X-Planes: Martin Marietta X-23 PRIME and a Contested Assignment

The Martin Marietta X-23A PRIME, whose name stood for Precision Recovery Including Maneuvering Entry, was six feet eight inches long, weighed 894 pounds, and was thrown at the Pacific Ocean three times from the top of an Atlas. On the third attempt, on 19 April 1967, it flew more than 710 miles to one side of the path a stone would have taken, deployed a parachute, and was caught in mid-air by a transport aeroplane near Kwajalein, as the official history of the project records. It is the smallest vehicle in this series so far and it answered a larger question than most of the aircraft that dwarf it. This article is the twenty-fourth 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, and the X-22.

The number also presents a serious difficulty. The designation X-23A is attached to this vehicle by encyclopaedias and by the historical literature. Available United States Air Force nomenclature records show that it was never assigned, and further that it was never even requested, in the standard reference on United States military aircraft designations. This article treats the vehicle and the paperwork as two separate subjects, because they are, and because the paperwork, far from being a clerical footnote, is evidence about how the designation system worked.

The Research Question

Can a vehicle returning from orbit choose where it lands?

In 1964 that question was open. A ballistic capsule cannot choose. It falls where the atmosphere and its entry conditions put it, and the only control available is when to start. The landing point is therefore wherever the orbital ground track happens to be at the moment of the deorbit burn, and if the track then crosses the middle of an ocean, the vehicle comes down in the ocean.

The alternative was known in principle. A body that generates lift as well as drag can hold itself up, glide, and by rolling that lift vector to one side, turn. The open question was how much of it a returning vehicle could obtain, because the lift available to a shape that must also survive entry heating is very small. A lifting body of the period had a hypersonic lift-to-drag ratio somewhere near one, in Reed, against roughly seventeen for a transport aeroplane at cruise, in the encyclopaedia entry on the lift-to-drag ratio. The article turns on this ratio, defined as

\[\frac{L}{D} = \frac{C_L}{C_D} \tag{1}\]

so a value near unity means a vehicle that produces as much drag as lift. The lifting body gives up a factor of about fourteen against a transport wing, and the question is what the remaining lift can achieve.

The keystone of this article is the conversion of that small lift-to-drag ratio into lateral distance, which the period literature calls lateral range and the modern literature calls crossrange, in Garland and Hall 1958, Jackson 1961, Baradell 1962, Baradell and McLellan 1963, Kornreich 1963, Wang 1963a, Wang and Skulsky 1963, Lessing et al. 1964, Ashford 1965, Wagner 1965, Lau 1967, Pritchard and Holloway 1967, Holloway 1968, NlEMANN 1968, Moote 1970, Bump 1977, Vinh et al. 1977, Johnson et al. 1982, Kelley et al. 1982. Every part of the vehicle was dimensioned against it. The shape exists to produce the lift, the ablator exists to let the vehicle stay in the atmosphere long enough to use it, the reaction controls and flaps exist to hold the bank angle that converts it, and the recovery system exists so that the measurement survives.

The X-20 Dyna-Soar had asked a version of this question and had been cancelled in December 1963 without flying, as a programme of 458 million dollars, in Reed’s history of the lifting bodies. PRIME asked the narrowest possible form of it, without a pilot, for a small fraction of the money. A programme memorandum of May 1967 puts the investment in PRIME at about 70 million dollars, not counting PILOT, in Vitelli and Hallion’s history of the project, so the ratio is

\[\frac{70}{458} = 0.153 \tag{2}\]

or about a seventh of the X-20’s cost.

Programme Origin

PRIME was one part of a United States Air Force programme called START, for Spacecraft Technology and Advanced Reentry Tests, which Reed dates to January 1964. The accounts divide the programme differently. Hallion’s history of the Dryden centre and the inventory of American X-vehicles published by the National Aeronautics and Space Administration, NASA, describe three phases, ASSET, PRIME and PILOT, for Piloted Low-Speed Tests. Reed names only PRIME and PILOT. The START development plan forwarded in January 1965, in Vitelli and Hallion, comprised the PRIME project, the PILOT project, configuration and design studies, and the ASSET project. ASSET, for Aerothermodynamic Elastic Structural Systems Environmental Tests, was a small unmanned McDonnell glider launched between September 1963 and March 1965, according to Hallion, and addressed structures and heating. PRIME addressed manoeuvring, which ASSET had not. ASSET had flown simple hypersonic glides, and PRIME was to fly far to one side of its path, in Heppenheimer’s history of the Space Shuttle decision.

The institutional context is the cancellation of Dyna-Soar. The Air Force had spent years and a great deal of money on a piloted, winged, manoeuvring re-entry vehicle and had been left with the question unanswered and the answer still wanted, in Reed. START was the cheap route to the same information. Two small unmanned vehicles, launched on existing boosters, instrumented and recovered, could measure heating and manoeuvring without a pilot, without a runway, and without a programme large enough to be worth cancelling.

Martin Marietta supplied the airframe. The company had been developing a family of lifting-body shapes under the designation SV-5, and the family is the reason three vehicles appear here where the title names one. The SV-5D was the small unmanned entry vehicle that became PRIME. The SV-5P was the larger piloted low-speed vehicle that became the X-24A, in Reed. The two are the same aerodynamic idea at different sizes and different ends of the speed range, and that kinship is why the designation question became tangled.

The PRIME contract followed in November 1964. The Space Systems Division of the Air Force Systems Command engaged Martin to design, build and test a manoeuvring re-entry vehicle, in Reed and Hallion, and the project’s own statement of May 1967 says it was approved in November 1964 with first flight due in 24 months, in Vitelli and Hallion. Both Reed and Vitelli and Hallion record the six features on which Martin argued for the SV-5 shape. The second is the subject of this article, a hypersonic lift-to-drag ratio of 1.2 or better, permitting a lateral range of 1,000 miles, which would allow a recall to any preselected site at least once a day and an emergency recall to a suitable location from every orbit.

The wider programme record is in Ingber 1965, Atlas-Centaur AC-12 Flight Performance 1968, Atlas-Centaur Flight Performance 1968, Adimurthy 1976, Shrivastava and Reddy 1976, Brusch 1977, Adimurthy 1987, Rasky 1998, Trefny 1999, Wallace 1999, Calhoun 2000, Naughton 2002, and the survey’s cluster on lifting bodies and the SV-5 family collects the family of shapes the vehicle came from.

The Vehicle

The SV-5D was a teardrop-shaped lifting body fitted with fins, in Heppenheimer, and Vitelli and Hallion add two hydraulically driven flaps at the rear. It was 6 feet 8 inches long, 3 feet 10 inches across and 2 feet 10 inches high, and weighed 894 pounds, in the encyclopaedia entry.

The record gives its weight several ways. The official history records the first vehicle lifting off at 895 pounds, about 4 percent below the weight goal, and states that all three were more than 3 percent below the specification maximum launch weight, in Vitelli and Hallion’s history of the project, whose press statement of May 1967 calls them 860-pound vehicles. Reed gives 880 pounds, Hallion 400 kilograms, and Cochrane and Graham about 800 pounds. This article uses 894 pounds, which differs from the first vehicle’s lift-off weight by

\[\frac{895}{894} - 1 = 0.11\% \tag{3}\]

Almost the whole of its surface was thermal protection. The primary structure was aluminium, and Vitelli and Hallion describe an elastomeric ablative heat shield, Martin’s ESA 3560HF, bonded directly to it, with a mechanically attached carbon phenolic nose cap. The flaps were beryllium plates faced with carbon phenolic beneath and with ESA 3560HF above, and the fins were beryllium sheet on a steel honeycomb. The shield was to hold the aluminium to 400 degrees Fahrenheit and the flaps and fins to 800. The encyclopaedia entry gives the shield’s thickness as between 0.75 and 2.75 inches and lists titanium among the structural metals, which the official history does not mention. Attitude was held by nitrogen gas reaction jets and by the two hydraulically driven flaps, which took over as the air became thick enough to be useful.

One quantity that the analysis below needs is not published. The reference area of the SV-5D does not appear in the accessible record, so it is derived here from the X-24A, the same shape at larger scale. The X-24A’s conventional reference area is 162 square feet on a reference length of 23 feet and a reference span of 10 feet, in Falarski and Mort, and those are reference quantities rather than the vehicle’s outline. Its whole planform is 195.0 square feet against a length of 24.50 feet and a tip-to-tip span of 13.63 feet in Saltzman, Wang and Iliff, and the ratio of that area to the length-times-span box is

\[k_S = \frac{S_\text{X-24A}}{l\,b} = \frac{195.0}{24.50 \times 13.63} = 0.5839 \tag{4}\]

and applying that ratio to the SV-5D’s own length and span gives

\[S = k_S\, l\, b = 0.5839 \times 2.032 \times 1.168 = 1.386\ \text{m}^2 \tag{5}\]

or 14.9 square feet. McTigue gives the X-24A body 191 square feet against 24.5 and 13.5, which makes the ratio

\[\frac{191}{24.5 \times 13.5} = 0.5775 \tag{6}\]

and the derived area 1.1 percent smaller. This is an assumption and every number that depends on it inherits that status. The crossrange result does not depend on it at all.

One check on the scaling fails, and the failure is informative. The two vehicles are in a linear ratio of

\[\frac{l_\text{SV-5D}}{l_\text{X-24A}} = \frac{2.032}{7.47} = 0.272 \tag{7}\]

so if they were the same thing at different sizes their weights would stand as the cube of that, or 0.020. The X-24A weighed about 12,000 pounds at launch, in Reed, and about 5,500 pounds empty, in Cochrane and Graham, so the actual ratio is

\[\frac{894}{12{,}000} = 0.075, \qquad \frac{894}{5{,}500} = 0.163 \tag{8}\]

Between nearly four and eight times what geometric scaling predicts. The reason is that the SV-5D is densely packed, its inboard profile filling the body with ballast, electronics, instrumentation, recovery gear and reaction controls beneath a bonded heat shield, in Vitelli and Hallion, while the X-24A is mostly enclosed volume with a pilot and a rocket engine inside it. Areas scale and contents do not. That difference makes the reference area derived above defensible where a weight derived the same way would not have been. Estimating what a vehicle will weigh, and knowing which parts of it obey a scaling law and which do not, is a methodical discipline, with a literature collected in the survey’s cluster on weight estimation and vehicle sizing.

Sizing From First Principles

The Force Balance That Makes a Glide an Equilibrium

A vehicle at orbital speed needs no lift, because the centrifugal effect of travelling that fast round a curved Earth supports it entirely. At rest it needs lift equal to its full weight. In between, an equilibrium glide is one that holds the difference.

Written out, the radial balance carries three terms rather than two, and the middle one is the effect the previous sentence names,

\[L\cos\phi + \frac{m V^2}{R} = W \tag{9}\]

Writing $\bar V = V/V_c$ for speed as a fraction of circular satellite speed, and $\phi$ for the angle through which the lift vector has been rolled away from vertical, and using $V_c^2 = gR$ to turn the centrifugal term into $W\bar V^2$, the balance collapses to

\[L\cos\phi = W\left(1 - \bar V^2\right) \tag{10}\]

which says that the lift a gliding vehicle needs is its weight less whatever its own speed is already carrying. At $\bar V = 1$ it needs none. At three quarters of circular speed it needs

\[1 - 0.75^2 = 0.4375 \tag{11}\]

of its weight, and at entry, where $\bar V = 0.972$, it needs 0.056 of it. That entry speed, 25,200 feet per second, is assumed throughout, and the flight record below sets it against the speeds the record gives. The glide therefore begins almost unloaded, a fact that explains the deceleration figures further down.

The circular speed itself follows from equating gravitational and centripetal acceleration at the surface, giving

\[V_c = \sqrt{g R} = \sqrt{9.80665 \times 6.371\times 10^6} = 7{,}904\ \text{m/s} \tag{12}\]

which is 25,933 feet per second. The equilibrium glide is the reference trajectory of the subject, and the survey devotes a cluster to it under the equilibrium glide and analytic entry trajectories.

Why the Turn Rate Does Not Depend on the Atmosphere

Two further statements complete the mechanics. Drag decelerates the vehicle along its path, and the sideways component of the rolled lift vector turns it,

\[m\frac{dV}{dt} = -D, \qquad m V \frac{d\psi}{dt} = L\sin\phi \tag{13}\]

where $\psi$ is the heading. Dividing the second by the first eliminates time, and substituting the force balance eliminates the weight, leaving

\[\frac{d\psi}{dV} = -\frac{L}{D}\,\frac{\sin\phi}{V} \tag{14}\]

Every property of the vehicle except its lift-to-drag ratio has dropped out, and so has the atmosphere. Mass, size, reference area and air density are all gone. That is the reason this analysis can be done at all for a vehicle whose reference area is not published. Integrating from the entry speed gives

\[\psi(V) = \frac{L}{D}\sin\phi \, \ln\frac{V_e}{V} \tag{15}\]

The heading change is logarithmic in the speed ratio, which means the great majority of the turning happens late, when the vehicle is slow. None of this is original to this article. The equilibrium glide and the relations that follow from it are standard material, set out in Vinh’s treatment of atmospheric flight trajectories and in Regan and Anandakrishnan on re-entry dynamics. What is done here is to carry them through to a requirement and then to invert them on a measurement. At a lift-to-drag ratio of 1.2 and a bank of 45 degrees, slowing from circular speed to a quarter of it turns the vehicle through

\[\psi = 1.2 \times \sin 45^\circ \times \ln 4 = 1.176\ \text{rad} = 67.4^\circ \tag{16}\]

The Crossrange Integral

Crossrange accumulates at $\dot y = V\sin\psi$. The classical treatment replaces $\sin\psi$ by $\psi$ at this point, the substitution that makes a closed form available at all. That step is examined below and it turns out to cost about a tenth of the answer, but it is kept here because it is the step the period literature took and the closed form it produces is the relation the subject is built on. Dividing the lateral rate by the deceleration removes time here as well,

\[\frac{dy}{dV} = -\,\frac{V\psi\,(L/D)\cos\phi}{g\left(1-\bar V^2\right)} \tag{17}\]

and the substitution $u = \bar V^2$, for which

\[V = V_c\sqrt{u}, \qquad dV = \frac{V_c}{2\sqrt{u}}\,du, \qquad g = \frac{V_c^2}{R} \tag{18}\]

makes every factor of $V_c$ cancel, leaving

\[dy = -\frac{R}{2}\,\frac{L}{D}\cos\phi\,\frac{\psi\,du}{1-u} \tag{19}\]

Substituting the heading solution, in which $\ln(V_e/V) = \tfrac{1}{2}\ln(u_e/u)$, turns the accumulated lateral distance into a single integral,

\[y = \frac{R}{4}\left(\frac{L}{D}\right)^2 \sin\phi\cos\phi \; I(u_e), \qquad I(u_e) = \int_0^{u_e} \frac{\ln(u_e/u)}{1-u}\,du \tag{20}\]

For entry at exactly circular speed the integral has a closed form, and deriving it is more instructive than quoting it. Expand the denominator as a geometric series,

\[\frac{1}{1-u} = \sum_{n\ge 0} u^n \qquad \text{for} \quad 0 \le u < 1 \tag{21}\]

and integrate term by term. Each term is a standard integral,

\[\int_0^1 (-\ln u)\,u^n\,du = \frac{1}{(n+1)^2} \tag{22}\]

so the sum is over the reciprocal squares, which is the Basel series,

\[I(1) = \int_0^1 \frac{-\ln u}{1-u}\,du = \sum_{k\ge 1} \frac{1}{k^2} = \frac{\pi^2}{6} = 1.6449 \tag{23}\]

A constant from elementary number theory turns up in the range of a re-entry vehicle. The coincidence arises in the integral and carries no information about spacecraft, but it is a pleasing one.

The Bank Angle Is Already Decided

The only free choice in the expression is $\phi$, and it appears as

\[\sin\phi\cos\phi = \tfrac{1}{2}\sin 2\phi \tag{24}\]

Differentiating and setting the result to zero gives the condition, and the second derivative confirms which kind of stationary point it is,

\[\frac{d}{d\phi}\left(\tfrac{1}{2}\sin 2\phi\right) = \cos 2\phi = 0, \qquad \frac{d^2}{d\phi^2} = -2\sin 2\phi = -2 < 0 \tag{25}\]

so the stationary point is a maximum and it sits at

\[\phi_\text{opt} = 45^\circ, \qquad \sin\phi\cos\phi = \tfrac{1}{2} \tag{26}\]

This does not depend on the lift-to-drag ratio, on the entry speed, or on anything about the vehicle. Any vehicle wanting maximum crossrange banks 45 degrees, and the guidance system’s apparently central decision turns out to have been made in advance by the arithmetic.

Putting the optimum and the closed form together gives the governing relation of the subject,

\[\frac{y_\text{max}}{R} = \frac{\pi^2}{48}\left(\frac{L}{D}\right)^2 = 0.2056\left(\frac{L}{D}\right)^2 \tag{27}\]

Crossrange goes as the square of the lift-to-drag ratio. Worked at a ratio of 1.2, for a vehicle entering at circular speed,

\[y_\text{max} = 0.2056 \times 1.2^2 \times 6.371\times 10^6 = 1.886\times 10^6\ \text{m} = 1{,}019\ \text{nmi} \tag{28}\]

and the same arithmetic gives 1,310 kilometres at a ratio of 1.0 and 2,568 at 1.4. A ballistic capsule at zero gets nothing. For it the capability is absent altogether, a difference of kind from a small value.

What the Small-Angle Step Costs

The closed form above was checked against a numerical integration that keeps $\sin\psi$ exactly, and the two disagree by more than a rounding error.

The reason is visible in the heading solution, which can be evaluated directly at the end of the glide. Taking that to be one percent of circular speed,

\[\psi_\text{end} = \frac{L}{D}\sin 45^\circ \ln\frac{V_e}{0.01\,V_c} \tag{29}\]

which gives 148 degrees at a ratio of 0.8, 185 degrees at 1.0, 222 at 1.2 and 260 at 1.4. Beyond 180 degrees $\sin\psi$ does not merely differ from $\psi$, it has the opposite sign. The approximation does not degrade gracefully. It inverts.

The exact treatment makes a related point precise. Lateral displacement accumulates as $\dot y = V\sin\psi$, so it stops accumulating exactly where the heading passes half a turn,

\[\sin\psi = 0 \quad \Longrightarrow \quad \psi = 180^\circ, \qquad V_{180} = V_e\exp\left(-\frac{\pi}{(L/D)\sin\phi}\right) \tag{30}\]

At a ratio of 1.2 that speed is 189 metres per second, reached very near the end of the flight. Crossrange is therefore maximised at the moment the vehicle finishes turning round, and everything after that is spent flying back toward the plane it started in.

Lift-to-drag ratio	Closed form	Exact	Over-prediction
0.8	838 km	797 km	5.2 percent
1.0	1,310 km	1,214 km	7.9 percent
1.2	1,886 km	1,696 km	11.2 percent
1.4	2,568 km	2,233 km	15.0 percent

The classical relation is optimistic, and increasingly so as the lift-to-drag ratio rises, because a better gliding vehicle turns further and the approximation is worse the further it turns. Both numbers are given from here on.

That table hides a physical statement. A vehicle holding 45 degrees of bank through a full lifting entry turns through half a circle. It arrives pointing the way it came. Real entry guidance reverses the bank part way through for this reason, and the Space Shuttle flew a series of such roll reversals, in the encyclopaedia entry on the Space Shuttle. The constant-bank assumption that makes the mathematics tractable is not a trajectory anyone would fly.

The Requirement

Now the other half. How much crossrange does a returning vehicle need?

Successive orbits do not retrace the same ground. The Earth turns underneath, so each pass lays its track to the west of the last by the rotation accumulated in one orbital period. The rate wanted here is the rotation relative to the fixed stars, because the orbit plane is fixed in that frame and not in the one that tracks the Sun,

\[\omega_E = \frac{2\pi}{86{,}164\ \text{s}} = 7.292\times 10^{-5}\ \text{rad/s} \tag{31}\]

Using the solar day of 86,400 seconds instead would overstate the interval by 0.27 percent, which is small but is an avoidable error. The track spacing in longitude is then

\[\Delta\lambda = \omega_E T = 7.292\times 10^{-5} \times 5400 = 0.3937\ \text{rad} = 22.56^\circ \tag{32}\]

for a nominal ninety-minute low orbit. The geometry of ground tracks, and of the orbits that lay them down, is standard astrodynamics, in Bosanquet 1958, Ambrosio et al. 1961, Musen and Squires 1965, Alderson 1967, Endres 1967, Mullins 1981, Teles 1989, Shapiro and Bhat 1993, Shapiro et al. 1993, Shapiro 1994, Bettner 1995. At the equator that is a ground distance of

\[d = R\,\Delta\lambda = 6.371\times 10^6 \times 0.3937 = 2{,}509\ \text{km} \tag{33}\]

An arbitrary landing site lies somewhere between two adjacent tracks, so it is at most half that distance from the nearer one. And those two tracks are consecutive in time. The requirement to reach a chosen site on one pass or the next is therefore

\[y_\text{req} = \tfrac{1}{2} R\,\Delta\lambda = 1{,}254\ \text{km} \tag{34}\]

The Answer

Inverting the crossrange relation on that requirement gives the lift-to-drag ratio a returning vehicle must have,

\[\frac{L}{D} = \sqrt{\frac{y_\text{req}/R}{\pi^2/48}} = \sqrt{\frac{0.1968}{0.2056}} = 0.978 \tag{35}\]

Solving the same requirement against the exact integration instead, which cannot be done in closed form and has to be bisected, gives

\[\left(\frac{L}{D}\right)_\text{exact} = 1.018 \tag{36}\]

The correction moves the answer toward unity, a fortunate accident that argues for neither number. Both are reported because the first is what the period could compute and the second is what is true.

A lift-to-drag ratio near unity is not a round number chosen for convenience. It is the threshold at which a spacecraft stops being a passenger of its orbit and starts being able to come home when it wants to. Below it the vehicle waits for the ground track to come back, which for a general orbit means a day or more and may mean never. At it, the longest wait is one orbit.

The requirement falls at higher latitudes, because the tracks crowd together as the meridians converge. The spacing carries a cosine, so the required ratio carries its square root,

\[y_\text{req}(\varphi) = \tfrac{1}{2} R\,\Delta\lambda\cos\varphi, \qquad \left(\frac{L}{D}\right)_\text{req}(\varphi) = \left(\frac{L}{D}\right)_\text{req}(0)\sqrt{\cos\varphi} \tag{37}\]

At 28.5 degrees that is 0.917, at Vandenberg’s 34.7 degrees it is 0.887, and at 45 degrees it is 0.823. The hardest case is the equator, and a vehicle sized for the equator is sized for everywhere.

What the Flight Record Says About a Disputed Number

The sources do not agree on this vehicle’s hypersonic lift-to-drag ratio. One gives 1.0, in the encyclopaedia entry, and another gives 1.2 for the SV-5 shape, in Vitelli and Hallion.

As ratios those differ by twenty percent, which sounds tolerable. They do not differ by twenty percent in the quantity this article is about, because crossrange goes as the square,

\[\frac{y(1.2)}{y(1.0)} = \left(\frac{1.2}{1.0}\right)^2 = 1.44 \tag{38}\]

A twenty percent disagreement about the vehicle is a forty-four percent disagreement about what it can do, and it cannot be waved away.

It can, however, be attacked, because two facts about the third flight are independently known and both are consequences of the same trajectory. The vehicle achieved 1,143 kilometres of crossrange, and it flew from Vandenberg Air Force Base to a recovery area near Kwajalein, in Vitelli and Hallion, a great-circle distance of

\[d = 2R\arcsin\sqrt{\sin^2\frac{\Delta\varphi}{2} + \cos\varphi_1\cos\varphi_2\sin^2\frac{\Delta\lambda}{2}} = 7{,}787\ \text{km} \tag{39}\]

The equilibrium glide gives a downrange to go with the crossrange, and it comes from the same two statements. Distance along the path accumulates at $\dot x = V$, and dividing by the deceleration gives

\[\frac{dx}{dV} = -\frac{V\,(L/D)\cos\phi}{g\left(1-u\right)} \tag{40}\]

Applying the same substitution as before, every factor of $V_c$ again cancels and the integrand becomes elementary,

\[dx = -\frac{R}{2}\,\frac{L}{D}\cos\phi\,\frac{du}{1-u} \tag{41}\]

which integrates directly to

\[x = \frac{L}{D}\cos\phi \;\frac{R}{2}\ln\frac{1}{1-u_e} \tag{42}\]

Downrange is linear in the lift-to-drag ratio where crossrange is quadratic in it, which is the reason the two together determine both unknowns. Banking to gain crossrange costs downrange as $\cos\phi$, so at the optimum the vehicle gives up

\[1 - \cos 45^\circ = 0.293 \tag{43}\]

or twenty-nine percent of the distance it could have flown straight ahead.

Two equations, two unknowns. Writing $A$ and $B$ for the two geometric factors, the pair is $\;(L/D)\cos\phi = x/A\;$ and $\;(L/D)^2\sin\phi\cos\phi = y/B$, and dividing one by the square of the other gives the bank angle without needing the lift-to-drag ratio first,

\[\tan\phi = \frac{y/B}{(x/A)^2}, \qquad \frac{L}{D} = \frac{x/A}{\cos\phi} \tag{44}\]

Assuming a bank angle of 45 degrees and recovering 45.13 looks like a confirmation and is nothing of the kind. A check that assumes the bank angle feeds the assumed lift-to-drag ratio of 1.2 straight back in. A suspiciously clean agreement is the signal that such a check is circular, so the solution here assumes neither quantity and solves for both.

The glide does not begin at the launch pad. The Atlas covers part of that great circle before entry interface, and the table varies that boost range so that its effect is visible. The pair is solved twice, once with the closed form and once against the exact integration.

Boost range before entry	Bank, closed form	Ratio, closed form	Bank, exact	Ratio, exact
0 km	35.1 degrees	1.035	37.0 degrees	1.060
500 km	38.8 degrees	1.016	41.0 degrees	1.050
1,000 km	42.8 degrees	1.006	45.5 degrees	1.052
1,500 km	47.2 degrees	1.006	50.3 degrees	1.070
2,000 km	51.9 degrees	1.019	55.5 degrees	1.111
2,500 km	56.8 degrees	1.049	60.9 degrees	1.183

Each solve carries its own bank angle, because the two models do not agree on what bank produces a given crossrange and pairing one model’s ratio with the other’s angle would be meaningless.

The bank angle swings through twenty-four degrees and the lift-to-drag ratio moves very little. Across the range of boost distances in the table the exact solution stays between 1.05 and 1.18. The flight record determines one of the two unknowns much better than the other. That uneven result is more useful than a single number would have been.

The result sits between the two disputed figures and is nearer the lower one. Flying the exact model at a ratio of 1.0 produces 1,043 kilometres against the 1,143 demonstrated, an under-prediction of 8.8 percent. Flying it at 1.2 produces 1,453 kilometres, an over-prediction of 27 percent,

\[\frac{1{,}042.7}{1{,}143} - 1 = -8.8\%, \qquad \frac{1{,}452.9}{1{,}143} - 1 = +27\% \tag{45}\]

Neither published figure reproduces the flight and the truth is in between, somewhere near 1.05 to 1.10.

The point needs plain statement, because the closed form alone appears to vindicate the 1.0 figure to within one percent, and removing the approximation takes that vindication away and replaces it with a value that neither source gives.

It does not settle the conflict and this article does not claim that it does. Several readings survive. If 1,143 kilometres was the vehicle’s maximum capability, the solution above is a measurement and both published figures are somewhat wrong. If it was a demanded value below capability, the solution is a lower bound and the 1.2 figure survives comfortably while 1.0 does not. There is also a reading in which both sources are right about different things, with 1.2 the maximum trimmed ratio the shape can reach and 1.0 a nominal or rounded value, since nothing obliges a vehicle to fly at its best lift-to-drag ratio. The record bears on the second reading. The third flight was planned as the maximum crossrange trajectory, yet Vitelli and Hallion record that the fourth was to reach about 790 nautical miles by flying a lower angle of attack and a steeper bank, so the third flight’s crossrange was the most the vehicle reached at the attitude it flew, short of the shape’s ceiling. A lift-to-drag ratio inferred from it describes that attitude rather than the shape’s maximum.

The two disputed figures do not have equal standing. The 1.2 is Martin’s design figure for the SV-5 shape, quoted above. The 1.0 appears in the encyclopaedia entry, which gives no source for it. Martin’s claim of 1,000 miles at 1.2 is itself consistent with the relation derived here, since the exact integration from circular speed at 1.2 gives 1,696 kilometres, which is

\[\frac{1{,}696}{1.609} = 1{,}054\ \text{statute miles} \tag{46}\]

The record fixes the boost range, and the pair solve does not survive it. The chart of the maximum crossrange ground track that accompanies the third flight’s account, figure 19 in Vitelli and Hallion’s history of the project, marks re-entry at 400,000 feet, 26,808 feet per second and a flight path angle of 2.03 degrees, 1,360 nautical miles from launch, which is

\[1{,}360 \times 1.852 = 2{,}518.7\ \text{km} \tag{47}\]

just beyond the last row of the table. Solved exactly at that boost range, the pair gives a bank of 61.1 degrees and a lift-to-drag ratio of 1.187. The record contradicts that bank angle. The second flight was programmed to hold a constant bank of 46 degrees through re-entry until terminal guidance began, and a memorandum of May 1967 proposing the fourth flight describes its planned 47 degrees as higher than the 39 degrees previously flown, both in Vitelli and Hallion. The downrange relation is the weak half of the pair. It grows without bound as the entry speed approaches circular, through the factor $\ln(1/(1-u_e))$, and the documented entry speed lies above the circular speed the model uses,

\[u_e = \left(\frac{26{,}808}{25{,}933}\right)^2 = 1.069 > 1 \tag{48}\]

where the relation has no finite value at all. The pair solve therefore depends on the assumed entry speed, and the record’s bank angles show that it does not describe the flight.

The crossrange alone, at a documented bank, is the firmer inversion. Holding the bank fixed removes the downrange from the problem. At the second flight’s 46 degrees, the exact integration needs a lift-to-drag ratio of 1.007 to reach the 654 miles, or 1,052.5 kilometres, that the narrative gives for that flight. The third flight’s bank is not stated, and at either 39 or 46 degrees its 710 miles, 1,142.6 kilometres, need 1.053,

\[y_\text{exact}\left(1.007,\ 46^\circ\right) = 1{,}052.5\ \text{km}, \qquad y_\text{exact}\left(1.053,\ 46^\circ\right) = 1{,}142.6\ \text{km} \tag{49}\]

The programme’s own curve sits close to these values. Figure 20 of the same history, presented among the quantities analysed from the flights, plots the SV-5D’s trimmed hypersonic lift-to-drag ratio against angle of attack. Read from the figure, it rises to a maximum of about 1.1 near 20 degrees at 200,000 feet, against about 1.4 for the inviscid estimate, and falls to about 0.9 at 35 degrees, the angle of attack that the fourth-flight memorandum gives for the flights already flown. The inversions, 1.007 and 1.053, lie between the curve’s value at the flown angle of attack and its maximum, and Martin’s 1.2 lies above the viscous curve everywhere.

The record also disagrees with itself about the crossranges. The narrative in Vitelli and Hallion gives 654 miles for the second flight and more than 710 miles for the third, and Heppenheimer also gives 710 miles for the third. This article uses that reading. The same history’s summary table gives 499 and more than 710 nautical miles instead. Read as nautical miles, the third flight’s crossrange is

\[710 \times 1.852 = 1{,}314.9\ \text{km} \tag{50}\]

and the inversion at a documented bank gives 1.14 rather than 1.05, while the second flight’s 499 nautical miles, 924.1 kilometres, give 0.94 at 46 degrees. The two figures for the second flight cannot be one distance in two units, since 654 statute miles is 568.3 nautical miles.

What can be said without qualification is narrower and firmer. The vehicle’s effective lift-to-drag ratio through the manoeuvring phase of the third flight was close to one, it was not close to zero, and a ballistic vehicle on the same trajectory would have landed 1,143 kilometres from where this one did.

Dependent Systems

The Shape

A lifting body generates its lift with its body instead of with wings. For a re-entry vehicle this is not an aesthetic choice. A wing is thin, and thin things have small radii, and small radii get hot. The survey’s cluster on stagnation-point, convective and radiative heating treats that problem. Removing the wing removes the worst heating problem and the structure that would have to survive it, at the cost of a lift-to-drag ratio that a winged vehicle would consider a failure.

The lifting-body shapes the SV-5 belongs to were worked out through the late 1950s and early 1960s, the SV-5D lying between the cone-like M2 and the modified delta HL-10, in Hallion, and their aerodynamics are documented in the survey’s clusters on lifting bodies and on hypersonic aerodynamics. Holding such a shape at a chosen attitude through the whole speed range is a separate subject, in Magnus A Haw and Sebastian V Colom, Nonweiler 1959, Arabian 1960, Demetriades 1960, Kaufman 1963, Kaufman and Louis G. 1963a, Kaufman and Louis G. 1963b, Whitfield and Wolny 1963, Flight Sciences Lab INC Buffalo NY 1964, Kaufman and Louis G. 1964, Meckler 1964, Meckler 1965, Walchner and Clay 1965, Kyriss and Rie 1967, Pottsepp and Shi 1968, Walchner 1974, Compton et al. 1983, Markopoulos and Mease 1990, Tarpley and Lewis 1993, Brauckmann et al. 1995, Reed 1997, Nydick and Friedmann 1999, Bowersox and Fan 2000, Groves et al. 2005, Stueber et al. 2009.

Thermal Protection

The equilibrium glide fixes the density at every speed, because the force balance demands it. Rearranging,

\[\rho = \frac{2\beta_L(1-u)}{V^2\cos\phi}, \qquad \beta_L = \frac{W}{S\,C_L} \tag{51}\]

so the heating history follows from the trajectory and leaves the designer no choice. The companion quantity is the ballistic coefficient, the same construction on the drag side,

\[\beta = \frac{W}{S\,C_D} \tag{52}\]

and the two stand in a fixed ratio, and that ratio offers a useful consistency check on the assumed coefficients,

\[\frac{\beta}{\beta_L} = \frac{C_L}{C_D} = \frac{L}{D} \tag{53}\]

With the derived reference area and an assumed hypersonic drag coefficient of unity,

\[\beta = \frac{3{,}977}{1.386 \times 1.0} = 2{,}869\ \text{N/m}^2 = 60\ \text{lb/ft}^2 \tag{54}\]

and the lift parameter is 2,391 newtons per square metre. That is a low ballistic coefficient, and low is what a research vehicle wants, because it decelerates high up where the air is thin. The quantity is the single most compressed description of an entry vehicle there is, and the period literature treats it as such, in Scherberg and Rubin 1953, Schweppe 1964, Chen 1965, Schoenenberger et al. 2005.

Stagnation-point heat flux at a blunt nose is one of the most heavily worked correlations in the subject, and the accumulated body of it is Eggers et al. 1958, Goulard 1961, Kivel 1961, Scala 1961b, Wittliff and Wilson 1961, Scala 1962b, Chow 1963, Fay and Kemp 1963, Rose and Stankevics 1963, Reilly 1964, Horton and Zeh 1966, Tokuda and Yang 1966, Derienzo and Pallone 1967a, Derienzo and Pallone 1967b, Anderson 1968, Vidal 1974, Bade 1975, Nomura 1983, Gupta et al. 1992. The form used here is that of Sutton and Graves,

\[\dot q_s = k\sqrt{\frac{\rho}{R_n}}\,V^3, \qquad k = 1.7415\times 10^{-4} \tag{55}\]

in metric units for air, with the density in kilogrammes per cubic metre, the nose radius in metres and the speed in metres per second. Substituting the glide density collapses the speed dependence. Since $\rho \propto (1-u)/V^2$, the square root carries $\sqrt{(1-u)/u}$ and the cube carries $u^{3/2}$, so

\[\dot q_s \propto \sqrt{\frac{1-u}{u}}\;u^{3/2} = u\sqrt{1-u} \tag{56}\]

Maximising is easiest on the square, whose derivative is a quadratic,

\[\frac{d}{du}\left[u^2(1-u)\right] = 2u - 3u^2 = 0 \quad \Longrightarrow \quad u = \tfrac{2}{3} \tag{57}\]

so the worst heating happens at

\[u = \tfrac{2}{3}, \qquad V = 0.8165\,V_c = 6{,}454\ \text{m/s} \tag{58}\]

In the equilibrium glide, peak heating is at eighty-two percent of circular speed regardless of the vehicle, because every property of it cancelled on the way to that quadratic.

The density there follows from the glide balance,

\[\rho = \frac{2 \times 2{,}391 \times \tfrac{1}{3}}{6{,}454^2 \times \cos 45^\circ} = 5.41\times 10^{-5}\ \text{kg/m}^3 \tag{59}\]

and with an assumed nose radius of 0.1 metres the peak is

\[\dot q_{s,\text{max}} = 1.7415\times 10^{-4}\sqrt{\frac{5.41\times 10^{-5}}{0.1}}\,\left(6{,}454\right)^3 = 109\ \text{W/cm}^2 \tag{60}\]

which is modest by the standards of a ballistic capsule and sustained for far longer.

That figure comes from the model glide and does not hold for the flight. The programme’s computed trajectory for a 700 nautical mile crossrange, figure 21 of Vitelli and Hallion’s history of the project, is not an equilibrium glide. Read from the figure, its altitude oscillates through several cycles over about 1,200 seconds, and its stagnation heating rate peaks above 480 British thermal units per square foot per second in the first dip, about 200 seconds after entry, which is

\[480 \times 1.1357 = 545\ \text{W/cm}^2 \tag{61}\]

or five times the equilibrium value. The same history notes that the heat flux on the small PRIME vehicles was considerably more extreme than larger operational vehicles would meet.

That correlation omits radiation, and the omission is deliberate. Shock-layer radiation becomes a significant part of the heat load only above roughly ten kilometres per second, the regime of a lunar or interplanetary return. An orbital return stays below it. PRIME entered at 8.2 kilometres per second, the 26,808 feet per second of the programme’s ground-track chart in Vitelli and Hallion, so the radiative term is small and the convective correlation carries the analysis. At Apollo’s entry speed it would not, and the literature of that regime is Christopher O Johnston, Yoshikawa and Wick 1961, Koh 1962, Nerem and Stickford 1964, Cooper 1966a, Cooper 1966b, Analytical Experimental and Developmental 1967, Bloor 1967, Engel and Spradley 1968, Liu 1968, Olstad 1969, Biberman et al. 1972, Golovachev 1972, Page and Woodward 1972, Edquist 1974, Sutton 1976, Golovachev 1979a, Nelson 1980, Nelson 1983.

The altitude of the peak follows from the density. No altitude quoted here was measured. Each comes from a model of the atmosphere, and the modelling of atmospheric density and its scale height has a long and careful literature, which the survey collects in its cluster on the atmosphere that entry is computed against. Inverting an exponential atmosphere of scale height 7,160 metres,

\[h = -H\ln\frac{\rho}{\rho_0} = -7{,}160\ln\left(4.42\times 10^{-5}\right) = 71.8\ \text{km} \tag{62}\]

or about 236,000 feet. The vehicle takes its worst heating some seventy kilometres up and never comes near the speeds involved again. Integrating the flux over the glide, using $dt = -(L/D)\cos\phi\,dV/(g(1-u))$, gives a closed form,

\[Q = k\,\frac{L}{D}\sqrt{\cos\phi}\sqrt{\frac{2\beta_L}{R_n}}\frac{V_c^3}{g}\cdot\frac{\arcsin a - a\sqrt{1-a^2}}{2} \tag{63}\]

with $a = \sqrt{u_e}$, evaluating to 107 kilojoules per square centimetre. The same integral gives the duration,

\[t = \frac{L}{D}\cos\phi\,\frac{V_c}{g}\,\text{artanh}\,\sqrt{u_e} = 1{,}452\ \text{s} \tag{64}\]

Twenty-four minutes. That is the price of using the lift.

A heat shield’s thickness and a heat load together imply an effective heat of ablation,

\[H_\text{eff} = \frac{Q}{\rho_\text{abl}\,t_\text{abl}} \tag{65}\]

At the thick end of the encyclopaedia’s range, 2.75 inches at an assumed charring-ablator density of 550 kilograms per cubic metre, the model’s heat load gives an areal mass and a heat of ablation of

\[\rho_\text{abl}t_\text{abl} = 550 \times 0.0699 = 38.4\ \text{kg/m}^2, \qquad H_\text{eff} = \frac{1.067\times 10^9}{38.4} = 27.8\ \text{MJ/kg} \tag{66}\]

and at the thin end, 0.75 inches, it gives 102 megajoules per kilogram. The primary record does not allow this to serve as a check. The one heat load the programme states appears in Vitelli and Hallion as a stagnation heat load of 7,000 British thermal units per square foot, planned for the fourth flight’s harsher entry, which is

\[7{,}000 \times 11{,}357 = 7.95\times 10^7\ \text{J/m}^2 = 7.95\ \text{kJ/cm}^2 \tag{67}\]

one thirteenth of the model’s figure. It is also hard to reconcile with the same history’s figure 21, whose heating rate, read from the figure, stays above 160 British thermal units per square foot per second for more than 300 seconds in all, so that

\[160 \times 300 = 48{,}000\ \text{BTU/ft}^2 \tag{68}\]

is a floor under the load that curve implies. The history also says the shield was conservative, since the SV-5D’s shield could be redesigned for the same environment with substantial reductions in thickness and weight, and that its task was to hold the aluminium to 400 degrees Fahrenheit. The thickness was set by insulation and margin rather than by the heat load, so dividing a heat load by it measures neither the material nor the heating, and the two thicknesses cannot be assigned to the stagnation region and to lightly heated surfaces on this arithmetic.

The survey’s cluster on ablation and thermal protection covers the materials, running from the thermal protection of the Apollo command module in Curry et al. 1966 and the flight test of its heat shield material on the Pacemaker vehicle in Graves and Witte 1968 to thermal protection materials for re-entry in Johnson et al. 2001. The ablation physics is in the same cluster, and the flow conditions that set the heating, such as the real gas effects of hypersonic flow over blunt bodies in Nagamatsu et al. 1960 and the laminar boundary layer of dissociated air in Beckwith and Cohen 1963, are in the cluster on hypersonic aerodynamics, flow fields and the boundary layer.

Control

The vehicle’s guidance task through the glide was to hold a bank angle. Vitelli and Hallion report that the second flight was programmed to hold 46 degrees from re-entry until terminal guidance began, one degree from the optimum derived above, and that a ground-based terminal guidance system then steered toward the recovery point. The derivation above explains why the glide law could be that simple. Attitude was held by nitrogen reaction jets at high altitude and by flaps once the dynamic pressure was sufficient, as the description of the vehicle above records, and the reaction-jet literature of the period, such as the performance of low-thrust cold-gas jets in a vacuum in Greer and Griep 1967, falls within the survey’s cluster on reaction control, attitude control and control surfaces. The guidance methods of the era, surveyed at the time in Wingrove 1963, and the entry guidance later flown by the Shuttle, in Harpold and Graves 1978, appear in the clusters on entry guidance and on the Space Shuttle orbiter, and the question of what ground the vehicle could reach, treated for orbital lifting re-entry vehicles in Stern and Chu 1964, is the subject of the cluster on crossrange, lateral range and the entry footprint.

Deceleration

The same balance that sets the density sets the deceleration. In equilibrium glide it is

\[\frac{a}{g} = \frac{1-u}{(L/D)\cos\phi} \tag{69}\]

which is smallest at the beginning and greatest at the end. At entry, where $u = 0.944$, it is

\[\frac{a}{g} = \frac{1 - 0.944}{1.2\cos 45^\circ} = 0.066 \tag{70}\]

so the vehicle barely feels the atmosphere at first, and by the end of the glide it has risen only to

\[\frac{a}{g} = \frac{1}{1.2\cos 45^\circ} = 1.18 \tag{71}\]

The entire lifting entry is gentler than standing up. The same entry flown ballistically, from the 26,808 feet per second and 2.03 degree flight path angle at 400,000 feet that the programme’s ground-track chart gives, in Vitelli and Hallion, yields the Allen and Eggers result

\[a_\text{max} = \frac{V_e^2\sin\gamma_e}{2eH} = \frac{\left(8{,}171\right)^2\sin 2.03^\circ}{2e \times 7{,}160} = 60.8\ \text{m/s}^2 = 6.20\ g \tag{72}\]

where $H$ is the atmospheric scale height. The unlifted case is no strawman, since ballistic warheads and the first capsules came back that way, and it has a large literature, collected in the survey’s cluster on capsules and ballistic entry, from which the lifting case is the departure. The ratio is

\[\frac{6.20}{1.18} = 5.25 \tag{73}\]

A factor of about five. The lift purchases a far gentler deceleration as well as crossrange, and for the piloted vehicles that this programme was clearing the way for, that was the more immediately valuable of the two.

Recovery as Data Return

A vehicle that measures something and then sinks has measured nothing that cannot be telemetered. The recovery system is therefore instrumentation, and twice it was the part of PRIME that failed.

The sequence in Vitelli and Hallion was a drogue ballute at about Mach 2 and 100,000 feet, then the main parachute at 45,000 to 50,000 feet, then mid-air retrieval by a JC-130B at about 10,000 feet, using the technique already in service for returning film capsules. The encyclopaedia entry gives the main parachute as 47 feet across, while the parachute drawing in the official history, its figure 17, marks a dimension of 32 feet labelled $D_p$.

On the first flight the ballute deployed at 99,850 feet, or 30.4 kilometres, in Vitelli and Hallion, where the speed of sound follows from the local temperature,

\[a = \sqrt{\gamma R_\text{air} T} = \sqrt{1.4 \times 287 \times 226.5} = 302\ \text{m/s} \tag{74}\]

so Mach 2 is 603 metres per second and the fabric has to be opened against a load that the supersonic-decelerator literature exists to predict, in Alejandro Pensado et al, Modeling and Simulation of the Dr, Alejandro R Pensado et al, Evan Roelke and Justin Green, Evan Roelke et al, Advanced Supersonic Parachute Inf, F Cadieux and M Barad, Francois Cadieux and Michael F Barad, Fluid-Structure Interaction Simul, Francois Cadieux and Michael F Barad, Supersonic Parachute Inflation Si, Francois Cadieux et al, Jonathan Boustani et al, Sims 1963, Heinrich 1966a, McEwan 1970, Poole 1973, Brinkman 1992, Gnoffo and Anderson 2002, Cruz et al. 2003, Miller et al. 2003,

\[q = \tfrac{1}{2}\rho V^2 = \tfrac{1}{2} \times 0.0184 \times 603^2 = 3{,}350\ \text{Pa} = 70\ \text{lb/ft}^2 \tag{75}\]

That is a mild load by supersonic-decelerator standards, and keeping it mild is the point of deploying that high and that late.

The recovery parachute’s area follows from its diameter,

\[S_p = \frac{\pi D^2}{4} = \frac{\pi \times 14.33^2}{4} = 161\ \text{m}^2 \tag{76}\]

and under it the vehicle descends at

\[V_d = \sqrt{\frac{2W}{\rho\,C_D S_p}} = \sqrt{\frac{2 \times 3{,}977}{1.225 \times 0.75 \times 161}} = 7.33\ \text{m/s} \tag{77}\]

or 24 feet per second at sea level. The recovery sequence in Vitelli and Hallion specifies 25 feet per second at 10,000 feet, where the standard atmosphere’s density is 0.9046 kilograms per cubic metre, and there the same relation gives

\[V_d = 7.33\sqrt{\frac{1.225}{0.9046}} = 8.53\ \text{m/s} = 28.0\ \text{ft/s} \tag{78}\]

so the specified rate needs a drag coefficient of

\[C_D = 0.75\left(\frac{28.0}{25}\right)^2 = 0.94 \tag{79}\]

on a 47 foot canopy, against the 0.75 assumed. The literature of that technique is Braun 1953, Downing et al. 1956, French 1965, French 1966, Jamison 1966, Eckstrom and Preisser 1967, Jamison 1967, Neustadt et al. 1967, Preisser et al. 1967, Cassanto et al. 1968, Brearley 1969, Chakoian 1969, Goodrick 1969, Pepper and Cronin 1969, Eckstrom 1970, Michal et al. 1970, Wolf 1971, Pearson 1972, Pepper and Biesterveld 1973, Whitlock et al. 1973, Wei and Pearson 1974, Fu and Koch 1977, Pepper 1980, Roberts 1980, Schatzle and Curry 1980, Pepper and Collins 1982, High Drag Rotating Parachute 1985, Knacke 1985, Yavuz 1985, Sengupta et al. 2009.

The Flight Test Record

Four vehicles were built and three flew, launched by SLV-3 Atlas boosters from Space Launch Complex 3 East at Vandenberg, in the NASA inventory of American X-vehicles and in Vitelli and Hallion. The fourth completed its checkout, and its flight was cancelled on 12 May 1967 because the third had met every objective.

Flight	Date	Crossrange flown	Miss distance	Outcome
PRIME 1	21 December 1966	zero	0.15 nmi	Main parachute never left its container. Vehicle lost in the Pacific.
PRIME 2	5 March 1967	654 miles, 1,053 km	1.91 nmi	Line cutters installed without charges. Catch not attempted, vehicle sank.
PRIME 3	19 April 1967	more than 710 miles, 1,143 km	4.27 nmi	Terminal guidance radar inoperative. Caught in mid-air at 12,000 ft.

The dates, crossranges and miss distances are those of Vitelli and Hallion, whose summary table gives the crossranges as 499 and more than 710 nautical miles instead, the disagreement discussed above.

The programme’s three flights were a failure, a failure and a success, and what failed needs to be stated precisely. In neither of the first two cases did the vehicle fail to fly the entry. Both flew their profiles and both telemetered, and the telemetry recovered on the three flights was 91.2, 99.3 and 99.5 percent. What failed was the recovery chain, twice, in two different components. On the first flight the ballute deployed about 4,300 miles downrange and within 900 feet of the preselected point, but the main parachute was never pulled from its container, and a premature power shutdown had already disabled the flaps. On the second the explosive line cutters had been installed without their charges, a human error, so the vehicle hung nose down from three points instead of one and the aircraft did not attempt the catch. The third flight demonstrated the largest crossrange of the three and was the one that came back, and post-flight tests found it capable of flying again, all in Vitelli and Hallion.

The record does not agree on how fast PRIME flew. Reed gives 14,900 miles an hour, Hallion 24,000 kilometres an hour, the inventory of X-vehicles about 16,500 miles an hour at re-entry, and Heppenheimer a peak above 17,000. The programme’s ground-track chart in Vitelli and Hallion gives 26,808 feet per second at 400,000 feet on the third flight. The quoted values span

\[14{,}900\ \text{mph} = 21{,}853\ \text{ft/s}, \qquad 26{,}808\ \text{ft/s} = 18{,}278\ \text{mph} \tag{80}\]

and the 25,200 feet per second assumed for the model lies inside that span. The sources do not say at what point of the flight the lower figures apply.

The vehicle that flew PRIME 3 is at the National Museum of the United States Air Force.

Comparison With Ground Prediction

The equilibrium-glide model in this article is what could be computed with a slide rule in 1964, and this section sets out how well it does. The comparison is only meaningful against what the period knew, and the body of work it knew is large, since 581 of the survey’s research records were published in 1967 or earlier.

Quantity	Model	Flight
Crossrange at a lift-to-drag ratio of 1.0, closed form	1,133 km	1,143 km
Crossrange at a lift-to-drag ratio of 1.0, exact	1,043 km	1,143 km
Crossrange at a lift-to-drag ratio of 1.2, exact	1,453 km	1,143 km
Downrange at the solved bank angle	7,787 km by construction	Vandenberg to Kwajalein
Bank angle at the documented boost range	61.1 degrees	46 degrees on flight 2, 39 degrees reported as flown
Lift-to-drag ratio at a documented bank	1.007 and 1.053	about 1.1 at most, about 0.9 at the flown 35 degrees
Peak deceleration	1.18 g	not published in the accessible record
Peak stagnation heating	109 W/cm²	above 545 W/cm² in the programme’s computed trajectory
Glide duration	24.2 min	about 20 min in the programme’s computed trajectory

The closed form is good to one percent at the lower of the two disputed lift-to-drag ratios, and that agreement is an accident of two errors cancelling. The small-angle step over-predicts by eight percent and the assumed ratio is low by about the same, so the product comes out right for the wrong reason. Removing the approximation removes the coincidence and leaves the flight sitting between the two published figures.

Here the lesson concerns method more than the vehicle. A model that agrees with a measurement to one percent is not thereby correct, and the way to find out is to improve the model and see whether the agreement survives. Here it did not.

The comparison is weaker than it looks in one respect that must be said. PRIME entered at a shallow 2.03 degrees but above circular speed, and the programme’s computed trajectory dips deep and then oscillates through several cycles of altitude rather than settling into an equilibrium glide, in figures 19 and 21 of Vitelli and Hallion. The model describes the mission being simulated more faithfully than the trajectory flown.

What the Data Changed

PRIME fed the X-24A directly. The same shape, at larger scale and with a pilot, first flew at Edwards on 17 April 1969, in the inventory of X-vehicles, and McTigue describes the X-24A as having evolved from the SV-5 PRIME vehicle. Vitelli and Hallion state that the SV-5D’s external shape was held rigorously to the SV-5 configuration so that its data would serve larger vehicles. Between them the two programmes flew the one shape from Mach 24 to Mach 2.0 and from Mach 1.6 to landing, in Reed, though the fourth-flight memorandum puts the end of PRIME’s flights at Mach 2.4. The vehicles that followed, and the manned entry programmes this one was clearing ground for, are Driscoll et al. 1966, Mueller et al. 1967, Minott et al. 1976, Duggan 1977, Space Shuttle Maiden 1979, Waldrop 1980, Grooms et al. 1984, Joosten 1985, Logsdon 1986, Space Shuttle Log 1986, Space Shuttle Flight Rates 1987, Space shuttle flight rates and ut, Space Shuttle Setback 1987, Space shuttle setback, Brookfield et al. 1989, Whitesides et al. 1990, Ware et al. 1991, Cruz and Ware 1992, Sawko and Goldstein 1992, Iliff and Shafer 1993, Pielke 1993, Ware and Cruz 1993, Pielke 1994, Chaudhary et al. 2001, Straube et al. 2002, McCluskey 2004.

The larger consequence is the Space Shuttle’s crossrange requirement, and the arithmetic connects the two. The requirement, the entry it drove, and the guidance built to fly it are documented at length, in Adams 1971, Dejarnette and Jones 1971, Deyst et al. 1971a, Deyst et al. 1971b, Deyst et al. 1972, McGlathery 1973, Space Shuttle Guidance Navigation 1973, Stolarski et al. 1974, Kriegsman and Tao 1975, Ramnath and Sinha 1975, Jeffs 1979, Emero 1980, Park and Rakich 1980, Rowell et al. 1980, Iliff et al. 1981, Compton et al. 1982, Fraser 1983, Kanipe 1983, Romere and Young 1983, Romere et al. 1983, Bayle 1984, Campbell et al. 1989, Rosello 1995, Restrepo and Valasek 2006, Campbell 2007, Wood and Alter 2008. The Shuttle was required to achieve 1,100 nautical miles of crossrange, a figure that came from the Air Force and was driven by a once-around polar mission returning to its launch site, in Heppenheimer’s history of the Space Shuttle decision, who gives the reason in the same terms, that after one orbit from Vandenberg the base has moved 1,100 nautical miles to the east. The launch site moves with the Earth, so in one orbit it displaces by the full track spacing at its own latitude rather than half of it,

\[d_\text{VAFB} = R\,\Delta\lambda\cos\varphi = 6.371\times 10^6 \times 0.3937 \times \cos 34.74^\circ = 2{,}061\ \text{km} \tag{81}\]

against a stated requirement of 1,100 nautical miles, which is 2,037 kilometres. The agreement is

\[\frac{2{,}061 - 2{,}037}{2{,}037} = 1.2\ \text{percent} \tag{82}\]

and nothing here was fitted to anything. The requirement that shaped the Space Shuttle’s wing, and through it a great deal of the vehicle, is the distance Vandenberg travels while a spacecraft goes round once.

That requirement also explains why the Shuttle has wings and PRIME did not. Putting 1,100 nautical miles through the same relation that gave 0.978 for the general case,

\[\frac{L}{D} = \sqrt{\frac{2{,}037/6{,}371}{0.2056}} = 1.25 \tag{83}\]

which is above the SV-5D’s own trim curve and at the upper end of the 1.0 to 1.4 that Reed gives for the piloted lifting bodies. Reed records the Air Force projecting a need for ratios as high as 2.0, a requirement that made winged vehicles more attractive, and Heppenheimer reproduces a NASA comparison in which a delta-wing orbiter reaches 1.7 against 0.5 for a straight-wing design. The once-around requirement bought the Shuttle its wing.

PRIME demonstrated a fraction

\[\frac{1{,}143}{2{,}037} = 0.56 \tag{84}\]

of that figure with a vehicle weighing 894 pounds.

The programme is also a data point about unmanned research vehicles, which the designation section below turns out to bear on directly.

A Designation That Was Never Requested

The encyclopaedias call it the X-23A, and so do NASA’s histories. Hallion’s history of the Dryden centre says the Air Force ordered four SV-5D vehicles and designated them X-23A, Reed says the same, and the NASA inventory of American X-vehicles lists the vehicle as the X-23. The nomenclature records, as reported by the standard reference on United States military aircraft designations, show that the designation was never assigned, and further that it was never requested.

The sequence, which is stranger than a simple omission, runs as follows.

On 16 November 1965 a request was submitted for the designation X-23A. It was submitted for the SV-5P, the piloted low-speed vehicle, and the vehicle description accompanying the request clearly described a manned lifting-body aircraft flying from Mach 2 to landing.

On 15 December 1965 the request was disapproved, on the ground that the subject aircraft was unmanned. At that date the designation system applied to manned aircraft only, so the reason was a valid one in general. It was not true of this aircraft, and the paperwork accompanying the request said so.

In late 1966 the offices responsible reconsidered the question. A proposal to create an entirely new designation category for gliding re-entry vehicles was raised and abandoned. The decision instead was to request X-23A for the unmanned SV-5D and X-24A for the piloted SV-5P. X-24A was requested and approved. No request for X-23A appears ever to have been sent. The sequence is documented in the standard reference on designations.

The reason is not recorded. The plausible reading, offered as a reading and not as a finding, is that having been told a year earlier that unmanned aircraft need no designation, nobody saw the point of asking.

Three points here should be kept separate.

First, the designation is in universal use and is not official. This article uses it, as its title does, because refusing to would make the vehicle harder to find without making it more accurately described.

Second, the disapproval was wrong on its facts. The 1965 refusal turned on the vehicle being unmanned, and the vehicle in that request was the piloted one. The manned vehicle was refused a number for being unmanned, and a year later received a different number for being manned.

Third, and most useful to this series, the system briefly considered growing a new limb and did not. A separate designation category for gliding re-entry vehicles was proposed and dropped. The X-series absorbed the problem instead, informally and without paperwork. The episode is a small piece of evidence about how the designation system accommodated things it was not built for. The series’ closing article argues that the designation system is not a counter. This is one of the cases behind that argument, and it should be read alongside the reserved-but-never-allocated X-39 and the refused X-52, both in the standard reference on designations.

This article states the conflict and does not resolve it. The records say the number was never assigned. The world says the vehicle is the X-23A. Both statements are true about different things, and collapsing them would destroy the evidence.

The Contemporary Literature

Cluster	Records
Parachutes, decelerators and recovery	650
Hypersonic aerodynamics, flow fields and the boundary layer	496
Ablation and thermal protection	462
Planetary and superorbital entry, descent and landing	442
Entry guidance, trajectory optimisation and hypersonic flight control	412
Lifting bodies and the SV-5 family	264
Hypersonic glide vehicles, their tracking and their interception	252
Stagnation-point, convective and radiative heating	243
Capsules and ballistic entry	232
The equilibrium glide and analytic entry trajectories	227
The Space Shuttle orbiter and its requirement	218
Reusable launch vehicles, spaceplanes and booster return	153
Entry flight experiments, measurements and programmes	120
Debris, casualty risk and range safety	97
Reaction control, attitude control and control surfaces	90
The atmosphere that entry is computed against	63
Crossrange, lateral range and the entry footprint	61
Entry vehicles in general	60
Weight estimation and vehicle sizing	57
Orbits, ground tracks and astrodynamics	43
Total	4,642

The problem PRIME was built for did not go away. What happened instead is stranger and is the organising fact of this survey. The capability was demonstrated, it was adopted, it was then given up by the very class of vehicle it had been built for, and it was adopted again by a different class of vehicle for the opposite reason.

The field as it currently stands is large, since 2,237 of the survey’s research records were published in 2010 or later, and the clusters below divide it by subject.

The Vehicles It Was Built For Gave the Capability Up

Every crewed spacecraft flying to orbit today comes home as a blunt capsule, as Mercury did. The Space Shuttle is the only crewed spaceplane to have flown in orbit, and Orion, Dragon, Soyuz and Shenzhou are the current capsules, in the encyclopaedia entry on space capsules, and the literature of that choice is gathered below under capsules and ballistic entry.

The relation derived here is still the quickest way to see what that costs. A blunt capsule trims at a lift-to-drag ratio near 0.3, a nominal value assumed here, and the crossrange it yields is

\[y = \pi^2/48 \times 0.3^2 \times 6.371\times 10^6 = 118\ \text{km} \tag{85}\]

or 117 kilometres by the exact integration, the two being close here because at so small a lift-to-drag ratio the heading barely turns and the small-angle step costs almost nothing. Set against the once-per-orbit requirement of 1,254 kilometres derived earlier, that is

\[\frac{117}{1{,}254} = 0.09 \tag{86}\]

Nine percent. A modern crewed spacecraft has, by deliberate choice, about one eleventh of the crossrange that would let it come home when it wants to.

The ratios in the table are nominal values assumed for illustration. The lifting-body rows sit within the 1.0 to 1.4 that Reed gives for the piloted lifting bodies.

Vehicle	Lift-to-drag ratio	Crossrange, exact
A ballistic capsule with no lift	0	0 km
Mercury and Vostok	0.05	3 km
Apollo, Orion and Soyuz	0.30	117 km
PRIME, at the lower disputed figure	1.00	1,214 km
The Space Shuttle orbiter	1.10	1,447 km
The X-24A	1.40	2,233 km

The regression came from the requirement disappearing, and engineering did not fail. The once-around polar mission that generated the Shuttle’s 1,100 nautical miles was an Air Force requirement, in Heppenheimer, and when Shuttle operations from Vandenberg were cancelled before they began, in the history of Space Launch Complex 6, nothing else needed that number. An ocean landing needs no runway, a parachute weighs less than a wing, and a capsule’s heat shield is a simpler object than an orbiter’s. The Shuttle’s wing was the last time crossrange drove a crewed vehicle’s shape, and PRIME is part of the reason that wing could be drawn with confidence.

Crossrange Became a Weapon’s Virtue

The capability did not disappear. It moved to weapons, whose literature appears below under hypersonic glide vehicles, their tracking and their interception.

A hypersonic glide vehicle wants lateral range for exactly the reason a spacecraft did not. A returning spacecraft wanted to reach a chosen site. A glide vehicle wants a trajectory that cannot be extrapolated, because an interceptor must be committed early and a manoeuvring target invalidates the prediction it was committed against. The literature reflects that inversion, being largely about estimating and tracking a manoeuvring entry body, where the period literature was about designing one.

The relation is the same and the motive is not, and the equation cannot tell the difference. The derivation above contains nothing that distinguishes a landing site from an evasive manoeuvre.

One limit constrains the treatment given here, though not the literature. A slender glide vehicle may reach a lift-to-drag ratio of 2.5, which Reed reports for the slender lifting bodies, and the closed form would offer 8,187 kilometres for it. That number should not be believed. At such a ratio the closed form over-predicts by 41 percent, the accumulated heading change passes 400 degrees, and even the exact constant-bank integration is describing a trajectory no vehicle would fly. The relation that describes PRIME does not describe its successors, and saying so is more useful than extrapolating it past its assumptions.

The Computation Became Free

What changed most is not the physics but the cost of solving it, as the cluster below on entry guidance, trajectory optimisation and hypersonic flight control shows.

The crossrange relation derived above is a closed form obtained by forcing the trajectory to be an equilibrium glide at constant bank. That was necessary in 1964 because the alternative was unaffordable. The modern equivalent solves the trajectory numerically, onboard, in real time, and increasingly by convex optimisation whose convergence can be guaranteed rather than hoped for. It arrives at very nearly the same answer, because the physics did not move.

The closed form’s role has changed rather than ended. It is no longer how a vehicle is sized. It is now how an optimiser’s answer is checked, the same use made of it above.

The Ablator Is Computed Rather Than Tested

The 1960s route to a heat shield thickness was arc-jet testing and margin. Vitelli and Hallion write that PRIME’s design procedures rested on a mathematical model and plasma arc testing and that its shield proved conservative. The modern route computes the material response, in Arnold et al. 2013, Li et al. 2015e, Milos et al. 2015, Chen 2016b, Kumar and Mahulikar 2016b, Brune et al. 2017, Harpale et al. 2018, Meurisse et al. 2018, Cinquegrana et al. 2019, Gulli and Maddalena 2019, Rivier et al. 2019, Wang et al. 2019a, Shilav and Khosid 2020, Raghunandan et al. 2021, Hasan 2022, He et al. 2022b, Price et al. 2022, Chinnaraj et al. 2023b, He et al. 2023, Lai and Leu 2023a, Lai and Leu 2023b, Scandelli et al. 2023, Chen and Gökçen 2024, Yang et al. 2024, Price et al. 2025, Wang et al. 2025a, Cutrone et al. 2026, Zibitsker and Martin 2026.

That is the largest single practical change in the subject. The cross-check performed earlier in this article, inverting a published thickness to recover an effective heat of ablation of 27.8 megajoules per kilogram, is the crude version of what a material response code now does properly, with pyrolysis chemistry, in-depth conduction and a quantified uncertainty on the answer. Arc-jet testing did not go away. It became validation instead of design.

Lifting Bodies Came Back Mostly Uncrewed

The shape survived, and the clusters below on lifting bodies and the SV-5 family and on reusable launch vehicles, spaceplanes and booster return record that work.

What is flying now is closer to PRIME than to the X-24A, in the sense that it is mostly uncrewed and mostly automatic. Alongside them sits the deployable or inflatable aeroshell that packs small and opens to a large low-ballistic-coefficient decelerator. That attacks the problem from the opposite end. PRIME lowered its ballistic coefficient to 60 pounds per square foot by being light. A deployable aeroshell lowers it by growing.

Catching Things in the Air Is Now Routine

The part of PRIME that failed twice in three flights is the part that has been most thoroughly vindicated. The cluster below on parachutes, decelerators and recovery documents that outcome.

Mid-air retrieval by helicopter has since been demonstrated on a returning orbital booster, in the encyclopaedia entry on mid-air retrieval, and the supersonic parachute work that Mars entry demanded has produced a decelerator literature far deeper than anything available in 1967. The technique outlived the aerodynamics, which is not the outcome anyone would have predicted from a programme that lost two vehicles to a main parachute that never left its container and to line cutters fitted without their charges, in Vitelli and Hallion.

The Footprint Became a Safety Calculation

Here the inversion is at its sharpest, in Falsone and Prandini 2017, Kim et al. 2018, Lee et al. 2018, Annaloro et al. 2020, Braun et al. 2020, Jorgensen and Sharf 2021, Santos and Sampaio 2021, Bohman et al. 2024, Chen et al. 2025e, Chen et al. 2025g, Jain and Hastings 2025, Navaz and Ntantis 2026, Park et al. 2026, Yuricich 2026.

PRIME wanted a large footprint. Modern practice wants a small and precisely predicted one. The reachable area treated above as a capability is, for a spent stage or a decaying satellite, a hazard to be bounded, and the same trajectory mathematics now serves debris casualty risk, controlled disposal and range safety. A quantity computed to show what a vehicle could reach is now computed to prove what it cannot.

The Same Relations, on Other Planets

Nor can the equation tell which planet it is being asked about, and the cluster below on planetary and superorbital entry, descent and landing is the evidence.

The equilibrium glide with a different gravitational parameter and a different atmosphere is what every planetary entry and every aerocapture study solves. Mars is where the modern work concentrates, because it has enough atmosphere to matter and not enough to make entry easy, and because the crossrange question there is the same question PRIME asked, being whether a vehicle can reach a chosen site rather than wherever the ballistic track puts it.

How It Flies, Computed to a Standard Nobody Had

Underneath all of it is the aerodynamic and aerothermodynamic prediction that the period could only estimate, surveyed below under hypersonic aerodynamics and under heating.

The decades between PRIME and the current revival were not empty, and 1,411 of the survey’s research records were published between 1973 and 2009.

What the Survey Shows

The arithmetic has not moved at all. Crossrange still goes as the square of the lift-to-drag ratio, the optimal bank angle is still 45 degrees, the footprint still goes as the cube, and the once-per-orbit requirement is still about a lift-to-drag ratio of one.

What moved twice is the requirement. It went from the Air Force wanting a spacecraft that could come home on the next pass, to nobody wanting that and crewed vehicles giving up ninety-one percent of the capability, to a different community wanting lateral range specifically because it defeats prediction.

And the thing PRIME was worst at turned out to be the thing that lasted. The programme lost two of three vehicles to the recovery system. Mid-air retrieval is now a demonstrated commercial technique, in the encyclopaedia entry on mid-air retrieval, and the aerodynamic configuration it was carrying is not flown by anyone.

Parachutes, decelerators and recovery

The recovery system and its descendants, being parachutes and their deployment, inflation, reefing and fabrics, ballutes and inflatable or deployable decelerators, and the mid-air retrieval of a descending payload. It is the largest cluster, and it includes parachute engineering for aircraft, ordnance and personnel because they share the deployment and inflation problem. 135 of the 650 titles say supersonic and 161 name a ballute, an aeroshell or an inflatable or deployable decelerator.

650 records. [A Supersonic Parachute 1949] [Abramova 2021] [Abramova and Reznik 2020] [Accorsi and Leonard 2002] [Adams 2014] [Aebischer and Suters 1970] [Al-Ebiary et al. 2017] [Averyanov 2022] [Braun and Walcott 1963] [Carten and Wuest 1980] [Figucia and McCafferty 1966] [French 1963] [French 1969a] [French 1969b] [Garrard and Konicke 1981] [Greene and Preisser 1970] [Guan et al. 2025b] [Guruswamy 2015] [Heinrich and Jamison 1966] [Heinrich and Saari 1978] [Heinrich and Rust 1965b] [Jailer et al. 1960] [Kim 2016] [Klimas 1972] [Landman 2020] [Lavrakas 1955] [Lorenz et al. 2021] [Nicolaides 1971] [Niemi 1992] [Pan and Yu 2023] [Pensado et al] [Pensado et al] [Amirkhizi et al. 2024] [Kim 2002] [Lee 2008] [An Overview of Munition 1984] [Analysis of the Working 2016] [Anderson 2004] [Andrianov et al. 2015] [Androsenkov et al. 2007] [Anton et al. 2023] [Antonenko and Belavskiy 2009] [Armand 2013] [Arnold et al. 2011] [Arnold et al. 2013] [As’ad et al. 2022] [Askins et al. 1997] [As’ad et al. 2025] [Autonomously Guided Ram-Air Parachute 2009] [Axdahl et al. 2009] [Babakov 2025] [Babakov 2026] [Babish 1970] [Baginski et al. 2013] [Bahrami 2012] [Bai et al. 2022] [Baker] [Baker and Swallow 1956] [Banerjee and Utreja 1975] [Banerji et al. 2018] [Barlog 1979] [Barnhardt et al. 2007] [Bartz and Miklosovic 2003] [Bassett et al. 2017] [Behr 1989b] [Behr 1989a] [Behr et al. 1991] [Bennett et al. 1976] [Berexa et al. 2019] [Bergeron et al. 2015] [Bohon and Miserentino 1970] [Bohon et al. 1974] [Bose et al. 2013] [Boulware et al. 2007] [Boundy et al. 1968] [Boustani et al. 2019] [Boustani et al. 2020] [Bowman] [Brandeau et al. 2015] [Purvis 1982] [Reddish et al] [Braun 1953] [Brearley 1969] [Brinkman 1992] [Brock et al. 2019] [Brookfield et al. 1989] [Brown 1989] [Brown et al. 2001] [Brown et al. 2003] [Brune et al. 2015] [Brune et al. 2016] [Brune et al. 2017] [Cadieux and Barad 2025] [Campos 1977] [Cannon and Koch 1989] [Cao et al. 2017] [Caqueo Jara et al. 2023] [Carandente et al. 2015] [Carten and Wuest 1979] [Cassanto et al. 1968] [Cassell et al. 2011] [Cassell et al. 2018] [Cassell et al. 2019] [Cassell et al. 2021] [Catch a Falling Star 1993] [Chakoian 1969] [Chambe et al. 2024] [Chandler 1967] [Charles 2017] [Chen et al. 2015c] [Chen et al. 2025c] [Chen et al. 2026b] [China Achieves First Reusable 2026] [Civelek and Kıvrak 2024] [Clapp et al. 2015] [Clark et al. 2006] [Clark et al. 2009] [Clark et al. 2015a] [Clark et al. 2015b] [Clark et al. 2021a] [Coatta et al. 2013] [Coleman et al. 2026] [Cook 2013] [Cowan et al. 2025] [Craley and Desabrais 2007] [Crimi 1986] [Crimi and Jorgensen 1991] [Cruz et al. 2003] [Currin et al. 2012] [Dahal et al. 2018b] [Dahal et al. 2018a] [Dahal et al. 2020] [Day 2013] [Defense Documentation Center Alexandria VA 1971] [Deitering and Hilliard 1965] [Delurgio et al. 1981] [Derkevorkian et al. 2019] [Desabrais et al. 2015] [Deshmukh et al. 2025] [Desimone 1981] [Di Caprio et al. 2021] [Dillman 2015] [Dillman et al. 2010] [Dillman et al. 2013a] [Dillman et al. 2013b] [Dillman et al. 2024] [Dimino et al. 2023] [Dinh] [DiNonno and Cheatwood 2026] [Dinonno et al. 2016] [Downing et al. 1956] [Downs and Bartlett 1989] [Drynan] [Dunker and Berland 2007] [Dutta et al. 2020] [D’Amato et al. 2022] [Eckstrom 1970] [Eckstrom 1975] [Eckstrom and Mayhue 1969] [Eckstrom and Preisser 1967] [Ericksen et al. 1984] [Eslambolchi and Johari 2013] [Roelke and Green] [Roelke et al] [Everett and Henke 1981] [Cadieux and Barad] [Fallon 1991] [Fallon and Fallon 1997] [Fallon et al. 1986] [Fan et al. 2022] [Farhall et al. 2007] [Fedele et al. 2021] [Fields and Basore 2015] [Fields et al. 2026] [Fogell et al. 2017] [Fomichev and Yadrenkin 2013] [Fomichev et al. 2011] [Cadieux and Barad] [Cadieux and Barad] [Cadieux et al] [French 1965] [French 1966] [French 1967] [French 1979] [French 1980] [French 1988] [Fu and Koch 1977] [Fukiba et al. 2023] [Further Development and Flight 1994] [Gaglio et al. 2026] [Gallon and Witkowski 2015] [Gallon et al. 2013] [Gao et al. 2015b] [Gao et al. 2016a] [Gao et al. 2016b] [Garba 1968] [Gasparoni et al. 2026] [Gates et al. 2010] [Gates Medlock and Longuski 2008] [Ghasimi and Rabinovitch 2023] [Ghoreyshi et al. 2014] [Ghoreyshi et al. 2015] [Giersch et al. 2015] [Gionfriddo 2011] [Gnoffo and Anderson 2002] [Goglia 1952] [Goglia et al. 1955] [Goldman et al. 2015] [Gombos and Reed 1975] [Gong and Wu 2021] [Goodrick 1969] [Goulding and Adams 2010] [Graham 1965] [Graham 2001] [Gramola et al. 2021] [Green et al. 2013] [Griebel 2010] [Griebel 2011a] [Griebel 2011c] [Griebel 2011b] [Grippon 2022] [Grychanyuk et al. 2015] [Guo et al. 2017a] [Guruswamy 2017] [Guruswamy 2025] [Güven and Şamiloğlu 2022a] [Güven and Şamiloğlu 2022b] [Ham 1963] [Hao et al. 2018b] [Hara and Yokoo 2018] [Haubelt et al. 2001] [He 2024] [He et al. 2022a] [Heinrich 1966b] [Heinrich 1966a] [Heinrich and Rust 1965a] [Henke and Nerem 1968] [Herrington et al. 2019] [Higgins and Speelman 1973] [High Drag Rotating Parachute 1985] [Highley 1970] [Hinada et al. 1991] [Hintzke and Haggard 1991] [Hiraki et al. 1997] [Hirst and Jorgensen 1995] [Hollis 2018] [Hornung 2001] [Hoter et al. 2026] [Huang et al. 2020b] [Hughes et al. 2011] [Iacovazzo et al. 2015] [Ibos et al. 1999] [Inatani et al. 1999] [Irving Air Chute 1968] [Ivanov et al. 2020] [Izadi and Razzaz 2008] [Jain et al. 2022] [Jamison 1966] [Jamison 1967] [Janda et al. 2013] [Jann 2015] [Jann and Ward 2019] [Jaremenko 1967] [Jasztal and Kłosiński 2024] [Jasztal et al. 2022] [Johari and Desabrais 2002] [DiNonno and Cheatwood] [Johnson 1986] [Johnson 1989] [Johnson and Lyons 2004] [Boustani et al] [Jorgensen 1991] [Jorgensen et al. 2005] [Just 1991] [Kanai et al. 2018] [Kandis and Witkowski 2019] [Karlgaard et al. 2019a] [Karlgaard et al. 2019b] [Kelly et al. 2016] [Kelly et al. 2018] [Kenig et al. 2013] [Kenig et al. 2015] [Kennedy and Lowry 1995] [Kennedy et al. 1997] [Kimata et al. 2015] [King et al. 2011] [Knacke 1985] [Knapik et al. 2011] [Koenig et al. 1995] [Koike et al. 2018] [Kou and Zhan 2022] [Kozlov 2013] [Kramer et al. 2011] [Kross and Webb 1979] [Kurinnyy 2020] [Kustas et al. 2000] [Křemenáková et al. 2026] [Langston et al. 2016] [Lavier 1955a] [Lavier 1955b] [Ledyankina et al. 2018] [Lee 1993] [Lee et al. 2007] [Levin and Shpund 1995] [Lewis 1964] [Li 2015] [Li et al. 2023a] [Liang and Mease 2019] [Lin 1986] [Lin et al. 1979] [Lingard 2015] [Lingard and Darley 2005] [Lingard et al. 2013] [Lingard et al. 2015] [Lingard et al. 2017] [Liu et al. 2000] [Long 1993] [Lorenz and Allen 2023] [Lorenz and Lam 2026] [Lucas 2022] [Ludtke 1991] [Lyalin and Morozov 2005] [Lyons and Johnson 2004] [MacCarthy 1954] [Machin and Daum 2026] [Machin et al. 2001] [MacNeal and Schuerch 1963] [Manjith 2026] [Mars Parachute Testing Suffers 2019] [Matsunaga et al. 2015] [Matsunaga et al. 2017] [Maydew and Johnson 1972] [Mayhue and Eckstrom 1969] [McCarty 1978] [McEwan 1970] [McMenomy 2022] [McRonald 2000] [Meacham et al. 2013] [Melzig and Schmidt 1965] [Meyer 1958] [Meyerson 2001] [Michal et al. 1970] [Mickey and Stuart 1967] [Miller 1954] [Miller et al. 2003] [Галимджанович et al. 2020] [Галимджанович et al. 2021] [Minnesota Univ Minneapolis Inst Of Tech 1962] [Mizukaki et al. 2019] [Mkrtchyan and Johari 2011] [Modular Heavy Payload Autonomously 2009] [Mohaghegh and Jahannama 2007] [Montanez and Pantano 2026] [Montanez et al. 1997] [Moog 1975] [Moog et al. 1979] [Moore 2013] [Moore and Morris 2011a] [Moore and Morris 2011b] [Moorman and Yechout 2009] [Mori and Kuzuo 2018] [Morris and Olson 2011] [Mortaloni and Stewart 1999] [Moss 2005] [Mosseev 1999] [Mungiguerra et al. 2017] [Muppidi et al. 2015] [Murman 2009] [Murray 1961] [Nadal Mora et al. 2005] [Nadal Mora et al. 2007] [Nagata et al. 2013] [Nakao et al. 2022] [Nelsen 1995] [Nerem 1966] [Neustadt et al. 1967] [Newberg et al. 2026] [Nie et al. 2023a] [Nie et al. 2023b] [Nie et al. 2024] [Noel et al. 2026] [O’Farrell et al. 2016] [O’Farrell et al. 2018] [O’Farrell et al. 2019] [O’Farrell et al. 2022] [O’Farrell et al. 2023] [O’Farrell et al. 2024] [Ohashi et al. 2018] [Orlandini et al. 2026] [Ortega et al. 2017] [Otsu 2008] [Otsu 2011] [Otsu and Abe 2008] [Otsu and Abe 2015] [Otsu and Abe 2016] [Otsu and Takama 2012] [Ouyang and Zhang 2026] [Ouyang et al. 2026] [O’Farrell and Clark 2024] [Palharini 2020] [Pantano and Montanez 2024] [Parachutes 1989] [Parate 2020] [Park 1986] [Payne and Band 1976] [Peacocke et al. 2019] [Pearson 1972] [Pedersen 1961] [Pepermans et al. 2018] [Pepper 1967] [Pepper 1977] [Pepper 1980] [Pepper 1984b] [Pepper 1984a] [Pepper and Biesterveld 1973] [Pepper and Collins 1982] [Pepper and Cronin 1969] [Pepper et al. 1984] [Peralta and Johari 2015] [Peri et al. 2024] [Perin and Patoux 2022] [Perschbacher and Potvin 1999] [Peterson et al. 1986] [Peterson et al. 2018] [Peterson et al. 2024] [Pilyugin and Khlebnikov 2010] [Placco 2023a] [Placco 2023b] [Placco et al. 2025] [Placco et al. 2026] [Pleasants 1973] [Pleasants 1975] [Ploskov 2020] [Pm et al. 2024] [Poole 1973] [Potvin 1997] [Potvin 2001b] [Potvin 2001a] [Potvin 2023] [Potvin and Peek 1998] [Potvin and Potvin 1997] [Potvin et al. 1997] [Prabhu et al. 2013] [Pratap et al. 2019] [Preisser et al. 1967] [Priyadarshi et al. 2020] [Purvis 1983] [Purvis 1984a] [Purvis 1984b] [Puskas 1984] [Puskas 1989] [Puthalapattu 2025] [Pyle et al. 1973] [Qingsong and Surong 2024] [Qiu et al. 2021] [Bodkin et al] [Rabinovitch et al. 2018] [Rabinovitch et al. 2019a] [Rabinovitch et al. 2019b] [Rabinovitch et al. 2020] [Rabinovitch et al. 2022] [Raghunandan et al. 2023] [Rasheed et al. 2001] [Ravnitzky 1989] [Ray 2013] [Reinhard et al. 1997] [Reza et al. 2007] [Reznik et al. 2020] [Richards 2022] [Richardson et al. 2005] [Rioseco Olave et al. 2023] [Roberts 1974] [Roberts 1980] [Rodier 1979] [Roland et al. 2016] [Rollstin 1986] [Rong et al. 2015b] [Runkle and Drobnik 1979] [Runkle and Woodis 1979] [Rybakiewicz and PlachÁ 2023] [Rysev 1993] [Sandstrom 1971] [Sanganeria 2025] [Santos et al. 2021] [Santos et al. 2022] [Saxena et al. 2021] [Schaefer et al. 2001] [Schatzle and Curry 1980] [Schuerch 1965] [Seidel and Bergeron 2017] [Seidel et al. 2016] [Sengupta et al. 2007] [Sengupta et al. 2008b] [Sengupta et al. 2008a] [Sengupta et al. 2009] [Shankar et al. 2018] [Shepardson 1954] [Sheta et al. 2015] [Shi et al. 2022] [Siegel et al. 2022] [Siegel et al. 2024] [Silbert 1983] [Silbert et al. 1986] [Silbert et al. 1989] [Sims 1963] [Sivasubramanian et al. 2026] [Skelton and Abbott 1974] [Smith et al. 2001] [Smollett 1955] [Sonneveldt et al. 2019] [Speelman 1975] [Speelman 1977] [Steeves 1986] [Steltzner et al. 2003] [Hughes et al] [Hughes et al] [Stewart 2013] [Study on Critical Parachute 2024] [Suit et al. 1964] [Sun et al. 2025b] [Sundberg 1975] [Swanson et al. 2025] [Sweeney 1955] [Szafran and Kramarski 2019] [Taguchi et al. 2015b] [Taguchi et al. 2015a] [Taguchi et al. 2021] [Takabayashi and Kitamura 2019] [Takabayashi et al. 2019] [Takahashi and Yamada 2018] [Takahashi et al. 2012] [Takahashi et al. 2013] [Takahashi et al. 2015] [Takahashi et al. 2018] [Takahashi et al. 2020] [Takayanagi et al. 2021] [Takizawa et al. 2016] [Tang and Qian 2015] [Tang et al. 2015] [Tang et al. 2021] [Tanner et al. 2015] [Tatsuta et al. 2025] [Teichroew 1954] [Terahara et al. 2025] [Thomas and Thomas 2008] [Thomas et al. 2007] [Tiaden and Yakimenko 2008] [Tiaden and Yakimenko 2009] [Tibbits and Ivanov 2015] [To] [Tomcsak 1960] [Toni 1968] [Townend 1970] [Trabandt et al. 2003] [Tutt et al. 2003] [Tutt et al. 2015] [Tutt et al. 2022] [Usry 1968] [Usry 1969] [Vardi] [Vishnyak 1995] [Vo et al. 1993] [Votta et al. 2009] [Votta et al. 2010] [Wailes and Carlson 1986] [Walcott 1963] [Wang and Shih 1991] [Wang et al. 2020f] [Wang et al. 2021] [Wang et al. 2022f] [Watkins 1995] [Way 2018] [Waye 1991] [Waye et al. 1986] [Webb 1986] [Wegereef et al. 2011] [Wei 1991] [Wei and Pearson 1974] [Wei et al. 2024] [Wercinski et al. 2015] [Wernet et al. 2009] [Whalley 1973] [Whitlock et al. 1973] [Whitmore et al. 2004] [Wijaszka et al. 2023] [Williams 2017] [Williamson 1979] [Witkowski 1999] [Witkowski and Kandis 2010] [Witkowski et al. 2009] [Witkowski et al. 2022] [Wolf] [Wolf 1971] [Wolf 1974] [Wolf 1999] [Wolf and Croll 1979] [Wolf and Fallon 2011a] [Wolf and Fallon 2011b] [Wolf and Ivanov 2008] [Woodruff et al. 2015] [Wu et al. 2021b] [Xie et al. 2015a] [Xing and Liang 2025] [Xing et al. 2022] [Xing et al. 2024] [Xing et al. 2025] [Xu et al. 2025b] [Xue and Nakamura 2011] [Xue and Nakamura 2013] [Xue et al. 2013] [Xue et al. 2015a] [Xue et al. 2015b] [Xue et al. 2016] [Xue et al. 2019b] [Xue et al. 2019a] [Xue et al. 2022] [Yakimenko et al. 2008] [Yamada et al. 2011a] [Yamada et al. 2013] [Yamada et al. 2015] [Yamada et al. 2022] [Xue 2021] [Yang et al. 2017] [Yang et al. 2018b] [Yang et al. 2019a] [Yang et al. 2020] [Yang et al. 2022] [Yasumura and Kitamura 2021] [Yavuz 1985] [Ye et al. 2026] [Yeakle et al. 2009] [Young 1976] [Young et al. 2018] [Yount et al. 2012] [Yu et al. 2023b] [Yu et al. 2025b] [Yun and Liu 2023] [Yun and Liu 2024] [Zhang 2003] [Zhang and Gao 2018] [Zhang and Gao 2019] [Zhang et al. 2024c] [Zhang et al. 2025e] [Zhao and Li 2019] [Zhao et al. 2019b] [Zhao et al. 2020a] [Zhao et al. 2022b] [Zhu et al. 2023] [Zuppardi et al. 2016] [Бабаков and Финченко 2022]

Hypersonic aerodynamics, flow fields and the boundary layer

The flow the vehicle flies through, being blunt-body and slender-body hypersonic aerodynamics, nonequilibrium and rarefied flow, the boundary layer and its transition, wakes, the plasma sheath and communications blackout, and the computational test cases of the double ellipse and the double ellipsoid.

496 records. [Abarbanel 1977] [Abdel-Gawad et al. 2019] [Abe et al. 2003] [Abgrall and Merlo 1992] [Air Force Test Pilot School Edwards Afb Ca 1987] [Albertson 1989] [Albisser et al. 2017] [Allegre et al. 1992] [Allouche et al. 2011] [Alsalihi and Deconinck 1991] [Amato et al. 2026] [An et al. 2021] [An et al. 2025] [Andersen and Connor 1970] [Anfuso et al. 2026] [Angrand et al. 1991] [Archer and Hermann 1965] [Argyris et al. 1991] [Argyris et al. 1992] [Arkhipov and Polenov 1971] [Arney and Boylan 1963] [Artamonov and Arkhipov 1979] [Asif et al. 2004] [Atkins 2026] [Atkinson et al. 2013] [Baganoff 1990] [Balakumar and Chou 2018] [Barbera 1980] [Bartel et al. 1988] [Becker 1964] [Beckwith and Cohen 1963] [Berry et al. 2021] [Bhutani and Chandran 1978] [Bhutta and Lewis 1988] [Bhutta and Lewis 1989b] [Bhutta and Lewis 1989a] [Bingyan et al. 2015] [Bloor 1965] [Blum and Yoshihara 1988] [Boccaccio et al. 1992] [Boeing Scientific Research Labs Seattle WA 1963] [Bogdonoff 1970] [Bogdonoff 1999] [Boppe and Davis 1989] [Borrelli and Pandolfi 1991] [Borrelli et al. 2010] [Boudreau 1979] [Bowersox and Fan 2000] [Boyd 2004] [Boyd 2008] [Boylan 1965] [Brauckmann 1986] [Breeza Paulose et al. 2016] [Brooke and Thomas 1964] [Brunk 1963] [Bulakh 1964] [Bush 1958] [Bush 1959] [Bykerk et al. 2020a] [Bykerk et al. 2020b] [Campbell et al. 2012] [Candler 2001] [Carden and Potter 1968] [Carlomagno et al. 1993] [Cassanto 1966] [Chalot et al. 1991] [Chao et al. 2015] [Chapter 5 2013] [Chapter 9 2013] [Chasovnikov 2020] [Chaussee et al. 1975] [Chavez and Schmidt 1993] [Cheah et al. 2025] [Chen and Gibbons 2022] [Chen et al. 2016c] [Chen et al. 2022b] [Chen et al. 2022e] [Chen et al. 2023b] [Cheng et al. 2011b] [Cheng et al. 2023a] [Chrusciel 1975] [Chu 1967] [Chuanzhen et al. 2022] [Chung 2023] [Computational Fluid Dynamics Design 1990] [Cox et al. 1966] [Cresci 1966] [Cunningham 1985] [Dai et al. 2020] [Davenport 1972] [Kessler et al. 2021] [de Moura and Ribeiro 2026a] [de Moura and Ribeiro 2026b] [Decker and Laschka 2001] [Demele and Brownson 1961] [Demetriades 1960] [Denman et al. 1991] [Device May Eliminate Communications 1962] [Dietrick 2013] [Ding et al. 2015] [Ding et al. 2018] [Ding et al. 2019] [Dirling et al. 1975] [Divitiis and Vitale 2010] [Dix 1962] [Dong and Li 2021] [Dongre 2024] [Dortmann 1991] [Dortmann 1992] [Druguet et al. 1992] [Dubois and Michaux 1992] [Eliasson et al. 1991] [Ericsson 1969] [Ericsson 1971] [Ericsson 1977a] [Ericsson 1977c] [Ericsson 1977b] [Ericsson 1979] [Ericsson and Scholnick 1969] [Evans et al. 1970] [Fante et al. 1970] [Fedele et al. 2014] [Feiereisen 1991] [Fey et al. 1992] [Finke 1970] [Finley 1990] [Finson 1973] [Finson 1975] [Fournier 1960] [Frayssinet 2019] [Frayssinet et al. 2013] [Galkin and Gladkov 1961] [Gamertsfelder et al. 2022] [Gao 2023] [Gao et al. 2020a] [Gao et al. 2026c] [Garvine 1966] [Gazaix 1992] [Gielda et al. 1990] [Ginoux 1966] [Gnoffo 1991] [Gockel 1993] [Goldberg and Scala 1965] [Golden 1969] [Goldman 1958] [Goldman and Obremski 1973] [Golovachev 1979b] [Golovachev 1981] [Gong et al. 2006] [Gonor 1964] [Gorenbukh and Nikolaev 1988] [Grasso et al. 1992] [Grawe and Häuser 1992] [Gregorek et al. 1963] [Griffith 1958] [Groves et al. 2005] [Gruhn and Gülhan 2018] [Gui et al. 2023] [Guillen and Borrel 1991] [Guo et al. 2019b] [Guo et al. 2020c] [Gupta and Hall 1977] [Guruswamy 2016] [Gökçen 1991] [GÜlçat 2021] [Han and Cao 2019] [Harloff 1987] [Harney 1963] [Harney and Petrie 1971] [Harris et al. 1980] [Hartsell 1961] [Haya Ramos et al. 2009] [Hayes 1959] [Hayes et al. 1960] [Heinrich 1961] [Heller and Widnall 1968] [Henckels and Maurer 1991] [Henckels and Maurer 1992] [Herdrich et al. 2000] [Hettena et al. 1992] [Hillier 1978] [Hitzel 1991] [Holland et al. 2000] [Horlock 1964] [Horstman 1963] [Hossan and Srinivas 2023] [Hu et al. 2017] [Huang 1968] [Hughson and Beran 1991] [Hui 1969] [Hui 1972] [Huynh and Kriz 2009] [Hypersonic Aerodynamics 1988] [Hypersonic Aerodynamics 2019] [Hypersonic Aerodynamics Slender Bodies 2025] [Volkov 2023] [Hypersonic Flows 2025] [Désidéri et al. 1991] [Hypersonic Reentry 2011] [Hypersonic Research Facilities Study 1970] [Hypersonic Thin Viscous Shock 2018] [Inger 1989] [Inger 1995] [Introduction to the Virtual 2026] [Исмагилов and Сидельников 2015] [Ivanov et al. 2006] [Jaffe 1970] [Ji et al. 2019a] [Jiang and Richards 1991] [Jin et al. 2026] [Johnson and Joseph A. 1977] [Johnston et al. 2026] [Joint Conference on Lifting 1960a, Joint Conference on Lifting Manne] [Joint Conference on Lifting 1960b, Joint Conference on Lifting Manne] [Jung et al. 2018] [Jurak et al. 1972] [Kaiser and Fluegge-Lotz 1968] [Kang 1969] [Kang 1970] [Kaplan and Oran 2021] [Kelly 1973b] [Kelly 1973a] [Kenyon 1961] [Kenyon and Sutton 1961] [Khalil et al. 2023] [Kim and Park 2000] [Kim et al. 2025b] [Klothakis and Nikolos 2024] [Knight 2015] [Kordulla et al. 1991] [Krause 1992] [Kryvoruka and Ashurst 1973] [Kubota and Berg 1977] [Lacomb and Lerat 1992] [Ladyzhenskii and Lipin 1966] [Ladyzhenskij 1963] [Lapygin and Tret’yakov 1986] [Lapygin and Yakunina 2009] [Laser Power May Lift 1963] [Lawrence 1991] [Ledu and Pollak 1968] [Lee 1965] [Lee and Chen 2018] [Lees and Hromas 1961] [Lees and Kubota 1972] [Levermore and Brio 1994] [Lew 1973] [Lewis 1991] [Leyland 1991] [Leyland 1992] [Li 1985] [Li et al. 2011] [Li et al. 2015b] [Li et al. 2017a] [Li et al. 2021c] [Li et al. 2024d] [Lin and Rubin 1979] [Lin et al. 2006] [Liu and Lu 2015] [Liu et al. 2018a] [Lobanovskii 1983] [Lobb et al. 1955] [Lobbia 2017b] [Lobbia and Suzuki 2003] [Lukasiewicz 1961] [Lunev et al. 1966] [Lusty and Miele 1966] [Haw and Colom] [Magomedov 1970] [Manna and Deconinck 1992] [Markopoulos and Mease 1990] [Mason 1991] [Maurer and Henckels 1992] [Mayne 1976] [Mbagwu et al. 2023] [McCOWN et al. 1966] [McDowell and Williamson 1980] [McDowell and Williamson 1982] [McKiernan et al. 2026] [Menne and Schröder 1992] [Meyer 1969] [Miles and Macheret 2006] [Miró Miró and Pinna 2018] [Miró Miró and Pinna 2020] [Monaghan 1959] [Moreira et al. 2022a] [Morimoto and Kinefuchi 2025] [Morrison and Fiscina 1982] [Morrison et al. 1981] [Morrison et al. 1982] [Moss and Bird 1984] [Muchnaya 1979] [Mudford et al. 1980] [Mulard and Moules 1992] [Mundt 1992] [Murzinov 1966] [Musal 1962] [Müller 1992] [NACA Conference on High-Speed 1958] [Nagamatsu et al. 1960] [Nakasato et al. 2015] [Nance 2013] [Narain et al. 1991] [Nark and Lee 1963] [Nauleau] [Nelson and Nelson 1997] [Netterfield 1991] [Netterfield 1992] [Newman et al. 1992] [Nikiforov and Omelik 1976] [Nishino 1993] [Niu and Su 2023] [Non-Contact Measuring Section 2019] [Nonweiler 1959] [Nydick and Friedmann 1999] [Oertel 1991] [Ortell 1967] [Osiptsov 1979] [Otsu et al. 2009a] [Ozawa et al. 2014] [Panaras et al. 1992] [Park et al. 2024] [Peng and Wang 2026] [Perrel and Lafon 1992] [Petrova and Ryzhov 1969] [Pezzella and Viviani 2016] [Pfaff 1968] [Phillips and Cruz 1991] [Phillips and Cruz 1993] [Pironneau 1991] [Pironneau 1992] [Pittman and Dillon 1977] [Poddar and Sharma 2015] [Potter 2006] [Qiao et al. 2025] [Qin and Richards 1991] [Qin and Richards 1992] [Qin et al. 1997] [Qiu et al. 2020] [Qiu et al. 2024] [Radespiel 1992] [Radespiel et al. 1991] [Rarity 1966] [Rathakrishnan 2025] [Rault 1992] [Reed 1997] [Reed 2005] [Reed 2006] [Reggiori 1971] [Rehder 1973] [Reshotko 1987] [Reshotko 1991] [Riabov 2011] [Riedelbauch 1991] [Riedelbauch 1992b] [Riley and McNamara 2017] [Rizk et al. 1987] [Rochefort et al. 1974] [Rona and Zavalan 2022] [Rouhi Youssefi and Knight 2017] [Ruble 1964] [Rudy et al. 1992] [Ryzhov and Terent’bev 1978] [Ryzhov and Terent’ev 1974] [Ryzhov and Terent’ev 1983] [Sanders 1991] [Santos 2007] [Santos 2009] [Santos 2011] [Satofuka and Morinishi 1991] [Sawley and Wüthrich 1992] [Sayapin 1966] [Scaggs 1966] [Scalabrin and Boyd 2006] [Schmatz 1989] [Schneider 2015] [Schröder and Menne 1992] [Schröder et al. 1992] [Schwane and Hänel 1991] [Segal 2011] [Selmin and Formaggia 1991] [Sforza 2020] [Sha et al. 2026] [Shang and Yan 2020] [Shannon] [Shao et al. 2016] [Shope 1991] [Shope 2006] [Shope and Spinetti 1993] [Simons 1975] [Singh 1995] [Singh et al. 1989] [Singh et al. 2022b] [Skujins and Cesnik 2010] [Skujins and Cesnik 2011] [Smith 1973a] [Smith and Wu 1964] [Sobieczky 1991] [Spearman 2003] [Spekreijse 1991] [Spencer 1971] [Spravka and Jorris 2015] [Srinivas 1992] [Srinivasan et al. 1992] [Stetson 1990] [Stetson and Lewis 1977] [Stueber et al. 2009] [Subramanian and Dwarakanath 1969] [Supersonic/Hypersonic Euler Flowfield Prediction 1990] [Suzuki et al. 2001] [Swain 1975] [Swain et al. 1975] [Swigart 1962] [Swigart 1963] [Swigart 1964] [Tao et al. 2016] [Tao et al. 2017b] [Tao et al. 2017a] [Thomas et al. 1991] [Thompson and Hull 1970] [Tirumalesa 1968] [Tittmann and Bömmel 1968] [Tong 1991] [Tu et al. 2021] [Turri et al. 2011] [Tuttle et al. 1994] [Uffelman and Deffenbaugh 1979] [Upadhyay et al. 2019] [Van 1963] [Vankeirsbilck and Deconinck 1991] [Varwig 1963] [Vendemia 1965] [Vigdorovich 1982] [Viviand 1991] [Viviani and Pezzella 2010] [Viviani et al. 2020] [Voland et al. 2005] [Voronin 1967] [Vos and Bergman 1991] [Vos and Bergman 1992] [Walchner 1974] [Wang and Richards 1991] [Wang et al. 2024f] [Wang et al. 2026c] [Wang et al. 2026h] [Watt and Aronson 1964] [Wells and Thornley 1996] [Wen et al. 2023b] [West and Hosder 2014] [White 1993] [Whitfield and Wolny 1963] [Wilcox 1974] [Dukes 1962] [Woods and Thompson 1993] [Wray 2008] [Xie et al. 2022] [Xiong et al. 2021] [Xu et al. 2013] [Yang et al. 2025c] [Yang et al. 2026d] [Yanow 1972] [Yasuhara and Kondo 1971] [Yates and Bennett 1972] [Ye 2015] [Ye et al. 2015] [Yin et al. 2023b] [Young 1966] [Yu and Yuan 2016] [Yu et al. 2022a] [Yuan et al. 2017] [Yushchenkova et al. 1967] [Zana and Thomas 1970] [Zeitoun et al. 1991] [Zemlyanskii 1966] [Zeng et al. 2026] [Zhang 1992] [Zhang and Li 2019] [Zhang et al. 2018a] [Zhang et al. 2019c] [Zhang et al. 2020] [Zhang et al. 2022d] [Zhang et al. 2022f] [Zhang et al. 2023a] [Zhang et al. 2025g] [Zhao et al. 2018a] [Zhi et al. 2015a] [Zhi et al. 2026] [Zhong 2009] [Zhou et al. 2015] [Zhou et al. 2016] [Zhou et al. 2018] [Zhu 2022] [Zhu et al. 2016a] [Zhu et al. 2020] [Zubin et al. 1997] [Калиновский 2016, Comparison of hypersonic aircraft]

Ablation and thermal protection

The ablator and what it protects, being charring and non-charring ablators, their material response, arc-jet testing, nose tips, heat shields, and reusable and active thermal protection.

462 records. [Abdullah et al. 2020] [Achenbach 1971] [Adarkar and Hartsook 1966] [Agrawal and Chavez-Garcia 2011] [Akers et al. 1970] [Alberts et al. 2026] [Alexander 1986] [Alkandry et al. 2014] [Amar et al. 2016] [Amokrane et al. 2024] [Anderson 1969] [April] [April et al. 1970] [Arne 1965] [Aronov and Klyagin 2021a] [Aronov and Klyagin 2021b] [Babashov and Varrik 2020] [Badea et al. 2025a] [Badea et al. 2025b] [Bailet et al. 2021] [Bailet et al. 2022] [Baker 1972] [Baker and Kramer 1982] [Balhoff and Pike 1973] [Bauer and Kummer 1965] [Bauer and Kummer 1966] [Guo et al. 2020a] [Huang et al. 2019c] [Libben et al] [Berardi et al. 2026] [Bhatia and Roy 2010] [Bhesania et al. 2022] [Bhutta and Lewis 1992] [Biberman et al. 1980] [Bisek et al. 2011] [Bishop and Dicristina 1967] [Blome et al. 1975] [Blosser et al. 2015] [Boehrk 2017] [Bose 2014] [Brewer 1967] [Brewer 1970] [Brewer and Pittman 1966] [Hollis and Hollingsworth 2025] [Budnik et al. 2020] [Butler et al. 2016] [Böhrk et al. 2010] [Campbell et al. 1966] [Carman 1966] [Anderson et al] [Cas et al. 2026] [Chaboki et al. 1990] [Champman 1972] [Chang et al. 2011a] [Chang et al. 2011b] [Chang et al. 2022b] [Channon and Barry 1967] [Chaturvedi et al. 2024] [Chen 2016a] [Chen 2016b] [Chen 2022] [Chen and Chang 1971] [Chen and Gokcen 2013] [Chen and Gokcen 2015] [Chen and Gökçen 2024] [Chen and Milos 2000] [Chen and Milos 2011] [Chen and Milos 2013] [Chen et al. 1993] [Chen et al. 1995] [Chen et al. 2021a] [Cheng et al. 2011a] [Chinnaraj et al. 2023b] [Chinnaraj et al. 2023a] [Cinquegrana et al. 2019] [Clarke 1980] [Clarke 2008] [Clayton 1971] [Clever and Denny 1975] [Coheur et al. 2017] [Combs et al. 2014] [Condren et al. 2024] [Congdon et al. 2002] [Congdon et al. 2003] [Coria and Parisse 2026] [Coskun and Sert 2024] [Coskun et al. 2019] [Couch 1973] [Covington et al. 2004] [Crose and McKinley 1972] [Cross 1967] [Curry 1965a] [Curry 1965b] [Curry et al. 1966] [da Costa and Sachs 2005] [Dang et al. 2022] [Daryabeigi et al. 2006] [Davuluri et al. 2021] [Davuluri et al. 2023] [Determination of the Density 1968] [Diaconis et al. 1961] [Dickey and Haacker 1963] [Dicristina and Richards 1977] [Dirling 1973] [Dow and Tompkins 1966] [Drawin 1993] [Duston et al. 2004] [Atomics International Div., Canoga Park, Calif. (USA) and Elliott 1969] [Ericsson 1967] [Erzincanli et al. 2010] [Evaluation of Resin-Ceramic Heat-Shield 1965] [Ewing and Pincock 2016] [Experimental Evaluation of Thermostructural 1979] [Fahy et al. 2019] [Farmer 1970] [Feild 1964] [Feldman et al. 2012] [Feng et al. 2025b] [Fleming 1965] [Fleurotte et al. 2022] [Friedman 1961] [Friedman et al. 1967] [Fu et al. 2020b] [Fu et al. 2020a] [Gao 2014] [Gao and Zhu 2025] [Gao et al. 2020b] [Gao et al. 2021] [Gao et al. 2026b] [Gerasimov 2025] [Gluck et al. 1964] [Gluck et al. 1968] [Gomez et al. 1970] [Gramola 2020] [Graves and Witte 1968] [Greenwald 1972] [Grigat et al. 2020] [Grinberg et al. 1968] [Groener et al. 1980] [Gui et al. 1999] [Gulli and Maddalena 2019] [Guo and Huang 2018] [Guo et al. 2023a] [Hains 1970] [Hakkaki-Fard and Kowsary 2007] [Hall and Nowlan 1978] [Hamaker 1960] [Han et al. 2023] [Hannah and Muessig 1970] [Harpale et al. 2018] [Hasan 2022] [Havstad and Ferencz 2002] [He et al. 2022b] [He et al. 2023] [Heat Shield 1971] [Heat Shield Delivery 2001] [Heat-Shield Ablation and Sublimation 1965] [Helber et al. 2014] [Helber et al. 2016] [Heller 1967] [Hollis 2011] [Hou et al. 2022] [Howell 1974] [Huang and Dai 2023] [Huang and Fan 2022] [Huang and Yao 2018] [Huang and Yao 2019b] [Huang and Yao 2019a] [Huang and Yao 2020] [Huang et al. 2019b] [Huang et al. 2019a] [Huang et al. 2023b] [Huang et al. 2025b] [Huang et al. 2026a] [Hull et al. 1981] [Hunter et al. 1985] [Hurwicz et al. 1964] [Hypersonic Materials for Thermal 2023] [Islam and Dutta 2025] [Jia et al. 2021] [Jin et al. 2024] [Johnson and Boisseau 1961] [Johnson et al. 2001] [Johnson et al. 2006] [Johnson et al. 2007] [Jones and Shukla 1999] [Jones et al. 1965] [Juneau et al. 1970] [Калашников 2021] [Kalugin and Slobodyanyuk 2020] [Kannan and Katte 2018] [Karim et al. 2026] [Kato et al. 2016] [Kennedy et al. 2024] [Kianifar and Mohammadiun 2010] [Kim 2017] [Kim et al. 2024] [Knight and Quinn 1971] [Kobayashi and Saperstein 1981] [Koenig et al. 2019] [Komurasaki and Candler 2000] [Koo and Mensah 2017] [Koo et al. 2018] [Kowal 2010] [Krusos 1968] [Kryvoruka 1976] [Kubota and Uchida 1999] [Kubota et al. 2017] [Kubota et al. 2018] [Kubota et al. 2020] [kumar et al 2017] [Kundu 2013] [Kuznetsov 1996] [Laganelli et al. 1974] [Lai and Leu 2023a] [Lai and Leu 2023b] [Langston et al. 2018] [Langston et al. 2021] [Lazic and Hrabar 1992] [Le and Goo 2025] [Le Bel and Russell 1965] [Le Bel and Russell 1966] [Le et al. 2019] [Le Maout et al. 2025] [Lee and Kim 2021] [Lee and Kim 2022] [Lei et al. 2026] [Li et al. 2015e] [Li et al. 2015c] [Li et al. 2020a] [Li et al. 2020b] [Li et al. 2021d] [Li et al. 2025a] [Li et al. 2025d] [Liang et al. 2023a] [Libby and Hendricks 1970a] [Libby and Hendricks 1970b] [Lin et al. 1984] [Lincoln 1981] [Liu et al. 2002] [Liu et al. 2018b] [Liu et al. 2019b] [Liu et al. 2021b] [Long et al. 2025] [Low Density Ablator Compositions 1978] [Lundell and Wakefield 1969] [Luo et al. 2025] [Lv et al. 2026] [Löhle et al. 2017] [Machado 2018] [Maddu et al. 2023] [Mehta et al] [Mehta et al] [Mansour et al. 2011] [Mansour et al. 2024] [Marquis et al. 2016] [Martin 2013] [Martin and Boyd 2010] [Martin and Panesi 2022] [Martin Co Denver Co 1965] [Martinez et al. 2011] [Maslen and Ostrach 1957] [Mastanaiah 1976] [Mazzaracchio 2018] [McAfee et al. 2026] [Mei et al. 2020] [Meurisse et al. 2018] [Miller et al. 2011] [Miller et al. 2023] [Mills 1971] [Mills et al. 1971] [Milos and Chen 2009] [Milos and Gasch 2015] [Milos et al. 2015] [Mishra et al. 2021] [Mitchel 1971] [Mizuno et al. 2007] [Mohammadiun and Mohammadiun 2012] [Moody et al. 1982] [Morrison 1975] [Moyer and Wool 1970] [Mullen] [Mullenix and Povitsky 2016] [Multi-Dimensional Thermal Properties of] [Muppidi et al. 2014] [Nagata et al. 2020] [Natali et al. 2016] [Nathan and Bindu 2005] [Nikolaev et al. 2006] [Nix 1959] [Olson et al] [Nenarokomov et al. 2016] [Nichols and Sichel 1967] [Iyinomen 2022] [Ogawa et al. 2019] [Olsen and Chapman 1972] [Ono et al. 2024] [Oruganti et al. 2026] [Otsu et al. 1999] [Otsu et al. 2005] [Otsu et al. 2010] [Otsu et al. 2012] [Oz and Kara 2024] [Paciorri et al. 2026] [Paglia et al. 2019] [Panesi and Martin 2020] [Park 1983] [Park and Shin 2024] [Park et al. 1998] [Parmenter et al. 2001] [Pastore et al. 2021] [Paydayesh and Kokabi 2015] [Penide-Fernandez and Sansoz 2019] [Pfahl and Dropkin 1966] [Pfahl and Mitchel 1970] [Pitts and Kourtides 1989] [Platus 1983] [Poovathingal and Chen 2022] [Pope and Vojvodich 1964] [Pope et al. 2021] [Potts 1984] [Potts 1990] [Prasad 1978] [Prasad and Agrawal 1974] [Pratibha Raghunandan et al] [Raghunandan et al. 2021] [Price et al. 2022] [Price et al. 2025] [Prussing and Krier 1978] [Puiroux et al. 2002] [Putz and Bartlett 1972] [Qian et al. 2015] [Qin et al. 2026] [Quinn et al. 2024] [Rabinskiy and Tushavina 2019] [Rahimi 2012] [Raper 1981] [Re-radiating heat shield assembly 1989] [Reda et al. 2004] [Reentry Experiment Will Test 1963] [Reentry Vehicle Nosetip Material 1977] [Reinikka and Sartell 1965] [Reinikka and Wells 1963] [Ren 2025] [Ren et al. 2021] [Riccio et al. 2017] [Riley and Landahl 1968] [Rindal et al. 1967] [Rivier et al. 2019] [Rong 2017] [Rostkowski and Panesi 2022] [Rostkowski et al. 2019] [Rostkowski et al. 2022] [Ruperti et al. 2004] [Rusert et al. 1978] [Sabarilal and Kumar 2018] [Sai Naga Bharghava et al. 2024] [Sakai et al. 2017] [Salazar and Amar 2021] [Salazar et al. 2016a, Development and Verification of E] [Salazar et al. 2016b, Development, Verification and Val] [Salvi et al. 2026] [Santos et al. 2008] [Satheesh Chandran et al. 2021] [Sawant et al. 2019] [Schmitt 1972] [Schneider et al. 1973] [Schrooyen et al. 2017] [Sessim et al. 2024] [Shang and Surzhikov 2010] [Shao et al. 2026] [Sharma et al. 2019] [Shen and Liu 2018] [Shen and Liu 2020] [Sherman 1978] [Shi et al. 2023b] [Shilav and Khosid 2020] [Shu et al. 2024] [Simon et al. 2014] [Skolnik and Putnam 2022] [Smith et al. 2015] [Sohn et al. 2011] [Son and Shin 2019] [Sperow 1965] [Spokes et al. 1971] [Stroud and Swann 1965] [Sugavanam and Sastry 1975] [Sullivan and Kobayashi 1987] [Sun and Zhu 2019] [Suzuki et al. 2007] [Suzuki et al. 2010a] [Suzuki et al. 2010b] [Suzuki et al. 2012] [Szasz et al. 2015] [Tahmasbi and Noori 2018] [Tahsini and Mousavi 2014] [Tatar 2019] [Tatar 2021] [Thareja and Lewis 1982] [Thermal Protection 1970] [Thermal Protection 2015] [Titov and Levin 2011] [Titov et al. 2011] [Tolstykh 1969] [Tompkins and Kabana 1973] [Triebes et al. 1978] [Tsukamoto et al. 2022] [Tushavina 2025] [Ungar 1967] [Kam 2022] [Vander Kam and Gage 2021] [Vaulin et al. 2023] [Venkatapathy et al. 2016] [Verbinski et al. 1976] [Viviani and Pezzella 2007b] [Vojvodich 1973] [Vojvodich and Pope 1963] [Wakefield and Lundell 1971] [Walker and Zeigler 1968] [Wang et al. 2019a] [Wang et al. 2022b] [Wang et al. 2023f] [Wang et al. 2024d] [Wang et al. 2025a] [Welsh and Chung 1963] [Wen et al. 2023a] [Weng and Martin 2013] [Weng and Martin 2014a] [Weng and Martin 2014b] [Weng and Martin 2015] [Weng et al. 2012] [Weng et al. 2015] [White et al. 2019] [Whitnah 1967] [Wilder and Reda 2004] [Willard 2022] [Williamson 1977] [Winter et al. 2014] [Winters 1964] [Wu 2019] [Wu et al. 2025] [Wuxing et al. 2015a] [Xiao et al. 1991] [Xiao et al. 2022] [Xin et al. 2026] [Xu et al. 2023b] [Yamada and Inatani 2002] [Yamada et al. 2002] [Yang et al. 2024] [Yang et al. 2026b] [Yoko et al. 2018] [Yoko et al. 2019] [Yu et al. 2025a] [Yuan et al. 2024] [Zhang et al. 2023c] [Zhang et al. 2024d] [Zheng et al. 2025b] [Zhu et al. 2016b] [Zibitsker and Martin 2026] [Zibitsker et al. 2022] [Zibitsker et al. 2023] [Hoter et al]

Planetary and superorbital entry, descent and landing

The same relations on other planets, and Earth entry faster than orbital speed, including Mars, Venus, Titan and the outer planets, aerocapture, powered descent, sample return capsules and lunar return. 162 of the 442 titles name Mars, which is where the analytic subsection above places the modern work.

442 records. [Abilleira 2013] [Adler 1998] [Afzal et al. 2009] [Ai et al. 2016] [Albert et al. 2022] [Alejandro Pensado et al, Uranus Probe Entry and Descent Tr] [Ali and Braun 2018] [Alkandry et al. 2012] [Allen et al. 1963] [Amato 2021] [Andrade and Deacon 1969] [Armenise et al. 2016] [Atlas-Centaur AC-12 Flight Performance 1968] [Atlas-Centaur Flight Performance 1968] [Babineaux 1966] [Baird et al. 2004] [Ball et al. 2022] [Bannova 2006] [Bansal et al. 2012] [Beck et al. 2018] [Beck et al. 2021] [Beuf et al. 1966] [Bhaskaran and Stern 2024] [Bigham 1970] [Birch et al. 2022a] [Birch et al. 2022b] [Bishop et al. 2025] [Blette and Braun 2016] [Braun et al] [Broome and Johnson 2007] [Bryson and Denham 1962] [Bryson et al. 2018] [Burkhart et al. 2005] [Burkhart et al. 2006] [Burkhart et al. 2013] [Byrne 2020] [Cabrera and Spencer 2024] [Cabrera and West 2026] [Cabrera et al. 2022] [Calhoun and Queen 2002] [Calise and Bae 1990] [Casani 1968] [Chakrabarti et al. 2024] [Chang et al. 2026b] [Chapman 1959] [Chapman 1960] [Chapman 1965] [Cheng-Chih Chu] [Chevalier et al. 2026] [Chin et al. 1964] [Ching et al. 2022] [Cho et al. 2024] [Choi and Kim 2024] [Christensen and Ko 1969] [Christian et al. 2007] [Dickmanns 1986] [Girija 2023] [Gomez-Delrio and Dutta n.d.] [Hull et al. 1985] [Karlgaard et al] [Karlgaard et al. 2020] [Clark et al. 2021b] [Coate and Lessing 1965] [Coelho and Lino da Silva 2023] [Congdon 1973] [Congdon 1974] [Congdon and Curry 2001] [Cornette and Sullivan 1971] [Crowe and Panda 2026] [Cruden 2012] [Cruz et al. 2005] [Dai et al. 2017] [Engel et al] [Engel et al] [De Zaiacomo et al. 2009] [Dees 2015] [Deng et al. 2022] [Desai and Lyons 2008] [Desai et al. 1999] [Desai et al. 2006] [Desai et al. 2008] [Desautel 1984] [Dieriam 1990] [Djamshidpour] [Doihara 2001] [Doihara and Nishida 2001] [Doihara and Nishida 2004] [Duan et al. 2023] [Dutta 2025] [Dutta and Braun 2014] [Dutta et al. 2012a] [Dutta et al. 2012b] [Dutta et al. 2023b] [Dutta et al. 2023a] [Dutta et al. 2024] [Dutta et al. 2025] [Edquist 1974] [Edquist et al. 2023] [Foudriat and Wingrove 1961] [Engel and Putnam 2025] [Engel et al. 2022] [Engel et al. 2025] [Esch] [Esposito et al. 2020] [Fawley and Putnam 2021] [Ferri et al. 2017] [Flight Performance of Atlas-Agena 1969, Flight performance of Atlas-Agena] [Fonseca et al. 2019] [French et al. 1971] [Friz and Samareh 2020] [Fujino and Ishikawa 2013] [Fujita et al. 1997] [Fujita et al. 2011] [Fukuda et al. 2017] [Furfaro and Wibben 2012] [Gao et al. 2015a] [Gao et al. 2024a] [Gao et al. 2025] [Gao et al. 2026a] [Gao et al. 2026d] [Garcia et al. 2010] [Gebbie et al. 2004] [Genge 2016a] [Genge 2016b] [Genge 2017] [Genge et al. 2020] [Girija et al. 2021] [Girija et al. 2023] [Gnoffo et al. 2016] [Golovachov and Lunkin 1979] [Gong et al. 2020] [Grasso et al. 2010] [Green and Nicolet 1978] [Grover et al. 2008] [Guan et al. 2025a] [Gulick and Edquist 1998] [Gupta et al. 1992] [Gülhan et al. 2019] [Hamilton et al. 1991] [Hao et al. 2018a] [Harms et al. 2010] [Harrison and Slocumb 1969] [Havill et al. 1966] [Hilary L. Justh, Status of Venus Global Reference] [Hoelscher 2007] [Holstein-Rathlou et al. 2016] [Horvath et al. 2002] [Hu et al. 2016b] [Hu et al. 2022b] [Huang 2019] [Huang and Li 2016] [Huang et al. 2021c] [Huang et al. 2023c] [Ilgen et al. 1991] [Inatani 2018] [Interplanetary Guidance Systems Requirements 1966] [Ito and Sakai 2023] [Jenniskens et al. 2012] [Ji 2020] [Jiang and Li 2019] [Jiang et al. 2018a] [Jiang et al. 2019a] [Jianwei et al. 2019] [Pei et al. 2025a] [Johannesen et al. 1985] [Johnson and Arnold 2001] [Johnson et al. 2020] [Johnston and Brandis 2022] [Julian Allen 1967] [Jupiter Probe Heat-Shield Configuration 1979] [Kangas et al. 2021] [Karlgaard et al. 2021] [Karlgaard et al. 2023] [Katsurayama and Abe 2010] [Katsurayama and Abe 2012] [Katsurayama et al. 2011] [Keys et al. 2006] [Mease and Vinh 1985] [Ray et al] [Kc et al. 2025] [Kennet and Taylor 1966] [Khan and Hoffman 2009a] [Khan and Hoffman 2009b] [Kihara et al. 2013] [Kipp et al. 2007] [Kitting et al. 2012] [Kluever 2008a] [Koelsch 2011] [Korchagin 2019] [Korzun et al. 2020] [Kraetzig et al. 2014] [Kumar and Bansal 2023] [Kuwata and Balaram 2011] [Kwon et al. 2021b] [Kyriss and Rie 1967] [Lakshminarayana et al. 2026] [Lasher and Wilson 1968] [Laure and Auweter-Kurtz 1994] [Lee and Lee 2023] [Lee et al. 2024] [Lee et al. 2025] [Lee et al. 2026b] [Lefevre] [Lefevre et al. 2022] [Lefland and Stehura 2022] [Leibowitz and Kuo 1975] [Леонов and Grishko 2019] [Lessing et al. 1964] [Levine 1966] [Li et al. 2015a] [Li et al. 2021e] [Liu et al. 2008] [Liu et al. 2021a] [Liu et al. 2024d] [Liu et al. 2026c] [Lockwood et al. 2005] [Longitudinal Range Control 1962] [Lorenz and Putnam 2019] [Lu 2018] [Lu 2019] [Lu 2020] [Lu and Callan 2023] [Lu and Davami 2024] [Lu et al. 2024] [Luidens 1961] [Lundell 1982] [Lyons and Desai 2005] [Moul et al. 1964] [Ma et al. 2025b] [Maddock et al. 2021b] [Maddock et al. 2021a] [Maigler et al. 2024] [Mall et al. 2024] [Maringer and Manning 1960] [Martin and Boyd 2015] [Martin et al. 2015] [Marvin and Pope 1966] [Marvin and Pope 1967] [Marwaha et al. 2009] [Mathavaraj and Padhi 2017] [Mathavaraj et al. 2016] [Mazzaracchio 2015] [McGilvray et al. 2024] [McGruer] [Methods for Predicting off-Stagnation-Point 1980] [Metzger 2024b] [Metzger 2024a] [Milos 1996] [Milos et al. 1995] [Mischna 2024] [Mischna 2025] [Mischna et al. 2022] [Mitchel 1967] [Mitcheltree and Gnoffo 1990] [Miyayama et al. 2025] [Modenini et al. 2019] [Molina et al. 2005] [Mooij 2024] [Moul et al. 1961] [Mu et al. 2023] [Murakami and Fujiwara 2001] [Murphy et al. 1981] [Murray and Tartabini 2001] [Mustafa and Shofiqul 2016] [Nakazawa et al. 2022] [Nelson 1980] [Nelson 1983] [Nelson and Mezines 1978] [Nicolet 1975] [Nishikawa et al. 2026] [Niu et al. 2026] [NlEMANN 1968] [Nurre and Taheri 2026] [Ogino et al. 2015] [Olstad 1974] [Onishi and Azimov 2020] [Otsu et al. 1998] [Otsu et al. 2006a] [Otsu et al. 2008] [Otsu et al. 2009b] [Otsu et al. 2014] [Ozawa et al. 2011] [Page and Woodward 1972] [Palaszewski 2009] [Palazzo 2025] [Pardha Sai Chadalavada et al] [Park 2005] [Park 2008] [Pastor et al. 2000] [Peng et al. 2018] [Placco et al. 2023] [Polsgrove and Dwyer-Cianciolo 2016] [Prakash and Zhong 2008] [Prince et al. 2008] [Qiao and Zhang 2026] [Quadrelli et al. 2011] [Rairden and Jenniskens 2010] [Rao et al. 2022] [Rataczak et al. 2025a] [Ray 2021] [Reynier 2021] [Reynolds and Mesbahi 2020] [Ridderhof and Tsiotras 2021] [Rimer and Sperling 1966] [Robbiani et al. 2025] [Rodi 2021] [Wercinski and Langhoff 1997] [Wingrove and Coate 1962] [Rouzaud et al] [Rui Teng et al. 2016] [Sagliano 2018] [Sagliano 2019] [Samareh 2020] [Samareh and Komar 2011] [Sandoval et al. 2024] [Santini De Leon et al. 2020] [Santini De Leon et al. 2022] [Saranathan 2025] [Sato et al. 2012] [Scala 1961a, Heating problems of entry into pl] [Scamfer et al. 2026] [Scandelli et al. 2023] [Schoenenberger et al. 2005] [Schroenenberger et al. 2009] [Seedhouse 2009] [Seiff and Kirk 1976] [Sharma et al. 2024] [Shevelev 2018] [Shi et al. 1971] [Shoemaker et al. 2012] [Silber 2026] [Silber and Bowman 2025] [Silber and Scamfer 2026] [Skalecki et al. 1984] [Smith and Yound 1967] [Smith et al. 2022] [Son et al. 2025] [Sonandres et al. 2025] [Sonandres et al. 2026] [Song et al. 2021] [Sostaric et al. 2017] [Southworth 1962] [Spiegel et al. 1969] [Stadter and Weiss 1976] [Stafford and Von Struve 1969] [Steiner 1964] [Stiltner et al. 2017, Cold Gas Reaction Control System] [Strahan and Sostaric 2016] [Strauss 1966] [Striepe et al. 2002] [Su et al. 2026a] [Su et al. 2026b] [Subrahmanyam and Rasky 2017] [Sun and Rao 2022] [Sun et al. 2015] [Surzhikov 2016] [Surzhikov 2024] [Surzhikov and Yatsukhno 2022] [Sutton 1976] [Suzuki et al. 1997] [Suzuki et al. 2011] [Suzuki et al. 2014] [Tang et al. 2025] [Tang et al. 2026] [Tauber 1969] [Tauber and Sutton 1991] [Tauber and Yang 1988] [Tauber et al. 1988] [Tigges and Ling 1989] [Tiwari and Subramanian 1983] [Tobak and Peterson 1964] [Trent et al. 2021] [Tsurumoto et al. 2018] [Urraza Atue and Bruce 2025] [V Jha et al] [Venkatapathy and Hash 2026] [Venkatapathy et al. 2021] [Vigil and Pérez 2026] [Vinh et al. 1977] [Vinh et al. 1980] [Vinh et al. 1984] [Vinh et al. 2000] [Vivek Jacob 2025] [Vorreiter 1972] [Wan 2023] [Wan et al. 2022] [Wang 1963b] [Wang and Chen 2026] [Wang and Grant 2017] [Wang and Yao 2017] [Wang et al. 2024c] [Warga and Hailey 1964] [Way 2011] [Way 2013] [Way et al. 2006] [Way et al. 2007] [Way et al. 2022] [Wei et al. 2021] [Weng et al. 2021] [Werner and Braun 2019] [West et al. 2016] [White et al. 2013] [Wibben and Furfaro 2016] [Williams et al. 2012] [Williams et al. 2025b] [Wilson and Riccardi 2021] [Wingrove 1965a] [Wingrove 1965b] [Wingrove 1966] [Winter et al. 2012] [Winter et al. 2019] [Worth 1966] [Xia et al. 2015] [Xiao et al. 2025] [Xu et al. 2018] [Xu et al. 2022b] [Yamada 2022] [Yamada et al. 2010] [Yamada et al. 2011b] [Yamagishi et al. 2024] [Yang and Liu 2020] [Yang et al. 1991] [Ye et al. 2022b] [Yeh] [Yoshikawa and Wick 1961] [You et al. 2021] [You et al. 2022] [Zander et al. 2024] [Zewge and Bang 2023] [Zhang 2017] [Zhang et al. 2017a] [Zhang et al. 2018b] [Zhang et al. 2021d] [Zhang et al. 2025c] [Zheng and Cui 2015a] [Zheng and Cui 2015b] [Zheng et al. 2017] [Zhong et al. 2019] [Zuppardi 2021] [Zuppardi and Mongelluzzo 2023a] [Zuppardi and Mongelluzzo 2024] [Дугин 2017, Flight module and Venus entry veh]

Entry guidance, trajectory optimisation and hypersonic flight control

Steering an entry vehicle and computing the trajectory it should fly, including predictor-corrector guidance, numerical trajectory optimisation and the attitude control of hypersonic vehicles. 277 of the 412 records date from 2010 or later. 85 titles name a convex, pseudospectral, predictor-corrector, evolutionary, swarm, neural or learning method, which is what the free computation described above looks like in a title.

412 records. [Adams and Stoll 1969] [Adimurthy 1976] [Adimurthy 1987] [Alexander 1978] [Batcha et al] [An et al. 2019] [Anhtuan D. Ngo] [Archer and Sworder 1979] [Automatic Re-Entry Guidance 1962] [Bae et al. 2024] [Balakrishnan et al. 1997] [Baltrum] [Bao et al. 2023] [Bao et al. 2024] [Bibeau and Rubinstein 2000] [Bin Jiang and Qi 2017] [Boutelle et al] [Brinda et al. 2006] [Brusch 1977] [Bryson 1969] [Bu and Lei 2018] [Bu et al. 2015] [Buchanan and Crosby 1983] [Burchett 2003] [Byczkowski and Rao 2026] [Byrne et al. 1996] [Cai and Huang 2022] [Cai et al. 2013] [Cai et al. 2015] [Carter 1965] [Carter et al. 2005] [Cavallo et al. 1996b] [Chai et al. 2020b] [Chander and Krishna 2013] [Chang et al. 2018a] [Chang et al. 2022a] [Changsheng et al. 2006] [Chao Song et al. 2011] [Chen and He 2025] [Chen and Liu 2013] [Chen and Tan 2019] [Chen and Tseng 2011] [Chen et al. 2018b] [Chen et al. 2020e] [Chen et al. 2021b] [Chen et al. 2026a] [Cheng et al. 2016] [Cheng et al. 2019a] [Cheng et al. 2023b] [Chi et al. 2024] [Childs 1970b] [Chimonas 1986] [Chirayath and Bindu 2014] [Chu et al. 2026] [Chudej and Bulirsch 1993] [Cole and Aroesty 1965] [Cui et al. 2022] [Cui et al. 2024] [D’Souza 2015] [D’souza et al. 2014] [da Costa and Sachs 2003b] [Dai et al. 2025] [Dan et al. 2022] [Daxini et al. 2024] [De Does 1969] [DeMarinis and Huttenlocher 1964] [Deng et al. 2017b] [Deng et al. 2025] [Dewell and Speyer 1993] [Deyst 1968] [Divya and Jayashree 2023] [Dou et al. 2018] [Doupe 2015] [Du et al. 2015] [Du et al. 2024] [Duan et al. 2011] [Dukeman 2002] [Dulikravich and Sheffer 1992] [Dulov 1976] [Efremov et al. 2023] [Elliott and Rau 1968] [Elsey and Carlson 1968] [Ely et al. 2001] [Ernst et al. 2024] [Erzberger and Lee 1980] [Eyi et al. 2019] [Filatyev 2000] [Fiorentini and Serrani 2012] [Fogarty 1967] [Franze and Barz 2025] [Fu et al. 2019] [Fuhry 1999] [Gaiduchenko and Gritsyk 2019] [Gao and Yao 2018] [Gao et al. 1997] [Gao et al. 2018b] [Gao et al. 2019] [Gao et al. 2022] [Gao et al. 2023a] [Gao et al. 2024b] [Gao et al. 2024c] [Gaohua et al. 2014] [Gefert and Wright 2014] [Geng et al. 2013] [Geng et al. 2014] [Girerd and Barton 2000] [Gohatre and Singla 2019] [Good 1975] [Gracey et al. 1981] [Grasso and Passalacqua 1991] [Grimm and Rotärmel] [Gui et al. 2020] [Guidance and Navigation 1968] [Guo and Liu 2024] [Guo and Lu 2021] [Guo et al. 2017b] [Guo et al. 2018b] [Guo et al. 2019a] [Guo et al. 2020b] [Hankey 1963] [Hanson and Jones 2004] [Harpold 1980] [Harpold and Gavert 1982] [Hassan et al. 1991a] [He et al. 2019] [Heller et al. 2000] [Hoge and Vaughn 2001] [Hongbo and Yongyuan 2016] [Hooks and Hankey 1965] [Horing et al. 2025] [Horneman et al. 2010] [Hu et al. 2015] [Hu et al. 2016a] [Hu et al. 2021a] [Hu et al. 2022d] [Hu et al. 2022a] [Hu et al. 2022e] [Hu et al. 2024a] [Hu et al. 2024b] [Huang et al. 2018a] [Huang et al. 2025a] [Huang et al. 2026b] [Ishikawa and Yamazaki 2021] [Ishizuka et al. 1998] [Islam 2024] [Jaensch and Markl 1991] [Ji et al. 2019b] [Ji et al. 2025a] [Ji et al. 2025b] [Jiang et al. 2018b] [Jiang et al. 2019b] [Johnson 2019] [Jouhaud et al. 2007] [Junchun et al. 2006] [Jurovics 1961] [Kamm and Johnson 1973] [Keshmiri et al. 2006] [Kidner 1993] [Kieszek et al. 2024] [Kim and Mavris 2023] [Kim et al. 2026d] [Klafin and Barnhart 1973] [Klimin and Yaroshevski 1970] [Komorowski and Zalewski 2026] [Kong and Zhang 2024] [Kumar et al. 2018b] [Langston 1967] [Lee] [Leite et al. 2022] [Leonardi 2023] [Leondes and Niemann 1966] [Li et al. 2016b] [Li et al. 2016c] [Li et al. 2018a] [Li et al. 2021b] [Li et al. 2022a] [Li et al. 2023b] [Li et al. 2024a] [Lian et al. 2004] [Liang and Zhu 2021] [Liang et al. 2017b] [Liang et al. 2020] [Liao and Li 2013] [Lim et al. 2007] [Lin-lin et al. 2015] [Liu 2020] [Liu et al. 2005] [Liu et al. 2016] [Liu et al. 2020a] [Liu et al. 2024b] [Liu et al. 2026e] [Liwei Zheng and Wuxing Jing] [Lobbia 2017a] [Love and Neustadt 1963] [Lu 1991] [Lu 1999b] [Lu 2007] [Lu 2014] [Lu and Xue 2009] [Lu et al. 2000] [Lu et al. 2017b] [Luo et al. 2023] [Lv et al. 2023] [Lysenko and Tachinina 2019] [Ma and Cai 2018] [Ma et al. 2018] [Ma et al. 2023] [Ma et al. 2024a] [Ma et al. 2025a] [Mackle] [Mackle et al. 2024] [Mallick et al. 2024] [Mallick et al. 2026] [Marchetti and Minisci 2021] [Marchetti and Minisci 2023] [Marinescu 1973] [Mease et al. 2000] [Meng et al. 2016] [Meng et al. 2019] [Menon et al. 1992] [Merlinge et al. 2019] [Miele 1962] [Miele and Saaris 1963] [Miller and Barton 2008] [Miyazawa et al. 1993] [Miyazawa et al. 1999] [Moch 1966] [Mooij 2001] [Mooij 2004b] [Mooij 2005] [Mooij 2014] [Mooij 2017] [Mooij 2018b] [Mooij 2018a] [Mooij and Barkana 2005] [Mooij and Hanninen 2009] [Mooij et al. 2007] [Mor and Livne 2007] [Mu and Wang 2012] [Munipalli et al. 2005] [Nair et al. 2022] [Naresh Kumar et al. 2017] [Nassif et al. 2026] [Ni et al. 2019] [Niu et al. 2018] [Okuno and Watanabe 1992] [Omar and Bevilacqua 2019] [Oñate et al. 1991] [Page and Rogers 1977] [Peng et al. 2019a] [Peng et al. 2019b] [Peng et al. 2022] [Pengxin et al. 2015] [Piet-Lahanier and Serre 2017] [Porcelli 1968] [Potsawat et al. 2019] [Pratap and Pratap 2025] [Pu et al. 2016] [Qu et al. 2023b] [Rao et al. 2023] [Rataczak et al. 2025b] [Richmond 2022] [Ridderhof et al. 2022] [Roenneke 2001] [Roenneke and Cornwell 1992] [Roenneke and Well 1996] [Rosenbaum 1971] [Sachs and Schoder 1991] [Sachs and Schoder 1992] [Sagliano and Mooij 2021] [Shan et al. 2015] [Shao and Wang 2015] [Shao and Wang 2016] [Shao et al. 2015] [Shen et al. 2016] [Shen et al. 2018] [Shen et al. 2023] [ShengZe Chen et al. 2014] [Shenming et al. 2017] [Shi et al. 2014] [Shi et al. 2025] [Shou et al. 2021] [Shrivastava and Reddy 1976] [Shu-Chun Zhang et al] [Skaar and Kraige 1982] [Son et al. 2022] [Song and Choi 2020] [Song et al. 2019] [South 1974] [Starkey et al. 2006] [Stengel 1971] [Stoffel et al. 2024] [Su et al. 2023] [Su et al. 2025] [Sun and Duan 2012] [Sun and Zhang 2011] [Sworder and Archer 1977] [Sworder and Wells 1976] [Talole et al. 2007] [Tang et al. 2022] [Tang et al. 2023] [Tannas 1966b] [Tao Xu et al. 2011] [Tarpley and Lewis 1993] [Taylor 1970] [Teng et al. 2016] [Tian and Shen 2022] [Tracy et al. 2023] [Trent et al. 2007] [Tsuchiya et al. 1982] [Vemuri 1982] [Verderese 1971] [Verma et al. 2007] [Villanueva 2022] [Vinh and Chern 1979] [Vinh et al. 1972] [Wagner 1966] [Wan et al. 2023] [Wang and Grant 2018] [Wang and Ren 2011] [Wang and Zhang 2018] [Wang et al. 2013a] [Wang et al. 2014a] [Wang et al. 2015d] [Wang et al. 2015b] [Wang et al. 2017e] [Wang et al. 2017d] [Wang et al. 2017b] [Wang et al. 2017c] [Wang et al. 2018b] [Wang et al. 2019c] [Wang et al. 2019d] [Wang et al. 2020a] [Wang et al. 2022g] [Wang et al. 2022e] [Wang et al. 2022c] [Wang et al. 2023b] [Wang et al. 2024a] [Wang et al. 2025d] [Wang et al. 2026e] [Wang et al. 2026i] [Weiner and Homsley 1977] [Weiwei et al. 2022] [Wenming et al. 2015] [Wingrove 1963] [Wingrove and Coate 1961] [Wu 2018] [Wu and Guo 2018] [Wu et al. 2015] [Wu et al. 2017] [Xia et al. 2020] [Xiao Jiaping and Shen Zuojun 2016] [Xie and Wang 2012] [Xie et al. 2024c] [Xingling and Honglun 2014] [Xu 2015] [Xu and Zhang 2015] [Xu et al. 2011a] [Xu et al. 2015] [Xu et al. 2025a] [Xue and Haibin 2017] [Yafei et al. 2015] [Yan et al. 2020] [Yan et al. 2026] [Yang and Li 2023] [Yang and Wang 2012] [Yang et al. 2026c] [Yao and Jia 2023] [Yao and Xia 2023] [Yao and Xia 2024] [Yao et al. 2024] [Ye and Jiang 2020] [Ye et al. 2017a] [Ye et al. 2017b] [Yeo and Sng 1980] [Yin et al. 2023a] [Yongfeng Xie and Shuo Tang 2010] [Yu et al. 2023a] [Zeng et al. 2018] [Zeng et al. 2021] [Zerar et al] [Zhai et al. 2016] [Zhai et al. 2019] [Zhang 2015] [Zhang and Chen 2011a] [Zhang and Chen 2011b] [Zhang and Ding 2023] [Zhang and Duan 2016] [Zhang and Han 2024] [Zhang and Tang 2008] [Zhang and Wang 2022] [Zhang et al. 2012] [Zhang et al. 2016] [Zhang et al. 2017d] [Zhang et al. 2021b] [Zhang et al. 2022e] [Zhang et al. 2022a] [Zhang et al. 2023b] [Zhang et al. 2025d] [Zhang et al. 2026c] [Zhao and Liang 2019] [Zhao et al. 2021] [Zhao et al. 2022c] [Zheng 2021] [Zheng and Selezneva 2022] [Zhi and Yang 2015] [Zhongjie Meng et al. 2008] [Zhou 2023] [Zhou and Wang 1987] [Zhou et al. 2020a] [Zhou et al. 2025a] [Zhu and Shen 2015]

Lifting bodies and the SV-5 family

The shape PRIME flew and the vehicles that share it, from the M2, HL-10 and X-24 lifting bodies and their flight tests to the HL-20, the X-38, Dream Chaser and the Intermediate eXperimental Vehicle, with the hypersonic aerodynamics of lifting-body shapes.

264 records. [Adams 1975] [Adams and Martindale 1973] [Adams and Martindale 1974] [Adams et al. 1973] [Aerothermodynamic Design 1993] [Allen 2024] [Almosnino 2016] [Anderson et al. 1963] [Anderson et al. 1967] [Angelini and Denaro 2016] [Aradag et al. 2007] [Arrington and Woods 1972] [Aso et al. 2004] [Balepin and Hendrick 1998] [Banks and Fisher 2006] [Barret 1998] [Barret 1999] [Baumgartner and Elvin 1995] [Benson 2006] [Billig et al. 2016] [Biswell and Puig-Suari 1996] [Bogar et al. 1996] [Bohn 1967] [Bonasia et al. 1967] [Boylan and Potter 1967] [Brumley and Perich 2022] [Brunner 1966] [Brunner et al. 1966] [Bryson et al. 1968] [Bugg and Sleeman 1967] [Burkhardt et al. 1999] [Béjar-Romero et al. 2016] [Campbell et al. 1996a] [Campbell et al. 2004] [Chen et al. 2022a] [Chen et al. 2025a] [Chen et al. 2026d] [Chen et al. 2026f] [Chernyi and Gonor 1973] [Chin 1970] [Clapp 1965] [Colvin 2021] [Couch and Morris 1968] [Crouch 1999] [Cruz and Ware 1992] [Cutrone et al. 2026] [D’Angelo et al. 1999] [Dana 1968] [Dana et al. 1969] [Davenport et al. 1992] [Davis 1966] [Delgado et al. 2000] [Delgado et al. 2001] [Deng et al. 2017a] [Deng et al. 2017c] [Deng et al. 2018] [Deng et al. 2024] [МГТУ им. Н.Э. Баумана et al. 2013] [Dingell et al. 1999] [Direct Numerical Simulations 2023] [Dolan et al. 1966] [Dong et al. 2024] [Draper and Buck 1968] [Dussy et al. 2011] [Eckhardt 2001] [Eggers and Swenson 1966] [Eliseev et al. 2014] [Elliott and Hankey 1968] [Erwin 1990] [Falarski and Mort 1970] [Fannelop 1967] [Filatov 1972] [First Glide Flight 1966] [Fong et al. 1970] [Foss and Whitcomb 1960] [Fuhrmann 2003] [Layton 1970] [Gawehn et al. 2011] [Gentry 1972] [Gentry et al. 1966] [Gibson and Goetz 1971] [Goldberg 1966] [Golubkin and Negoda 1995] [Gérard and Tumino 2006] [Hallion 1998] [Hassell 1960] [Hodge et al. 1981] [Holmes 1970] [Holt et al. 2016] [Hook and Freeman 1989] [Horvath et al. 1990] [Horvath et al. 2000] [Ishimoto 1995] [Jackson and Rivers 1998] [Jackson et al. 1993b] [Jackson et al. 1993a] [Jackson et al. 1994] [Stevens et al. 1966] [Jeong et al. 2007] [Jeong et al. 2009] [Jernell 1971] [Jie Gu et al. 2016] [Cochrane and Graham 1971] [McTigue 1970] [Johnson et al. 1982] [Kaminsky and Johnson 1964] [Katz and Roglin 2000] [Katz et al. 1998] [Kawato et al. 2002] [Kawato et al. 2003] [Kawato et al. 2005] [Kazi et al. 2019] [Kempel and Painter 1993] [Kempel and Thompson 1971] [Kempel et al. 1971] [Kempel et al. 1975] [Kempel et al. 1994] [Khurana and Suzuki 2012] [Khurana and Suzuki 2013b] [Khurana and Suzuki 2013a] [Khurana and Suzuki 2013c] [Khurana and Suzuki 2014] [Khurana et al. 2012] [Kotfila and Painter 1969] [Krevor et al. 2011b] [Krevor et al. 2011a] [Krusos 1967] [Kumar and Mahulikar 2016a] [Kurita et al. 2006] [La et al. 1993] [Ladson 1970] [Lagimoniere and Avram 2024] [Laporte 1966] [Larson 1972] [Layton and McTigue 1969] [Lewellen and Mirels 1966] [Li et al. 2010] [Liang et al. 2014] [Ling 2017] [Liu et al. 2019a] [Loddoni et al. 2010] [Lusty 1966] [Lynch 1966] [M2-F2 Lifting Body Accident 1967] [MacConochie 2000] [Machin et al. 1999] [Maikapar 1967] [Masaki and Yakura 1968] [McGhee 1970] [McTigue and Ryan 1968] [Merlin 2014] [Meyer-Allyn et al. 2012] [Micol 1990] [Miele 1968] [Minami and Tsukamoto 2006] [Tang 1970] [Morio et al. 2009] [Naeseth 1970] [Nelson et al. 1997] [Nietubicz 1975] [Otsu 2016] [Otsu 2018] [Sreena and Laxman 2023] [Page and Anderson 1996] [Painter and Sitterle 1974] [Palmer et al. 1995] [Peipei et al. 2017] [Penland 1975] [Peterson 2004] [Petrov and Soudakov 2016] [Powell 1993] [Powell and Cruz 1991] [Pyle 1971] [Qi et al. 2021] [Reed et al. 1997] [Raible and Jacob 2003] [Rana and Chudoba 2016] [Rana et al. 2017a] [Rana et al. 2017b] [Rasmussen 1978] [Rasmussen 1979] [Reaser 1997] [Recasens et al. 2005] [Reimann 2016] [Rice and Cheng] [Rivers et al. 1994] [Rizvi et al. 2012] [Rizvi et al. 2013] [Rizvi et al. 2015] [Kempel et al. 1970] [Ruf et al. 1996] [Saccani 2020] [Sager 1995] [Saltzman et al. 1999] [Saltzman et al. 2002] [Saltzman et al. 2007] [Savino et al. 2015] [Scallion 1999] [Schouler et al. 2021b] [Schouler et al. 2021a] [Schwelkart and Hallion 1997] [Seegmiller 1968] [Shi et al. 1969] [Shin et al. 1999] [Shin et al. 2001] [Slender Lifting Body Axial 1994] [Smith 1965] [Smith et al. 1998] [Soccini et al. 2015] [Soistmann and Spain 1993] [Spearman 1985] [Squire 1971] [Stadler 1993] [Stalony-Dobrzanski 1966] [Stone and Piland 1991] [Stubbs 1966] [Study of the Influence 1967] [Sun et al. 2026e] [Talay 1992a] [Talay 1992b] [Talay and Stone 1991] [Tang and Pearson 1973] [Tartabini et al. 2000] [Tartabini et al. 2002] [Taylor and Allison 2015] [Taylor and Howard 2008] [Thompson 1964b] [Thompson 1964a] [Thompson 1966] [Thompson 1970a] [Thompson 1970b] [Tongue and Dingell 1999] [Trifoni and Lafferty 2025] [Trifoni et al. 2026] [Van Ghele et al. 2018] [van Oort et al. 2007] [Vella] [Vetter 1966] [Vidal 1974] [Viladegut 2018] [Ware and Cruz 1993] [Ware et al. 1991] [Wartemann et al. 2018] [Webb and Bettinger 2024] [Weber et al. 2000] [Dana and Gentry 1970] [Winnick 1996] [Woffinden et al. 2011] [Wu et al. 2009] [Wurster 1983] [Xia et al. 2016] [Xiang and Kun 2017] [Xue et al. 2023b] [Yang et al. 2014] [Yang et al. 2025a] [Yin et al. 2024] [Young et al. 1972] [Zea et al. 2012] [Zhang et al. 2019d] [Zhang et al. 2024b] [Zhang et al. 2024e] [Zhang et al. 2026a] [Zhang et al. 2026b] [Zou et al. 2025]

Hypersonic glide vehicles, their tracking and their interception

The glide vehicle as a weapon, with its trajectory design and control, and the tracking, prediction and interception of it. 235 of the 252 records date from 2010 or later, and 91 of the titles name tracking, prediction, estimation, detection, radar, interception, intention or defence, which is the inversion the analytic subsection above describes, from designing a manoeuvring entry body to predicting one.

252 records. [Acton 2015] [Ansari and Bernstein 2019] [Arabian 1960] [Arputharaj and Mukherjee 2026] [Ashford 1965] [Autenrieb and Gruhn 2025] [Autenrieb and Gruhn 2026] [Autenrieb et al. 2025] [Bahman Zohuri et al. 2019] [Bai et al. 2025] [Barr et al. 2026] [Bartusiak et al. 2022] [Barz 2026] [Baxter and Arthur 1965] [Bedrov et al. 1965] [Berthelot et al. 2026] [Bonavita et al. 2026] [Brockmann and Stefanovich 2022] [Burns 2020] [Butler et al. 2022] [Butler et al. 2023] [Cai and Zhuang 2025] [Cai et al. 2026] [Candler and Leyva 2022] [Cangelosi et al. 2024] [Chen 2017] [Chen et al. 2015b] [Chen et al. 2016d] [Chen et al. 2018a] [Chen et al. 2020d] [Chen et al. 2020f] [Chen et al. 2020h] [Chen et al. 2020i] [Chen et al. 2021d] [Chen et al. 2022d] [Chen et al. 2025f] [Cheng et al. 2019b] [Cheng et al. 2020] [Cheng et al. 2021] [Cheng et al. 2022] [Chiriac 2022] [Coupled Dynamic Model 2018] [Dai et al. 2026a] [Dendy et al. 2026] [Deng 2026] [Deng and Zhao 2026] [Ding et al. 2016] [Dong and Cai 2017] [Dong et al. 2021] [Dong et al. 2023a] [Doronzo 2026] [Du et al. 2026] [Fan et al. 2016b] [Fan et al. 2017] [Fang et al. 2024] [Feng and Zhang 2016] [Feng et al. 2017] [Feng et al. 2025a] [Fergusson] [Froning et al. 1996] [Fu et al. 2024] [Gao et al. 2018a] [Gottlieb et al. 2024] [Graves and Carmel 1968] [Guo et al. 2018a] [Guo et al. 2023b] [Hall et al. 2026] [Han et al. 2024a] [Hao and Yongqi 2024] [Hao et al. 2025] [Harris and Davidson 1962] [He et al. 2016] [He et al. 2017b] [He et al. 2024] [He et al. 2025] [He et al. 2026a] [He et al. 2026c] [He et al. 2026b] [Herrmann et al. 2025] [Hou et al. 2023] [Hu et al. 2021b] [Hu et al. 2022c] [Hu et al. 2025] [Huang et al. 2017] [Huang et al. 2018b] [Huang et al. 2020a] [Huang et al. 2021b] [Huang et al. 2023a] [Huang et al. 2024a] [Jaeger and Hemati 2025] [Jewel and Whitten 1960] [Jia et al. 2018] [Jian-bo et al. 2017] [Jiang et al. 2022] [Jung et al. 2024a] [Kelley et al. 1982] [Kessler 2022] [Knight et al. 2026] [Kumar et al. 2018a] [Kurilova and Li 2026] [Kwon et al. 2021a] [Le et al. 2023] [Lee and Ryoo 2018] [Leng et al. 2025] [Li 2021] [Li and Nan 2023] [Li et al. 2009] [Li et al. 2014] [Li et al. 2015d] [Li et al. 2016a] [Li et al. 2017b] [Li et al. 2018d] [Li et al. 2021a] [Li et al. 2022d] [Li et al. 2022c] [Li et al. 2024c] [Li et al. 2024b] [Li et al. 2025c] [Li et al. 2026a] [Li et al. 2026c] [Liang et al. 2015] [Liang et al. 2025a] [Liang et al. 2025b] [Liu and Shen 2015] [Liu et al. 2010] [Liu et al. 2021c] [Liu et al. 2022b] [Liu et al. 2023b] [Liu et al. 2024a] [Liu et al. 2024c] [Liu et al. 2025c] [Liu et al. 2025d] [Liu et al. 2025a] [Liu et al. 2025b] [Liu et al. 2025e] [Liu et al. 2026d] [Liu et al. 2026a] [Liu et al. 2026b] [Lock et al. 2025] [Lu and Qian 2024] [Luo et al. 2022] [Ma et al. 2024b] [Mai et al. 2026] [Malinowski 2020] [Matheny and Smith 2026] [McGrory 2001] [Melville and Helmich 2021] [Meng and Tian 2020] [Meng et al. 2021] [Müller and Petervari 2025] [Nguyen et al. 2026] [Paulson and Shanks 1959] [Paulson and Shanks 1961a] [Ping et al. 2017] [Pinto et al. 2023a] [Pinto et al. 2023b] [Pottsepp and Shi 1968] [Pulimidi et al. 2018] [Qiu et al. 2016] [Radhakrishnan and Ozana 2025] [Ragnoli et al. 2024] [Rataczak et al. 2024] [Raza and Mehmood 2023] [Reentry Maneuvering Vehicle Ascent 2025] [Ren et al. 2023] [Rizvi et al. 2017] [Rodi 2020] [Rosner and Cibrian 1974] [Sayadi et al. 2018] [Scala and Nolan 1960] [Sethi 2025] [Shan et al. 2018] [Shao et al. 2025] [Shi et al. 2023a] [Su et al. 2024] [Sun 2026] [Sun and Zhang 2020] [Sun et al. 2017] [Sun et al. 2024a] [Sun et al. 2025c] [Sun et al. 2025a] [Sun et al. 2026d] [Sun et al. 2026g] [Sun et al. 2026c] [Tan et al. 2019] [Tarjáni 2023] [Tianyang et al. 2024] [Tong et al. 2026b] [Tracy and Wright 2020] [ul Islam Rizvi et al 2015] [Wan et al. 2019] [Wang 2019a] [Wang 2019b] [Wang and Chen 2023] [Wang et al. 2019e] [Wang et al. 2022a] [Wang et al. 2024b] [Wang et al. 2025b] [Wang et al. 2026b] [Wang et al. 2026d] [Way et al. 2024] [Wei et al. 2026] [Wei-wei et al. 2013] [Weidong et al. 2015] [Weijie et al. 2016] [Williams 2021] [Williams et al. 2024] [Williams et al. 2025a] [Williamson et al. 2026] [Wright 2015] [Wu and Ma 2019] [Wu et al. 2018b] [Wu et al. 2019] [Xie et al. 2021a] [Xie et al. 2024b] [Xie et al. 2024a] [Xu et al. 2023a] [Xu Mingliang et al. 2010] [Xue et al. 2023a] [Xue et al. 2026] [Yakubayev et al. 2026] [Yan and Wang 2012] [Yan et al. 2014] [Yan et al. 2017] [Yan et al. 2024] [Yang et al. 2026a] [Yanli et al. 2016] [Yao et al. 2023] [Ye et al. 2022a] [Yogaswara et al. 2017] [Yu et al. 2022b] [Yuan et al. 2026] [Zhai and Yang 2020] [Zhan et al. 2017] [Zhang and Du 2017] [Zhang and Zhou 2022a] [Zhang and Zhou 2022b] [Zhang et al. 2015a] [Zhang et al. 2015b] [Zhang et al. 2019e] [Zhang et al. 2022g] [Zhang et al. 2022b] [Zhang et al. 2022c] [Zhang et al. 2022h] [Zhang et al. 2023d] [Zhang et al. 2025a] [Zhang et al. 2025b] [Zhang et al. 2026d] [Zhao et al. 2018b] [Zhou et al. 2026] [Zhu et al. 2018] [Zope et al. 2026]

Stagnation-point, convective and radiative heating

The heat load the ablator answers, being stagnation-point and convective heating correlations, shock-layer radiation and the aerothermal prediction of entry vehicles.

243 records. [Aerothermodynamic Predictions for Hypersonic 2004] [Anderson 1968] [Anoop et al. 2026] [Appar et al. 2022] [Arc-Heated Facilities as 2002] [Avduevskii and Ivanov 1968] [Bade 1975] [Beier 1988] [Bettis and Hosder 2010] [Biberman et al. 1972] [Bird 1960] [Blackwell et al. 1972] [Bloor 1967] [Boiarski and Parobek 1980] [Bonin et al. 2017] [Bose 2009] [Bourdon and Bultel 2008] [Bouslog et al. 1993] [Boyd 2002] [Hollis 2020] [Brunner 1959] [Bryson et al. 1962] [Bulmer 1975] [Nath 1971] [Pavlov 1967] [Potter and Bailey 1963] [Varghese et al. 2023] [Carlozzi] [Cauchon 1967] [Cauchon et al. 1967] [Chapman 1967] [Chapter 1 2013] [Chapter 13 2013] [Chen 1958a] [Chen 1958b] [Chen and Fan 2025] [Chen et al. 2023a] [Chew] [Chou and Smith 1974] [Johnston] [Chun 1991] [Clark et al. 1978] [Compton and Cooper 1965] [Conti 1964] [Cooper 1966a] [Cooper 1966b] [Cozzarelli and Vito 1969] [Maciel 2022] [DeChant and Wagnild 2020] [Derienzo and Pallone 1967a] [Derienzo and Pallone 1967b] [Dicristina 1979] [Dobrov et al. 2023] [Dogra et al. 1987] [Dohnanyi 1964] [Dreyer et al. 2021] [Druguet 2012] [Dusinberre 1958] [Eggers et al. 1958] [Eliseev and Cherkez 1978] [Engel and Spradley 1968] [Ermak and Neiland 1967] [Fay and Kemp 1963] [Feldick et al. 2008] [Finke 1990] [Finson et al. 1980] [Fomin 1966] [Fontenot 1965] [Francis 1972] [Fujino et al. 2008] [Gai and Cao 2025] [Gally and Campbell 2002] [Gershbein and Kolesnikov 1980] [Glawe et al. 1963] [Gnoffo 2007] [Goates et al. 2026] [Goekcen and Edwards 1996] [Golovachev 1972] [Golovachev 1979a] [Goulard 1961] [Gros 1963] [Gu 2026b] [Gu 2026a] [Guinn 1961] [Gülhan et al. 2001] [Hankey and Hooks 1963] [Hao et al. 2017] [Harloff and Petrie 1987] [Hartung et al. 1991] [Harvey 1965] [Hassan et al. 1991b] [Hawkins et al. 1999] [Hayes 1964] [Hollis and Hollingsworth 2012] [Hong and Neuenschwander 1991] [Horton and Babineaux 1967] [Horton and Zeh 1966] [Hossain 2025] [Hove and Shih 1977] [Huber 1966] [Husson 1963] [Inger 1991] [Ivanov et al. 2011] [Jenke 1979] [Jischke 1968] [Jischke 1970] [Jo et al. 2019] [Jo et al. 2020] [Judd 1963] [Jumper and Seward 1992] [Kao 1964b] [Kashkovsky 2014] [Kaufman 1963] [Kaufman and Louis G. 1963a] [Kaufman and Louis G. 1963b] [Kaufman and Louis G. 1964] [Kaushikh et al. 2018] [Kemp 1960] [Kianvashrad and Knight 2019] [Kim et al. 2026c] [Kivel 1961] [Koh 1962] [Kozlov 1969] [Kremeyer and Pakhomov 2008] [Krishnamoorthy and Clarke 2016] [Kumar and Jain 1974] [Lee and Pappas 1969] [Lee and Pappas 1970] [Lee et al. 1992] [Lee et al. 1994] [Lenard 1962] [Li and Geiger 1957] [Li and Zhang 2021] [Libby 1967a] [Libby 1967b] [Libby and Sepri 1968] [Liechty et al. 2011] [Liu 1968] [Liu and Liu 2016] [Liu et al. 2019c] [Liu et al. 2021d] [Loehle et al. 2021] [Lunev and Khramov 1970] [Haw et al] [Maise 1971] [Martin 1968] [Masters and Cohen 1957] [McAnally and Engel 1979] [McLellan 1955] [Meckler 1964] [Meyer 1959] [Miles and Brown 2002] [Miller 2005] [Morgado et al. 2022] [Mori 1965] [Muthanna and Nath 1976] [Muthu et al. 2020] [Atomics International, Canoga Park, Calif. and Nelson 1967] [Nerem and Stickford 1964] [Nishida and Sugimoto 1973] [Nishio 1996] [Nomura 1983] [Oguchi 1958] [Olivier 1995] [Olstad 1969] [Olynick 1996] [Otsu et al. 2001] [Otsu et al. 2004] [Pal 1970b] [Pal 1970a] [Park 1984] [Parton 2018] [Patrick 2019] [Perini 1972] [Perini 1975a] [Pervushin 1982] [Peterson and Frantz 1982] [Plumb 1971] [Pollin 1963] [Pollin 1964] [Pope 1968] [Porter and Cambel 1966] [Radiation and Reentry 1968] [Radiation Properties of Hypersonic 2018] [Radiative Heat Transfer 2018] [Raju et al. 1978] [Ravichandran et al. 2023] [Reba 1964] [Reba and Christian 1963] [Reilly 1964] [Reynerson 2006] [Rieken et al. 2021] [Rose and Stankevics 1963] [Sasoh and Fujiwara 1990] [Satchell et al. 2018] [Scala 1962a] [Schmidt 1966] [Schwartzentruber et al. 2012] [Sheldon 1967] [Smith et al. 1965] [Sockalingam and Tabiei 2009] [Sohn et al. 2008] [Sprinks 1963] [Srinivas 2026] [Stewart and Golden 1970] [Strike 1982] [Sun et al. 2020] [Sun et al. 2023] [Suslov 1969] [Suzuki 1978] [Talbot 1960] [Talbot 1962] [Tashakkor et al. 2011] [Test Method for Calculation] [Thompson 1968] [Tokuda and Yang 1966] [Tong 1965] [Tong and Giedt 1963] [Trimmer 1968] [Türkoğlu et al. 2026] [Ueno 1963] [Utyuzhnikov and Tirskiy 2013] [Vandrey 1957] [Vasil’kov 1975] [Viviani and Pezzella 2007a] [Viviani et al. 2008] [Voronkin 1971] [Wang et al. 2023c] [Warmbrod 1963] [Weeks 1969] [Williams 1968] [Wilson 1970] [Wind-Tunnel Study of Ascent 1981] [Wing 1971] [Winkler 1952] [Winkler 1954] [Winovich 1968] [Wortman 1970] [Zhao et al. 2019c] [Zhao et al. 2022a] [Zhou et al. 2023] [Zoby et al. 1993] [Zuo and Hu 2021]

Capsules and ballistic entry

The unlifted case and the low-lift capsule, being ballistic entry, re-entry vehicle dispersion and tracking, crew return vehicles and capsule aerodynamics, heating and dynamic stability.

232 records. [Gemini Spacecraft Orbital Simulation 1966] [Abe et al. 2000] [안미치코 2013] [Allen 1969] [Arho 1971] [Asad et al. 2020] [Aslanov 2016] [Aslanov 2017a] [Aslanov and Ledkov 2016] [Bairstow and Barton 2007] [Barbara 1981] [Barth and Bailey 2007] [Bate and Johnson 1962] [Bihari et al. 2011] [Bilimoria and Mueller 2010] [Bouyahiaoui et al. 2020] [Brunner and Lu 2010] [Bui et al. 2006] [Burgio et al. 1993] [Burkhardt and Schoettle 1996] [Burns 1974] [Mehta 2019] [Campbell 2025] [Campbell et al. 1996b] [Chandler 1992] [Chang 1980] [Chang et al. 2006] [Chen 1965] [Chen et al. 2015a] [Cooper et al. 2005] [Costa et al. 2000] [Cowings et al. 2018] [Crenshaw 1983] [Crespo et al. 2026a] [Crespo et al. 2026b] [Crowder and Moote 1969] [Culbertson 1970] [Dean et al. 2026] [Di Clemente and Ferrarella 2010] [Di Giovanni and Stemmer 2019a] [Di Giovanni and Stemmer 2019b] [Dingell and Hurlbert 1997] [Dobies 1957] [Driscoll et al. 1966] [Duda 2016] [Duda and Nakamura 2017] [e-CRV 2004] [Endo et al. 2024] [Ericsson and Reding 1970] [Experimental Dynamic Stability Investigation 2025] [Fan et al. 2016a] [Fink 1961] [Fitzgerald 1974] [Foster 1960] [Fujimoto et al. 2017] [Garland and Hall 1958] [General Dynamics/Astronautics San Diego Ca 1961] [General Dynamics/Astronautics San Diego Ca 1962] [General Dynamics/Astronautics San Diegoca 1961] [Miller 1961] [Mueller et al. 1967] [Ghaedamini Harouni and Hashemi Mehneh 2019] [Gillespie and Saha 2003] [Glebova et al. 2022] [Glover 1965] [Goldburg et al. 1965] [Govindaraj and Ganesan 2024] [Han et al. 2024b] [Han et al. 2025] [Harrison and Aronson 1969] [Hashimoto et al. 2016] [Heidrich and Braun 2017] [Hertz 2003] [Hiraki et al. 2018] [Hiraki et al. 2020] [Hooks and Stone 1992] [Hosaka et al. 2026] [Hough 1982a] [Hough 1982b] [Huang 2022] [Iizuka and Fujii 2006] [Ishihara et al. 2015] [Ishii et al. 2008] [Jayanthi and Jain 2019] [Johnston 2026] [Kachadourian 1970] [Kadam and Hablani 2014] [Kalil 1966] [Kang et al. 2025] [Karthikeyan Kalirajan and Ashok Joshi 2023] [Kashiwagi 1968] [Kazemba et al. 2013] [Kennedy and Fields 1962] [Kim et al. 2026a] [Kim et al. 2026b] [King 1980] [Koga et al. 2014] [Komurasaki and Candler 1998] [Koppa et al. 2026] [Kornreich 1963] [Kornuta] [Krupa 1990] [Krysenko 1963] [Kumagai 1964] [Kutkan and Eyi 2018] [Laitone 1959] [Leondes and Volgenau 1967] [Li and Gong 2018] [Liang and Han 2008] [Liang and Ji 2021] [Liang and Liu 2009] [Liang et al. 2010] [Licata 1977] [Loh 1962a] [Loh 1962b] [Lu and Zhou 2016] [Lu et al. 2017a] [Luo and Liu 2009] [Neal 1963] [Lykoudis 1964] [Ma et al. 2024c] [Marichalar et al. 2012] [Matsuda et al. 2013] [Matsumoto et al. 2016] [McNamara and Braun 2014] [Mehra 1971] [Mehta 2005] [Mehta 2023a] [Mehta 2023b] [Miele 1957] [Miki and Fujii 2018] [Montella et al. 2025b] [Montella et al. 2025a] [Montella et al. 2026] [Moreira et al. 2022b] [Moseley 1969] [Moss et al. 2006b] [Mu and liCai 2016] [Murphy and Rubesin 1965] [Nagata et al. 2016] [Nakamura et al. 2014] [Nebylov and Nebylov 2024] [Neto et al. 2021] [Rahaim and Wood] [Niculescu et al. 2018] [Nomura et al. 2018] [Nomura et al. 2019] [Norfleet et al. 1975] [O’Hare and Anderson 1993] [Ohmichi et al. 2019] [Okano et al. 2023] [Okano et al. 2024b] [Okano et al. 2024a] [Otsu 2021] [Palharini et al. 2019] [Park 2001] [Patil et al. 2004] [Pezzella and Votta 2009] [Phillips and Cohen 1959] [Phillips and Kryvoruka 1973] [Plastinin et al. 2007] [Platus 1967a] [Platus 1967b] [Platus 1980c] [Platus 1982] [Platus 1998] [Pollak 1962] [Price and Ericsson 1970] [Probst et al. 2022] [Putnam and Braun 2015] [Raeisi et al. 2019] [Rasmussen 1969] [Bhaskaran 2024] [Morth 1966] [Rea 2008] [Rea and Putnam 2007a] [Reitz 1972] [Rong et al. 2015a] [Rossman et al. 2017] [Ruffner et al. 2023] [Rugescu 2013] [Sabin 1975] [Scherberg and Rubin 1953] [Schoettle et al. 1997] [Schrijer and Walpot 2010] [Schweppe 1964] [Seeley and Cole 1965] [Sepahban and Williams 1993] [Shetu et al. 2026] [Shi et al. 2020] [Smith et al. 1990] [Sostaric et al. 2019] [Soumya et al. 2018] [Stiles 1970] [Strand 1959] [Surzhikov 2017] [Suzuki and Sawada 2000] [Takahashi et al. 2016] [Takii et al. 2014] [Tang and Wright 2007] [Tanno et al. 2010] [Tanno et al. 2013] [Tauber 1970] [Teramoto and Fujii 2002] [Teramoto et al. 1998] [Theiss and Hein 2017] [Tendeland and Pearson 1962] [Tigges et al. 2011] [Timofeev 2020] [Valentini et al. 2026] [Viviani and Pezzella 2009] [Viviani and Pezzella 2015] [Viviani et al. 2006] [Wang et al. 2023a] [Watkins et al. 2008] [Weilmuenster et al. 1990] [Williamson 1978] [Willier et al. 2026] [Withers 2015] [Wood et al. 1996] [Xie et al. 2015b] [Xu 2022] [Xu et al. 2020] [Yang and Radespiel 2017] [Yang et al. 2016a] [Yang et al. 2018a] [Yang et al. 2019b] [Yuntong et al. 2025] [Zhang et al. 2017b] [Zhao 1993] [Zhou et al. 2012b] [Zimmermann et al. 1996]

The equilibrium glide and analytic entry trajectories

The trajectory the article’s derivation assumes, being the equilibrium glide, approximate and analytic solutions of lifting entry, skip entry, entry corridors and the optimisation of the entry trajectory itself.

227 records. [Allen 1964] [Allen 1966] [Analytical Experimental and Developmental 1967] [Antonova and Skiba 1968] [Approximate Analysis of Atmosphere 1965] [Arora 2002] [Aslanov 2017b] [Atmospheric Entry 2004] [Babineaux et al. 1963] [Bao et al. 2021] [Bass 1980] [Bayle 1982] [Bell 1965] [Bequaert and Chin 1963] [Betz 1967] [Boylan et al. 1976] [Breitner and Pesch 1994] [Broglio 1961] [Brunner] [Bulmer 1974] [Burton 1974] [Busemann et al. 1969] [Byczkowski and Rao 2024] [Carlson and Swenson 1966] [Chai et al. 2020a] [Chao et al. 2026] [Cheatham 1959] [Chen et al. 2016a] [Chen et al. 2020c] [Chen et al. 2020b] [Chen et al. 2020g] [Chen et al. 2020a] [Chen et al. 2021c] [Cheng et al. 2017] [Chern and Vinh 1978] [Chern and Vinh 1980] [Chern et al. 1988] [Craig et al. 1994] [Crawford 1971] [Dai et al. 2026b] [Das et al. 2023] [Das et al. 2024] [Delpino et al. 1967] [Dix et al. 1967] [Dong et al. 2025] [Duan and Li 2015] [Duncan 1968] [Dunkley 1970] [Eggers and Wong 1961] [Enmi et al. 2018] [Giraldo-Grueso et al. 2025] [Fine 1967] [Fletcher and Jaquet 1962] [Garcia-Llama 2007] [Geiger 1962] [Giraldo-Grueso et al. 2026] [Glover 1966] [Grant 1960] [Greene and Williamson 1982] [Guo et al. 2021] [Han and Jia 2023] [Hao et al. 2019] [Haoui 2011] [He et al. 2017a] [Holleman 1966] [Huang et al. 2021a] [Huang et al. 2024b] [Igra 2019] [Inatani et al. 1992] [Ji et al. 2018] [Jinchuan Hu et al. 2015] [Jordan and Barrett 1961] [Kao 1964a] [Kelley and Sullivan 1972] [Khramov and Chekmarev 1982] [Kluever 2008b] [Krupp 1965] [Kumar et al. 2018c] [Laganelli 1980] [Leavitt and Mease 2007] [Lebedev et al. 1969] [Lee and Mason 1960] [Lees et al. 1959] [Lennon and Poirter 1974] [Li et al. 2016d] [Li et al. 2025b] [Liang and Ren 2018] [Liang et al. 2024] [Lin et al. 2020] [Liu and He 2017] [Liu et al. 2020b] [Liu et al. 2021e] [Liu et al. 2022a] [Liu et al. 2022c] [Liu et al. 2023a] [Logan 1968] [Love 1966] [Lu 2005] [Lu 2008] [Luo and Su 2016] [Luo et al. 2015] [Luo et al. 2026] [Ma et al. 2022] [Mahmoud et al. 2017] [Mao et al. 2016] [Maorui Zhang et al. 2010b] [Maorui Zhang et al. 2010a] [Martin 1966] [Masuda et al. 2016] [Matsumoto et al. 2015] [Ming-Guang et al. 2006] [MingLin 2022] [Moe 1960] [Mooij 2004a] [Mori et al. 2002] [Morth 1970] [Multi-Objective Reentry Trajectory Optimization 2017] [Musen and Squires 1965] [Nachtsheim and Lehman 1980] [Norman and Meier 1963] [Ohya and Kato 1985] [Optimal Glide of Reentry 1981] [Otsu et al. 2011] [Parsons 1964] [Pei et al. 2021] [Peigin and Désidéri 2001] [Ping Li et al. 2010] [Platus 1994] [Project EGRESS 1990] [Putnam and Braun 2016] [Qi et al. 2025] [Qu et al. 2016] [Rahman 1962] [Rahman 1963] [Randall 1970] [Re-Entry Trajectory with Diveline 1993] [Rea and Putnam 2007b] [Reding and Svendsen 1988] [Reentry Flight Predictions around 1994] [Reentry Trajectory Estimation 2024] [Ren et al. 2019] [Ruger 1964] [Savage and Tinling 1959] [Scala 1961b] [Scala 1962b] [Schadt 1968] [Shen 1963] [Shen et al. 2002] [Shi et al. 2012] [Short 1961] [Spearman 1984] [Speyer and Womble 1971] [Srivastava et al. 2022] [Starkey and Lewis 2000] [Steinfeldt and Tsiotras 2010] [Stern 1968] [Sun et al. 2025d] [Sun et al. 2026a] [Sun et al. 2026b] [Sushnigdha 2022] [Sushnigdha and Joshi 2018] [Tang et al. 2020] [Tannas 1966a] [Tartabini et al. 2011] [Teofilatto 2024] [Terasaki 1963] [Thomas et al. 2022] [Timchenko et al. 2004] [Tong et al. 2026a] [Townend 1979] [Trella and Vaglio-Laurin 1964] [Tu and Yuan 2006] [V. a. Yaroshevskii 1965] [Vinh and Johannesen 1985] [Vinh et al. 1981] [Vorreiter et al. 1973] [Walker 1965] [Wang 1963a] [Wang and Dong 2013] [Wang and Ting 1961] [Wang et al. 2013b] [Wang et al. 2015c] [Wang et al. 2016] [Wang et al. 2017a] [Wang et al. 2019b] [Wang et al. 2020b] [Wang et al. 2025c] [Wang et al. 2026j] [Wang et al. 2026g] [Wang et al. 2026a] [Wei et al. 2018] [Wong et al. 1960] [Wu et al. 2018a] [Wu et al. 2021a] [Wu et al. 2026] [Xiao-tian et al. 2022] [Xie et al. 2021b] [Xie et al. 2023] [Xu et al. 2011b] [Xu et al. 2012] [Xu et al. 2019] [Xu et al. 2022c] [Yan et al. 2023] [Yang and Meng 2012] [Yang and Sun 2011] [Yang and Wang 2015] [Yang et al. 2016b] [Yoshino et al. 2007] [Yu and Chen 2011] [Yu et al. 2026] [Zhang et al. 2017c] [Zhang et al. 2018c] [Zhang et al. 2019a] [Zhang Qingzhen et al. 2007] [Zhao and Pan 2025] [Zhao and Zhou 2013] [Zhao et al. 2014] [Zhao et al. 2019a] [Zhengchun 2018] [Zhiqiang Zhao and Zhengdong Hu 2010] [Zhongjie Meng et al. 2010] [Zhou 2009] [Zhou et al. 2012c] [Zhou et al. 2019] [Zhu et al. 2026] [Zhuo et al. 2011] [Zou et al. 2013]

The Space Shuttle orbiter and its requirement

The vehicle that PRIME’s crossrange fed, being the orbiter’s entry, guidance, aerothermodynamics, thermal protection, flight control and landing. 162 of the 218 records date from before 1990, which is the shape of a literature about a vehicle that was designed in the 1970s and flew its entries from 1981.

218 records. [Adams 1971] [Alber 2012] [Albright and Wichmann 1994] [Alred 1983] [An et al. 1996] [Andrews 1977] [Anthony et al. 1972] [Approximate Method of Predicting 1983] [Assessment of Alternate Thermal 1983] [Audley and Hodge 1982] [Balakrishnan 1984] [Barton and Culp 1985] [Bayle 1984] [Blanchard et al. 2001] [Blazek and Carrier 1974] [Blevins and Hohmann 1975] [Bradley et al. 1983] [Brauckmann and Scallion 2004] [Brauckmann et al. 1994] [Brauckmann et al. 1995] [Brice and Sugano 1978] [Campbell 2007] [Campbell et al. 1989] [Caram et al. 1993] [Carter and Kaul 1975] [Cassanto et al. 1988] [Causey and Sohoni 1973] [Champion 1993] [Chi et al. 1996] [Christiansen and Ortega 1990] [Cohen and Silveira 2003] [Compton et al. 1982] [Cooper 1982] [Cowling 2011] [Cunningham 1972] [Curry et al. 1982] [Curry et al. 1983] [Curry et al. 1986] [Curry et al. 2002] [Daforno et al. 1973] [Danesi 1982] [Daniels and Brooks 1991] [Daugherty and Stubbs 1987] [Daugherty and Stubbs 1988] [Debevoise and McGinnis 1972] [Dejarnette and Jones 1971] [Deriugin et al. 1973] [Diffusion Bonded Columbium Panels 1973] [Doggett 2008] [Dotts et al. 1982b] [Dotts et al. 1982a] [Doyle 1981] [Doyle et al. 1986] [Duggan 1977] [Dziubala et al. 1973] [Elder 1975] [Elias 1974] [Emero 1980] [Ericsson and Reding 1978] [Fester et al. 1975] [Forsberg and Anderson 1972] [Fraser 1983] [Gallegos 1978] [Gatto 1983] [Gilmore et al. 2011] [Gong et al. 1984] [Green et al. 1983] [Grooms et al. 1984] [Haeuser et al. 1992] [Harpold and Gavert 1983] [Harpold and Graves 1978] [Harpold and Hill 1980a] [Harpold and Hill 1980b] [Helms 1981] [Henderson and Nguyen 2011] [Hiltz 1972] [Hoopes and Takahashi 2024] [Horvath et al. 2013] [Ikawa 1977a] [Ikawa 1977b] [Iliff and Shafer 1993] [Iliff et al. 1981] [Iliff et al. 1983] [Jeffs 1979] [Johnson et al. 1986] [Jones 1973] [Joosten 1985] [Kafer 1982] [Kafer et al. 1976] [Kanipe 1983] [Ko et al. 1981] [Krek] [Kremer and Mease 1994] [Kriegsman and Tao 1975] [Kyle 1975] [Lee and Harthun 1982] [Letts and Castle 1981] [Lewis 1983] [Li 1981] [Logsdon 1986] [Longo and Radespiel 1991] [Lorincz 1980] [Lowry 2013] [Lutes and Hodge 1984] [Ma 1992] [Maglieri et al. 2011a] [Maglieri et al. 2011b] [Marichalar et al. 2006] [Martin 1985] [Martindale and Carter 1975] [Matienzo et al. 1985] [Maus et al. 1984] [McCluskey 2004] [McDonnell Douglas 1972] [McGlathery 1973] [McNamara 1971] [Mease and Kremer 1992] [Mease and Kremer 1994] [Merlin 2006] [Minott and O’Hern 1974] [Minott et al. 1976] [Monopropellant Engine Investigation 1975] [Montez and Madden 1982] [Moser and Schneider 1981] [Murad 1985] [Nagle and Sinclair 1989] [NDE Nondestructive Evaluation 1994] [North 1978] [Nutt et al. 1979] [O’Brien 1972] [Papadopoulos et al. 2001] [Park and Rakich 1980] [Pejsa 1972] [Pesch 1980] [Peterson and Uney 1978] [Pielke 1993] [Pielke 1994] [Powell 1977] [Powell and Freeman 1984] [Powell et al. 1976] [Prabhu and Tannehill 1984] [Prabhu et al. 2003] [Pruett et al. 1981] [Pulsonetti and Wood 2005] [Ragsdale and Bown 1977] [Rajagopal and Ortiz 1998] [Ramnath and Sinha 1975] [Rault 1993] [Rausch and Roberts 1974] [Rehder and Holloway 1972] [Restrepo and Valasek 2006] [Reuther et al. 2004] [Richie and Rish 1982] [Rizk and Ben-Shmuel 1985] [Rochelle et al. 1972] [Romere and Young 1983] [Romere et al. 1978] [Romere et al. 1983] [Ronquillo and Williams 1984] [Rosello 1995] [Rowell et al. 1980] [Sawko and Goldstein 1992] [Scallion 2005] [Scott 1978] [Shuttle Orbiter Reusable Surface 1983] [Siemers and Larson 1978] [Siemers and Larson 1979] [Siemers et al. 1983] [Smith 1973b] [Sohoni 1973] [Sohoni 1976] [Space Shuttle Flight Rates 1987, Space shuttle flight rates and ut] [Space Shuttle Guidance Navigation 1973] [Space Shuttle Log 1986] [Space Shuttle Maiden 1979] [Space Shuttle Orbiter Leading 1983] [Space Shuttle Setback 1987, Space shuttle setback] [Stallings 1981] [Stengel 1972] [Stolarski et al. 1973] [Stolarski et al. 1974] [Stone and Powell 1976] [Straube et al. 2002] [Strauss 1975] [Streb 1972] [Stuckey 2001] [Sund and Hill 1979] [Suppanz and Schroeder 1978] [Surber and Olsen 1974] [Tartaglione and Mazzola 1982] [Tewell et al. 1983] [Thompson 1985] [Thompson et al. 1972] [Throckmorton 1981] [Throckmorton 1982] [Throckmorton 1993] [Tile-Gap Flow 1983] [Ting 1982] [Ting et al. 1986] [Tow et al. 1989] [Townend 1972] [Treybig 1975] [Trujillo 1986] [Venkatapathy et al. 1982] [Vinh and Laitone 1972] [Wada and Kubota 1992] [Waldrop 1980] [Wang and Caram 1994] [Ware and Spencer 1986] [Weilmuenster and Hamilton 1982] [Weiss 1971] [Wells 1983] [Whitesides et al. 1990] [Williams and Curry 1983] [Wittliff 1984] [Wood and Alter 2008] [Wood and Oliver 2011] [Young and Underwood 1982]

Reusable launch vehicles, spaceplanes and booster return

Winged and reusable successors and the return of boosters, being reusable launch vehicle entry and landing, spaceplanes, and the recovery of launch vehicle stages.

153 records. [2018, ISRO Releases the Special Issue o] [Agarwalla 2025] [AL-Bakri and Kluever 2017] [Allard 2024] [Aprovitola et al. 2019] [Aprovitola et al. 2021] [Ashikhmina et al. 2021] [Aslanov and Ledkov 2018] [Bae et al. 2022] [Bagal 2026] [Bojun et al. 2019] [Bollino et al. 2006] [Botelho et al. 2022] [Brandenburg et al. 2022] [Brociek et al. 2023] [Calhoun 2000] [Carman et al. 2026] [Carradori et al. 2026] [Chang et al. 2026a] [Chapter 12 2013] [Chaudhary et al. 2001] [Chavagnac 2003] [Chen et al. 2005] [Chen et al. 2025d] [Chen et al. 2026c] [Chowdhry et al. 2001] [Cinquegrana et al. 2015] [Das et al. 2008] [De Oliveira and Lavagna 2023] [De Oliveira and Lavagna 2024] [Fumo et al. 2013] [Desikan and Srinivasan 2018] [Dong et al. 2023b] [Dufour et al. 2015] [Ernst and Leidinger 1988] [European Space Agency Launches 2015] [Fang et al. 2017] [Foster 1959] [Gang et al. 2005] [Gibney 2015] [Gray et al. 2009] [Guadagnini et al. 2023] [Gulli et al. 2015] [Gupta and Ramkumar 2015] [Gupta et al. 2018] [Halbe et al. 2010] [Hwang et al. 2026] [Ishijima et al. 1998] [Ivanov et al. 2007] [Jayan et al. 2024] [Jee et al. 2022] [Jianguo et al. 2016] [Junaid R and Beebi M 2015] [Kaufman 1970] [Khamlak 2026] [Kharchenko and Kryukov 2018] [Kiehn 2020] [Kim et al. 2021] [Kluever and Neal 2015] [Koch et al. 2025] [Kolga and Rundau 2024] [Kumar and Mahulikar 2016b] [Kumar and Mahulikar 2017] [Le and Goo 2021] [Lee et al. 2026a] [Li and Gong 2022] [Li and Hu 2018] [Li et al. 2026b] [Liaoni Wu et al. 2008] [Liu 2019] [Liu et al. 2017] [Lu 1993] [Lu 1996] [Lu 1997] [Lu 1999a] [Mahmoud and Maaruf 2021] [Marchetti et al. 2024] [Mathavaraj and Padhi 2020] [Mathavaraj et al. 2010] [Meckler 1965] [Moreira et al. 2022c] [Mukundan et al. 2022] [Nag et al. 2023] [Nelson 2003] [Nugroho et al. 2024] [Numerical Optimization on Approach 2016] [Oakes 2021] [Paletta et al. 2015] [Parhi et al. 2018] [Parmenter et al. 2002] [Pei et al. 2025b] [Qu et al. 2023a] [Rasky 1998] [Reusable Reentry Satellite RRS 1990a, Reusable Reentry Satellite RRS Co] [Reusable Reentry Satellite RRS 1990b, Reusable Reentry Satellite RRS Re] [Reusable Reentry Satellite RRS 1991a, Reusable Reentry Satellite RRS sy] [Reusable Reentry Satellite RRS 1991b, Reusable Reentry Satellite RRS sy] [Ricciardi et al. 2019] [Roche and Kosareo 2001] [Roche et al. 2000] [Hameed and Bindu 2021] [Sarkar et al. 2021] [Simplício et al. 2019] [Singh et al. 2022a] [Singh et al. 2023] [Sivan and Pandian 2018] [Strauss and Boensch 1973] [Su and Liu 2025] [Su and Wang 2015] [Su et al. 2021] [Morlang 2019] [Tariq et al. 2026] [Tejtel et al. 2011] [Tewell 1984] [Thies 2022] [Tian et al. 2025] [Tillier 1998] [Trefny 1999] [Vinh and Lin 1982] [Wang et al. 2015a] [Wang et al. 2018a] [Wang et al. 2020c] [Wang et al. 2020e] [Wang et al. 2022d] [Wang et al. 2024e] [Wen et al. 2021] [Wu et al. 2020] [Xiong et al. 2022] [Xu and Lan 2018] [Xu and Tang 2010] [Xu et al. 2016] [Xu et al. 2024] [Yang 2025a] [Yang 2025b] [Yue et al. 2018] [Yue et al. 2019] [Yue et al. 2022a] [Yue et al. 2022b] [Zang and Tang 2012] [Zaragoza Prous et al. 2025] [Zhang and Liu 2011] [Zhang et al. 2014] [Zhang et al. 2021a] [Zhang et al. 2021c] [Zhang et al. 2024a] [Zhang et al. 2025h] [Zhao et al. 2020b] [Zhi et al. 2015b] [Zhou et al. 2025b] [Zou et al. 2015] [Zuo et al. 2026] [Zuppardi and Mongelluzzo 2023b] [Çelik and Demirezen 2024]

Entry flight experiments, measurements and programmes

Entry flight tests and the measurements taken on them, together with the period programmes and the launch vehicles that flew them, the Atlas among them.

120 records. [Abe et al. 2001] [Adams] [Armstrong 1977] [Asl and Farahani 2013] [Bakulin et al. 2016] [Bettis and Hosder 2011] [Bifurcation Analysis 2004] [Bityurin and Bocharov 2014] [Blanchard 1961] [Blodgett et al. 1986] [Borrelli et al. 2009] [Cain and Snelling 2022] [Chang et al. 2018b] [Chaw-Bing Chang et al. 1977] [Christoph 1985] [Compilation of Papers Presented 1962] [Cooper 1968] [Costa and Sachs 2002] [da Costa and Sachs 2002] [da Costa and Sachs 2003a] [An Airborne Telescope-Camera System 1974] [Daw 1966] [de Góes Maciel 2015] [Derbidge and Dahm 1976] [Donahue and Farrell 1979] [Dubois-Matra and Bishop 2003] [Ehmsen 1971] [Ehret 1993] [Finson et al. 1978] [Frankenthal 1964] [Franze and Basov 2026] [Gaitonde and Shang 1993] [Gallais] [Gallais] [Gallais] [Golenko and Sychev 2020] [Grabowsky et al. 1981] [Gravlee et al. 2008] [Wilson 1964] [Hollars 1982] [Hongbo Chen and Di Yang] [Hunt et al. 2015] [Ingber 1965] [Jian et al. 2006] [Johnis 2023] [Johnson 2008] [Joshi et al. 2015] [Joshi et al. 2023] [Jung et al. 2024b] [Kameda et al] [Kamimura et al. 2012] [Keith Soo Hoo et al. 1972] [Knott 1969] [Kovtunenko et al. 1986] [Le Maout et al. 2023] [Leveugle and Reinhard 1999] [Li 1989] [Li et al. 2018b] [Li Ruikang et al. 2006] [Lin et al. 2003] [Lyons 1977] [Maciel and Andrade 2017b] [Maciel and Andrade 2017a] [Macret and Leveugle 1999] [Martin Co Denver Co 1966] [McAlees 1968] [Minisci and Vasile 2013] [Moshman and Proulx 2014] [Naigang Cui et al. 2009] [NASA to Launch 5th 1966] [Naughton 2002] [Ogasawara and Nishioka 2001] [Ostrom] [Otsu et al. 2006b] [Paletta et al. 2014] [Park 1976] [Peicheng et al. 2018] [Persen 1969] [Platus 1975] [Platus 1980b] [Potter 1985] [Potts 1981] [Precise Reentry Estimation Using 2024] [Priceman and Sama 1966] [Pritchard 1963] [Reed et al. 2016] [Reentry Acceleration Characterization 2024] [Rigali et al. 1980] [Coate et al. 1962] [Burns et al] [Setterfield et al. 2021] [Shahzad and Weiduo 2019] [Shang and Gaitonde 1994] [Sharenson 1966] [Sheeley et al. 2006] [Skaggs et al. 1967] [Skalandunas 1963] [Starkey et al. 2003] [Sun et al. 2024b] [Sunken Reentry Vehicle 2013] [Szu 2023] [Thomas and Perlbachs 1967] [Thompson 1967] [Thompson and Horton 1981] [Thompson et al. 1982] [Touryan and Sluyter 1966] [Vibration of a Reentry 1975] [Vijay and Jayashree 2024] [Wallace 1999] [Wang et al. 2014b] [Watson 1970] [Watts 2005a] [Watts 2005b] [Whittenberger 1977] [Wolfe 1966] [Wortman 1969] [Wuxing et al. 2015b] [Zheng et al. 2004] [Zheng et al. 2025a] [Zhou et al. 2012a]

Debris, casualty risk and range safety

The footprint as a hazard, being the re-entry of debris and spent stages, casualty risk, breakup and survivability, and range safety for launch and entry.

97 records. [Adams and Kao 2001] [Ailor et al. 2006] [Al-Zaidi et al. 2020b] [Al-Zaidi et al. 2020a] [Annaloro et al. 2020] [Anz-Meador and Potter 1991] [Aoping et al. 2026] [Aslanov and Sizov 2020] [Bacon and Matney 2016] [Baeker et al. 2005] [Basar and Ghosh 2023] [Bigham and Puri 2025] [Bohman et al. 2024] [Braun et al. 2020] [Capristan and Alonso 2014] [Chen et al. 2025b] [Chen et al. 2025e] [Chen et al. 2025g] [Chen et al. 2026e] [Cho et al. 2021] [Chris Ostrom et al] [Collins et al. 2005] [Da Costa 2003] [De Vita et al. 2015] [Dreher et al. 1980] [Dunker and Hill 2025] [Edrington 1966] [Falsone and Prandini 2017] [Falsone et al. 2014] [Fernando and Charalambous 2026] [Ferreira et al. 2023] [Ferreira Santos 2022] [Findley 1961] [Gao et al. 2023b] [Glaese and Kennel 1979] [Glaese and Kennel 1981] [Gruber et al. 2023] [Haber 2017] [Hakima and Bazzocchi 2021] [Koehler et al. 2025] [Hong and Kim 2024] [Jain and Hastings 2025] [Jain et al. 2023] [Jenkin et al. 2024] [Jie Liang 2019] [Holladay et al. 2026] [Jorgensen and Sharf 2021] [Kaplan and Alexander 1979] [Kessler 1981] [Kezirian and Lloyd 2024] [Kim et al. 2018] [Kim et al. 2019] [Kim et al. 2025a] [Kurtz et al. 1965] [Ledermann] [Lee et al. 2018] [Leiser et al. 2022] [Longlune et al. 2026] [Matney 2008] [Megner 2024] [Millard and Acon-Chen 2010] [Mueller 1985] [Murcia P et al. 2019] [Navaz and Ntantis 2026] [Omar and Bevilacqua 2017] [Park and Park 2017] [Park et al. 2018] [Park et al. 2026] [Patera 2005] [Patera 2006] [Perini 1975b] [Prevereaud et al. 2012] [Rao 2000] [Rao and Woeste 1979] [Reyhanoglu and Alvarado 2013] [Reynerson 2005] [Rochelle et al. 1997] [Ross and Madden 1994] [Sampaio and dos Santos 2020] [Sampaio and Santos 2021] [Sanson et al. 2019] [Santos and Sampaio 2021] [Sawal et al. 2024] [Smith et al. 1989] [Spahr 1969] [Standard Classification for Space] [Stern 2008] [Suwantong et al. 2012] [Suwantong et al. 2013] [Twiss 1965] [Wang et al. 2026f] [Wei 2024] [Westerman 1963] [Wu et al. 2011] [Yoon and Ahn 2016] [Yuricich 2026] [Öztürk et al. 2026]

Reaction control, attitude control and control surfaces

Holding the bank angle, being reaction jets, flaps and control surfaces at hypersonic speed, and the attitude control of spacecraft and entry vehicles.

90 records. [Agustin et al. 1998] [Amaratunga et al. 1996] [Andrew et al. 1966] [Autenrieb and Fezans 2024] [Bailey et al. 2008] [Bedrossian et al. 1990] [Bernussou 1973] [Besco 1965] [Bevacqoa et al. 2004] [Bittner et al. 1983] [Buerger and Glanzmann 1970] [Cai et al. 2014] [Cannon and Eppler 1965] [Cavallo et al. 1996a] [Childs 1970a] [Colburn and White 1977] [Compton et al. 1983] [De Angelis and Tang 1969] [de Rosa et al. 2016] [Di Clemente et al. 2006] [Du et al. 2016] [Dunavant and Edwards 1966] [Etheridge and Boudreaux 1970] [Flight Sciences Lab INC Buffalo NY 1964] [Flora et al. 2019] [Garg 1979] [Gevarter 1967] [Ghori et al. 2023] [Greer and Griep 1967] [Guo et al. 2025] [Guo Jianguo et al. 2016] [Gutman 1967] [Hill and Smith 1969] [Hong et al. 2014] [Hooker et al. 1970] [Hughes 1964] [Hui and East 1971] [Huston 1966] [Ito et al. 2002] [Jiang et al. 2020] [Jianguo et al. 2017] [Jiayuan et al. 2018] [Jordan and Buffington 1987] [Kanning 1966] [Kind and Orlik-Rueckemann 1966] [Kirsten and Ash 1974] [Kontis and Stollery 1996] [Kumar and Stollery 1995] [Kumar and Stollery 1996] [Kuntz et al. 1987] [Lappas 2008] [Lecompte and Bland 1964] [Likins 1977] [Likins and Fleischer 1971] [Lopez and Ratcliff 1964] [Moran and Dishman 1970] [Musser and Ebert 1989] [Neumeyer 1968] [Orlik-Rueckemann 1966] [Pande 1976] [Patapoff 1961] [Paulson and Shanks 1961b] [Psiaki and D’Andrea 2000] [Ren et al. 2017] [Roberson 1979] [Roenneke and Well 1995] [Scarboro 1982] [Scott and Rubbo 1975] [Seltzer 1968] [Seltzer 1969] [Seltzer 1970] [Shenming et al. 2018] [Sorensen 1971] [Stickler and Alfriend 1976] [Sun et al. 2026f] [Tinling 1962] [Todosiev 1973] [Tsiotras 2002] [Tsiotras 2004] [Turner 1977] [Walchner and Clay 1965] [Walker and Wolowicz 1960] [Wallner and Well 2002] [Wu] [Wu] [Weil 1981] [Wheeler 1967] [Yu and Liu 2017] [Zhang et al. 2019b] [Zhao et al. 2023]

The atmosphere that entry is computed against

The model atmosphere and its density, being the standard atmospheres, upper-atmosphere density models and the measurements behind them.

63 records. [Air Density 1960] [Hïgh-Altitude Atmospheric Density 1960] [Comparison of High-Altitude Rocket 1960a] [Aerodynamic Stability 1966] [Air Force Test Pilot School Edwards Afb Ca 1962] [Allegre et al. 1991] [B-34. U. S. Standard 1963] [Blish 1980] [Bobylev et al. 2008] [Brown and Bergles 1963] [Brunt 1955] [Carroll and Brandis 2023] [Chapter 10 2013] [Chen et al. 2016b] [Chow 1963] [Comparison of High-Altitude Rocket 1960b] [Dean 1982] [Detra and Hidalgo 1961] [Dubin et al. 1962] [Dubin et al. 1966] [Fischbach et al. 1965] [Forbes 1981] [Gardner and Whitaker 1967] [Grantham 1970] [Grimminger 1959] [Groves 1956] [Harris and Priester 1965] [High-Altitude Atmospheric Density 1960] [Justh] [Jacchia 1965b, Static diffusion models of the up] [Jacchia 1965a, Static diffusion models of the up] [Jacchia and Kopal 1952] [Johnson et al. 2002] [Kennedy and Niemann 1966] [King-Hele 1964] [Krueger and Minzner 1976] [La Glow 1963] [Lemal et al. 2018] [Lien and Eckerman 1966] [Lunev 1971] [Minzner 1966a, Atmospheric density models and ob] [Minzner 1966b, Studies of atmospheric structure] [Minzner 1967] [Minzner et al. 1967] [Minzner et al. 1976] [Moss et al. 2006a] [Newton and Pelz 1973] [Other Publications 1987] [Ouseph and Link 1984] [Parks 1982] [Peters 1977] [Pisharoty 1959] [Pressly et al. 1954] [Ru-ren Chow 1963] [Singer 1956] [Stein and Walker 1965] [Sterne 1958] [Stone 1966] [U.S. Standard Atmosphere Supplements 1966, U.S. Standard Atmosphere Suppleme] [U.S. Standard Atmosphere 1962 1962] [U.S. Standard Atmosphere 1976 1976] [Wahl 1963] [Wittliff and Wilson 1961]

Crossrange, lateral range and the entry footprint

The keystone’s own literature, being lateral range, crossrange, the landing footprint and the reachable set of a lifting entry vehicle. The vocabulary changed and the subject did not. The 7 titles in this cluster that say lateral range date from 1961 to 1970, and the 9 that say crossrange date from 1979 to 2023, so no title in it says lateral range after 1970 or crossrange before 1979.

61 records. [Bao et al. 2026] [Baradell 1962] [Bryant 2002] [Bump 1977] [Chang et al. 2012] [Chao et al. 2010] [Cheng et al. 2025] [Chern et al. 1985] [Clark 2012] [Deyst et al. 1971a] [Deyst et al. 1971b] [Deyst et al. 1972] [Baradell and McLellan 1963] [Evdokimov et al. 2012] [Fenghua et al. 2021] [Florence 1979] [Gonzalez-Puerta et al. 2018] [Handler 1989] [Holloway 1968] [Hsu et al. 1990] [Huang and Li 2018] [Huo et al. 2014] [Jackson 1961] [Kozynchenko 2009] [Lau 1967] [Li and Cui 2009] [Li et al. 2012] [Li et al. 2019] [Li et al. 2022b] [Liang et al. 2017a] [Liang et al. 2023b] [Liu et al. 2015] [Long et al. 2026] [Moote 1970] [Ning Zhang et al. 2016] [Pandie et al. 2026] [Patel and Subbarao 2024] [Patel and Subbarao 2025] [Ploen et al. 2003] [Ploen et al. 2009] [Pritchard and Holloway 1967] [Rataczak et al. 2023] [Saraf et al. 2004] [Shen and Lu 2004] [Stern and Chu 1963] [Stern and Chu 1964] [Wagner 1965] [Wang and Skulsky 1963] [Wang et al. 2020d] [Wang et al. 2023d] [Wang et al. 2023e] [Webb et al. 2026] [Xi et al. 2021] [Xu et al. 2022a] [Xue and Lu 2009] [Yang et al. 2025b] [Yu and Chen 2021] [Yu Li and Nai-gang Cui 2008] [Zhang et al. 2025f] [Zhou et al. 2020b] [Zou et al. 2024]

Entry vehicles in general

The residual, reported and not hidden. Entry vehicle titles that name no subsystem the clusters above describe, such as general design, landing and dispersion studies of re-entry vehicles. No further subject in it is large enough to name.

60 records. [A Look 1964] [Allison and Newman 1966] [Atmospheric Re-Entry Vehicle Mechanics 2007] [Barte 1968] [Brown 1975] [Cavallo and Ferrara 1996] [Configuration Design for High-Lift 1972] [Coward and Nelson 1968] [Crenshaw 1971] [Crenshaw 1972] [Kummer and Siegel 1962] [DiFranco 1971] [Dohner 1968] [Fasola et al. 1955] [Ferraiuolo et al. 2006] [Fisher 1970] [Freeman et al. 1985] [Gardner 1966] [Grodsky and Mandour 1967] [Highley and Stone 1968] [Hough 1982c] [Houwink and Richards 1973] [Huot et al. 1992] [Johannessen 1964] [Kellas 2017] [Kirsch 1973] [Koryanov 2020] [Krenz 1965] [Kulleseid and Haas 1963] [Larson 1970] [Levin and Smith 1969] [Li et al. 2018c] [Martin 1989] [Montella et al. 2024] [Nelson 1985] [Nelson and Coward 1968] [Nikolaev et al. 1976] [Ohara et al. 2001] [Okolo et al. 2022] [Pavlov and Simakova 2021] [Pettus 1970] [Pfitzer 2018] [Platus 1979] [Platus 1980a] [Powell et al. 1986] [Rasky et al. 1993] [Re-Entry and Vehicle Design 1960] [Re-Entry Vehicle Particle Mechanics 1993] [Re-Entry Vehicle Soft-Recovery Techniques 1981] [Riedelbauch 1992a] [Deshmukh and Manwell 2024] [Schermerhorn and Demeritte 1960] [Seiff 1964] [Soumya et al. 2022] [Tausche et al. 2009] [Our Cosmology Correspondent 1970] [Vetter et al. 1992] [Waibel 1977] [Weiss 1969] [Луковкин 2018, Energy-absorbing characteristics]

Weight estimation and vehicle sizing

What the vehicle weighs and why, being structural weight estimation, mass properties and vehicle sizing for aircraft, launch vehicles and spacecraft.

57 records. [A Rapid Technique 1969] [Abensur 1994] [Adams 1974] [Ascani 1974] [Best 1964] [Bootle 1973] [Carreyette 1950] [Cerro et al. 2002] [Chaloff et al. 1974] [Chen et al. 2022c] [de Jong and Mulder 1987] [DeBilzan 1975] [Ding et al. 2023] [Figueiredo 2003] [Forrette 1964] [Fusaro et al. 2019] [Hajela and Chen 1988] [Handbook for Weight Estimating 1970] [Hayase 1974f] [Hayase 1974b] [Hayase 1974d] [Hayase 1974e] [Hayase 1974a] [Hayase 1974c] [Hayase 1974g] [Heineman 1969] [Hiyama 1974b] [Hiyama 1974a] [Holt and Monk 2009a] [Holt and Monk 2009b] [Hunter et al. 2002] [Cerro and Shore 1990] [Jex 1958] [Kibbey 2019] [Kihara et al. 2012] [Klein and Viswanathan 1975] [Martindale et al. 1974] [Miura et al. 1988] [Petts 1964] [Richie et al. 2006] [RlDHA 1969] [Saelman 1964] [Samuels 1982] [Sexstone 1998] [Simodynes 1974] [Solvey 1951] [Spunt 1970] [Swann 1960] [Switzky 1965] [Torenbeek 1972] [Waters 2013] [Wildermuth et al. 1974b] [Wildermuth et al. 1974a] [Wilkinson et al. 1976] [Williams 1989, Weight and cost forecasting for a] [Wu et al. 2012] [Zihao et al. 2014]

Orbits, ground tracks and astrodynamics

Where the ground track goes, being orbital mechanics, ground-track geometry and the satellite orbit theory that sets where a returning vehicle starts from.

43 records. [Alderson 1967] [Allan 1961] [Ambrosio et al. 1961] [Benedict 1963] [Bettner 1995] [Blitzer 1971] [Bosanquet 1958] [Bruce 1961] [Cohen and Spielberg 1965] [Diehl et al. 1992] [Endres 1967] [Enriquez 2025] [Etkin 1961] [Flight Performance 1969, Flight performance of the Atlas-A] [Garfinkel 1959] [Guan and Li 2025] [Holloway 1966] [I. V. Ioslovich 1965] [Jacchia and Slowey 1963] [Jacchia and Slowey 1964] [Kelley et al. 2010] [Kozak and Sharipov 2012] [Kraft and Townsend 1963] [Lavine 1963] [Moreira et al. 2020] [Mullins 1981] [Nelson 1965] [Preliminary Launch Vehicle Flight 1967] [Schooley 1962] [Sconzo 1966] [Shapiro 1994] [Shapiro and Bhat 1993] [Shapiro et al. 1993] [Space systems. Re-entry risk] [Space systems. Re-entry risk] [Stern 2004] [Surzhikov 2018] [Teles 1989] [Teles and Samii 1993] [The Orbit 1963] [The Orbit of Sputnik 1958] [Vinh and Dobrzelecki 1971] [Yamamoto et al. 1996]

Where the Framing Breaks Down

Treating PRIME through crossrange alone gets the programme wrong in at least three ways.

The vehicle was not only a manoeuvring experiment. It carried a heat shield the programme wanted measured, and ASSET had already been devoted to structures and heating. The sources disagree on how far PRIME was a heating experiment. The official history lists the acquisition of heat shield and aerodynamic data first among the five flight objectives, in Vitelli and Hallion, while Heppenheimer says that PRIME did not attempt to produce heating data because ASSET had covered it. Heating and manoeuvring were both objectives and the article’s keystone selects one. The wider class of entry vehicles, most of which never manoeuvred at all, fills the survey’s cluster on capsules and ballistic entry, and the field it sits inside is the survey as a whole.

The equilibrium glide is not what it flew. The model assumes a smooth glide that begins below circular speed. PRIME entered at 2.03 degrees from 400,000 feet, faster than the circular speed the model uses, and the programme’s computed trajectory dips and oscillates rather than gliding in equilibrium, so it reached the crossrange it did under conditions the model describes only approximately, in Vitelli and Hallion. That the numbers agree to one percent at the lower disputed lift-to-drag ratio is encouraging and is not proof.

The reference area is derived, not published. Everything in the thermal section inherits that. The crossrange result does not, and for that reason the crossrange is the keystone and the heating is not.

A fourth concerns the article’s framing. A vehicle whose recovery system failed twice in three flights is a programme about recovery at least as much as about entry, and it gets one short section here.

The Source Base

The research survey holds 4,642 research records drawn from the Technical Reports Server of the National Aeronautics and Space Administration, NASA, from the Defense Technical Information Center and from the Crossref index, of which 585 link to the NASA Technical Reports Server, 281 are Defense Technical Information Center reports by host or by that center’s identifier prefix, and the remaining 3,776 are other records reached through Crossref. The report servers therefore hold 866 records, being 18.7 percent of the survey, and its median publication year is 2009.

The subject has a deep period record. Of the 4,554 research records that carry a year, 1,056, or 23.2 percent, predate 1976, which reflects that lifting entry was worked out in a concentrated burst between about 1958 and 1972 and then largely left alone until the current revival. The period record names the subject in its own vocabulary. Where the modern literature says crossrange, the period reports say lateral range, roll modulation and maneuvering range, and the period work is found under those words.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when its address is on the NASA Technical Reports Server or on the Defense Technical Information Center’s own host, or when it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. The records this article’s own argument rests on are report primaries under that rule, among them the project’s official history in Vitelli and Hallion, Reed’s history of the lifting bodies, the X-24A data in Cochrane and Graham and McTigue, and the planform figures in Saltzman, Wang and Iliff. The rule does not reach the journal papers of the period, such as the lateral range analyses published by the American Institute of Aeronautics and Astronautics, so 18.7 percent is a lower bound on how much of the survey is first-hand.

Thin Subjects

Five subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with a hyphen read as a space. Where a row joins two groups of terms with the word together, a title must carry a term from each group.

Subject	Title terms counted	Records
the vehicle itself, by its own names	SV-5D, SV-5, X-23, X-23A, Project PRIME, PRIME vehicle, program, programme, reentry or re-entry	3
the bank angle that maximises crossrange	crossrange, cross range, lateral range together with bank, banking, roll, rolling	2
mid-air retrieval of a returning payload	mid air, midair, aerial recovery, aerial retrieval, in air capturing, in air capture, air snatch	20
the once-around recall requirement	once around, abort once, landing site access, recall, return to launch site, global landing	2
the effective heat of ablation	heat of ablation, heats of ablation, ablation heat	0

The vehicle itself is almost absent from the titles. Three titles name it by SV-5, X-23 or PRIME. One is the project’s official history in Vitelli and Hallion, one defines the entry environment of an assured crew return vehicle derived from the X-23 and X-24A in Campbell et al. 1996a, and the third, of 2023, gives the designation X-23 to a hypersonic glide vehicle in its title, in Butler et al. 2023. The flight record this article reconstructs therefore rests on the official history and on Reed rather than on a technical literature of the vehicle.

The bank angle that maximises crossrange has two titles, both of the period, lateral range control by banking in Baradell 1962 and roll modulation for maximum lateral range in Wagner 1965. The optimum of 45 degrees derived above is standard and is rarely the subject of a title.

Mid-air retrieval has a small literature of its own. Of the 20 titles, 5 concern returning boosters or reusable launch vehicles, and Catch a Falling Star 1993 records the parachute lessons of the Air Force space capsule mid-air recovery programme from 1959 to 1985, the technique this article records as already in service for returning film capsules when PRIME flew.

The recall requirement that motivated the vehicle has two titles, abort-once-around dispersion in Kyle 1975 and global landing site access by skip trajectories in Bryant 2002. The requirement’s history is in Heppenheimer rather than in a research literature.

No title names the effective heat of ablation, so the cross-check above that recovers 27.8 megajoules per kilogram from a published thickness stands on the relation shown rather than on a measured value in the survey.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. The programme acronyms do not identify its literature. PRIME collides with prime numbers and prime movers, and START with the Strategic Arms Reduction Treaty and with the ordinary English verb, so neither word admits a record to the survey. Beyond the acronyms, footprint belongs to carbon, water and ecological accounting and to tyre contact, recovery to economics and to waste heat, ablation to medicine, to laser materials processing and to the ablators of inertial fusion targets, charring to fire science, and entry to almost everything. Re-entry is also the return of prisoners to the community, the subject of a large criminal justice literature, and a term of cardiac electrophysiology and of software, and parachute also names a golden parachute in finance, a heart valve malformation, a mine ventilation stopping and a game for schoolchildren.

Several further families share this subject’s words and nothing else. Lateral motion of a vehicle is a term of art in railway dynamics and in road-vehicle lane keeping. Maneuvering range names an instrumented air combat facility off the East Coast, so the phrase also titles a construction quality assurance plan. Lateral range is also a term in search and detection theory. Glider, maneuvering and hovering all belong to underwater vehicles as well as to aircraft. Guidance, landing and control are shared with tactical missiles, small unmanned aircraft, rotorcraft and spacecraft operating in orbit, and a reading of this subject’s titles removes records of all four. Impact-angle and homing guidance of tactical missiles, the landing and flight control of drones and multirotors, helicopter flight test, and rendezvous, formation flight and debris impact on orbit are excluded, because none of them concerns a vehicle returning through the atmosphere.

Records that share a word with the subject and nothing else are excluded. Beyond the families above, the excluded classes include road, rail and ground transport, clinical medicine and biology, ion, surface and plasma physics, robotics and manufacturing, building heating and energy systems, combustion, fire science, boiling, critical heat flux and industrial heat exchange, thermal analysis as a laboratory chemistry discipline, atmospheric remote sensing and radio propagation, boundary-layer meteorology, airline operations, generic fluid mechanics and numerical mathematics, satellite communications, and electronics and materials. Records that are not works are excluded as well, meaning figures, tables, supplementary files, peer-review reports, notices of erratum, correction, retraction or withdrawal, and journal front matter such as reviewer lists and indexes, because a survey counts research works and those are parts of works or editorial events rather than works. A review of a book, a reference or definition entry, a notice such as a news item, a press release or an editorial preface, and a second deposit of a document the survey already holds, such as a report server copy or a reprint of a journal article, are not admitted either, because none of them is a further research work.

Some records of doubtful relevance are kept, because they bear on entry, flight or the design of a vehicle like this one without being about it. They are spacecraft attitude control by reaction jets, wheels and gyroscopes, crew physiology during entry and landing, the entry heating of meteoroids and micrometeorites, lunar and planetary landing and the erosion a landing rocket causes, aircraft structural weight estimation, rocket engine components, the propulsive landing of returning boosters, and the air-breathing hypersonic vehicle control literature, whose vehicles fly the same speed range without returning from orbit. 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, as reported by the accessible record. The SV-5D PRIME was built by Martin Marietta for the United States Air Force under the START programme. Four were built, three were launched on SLV-3 Atlas boosters from Vandenberg on 21 December 1966, 5 March 1967 and 19 April 1967, and the fourth flight was cancelled on 12 May 1967. The first two were lost to recovery-system failures and the third was recovered in mid-air by a JC-130B at 12,000 feet. The crossranges flown were zero, 654 miles and more than 710 miles in the official history’s narrative, taken here as 1,053 and 1,143 kilometres, while its summary table gives 499 and more than 710 nautical miles. The second flight held a constant bank of 46 degrees until terminal guidance. The third re-entered at 400,000 feet, 26,808 feet per second and 2.03 degrees, 1,360 nautical miles from launch. Martin’s design figure for the hypersonic lift-to-drag ratio was 1.2 or better. All of this is in Vitelli and Hallion. The vehicle was 6 feet 8 inches long, and its recorded weights run from about 800 to 895 pounds, with 894 used here. The surviving vehicle is at the National Museum of the United States Air Force.

Historical fact, on the designation. The nomenclature record shows a request for X-23A submitted on 16 November 1965 for the SV-5P, disapproved on 15 December 1965 on the stated ground that the aircraft was unmanned, and a late-1966 decision to seek X-23A for the SV-5D and X-24A for the SV-5P, of which only the second was ever submitted, in the standard reference on designations. This article reports that record and does not adjudicate between it and universal usage.

Engineering analysis, performed here and checkable. The equilibrium-glide crossrange relation, its closed form, the optimal bank angle of 45 degrees, the required crossrange of half the ground-track spacing, and the resulting lift-to-drag requirement of 0.978 by the closed form and 1.018 by exact integration, are all derived in this article from stated assumptions. The simultaneous solution of downrange and crossrange for the bank angle and lift-to-drag ratio, and the inversion of crossrange alone at a documented bank angle, are likewise derived here. The heating figures follow from the Sutton and Graves correlation applied to the equilibrium-glide density.

Inference, and flagged as such. That the vehicle’s effective lift-to-drag ratio through the manoeuvring phase was about 1.01 on the second flight and 1.05 on the third is an inference from the documented crossranges at the documented bank angles under the equilibrium-glide model. It rises to about 1.14 if the summary table’s nautical miles are right, and it lies between the programme’s trim curve at the flown angle of attack and that curve’s maximum, below Martin’s design figure of 1.2. The simultaneous solution of downrange and crossrange is not used as a measurement, because at the documented boost range it demands a bank angle the record contradicts. That nobody submitted the X-23A request because the 1965 refusal had said unmanned vehicles need none is a reading offered by the designation reference and is not documented.

Assumptions that everything downstream inherits. The reference area of 1.386 square metres is scaled from the X-24A and is not published for this vehicle. The entry speed of 25,200 feet per second, the nose radius of 0.1 metres, the hypersonic drag coefficient of unity, the ablator density of 550 kilograms per cubic metre, the parachute drag coefficient of 0.75, and the nominal lift-to-drag ratios of the capsules and the Space Shuttle orbiter in the comparison table are all assumed. The record’s own speeds run from 21,853 to 26,808 feet per second.

What the record does not settle. The vehicle’s lift-to-drag ratio in flight, beyond what the programme’s trim curve shows. Its actual reference area. Whether the crossranges are statute or nautical miles. The bank angle flown on the third flight. The stagnation heat load, which the programme’s stated figure and its computed heating curve give very differently. The peak deceleration and heating as measured, which were certainly telemetered and are not in the accessible literature. And the reason the X-23A request was never sent.

Out of Scope

The ASSET phase of the START programme, which deserves its own treatment. The Atlas SLV-3 as a launch vehicle. The X-24A and X-24B, which follow in this series. The mid-air retrieval technique and its origins in satellite film return. The detailed chemistry of charring ablators. The Space Shuttle crossrange requirement’s full political history, of which only the arithmetic is treated here.

Conclusion

PRIME asked whether a spacecraft could steer on the way home, and the answer was yes, by about a thousand kilometres.

The number matters more than it looks. A returning vehicle needs roughly half a ground-track spacing of crossrange to reach a chosen site without waiting, and at the equator that requires a lift-to-drag ratio of 0.978 by the relation the period used and 1.018 when the approximation in that relation is removed. A lifting body near unity is therefore not a modest capability but the threshold one, and the difference between it and a ballistic capsule is not a matter of degree. One can come home when it chooses and the other cannot.

One more measure shows how steeply that capability is bought. The reachable ground area scales as the crossrange half-width times the downrange depth, and those go as the square and the first power of the lift-to-drag ratio respectively, so

\[A_\text{footprint} \propto \left(\frac{L}{D}\right)^3 \tag{87}\]

The footprint goes as the cube. Raising the ratio from 1.0 to 1.2 enlarges the region a vehicle can reach by a factor of 1.73. Twenty percent of lift-to-drag ratio was therefore worth arguing about, and the disagreement in the sources matters.

The vehicle that demonstrated this weighed 894 pounds, flew three times, was lost twice on the way back, and carries a designation that was never requested for it. All four of those facts deserve to be kept.

Equations

This section collects the 87 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 87, 55 are established and 32 are bespoke. Mechanics are in International System units, with distances in metres or kilometres and speeds in metres per second, while the record quotes feet, statute miles, nautical miles and British thermal units, so each conversion is stated where it is made, and the entry speed of 25,200 feet per second, the working weight of 894 pounds and the derived reference area of 1.386 square metres are values the article assumes.

Equation 1, Lift-to-Drag Ratio. The lift-to-drag ratio is the ratio of lift to drag, equal to the ratio of the lift and drag coefficients. encyclopaedia entry on the lift-to-drag ratio

\[\frac{L}{D} = \frac{C_L}{C_D} \tag{1}\]

Equation 2, Cost of PRIME Relative to the X-20. The documented 70 million dollars of the Precision Recovery Including Maneuvering Entry programme against the 458 million dollars of the cancelled X-20 is a ratio of about one seventh. Reed official history of the project

\[\frac{70}{458} = 0.153 \tag{2}\]

Equation 3, Bespoke Departure of the Working Weight from the Lift-Off Weight. The working weight of 894 pounds that the article chooses among conflicting figures differs from the first vehicle’s documented lift-off weight of 895 pounds by about one tenth of a percent.

\[\frac{895}{894} - 1 = 0.11\% \tag{3}\]

Equation 4, Bespoke Planform Fill Ratio of the X-24A. The article defines the ratio of planform area to the product of length and span and evaluates it on the X-24A at about 0.58. Saltzman, Wang and Iliff

\[k_S = \frac{S_\text{X-24A}}{l\,b} = \frac{195.0}{24.50 \times 13.63} = 0.5839 \tag{4}\]

Equation 5, Bespoke Reference Area of the SV-5D. Applying the X-24A planform fill ratio to the length and span of the SV-5D assumes that the two shapes fill their bounding boxes alike and gives about 1.39 square metres.

\[S = k_S\, l\, b = 0.5839 \times 2.032 \times 1.168 = 1.386\ \text{m}^2 \tag{5}\]

Equation 6, Bespoke Planform Fill Ratio from an Alternative Source. The same fill ratio evaluated on the alternative X-24A dimensions is about 0.58, which makes the derived area 1.1 percent smaller. McTigue

\[\frac{191}{24.5 \times 13.5} = 0.5775 \tag{6}\]

Equation 7, Linear Scale Ratio of the SV-5D to the X-24A. The ratio of the documented lengths of the two vehicles is about 0.27.

\[\frac{l_\text{SV-5D}}{l_\text{X-24A}} = \frac{2.032}{7.47} = 0.272 \tag{7}\]

Equation 8, Weight Ratios of the SV-5D to the X-24A. The documented SV-5D weight is 7.5 percent of the X-24A launch weight and 16 percent of its empty weight. Reed Cochrane and Graham

\[\frac{894}{12{,}000} = 0.075, \qquad \frac{894}{5{,}500} = 0.163 \tag{8}\]

Equation 9, Radial Force Balance in a Gliding Entry. In the radial direction the vertical component of the rolled lift and the centrifugal force of the curved path together support the weight.

\[L\cos\phi + \frac{m V^2}{R} = W \tag{9}\]

Equation 10, Equilibrium Glide Lift Requirement. With the centrifugal term written through the speed as a fraction of circular speed, the lift a gliding vehicle needs is its weight less the part its speed already carries.

\[L\cos\phi = W\left(1 - \bar V^2\right) \tag{10}\]

Equation 11, Lift Required at Three Quarters of Circular Speed. At three quarters of circular speed the equilibrium glide needs a vertical lift of 0.44 of the weight.

\[1 - 0.75^2 = 0.4375 \tag{11}\]

Equation 12, Circular Satellite Speed at the Surface. Equating gravitational and centripetal acceleration at the mean Earth radius with standard gravity gives a circular speed of about 7,900 metres per second.

\[V_c = \sqrt{g R} = \sqrt{9.80665 \times 6.371\times 10^6} = 7{,}904\ \text{m/s} \tag{12}\]

Equation 13, Equations of Motion Along and Across the Path. Drag decelerates the vehicle along its path and the sideways component of the rolled lift turns its heading.

\[m\frac{dV}{dt} = -D, \qquad m V \frac{d\psi}{dt} = L\sin\phi \tag{13}\]

Equation 14, Heading Change per Unit Speed. Dividing the turning equation by the deceleration and substituting the force balance leaves a heading rate per unit speed that depends on the vehicle only through its lift-to-drag ratio. Vinh’s treatment of atmospheric flight trajectories Regan and Anandakrishnan on re-entry dynamics

\[\frac{d\psi}{dV} = -\frac{L}{D}\,\frac{\sin\phi}{V} \tag{14}\]

Equation 15, Heading Change in an Equilibrium Glide. Integrating from the entry speed gives a heading change proportional to the logarithm of the speed ratio at constant bank and lift-to-drag ratio. Vinh’s treatment of atmospheric flight trajectories Regan and Anandakrishnan on re-entry dynamics

\[\psi(V) = \frac{L}{D}\sin\phi \, \ln\frac{V_e}{V} \tag{15}\]

Equation 16, Heading Change from Circular to Quarter Circular Speed. At Martin’s design lift-to-drag ratio of 1.2 and a bank of 45 degrees, slowing to a quarter of circular speed turns the vehicle through about 67 degrees.

\[\psi = 1.2 \times \sin 45^\circ \times \ln 4 = 1.176\ \text{rad} = 67.4^\circ \tag{16}\]

Equation 17, Crossrange Rate per Unit Speed in the Small-Angle Form. Dividing the lateral rate by the deceleration with the heading taken as small, the step the period literature took, gives the crossrange accumulated per unit speed.

\[\frac{dy}{dV} = -\,\frac{V\psi\,(L/D)\cos\phi}{g\left(1-\bar V^2\right)} \tag{17}\]

Equation 18, Substitution in the Squared Speed Fraction. Writing the speed through the squared speed fraction $u$ and gravity through the circular speed prepares every factor of circular speed to cancel.

\[V = V_c\sqrt{u}, \qquad dV = \frac{V_c}{2\sqrt{u}}\,du, \qquad g = \frac{V_c^2}{R} \tag{18}\]

Equation 19, Crossrange Increment in the Squared Speed Fraction. After the substitution the crossrange increment depends on the Earth radius, the lift-to-drag ratio, the bank and the heading alone.

\[dy = -\frac{R}{2}\,\frac{L}{D}\cos\phi\,\frac{\psi\,du}{1-u} \tag{19}\]

Equation 20, Closed Crossrange Integral. Substituting the logarithmic heading solution turns the accumulated crossrange into the Earth radius times the squared lift-to-drag ratio, a bank factor and a single integral in the entry speed fraction.

\[y = \frac{R}{4}\left(\frac{L}{D}\right)^2 \sin\phi\cos\phi \; I(u_e), \qquad I(u_e) = \int_0^{u_e} \frac{\ln(u_e/u)}{1-u}\,du \tag{20}\]

Equation 21, Geometric Series Expansion. The reciprocal of one minus $u$ expands as a geometric series that converges for $u$ below one.

\[\frac{1}{1-u} = \sum_{n\ge 0} u^n \qquad \text{for} \quad 0 \le u < 1 \tag{21}\]

Equation 22, Logarithmic Moment Integral. Each term of the expanded integrand integrates to the reciprocal square of one more than its power.

\[\int_0^1 (-\ln u)\,u^n\,du = \frac{1}{(n+1)^2} \tag{22}\]

Equation 23, Crossrange Integral at Circular Entry as the Basel Sum. For entry at circular speed the integral is the sum of reciprocal squares, which equals $\pi^2/6$.

\[I(1) = \int_0^1 \frac{-\ln u}{1-u}\,du = \sum_{k\ge 1} \frac{1}{k^2} = \frac{\pi^2}{6} = 1.6449 \tag{23}\]

Equation 24, Double-Angle Identity for the Bank Factor. The product of the sine and cosine of the bank angle is half the sine of twice the angle.

\[\sin\phi\cos\phi = \tfrac{1}{2}\sin 2\phi \tag{24}\]

Equation 25, Stationarity Condition of the Bank Factor. The first derivative of the bank factor vanishes where the cosine of twice the bank is zero and the second derivative there is negative, so the point is a maximum.

\[\frac{d}{d\phi}\left(\tfrac{1}{2}\sin 2\phi\right) = \cos 2\phi = 0, \qquad \frac{d^2}{d\phi^2} = -2\sin 2\phi = -2 < 0 \tag{25}\]

Equation 26, Optimum Bank Angle for Crossrange. Crossrange is maximised at a bank of 45 degrees, where the bank factor is one half, independent of the vehicle.

\[\phi_\text{opt} = 45^\circ, \qquad \sin\phi\cos\phi = \tfrac{1}{2} \tag{26}\]

Equation 27, Maximum Crossrange of an Equilibrium Glide. Combining the optimum bank with the circular-entry integral gives a maximum crossrange equal to $\pi^2/48$ of the Earth radius times the square of the lift-to-drag ratio.

\[\frac{y_\text{max}}{R} = \frac{\pi^2}{48}\left(\frac{L}{D}\right)^2 = 0.2056\left(\frac{L}{D}\right)^2 \tag{27}\]

Equation 28, Maximum Crossrange at a Lift-to-Drag Ratio of 1.2. At Martin’s design ratio of 1.2 the closed form gives about 1,890 kilometres of crossrange from circular entry.

\[y_\text{max} = 0.2056 \times 1.2^2 \times 6.371\times 10^6 = 1.886\times 10^6\ \text{m} = 1{,}019\ \text{nmi} \tag{28}\]

Equation 29, Bespoke Final Heading at the End of the Glide. Evaluating the heading solution at a glide end taken by the article as one percent of circular speed shows the heading passing half a turn for ratios near one.

\[\psi_\text{end} = \frac{L}{D}\sin 45^\circ \ln\frac{V_e}{0.01\,V_c} \tag{29}\]

Equation 30, Speed at Which the Heading Reaches Half a Turn. Lateral displacement stops accumulating where the sine of the heading returns to zero, which the logarithmic heading solution places at a speed exponentially small in the reciprocal of the ratio times the bank sine.

\[\sin\psi = 0 \quad \Longrightarrow \quad \psi = 180^\circ, \qquad V_{180} = V_e\exp\left(-\frac{\pi}{(L/D)\sin\phi}\right) \tag{30}\]

Equation 31, Sidereal Rotation Rate of the Earth. The rotation rate relative to the fixed stars is two pi radians per sidereal day of 86,164 seconds.

\[\omega_E = \frac{2\pi}{86{,}164\ \text{s}} = 7.292\times 10^{-5}\ \text{rad/s} \tag{31}\]

Equation 32, Bespoke Ground Track Spacing in Longitude. The Earth turns through about 22.6 degrees in one orbit for a period the article takes as a nominal 90 minutes.

\[\Delta\lambda = \omega_E T = 7.292\times 10^{-5} \times 5400 = 0.3937\ \text{rad} = 22.56^\circ \tag{32}\]

Equation 33, Bespoke Ground Track Spacing at the Equator. The longitude spacing of the nominal 90 minute orbit becomes about 2,510 kilometres of ground distance at the equator.

\[d = R\,\Delta\lambda = 6.371\times 10^6 \times 0.3937 = 2{,}509\ \text{km} \tag{33}\]

Equation 34, Bespoke Once-per-Orbit Crossrange Requirement. The article requires that any site be reached on one pass or the next, which sets the crossrange at half the equatorial track spacing of the nominal 90 minute orbit.

\[y_\text{req} = \tfrac{1}{2} R\,\Delta\lambda = 1{,}254\ \text{km} \tag{34}\]

Equation 35, Bespoke Required Lift-to-Drag Ratio in Closed Form. Inverting the maximum crossrange relation on the once-per-orbit requirement gives a required lift-to-drag ratio of about 0.98.

\[\frac{L}{D} = \sqrt{\frac{y_\text{req}/R}{\pi^2/48}} = \sqrt{\frac{0.1968}{0.2056}} = 0.978 \tag{35}\]

Equation 36, Bespoke Required Lift-to-Drag Ratio by Exact Integration. Bisecting the exact integration against the same requirement, rather than using the small-angle closed form, gives a required ratio of about 1.02.

\[\left(\frac{L}{D}\right)_\text{exact} = 1.018 \tag{36}\]

Equation 37, Bespoke Latitude Dependence of the Requirement. Because the track spacing carries the cosine of latitude, the once-per-orbit requirement falls with latitude and the required ratio falls with its square root.

\[y_\text{req}(\varphi) = \tfrac{1}{2} R\,\Delta\lambda\cos\varphi, \qquad \left(\frac{L}{D}\right)_\text{req}(\varphi) = \left(\frac{L}{D}\right)_\text{req}(0)\sqrt{\cos\varphi} \tag{37}\]

Equation 38, Crossrange Ratio between the Disputed Lift-to-Drag Ratios. Because crossrange goes as the square of the ratio, the twenty percent difference between 1.2 and 1.0 becomes a forty-four percent difference in crossrange.

\[\frac{y(1.2)}{y(1.0)} = \left(\frac{1.2}{1.0}\right)^2 = 1.44 \tag{38}\]

Equation 39, Haversine Great-Circle Distance. The haversine formula gives the great-circle distance between Vandenberg Air Force Base and the recovery area near Kwajalein as about 7,790 kilometres. official history of the project

\[d = 2R\arcsin\sqrt{\sin^2\frac{\Delta\varphi}{2} + \cos\varphi_1\cos\varphi_2\sin^2\frac{\Delta\lambda}{2}} = 7{,}787\ \text{km} \tag{39}\]

Equation 40, Downrange Rate per Unit Speed. Dividing the along-path rate by the deceleration gives the downrange accumulated per unit speed in the equilibrium glide.

\[\frac{dx}{dV} = -\frac{V\,(L/D)\cos\phi}{g\left(1-u\right)} \tag{40}\]

Equation 41, Downrange Increment in the Squared Speed Fraction. The same substitution cancels every factor of circular speed and leaves an elementary integrand.

\[dx = -\frac{R}{2}\,\frac{L}{D}\cos\phi\,\frac{du}{1-u} \tag{41}\]

Equation 42, Downrange of an Equilibrium Glide. Integrating gives a downrange linear in the lift-to-drag ratio and logarithmic in one over one minus the entry speed fraction.

\[x = \frac{L}{D}\cos\phi \;\frac{R}{2}\ln\frac{1}{1-u_e} \tag{42}\]

Equation 43, Downrange Lost at the Optimum Bank. Banking at 45 degrees costs the fraction one minus the cosine of the bank, about twenty-nine percent, of the downrange flown wings level.

\[1 - \cos 45^\circ = 0.293 \tag{43}\]

Equation 44, Bespoke Pair Solve for Bank and Lift-to-Drag Ratio. The article treats the documented crossrange and downrange as two equations and divides one by the square of the other to recover the bank angle and then the ratio, an inversion that rests on the entry speed and boost range it assumes.

\[\tan\phi = \frac{y/B}{(x/A)^2}, \qquad \frac{L}{D} = \frac{x/A}{\cos\phi} \tag{44}\]

Equation 45, Bespoke Exact Model Errors at the Disputed Ratios. The exact model, flown from the assumed entry speed, under-predicts the demonstrated 1,143 kilometres by 8.8 percent at a ratio of 1.0 and over-predicts it by 27 percent at 1.2.

\[\frac{1{,}042.7}{1{,}143} - 1 = -8.8\%, \qquad \frac{1{,}452.9}{1{,}143} - 1 = +27\% \tag{45}\]

Equation 46, Bespoke Exact Crossrange at Martin’s Design Ratio. The exact integration from circular speed at a ratio of 1.2 gives 1,696 kilometres, which converts to about 1,054 statute miles, close to Martin’s claim of 1,000 miles.

\[\frac{1{,}696}{1.609} = 1{,}054\ \text{statute miles} \tag{46}\]

Equation 47, Documented Boost Range in Kilometres. The 1,360 nautical miles from launch to entry interface on the ground-track chart is about 2,519 kilometres. official history of the project

\[1{,}360 \times 1.852 = 2{,}518.7\ \text{km} \tag{47}\]

Equation 48, Documented Entry Speed Fraction Above Unity. The documented entry speed of 26,808 feet per second exceeds circular speed, so the squared speed fraction is above one, where the downrange relation has no finite value. official history of the project

\[u_e = \left(\frac{26{,}808}{25{,}933}\right)^2 = 1.069 > 1 \tag{48}\]

Equation 49, Bespoke Exact Crossrange Inversions at a Documented Bank. At the second flight’s documented bank of 46 degrees the exact integration from the assumed entry speed needs ratios of 1.007 and 1.053 to reach the second and third flight crossranges.

\[y_\text{exact}\left(1.007,\ 46^\circ\right) = 1{,}052.5\ \text{km}, \qquad y_\text{exact}\left(1.053,\ 46^\circ\right) = 1{,}142.6\ \text{km} \tag{49}\]

Equation 50, Third Flight Crossrange Read as Nautical Miles. Read as nautical miles, the 710 miles of the third flight is about 1,315 kilometres. official history of the project

\[710 \times 1.852 = 1{,}314.9\ \text{km} \tag{50}\]

Equation 51, Equilibrium Glide Density and Lift Parameter. The equilibrium glide force balance fixes the density at each speed in terms of the lift parameter, the weight per unit lifting area.

\[\rho = \frac{2\beta_L(1-u)}{V^2\cos\phi}, \qquad \beta_L = \frac{W}{S\,C_L} \tag{51}\]

Equation 52, Ballistic Coefficient. The ballistic coefficient is the weight divided by the product of reference area and drag coefficient.

\[\beta = \frac{W}{S\,C_D} \tag{52}\]

Equation 53, Ratio of Ballistic Coefficient to Lift Parameter. The ballistic coefficient and the lift parameter stand in the ratio of the lift to the drag coefficient, which is the lift-to-drag ratio.

\[\frac{\beta}{\beta_L} = \frac{C_L}{C_D} = \frac{L}{D} \tag{53}\]

Equation 54, Bespoke Ballistic Coefficient of the SV-5D. The working weight on the derived reference area at an assumed hypersonic drag coefficient of one gives a ballistic coefficient of about 2,870 newtons per square metre.

\[\beta = \frac{3{,}977}{1.386 \times 1.0} = 2{,}869\ \text{N/m}^2 = 60\ \text{lb/ft}^2 \tag{54}\]

Equation 55, Sutton and Graves Stagnation Heating. The Sutton and Graves relation gives the stagnation-point convective heat flux as a constant times the square root of density over nose radius times the cube of speed, in metric units for air.

\[\dot q_s = k\sqrt{\frac{\rho}{R_n}}\,V^3, \qquad k = 1.7415\times 10^{-4} \tag{55}\]

Equation 56, Stagnation Heating Along the Equilibrium Glide. Substituting the glide density makes the stagnation heat flux proportional to $u\sqrt{1-u}$.

\[\dot q_s \propto \sqrt{\frac{1-u}{u}}\;u^{3/2} = u\sqrt{1-u} \tag{56}\]

Equation 57, Condition for Peak Stagnation Heating. Setting the derivative of the squared heating function to zero places its maximum at a squared speed fraction of two thirds.

\[\frac{d}{du}\left[u^2(1-u)\right] = 2u - 3u^2 = 0 \quad \Longrightarrow \quad u = \tfrac{2}{3} \tag{57}\]

Equation 58, Speed of Peak Stagnation Heating. Peak heating in an equilibrium glide falls at about 82 percent of circular speed, about 6,450 metres per second, for any vehicle.

\[u = \tfrac{2}{3}, \qquad V = 0.8165\,V_c = 6{,}454\ \text{m/s} \tag{58}\]

Equation 59, Bespoke Density at Peak Heating. The glide balance at the derived lift parameter of 2,391 newtons per square metre and a bank of 45 degrees gives the density at the peak heating speed.

\[\rho = \frac{2 \times 2{,}391 \times \tfrac{1}{3}}{6{,}454^2 \times \cos 45^\circ} = 5.41\times 10^{-5}\ \text{kg/m}^3 \tag{59}\]

Equation 60, Bespoke Peak Stagnation Heat Flux. The Sutton and Graves relation at the peak heating speed and density with a nose radius the article assumes as 0.1 metres gives about 109 watts per square centimetre.

\[\dot q_{s,\text{max}} = 1.7415\times 10^{-4}\sqrt{\frac{5.41\times 10^{-5}}{0.1}}\,\left(6{,}454\right)^3 = 109\ \text{W/cm}^2 \tag{60}\]

Equation 61, Flight Heating Rate in Watts per Square Centimetre. The heating rate of 480 British thermal units per square foot per second read from the programme’s figure is about 545 watts per square centimetre. official history of the project

\[480 \times 1.1357 = 545\ \text{W/cm}^2 \tag{61}\]

Equation 62, Bespoke Altitude of Peak Heating. Inverting an exponential atmosphere of an assumed scale height of 7,160 metres at the inferred peak heating density places the peak near 72 kilometres.

\[h = -H\ln\frac{\rho}{\rho_0} = -7{,}160\ln\left(4.42\times 10^{-5}\right) = 71.8\ \text{km} \tag{62}\]

Equation 63, Stagnation Heat Load of an Equilibrium Glide. Integrating the Sutton and Graves flux over the glide in closed form gives the stagnation heat load in terms of the lift-to-drag ratio, the bank, the lift parameter, the nose radius and the entry speed fraction.

\[Q = k\,\frac{L}{D}\sqrt{\cos\phi}\sqrt{\frac{2\beta_L}{R_n}}\frac{V_c^3}{g}\cdot\frac{\arcsin a - a\sqrt{1-a^2}}{2} \tag{63}\]

Equation 64, Bespoke Duration of the Equilibrium Glide. Integrating the time over the glide from the assumed entry speed of 25,200 feet per second at a ratio of 1.2 and a bank of 45 degrees gives about 24 minutes.

\[t = \frac{L}{D}\cos\phi\,\frac{V_c}{g}\,\text{artanh}\,\sqrt{u_e} = 1{,}452\ \text{s} \tag{64}\]

Equation 65, Effective Heat of Ablation. The effective heat of ablation is the heat load divided by the areal mass of the heat shield.

\[H_\text{eff} = \frac{Q}{\rho_\text{abl}\,t_\text{abl}} \tag{65}\]

Equation 66, Bespoke Heat of Ablation at the Thick Shield. The model heat load over a shield of 2.75 inches at an assumed charring-ablator density of 550 kilograms per cubic metre implies about 28 megajoules per kilogram.

\[\rho_\text{abl}t_\text{abl} = 550 \times 0.0699 = 38.4\ \text{kg/m}^2, \qquad H_\text{eff} = \frac{1.067\times 10^9}{38.4} = 27.8\ \text{MJ/kg} \tag{66}\]

Equation 67, Documented Stagnation Heat Load in Metric Units. The documented 7,000 British thermal units per square foot is about 7.95 kilojoules per square centimetre. official history of the project

\[7{,}000 \times 11{,}357 = 7.95\times 10^7\ \text{J/m}^2 = 7.95\ \text{kJ/cm}^2 \tag{67}\]

Equation 68, Floor on the Heat Load from the Flight Heating Curve. A heating rate above 160 British thermal units per square foot per second for more than 300 seconds, read from the programme’s figure, implies a heat load of at least 48,000 British thermal units per square foot.

\[160 \times 300 = 48{,}000\ \text{BTU/ft}^2 \tag{68}\]

Equation 69, Deceleration in an Equilibrium Glide. The glide balance gives a deceleration in units of gravity of one minus the squared speed fraction over the lift-to-drag ratio times the cosine of bank.

\[\frac{a}{g} = \frac{1-u}{(L/D)\cos\phi} \tag{69}\]

Equation 70, Bespoke Deceleration at Entry. At the squared speed fraction of 0.944 that the assumed entry speed of 25,200 feet per second implies, the deceleration is about 0.07 of gravity.

\[\frac{a}{g} = \frac{1 - 0.944}{1.2\cos 45^\circ} = 0.066 \tag{70}\]

Equation 71, Deceleration at the End of the Glide. As the speed fraction falls to zero the deceleration at a ratio of 1.2 and a bank of 45 degrees rises to about 1.18 of gravity.

\[\frac{a}{g} = \frac{1}{1.2\cos 45^\circ} = 1.18 \tag{71}\]

Equation 72, Bespoke Allen and Eggers Peak Ballistic Deceleration. The Allen and Eggers peak deceleration of a ballistic entry from the documented entry state, with the scale height the article assumes as 7,160 metres, is about 6.2 of gravity. official history of the project

\[a_\text{max} = \frac{V_e^2\sin\gamma_e}{2eH} = \frac{\left(8{,}171\right)^2\sin 2.03^\circ}{2e \times 7{,}160} = 60.8\ \text{m/s}^2 = 6.20\ g \tag{72}\]

Equation 73, Bespoke Ratio of Ballistic to Lifting Peak Deceleration. The ballistic peak deceleration is about five times the lifting one, a ratio that inherits the assumed scale height.

\[\frac{6.20}{1.18} = 5.25 \tag{73}\]

Equation 74, Speed of Sound at Ballute Deployment. At the standard atmosphere temperature of 226.5 kelvin at 30.4 kilometres the speed of sound is about 302 metres per second.

\[a = \sqrt{\gamma R_\text{air} T} = \sqrt{1.4 \times 287 \times 226.5} = 302\ \text{m/s} \tag{74}\]

Equation 75, Dynamic Pressure at Ballute Deployment. At Mach 2 and the standard atmosphere density at deployment altitude the dynamic pressure is about 3,350 pascals.

\[q = \tfrac{1}{2}\rho V^2 = \tfrac{1}{2} \times 0.0184 \times 603^2 = 3{,}350\ \text{Pa} = 70\ \text{lb/ft}^2 \tag{75}\]

Equation 76, Area of the Recovery Parachute. The documented 47 foot canopy diameter gives a nominal area of about 161 square metres.

\[S_p = \frac{\pi D^2}{4} = \frac{\pi \times 14.33^2}{4} = 161\ \text{m}^2 \tag{76}\]

Equation 77, Bespoke Descent Rate under the Recovery Parachute. The terminal descent rate of the working weight under the canopy at sea level with an assumed drag coefficient of 0.75 is about 7.3 metres per second.

\[V_d = \sqrt{\frac{2W}{\rho\,C_D S_p}} = \sqrt{\frac{2 \times 3{,}977}{1.225 \times 0.75 \times 161}} = 7.33\ \text{m/s} \tag{77}\]

Equation 78, Bespoke Descent Rate at 10,000 Feet. Scaling the descent rate by the square root of the standard atmosphere density ratio to 10,000 feet gives 28 feet per second at the assumed drag coefficient.

\[V_d = 7.33\sqrt{\frac{1.225}{0.9046}} = 8.53\ \text{m/s} = 28.0\ \text{ft/s} \tag{78}\]

Equation 79, Bespoke Drag Coefficient for the Specified Descent Rate. The documented 25 feet per second at 10,000 feet requires a drag coefficient of about 0.94 for the working weight on the nominal canopy area.

\[C_D = 0.75\left(\frac{28.0}{25}\right)^2 = 0.94 \tag{79}\]

Equation 80, Unit Conversions of the Quoted Entry Speeds. The quoted entry speeds of 14,900 miles an hour and 26,808 feet per second convert to 21,853 feet per second and 18,278 miles an hour.

\[14{,}900\ \text{mph} = 21{,}853\ \text{ft/s}, \qquad 26{,}808\ \text{ft/s} = 18{,}278\ \text{mph} \tag{80}\]

Equation 81, Bespoke Launch Site Displacement in One Orbit. Vandenberg moves through the full track spacing of the nominal 90 minute orbit at its own latitude, about 2,060 kilometres.

\[d_\text{VAFB} = R\,\Delta\lambda\cos\varphi = 6.371\times 10^6 \times 0.3937 \times \cos 34.74^\circ = 2{,}061\ \text{km} \tag{81}\]

Equation 82, Bespoke Agreement with the Shuttle Crossrange Requirement. The displacement from the nominal 90 minute orbit agrees with the stated 1,100 nautical mile requirement to 1.2 percent.

\[\frac{2{,}061 - 2{,}037}{2{,}037} = 1.2\ \text{percent} \tag{82}\]

Equation 83, Lift-to-Drag Ratio for the Shuttle Crossrange Requirement. Putting the stated 1,100 nautical mile requirement through the closed-form maximum crossrange relation gives a required ratio of about 1.25. Heppenheimer’s history of the Space Shuttle decision

\[\frac{L}{D} = \sqrt{\frac{2{,}037/6{,}371}{0.2056}} = 1.25 \tag{83}\]

Equation 84, Demonstrated Fraction of the Shuttle Requirement. The demonstrated 1,143 kilometres is 56 percent of the 2,037 kilometre Shuttle requirement.

\[\frac{1{,}143}{2{,}037} = 0.56 \tag{84}\]

Equation 85, Bespoke Crossrange of a Blunt Capsule. The closed form at a capsule lift-to-drag ratio the article assumes as a nominal 0.3 gives about 118 kilometres of crossrange.

\[y = \pi^2/48 \times 0.3^2 \times 6.371\times 10^6 = 118\ \text{km} \tag{85}\]

Equation 86, Bespoke Capsule Fraction of the Once-per-Orbit Requirement. The capsule’s crossrange by exact integration is about nine percent of the once-per-orbit requirement of the nominal 90 minute orbit.

\[\frac{117}{1{,}254} = 0.09 \tag{86}\]

Equation 87, Bespoke Footprint Scaling with Lift-to-Drag Ratio. Taking the reachable area as the crossrange half-width times the downrange depth, the article finds it grows as the cube of the lift-to-drag ratio.

\[A_\text{footprint} \propto \left(\frac{L}{D}\right)^3 \tag{87}\]

Notation

• $L$, the lift
• $D$, the drag, and in Equation 76 the parachute diameter
• $C_L$, the lift coefficient
• $C_D$, the drag coefficient
• $k_S$, the ratio of planform area to the product of length and span
• $\phi$, the bank angle, the angle through which the lift vector is rolled from vertical
• $\bar V$, the speed as a fraction of circular satellite speed
• $V_c$, the circular satellite speed at the surface
• $V_e$, the entry speed
• $R$, the mean radius of the Earth
• $\psi$, the heading angle
• $u$, the square of the speed as a fraction of circular speed, with $u_e$ its value at entry
• $y$, the crossrange, with $y_\text{max}$ its maximum and $y_\text{req}$ the requirement
• $x$, the downrange
• $\omega_E$, the sidereal rotation rate of the Earth
• $\Delta\lambda$, the spacing in longitude of successive ground tracks
• $\varphi$, the latitude
• $\beta_L$, the lift parameter, the weight per unit area per unit lift coefficient
• $\beta$, the ballistic coefficient
• $\dot q_s$, the stagnation-point heat flux
• $R_n$, the nose radius
• $H$, the atmospheric scale height
• $Q$, the stagnation heat load
• $H_\text{eff}$, the effective heat of ablation
• $\rho$, the air density
• $\gamma_e$, the flight path angle at entry
• $S_p$, the nominal area of the recovery parachute
• $V_d$, the descent rate under the parachute

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