is a separate question from whether it can fly. Tracking filters, trajectory prediction, radar and infrared detection, interception and missile defence. 66 titles name a glide vehicle and 143 of the 196 records date from 2015 or later. This cluster is surveyed and not analysed, since the article makes no claim about it.

195 records. [Bao et al. 2020] [Barr et al. 2026] [Bartusiak et al. 2022] [Bartusiak et al. 2023] [Bartusiak et al. 2024] [Battistini and Menegaz 2017] [Benson et al. 2025] [Bishop 2013] [Cai and Zhuang 2025] [Candler and Leyva 2022] [Cassabaum et al. 2000] [Chaw-Bing Chang et al. 1977] [Chen et al. 2008] [Chen et al. 2015b] [Chen et al. 2019c] [Chen and Tseng 2011] [Chen Chen et al. 2015] [Hailong et al. 2021] [Cheng et al. 2019c] [Cheng et al. 2021a] [Cheng et al. 2023b] [Cooper and James 1979] [Cui et al. 2010] [Dai and Wang 2016] [Dan et al. 2022] [Ding et al. 2020] [Ding et al. 2023b] [Du et al. 2026] [Dubois-Matra and Bishop 2003] [Edwards and Babikian 1987] [Fan et al. 2016] [Fan et al. 2017b] [Fan et al. 2021b] [Feng et al. 2017b] [Feng et al. 2025a] [Fitzgerald 1974] [Fu et al. 2024a] [Golenko and Sychev 2020] [Greene and Williamson 1981] [Grego 2018] [Gronlund et al. 2002] [Guangjun et al. 2013] [Guo and Fan 2022] [Han and Xiong 2016] [Hao et al. 2025] [Hao and Yongqi 2024] [He 2015b] [He et al. 2025b] [He et al. 2026a] [He et al. 2026b] [He et al. 2026c] [Holdsworth and Leondes 1990] [Hu et al. 2022c] [Huang et al. 2017a] [Huang et al. 2018b] [Huang et al. 2020] [Huang et al. 2021b] [Huang et al. 2023a] [Hutchins and San Jose 1998] [Jazwinski 1972] [Jeong et al. 2025] [Ji et al. 2025] [Kalil 1966] [Kameda et al. 2000] [Kim et al. 2025a] [Knight et al. 2026] [Kumar et al. 2018c] [Kurilova and Li 2026] [Kuroda and Imado 1990] [Lau 1979] [Law et al. 2023] [Lee and Liu 1999] [Li et al. 2019b] [Li et al. 2022g] [Li et al. 2022d] [Li et al. 2022e] [Li et al. 2023a] [Li et al. 2025h] [Li Zhi-huai et al. 2011] [Liang and Han 2008] [Liang et al. 2010] [Liang et al. 2015b] [Liang et al. 2016a] [Liang et al. 2023b] [Licata 1977] [Lin et al. 2025b] [Lin et al. 2025c] [Liquan et al. 2020] [Liqun et al. 2017] [Liu 2009] [Liu and Liang 2025] [Liu et al. 2005] [Liu et al. 2012b] [Liu et al. 2020f] [Liu et al. 2020a] [Liu et al. 2021c] [Liu et al. 2022h] [Liu et al. 2023e] [Liu et al. 2024b] [Liu et al. 2025e] [Liu et al. 2025b] [Liu et al. 2025g] [Liu et al. 2025a] [Liu et al. 2026f] [Liu Yuan et al. 2015] [Lu and Qian 2024] [Lukacs and Yakimenko 2007] [Lukacs and Yakimenko 2008] [Mehra 1971] [Meng et al. 2021] [Meng and Tian 2020] [Merritt and Kramer 1997] [Merritt et al. 1996] [Mitanchey et al. 2024] [Molchanov 2024] [Mostafa and Nooraliei 2009] [Mu and Wang 2025] [Müller and Petervari 2025] [Nam et al. 2025] [Nguyen et al. 2026] [Niu et al. 2019b] [Niu et al. 2019a] [O’Connor 2019] [Ohlmeyer et al. 2010] [Paiva 1998] [Pakula et al. 1990] [Peng Peng et al. 2013] [Pinto et al. 2023b] [Pinto et al. 2023a] [Pulimidi et al. 2018] [Qiao Yongjie et al. 2011] [Qilun et al. 2015] [Rakdham et al. 2007] [Reentry Trajectory Estimation 2024] [Ren et al. 2023] [Sankowski 2011] [Savage et al. 2000] [Schweppe 1964] [Shan et al. 2018] [Shao et al. 2014b] [Shao et al. 2025a] [Sharma et al. 2023] [Shen et al. 2022] [Simas 1963] [Skaggs et al. 1967] [Sun et al. 2025d] [Sun et al. 2025a] [Tao Xu et al. 2011] [Tian and Zhang 2013] [Tracy and Wright 2023] [Vemuri 1982] [Walenczykowska et al. 2024] [Wang and Li 2016a] [Wang et al. 2026e] [Wang et al. 2026c] [Wei et al. 2023] [Wei et al. 2024] [Wei-feng et al. 2015] [Wu and Chen 2011] [Xia et al. 2025] [Xiao et al. 2014] [Xu et al. 2020] [Xu et al. 2022a] [Xu et al. 2023b] [Xu et al. 2026b] [Xue et al. 2023a] [Yang et al. 2017b] [Yang et al. 2018] [Yang et al. 2025a] [Hong et al. 2016] [Ye et al. 2022] [Yu et al. 2019b] [Yu et al. 2022b] [Yu et al. 2025c] [Yuanjie et al. 2023] [Zeng et al. 2019] [Zeng et al. 2021] [Zewge and Bang 2022] [Zhan et al. 2017] [Zhang et al. 2018b] [Zhang et al. 2017b] [Zhang et al. 2020a] [Zhang et al. 2022f] [Zhang et al. 2025l] [Zhang et al. 2025a] [Zhang et al. 2025b] [Zhang et al. 2025i] [Zhao 1993] [Zhao et al. 2020a] [Zhao et al. 2023] [Zhou et al. 2017a] [Zhou et al. 2025] [Zhou et al. 2026b] [Jinwei et al. 2015] [Zope et al. 2026]

Launch vehicles, boost and stage separation

The boost requirement derived here is most of a space launch. Launch vehicles, ascent trajectories, staging and the separation of a glider from its booster. 57 titles name a small launch vehicle, the class the programme’s launch task was meant to produce.

173 records. [No 2002] [Aerospace Corp El Segundo Ca 1963] [Bailey 2020] [Barber 1976] [Baysal and Luo 1999] [Beers et al. 2013] [Benton 1990] [Boost Vehicle Trajectories 1964] [Boyden and McKinney 1968] [Breitsamter et al. 2001] [Browning 1993] [Burleigh 1999] [Butler et al. 1991] [Carr et al. 2012] [Chandler 2019] [Chase and McKinney 2005] [Chen 2019] [Chen and Wu 2018] [Cheng et al. 2023a] [Chiesa et al. 2005] [Cho et al. 2021] [Choi et al. 2022] [Chou et al. 1997] [Chudej 1993] [Chudej and Bulirsch 1993] [Cowling 2011] [Cremaschi 2012] [Cross and Vesely 2018] [Cvrlje 1999] [Dalle et al. 2014] [Decker and Laschka 2001] [Degelsmith et al. 1993] [Lee 2004] [Duan et al. 2024] [Duret and Fabrizi 1999] [Ebrahimi et al. 2011] [Eklund 2004] [Escher and Ehrlic 2000] [Fisher et al. 1985] [Foust and Smith 2004] [Freeborn et al. 2005] [Fruncillo et al. 2026] [Fu et al. 2019] [Gao 2000] [Garvey et al. 2003] [Giri and Ghose 2010] [Fernandez 2024] [Gong et al. 2014b] [Gong et al. 2015] [Gong et al. 2022] [Greene et al. 1990] [Gruber et al. 2023] [Guo et al. 2025c] [Hamilton et al. 2007] [Hanai et al. 2007] [Haws and Bowman 2022] [Haynes et al. 1960] [Hayward and Urdiales 2018] [He et al. 2018] [He et al. 2023a] [Heinze and Bardenhagen 1998] [Hellman et al. 2011] [Hermann and Schmidt 1995] [Hohn and Gülhan 2017] [Holguin and Labbee 1988] [Hu et al. 2025c] [Huang et al. 2023b] [Hwang 2019] [Jeyakumar et al. 2005] [Jia et al. 2020] [Jo et al. 2021] [Johnson 2002] [Jutty K et al. 2000] [Kaushal 2024] [Kim et al. 2023] [Kim et al. 2024] [Kim et al. 2025c] [Kinnersley et al. 2002] [Kokan et al. 2014] [Kothari et al. 2011] [Ledbetter 1960] [Leng et al. 2024] [Lepore 2006] [Li et al. 2024c] [Long et al. 2026] [Luo and Baysal 1999] [Mahato et al. 2023] [Mani and Haney 1994] [Marcum 2001] [Markusic et al. 2018] [Martin Co Baltimore Md 1963] [Mayrhofer and Sachs 1999] [McCormick et al. 2010] [McCurry 1996] [Menees et al. 1987b] [Michna and Allayaud 1972] [Miller 1963] [Mocio 2001] [Moog and Kross 1982] [Morani et al. 2026] [Mowry and Grasso 2020] [Murillo and Lu 2010] [Murphy et al. 2004] [Najam 2014] [Naughton 2002] [Nelson 1996] [Newman et al. 1992] [Ngo et al. 2017] [Nguyen and Aleti 2025] [Niederstrasser 2022] [Nikolaevich Blinov et al. 2016] [Okamoto et al. 2002] [Okuno and Watanabe 1992] [Palmer 2020] [Pamadi and Brauchman 1999] [Parsons Engineering Sciences INC Pasadena CA 1991] [Pelton and Madry 2019] [Pelton and Madry 2020] [Prasanna et al. 2005a] [Price et al. 1971] [Qi et al. 2023] [Rafique and LinShu 2009] [Raible and Jacob 2003] [Reaser 1997] [Reentry Maneuvering Vehicle Ascent 2025] [Runyan et al. 1960] [Sachs and Schoder 1991] [Sachs and Schoder 1992] [Sarzi-Amade et al. 2016] [Schafer 2002] [Schmidt et al. 1993] [Schoneman et al. 2000] [Schoneman et al. 2005] [Schoneman et al. 2007] [Schumacher et al. 2003] [Seo et al. 2022] [Shaju et al. 2023] [Shi et al. 2013a] [Shi et al. 2013b] [Sponaugle and Fernandes 1987] [Steele 2009] [Stender and Loghry 2017] [Stevens et al. 1995] [Sun and Zhao 2013] [Suzuki 2001] [Suzuki 2016] [Tartabini et al. 2011] [Tharratt 1975] [The FALCON Small Satellite 2004] [Thornton 1977] [Unsteady Interaction Mechanism 2023] [Villanueva 2022b] [Villanueva et al. 2013] [Villanueva et al. 2014] [Wang et al. 2017g] [Wang and Wang 2024] [Watts 1971] [Weeks et al. 2004] [Wenbo and Qiang 2012] [Wilke et al. 2000] [Wu et al. 2015a] [Wuenscher 1967] [Wunderlin et al. 2018] [Yoon and Ahn 2016] [Yu et al. 2014a] [Zaehringer et al. 2003] [Zhai and Yang 2020] [Zhang et al. 2021b] [Zhang et al. 2025d] [Zheng et al. 2020a] [Zhong et al. 2022] [Zhong and Wu 2021] [Zhou et al. 2017b]

Structures, aerothermoelasticity and loads

What the heating does to the airframe. Hot structures, aerothermoelasticity, panel flutter, thermal stress and the loads of entry, which join the heating clusters to the structure that carries them.

129 records. [Ahmed and Lane 2017] [Anderson and Swann 1960] [Barz 2026] [Bell et al] [Blevins et al. 1993] [Boensch et al. 1968] [Bolender and Doman 2006] [Brune et al. 2015] [Chavez and Schmidt 1994] [Chen 1958b] [Chen 1958a] [Chen et al. 2009] [Chen et al. 2018d] [Chen et al. 2025g] [Cheng et al. 2018] [Clapp et al. 2015] [Clark et al. 2006] [Cohen 1973] [Cristillo et al. 2019] [Czarnecki and Davison 1960] [Dabas et al. 2025] [De-qing et al. 2021] [Deriugin et al. 1972] [Doggett 1959] [Du et al. 2017] [Duda 2016] [Dusinberre 1958] [Falkiewicz et al. 2009] [Falkiewicz et al. 2010] [Falkiewicz et al. 2011b] [Ferraiuolo and Manc 2011] [Fusco et al. 2026] [Garba and Heer 1968] [Gladden and Melis 1988] [Goldman et al. 1967] [Goldman et al. 1968] [Gong et al. 1984] [Gopinath et al. 2017] [Guo et al. 2019b] [Gupta and Petersen 1993] [Gupta and Voelker 2012] [Guy 1968] [Guy 1969] [Hall et al. 2026] [Hao et al. 2017a] [Harris and Davidson 1962] [Heard et al. 1972] [Heeg et al. 1993] [Helper et al. 1960a] [Hernandez et al. 2020] [Hu and Mahadevan 2019] [Hu et al. 2008b] [Hudson and Stephens 2009] [Huo et al. 2016] [Huo and Yang 2017] [Jayanthi and Jain 2019] [Johnson 1966] [Jones and Cesnik 2024] [Klock and Cesnik 2015] [Klock and Cesnik 2016] [Ko and Jenkins 1989] [Ko et al. 1987] [Ko et al. 2007b] [Ko et al. 2007a] [Kozlov 1969] [Kuipers et al. 2007] [La Porte 1966] [Langston et al. 2018] [Lazarev 1999] [Levin et al. 2008] [Li et al. 2021a] [Liguore and Tzong 2011] [Ling et al. 2025] [Liu et al. 2019f] [Lu et al. 2016b] [Lu et al. 2025] [Ma et al. 2012] [Ma et al. 2026a] [McCOWN et al. 1966] [McINTOSH 1973] [Melis et al. 2004] [Mor and Livne 2007] [Moran et al. 2021] [Morita et al. 2020] [Nakamura et al. 2014] [Newell 1965] [Ngo et al. 1993] [Odabas and Sarigul-Klijn 1992] [Olsen 1965] [Onozeki et al. 2026] [Oppenheimer et al. 2007] [Pozefsky 1989] [Pulok and Chakravarty 2020] [Quadrelli et al. 2009a] [Quadrelli et al. 2009b] [Quadrelli et al. 2011] [Rafla 2019] [Raney et al. 1995] [Rauh et al. 2026] [Rodríguez-Segade et al. 2022] [Rodríguez-Segade et al. 2024] [Smith and Benedetti 1965] [Spain et al. 1993] [Steelant and van Duijn 2011] [Stephens and Anderson 1976] [Sudalagunta et al. 2018] [Swanson et al. 2007] [Swanson et al. 2015] [Swanson et al. 2019] [Tabiei and Sockalingam 2012] [Taylor and Jackson 1980] [Wang et al. 2023c] [Weston and Cesnik 2024] [Williams et al. 2006] [Wu et al. 2021b] [Wurster 1980] [Wurster 1983] [Xiaoxuan et al. 2018] [Xie et al. 2020] [Yount et al. 2012] [Yu et al. 2013] [Yu et al. 2014b] [Yu et al. 2025b] [Zhang et al. 2019b] [Zhang et al. 2019c] [Zhang et al. 2020b] [Zhang et al. 2026g] [Zhang and Zong 2014] [Zuchowski 2013]

Hypersonic weapons, prompt global strike and policy

The smallest cluster, and small for a reason. Prompt global strike, hypersonic weapons, strategic stability and arms control. 18 titles name global strike, and the earliest record dates from 1999, so open scholarship on the policy question is recent and thin next to the engineering literature, which is itself a fact about how this vehicle was discussed.

38 records. [Acton 2015b] [Anin 2011] [Bahman Zohuri et al. 2019] [Baker et al. 2004] [Bille and Lorenz 2001] [Chudoba et al. 2015] [Conventional Prompt Global Strike 2007] [Douglas and Lindgren 1999] [Gormley 2005] [Gormley 2015] [Hopkins et al. 2010] [Hwang and Huh 2020] [Kessler 2022] [Kong et al. 2023] [Kong et al. 2024] [Lewis 2017] [Malinowski 2020] [Melville and Helmich 2021] [Miller 2004] [Kupach 2018] [Peter Korzun 2017] [Pollack 2009] [Pollack 2015] [Raza and Mehmood 2023] [Savelsberg et al. 2026] [Scheber and Guthe 2013] [Sills 2000] [Sills 2001] [Singh 2026] [Spinardi 2008] [Tarjáni 2023] [Thornton 2019] [U.S. Conventional Prompt Global 2008] [West 2012] [Williams 2019] [Williams 2021] [Wright 2015] [Zvedre 2016]

Where the Framing Breaks Down

Deriving a classified vehicle from its mission is a method with three specific weaknesses, and this article exhibits all of them.

First, the requirement may not be the requirement. The 9,000 nautical mile figure is attached in the public record to the reusable cruise vehicle that would have carried several of these gliders rather than to the glider alone [DARPA Falcon Project]. The glider’s own requirement is stated as a reach to anywhere on Earth [Woolf 2011], and the 17,000 kilometre range goal that a published analysis gives for the vehicle that flew [Acton 2015a] matches the cruise vehicle’s figure, but neither is a programme specification. If the glider was only ever meant to fly a fraction of that range, the entire chain above is answering the wrong question, and the article cannot exclude it.

Second, equilibrium glide is an idealisation and real trajectories are not equilibrium glides. A flown vehicle skips, phugoids and banks, and a banked turn spends lift on turning rather than on range. Every deviation from the idealisation reduces range for a given ratio, so the required ratios in the table are lower bounds and the argument is if anything understated.

Third, the two quantities the corridor calculation needs are exactly the two the record withholds. The effective $S C_{L}$ and the leading-edge radius are swept rather than known, and a reader who prefers different values will get different temperatures. The table is offered so that the reader sees the sweep that a single number would hide.

The Source Base

44 curated sources carry the argument, and a survey of 5,417 research records maps the field the vehicle sits in. The 27 curated research records are members of the survey, and no other survey record is cited in support of a claim about the X-41.

36 of the 44 are primary or canonical sources, which is 82 percent of the curated set. Twenty-nine are technical, being 25 reports from NASA’s Technical Reports Server and 4 papers, one of which is the published analysis of the flight tests that estimates the vehicle’s lift to drag ratio. Seven are government programme documents, being the Defense Advanced Research Projects Agency’s fact sheet, its programme page, its four releases on the flights and their review boards, and the Congressional Research Service report on the programme. The other eight are one newspaper report and seven reference works, being one designation reference and six encyclopaedia articles. The flight dates, the flight plan, both review boards’ findings and the funding restriction are cited to the government documents, and the relations the derivation uses are cited to their primary technical sources rather than to the reference works. The vehicle’s mass and length, the cancellation of its first design and of a third flight, and its construction and planform rest on the designation reference and an encyclopaedia article, because no government document in the curated set states them.

Six of them carry relations or values this article uses numerically. The lift to drag ratio of 2.6 is the flight-test analysis’s estimate, made with the same range relation and ceiling this article uses. The equilibrium glide range relation is Eggers and colleagues’ comparative analysis of long-range hypervelocity vehicles, published in 1955 and refined through 1958, before any such vehicle existed. The lift to drag ceiling is Küchemann’s correlation. The stagnation-point heating form belongs to a family running from Fay and Kemp through free-flight measurement to modern blunt-body procedures, and its coefficient is checked against Sutton and Graves’ correlation for air. The speed of sound, sea-level density and scale heights are the 1976 standard atmosphere’s.

One source speaks directly to the central contradiction. An aerothermal performance constraint analysis of sharp nosecaps and leading edges works the sharp-versus-blunt trade from the materials side, and a flight experiment programme was built to attack it. The contradiction derived here is a recognised design problem with its own literature, which is a stronger position than deriving it alone.

The research survey holds 5,417 research records drawn from Crossref, NASA’s Technical Reports Server and the Defense Technical Information Center, of which 1,492 are report primaries, being 27.5 percent, by the identifier rule set out under The Definition of Primary. 1,321 are Technical Reports Server records and 171 are Defense Technical Information Center reports. The median publication year is 2011. Of the 5,297 dated records, 492 were published before 1970 and 2,204 in 2015 or later.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when its address is on NASA’s 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 24 curated research reports that carry the glide relation, the heating correlations and the sharp leading-edge programme are report primaries under this rule. A journal or conference paper is not counted as a report primary, however close its subject stands to the vehicle.

Thin Subjects

Six 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.

Subject Title terms counted Records
the entry corridor corridor, corridors 30
cross-range and the landing footprint cross range, crossrange, footprint, footprints 26
the equilibrium glide equilibrium glide, steady glide 20
the ceiling on hypersonic lift to drag maximum lift to drag, maximum lift-drag, maximum L/D, maximal lift-drag, Kuchemann 7
the radiative equilibrium temperature of a radiation-cooled surface radiative equilibrium, radiation equilibrium, radiation cooled, radiative cooling 2
the vehicle itself HTV-2, HTV 2, Falcon, Common Aero Vehicle, CAV, Hypersonic Technology Vehicle 19

The corridor is the construct the sizing argument turns on, and 30 titles name it. Cross-range is the quantity the guidance paragraph leans on, and 26 titles name it or the landing footprint.

The equilibrium glide is the whole argument of the sizing section, and 20 titles name an equilibrium or steady glide. The count measures the titles in which the glide is the subject, not the studies that use it.

The ceiling on hypersonic lift to drag has almost no titles of its own. Only 7 titles name a maximum lift to drag ratio, all published between 1961 and 1985, and none names Küchemann, so the correlation that bounds the sizing table rests on its primary source rather than on a literature that tests it.

The radiative equilibrium temperature that decides the leading edge appears in 2 titles, so the last link in the sizing chain is used as a standard relation rather than studied as a subject.

The vehicle itself is named in 19 titles, and thirteen of them are trajectory, guidance, configuration or control studies that take the Common Aero Vehicle or the Hypersonic Technology Vehicle as a model. The rest concern the flight demonstration and its environmental assessment, the programme’s small launch vehicle, the radar signature of the ablating vehicle and the boost phase of the published flight-test analysis.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. The subject is a hypersonic boost-glide entry vehicle, read through the eleven clusters above. Entry into the atmospheres of other planets and return from the Moon are admitted, because the relations of trajectory, heating and guidance are the same.

Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Glide, trajectory, range and vehicle also describe the underwater oceanographic glider, and block glide and front range describe landslides. Stagnation point and heat transfer also name the nanofluid stagnation-point flow literature, a large applied-mathematical field concerning flow over stretching sheets, spinning spheres and non-Newtonian fluids that shares no physics of interest with reentry aerothermodynamics. Corridor and long range also describe road traffic, automated cars and ship routing, corridor, terminal guidance and reentry also describe drones, quadrotors and ground robots, and Waverider is also the name of an oceanographic wave-measurement buoy. Trajectory also names atmospheric pollutant transport, reentry also names a mechanism of cardiac arrhythmia that ablation treats, glide also names gliding animals and dislocation glide in metals, and boost, range and entry recur in business news. Entry also names data entry, market entry, forcible entry by airborne forces, military initial entry training and the entry of a body into water. Hypersonic also names a band of acoustic frequencies, Minotaur also names a university sounding rocket, and HTV also names the Japanese transfer vehicle that supplies the International Space Station. Correction, erratum, addendum, retraction and withdrawal notices, figure and supplementary-material records, peer-review reports and journal front matter are excluded as well, because the survey counts research works and those are parts of works or editorial events rather than works. Twin deposits of one document, carrying the same title in the same year, are counted once. A review of a book, a dictionary entry, a short or unsigned encyclopedia entry and a notice such as an editorial, an announcement or a news item, signed or unsigned, are not research works either and are excluded.

Several neighbouring literatures are excluded by rule. Studies whose object is an inlet, intake, combustor, nozzle, fuel system or engine are excluded, because this article places scramjet propulsion out of scope, while studies of a vehicle that integrates an engine with its airframe are kept. Guidance laws for tactical missiles, aircraft, unmanned aerial vehicles, lunar and asteroid landers and orbital rendezvous are excluded unless the vehicle is entering an atmosphere or flying hypersonically, and gun-launched and artillery projectiles are excluded with them. Stagnation-point heat transfer is admitted in high-temperature, dissociated, ionised or hypersonic flow and excluded in low-speed, turbulent, flame, jet and turbine flows. Supersonic aerodynamics with no hypersonic or entry element, meteors and other natural bodies entering an atmosphere, and the reentry of reactor and isotope heat sources are excluded.

Some records of doubtful relevance are kept. Ultra-high temperature ceramic processing and property studies that name no vehicle are kept, because the class is defined by its use at sharp leading edges and nose tips. Thermal management systems of hypersonic vehicles, and Space Shuttle debris impact and repair at the wing leading edge, are kept as thermal protection. The generic air-breathing hypersonic vehicle of the control literature is kept, because its flight dynamics are those of a hypersonic vehicle even though it is powered. A reader may weigh each accordingly.

No cluster is a residual. Every record belongs to a named cluster whose scope is stated above, so no record is admitted as merely adjacent to the subject.

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

Epistemic State

Historical Fact

The Common Aero Vehicle was a manoeuvrable hypersonic reentry vehicle intended to dispense payloads inside the atmosphere, with Aero standing for aeroshell. In December 2002 the Air Force programme was merged with a Defense Advanced Research Projects Agency effort into the Force Application and Launch from the Continental United States programme, carrying a small launch vehicle task and an aero vehicle task. By 2004 the offensive strike element was cancelled and weaponisation research ended, and the vehicle was renamed the Hypersonic Technology Vehicle in 2004 or in 2006, the two dates given by different sources. Congress increased the vehicle’s funding while questioning its strike mission, and the appropriations act for fiscal year 2005 barred any variant that included weapons. The programme’s reusable cruise vehicle was to strike targets 9,000 nautical miles distant, and the glider was to carry about 1,000 pounds of payload anywhere on Earth from the continental United States with a cross-range of 3,000 nautical miles. The first design was cancelled in 2006 after its leading edges delaminated. Vehicles were about 3.5 to 4.5 metres long and about 900 kilograms. The second Hypersonic Technology Vehicle was built by Lockheed Martin from carbon composite in an arrowhead planform, was expected to reach a surface temperature of more than 3,500 degrees Fahrenheit, and was launched on a Minotaur IV Lite from Vandenberg Air Force Base on a plan of about 4,100 nautical miles in less than thirty minutes. It flew on 22 April 2010, when yaw higher than predicted coupled into a roll beyond its control authority, and on 11 August 2011, when unexpected aeroshell degradation ended the flight. Each flight ended near the ninth minute. A planned third flight was cancelled.

Engineering Analysis

Every quantitative result here is computed from published figures using standard relations, and each can be recomputed from the relations and figures shown. The circular speed, the equilibrium glide condition and the range relation carry no vehicle property, and they are cited to their primary sources rather than treated as common knowledge [Eggers et al. 1955] [Eggers et al. 1958]. The Küchemann correlation is empirical [Küchemann 1965] and bounds the problem without predicting it, with measurements on hypersonic configurations cited beside it. The lift condition is the definition of the lift coefficient, the stagnation-point heating coefficient is checked above against Sutton and Graves [Sutton and Graves 1971], and the radiative equilibrium temperature is the balance of that heating against emission at the stated emissivity. The atmosphere’s speed of sound, sea-level density and scale heights are taken from the 1976 standard atmosphere [U.S. Standard Atmosphere 1976 1976].

The model is checked against the one published performance figure before it is used to argue. The estimated lift to drag ratio of 2.6, with the published reconstruction’s speeds at the start and end of the planned glide, reproduces the planned glide’s distance and duration to within one percent. The estimate and the speeds come from a fit of a model in the same family, so the agreement checks consistency without validating the model independently. It is not good enough to size hardware.

Inference

That the leading edge is the binding constraint is an inference, though a well-supported one. It follows from the corridor calculation and is corroborated by the failure report, which attributes the loss to aeroshell degradation and states that the aerodynamic design was validated. No source frames the vehicle’s central problem this way.

That the vehicle would have needed boosting to 93 percent of orbital speed is an inference conditional on the 9,000 nautical mile figure applying to the glider, which no programme specification establishes, although the published 17,000 kilometre range goal for the vehicle that flew agrees with it.

That the first flight was lost before its glide began is an inference from the agency’s 139 seconds of Mach 22 to Mach 17 data and the published reconstruction of the planned trajectory, and it depends on reading those seconds as starting at re-entry.

What the Record Does Not Settle

Whether the X-41 designation belongs to this vehicle at all is not settled, and the authoritative survey says so. The designation was allocated in late 1997 or early 1998, years before the joint programme, was never used again officially, and its applicability to the Common Aero Vehicle is explicitly doubted [X-41 CAV]. This article uses the pairing because the public record does, and records that the pairing may be wrong.

No specifications or photographs of the Common Aero Vehicle have been released [X-41 Common Aero Vehicle], so every dimension used here comes from the Hypersonic Technology Vehicle that succeeded it, and there is arithmetic showing the two cannot be the same vehicle. The payload figure attached to the Common Aero Vehicle is 1,000 pounds [Woolf 2011] [X-41 Common Aero Vehicle], against a Hypersonic Technology Vehicle mass of about 900 kilograms [X-41 CAV].

\[\frac{1{,}000 \ \text{lb}}{900 \ \text{kg}} = \frac{454}{900} = 0.50 \tag{45}\]

A payload half the mass of the whole vehicle is not credible for a hypersonic glider, so either the payload figure describes a larger design than the one that flew, or the mass figure describes a stripped demonstrator carrying nothing. The record does not say which, and this article uses each figure only where it is safe to.

The reference area, the lift coefficient and the leading-edge radius are not published [X-41 CAV]. Instead of assuming them, the article sweeps them across a plausible range, and the conclusion is stated as holding throughout the sweep.

The design temperature rests on a single newspaper report, which gives more than 3,500 degrees without naming the scale [Pentagon releases results of 13,000-mph test flight over Pacific]. The Fahrenheit scale is therefore inferred, and the encyclopaedia article adopts the same reading [Hypersonic Technology Vehicle 2].

Whether the 9,000 nautical mile requirement applied to the glider or to the larger system that would carry several of them remains open, and the framing section sets out what that does to the argument.

The first flight’s review board names a most probable cause and not a certain one, and no public source names which aerodynamic parameters were poorly known or by how much the yaw exceeded prediction [DARPA concludes review of Falcon HTV-2 flight anomaly].

The relationship between this vehicle and later hypersonic glide programmes is outside what the record supports, and this article does not trace it.

Out of Scope

The Small Launch Vehicle task of the same programme, which deserves separate treatment. The air-breathing hypersonic cruise vehicle studied under the same name, which is a different vehicle with a different problem. Prompt global strike as a policy question, and the arms-control literature on distinguishing conventional from nuclear boost-glide payloads. The later Hypersonic Technology Vehicle 3 concept. Scramjet propulsion, which this vehicle did not use. Ablative thermal protection design, which is surveyed here and not analysed. The detection and tracking of hypersonic glide vehicles, which is surveyed and not analysed.

Conclusion

A vehicle with no published specifications can still be bounded, because its mission is a physics problem. A range of 9,000 nautical miles and the equilibrium glide relation demand a lift to drag ratio that the Küchemann barrier refuses below Mach 22.2, so the glider had to be boosted to at least 83 percent of orbital speed, and at the ratio of 2.6 estimated for the vehicle that flew, to 93 percent.

The vehicle breaks in the corridor that follows. Flying low enough to be held up by the air puts a 50 millimetre leading edge at about 2,921 kelvin, against an expected surface temperature of about 2,200. Holding that value needs an edge radius of 0.484 metres on a vehicle four metres long, and that much bluntness costs the range the sharpness was for. Five of the nine plausible combinations swept here exceed the design temperature.

Both flights ended near the ninth minute of a thirty minute mission, and for different reasons. The first was lost to yaw higher than predicted that coupled into roll, before its glide began. Once the centre of gravity and angle of attack had been changed, the second flew under control at Mach 20 for nearly three minutes, and its board found unexpected aeroshell degradation, larger than expected skin loss, and shock-induced rolls beyond the vehicle’s ability to recover. It also found that the aerodynamic design was validated and that the surprise was thermal.

Once the shape had been corrected, the edge was the problem, and the relations that say so were all published before the vehicle flew.

The next article returns to a vehicle whose designation is not in doubt.

Equations

This section collects the 45 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 45, 28 are established and 17 are bespoke. Mach numbers in this article are a fixed speed scale of 295 metres per second rather than local Mach numbers, ranges are quoted in both kilometres and nautical miles, and the letter $R$ alone is a glide range while $R_{e}$ is the radius of the Earth and $R_{n}$ the leading-edge radius.

Equation 1, Half Great Circle of the Earth. The farthest point on Earth from any launch site is half a great circle away, 20,015 kilometres or 10,807 nautical miles on the mean radius.

\[\pi R_{e} = \pi \times 6{,}371 \ \text{km} = 20{,}015 \ \text{km} = 10{,}807 \ \text{nautical miles} \tag{1}\]

Equation 2, Planned Range Against the Cruise Vehicle’s Figure. The published planned range of 17,000 kilometres stands within two percent of the cruise vehicle’s 9,000 nautical miles. Acton 2015a DARPA Falcon Project

\[\frac{17{,}000 \ \text{km}}{9{,}000 \times 1.852 \ \text{km}} = \frac{17{,}000}{16{,}668} = 1.020 \tag{2}\]

Equation 3, Circular Speed at the Surface. The speed at which a body would orbit at the surface is the square root of gravity times the Earth radius, 7,904 metres per second.

\[V_{c} = \sqrt{g R_{e}} = \sqrt{(9.80665)(6.371 \times 10^{6})} = 7{,}904 \ \text{m/s} \tag{3}\]

Equation 4, Equilibrium Glide Lift. The lift a steady glide requires is the weight less the centrifugal relief of the curved path.

\[L = W \left( 1 - \frac{V^{2}}{V_{c}^{2}} \right) \tag{4}\]

Equation 5, Equilibrium Glide Range of Eggers. Integrating the equilibrium glide from an initial speed to rest gives a range linear in the lift to drag ratio and logarithmic in the speed term. Eggers et al. 1955 Eggers et al. 1958

\[R = \left(\frac{L}{D}\right) \frac{R_{e}}{2} \ln \left( \frac{1}{1 - V^{2}/V_{c}^{2}} \right) \tag{5}\]

Equation 6, Sensitivity of Range to Lift to Drag Ratio. Since range is linear in the lift to drag ratio, a fractional loss of the ratio is the same fractional loss of range.

\[\frac{\partial R}{R} = \frac{\partial (L/D)}{L/D} \tag{6}\]

Equation 7, Lift to Drag Ratio Required for a Range. Solving the equilibrium glide range for the ratio gives the demand that a fixed distance places on the shape.

\[\frac{L}{D} = \frac{R}{\dfrac{R_{e}}{2} \ln\left(\dfrac{1}{1 - V^{2}/V_{c}^{2}}\right)} \tag{7}\]

Equation 8, Bespoke Fixed Speed Scale for Mach Numbers. Speeds are converted from Mach numbers on a fixed scale of 295 metres per second, the isothermal-layer speed of sound of the standard atmosphere, which the article adopts as a convention rather than a local value. U.S. Standard Atmosphere 1976 1976

\[V = M a \qquad a \approx 295 \ \text{m/s} \tag{8}\]

Equation 9, Küchemann Barrier for Hypersonic Lift to Drag Ratio. Küchemann’s correlation gives the attainable maximum lift to drag ratio of a hypersonic configuration as four times the Mach number plus three, over the Mach number. Küchemann 1965

\[\left(\frac{L}{D}\right)_{\max} \approx \frac{4(M + 3)}{M} = 4 + \frac{12}{M} \tag{9}\]

Equation 10, Bespoke Mach Number Where Demand Meets the Barrier. Equating the ratio required for a range of 9,000 nautical miles, which the article takes as the glider’s requirement, to the Küchemann ceiling on the fixed speed scale defines the minimum entry speed.

\[\frac{R}{\dfrac{R_{e}}{2} \ln\left(\dfrac{1}{1 - (M a / V_{c})^{2}}\right)} = \frac{4(M + 3)}{M} \tag{10}\]

Equation 11, Bespoke Minimum Entry Speed. The numerical root on the fixed speed scale and the attributed range requirement is Mach 22.2, or 83 percent of orbital speed.

\[M_{\min} = 22.2 \qquad V_{\min} = 6{,}537 \ \text{m/s} = 0.83 \ V_{c} \tag{11}\]

Equation 12, Bespoke Effect of Using the Local Speed of Sound. Replacing the fixed 295 metres per second scale with the local speed of sound at 40 kilometres raises the Küchemann ceiling at Mach 20 by about one percent.

\[\frac{4 + 12 \times 317.19/5{,}900}{4 + 12/20} = \frac{4.645}{4.600} = 1.010 \tag{12}\]

Equation 13, Planned Glide Duration and Distance. The published reconstruction of the trajectory gives a planned glide of 1,178 seconds covering 4,800 kilometres. Acton 2015a

\[t_{5} - t_{4} = 1{,}798 - 620 = 1{,}178 \ \text{s} \qquad x_{5} - x_{4} = 5{,}900 - 1{,}100 = 4{,}800 \ \text{km} \tag{13}\]

Equation 14, Equilibrium Glide Range Between Two Speeds. The range between two speeds is the difference of the two ranges to rest.

\[R = \left(\frac{L}{D}\right) \frac{R_{e}}{2} \ln \left( \frac{1 - V_{f}^{2}/V_{c}^{2}}{1 - V_{i}^{2}/V_{c}^{2}} \right) \tag{14}\]

Equation 15, Bespoke Range of the Planned Glide. The range between the reconstructed initial speed and a final speed of 2,250 metres per second, the midpoint of the reconstructed range, at the published ratio of 2.6 is 4,783 kilometres.

\[R = 2.6 \times 3{,}185.5 \ \text{km} \times \ln\left(\frac{1 - 0.2847^{2}}{1 - 0.6958^{2}}\right) = 2.6 \times 3{,}185.5 \times \ln(1.7815) = 4{,}783 \ \text{km} \tag{15}\]

Equation 16, Bespoke Entry Speed Needed for the Original Mission. Inverting the range relation at the published ratio of 2.6 for the 9,000 nautical miles the article attributes to the glider gives 93.1 percent of orbital speed.

\[\frac{V}{V_{c}} = \sqrt{1 - \exp\left(-\frac{16{,}668}{2.6 \times 3{,}185.5}\right)} = 0.931 \tag{16}\]

Equation 17, Bespoke Entry Speed in Metres per Second and Mach Number. The required fraction of orbital speed is 7,357 metres per second, which is Mach 24.9 on the fixed speed scale.

\[V = 7{,}357 \ \text{m/s} = \text{Mach } 24.9 \ \text{at } 295 \ \text{m/s} \tag{17}\]

Equation 18, Published Glide Start Speed as a Fraction of Orbital Speed. The published glide start speed of 6,900 metres per second is 87.3 percent of orbital speed. Acton 2015a

\[\frac{6{,}900}{7{,}904} = 0.873 \tag{18}\]

Equation 19, Deceleration in Equilibrium Glide. The deceleration along the path is the drag over the mass, the lift requirement divided by the lift to drag ratio.

\[\frac{dV}{dt} = -\frac{g\left(1 - V^{2}/V_{c}^{2}\right)}{L/D} \tag{19}\]

Equation 20, Time to Decelerate in Equilibrium Glide. Separating and integrating the glide deceleration gives the time between two speeds as a difference of inverse hyperbolic tangents.

\[t = \left(\frac{L}{D}\right) \frac{V_{c}}{g} \left[ \operatorname{artanh}\left(\frac{V_{i}}{V_{c}}\right) - \operatorname{artanh}\left(\frac{V_{f}}{V_{c}}\right) \right] \tag{20}\]

Equation 21, Bespoke Duration of the Planned Glide. The time between the reconstructed initial speed and the midpoint final speed of 2,250 metres per second at the published ratio is 1,187 seconds.

\[t = 2.6 \times \frac{7{,}904}{9.80665} \left[ \operatorname{artanh}(0.6958) - \operatorname{artanh}(0.2847) \right] = 2.6 \times 806.0 \times 0.5664 = 1{,}187 \ \text{s} \tag{21}\]

Equation 22, Density Required for Lift in Equilibrium Glide. The lift condition fixes the air density from the weight, the centrifugal relief, the speed and the product of reference area and lift coefficient.

\[\rho = \frac{2 W \left(1 - V^{2}/V_{c}^{2}\right)}{V^{2} S C_{L}} \tag{22}\]

Equation 23, Weight of the Glider. The published mass of about 900 kilograms gives a weight of 8,826 newtons. X-41 CAV

\[W = m g = (900)(9.80665) = 8{,}826 \ \text{N} \tag{23}\]

Equation 24, Bespoke Corridor Density at Seven Kilometres per Second. The density is evaluated with a product of reference area and lift coefficient of 0.45 square metres that the article assumes.

\[\rho = \frac{2 (8{,}826)(0.2157)}{(7{,}000)^{2}(0.45)} = 1.73 \times 10^{-4} \ \text{kg/m}^{3} \tag{24}\]

Equation 25, Exponential Atmosphere. An isothermal exponential atmosphere gives density from a sea-level value and a scale height, and inverts for altitude.

\[\rho = \rho_{0} \exp\left(-\frac{h}{H}\right) \qquad h = -H \ln\left(\frac{\rho}{\rho_{0}}\right) \tag{25}\]

Equation 26, Bespoke Corridor Altitude. The assumed corridor density converted through a single exponential fit with a scale height of 6.9 kilometres gives 61.2 kilometres, about three kilometres below the standard atmosphere value. U.S. Standard Atmosphere 1976 1976

\[h = -6{,}900 \ln\left(\frac{1.73 \times 10^{-4}}{1.225}\right) = 61.2 \ \text{km} \tag{26}\]

Equation 27, Bespoke Lift Coefficient at the Corridor. The lift coefficient implied at the corridor rests on an assumed reference area of two square metres.

\[C_{L} = \frac{2 W \left(1 - V^{2}/V_{c}^{2}\right)}{\rho V^{2} S} = 0.225 \ \text{at} \ S = 2 \ \text{m}^{2} \tag{27}\]

Equation 28, Stagnation Heating Coefficient From the Sutton and Graves Constant. Taking the stagnation pressure as the density times the speed squared and the enthalpy difference as half the speed squared, the usual hypersonic approximations, converts the published coefficient to 1.748 times ten to the minus four. Sutton and Graves 1971

\[k \approx \frac{0.1113}{2 \sqrt{101{,}325}} = \frac{0.1113}{636.6} = 1.748 \times 10^{-4} \tag{28}\]

Equation 29, Stagnation-Point Heat Flux. The convective stagnation-point flux is a constant times the square root of density over leading-edge radius times the cube of speed.

\[\dot{q} = k \sqrt{\frac{\rho}{R_{n}}} \, V^{3} \tag{29}\]

Equation 30, Radiative Equilibrium Temperature. A surface rejecting heat by radiation alone reaches the fourth root of the heat flux over the emissivity times the Stefan-Boltzmann constant.

\[T = \left(\frac{\dot{q}}{\varepsilon \sigma}\right)^{1/4} \tag{30}\]

Equation 31, Bespoke Heating of a Sharp Edge at the Corridor. The flux and equilibrium temperature are evaluated for a leading-edge radius of 50 millimetres, an assumed emissivity of 0.85 and the assumed corridor density.

\[\dot{q} = 3.51 \ \text{MW/m}^{2} \qquad T = 2{,}921 \ \text{K} \tag{31}\]

Equation 32, Published Surface Temperature in Kelvin. The published expected surface temperature of more than 3,500 degrees Fahrenheit converts to 2,200 kelvin. Pentagon releases results of 13,000-mph test flight over Pacific

\[T_{d} = \frac{5}{9}\left(3{,}500 - 32\right) + 273.15 = 1{,}926.7 + 273.15 = 2{,}200 \ \text{K} \tag{32}\]

Equation 33, Bespoke Heat Flux Rejected at the Design Temperature. A surface at 2,200 kelvin with an emissivity of 0.85, which the article assumes, can reject 1.13 megawatts per square metre.

\[\dot{q}_{d} = \varepsilon \sigma T_{d}^{4} = (0.85)(5.67 \times 10^{-8})(2{,}200)^{4} = 1.13 \ \text{MW/m}^{2} \tag{33}\]

Equation 34, Bespoke Leading-Edge Radius That Holds the Design Temperature. Equating the stagnation flux at the assumed corridor density to the radiation at the design temperature and assumed emissivity gives a leading-edge radius of 0.484 metres.

\[R_{n} = \rho \left(\frac{k V^{3}}{\varepsilon \sigma T_{d}^{4}}\right)^{2} = 0.484 \ \text{m} \tag{34}\]

Equation 35, Fraction of Orbital Energy Required. Specific kinetic energy goes as the square of speed, so the fraction of orbital energy required is the square of the speed fraction.

\[\frac{E/m}{(E/m)_{\text{orbital}}} = \frac{V^{2}}{V_{c}^{2}} \tag{35}\]

Equation 36, Bespoke Fractions of Orbital Energy at the Two Entry Speeds. The two speed fractions, which rest on the fixed speed scale and the attributed range requirement, require 69 and 87 percent of orbital energy.

\[\left(0.83\right)^{2} = 0.69 \qquad \left(0.931\right)^{2} = 0.87 \tag{36}\]

Equation 37, Mass Ratio From the Rocket Equation. The ratio of stack mass to delivered mass is the exponential of the velocity increment over the effective exhaust velocity.

\[\frac{m_{0}}{m_{f}} = \exp\left(\frac{\Delta V}{g I_{sp}}\right) \tag{37}\]

Equation 38, Bespoke Mass Ratio of a Solid Booster. The mass ratio is evaluated at an assumed solid-propellant specific impulse of 280 seconds and the lower entry speed of 6,537 metres per second.

\[\frac{m_{0}}{m_{f}} = \exp\left(\frac{6{,}537}{(9.80665)(280)}\right) = 10.8 \tag{38}\]

Equation 39, Launcher Mass Against Glider Mass. The published Minotaur IV launch mass over the published glider mass gives a ratio of order 96. Minotaur IV

\[\frac{86{,}300}{900} = 96 \tag{39}\]

Equation 40, Time of Mach 17 Against the Planned Glide Start. Counting the 139 seconds from the return to the atmosphere, as the published reconstruction does, places Mach 17 at 574 seconds, before the planned glide start at 620 seconds. Acton 2015a

\[t_{2} + 139 = 435 + 139 = 574 \ \text{s} < t_{4} = 620 \ \text{s} \tag{40}\]

Equation 41, Bespoke Mean Deceleration of the First Flight. The mean deceleration from the published re-entry speed to Mach 17, converted on the fixed speed scale, is 7.16 metres per second squared.

\[\bar{a} = \frac{6{,}010 - 5{,}015}{139} = 7.16 \ \text{m/s}^{2} = 0.73 \ g \tag{41}\]

Equation 42, Equilibrium Glide Deceleration at the Re-entry Speed. The glide relation at the published re-entry speed and lift to drag ratio of 2.6 gives 1.59 metres per second squared. Acton 2015a

\[\frac{g\left(1 - 0.760^{2}\right)}{2.6} = 1.59 \ \text{m/s}^{2} = 0.16 \ g \tag{42}\]

Equation 43, Flight Duration as a Share of the Planned Mission. Nine minutes against the planned 1,798 second mission is 0.30 of it. Acton 2015a

\[\frac{9 \times 60}{1{,}798} = 0.30 \tag{43}\]

Equation 44, Speed Scale Implied by the Agency’s Statement. The published 13,000 miles per hour at Mach 20 implies a scale of 290.6 metres per second, close to the 295 metres per second convention. Falcon HTV-2 fact sheet 2010

\[13{,}000 \ \text{mph} \times \frac{1{,}609.344 \ \text{m}}{3{,}600 \ \text{s}} = 5{,}812 \ \text{m/s} \qquad \frac{5{,}812}{20} = 290.6 \ \text{m/s} \qquad 20 \times 295 = 5{,}900 \ \text{m/s} \tag{44}\]

Equation 45, Payload Against Vehicle Mass. The published payload of 1,000 pounds over the published vehicle mass of about 900 kilograms is half the vehicle. Woolf 2011 X-41 CAV

\[\frac{1{,}000 \ \text{lb}}{900 \ \text{kg}} = \frac{454}{900} = 0.50 \tag{45}\]

Notation

  • $R_{e}$, the radius of the Earth
  • $V_{c}$, the circular speed at the surface
  • $R$, the glide range
  • $L/D$, the lift to drag ratio, with $\left(\frac{L}{D}\right)_{\max}$ the Küchemann ceiling
  • $M$, the Mach number on the fixed speed scale
  • $a$, the fixed speed scale of 295 metres per second
  • $V_{i}$, the initial glide speed, with $V_{f}$ the final glide speed
  • $M_{\min}$, the minimum entry Mach number, with $V_{\min}$ the corresponding speed
  • $t_{5}$, the planned end of the glide, with $t_{4}$ its start and $t_{2}$ the return to the atmosphere
  • $x_{5}$, the downrange position at the end of the glide, with $x_{4}$ its start and $x_{2}$ the point of re-entry
  • $C_{L}$, the lift coefficient
  • $\rho_{0}$, the sea-level air density
  • $H$, the scale height of the exponential atmosphere
  • $k$, the stagnation heating coefficient
  • $R_{n}$, the leading-edge radius
  • $\dot{q}$, the stagnation-point heat flux, with $\dot{q}_{d}$ the flux rejected at the design temperature
  • $\varepsilon$, the emissivity
  • $\sigma$, the Stefan-Boltzmann constant
  • $T_{d}$, the design temperature
  • $I_{sp}$, the specific impulse of the booster in seconds
  • $m_{0}$, the stack mass, with $m_{f}$ the delivered mass

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