The Orbital Sciences X-34 was cancelled in the same NASA announcement as the vehicle in the previous article, on 1 March 2001, and the General Accounting Office gives both terminations the same cause, significant cost increases. Almost nothing else about the two is alike. The X-33 was enormous, used liquid hydrogen, carried an untried engine architecture, and failed a structural test in a way that made a photograph. The X-34 was small, burned kerosene, used an engine designed to be cheap rather than good, was finished, was towed and carried through the air by an airliner turned launch aircraft, and was cancelled without anything on the vehicle breaking at all. This is the thirty-fifth article in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, the X-24, the X-25, the X-26, the X-27, the X-28, the X-29, the X-30, the X-31, the X-32, and the X-33.

The difference that matters is not size or propellant. It is that the two programmes had different kinds of unknown. The X-33’s binding unknown was mass. Mass obeys a conservation law, a demonstrator can be weighed, and what came back was a number that did not close. The X-34’s binding unknown was cost, and cost obeys nothing.

The Research Question

The keystone is whether cost can be attacked as an engineering quantity, and what it costs to try.

The keystone is unusual for this series, and the difficulty should be stated at once. Every previous article has dimensioned an aircraft against a physical unknown. A drag rise, a heating rate, a divergence speed, a mass fraction. Those quantities have units, conservation laws and instruments. Cost has none of the three. It has no equation of state, it cannot be measured on the article, and every number attached to it is a forecast and none is a reading.

Why That Is Not a Reason to Refuse the Subject

The cost argument left physical fingerprints, and those can be computed. A programme that attacks cost does it by simplifying, and every simplification has a performance price with units. The X-34 chose an engine cooled by being destroyed, a propellant of lower specific impulse and about three times the bulk density of hydrogen and oxygen, an aeroplane to carry it to altitude instead of a launch pad, and a level of system testing that a later review found insufficient. Three of those four choices can be priced in kilograms, seconds and newtons. The fourth could not be priced at all until somebody tried to fly the vehicle.

The Question Behind the Question

A cheap demonstrator demonstrates that demonstrators can be cheap. Whether it demonstrates that an operational vehicle can be cheap is a separate claim and a much weaker one, and the distinction runs through this article.

The programme’s answer did not come from a test. It arrived as an arithmetic correction. Working from the restructure plan of June 2000, the General Accounting Office estimated the total requirement at about 348 million dollars against roughly 86 million budgeted in 1996, and the reason the agency gave was that reaching an acceptable level of risk needed more government technical insight, more hardware testing and more integrated assessment. Those are the things a low-cost programme removes.

Programme Origin

What the Agency Wanted and What It Bought

The X-34 belongs to the same family as the X-33 and answers a different half of the same question. Both were technology demonstrators under a reusable launch vehicle programme whose stated ambition was an order-of-magnitude reduction in the cost of reaching orbit. The X-33 pursued that by attacking the mass fraction, which is the physics of the problem. The X-34 pursued it by attacking the price of the hardware, which is not.

The contract went to Orbital Sciences in August 1996 as a fixed-price award of 49.5 million dollars, and with its later options and the engine project the vehicle was budgeted at about 86 million dollars, which set it against the X-33 at more than a billion. A ratio of that size is the argument in a single number, and testing whether the ratio survives contact with the vehicles is the work of the Where the Framing Breaks Down section.

The Company and the Method

Orbital Sciences had already done the thing the X-34 needed. The company operated an air-launched satellite booster carried by a modified airliner, so the carrier aircraft, the release mechanism, the separation problem and the operating culture existed before the X-34 did. A programme that reuses an existing carrier does not pay for one, and the saving it makes is a real one.

The Fastrac Engine

The Fastrac engine, also designated MC-1, was designed by a government laboratory to be cheap. It used a gas generator cycle, commercial parts where they would serve, a simplified turbopump, and a combustion chamber and nozzle cooled not by circulating its own fuel but by being consumed. An engine reported at around 1.2 million dollars in its development phase, against a production target near 350,000, is a different kind of object from the X-33’s engine, and the Sizing section takes it apart.

Sizing From First Principles

Three Quoted Numbers That Do Not Close

Begin with the engine figures as they are usually quoted, because they contain a discrepancy that turns out to be informative. They are a vacuum thrust of 60,000 pounds force, a vacuum specific impulse of 314 seconds, and a total propellant mass flow of 91.90 kilograms per second, as the engine’s usual specification gives them.

Those three quantities are related by the definition of specific impulse. Writing $F$ for thrust, $\dot{m}$ for mass flow and $g_0$ for standard gravity,

\[I_{sp} = \frac{F}{\dot{m} \, g_0} \tag{1}\]

in the form Sutton sets out for propulsion analysis.

Converting the thrust to 266,893 newtons, which is 266.9 kilonewtons, and substituting,

\[I_{sp} = \frac{266{,}893}{91.90 \times 9.80665} = 296.14 \ \text{s} \tag{2}\]

against a quoted 314, which is 5.69 percent adrift. A disagreement of that size in a quoted set is either an error or a distinction, and here it is a distinction, though not the one it first appears to be.

The Gap Is the Nozzle

The engine’s development status report resolves it. Ballard, Olive and Turner state that the engine runs at one rated power level, nominally 60,000 pounds force in vacuum with the 15:1 nozzle used for ground testing and slightly higher with the 30:1 nozzle built for the X-34. Their engine schematic gives both sets, 59,956 pounds force at 296 seconds for the 15:1 nozzle and 63,939 pounds force at 314 seconds for the 30:1 nozzle, at an engine mixture ratio of 2.17 in both. The usual quotation pairs the ground nozzle’s thrust with the flight nozzle’s impulse.

The same schematic gives the flows, 195.5 pounds per second into the main chamber and 7.10 into the gas generator, so the total is

\[\dot{m} = \left(195.5 + 7.10\right) \times 0.45359237 = 202.6 \times 0.45359237 = 91.90 \ \text{kg/s} \tag{3}\]

which is the quoted flow, now derived from the primary record. Put back through the definition with each nozzle’s own thrust, 284,415 newtons for the flight nozzle and 266,698 for the ground nozzle,

\[I_{sp}^{30} = \frac{284{,}415}{91.90 \times 9.80665} = 315.6 \ \text{s} \qquad I_{sp}^{15} = \frac{266{,}698}{91.90 \times 9.80665} = 295.9 \ \text{s} \tag{4}\]

with the superscript naming the area ratio, against the published 314 and 296. Each configuration closes on its own figures to within half a percent, and the 5.69 percent gap was never in the engine. The 296.14 seconds the quoted set implies is, to within rounding, the ground nozzle’s impulse.

The Cycle Is Smaller Than the Gap

A gas generator engine does not send all its propellant through the nozzle. A small stream is burned fuel-rich in a separate chamber to drive the turbopump, and the exhaust from that turbine is dumped overboard rather than expanded through the main nozzle, where it would contribute thrust. So the engine’s specific impulse is lower than its chamber’s.

Writing $\dot{m}_c$ for the chamber flow and $\dot{m}_{gg}$ for the gas generator flow, the schematic gives the generator’s share directly,

\[\frac{\dot{m}_{gg}}{\dot{m}} = \frac{7.10}{202.6} = 0.0350 \tag{5}\]

which is 3.50 percent of the total. A gas generator typically spends between three and seven percent of the propellant it pumps, a range set out in Huzel and Huang’s design text on liquid propellant rocket engines, so the published cycle lands inside the range the architecture uses, near its economical end.

The same figures give what the cycle costs the vehicle. The chamber flow is 195.5 pounds per second, or 88.68 kilograms per second, and taking the turbine exhaust as contributing no thrust, the chamber alone would deliver

\[I_{sp,c} = \frac{F}{\dot{m}_c \, g_0} = \frac{284{,}415}{88.68 \times 9.80665} = 327.05 \ \text{s} \tag{6}\]

against the 315.59 seconds the whole flow gives, so

\[\Delta I_{sp} = 327.05 - 315.59 = 11.46 \ \text{s} \tag{7}\]

which is an upper bound, because a turbine exhaust duct recovers a little thrust. The two percentages are identical by necessity. The fractional impulse the cycle costs equals the fractional flow the cycle takes, exactly, because both are one minus the same ratio.

Two clusters below, on liquid rocket engines, turbopumps and combustion and on rocket nozzles, plumes and expansion, hold the gas generator and turbopump literature behind these figures. It includes the fuel-rich generator designs of Kwon et al. 2004 and Jeon et al. 2004 and the Fastrac’s generator testing in Nesman and Dennis 1999.

A Fourth Number That Closes on the Other Three

The vehicle’s propellant load and the engine’s flow rate give a burn time, and it can be checked against the longest engine test the programme published.

\[t_b = \frac{m_p}{\dot{m}} = \frac{13{,}600}{91.90} = 148.0 \ \text{s} \tag{8}\]

The longest hot fire in the engine development record ran 159.03 seconds against 159.0 planned, in a test on 14 May 1999 recorded in the test table of the development status report on the MC-1 engine. Writing $t_{\text{test}}$ for that duration, the margin over the mission burn is

\[\frac{t_{\text{test}}}{t_b} = \frac{159.03}{148.0} = 1.075 \tag{9}\]

The masses, the flow rate and the test duration were published separately and by different parts of the programme, and they describe one vehicle burning one propellant load with about seven and a half percent to spare. Had the tested duration come out below the mission burn, one of the four numbers would have been wrong.

What the Vehicle Could Reach

The engine’s figures do not by themselves say what the vehicle can do with it, and the answer is a check on the published masses. The effective exhaust velocity is the flight engine’s published impulse of 314 seconds, which already carries the cost of the cycle, times standard gravity,

\[v_e = I_{sp} \, g_0 = 314 \times 9.80665 = 3{,}079.3 \ \text{m/s} \tag{10}\]

which is 3,079.3 metres per second. The mass ratio is the release mass over the burnout mass,

\[\frac{m_0}{m_f} = \frac{21{,}800}{8{,}200} = 2.6585 \tag{11}\]

so the ideal velocity increment is

\[\Delta v = v_e \ln\!\left(\frac{m_0}{m_f}\right) = 3{,}010.9 \ \text{m/s} \tag{12}\]

The ideal increment is 3,010.9 metres per second, and adding the 236.1 the carrier aircraft already supplied gives 3,247.0, against a Mach 8 objective which at the burnout altitude is about 2,400 metres per second.

\[3{,}247.0 - 2{,}400 = 847.0 \ \text{m/s} \tag{13}\]

leaving 847.0 metres per second, or 26.1 percent of the ideal total, for gravity, drag and steering. A vehicle whose ideal increment exceeded its objective by only a few percent would be claiming no losses at all, and one that exceeded it by half would suggest an objective set well below what the vehicle could do. About a quarter is a plausible allowance for a suborbital ascent, which makes this a check on the published masses rather than on the trajectory.

The thrust to weight at release follows from the same figures,

\[\frac{F}{m_0 g_0} = \frac{284{,}415}{21{,}800 \times 9.80665} = 1.330 \tag{14}\]

and a vehicle released in level flight needs no more than one, because the wing is already carrying it. Being above one lets an air-launched vehicle pitch up immediately instead of sinking while it accelerates.

The masses also fix the propellant mass fraction,

\[\zeta = \frac{13{,}600}{21{,}800} = 0.6239 \tag{15}\]

or 62.4 percent, against 73.7 for the X-33 and the 89.0 percent an orbital vehicle needs. The X-34 is further from an orbital mass fraction than the X-33 was, and neither was required to be close, because neither was going anywhere near orbit. The distinction matters, because the temptation with a demonstrator is to read its numbers as predictions of the vehicle it stood for.

The Chamber That Is Consumed

The Fastrac’s combustion chamber and nozzle were cooled ablatively. There is no regenerative jacket circulating fuel through passages in the wall. Instead a silica-phenolic liner inside a composite overwrap absorbs heat by decomposing, and the gas that leaves the decomposing surface keeps the hot flow off the wall. The wall survives by being destroyed at a controlled rate.

Here the cost argument holds, and the manufacturing burden it avoids is set out in the same design text. A regeneratively cooled chamber is a precision assembly of hundreds of brazed passages and one of the most expensive parts of a rocket engine to make. An ablative liner is a moulding.

It has a consequence that the words reusable launch vehicle do not prepare anyone for. Taking the chamber flow, the chamber pressure $p_c$ and the characteristic velocity $c^{\ast}$ of liquid oxygen burning with RP-1 kerosene, the throat area follows from

\[A_t = \frac{\dot{m}_c \, c^{\ast}}{p_c} \tag{16}\]

Here the throat is published, so the relation can be run the other way. It is 8.25 inches across in the nozzle design report, which is 0.20955 metres, so

\[A_t = \frac{\pi D_t^2}{4} = \frac{\pi \times 0.20955^2}{4} = 0.034488 \ \text{m}^2 \tag{17}\]

and with the nominal chamber pressure of 652 pounds per square inch, or 4.495 megapascals, that the development status report lists among the engine’s requirements, and the chamber flow of 88.68 kilograms per second,

\[c^{\ast} = \frac{p_c A_t}{\dot{m}_c} = \frac{4.495 \times 10^6 \times 0.034488}{88.68} = 1{,}748 \ \text{m/s} \tag{18}\]

The same report’s engine schematic shows 633 pounds per square inch in the chamber at its operating point, which would lower the characteristic velocity by 2.9 percent, and the requirement figure is used here as the nominal one. The vacuum thrust coefficient at the flight nozzle’s thrust is then

\[C_F = \frac{F}{p_c A_t} = \frac{284{,}415}{4.495 \times 10^6 \times 0.034488} = 1.8345 \tag{19}\]

Those two quantities divide the engine’s performance between its two halves, since the characteristic velocity describes everything upstream of the throat and the thrust coefficient everything downstream,

\[I_{sp} = \frac{C_F \, c^{\ast}}{g_0} \tag{20}\]

That relation is shown for its structure and not as a check. The characteristic velocity above was derived from the same pressure, area and chamber flow, so multiplying the two factors returns the chamber impulse of 327.05 seconds by construction, and presenting the agreement as confirmation would be circular.

The area ratio then fixes the exit. The flight nozzle’s ratio is approximately 30 in both reports, so

\[A_e = \varepsilon A_t = 30 \times 0.034488 = 1.0346 \ \text{m}^2 \tag{21}\]

an exit 1.148 metres across, which is a check on the published ratio, because a nozzle wider than the vehicle could not have been fitted to it.

How Fast the Wall Is Destroyed

A recession rate is the output of an energy balance rather than an input to one, and running the balance is instructive because it fails.

Start with the heat the wall has to survive. The standard estimate for a rocket throat is the Bartz correlation, which gives the gas-side heat transfer coefficient as

\[h_g = \frac{0.026}{D_t^{0.2}}\left(\frac{\mu^{0.2} c_p}{\mathrm{Pr}^{0.6}}\right)\left(\frac{p_c}{c^{\ast}}\right)^{0.8}\left(\frac{D_t}{R_c}\right)^{0.1} \tag{22}\]

With a chamber at about 3,500 kelvin and gas properties typical of liquid oxygen burning with kerosene, that gives 8,674 watts per square metre per kelvin, taking the throat’s radius of curvature equal to its diameter. The heat arriving is the coefficient times the difference between the recovery temperature and the ablating surface,

\[q = h_g \left(T_{aw} - T_w\right) = 8{,}674 \times \left(3{,}150 - 1{,}900\right) = 10.84 \ \text{MW/m}^2 \tag{23}\]

Ten megawatts per square metre is the order of magnitude a rocket throat delivers. The correlation is good to perhaps a factor of two, a limit stated here because what follows depends on it.

Now the balance. A surface protecting itself by being destroyed removes heat at a rate set by how much energy each kilogram carries away, so writing $H_{\text{eff}}$ for that effective heat of ablation and $\rho_a$ for the material density,

\[\dot{s} = \frac{q}{\rho_a H_{\text{eff}}} \tag{24}\]

Run it forwards with the energy the material can actually absorb. On representative property values, heating silica phenolic from room temperature to 1,900 kelvin takes about 1.76 megajoules per kilogram and vaporising the silica about 12, so

\[H_{\text{absorb}} = 13.76 \ \text{MJ/kg} \qquad \Rightarrow \qquad \dot{s} = 0.463 \ \text{mm/s} \tag{25}\]

Over the 148 second burn that rate removes 68.6 millimetres, an absurd figure. A throat losing that much would not survive, and ablative chambers of this class do not behave that way.

So invert it. The nozzle design report set a throat erosion requirement of under 2 mils per second, which is 0.051 millimetres per second, and found no throat enlarged after 66 firings totalling 1,803 seconds, so a tenth of a millimetre per second is a generous upper figure, and putting that in gives

\[H_{\text{eff}} = \frac{q}{\rho_a \dot{s}} = \frac{10.84 \times 10^6}{1{,}700 \times 10^{-4}} = 63.8 \ \text{MJ/kg} \tag{26}\]

against 13.76 that the material can absorb, a ratio of 4.6, which a slower recession would only raise.

The ablator is not mostly absorbing the heat. It is blocking it. Pyrolysis gas leaving the decomposing surface blows into the boundary layer and thickens it, cutting the heat that arrives in the first place. Absorption is the small term and transpiration is the large one, by a factor of at least four, and an ablative wall survives because of the large term.

The forward calculation being wrong by that factor is the result. It explains why a recession rate is measured rather than predicted.

The Bartz correlation and the ablation balance are standard results and are not this article’s. This article’s contribution is the inversion, an arithmetic step on the balance that introduces no new relation, and the observation that the factor between the two answers is the transpiration term.

Both halves rest on literatures older than the programme. The convective heat transfer to a rocket nozzle was being estimated from the middle 1950s, as in Sibulkin 1956 and Mayer 1961, and the transpiration work that explains the blocking term runs alongside it, as in Bartle and Leadon 1960 and Librizzi and Cresci 1964, so the physics the X-34’s chamber depended on was some forty years settled when the engine was designed.

What That Costs the Chamber

At the upper figure of a tenth of a millimetre per second the liner loses

\[\Delta s = \dot{s} \, t_b = 10^{-4} \times 148.0 = 14.8 \ \text{mm} \tag{27}\]

over a full burn, so a chamber built to fly one mission needs a consumable layer of the order of a centimetre and a half, and at the published erosion requirement about half that.

Recession rate Liner consumed over the burn
0.05 mm per second 7.4 mm
0.10 mm per second 14.8 mm
0.15 mm per second 22.2 mm
0.20 mm per second 29.6 mm

The engine’s combustion chamber was a consumable on a vehicle whose entire purpose was reuse, and the engine’s fact sheet said so, with the ablative chamber and nozzle and the hypergolic ignition cartridge to be replaced after each flight and nearly all the rest reused. At the planned rate of twenty-five flights a year, that is twenty-five combustion chambers a year.

Whether that is cheap depends entirely on what a chamber costs. The article’s keystone has arrived as a component. A moulding at a few tens of thousands of dollars makes it right. A moulding at a few hundred thousand makes it wrong. The public record does not contain the number, and the Epistemic State records the gap without guessing at it.

What Air Launch Donates

The X-34 was carried to altitude under a modified airliner and released, and the usual argument for that is altitude and speed. It is the weakest of the several available.

Taking a release at 38,000 feet, which is 11,582 metres and is the approximate launch altitude that the engine development report gives for the X-34, at an assumed Mach 0.8, the specific energy the aircraft has already supplied is potential plus kinetic,

\[e = g_0 h + \frac{v^2}{2} \tag{28}\] \[e = 9.80665 \times 11{,}582 + \frac{236.1^2}{2} = 141{,}446 \ \text{J/kg} \tag{29}\]

The total is 141.4 kilojoules per kilogram. Expressed as the velocity increment that energy would buy,

\[\Delta v_{\text{equiv}} = \sqrt{2e} = 531.9 \ \text{m/s} \tag{30}\]

The figure is 5.7 percent of a 9,300 metre per second orbital budget. An argument for air launch from the altitude and the speed argues from the smallest of its benefits.

The larger measurable benefit is that the nozzle never sees sea level. Thrust falls below its vacuum value by the ambient pressure acting over the exit area,

\[F = F_{vac} - p_a A_e \tag{31}\]

so with the flight nozzle’s exit area of 1.0346 square metres, and ambient pressures of 101,325 pascals at sea level and 20,646 at the release altitude, the thrust recovered by launching high is

\[\left(101{,}325 - 20{,}646\right) \times 1.0346 = 83{,}470 \ \text{N} \tag{32}\]

which is 83,470 newtons, the difference between a loss at sea level of 104.83 kilonewtons and one at the release altitude of only 21.36. Launching from altitude recovers 83.47 kilonewtons, which is 29.3 percent of the flight nozzle’s vacuum thrust, about five times the share of an orbital budget that the altitude and speed donate. The simple relation overstates the sea-level case, because a 30:1 nozzle at sea level is badly overexpanded, and the nozzle design report records that the nozzle was sometimes truncated to 15:1 to prevent overexpansion and the side loads that come with it. That truncation is the 15:1 configuration whose thrust the usual quotation carries.

And the largest benefit is the one this article cannot compute. An air-launched vehicle needs no launch pad, no flame trench, no fixed azimuth and no launch window dictated by weather over a single site. For a programme whose keystone is cost, the ground infrastructure it never has to build is the argument, and it has no equation.

The Same Trade the Previous Article Answered With Hydrogen

Two consecutive vehicles in this series answered one question in opposite directions, and the question is which propellant to carry.

Writing $r$ for the mixture ratio, the bulk density of a propellant combination is

\[\rho_{\text{bulk}} = \left[\frac{1}{1+r}\frac{1}{\rho_f} + \frac{r}{1+r}\frac{1}{\rho_o}\right]^{-1} \tag{33}\]

The densities come from Huzel and Huang’s design text. Its table of cryogenic propellants gives liquid oxygen 1.142 grams per cubic centimetre at its normal boiling point, and its table of storable propellants gives RP-1 between 0.80 and 0.82 at 68 degrees Fahrenheit, so taking the middle of that range,

\[\rho_o = 1{,}142 \ \text{kg/m}^3 \qquad \rho_f = \frac{800 + 820}{2} = 810 \ \text{kg/m}^3 \tag{34}\]

and the hydrogen side keeps the previous article’s 70.85 kilograms per cubic metre. At the engine mixture ratio of 2.17 that the development status report publishes,

\[\rho_{\text{bulk}} = \left[\frac{1}{3.17}\frac{1}{810} + \frac{2.17}{3.17}\frac{1}{1{,}142}\right]^{-1} = 1{,}011.2 \ \text{kg/m}^3 \tag{35}\]

For kerosene and oxygen that is 1,011.2 kilograms per cubic metre, against 343.4 for hydrogen and oxygen at 5.5, a ratio of 2.945. The X-33 article, which assumed a generic kerosene mixture ratio of 2.56, found 1,024.1 and a ratio of 2.983 with the same densities. The difference is the mixture ratio alone, and the Fastrac’s published 2.17 is the value that applies to the X-34.

The fuel share of the propellant mass is fixed by the mixture ratio alone,

\[\frac{m_f}{m_p} = \frac{1}{1+r} = \frac{1}{3.17} = 0.3155 \tag{36}\]

or 31.5 percent, so the X-34 carried 4,290 kilograms of kerosene against 9,310 of oxygen.

The previous article’s central sentence inverts. Hydrogen is 15.4 percent of the propellant mass and 74.6 percent of its volume, so the fuel tank is the vehicle. Kerosene is about a third of the mass and 39.4 percent of the volume, so the fuel tank is a tank.

The consequence is easiest to see in the load the X-34 carried.

\[\frac{13{,}600}{1{,}011.2} = 13.45 \ \text{m}^3 \qquad \text{against} \qquad \frac{13{,}600}{343.4} = 39.61 \ \text{m}^3 \tag{37}\]

An extra 26.16 cubic metres, on a vehicle 17.77 metres long, is not a packaging problem. It is a different aeroplane.

Where the Previous Article’s Scale Invariance Stops Holding

The X-33 article proved that the membrane tank fraction contains no length. A thin vessel of volume $V$ at pressure $p$ has mass $k \rho_w p V / \sigma$ and holds $\rho_p V$ of propellant, so

\[\frac{m_{\text{tank}}}{m_{\text{prop}}} = \frac{k \, \rho_w \, p}{\sigma \, \rho_p} \tag{38}\]

and the size cancels. That cancellation is why a subscale tank was a valid test of a full-scale tank technology. It was the strongest thing the previous article had to say about demonstrators.

It cancels only while stress sets the thickness. The membrane thickness a pressure demands is

\[t = \frac{pR}{\sigma} \tag{39}\]

which falls with the radius, while the thinnest laminate anybody can lay up does not fall at all. Taking the same construction and pressure as the previous article so the comparison is controlled, and sizing the walls by the ordinary structural methods Bruhn sets out for flight vehicle structures,

Tank Radius Membrane thickness needed Per facesheet Minimum gauge as a multiple
X-33 hydrogen tank 2.15 m 1.384 mm 0.692 mm 1.45
X-34 tank, assumed 0.75 m 0.483 mm 0.241 mm 4.14

The smaller the tank, the more of its wall is material no load asked for. Once minimum gauge binds, the wall thickness stops depending on the pressure at all, and the tank fraction follows in three lines. For a cylinder of radius $R$ whose wall is two facesheets each at the minimum gauge, the wall mass and the propellant mass per unit length are

\[m'_{\text{wall}} = \rho_w \left(2 \pi R\right) \left(2 t_{\text{gauge}}\right) \qquad m'_{\text{prop}} = \rho_p \pi R^2 \tag{40}\]

so the length and the constant both cancel, leaving

\[\frac{m_{\text{tank}}}{m_{\text{prop}}} = \frac{4 \rho_w t_{\text{gauge}}}{\rho_p R} \tag{41}\]

which goes as one over the radius instead of being independent of it.

Tank radius Hydrogen and oxygen Kerosene and oxygen
0.50 m 3.66% 1.24%
0.75 m 2.44% 0.83%
1.00 m 1.83% 0.62%
1.50 m 1.22% 0.41%
2.15 m 0.85% 0.29%
3.00 m 0.61% 0.21%

Two things follow and they point in opposite directions.

The scale penalty is real, so a small demonstrator’s tank is proportionally worse than a large vehicle’s and cannot stand in for it. The X-33’s tank could. The X-34’s could not. That is the previous article’s best argument about demonstrators failing at a smaller size, and it fails because of manufacture rather than because of mechanics.

And the propellant more than pays for it. At the X-34’s assumed tank radius of 0.75 metres, with the previous article’s laminate density of 1,570 kilograms per cubic metre and minimum gauge of one millimetre, the gauge-limited fraction for the two bulk densities above is

\[\frac{4 \times 1{,}570 \times 0.001}{343.4 \times 0.75} = 0.0244 \qquad \text{against} \qquad \frac{4 \times 1{,}570 \times 0.001}{1{,}011.2 \times 0.75} = 0.0083 \tag{42}\]

so a hydrogen and oxygen tank is 2.44 percent of the propellant it holds and a kerosene and oxygen tank is 0.83, a factor of 2.945 which is exactly the ratio of the two bulk densities, since everything else in the numerator and denominator is common to both. The small vehicle is penalised by its size and rescued by what it chose to burn.

The Vehicle

The X-34 was a small winged rocket aeroplane, carried aloft under an airliner and released to fly a suborbital profile to about Mach 8. The agency’s fact sheet gives a length of 58.3 feet and a wingspan of 27.7 feet, which at 0.3048 metres to the foot are

\[L = 58.3 \times 0.3048 = 17.77 \ \text{m} \qquad b = 27.7 \times 0.3048 = 8.44 \ \text{m} \tag{43}\]

It had a composite airframe with composite propellant tanks, silica-based tiles and flexible blankets for thermal protection, and it was to land itself on a runway without a pilot.

The same fact sheet gives an unfuelled weight of 18,000 pounds and 30,000 pounds of liquid oxygen and kerosene. At 0.45359237 kilograms to the pound, and writing $m_e$ for the empty mass and $m_0$ for the release mass,

\[m_e = 18{,}000 \times 0.45359237 = 8{,}165 \ \text{kg} \qquad m_p = 30{,}000 \times 0.45359237 = 13{,}608 \ \text{kg} \tag{44}\] \[m_0 = m_e + m_p = 48{,}000 \ \text{lb} = 21{,}772 \ \text{kg} \tag{45}\]

This article rounds the 8,165, 13,608 and 21,772 kilograms to 8,200, 13,600 and 21,800, and the sum still closes after rounding. The closure holds by construction and is no check, because the fact sheet does not give the release mass separately, and it deserves mention only because the previous article’s did not.

What Was Deliberately Left Out

The list of things the X-34 did not have is the list a later review objected to, and it reads more fairly forwards than backwards. The vehicle had single-string avionics, meaning no redundant channel for a failure to fall back on. Its system-level testing was thin. Its automatic landing had not been validated in flight.

Every one of those is a defensible choice for a cheap demonstrator and an indefensible one for a vehicle about to be released over inhabited ground. The programme did not change its mind about engineering. It changed its mind about which of those two things it was building.

Dependent Systems

Thermal Protection

The X-34 used silica-based tiles on its nose and wing leading edges and flexible insulation blankets elsewhere rather than the metallic system the X-33 chose, as Wurster et al. 1998 describe, and the requirement that shaped it was unusual. The vehicle had to survive subsonic flight through weather, because an air-launched vehicle spends its climb attached to an aeroplane flying through whatever is between the runway and a launch altitude that the engine development report puts at about 38,000 feet. A launch pad does not fly through rain.

Autonomy and Landing

An unpiloted vehicle that lands on a runway has to be right the first time, and the X-34 was to demonstrate automatic landing including in a twenty-knot crosswind, with navigation from a combination of satellite and inertial systems.

This is where the cost argument and the risk argument meet most directly. Automatic landing is cheap to specify and expensive to prove, because proving it means flying it, and flying it is what the programme had not yet done when it was asked what its residual risk was.

Aerodynamics

The aerodynamic work was conventional and the vehicle was small enough to be tested honestly, one advantage of a small demonstrator that the mass-fraction argument does not capture. A wind tunnel model of a 17-metre vehicle is a larger fraction of full scale than a model of a 21-metre one, and the Reynolds number gap is correspondingly smaller.

The Flight Test Record

There is no powered flight test record. The X-34 never fired its engine in the air.

Ground Tests and Captive Flights

The first unpowered airframe was rolled out in 1999 at the agency’s flight research centre. It was towed on the ground behind a vehicle, and it was carried aloft beneath the carrier aircraft on a first captive flight on 29 June 1999, with two more captive flights later that year. Two airframes were completed of the three planned. The engine was tested extensively on the ground, and its longest firing, of 159.03 seconds in the engine’s test record, is the firing set against the mission burn earlier, under A Fourth Number That Closes on the Other Three.

No free flight was ever made, powered or unpowered. The vehicle was never released from the carrier aircraft.

The Review That Ended It

A joint review in 2000 found that the project needed its approach, scope, budget and schedule redefined, and named the risks. They were inadequate system testing, single-string avionics and an unvalidated automatic landing. Reaching an acceptable level of risk would require more government technical insight, more hardware testing and integrated systems assessment, as the agency’s fact sheet of the period records.

An estimate drawn from the restructure plan that followed put the total requirement near 348 million dollars against roughly 86 million budgeted in 1996, in the oversight body’s testimony, and the programme ended on 31 March 2001, after a funding decision announced together with the X-33’s, with the agency stating that the benefits did not justify continued investment and that the funds of the initiative that replaced both should go to higher priority needs. The oversight body examined the two cancelled programmes together later that year.

\[\frac{348 - 86}{86} = 3.05 \tag{46}\]

A growth of 305 percent on the rounded figures, and the arithmetic is not the interesting part. The oversight body, working from unrounded ones, gives 307 percent. What the number measures is.

Comparison With Ground Prediction

This section normally compares prediction with flight measurement. The X-34 produced no flight measurement at all, so what can be compared is prediction against the only two things the programme did produce, which are ground test results and a revised cost estimate.

Where the Ground Tests Agreed With Prediction

The engine worked. It was fired repeatedly, including for 159.03 seconds, which exceeds the 148 second burn a full propellant load implies, by the margin the burn-time check above derived. The published thrust, impulse and flow figures are mutually consistent to within half a percent once each nozzle’s thrust is paired with its own impulse, as the nozzle pairing above shows, and the generator fraction of 3.50 percent derived under The Cycle Is Smaller Than the Gap lands inside the range the cycle architecture uses. Nothing in the engine’s published numbers indicates a machine that was not doing what it was designed to do.

The airframe was built, twice. It was towed, it was carried, it held together, and the two airframes outlived the programme by nearly two decades.

Where Prediction and Outcome Diverged

The prediction that failed was the cost estimate, and it failed by a factor of four. No structure broke, the engine’s development problems were found and corrected on the ground, and no aerodynamic surprise appeared. The quantity that moved was the one with no conservation law.

That is a different kind of divergence from any this series has met. A drag rise that comes in higher than predicted is a fact about air. A cost estimate that comes in higher than predicted is a fact about what was left out of the estimate, and the review that produced the new figure named what had been left out.

The Comparison the Programme Never Got to Make

The X-34 was to demonstrate rapid turnaround, and turnaround is the one quantity that would have tested the whole cost argument. London and Lyles 1998 give the goal as 25 flights in a year with a surge of two flights within 24 hours. A vehicle that flies twenty-five times a year with a small crew is a different economic object from one that flies twice. The programme never flew once, so the number that mattered most was never measured, and the Epistemic State lists it as unsettled.

Work on operations and turnaround appears below under launch vehicle design, staging and operations and under risk, reliability, safety and health management. It includes the turnaround time model for conceptual rocket engines in Nix and Staton 2004 and the reliability and maintainability models for reusable launch vehicles in Unal et al. 2000 and Unal et al. 2004.

What the Data Changed

The Verdict on the Cost Argument, Tested Both Ways

Take the two programmes cancelled in the same announcement and divide what each spent by the mass of vehicle it produced. Mass is a poor denominator for cost. It is used here because it is the one comparable quantity both programmes published. Cost estimating for space systems has its own methods, set out in Wertz and Larson’s standard treatment of space mission design, and none of them is a division by mass. The article states that limit openly so that the ratio is not taken to mean more than it does.

The X-34’s release mass is the fact sheet’s 48,000 pounds, the sum displayed in the description of the vehicle above, against 285,000 for the X-33. The X-34’s spending is reported as just under 112 million dollars, and the X-33’s as about 1,280 million, being the 922 million the agency and 357 million Lockheed Martin put in.

\[\frac{112 \times 10^6}{48{,}000} = 2{,}333 \ \text{dollars per pound} \tag{47}\] \[\frac{1{,}280 \times 10^6}{285{,}000} = 4{,}491 \ \text{dollars per pound} \tag{48}\]

The X-34 comes to 2,333 dollars per pound against the X-33’s 4,491, so on money actually spent the low-cost vehicle was 1.92 times cheaper per pound of vehicle, and both programmes ended without a powered flight, so the comparison is between two equivalently incomplete efforts.

Now do it with the money it would have taken to fly the thing safely.

\[\frac{348 \times 10^6}{48{,}000} = 7{,}250 \ \text{dollars per pound} \tag{49}\]

The result, 7,250 dollars per pound, is 1.61 times the X-33’s actual spend per pound. The vehicle built to be cheap would have cost more per pound to finish than the vehicle everyone remembers as the expensive one.

Both figures are published and they answer different questions. The first says the programme was economical at building hardware. The second says that building hardware was not the expensive part.

What the Programme Settled

It settled that a small air-launched reusable demonstrator can be built for a fraction of the cost of a large one, which was never seriously in doubt and which the airframes themselves prove.

It settled that an ablatively cooled engine of that class can be built and run, and the Fastrac was fired far more than the X-34 ever flew.

It did not settle anything about the cost of an operational reusable launch vehicle, because the quantity that would have settled it, turnaround, was never measured.

These conclusions draw on the cluster on cost estimation, cost growth and acquisition, including the launch systems operations cost model of Prince and Hamaker 2001 and the cost analysis of a single-stage reusable ballistic launch vehicle in Koelle 1993.

What It Fed Into

The engine’s record after the vehicle is unclear, since one account dates the end of its programme to 2001 and the closure of its test project to 2009. The ablative low-cost approach did not become the standard route to a cheap engine, and the kerosene engine that followed the Fastrac’s methods is now regeneratively cooled.

What did become the standard route is visible in what replaced the programme’s premise. The decision history that produced this family of programmes is set out in Heppenheimer’s account of the shuttle decision. The reduction in launch cost that the reusable launch vehicle programme was chartered to pursue has since been sought through recovering and reflying an expensive engine many times, one Falcon 9 engine having flown twenty-two times, rather than through building a cheap one to throw away. The X-34’s bet was that the way to make launch cheap is to make the hardware cheap. The bet that paid was that the way to make launch cheap is to use expensive hardware more often.

That conclusion needs stating with care and without triumph. The two strategies are not opposites and a small launcher today may well be right to use a simple engine. What can be said is that the inference behind the X-34, that cheap hardware implies cheap access, was not the one that turned out to matter most.

What It Failed to Influence

The two airframes are the most direct evidence of influence, and they went to a scrapyard. They sat in storage at Edwards, moved to a desert airfield in 2010, then to a crane company’s yard, and were at a scrapyard by April 2020. A vehicle that is near completion and then abandoned teaches little beyond what was written down before it stopped. The programme appears in the agency’s history of the X-vehicles as a vehicle that was built and did not fly.

The Contemporary Literature

Cluster Records
The X-34, the Fastrac engine and the low-cost booster programme 87
Reusable launch vehicle programmes and demonstrators 109
Air launch, carrier aircraft and store separation 177
Launch economics, small launchers and reusability 112
Cost estimation, cost growth and acquisition 245
Ablative materials, charring and recession 455
Additive manufacturing and low-cost fabrication 258
Gas-side heat transfer and the cooling of chambers 504
Liquid rocket engines, turbopumps and combustion 678
Solid and hybrid rocket motors 338
Rocket nozzles, plumes and expansion 206
Thermal protection systems and hot structures 211
Propellant tanks and cryogenic storage 146
Composite structures and flight vehicle materials 186
Aerodynamics, aerothermodynamics and hypersonic flow 256
Automatic and autonomous landing 323
Guidance, control, avionics and trajectories 444
Risk, reliability, safety and health management 192
Design optimisation, uncertainty and computation 117
Launch vehicle design, staging and operations 305
Flight test, instrumentation and range operations 18
Total 5,367

The subjects this article computes are all active, and two of them are more active now than they were then, for reasons the programme would have found ironic.

Ablative Materials and Their Modelling

The ablation modelling the article treats as a recession rate is now a detailed thermochemical subject, with pyrolysis, char and surface chemistry resolved rather than lumped, and more of its recent titles concern planetary entry than cheap engines.

The cluster on ablative materials, charring and recession holds this literature. The pyrolysis of the phenolic impregnated carbon ablator is characterised in Wong et al. 2015 and Torres-Herrador et al. 2019, its arc-jet response in Smith et al. 2015 and Milos and Gasch 2015, and the full-scale Stardust heat shield is modelled in Weng et al. 2021. The engine application continues in Wunderlin et al. 2024, an ablative thrust chamber for a liquid engine, and in Chandler 2023, a test of an ablative chambered engine.

Low-Cost Propulsion Through Manufacture

The X-34’s answer to expensive engines was to make a cheap one badly on purpose. The modern answer is to make an expensive one quickly, with additive manufacturing cutting the fabrication time, the cost and the number of separate manufacturing steps of the regeneratively cooled chamber the Fastrac avoided. NASA’s low-cost upper stage propulsion project and its bimetallic chamber work with Virgin Orbit both report those reductions. The constraint the Fastrac was designed around has largely dissolved. This is the second time in two articles that a 1990s architecture has been overtaken by a change in how things are made rather than in how they work.

The additive manufacturing of that chamber is developed and hot-fired in Gradl et al. 2017 and Gradl et al. 2019a, summarised in Gradl et al. 2018a, and applied to a low-cost upper stage chamber in Protz et al. 2016. The remainder is spread across the clusters on additive manufacturing and low-cost fabrication, on gas-side heat transfer and the cooling of chambers and on liquid rocket engines, turbopumps and combustion.

Small Launch Vehicles and Their Economics

The market the X-34 was pointing at exists now, and the literature on small launch vehicle economics, reusability and cost per kilogram is where the argument the programme could not finish is being had.

Its cluster, launch economics, small launchers and reusability, includes the industry analyses of Sun 2022 and Puteaux et al. 2024, the survey of small launch vehicles in Niederstrasser 2022, and the cost analysis of the Starship system in Harris et al. 2022b.

The Commercial Verdict on Air Launch

The argument for air launch is no longer being had, because the market has spent the last decade running the experiment.

The operating method the X-34 borrowed was already commercial when the programme started, and the air-launched booster that supplied it flew for decades at a price that rose, from an initial offer of six million dollars to about forty million by 2017 for some 450 kilograms to low orbit,

\[\frac{40{,}000{,}000}{450} \approx 89{,}000 \ \text{dollars per kilogram} \tag{50}\]

A later attempt, Virgin Orbit’s LauncherOne, put a liquid-fuelled orbital rocket under a widebody airliner and flew it six times between 2020 and 2023. Four of the six reached orbit. The operator filed for bankruptcy in April 2023 and was wound up the following month, its remaining assets sold at auction for about thirty-six million dollars, and the carrier aircraft was bought by another company to carry a hypersonic test vehicle in place of a launcher.

Reaching orbit was not the problem. Four flights out of six did that. What failed was the thing the X-34 existed to demonstrate.

This is a harder verdict on the X-34’s premise than anything in the programme’s record, and it should be stated with its limits. One company failing is a fact about one company. But the claim that removing the launch pad removes enough cost to change the economics has now been tested with real money by people who believed it, and the answer that came back was the same one the restructure plan gave in 2000. The infrastructure a vehicle does not build is not where the cost is.

The literature on small launch economics is where this argument now lives, and most of it is recent. Of the 112 records gathered below on launch economics, small launchers and reusability, 67 date from 2015 or later, while 113 of the 177 records on air launch, carrier aircraft and store separation predate 2015.

The cluster on air launch, carrier aircraft and store separation runs from the Pegasus flight test programme in Elias and Knutson 1995 to the description of LauncherOne in Vaughn et al. 2017, the towed glider concept of Budd and Monheim 2015, the business-jet captive-carry demonstration in Miller et al. 2018a and the comparison of ground and airborne launch for hybrid small launchers in Casalino et al. 2022b.

Autonomy, Landing and the Risk Case

The unvalidated automatic landing that helped end the programme is now routine for reusable launch stages, and it is routine because vehicles fly it repeatedly rather than because anybody proved it on paper. Falcon 9 boosters land vertically under power, where the X-34 was to land on a runway. They first landed in December 2015 and have since landed nearly six hundred times. The risk argument against the X-34 has since been resolved by the method the X-34 could not afford.

Landing is covered below by the clusters on automatic and autonomous landing and on guidance, control, avionics and trajectories. The powered landing of reusable rocket stages is a large part of the recent work, with landing guidance in Sagliano et al. 2021, Ma et al. 2019 and Su et al. 2022a and trajectory optimisation in Wang and Song 2018.

Structures, Tanks and Thermal Protection

The clusters on thermal protection systems and hot structures, on propellant tanks and cryogenic storage and on composite structures and flight vehicle materials collect the literature on structures, tanks and thermal protection. Recent threads include linerless composite tanks for liquid hydrogen in Olsson et al. 2024 and flexible thermal protection in Tobin and Dec 2015 and Rossman and Braun 2016.

Method, Uncertainty and Computation

Method draws on the clusters on design optimisation, uncertainty and computation, on risk, reliability, safety and health management and on launch vehicle design, staging and operations. Uncertainty quantification for launch vehicle design is treated in Brevault and Balesdent 2021 and Novack et al. 2016.

The vehicle’s own record stops when the programme does. Of the 39 research records whose titles carry the X-34 designation, 37 date from 2001 or earlier, one from 2002, and one, a 2015 paper on the Fastrac’s memorandums of misunderstanding in Hawkins and Turner 2015, from 2015. A cancelled programme stops generating literature under its own name almost immediately, which means the documentary trace of a vehicle is not a measure of what it contributed but of how long it survived.

The X-34, the Fastrac engine and the low-cost booster programme

The vehicle, its Fastrac engine and the low-cost booster technology programme that produced the engine, with the programme’s status reports and its successors under the Future-X heading.

The record is the programme’s own and it stops when the programme does. Of the 87 records, 78 date from 2001 or earlier and 3 from 2015 or later. Of the 45 titles that name the Fastrac or the MC-1, 38 date from 2002 or earlier.

87 records. [Aron et al. 2001] [Ballard et al. 2000] [Barton and Tragesser 1999] [Beech and Chandler 1997] [Berry et al. 1998] [Beshears 2000a] [Beshears 2000b] [Blades and Redgrave 2000] [Brauckmann 1998] [Brown 2000] [Brown 2002] [Brown and Brunty 2001] [Brown et al. 1998a] [Brown et al. 2000] [Brown et al. 1998b] [Bullard 1998] [Burchett 2008] [Champion and Darrow 1998] [Christensen and Nesman 1998] [Component and System Level 1999] [Davis 2001] [Davis and Phelps 2001] [Dennis and Sanders 2000] [Dill et al. 2001] [Dobson et al. 2000] [Dragone 2000] [Fisher and Ise 1998] [Fisher et al. 1998] [Frady et al. 2000] [Garcia et al. 1998] [Goode 2001] [Griffin and Dorney 1999] [Griner and Lyles 1999] [Hawkins and Turner 2015] [Hedayat et al. 1998a] [Hedayat et al. 1998b] [Hedayat et al. 2000] [Heflin et al. 2000] [Hwang et al. 2020] [Kelb et al. 1998] [Kim and Kim 2012] [Klem 1999] [Koelbl and Van Hooser 2015] [Laszar 2003] [Lawerence et al. 2000] [Lawrence et al. 2001a] [London and Lyles 1998] [London and Sumrall 1999] [Ly and Roe 2001] [McDonald et al. 1998b] [McDonald et al. 1998a] [Miller 1999] [Miller 2000] [Milos and Squire 1999] [Milos et al. 1997b] [Moon and Beveridge 1997a] [Moon and Beveridge 1997b] [Nesman and Dennis 1999] [Nesman and Dennis 2001] [Nguyen 1998] [Pamadi and Brauchman 1999] [Pamadi et al. 2000] [Peters and Turner 2000] [Peters et al. 2000] [Prabhn and Weilmuenster 2001] [Prabhu 2001] [Riley and Kleb 1998] [Rocker and Jones 2002] [Rocker and Nesman 1998] [Rocker and Nesman 1999] [Rocker et al. 2001] [Rogers and Dragone 1996] [Santi 1999] [Shadoan et al. 2000] [Skelley and Zoladz 1999] [Skelley and Zoladz 2001] [Soots and Burchett 2008] [Springer and London 2000] [Springer 1999] [Tragesser and Barton 1999] [VanHooser and Turner 2001] [Vu et al. 2000] [Wallace 1999] [Wood 1999] [Wurster et al. 1998] [Zoladz 2000] [Zoladz and Turner 2001]

Reusable launch vehicle programmes and demonstrators

The other reusable and experimental launch vehicle programmes the article sets the X-34 beside, chiefly the X-33, the Space Shuttle, the DC-X and the Kistler K-1.

It is a literature of the programmes’ own period. Of the 109 records, 83 date from 2001 or earlier.

109 records. [Aggarwal 2018] [Andrews 1998] [Armstrong 1977] [Baumann et al. 2008] [Bell Aerospace Co Buffalo Ny 1955b] [Bell Aerospace Co Buffalo Ny 1955a] [Bell Aerospace Co Buffalo Ny 1957] [Bott et al. 1983] [Brauckman and Scallion 2003] [Chiesa et al. 2005] [Clayton 1989] [Cook 1996] [Cook and Coffey 1973] [Cook et al. 1989] [Curry et al. 1971] [Dean and Mena 1983] [DeMott and Bigler 2017] [Development of a Large 1993] [Donahue 1997] [Donahue 2001] [Dotts et al. 1982b] [Dotts et al. 1982a] [Dotts et al. 1983] [Dwoyer et al. 1982] [Edwards and Foster 1973] [Edwards et al. 1975] [Elegante and Bowman 1978] [Fagan et al. 2003] [Ferguson 2011] [Fitzsimmons 1996] [Foster 1989] [Foster et al. 1989] [Fullerton 1975] [Graves et al. 1989] [Greenberg 1993] [Gregory and Wilcox 1970] [Gregory et al. 1971] [Gupta et al. 2018] [Hanson et al. 1998] [Harris 1993] [Harris et al. 2018] [Harsh et al. 1991] [Hartman and Stallings 1982] [Health Monitoring and Controls 1994] [Henry and McLELLAN 1971] [Hudson 1988] [Ingalls and Cipolletti 2011] [ISRO Releases the Special 2018] [Jameson 2001] [Jensen 2000] [Justiz and Patel 1988] [Kai and Ohtake 1996] [Ketner and Hess 1979] [Kobald et al. 2017] [Koelle 1993] [Kuo 1976] [Lanshin and Sosunov 1995] [Lee 1974] [Lee et al. 2026b] [Lockheed Martin Skunk Works 1999] [Lomas et al. 2001] [London and Rogacki 2000] [Lui and Mason 1991] [Lycans 1998] [McWhorter and Ewing 2001] [McWhorter et al. 2004] [Meyerson 1998] [Molinari et al. 2024] [Mueller (HM) and Lepore 2000] [Naftel 2000] [Niedermeyer 2003] [Ohern 1975] [Olynick 1998] [Palmer et al. 1999] [Peebles 2007] [Perlo 2026] [Peterson and Uney 1978] [Picka and Glenn 2011] [Powers and Bailey 1980] [Powers and Bailey 1982] [Powers et al. 1981] [Rice 1979] [Roberts and Huynh 1998] [Ronquillo 1985] [Roush et al. 2026] [Rozycki et al. 1993] [Sawyer et al. 1999] [Schmidt and Mann 1996] [Schwabacher et al. 2002] [Schweikhard et al. 1998] [Schweikhard et al. 2001] [Seward and Jumper 1990] [Shoyama and Hirakawa 2024] [Sivan and Pandian 2018] [Smith et al. 1974] [Stanley and Powell 1990] [Support to X-33/Reusable Launch 2000] [Chambers 1977] [Tartaglione and Mazzola 1982] [The Air-Breathing Launch Vehicle 1970] [Trefny 1999] [Trimmer et al. 1972] [Patil 2025] [Wang et al. 2001] [Wang and Cornelison 1996] [Whitesides et al. 1990] [Whitmore et al. 2004] [Wierzbanowski and Ramasubramanian 2020] [Zubrin and Clapp 1996]

Air launch, carrier aircraft and store separation

Air launch to orbit, the Pegasus booster and LauncherOne, carrier aircraft and captive carry, and the store separation problem that release from a carrier shares with weapons.

The operating method has a continuous literature. Of the 177 records, 113 name air launch, Pegasus, LauncherOne or Virgin Orbit, and 64 date from 2015 or later.

177 records. [Небылов et al. 2019] [Aircraft Store Separation Motion 1980] [Arnodo et al. 2018] [Atwood 1994] [Atwood 1995] [Belbruno et al. 1992] [Bell and Moser 1999] [Black 1969] [Black and Picklesimer 1971] [Blackburn and George 1964] [Bolster and Googins 1967] [Boltz 2004] [Bonometti and Sorensen 2006] [Brooks 1971] [Budd 2015] [Budd 2018] [Budd and Jensen 2015] [Budd and Monheim 2015] [Budd and Webb 2016] [Butler 1975] [Butler 1976] [Cai et al. 2023] [Carlson et al. 1995] [Carriage and Launch Characteristics 1994] [Casalino et al. 2022b] [Cenko et al. 1994] [Chao et al. 1993] [Ching 2000] [Chow and Marconi 1989] [Clegern and Ostrander 1995] [Cline et al. 1996] [Coleman et al. 1996] [Coogan and Musgrove 2017] [Corda et al. 2018] [Fanggidae and Kusumahardi 2025] [Daniels and Clare 1973] [Davids and Cenko 2001] [Davis and Welterlen 2003] [Davis et al. 2006] [Deitchman 1957] [Demir 2018] [Deslandes and Seifert 2000] [Lee 2004] [Dileep et al. 2019] [Dillenius et al. 1974] [Dillenius et al. 1975] [Donegan and Fox 1991] [Doolan 2006] [Elias and Knutson 1995] [Elkman et al. 2022a] [Elkman et al. 2022b] [Elkman et al. 2022c] [Feaux et al. 1989] [Goerttler and Schnepf 2024] [Gothard and Granlund 2022] [Gregory 2001] [Guo et al. 2024a] [Hampsten 1996] [Hendrick and Saint-Mard 1999] [Hochstetler et al. 2016] [Hoffren and Salminen 1999] [Hoyt 2006] [Huan-Ding et al. 2018] [Hudson 2005] [Ito et al. 2019] [Jenkins 1982] [Joshi et al. 2023b] [Kansas Univ Lawrence 1952] [Kaykayoglu 1996] [Keen 1990] [Kelly et al. 2017] [Lasek and Sibilski 2002] [Lee and Sarigul-Klijn 2020] [Lempert 1975] [Lengyel and Sosa 2021] [Lepore 2006] [Li et al. 2022b] [Lijewski and Suhs 1992] [Lijewski and Suhs 1994] [Lindberg 1989] [Liu 2003] [Logan et al. 2006] [Lyu and Wang 2024] [Maddox 1980] [Maddox et al. 1979] [Markarian 1971] [Martineau et al. 1990] [Meyer et al. 1992] [Miller et al. 2018a] [Mizrahi and Raveh 2019] [Mosier et al. 1991b] [Mosier et al. 1991a] [Murman et al. 2004] [Newman et al. 1992] [Nichols and Denny 1999] [Noffz and Curry 1991] [Noh et al. 2007] [Kim 2005] [Olejnik et al. 2020] [Olejnik et al. 2022a] [Parkinson et al. 1995] [Pegasus 1990] [Peters et al. 2024] [Poth et al. 1993] [Pritts 1974] [Qian et al. 2017] [Rafique and LinShu 2009] [Rafique et al. 2009a] [Rafique et al. 2009b] [Rafique et al. 2009c] [Rafique et al. 2009d] [Rafique et al. 2009e] [Rafique et al. 2010a] [Rafique et al. 2010b] [Rafique et al. 2011] [Raharema et al. 2026] [Reed and Curry 1969] [Rovner 1991] [Roychowdhury et al. 2019] [Rutherford and Wells 1999] [Ryan 1966] [Salt 2015] [Sarigul-Klijn et al. 2004] [Sarigul-Klijn et al. 2005] [Sarigul-Klijn et al. 2006a] [Sarigul-Klijn et al. 2006b] [Sarigulklijn et al. 2012] [Shubov 2023] [Sikharulidze et al. 2005] [Silaidis et al. 2024] [Singh et al. 2022] [Sohier et al. 2014a] [Sohier et al. 2014b] [Sohier et al. 2015] [Song et al. 2020] [Sorensen and Schafer 2001] [Spahr 1974] [Spahr 1975] [Spahr and Sumlin 1974] [Spahr and Sumlin 1975] [Spivey et al. 2018] [Stallings 1982] [Stewart et al. 2026] [Stokes et al. 1999] [尹 2023] [Svob and Bills 1984] [Szalai 2025] [Talbot and Moyer 1993] [The Bigger Picture 2018] [Thomas et al. 2007] [Tomaro et al. 2000] [Tsybriy and Guskov 2025] [Urbahs et al. 2021] [van den Broek 1984] [Van Kesteren et al. 2014] [Vaughn et al. 2017] [Verstraete and Hendrick 2003] [Verstraete et al. 2009] [Virgin Orbit Could Have 2021] [Vishwajeet et al. 2025] [Vlasyk and Korshunova 2025] [Wang 2015b] [Wang and Ma 2024] [Waskiewicz et al. 1981] [Waters et al. 2013a] [Whitehead 2006] [Xu and Tang 2010] [Yang et al. 2016b] [Yang et al. 2021] [Yavuz 1997] [Yin et al. 2024] [Zhang and Xu 2025] [Zhang and Zhang 2020] [Zhang et al. 2013] [Zhao and Wang 2020] [Zheng and Zhang 2018] [Zhou et al. 2019]

Launch economics, small launchers and reusability

Launch cost, cost per kilogram, the small launch market, commercial launch and the economics of reusability.

The market literature is recent. Of the 112 records, 67 date from 2015 or later.

112 records. [Akiyama and Inatani 2009] [Beers et al. 2013] [Bos and Morrison 1964] [Buursink 1998] [Carrick et al. 1998] [Casalino et al. 2019b] [Casalino et al. 2019a] [Casalino et al. 2022a] [Chandler 2019b] [Chelaru et al. 2015] [Chelaru et al. 2017] [Chen 2019] [Chen and Wu 2018] [Choi et al. 2022] [Christie 2026] [Cordes and Hertzfeld 1997] [Daniel and Ramusat 2005] [Deschamps 1985] [Duret and Fabrizi 1999] [Ellery 2017] [Fanciullo 2000] [Felix Mwiya and Wisdom Simwila Kalunga 2024] [Ferrandon 1997] [Frazier and Moser 1995] [Garvey et al. 2003] [Goldsborough 2005] [Fernandez 2024] [Griffin and Claybaugh 1994] [Grim et al. 1969] [Gulliver et al. 2017] [Haws and Bowman 2022] [Hayward 2017] [Hemza et al. 2018] [Hubbel 2000] [Hutchison 2011] [Imamura et al. 1994] [Jiawei 2024] [Jo et al. 2021a] [Jo et al. 2021b] [Jones 2017b] [Jones 2017a] [Jones 2018b] [Jones 2018a] [Jung 2026] [Kaushal 2024] [Keith 1995] [Kim 2024] [Kim et al. 2022a] [Koelle 1989] [Koelle 1992b] [Kozedra et al. 2021] [Kumar et al. 2026] [Kuriakose et al. 2020] [Kutter 2006] [Larsen 2000] [Larsen 2003] [Lee et al. 2025c] [Mankins 1994] [Ortega et al. 2024] [Marcucci et al. 2026] [Merriam 2002] [Meserole 1993] [Mingireanu 2016] [Morrison and Festa 2000] [Moser and Frazier 1994] [Najam 2014] [Nguyen and Aleti 2025] [Niederstrasser 2022] [Oldson and Carroll 1995] [Onel et al. 2019] [Palac 1999] [Park et al. 2024a] [Park et al. 2024b] [Parkinson 1995] [Parkinson 2000] [Parsons 1970] [Parsons Engineering Sciences INC Pasadena CA 1991] [Pizzuto and Ziegler 2024] [Prince 1999] [Puteaux et al. 2024] [Ridosko et al. 2024] [Rouillon and Senegas 2026] [Battelle Columbus Labs., OH (USA) 1980] [Schilling 2016] [Schmierer et al. 2019] [Schneider and Breda 2024] [Schutte and Thoreau 2016] [Seo et al. 2022a] [Shaw and Greenberg 1998] [Shaw et al. 1997] [Skoczylas et al. 2019] [Sun 2022] [Tiffin and Friz 2021] [Torres and García 2018] [Ueda et al. 2026] [Villanueva and Abbas 2015] [Vital et al. 2025] [Vrankar 2026] [Waters et al. 2013b] [Webb 2016] [Whitfield 1998] [Wilken 2024] [Wilken 2025] [Williams et al. 2015] [Wolfe and Knight 1988] [Wunderlin et al. 2018] [Yaddala Somasekhar 2024] [Yang 2020] [Zapata 2012] [Zhang et al. 2018b] [Zhang et al. 2021c] [Zhang et al. 2021a]

Cost estimation, cost growth and acquisition

Cost estimation, cost growth, design to cost and acquisition, for launch vehicles and space systems and for the defence programmes whose cost-growth literature is the larger one.

The keystone’s literature is split between two customers. Of the 245 records, 118 name a launch vehicle, a rocket, a booster, an orbit or space, and 46 name acquisition, weapons, defence or a military service. 24 titles in the survey name faster, better, cheaper.

245 records. [Accola et al. 1990] [Aerojet-General Corp Sacramento Ca 1963] [Affordable in-Space Transportation 1996] [Affordable in-Space Transportation Phase 1996] [Aggarwal et al. 2010] [Alawadhi et al. 2025] [Alexander and Fournier 1963] [Alvey 1966] [Shibanov 2024] [Apgar 2003] [Arockiam et al. 2012] [Asher and Maggelet 1980] [Aso et al. 2018] [Avery et al. 2026] [Backlund and Rossen 1971] [Baldus et al. 2013] [Balut et al. 2003] [Baruah et al. 2025] [Bedzyk et al. 1987] [Bell et al. 1964] [Bignami 2000] [Blalack 2020] [Boehm 2012b] [Boehm 2012a] [Boger and Nussbaum 1990] [Bonnín Roca et al. 2019] [Borowski et al. 2015a] [Borowski et al. 2015b] [Borowski et al. 2014] [Borowski et al. 2016] [Bradford et al. 2004] [Bradshaw et al. 1971] [Braun et al. 1970] [Brennan and Finizie 1976] [Brown 1978] [Browning 1993] [Campbell and Schneider 1969] [Capitano and Eldridge 1984] [Catena et al. 2000] [Chace 2015] [Chase and McKinney 2005] [Cheaper Faster Better? Commercial 2000] [Cifani and Martino 2013] [Cloos and Nelson 1990] [Computer-Aided Conceptual Design 1988] [Cook] [Coopersmith 2011] [Cork and Mulcahy 1977] [Corso 1969a] [Corso 1969b] [Crispo and Kim 2026] [Crose 1965] [Cruz et al. 2025] [Curtis et al. 1996] [Davis 1973] [Davis 2011] [Davis 1988b] [Defense Acquisition Univ Ft Belvoir Va 2004] [Degelsmith et al. 1993] [DeLauer 1984] [Della Vecchia et al. 2022] [Dement 1990] [Deutsch et al. 1997] [DoD Office of Inspector General 2015] [Dodson 1978] [Donahue et al. 2008] [Dreier 2022] [Drenthe et al. 2019] [Drown and Graham 2010] [Du et al. 2025] [Duffy 1993] [Eaton et al. 2022] [Ehricke 1963] [Ehricke 1964] [Enthoven 2019] [ЗЕМЛЯНСКАЯ 2023] [Etzenbach et al. 2026] [“Faster Better Cheaper?” 2003] [Feltus 1979] [Fernandes et al. 2019] [Figueroa 2024] [Fisher 2000] [FOURTEEN. Faster Better Cheaper 2017] [Franck and Dillard 2006] [French 1983] [Friedland 1965] [Fritz and Sackheim 1982] [Friz et al. 2018] [Friz et al. 2022] [Gansler et al. 2010] [Graham and Hoffman 1999] [Greaves 1997] [Greer 2010] [Gstattenbauer et al. 2006] [Guinivan 2004] [Hagnell and Åkermo 2015] [Hamaker 1999] [Hamaker 2000] [Hamid and MacDermott 2015] [Hanford 1969] [Harris et al. 2022b] [Harvey 2017] [Hauer et al. 1963] [Hellman 2006] [Hertzfeld 2000] [Hinkle et al. 2011] [Hodson et al. 2017] [Ingalls and Scott 2011] [Ivkić et al. 2024] [Ivkić et al. 2025] [Jacobs 1999] [Jain 2022] [Jo and Ahn 2022] [Jorden and Siegel 1973] [Kang et al. 2025] [Kasunic 2004] [Keating 1979] [Keaton 2015] [Keeler 2005] [Kennedy and McClure 2005] [Kha and Hamaker 2015] [Knesek et al. 2025] [Koelle 1981] [Koelle 1984] [Koelle 1992a] [Koelle 1994] [Koelle 1998] [Koelle 1999] [Koelle 2000] [Kokan et al. 2014] [Komar 2017] [Krevor and Wilhite 2006] [Lee et al. 1969a] [Lee et al. 1969b] [Lehman et al. 2000] [Li 2022] [Long 2014] [Lynch 2011] [Maddux 1999] [Man 1996] [Marcopulos 1998] [Martin 1993] [Maykut 1977] [Maynard 1969] [Maze 1985] [McCleskey and Bartine 2006] [McCleskey et al. 2012] [McCown 2011] [McCurry 1995] [McDaniel 2004] [McNicol 2014] [McNicol and Wu 2014] [Meisl 1986] [Meisl 1988] [Meisl 1989] [Miles 1996] [Moore and Cozzolino 1978] [Morel et al. 1993] [Morgenthaler 1991] [Mossman and Perkins 2001] [Naseh and Jafarpanah 2022] [Neiss and Brown 1967] [Netzel et al. 2025b] [Novick 1979] [Oki 2024] [Osterbeck et al. 1979] [Parrish 1978] [Pate-Cornell and Dillon 2001] [Friz 2020] [Paxton 2007] [Peffley 1991] [Perry 1979] [Perry 1999] [Porter and Hewitson 2005] [Portz 2004] [Prince and Hamaker 2001] [Prosser 2003] [Puening 1990] [Ralph 1999] [Rasky et al. 2001] [Rasky et al. 2000] [Rhodes et al. 2009a] [Rhodes et al. 2009b] [Rice and Locksley 2000] [Roark and Cuda 2010] [Robinson and Smith 1999] [Robinson et al. 2008] [Rogacki 2000] [Rosch and Schor 1990] [Roschli et al. 2025] [Rozum 1992] [Rubinstein 2014] [Ruiz-Torres and McCleskey 2000] [Rush et al. 1967] [Rutledge 1993] [Sebring and Young 1981] [Shah et al. 2023] [Sharma 2019] [Shearer 1997] [Shi et al. 2025b] [Shuman 2002] [Sims 1978] [Sobel 2013] [Son and Ryu 2015] [Stahl et al. 1984] [Stekler 1982] [Stewart et al. 2011] [Stroup 1967] [Stuart 1983] [Swan and Swan 2025] [Syscon Corp Washington Dc 1983] [Systems Cost Analysis 1999] [Theisen et al. 2015] [Thomas and Hanagud 1975] [Toten et al. 1991] [Townsend and Hamilton 1981] [Unal 1990] [Van Wie 1979] [Voas 2001] [Waiss 1987] [Walton and Dumas 1999] [Wang and Stockton 2001] [Washington Univ Seattle Dept Of Statistics 2007] [Watson et al. 2014] [Watzin 2001] [West et al. 2016] [Westmoreland 1977] [Westwick 2006] [Whitehead 2000] [Wickert 1985] [Winbush and James O. 2012] [Wodele 2013] [Woeppel et al. 2014] [Woerner 1995] [Womer and Camm 2003] [Yang 2019] [Yang et al. 2016c] [Yao et al. 2016] [Yelverton 1995] [Yi et al. 2023b] [Yoo et al. 2011] [Young 1992] [Zhao and Tan 2026] [Zhou et al. 2026a] [Çam and Özkol 2023]

Ablative materials, charring and recession

Ablative materials, charring and pyrolysis, surface recession and throat erosion, in rocket chambers, nozzles and motor insulation and in entry heat shields, with the fire science of charring polymers.

The engine application is the older one. Of the 455 records, 232 date from 2001 or earlier. Of the 186 from 2015 or later, 58 name atmospheric entry, a heat shield or thermal protection, and 44 name a rocket, a motor, a nozzle, a chamber or insulation.

455 records. [Canfield et al. 1987] [Abdullah et al. 2020] [Ablative Material Tests 1969] [Achambath et al. 2019] [Acharya and Kuo 2007] [Acharya and Kuo 2010] [Achenbach 1971] [Adams 1960] [Adarkar and Hartsook 1966] [Aeschliman et al. 1975] [Agrawal et al. 2016] [Ahn et al. 1998] [Akers et al. 1970] [Amar et al. 2016] [Amokrane et al. 2024] [Ananth et al. 2003] [Anderson 1969] [Anderson et al. 2024] [Atreya and Baum 2002] [Auerbach and US Atomic Energy Commission (AEC) 1966] [SNL (Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)) and US Atomic Energy Commission (AEC) 1966] [Bae et al. 2017] [Baker 1969] [Baker 1972] [Balhoff and Pike 1973] [Bano et al. 2026] [Bartlett 1964] [Bartlett et al. 1971] [Bauer and Kummer 1965] [Başkaya and Hickel 2025] [Beck and Laub 1983] [Behrens and Minier 1998] [Benjamin 1966] [Bernstein et al. 2023] [Bhat et al. 2016] [Bianchi and Nasuti 2011] [Bianchi and Nasuti 2015] [Bianchi et al. 2019a] [Bishop and Dicristina 1967] [Bishop and Dicristina 1968] [Blackwell 1988] [Blome et al. 1975] [Blumenthal et al. 1966] [Boehrk 2017] [Borsch-Supan and Hunter 1987] [Boury et al. 2011] [Boyer 2017] [Brecheisen and Ehresman 1971] [Brewer 1970b] [Brewer 1970a] [Brewster 1989] [Bryan et al. 2026] [Budzinski et al. 2020] [Bueche 1977] [Bulmer 1972] [Bunker and Nelson 1985] [Butler et al. 2016] [Carman 1966] [Castets et al. 2001] [Chandler 2023] [Chang et al. 2021] [Chang et al. 2022] [Chang et al. 2023] [Chasman et al. 2005] [Chen and Boyd 2017] [Chen and Gokcen 2015] [Chen and Gökçen 2024] [Chen and Milos 1998] [Chen and Milos 2000] [Chen and Milos 2001] [Chen and Wu 2008] [Chen et al. 1993] [Chen et al. 2015c] [Chen et al. 2015b] [Chen et al. 1994] [Chiang and Ma 2004] [Chinnaraj et al. 2023] [Chiodi et al. 2022] [Clayton 1971] [Clayton and Back 1986] [Clayton 2017b] [Clayton 2017a] [Clever and Denny 1975] [Cline and Schultz 1967] [Clinton and Wendel 1998] [Cohen et al. 1974] [Coheur et al. 2017] [Coheur et al. 2023] [Cohz et al. 1966] [Coleman et al. 1968] [Colombo et al. 1994] [Condren et al. 2024] [Congdon 1973] [Congdon 1974] [Congdon 1995] [Congdon 1996] [Congdon and Curry 2001] [Congdon et al. 2002] [Congdon et al. 2003] [Cortopassi et al. 2008] [Cortopassi et al. 2009] [Coskun and Sert 2024] [Coskun et al. 2019] [Couch 1973] [Cross 1967] [Cross and Boyd 2017a] [Cross and Boyd 2017b] [Cross and Boyd 2018] [Dahm and Schaefer 1966] [Damane and Pitot 2024] [Davies and Park 1982] [Davis 1966] [Davis 1968] [Davis and Evensen 1969] [Davuluri et al. 2022] [De et al. 1990] [Dean et al. 1990] [Dec and Braun 2005] [Dec and Braun 2006] [Dec et al. 2011] [Delaney et al. 1964] [Di Blasi 1993] [Dickerson et al. 2004] [Dickey 1968] [Dickey and Jones 1967] [Dicristina and Richards 1977] [Dimitrienko 1997] [Divo et al. 1998] [Dolan 1970] [Droms et al. 1976] [Eberhart et al. 2016] [Effect of Water 1993] [Fabrizi et al. 1996] [Farmer 1970] [Feng et al. 2015] [Feng et al. 2016] [Fio Rito 1964] [Fleming 1965] [Fleurotte et al. 2022] [Flow Simulation over 2019] [Fortner et al. 2022] [Friedman et al. 1967] [Fu and Martin 2023] [Fu et al. 2019b] [Fu et al. 2020] [Fu et al. 2021a] [Fujita et al. 2015] [Funatsu and Hiroyuki 2001] [Gannon and Laszlo 1966] [Gao et al. 2019] [Gao et al. 2020] [Gao et al. 2023a] [Gao et al. 2024] [Giardini 1986] [Gilligan et al. 1989] [Gluck et al. 1964] [Gomez 1970] [Gosma et al. 2022] [Gosma et al. 2023] [Green and Nicolet 1978] [Noffz and Bowman 1996] [Grigat et al. 2020] [Gui et al. 1999] [Gulick and Edquist 1998] [Guo and Huang 2018] [Guo et al. 2020b] [Hagemaier and Kleint 1966] [Hahn 1964] [Hall 1988] [Hamad and Nagmeldin m. elamin 2021] [Hannah and Muessig 1970] [Hasan 2022] [Haviland and Medford 1967] [He and Zhou 1992] [He et al. 2023] [Henderson and Tant 1983] [Henderson et al. 1981] [Herrick 1968] [Hickey et al. 2000] [Hickey et al. 2001] [Hillberg 1967] [Hoffman et al. 2003] [Horiuchi et al. 2017] [Howse and Lawrence 2004] [Hsiao and Chung 1986] [Huang et al. 1996] [Huang et al. 2026] [Hui et al. 2023] [Humphrey and Madden 1971] [Ito et al. 2020a] [Joatton 1970] [Johnstun 2001] [Jones et al. 1986] [Joseph et al. 2024] [Jumper and Hitchcock 1986] [Kaminsky and Johnson 1964] [Kamps et al. 2016] [Kamps et al. 2019] [Katcher 2019] [Kaul et al. 2002] [Kawabata et al. 2019] [Keller 1968] [Kelley and Thompson 1989] [Kemp 1968] [Kendall and Rindal 1964] [Kennedy 1966] [Keswani et al. 1983] [Keswani et al. 1985] [Kim et al. 2000] [Kim et al. 2020b] [Kimura et al. 2019a] [Kishore Nath and Mallesham 2023] [Klein 1987] [Klein and Gentilman 1985] [Klein et al. 1987] [Knight and Quinn 1971] [Kobayashi and Saperstein 1981] [Kojima et al. 2022] [Koo et al. 1991] [Koo et al. 2023] [Kovach and Moise 1969] [Kryvoruka 1976] [Kuby 1962] [Laganelli et al. 1974] [Lai and Leu 2023b] [Lai and Leu 2023a] [Langston et al. 2018] [Lariviere and Kezirian 2019] [Laub and McHenry 1982] [Laub and White 2002] [Lee 1965] [Letson et al. 1989] [Lewis and Anderson 1998] [Li et al. 2015a] [Li et al. 2015b] [Li et al. 2015c] [Li et al. 2016d] [Li et al. 2016c] [Li et al. 2016a] [Li et al. 2019b] [Li et al. 2020d] [Li et al. 2021c] [Li et al. 2025a] [Liggett and Menon 2007] [Lin and Ma 2000] [Lin et al. 2000] [Lincoln 1981] [Liu and Qizhi 1996] [Liu et al. 2019b] [Lizhong et al. 2002] [Lundell 1969] [Lundell 1982] [Lundell et al. 1964] [Lundell et al. 1965] [Luo et al. 2003] [Maahs 1972] [Machado and Torsani 2020] [Maddu et al. 2023] [Marquis et al. 2016] [Martin and Boyd 2015] [Martin Co Denver Co 1965] [Mastanaiah 1976] [Mayberry et al. 1968] [Mazzaracchio 2018] [McGuire et al. 2018] [McHenry and Laub 1983] [McWhorter et al. 1999] [Medford 1964] [Menon and Liggett 2007] [Mezines 1968] [Migliorino et al. 2021] [Miller et al. 2018b] [Mills et al. 1971] [Milos 1996] [Milos 1997] [Milos and Gasch 2015] [Milos and Marschall 1994] [Milos et al. 1997a] [Milos and Chen 2010] [Minyushkin and Kryukov 2019] [Mitchel 1971] [Kumar et al. 2015a] [Mohan Ramu and Poovathingal 2024] [Morlang and Strassburger 2024] [Morris et al. 2026] [Mottram et al. 1992] [Moyer and Wool 1970] [Murugan et al. 2018] [Nagler 2026] [Narsai et al. 2016] [Naughton et al. 1998] [Navaneethan et al. 2024] [Navaneethan et al. 2025] [Nelson and Mezines 1978] [Nichols and Sichel 1967] [Nichols and Sichel 1969] [Nicolet et al. 1976] [Nix and Escher 1999] [North 1983] [Odak et al. 2025] [Ogawa et al. 2019] [Oliver 2017] [Oliver and Stephanou 1963] [Olsen and Chapman 1972] [Ono et al. 2024] [Orlik-Ruckemann 1968] [Paglia et al. 2019] [Palumbo and Begun 1977] [Papadopoulos et al. 2014] [Park and Kang 2002] [Park et al. 2004] [Parmenter et al. 2001] [Patton et al. 2001] [Piacquadio et al. 2023] [Pimentel et al. 2018] [Potts 1984] [Price et al. 2022] [Prussing and Krier 1978] [Puiroux et al. 2004] [Py and Daguerre 2000] [Qin et al. 2026] [Quinn et al. 2023] [Quinn et al. 2024] [Randall 1978] [razmjooei et al 2020] [Reich and Jahn 1996] [Research on Fabrication 2026] [Richman 1967] [Richter and Smith 1995] [Riley and Landahl 1968] [Rindal and Moyer 1968] [Ringel et al. 2022a] [Rinta-Paavola et al. 2023] [Risch 2017] [Risch and Laub 1990] [Rito 1965] [Romie 1967] [Rostkowski and Panesi 2022] [Rostkowski et al. 2022] [Rotondi et al. 2022] [Sabarilal and Kumar 2018] [Saha and Bhowmick 2017] [Saha Deuri et al. 1988] [Salazar and Amar 2021] [Salazar et al. 2016] [Salvi et al. 2026] [Scandelli et al. 2023] [Schrooyen et al. 2017] [Schrödter and Baltes 1991] [Scoggins et al. 2015] [Serio et al. 1994] [Shah and Navajas Ortega 2025] [Shi et al. 2015] [Shi et al. 2018] [Shi et al. 2021] [Shih and Cheung 1997] [Shinn 1967] [Shishov et al. 1990] [Shivakumar and Cozart 2002] [Shortland and Tsai 1995] [Silver et al. 2024] [Slattery 1993] [Slosarik and Swope 1964] [Smith et al. 1992] [Smith et al. 2015] [Snowdon 1974] [Sohn et al. 1999] [Sperow 1965] [Sprague 1963] [Sreejith and Krishnamurthy 1999] [Sreejith et al. 1999b] [Sreejith et al. 1999a] [Sreejith et al. 2000] [Stadter and Weiss 1976] [Strauss 1967] [Strauss 1974] [Stroud and Brinkley 1975] [Stroud et al. 1987] [Su et al. 2022b] [Sullivan and Kobayashi 1987] [Suzuki et al. 2003] [Suzuki et al. 2004] [Swann et al. 1964] [Swann et al. 2017] [Swann and South 1961] [Szasz et al. 2015] [Tahmasbi and Noori 2021] [Tatar 2019] [Tatar 2021] [Thakre and Yang 2009] [Thermal Investigation of Charring 2015] [Thermal Protection 2015] [Thibaudeau and Whitmore 2026a] [Thibaudeau and Whitmore 2026b] [Thongsri et al. 2022] [Tian et al. 2022] [Tian et al. 2025b] [Tian et al. 2025c] [Torres-Herrador et al. 2019] [Torres-Herrador et al. 2020] [Trevino and Candler 2015] [Triebes et al. 1978] [Trinh 1994] [Trotsky and Baccarella 2024] [Trotsky and Baccarella 2025] [Tsukamoto et al. 2022] [Verderaime 1986] [Viventi 1961] [Vural and Ak 1997] [DOE and Wagner 1992] [Wagner et al. 2025] [Wakefield and Lundell 1971] [Wakefield and Pitts 1980] [Walker and Zeigler 1968] [Wang and Li 1999] [Wang et al. 2019] [Wang et al. 2025a] [Wei and Zien 2000] [Wei and Zien 2001] [Weng and Martin 2015] [Weng et al. 2021] [Wernimont 1993] [White 2014] [Wichman 1985] [Wichman and Atreya 1987] [Wilhelm 1964] [Wilhelm 1965] [Williams and White 2001] [Williamson et al. 1973] [Winter et al. 2014] [Wise et al. 1999] [Wong et al. 2015] [Wong et al. 2016] [Wool et al. 1971] [Wu et al. 2024b] [Wu et al. 2025] [Wunderlin et al. 2024] [Xiao et al. 1991] [Xu and Yang 1993] [Yamada et al. 1997] [Yinda 1986] [Yoko et al. 2018] [Yoko et al. 2019] [Zhang et al. 2023d] [Zhang et al. 2024b] [Zheng 2009] [Zheng et al. 2023] [Zheng et al. 2024] [Zheng et al. 2025c] [Zheng et al. 2025a] [Zhu et al. 2022] [Zibitsker et al. 2022] [Zibitsker et al. 2023] [Zien 1978] [Zien and Wei 1999]

Additive manufacturing and low-cost fabrication

Additive manufacturing and other low-cost fabrication, of rocket chambers, injectors and thrusters and as a process in its own right.

It is almost all recent. Of the 258 records, 236 date from 2015 or later.

258 records. [A Review on Properties 2017] [A Simulation Study 2017] [Abdala et al. 2025] [Adamou et al. 2022] [Akbulatov et al. 2023] [Allison et al. 2019] [An and Li 2023] [Andrianov et al. 2025] [Ang et al. 2020] [Aqailan and Huh 2025] [Aremu et al. 2024] [Aryal et al. 2024] [Azhagan M. et al. 2023] [Balles 2022b] [Balles 2022a] [Barnes et al. 2010] [Barros et al. 2025] [Battegazzore et al. 2024] [Bauer et al. 2020] [Benkelman et al. 2017] [Betts et al. 2011b] [Betts and Hardin 2011] [Betts et al. 2011a] [Biberstein et al. 2021] [Biedermann and Meboldt 2020] [Blösch-Paidosh and Shea 2018] [Boyd and Fazelpour 2019] [Broomby and Trifoni 2024] [Bryant 2021] [Bua 1963] [Buchholz et al. 2022] [Buettner et al. 2023] [Capparelli et al. 2026] [Carneiro et al. 2020] [Catina et al. 2016] [Chandler 2024] [Chandler et al. 2026] [Charan and Tibrewal 2025] [Chaudhary et al. 2025] [Chekurov 2019] [Chen and Smith 2021] [Chen et al. 2021c] [Chen et al. 2023b] [Chen et al. 2025c] [Cheng and Chou 2017] [Cican et al. 2023] [Connell et al. 2019] [Cubeda et al. 2021] [Cui 2025] [Dangal and Jung 2023] [Deng et al. 2020] [Di Caprio et al. 2019] [Diegel et al. 2020] [Dobrodomov 2025] [Dong et al. 2020] [Dong et al. 2021a] [Dorrell et al. 2024] [Durkee et al. 2020] [Dziubek et al. 2026] [Easley et al. 2019] [Effinger et al. 1999] [Ehlers et al. 2021] [Eom and Hong 2025] [Ergin et al. 2024] [Ermakova and Mehmanparast 2022] [Ertugrul 2024] [Eskue 2023] [Fasel et al. 2020] [Векілов and Ліповський 2023a] [Fedotowsky et al. 2024] [Fodor 2017] [Fritz et al. 2017] [Fuller 1973] [Gawron et al. 2023] [Gaynor and Johnson 2020] [Giambelli et al. 2026] [Giurgiutiu and Lin 2004] [Gleadall 2021] [Godderidge et al. 2024] [Gotzig 2015] [Gradl and Protz 2020] [Gradl et al. 2017] [Gradl et al. 2018b] [Gradl et al. 2018a] [Gradl et al. 2021] [Gradl et al. 2024] [Gradl and Brandsmeier 2016] [Gradl et al. 2019a] [Gradl et al. 2019b] [Großmann et al. 2020] [Gu et al. 2017] [Gu et al. 2023] [Guo et al. 2020a] [Gupta et al. 2022] [Han and Lu 2018] [Hanks and Frecker 2019] [Hernandez et al. 2019] [Hernandez-McCloskey et al. 2023] [Hicks and Siddiqui 2026] [Hitt 2018b] [Hitt 2018a] [Hoppin et al. 1980] [Hudson and Fidan 2024] [Imani and Khanzadeh 2021] [Jansari et al. 2026] [Jere et al. 2025] [Jing et al. 2021] [Johnson and Kujawski 2025] [Prasad et al. 2025] [Kalia and Ameli 2024] [Kamps et al. 2018] [Kapelyushin et al. 2026] [Karakai and Karpovych 2026] [Keller et al. 2024] [Keller et al. 2025a] [Keller et al. 2025b] [Kennedy and Weldon 2024] [Kerstens et al. 2021] [Kim et al. 2019] [Kim et al. 2025d] [Knauer and Edman 1991] [Knauer et al. 1993] [Ko et al. 2021] [Krishnan and Thakur 2024] [Krishnanand and Taufik 2021] [Kumar et al. 2019] [Kumar et al. 2020] [Kunka and Jacob 2017] [Kuntanapreeda and Hess 2020] [Lan 2017] [Landau et al. 2020] [Lang et al. 2021] [Lazarets 2026] [Lee et al. 2020b] [Lee et al. 2023] [Leonetti et al. 2026] [Li 2020] [Li et al. 2020a] [Li et al. 2023a] [Lim et al. 2025] [Lindberg and Campbell 2019] [Liu et al. 2020] [Luo 2024] [Ma et al. 2024a] [Mackey et al. 2026] [Mahan and Menold 2020] [Malim et al. 2023] [Man’ko and Коzis 2019] [Stachulla et al. 2019] [Mathur et al. 2023] [McClain et al. 2019b] [McClain et al. 2019a] [McConaha and Anand 2020] [McCoy 1988] [McKnight et al. 2015] [Meier and Key 2025] [Melo et al. 2022] [Michell 2016] [Minguella-Canela et al. 2023] [Moetazedian et al. 2021] [Monokrousos et al. 2024] [Mosolov et al. 2021] [Mozaffar et al. 2023] [Muhammad 2021] [Murugan et al. 2023] [Nagulin et al. 2022] [Nair et al. 2019] [Norman et al. 2021] [Ntintakis et al. 2025] [Oh et al. 2018a] [Ortega et al. 2020] [Ortega et al. 2023] [Oztan and Coverstone 2021] [Oztan et al. 2021] [Palacios Hervas 2026] [Pantoja and Wallick 2023] [Patel et al. 2019] [Peng et al. 2020] [Peterson and Liu 2015] [Petsiuk and Pearce 2022] [Peugeot et al. 2014] [Phillips et al. 2020] [Polizzi et al. 2025] [Poulopoulos et al. 2026] [Prasad et al. 2022] [Protz et al. 2014] [Protz et al. 2016] [Pu et al. 2026] [Pustovyi 2026] [Qu et al. 2024b] [Rahimi et al. 2023] [Rastegarzadeh and Huang 2023] [Ringel et al. 2022b] [Rivas Santos et al. 2020] [Robertson et al. 2021b] [Rouina et al. 2021] [Rupert and King 2025] [Sandoval et al. 2018] [Schuller et al. 2024] [Shams et al. 2021] [Shen et al. 2020a] [Shynkarenko et al. 2024b] [Simpson 2021] [Sirenko 2025] [Slowik 2019] [Smith and Bardaweel 2018] [Snow and Hunsaker 2021] [Special Section 2017] [Springer et al. 2020] [Stickler and Keller 1998] [Sung and To 2026] [Swensen 2024] [Tam et al. 1996] [Tam et al. 1997] [Tam et al. 1998] [Tam et al. 2000] [Tam et al. 2002] [Teasley et al. 2021] [Векілов et al. 2023] [Thomas 2022] [Thomas 2023] [Thompson et al. 2019] [Thompson et al. 2026] [Thostenson et al. 2024] [Tian 2025] [Titotto 2024] [Tommila and Hartsfield 2017] [Tucker and Schmidt 2016] [Unternbaumen et al. 2026] [Van Den Berghe et al. 2020] [Veerasamy et al. 2025] [Wakefield 1986] [Walker et al. 2020] [Wang and Song 2025] [Wang and Xia 2022] [Wang et al. 2017a] [Wang et al. 2018b] [Wang et al. 2021a] [Wang et al. 2021c] [Warga 1970] [Weber and Ruff-Stahl 2017] [Whitmore 2015] [Whitmore and Heiner 2019] [Whitmore and Merkley 2019] [Wiberg et al. 2019] [Woodger et al. 2025] [Woods et al. 2016] [Wright et al. 2023] [Wu and Baur 2024] [Wu and Yuan 2025] [Wu et al. 2024a] [Xiong et al. 2022] [Yaghi et al. 2019] [Yang et al. 2023a] [You and Park 2021] [Zappino et al. 2026] [Zawaski and Williams 2020] [Zhuravlev et al. 2025]

Gas-side heat transfer and the cooling of chambers

Gas-side heat transfer in chambers and nozzles, and film, regenerative and transpiration cooling, with the conjugate heat transfer and cooling-channel studies that share their physics.

504 records. [Faizrakhmanova et al. 2025] [Ables and Davis 2014] [Abulawi et al. 2025] [Agarwal et al. 2021] [Aksonov et al. 2023] [Alves Avelino and Chalhub 2021] [Amato et al. 2016] [Amos et al. 1958] [Векілов and Ліповський 2023b] [Anderson et al. 1993] [Andrews et al. 1986] [Anum et al. 2022] [Arakeri 1980] [Arhami et al. 2025] [Martinez et al] [Armstrong 1986] [Arun and Prakash 2018] [Aslan et al. 2015] [Assadi et al. 2022] [Assonitis et al. 2024] [Azuma et al. 2016] [Azuma et al. 2019] [Bacci et al. 2025] [Back and Cuffel 1970] [Back and Cuffel 1971] [Back and Cuffel 1972] [Back et al. 1964] [Back et al. 1970b] [Back et al. 1970a] [Back et al. 1969] [Baek and Ahn 2020] [Barbato 2023] [Bartle and Leadon 1960] [Bassina et al. 2001] [Bates et al. 2002] [Batista et al. 2024] [Batista et al. 2026] [Becchi et al. 2016] [Beddini and Owano 1987] [Beitel 1991] [Bejan 1983] [Benderskii and Chernova 2022] [Benderskiy and Chernova 2021] [Benderskyi and Chernova 2020a] [Best 1982] [Betti et al. 2015] [Bi et al. 2025] [Bills et al. 2016] [Bobisud 1983] [Boden 1951] [Bohn and Moritz 2001] [Boldman et al. 1967] [Bolshov et al. 1996] [Bose 1978] [Broatch et al. 2019] [Broatch et al. 2020] [Brooker et al. 1998] [Brown et al. 1964] [Brown 1991] [Buchanan et al. 2018] [Bulat et al. 2024] [Burkhardt and Hayes 1992] [Busam et al. 1999] [Bäker et al. 2015] [Calhoon et al. 1973] [Campo et al. 1996] [Carden 1964] [Cardillo et al. 2023] [Champion and Deshaies 1995] [Chang 1956] [Chang et al. 1996] [Chang et al. 2026] [Chavez and Dawson 1978] [Chen et al. 2015a] [Chen et al. 2021a] [Cheng and Wong 2023] [Cherkupalli and Sandeep 2022] [Chiu 1986] [Choi et al. 1997] [Chou and Kalina 1982] [Chu et al. 2019] [Chu et al. 2025] [Clayton 1999] [Clayton 2001] [Cocirla et al. 2025] [Coleman 1986] [Concio et al. 2021] [Concio et al. 2023] [Connell et al. 1992] [Cooper and Martin 2021] [Coulbert 1963] [Crachi et al. 2024] [Croce et al. 2015] [Cui 2020] [Lise, i, M H N 1995] [Da Soghe and Bianchini 2019] [Daimon et al. 2017] [Darbandi and Jalali 2022] [Das et al. 1988] [Delogu et al. 2026a] [Delogu et al. 2026b] [Deng et al. 2016] [Deng et al. 2026] [Слюсарєв and Бучарський 2024] [Dharshan 2019] [Di et al. 2026] [Dicristina 1979] [Dillon and Line 1956] [Dinh and Trifoni 2023] [Djeffal et al. 2024] [Dmitrenko 1998] [Dresia et al. 2023] [Drobyshev 2026] [Du et al. 2019b] [Duan et al. 2022] [Dudareva 2025] [Dunlap and Kuethe 1961] [Dutta and Smith 2020] [Dutta et al. 2016] [Dzodzo 2022] [Eaton and Mathias 2000] [Eckert and Goldstein 1982] [Elkind 1964] [Elliott and Rose 1957] [Emidio et al. 1998] [Emory 2022] [Enomoto and Furuhama 1989] [Han 2004] [Fan and Cheung 1996] [Fan et al. 2024] [Fassin et al. 2016] [Fayyazi et al. 2025] [Fehr and Wensley 1970] [Feldkamp et al. 2025] [Ferreira and Dourado 2018] [Fidler and Hays 2026] [Fiedler et al. 2015] [Fiedler et al. 2019] [Fiore et al. 2024] [Fiore et al. 2025] [Fischer and Norris 1949] [Fragnaud 1996] [Franceschetti et al. 2025] [Froehkle et al. 1998] [Fu et al. 2026] [Furlong et al. 2025] [Garcia et al. 2020] [Garimella and Nenaydykh 1996] [Gelain et al. 2022] [Georgieva 2026] [Giovanetti et al. 1983] [Giovanetti et al. 1984] [Gordon 1950] [Gorelov 2019] [Gorelov 2023] [Gorelov and Tyul’kov 2018] [Graber and Clark 1972] [Hall et al. 1994] [Han et al. 2024] [Hao et al. 2017a] [Harvazinski and Houba 2022] [Harvazinski and Houba 2023] [Harvazinski et al. 2024] [Hasegawa and Yoshioka 2019] [He and Liu 2018] [He et al. 2019a] [Hegab and Kassoy 2001] [Heldens et al. 2021] [Herman and Melnik 1962] [Heyda 1957] [Hishida et al. 1982] [Ho et al. 2016] [Hodge and Taylor 1991] [Hoffman and Eaton 2021] [Hoffman et al. 2018] [Hoffmeyer et al. 2019] [Horton 1976] [Hou et al. 2017] [Howell 1968] [Hu and An 2024] [Huang et al. 2022] [Höglauer et al. 2015] [Hötte and Haupt 2020] [Ichiyanagi et al. 2020] [Indelicato et al. 2021] [Ingebo 1961] [Ishii et al. 2019] [Issakhov et al. 2024] [Campbell et al. 1964] [Jaiswal et al. 2024a] [Jennings and Morel 1987] [Jeon and Park 2026] [Jeong et al. 2023] [Jeong et al. 2024] [Jia 1987] [Jia and Chung 1996] [Jia et al. 2018] [Jiang et al. 2023] [Jing et al. 2018] [Johnson et al. 2026] [Kacynski and Hoffman 1994] [Kacynski et al. 1987] [Kang et al. 2024] [Karabey and Bozdogan 2022] [Kaufman and Louis G. 1964] [Kaye and Brown 1954] [Keener et al. 1995] [Kendall and Holman 1996] [Kilham and Dunham 2019] [Kim and Choi 2024] [Kim et al. 2015] [Kim et al. 2025a] [Knab et al. 1998] [Kolesnik and Novikov 2023] [Kringe et al. 2022] [Krinsky 1978] [Krishnamoorthy 1982] [Kumar and Bansal 2024] [Kumar et al. 2015b] [Kumar et al. 2021] [Kuwahara et al. 2001] [Kühlwein et al. 2024] [Laganelli 1970] [LaGraff 2001] [Lakshminarayana and Luo 1996] [Latini et al. 2022] [Lee 1963] [Lee 1964] [Lee and Lee 1995] [Lee and Smith 1974] [Lee et al. 2024a] [Leitner 1986] [Левихин and Musteikis 2025] [Li and Wang 2024] [Li et al. 2017b] [Li et al. 2024e] [Li et al. 2025g] [Librizzi and Cresci 1964] [Lienhard and Napolitano 1996] [Lieu 1964] [Lindqvist et al. 1997] [Linne 1993] [Liquid Rocket Engine Fluid-Cooled 1972] [Litchfield and Norton 1982] [Liu and Tiwari 1996] [Liu et al. 1998] [Liu et al. 2022b] [Liu et al. 2022a] [Liu et al. 2023c] [Liu et al. 2023e] [Liu et al. 2026] [Lobanov et al. 1998] [Longobardo et al. 2026] [Luan et al. 2017] [Ludescher and Olivier 2018] [Lv et al. 2023] [Lytle and Webb 1994] [Ma 2016] [MacFarlane and Madell 1964] [Machado 2025] [Maciejewski 1995] [Makhija et al. 2024] [Maldonado 1994] [Manjhi and Kumar 2019] [Marocco and Franco 2016] [Masiulaniec et al. 1995] [Mastanaiah 1978] [May and Burkhardt 1991] [Mayer 1961] [Mayer and Prickett 1986] [Mayo et al. 2016] [Mecklenburg 1966] [Mehdizadeh et al. 2017] [Mehta 1981] [Meinicke et al. 2018] [Mendu and Parameswaran 1995] [Merzlikin et al. 2019] [Michel 1983] [Micklow 1996] [Noel and Massier 1962] [Mirzamoghadam 1991] [Mitsuishi et al. 2020] [Miyashita et al. 2026] [Modise and Magalakwe 2022] [Modlin and Colwell 1992] [Mondal and Sharma 2025] [Moosaie 2024] [Mukambetov and Borovik 2022] [Mulla et al. 2023] [Multi-Dimensional Modeling of Convective 1989] [Murthy and Sheu 1988] [Nag et al. 2023] [Nakayama et al. 2019] [Narayanan et al. 1996] [Nasuti and Pizzarelli 2021] [Nasuti et al. 2021] [Negishi et al. 2015] [Nesbitt 1990] [Nesbitt 2000] [Nguyentat et al. 1991] [Ni et al. 2021a] [Nidhi et al. 2016] [Niino et al. 1982] [Nilesh and Kamlesh 2020] [Nourin and Amano 2023] [Aerojet-General Corp., Sacramento, Calif. (USA) 1972] [Nunome et al. 2019] [Obrien 1989] [Oh et al. 2019] [Okano and Haga 2026] [Olcucuoglu et al. 2018] [Olivero et al. 2018] [Olmeda and Stemmer 2019] [Olson and Allen 1998] [Ortiz and Acharya 2023] [Oyewola et al. 2022] [Oz and Kara 2024] [Ozturk et al. 2023] [O’Donnell et al. 2016] [Padmanabhan et al. 2022] [Palaszewski 1997] [Palaszewski and Zakany 1996] [Palej and Palacz 2018] [Paramo and Arizpe 2024] [Parent 2021] [Pattanaik and Anupindi 2025] [Pelevin and Ponomarev 2018] [Pelevin and Ponomarev 2021] [Pelevin et al. 2012] [Perakis et al. 2018] [Perakis et al. 2021] [Persh 1955] [Piergallini and Stoll 1980] [Pinheiro Maia and Marinho 2018] [Pizzarelli 2021b] [Pizzarelli 2021a] [Pizzarelli et al. 2015] [Pizzarelli et al. 2024] [Polidori et al. 1996] [Poovathingal et al. 2023] [Potier et al. 2022] [Potter et al. 1993] [Pourghasemi and Fathi 2022] [Prakash et al. 2017] [Preclik et al. 1998] [Price 1980] [Pu et al. 2018] [Pörtner et al. 2026] [Qi 2023] [Qiu et al. 1995] [Quinn 1966] [Radhakrishnan et al. 2024b] [Raghuraman et al. 1994] [Rahn et al. 2019] [Raju et al. 2021] [Reiss and Bölcs 2000] [Remiddi et al. 2022] [Ren et al. 1997] [Ren et al. 1998] [Ricci et al. 2022] [Ricci et al. 2023b] [Robles et al. 2017] [Rodriguez and Kalman 2024] [Roland et al. 1966] [Rose 1958] [Rubtsov and Ogurechnikova 1988] [Ruiz et al. 2021] [Sa et al. 2017] [Saha et al. 2017] [Sakai and Takahashi 2017] [Samkhaniani 2016] [Sandri et al. 2025] [Sankar et al. 2017] [Saravani et al. 2018] [Sarbu and Iosif 2017] [Satish and Venkatasubbaiah 2020] [Saums et al. 2016] [Sayed et al. 2024] [Sayyar and Saghafian 2017] [Sbutega and Catton 2015] [Scala 1962] [Scanlan and Alter 1953] [Schacht and Quentmeyer 1973] [Schoenman 1991] [Schoyer 1980] [Seidel 1974] [Seyed-Yagoobi et al. 1998] [Shanmugam and Sun Park 2024] [Sheremet 2021] [Sheremet 2023] [Shilwant and Mahulikar 2024] [Shin et al. 2022] [Shine and Nidhi 2018] [Shorter et al. 2025] [Sibulkin 1956] [Sichler et al. 2018a] [Singh et al. 2018] [Singh et al. 2020] [Singh et al. 2021] [Snyder 1990] [So and Speziale 1999] [Sobhani et al. 2017] [Sokolov and Tupitsyn 2019] [Somhorst and Oevermann 2024] [Song and Sun 2017] [Song et al. 2022] [Sounik and Wright 2024] [Spencer et al. 1978] [Sreekanth and Reddy 1994] [Sreekanth and Reddy 1995] [Srivastav et al. 2024] [Steinetz and Dunlap 2001] [Steinetz and Dunlap 1999] [Stepanov et al. 2016] [Stepha and Jacob 2021] [Stonehill et al. 2023] [Strobel and King 1993] [Strokach et al. 2020] [Sultana et al. 2024] [Sun et al. 2021b] [Sun et al. 2022] [Suresh et al. 2019] [Symons 1987] [Takita and Masuya 1999] [Talbot 1986] [Taylor 1970] [Teasley et al. 2025] [Thompson 2022] [Tiwari and Moharana 2019] [Tsongas 1966] [Tucker and Warsi 1993] [Turner and Ash 1990] [Vadasz 2018] [Valler 1979] [Vasilevsky 2022] [Velásquez et al. 2023] [Verstraete and Scholl 2016] [Vijaybabu and Dhinakaran 2018] [Vintsarevich et al. 2020] [Voisinet and Lee 1972] [Von Eckartsberg et al. 2025] [Vural and Ak 1996] [Wadel and Meyer 1996] [Wadel and Wadel 1997] [Wahid et al. 2025] [Wang 2015a] [Wang and Van 1992] [Wang et al. 2016c] [Wang et al. 2016a] [Wang et al. 2018c] [Wang et al. 2020d] [Wang et al. 2024b] [Waqas et al. 2021] [Weaver 1994] [Weaver and Gramoll 1996] [Wehofer 1963] [Wei et al. 2022b] [Willeke and Verstraete 2015] [Williams 1972] [Williams and Giedt 1977] [Witkowski and Rothamer 2023] [Wu 2019] [Wu and Zhou 2015] [Xiang et al. 2020] [Xiang et al. 2024] [Xiao et al. 2025] [Xie et al. 2019] [Xie et al. 2023] [Xiong et al. 2026] [Xu et al. 2021] [Xu et al. 2023a] [Xu et al. 2023d] [Xu et al. 2024b] [Yan 2020] [Yan et al. 2018b] [Yan et al. 2018a] [Yan et al. 2023b] [Yang et al. 2022b] [Yang et al. 2025b] [Yoon et al. 2023] [Yu and Chen 1969] [Zha et al. 2024] [Zhang 2000] [Zhang 2018] [Zhang and Men 2019] [Zhang and Xia 2026] [Zhang et al. 2023g] [Zhang et al. 2024f] [Zhang et al. 2024a] [Zhang et al. 2025b] [Zhao et al. 2022] [Zhao et al. 2024] [Zheng and Yao 2026] [Zhou et al. 2016a] [Zhou et al. 2020a] [Zhou et al. 2021b] [Zhou et al. 2023b] [Zhou et al. 2025] [Zhu et al. 2015] [Zhu et al. 2021a] [Zhukov and Suslov 2016] [Zhumali et al. 2026] [Zien 1974] [Zucrow and Graham 1957]

Liquid rocket engines, turbopumps and combustion

Liquid rocket engines, their cycles, gas generators, turbopumps, injectors and combustion, including combustion instability and kerosene, methane and hydrogen propellants.

678 records. [Adams 2004] [Adoua and Page 2017] [Aerojet-General Corp Sacramento Ca 1966] [Air Force Research Lab Edwards AFB CA 2000] [Alliot et al. 1990] [Altseimer 1952] [Alves Almeida et al. 2024] [Alvis and Chessman 1957] [Amateur Gas-Propelled Rocket Engine 2004] [Aminov et al. 2023] [An Experimental Study 1981] [Назаренко 2023] [Anderson et al. 2012] [Anderson et al. 2013] [Anderson et al. 2015b] [Andreadis et al. 2002] [Andreadis et al. 2003] [Andrews et al. 2018] [Anisimov et al. 2016] [Appel and Kruger 1980] [Barashkov 2024] [Ardema et al. 1995] [Arita et al. 2000] [Armbruster et al. 2021] [Atamanchuk 2025] [Augousti et al. 2018] [Ayran et al. 2026] [Bailey 1964] [Bairamov and Bairamov 2022] [Balcomb 1972] [Balepin 2001] [Balepin et al. 2001] [Barber and Schultheiss 1967] [Barrère 1977] [Beaurain et al. 1992] [Beck and Beach 2003] [Beltran and Kosvic 1966] [Belyakov 2022] [Berg 1968] [Berger et al. 2015] [Berggren et al. 1948] [Bermudez 2024] [Bernstein et al. 1949] [Betady et al. 2018] [Bewley 1989] [Binder 1993] [Bing and Gong 2015] [Bjorklund et al. 1979] [Blake and Esselman 1961] [Borowski et al. 2012a] [Borowski et al. 2012b] [Borowski et al. 2017] [Bortoloto et al. 2023] [Bosson and Goirand 1999] [Bragg 1963] [Breshears et al. 1966] [Brophy and Hawk 1990] [Broughton 1962] [Bruccoleri and Daniel 2009] [Burrows 2008] [Burton et al. 2008] [Butler 1999] [Börner et al. 2017] [Campbell and Riccio 1995] [Cha et al. 2024] [Chamis 1983] [Chandler 2019a] [Chandler and Herrera 2025] [Chandler et al. 2002] [Chandra et al. 2025] [Chelouati et al. 2021] [Chemnitz et al. 2018] [Chen et al. 2022c] [Chen et al. 2025b] [Cheng and Farmer 2002] [Chicatelli et al. 2006] [Childress-Thompson et al. 2016] [Chin 1994] [Chiu 1987] [Chiu et al. 1990] [Cho and Chang 2004] [Cho et al. 2004] [Cho et al. 2019] [Choi and Moon 2022] [Christenson and Holt 1995] [Christenson et al. 2003] [Christison 2024] [Chung et al. 2025] [Cichon et al. 2026] [Citarella et al. 2022] [Combs 1970] [Combs and Hoehn 1964] [Combs and Schuman 1965] [Cooper et al. 2024] [Coopersmith and Davis 2016] [Cox 1988] [Cox 1987] [Crocker and Peery 1998] [Cycle Analysis of Lox/Lh2 2025] [Czysz and Little 1993] [Dai and Huang 2021] [Dang and Nickerson 1987] [Das et al. 2024] [Dastanian et al. 2025] [Davidian 1989] [Davidian 1990] [de Groot 1998] [DeBonis and Yungster 1996] [Deiros et al. 2025] [DeJarnette 2018] [DeLong et al. 2007] [Denisov et al. 1960] [Diachenko and Temnov 2015] [Digumarthi and Chang 1984] [Dijkstra et al. 1995] [Dineshkumar et al. 2021] [Dolgih 2025] [Dong et al. 2019] [Dong et al. 2025a] [Dou et al. 2025] [Drake 1990] [Dressler et al. 1993] [Driscoll 1986] [Du 2017] [Dubois et al. 1995] [Duggleby et al. 2025] [Duke and Houghton 1966] [Duke and Houghton 1967] [Dunn 1990] [Durham and Kirk 1972] [D’Alessandro et al. 2021] [D’Souza et al. 2022a] [Edwards et al. 2003] [Effect of Distributed Injection 2017] [Eggleston 1995] [Eklund 2004] [Elias and Gordon 1952] [Ellis 2013] [Ellis et al. 2001] [Emdee 2001] [Enomoto and Furuhama 1985] [Enomoto and Furuhama 1986] [Erol and Ünsal 2026] [Etzenbach et al. 2025] [Fang 1984] [Fanqi et al. 2023] [Farmer et al. 1996] [Farmer et al. 1998] [Farmer et al. 1999] [Felix and Bohl 1959] [Feng et al. 1985] [Fernandez et al. 2018] [Ferraiuolo et al. 2023] [Frady et al. 2002] [Franklin and Tinsley 1970] [Freiherr 2016] [Friedman 1953] [Fujio and Ogawa 2024] [Fultyn 1900] [Funazaki et al. 2020] [Fusselman et al. 2019] [Gale and Moedt 1962] [Ganesan et al. 2025] [Gangeh et al. 2023] [Gao et al. 2023c] [Gao et al. 2025] [Garwol 2024] [Gavitt et al. 1997] [Gaynor and Cervisi 1984] [Gibart et al. 2024] [Gibson 1985] [Gompertz 1950] [Gong et al. 2015] [Gong et al. 2017] [Gorla et al. 2025] [Green 1966] [Green 1994] [Greene 2017] [Greene 2011] [Grey 1953] [Griffin et al. 1999] [Gro¨nstedt and Pilidis 2000] [Gu et al. 2021a] [Guidos and Seymour 2003] [Gulczynski et al. 2023] [Gulczyński et al. 2024] [Gulczyński et al. 2026] [Gunn and Hundal 1994] [Guo and Wehrmeyer 1997] [Guo et al. 2022a] [Gut et al. 2025] [Ha et al. 2020] [Hajar et al. 2025] [Hamid et al. 2025] [Han et al. 2026b] [Hardgrove and Krieg 1984] [Hargus et al. 2018] [Harris et al. 2000] [Harrje 1959] [Harstad and Bellan 1998a] [Harstad and Bellan 1998b] [Harvazinski et al. 2014] [Hautman 1995] [Heister 2008] [Herbertz 2016] [Herbertz et al. 2001] [Herget et al. 1969] [Herman et al. 2015] [Hicks 1992] [Higashi 2023] [Hirai 2015] [Hirai et al. 2021] [Ho 1992] [Ho et al. 1989] [Hoff 1967] [Hoffman 1970] [Hoffman et al. 2024] [Holmes and Hsia 1960] [Hooper and Kostusak 1991] [Horton 1964] [Howe 1986] [Hu and Zhang 2019] [Huang 2002a] [Huang 2002b] [Huff and Kerrebrock 1954] [Hulka 2010] [Hutt et al. 2001] [Hyde and Argueta 2025] [Hydrostatic Bearings for Cryogenic 1969] [Il’Yashenko 1963] [Ilegbusi 1996] [ДП «Конструкторське бюро «Південне» ім. М.К. 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Solid and hybrid rocket motors

Solid and hybrid rocket motors, their propellants, grains, cases and combustion.

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al. 2021] [Meadors et al. 2000] [Mehta et al. 2011] [Meichin and Tanaka 2019] [Miccio 1998] [Miccio 2016] [Michigan Univ Ann Arbor 1963] [Moon and Lee 2016] [Moore and Phelps 2011] [Moran and Houston 2011] [Morita 2020] [Morrow and Petersen 2017] [Moto et al. 2021] [Mugot et al. 2024] [Mugot et al. 2026] [Mungas et al. 2003] [Murari et al. 2019] [Naka 2021] [Nardozzo et al. 2019] [Naval Weapons Center China Lake CA 1963] [Naval Weapons Center China Lake CA 1964] [Neilson and Gilchrist 1968] [Nelson and Fields 1995] [Netzel et al. 2025a] [Nguyen 2020] [Nidagalkar et al. 2024] [Nielsen 1966] [Obreque and Díaz 2022] [Ogawa and Sasaki 2017] [Oishi et al. 2023] [On the Axial Velocity 1982] [Osborn and Bonnell 1961] [Osborn and Davis 1961] [Osherov and Natan 2000] [Osherov et al. 1996] [Passarani et al. 2026] [Pearson and Sutton 1966] [Perlmutter and DePierre 1965] [Person et al. 2026] [Pesqueira 1945] [Petrenko and Popov 1996] [Pinalia et al. 2021] [Plane 1963] [Plane 1964a] [Plane 1964c] [Plane 1964b] [Povinelli and Rosenstein 1964] [Prianto et al. 2021] [Price 1964] [Price 1965] [Price and Dehority 1967] [Price et al. 1971] [Prince et al. 1989] [Prins et al. 1992] [Qu et al. 2024a] [Quero Granado et al. 2021] [Quilici 1984] [Raji and Rose 2024] [Ramadhan et al. 2024] [Ramohalli and Magiawala 1981] [Rampazzo and Barato 2023] [Rastogi and Ouseph 1965] [Riehl et al. 2002] [Rison et al. 1967] [Rosciszewski 1965] [Rotondi et al. 2023] [Rowland and Grubelich 1996] [Roys 1977] [Ruesch et al. 2021] [Sagawa et al. 2019] [Saha and Chakraborty 2016] [Saiki et al. 2026] [Sakurai and Hayashi 2015] [Schulze and Meyer 1993] [Schöyer and Korting 1986] [Sebisty 1959] [Seidel 1965] [Setiadi et al. 2022] [Shannon 1970] [Sharn 1962] [Shiwa et al. 1990b] [Shiwa et al. 1990a] [Shiwa et al. 1994b] [Shiwa et al. 1994a] [Shynkarenko and Cunha Martins 2017] [Shynkarenko et al. 2024a] [Smallwood 1966] [Smallwood 1967] [Smith-Kent et al. 1993] [Song et al. 2023] [Sparks 1988] [Srivastava and Jayachandran 2022] [Srivastava and Jayachandran 2023] [Srivastava and Thakur 2022] [Srivastava et al. 2024] [States 2001] [Stehling 1952] [Stephenson 2018] [Stoker 1964] [Story 2014] [Story 2015] [Strahle and Handley 1978] [Strand et al. 1993] [Sethi et al. 2026] [Szatkowski 1985] [Tajima 1965] [Takaki et al. 2022] [Tamang 2025] [Terashima et al. 2021] [Thomas and Nandi 1976] [Thomas and Petersen 2022] [Thomas and Petersen 2023] [Tseng and Yang 1994] [Tsien 1952] [Valencia et al. 2026] [Villanueva 2016] [Villanueva 2018] [Villar and Rezende 2015] [Waesche and Summerfield 1965] [Wagner and Cleveland 1991] [Wang 1993] [Wang and Feng 1999] [Wang et al. 1996b] [Wang et al. 2016d] [Wang et al. 2022a] [Wang et al. 2024f] [Wang et al. 2025b] [Ward 1971] [Ward 1970] [Wardach-Święcicka and Kardaś 2024] [Wei 1987] [Wenzhi et al. 2024] [Whitney and Hennessey 1992] [Wong 1968] [Wormhoudt 2003] [Wyld 1947] [Xiao et al. 2001] [Xu et al. 2019] [Xu et al. 2020a] [Yoda et al. 2015] [Zhang et al. 2025e] [Zhu et al. 2021b] [Zinn 1972] [Zinn 1973] [Zolla et al. 2026]

Rocket nozzles, plumes and expansion

Rocket nozzles, their flow, expansion and thrust vector control, and exhaust plumes.

206 records. [Ahmed and Gross 2023] [Aikens et al. 2015] [Alexandrov 2026] [Altman and Penner 1949] [Application of Double Divergent 2022] [Ashforth-Frost and Jambunathan 1996] [Prasad et al. 2019] [Baetz 1974] [Balwanz 1965] [Bauer 1980] [Bekka et al. 2015] [Bennaceur et al. 2026] [Bhaskar and Sahu 2021] [Blades et al. 2017] [Boraas 1983] [Bowles and Tenney 1981] [Brazzel 1963] [Broadwell 1963] [Brodsky 1970] [Brogan 1984] [Brunner and Buse 1977] [Bryson 1968] [Bundy and Strong 1948] [Burdett 1946] [Butler 1964] [Cabello et al. 2025] [Cai 2015] [Cai et al. 2019] [Candler 2005] [Chaiaiad and Thongsri 2023] [Chang 1980] [Chaplin 1957] [Chen 2018] [Computational Analysis of Combustion 1981] [Conte et al. 2019] [Crowe 1967] [Crowe and Willoughby 1966] [Crowe and Willoughby 1967] [Crowe et al. 1968] [Crown 1950] [Daily 1989] [Davidian 1987] [Daviller et al. 2020] [Demetriades 1977] [Denton et al. 2025] [Dillaway 1957] [Ding et al. 2019] [Dominguez Calabuig et al. 2024] [Dougherty and Liu 1991] [Driggers 1975] [Ebrahimi et al. 1998] [Ederouich et al. 2021] [Eggers 1961] [Electrodeposition Forms Rocket Nozzle 1961] [Ellison and Ojala 1969] [Erhart 1992] [Ferrero and Pastrone 2019] [Fisher 1978] [Franco-Ferreira 1967] [Franco-Ferreira 1968] [Fredericks and Shorr 1972] [Gale et al. 2017] [Gandge et al. 2022] [Gates and Cochran 1961] [Ghosh and Gunasekaran 2021] [Glowacki 1971] [Gregg 1988] [Guimond et al. 2015] [Gummadidala et al. 2025] [Gundersen 2001] [Hadjadj et al. 1997] [Hale 1963b] [Harikrishnan and Lokavarapu 2021] [Harroun et al. 2020] [Hauptman 1965] [He et al. 2022] [Hiers and Knapke 2019] [Hoertel 1961] [Hosack and Stromsta 1969] [Huskey 1975] [Ilie and Sullivan 2022] [Isono and Fujikawa 2025] [Janardan and Zinn 1977] [Janardan et al. 1974] [Janardan et al. 1975] [Jayaprakash et al. 2022] [Jenkins 1990] [Jensen and Jones 1981] [Jensen and Wilson 1975] [Jiang et al. 2018] [Jones et al. 2013] [Jones et al. 2014] [Joseph et al. 2020] [Kanfoudi and Zgolli 2015] [Kimura et al. 2018] [Knickerbocker et al. 2026] [Krieger 1951] [Krishna 2020] [Krishnan and Tucker 1992] [Krzycki 1965] [Kumar and Ghosh 2018] [Kumar and Siddapureddy 2025] [Kurita et al. 2020] [Langford et al. 2007] [Lankford 1987] [Lebedev et al. 2000] [Lee 2018] [Lent 1944] [Lepicovsky 1990] [Lewis and Harrison 1961] [Lewis and Williams 1975] [Liao et al. 2023a] [Liu and Ramamurti 2018] [Maicke 2017] [Manda 1966] [Manski and Hagemann 1994] [Manski and Hagemann 1996] [Matveev et al. 2018] [Mehta et al. 2017] [Metghalchi 2009] [Micci 1975] [Mikhail 1979] [Miley et al. 2020] [Monroe 1945] [Muhammad et al. 2024] [Murphy 1999] [Naylor 1951] [Numerical Simulation Study 2025] [Oblanas 1968] [Onodera and Idomura 2018] [Patel et al. 2025] [Paxson et al. 2022] [Penner 1949] [Perez 1964] [Petrie 1982] [Pietrykowski et al. 2020] [Pike 1991] [Placzek et al. 1969] [Platov et al. 2003] [Pratt 1971] [Price et al. 1967] [Ramamurti 2001] [Ramsey et al. 2023] [Ranlet 1965] [Rao 1961] [Rastogi and Pandya 1956] [Reddy et al. 2023] [Ringuette et al. 2001] [Robinson 1978] [Robinson and High 1974] [Rothschild and Martin 1976] [Sampson and Gibson 1982] [US Atomic Energy Commission (AEC) and Samuelson 1967] [Saokhede et al. 2025] [Saxena et al. 2023] [Sichel and Yin 1966] [Silnikov and Chernyshov 2017] [Simons 1972] [Smith 1983] [Soni 2026] [Soto and Williams 2024] [Spencer and Beggs 1977] [Spencer et al. 1983] [Stephen 1974] [Stephenson 1958] [Stewart et al. 2020] [Streiff 1953] [Strome 1969] [Stubbs and US Atomic Energy Commission (AEC) 1964] [Sullivan 1999] [Takeishi et al. 2017] [Tempelman 1972] [Thayer et al. 2004] [The Pressure Analyzing 2023] [Thompson and Epstein 1977] [Thomson 1961] [Tian et al. 2026] [Tinney and Valdez 2026] [Varé and Bogey 2022] [Verma 2006] [Victor 1979] [Vijayakumaran and Lemma 2018] [Walker et al. 1963] [Wang et al. 2022f] [Wang et al. 2025d] [Wang 1995] [Watson 1961] [Watts 2016] [Williams et al. 1993] [Wong and Brown 1968] [Wongprapinkul et al. 2024] [Woods 1963] [Xie and Du 2024] [Xu and Jangi 2025] [Yagodnikov et al. 1995] [Yahiaoui and Olivier 2015] [Yan et al. 2017] [Yao et al. 2023] [Yin and Li 2015] [Yoshihara 1963] [Yu et al. 2019] [Zhang et al. 2015a] [Zhao et al. 2026a] [Zheng 2024] [Zhu et al. 2025] [Zirkind 1967]

Thermal protection systems and hot structures

Thermal protection systems, tiles, blankets and insulation, and hot structures for reusable and entry vehicles.

211 records. [4680010 Re-Radiating Heat Shield 1989] [Achambath and Schwartzentruber 2018] [Agrawal et al. 2010] [Ai et al. 2022] [Ajayi et al. 2021] [Akamine et al. 2026] [Anderson and Kinzel 2023] [Aprovitola et al. 2019] [Aronov and Klyagin 2021] [Babashov and Varrik 2020] [Banerjee and Poovathingal 2021] [Bao et al. 2019] [Bauer and Kummer 1970] [Bernstein et al. 2024] [Blosser 1997] [Bose et al. 2016] [Brociek et al. 2022] [Brociek et al. 2023b] [Brociek et al. 2023a] [Brockmeyer 1993] [Brown 2003] [Brune et al. 2016] [Cassell et al. 2016] [Castro Júnior and Andrianov 2025] [Chao et al. 2024] [Chaturvedi et al. 2024] [Chen et al. 2024a] [Chen et al. 2024b] [Chen et al. 2025f] [Chen et al. 2025a] [Cheng et al. 2026] [Chinnaraj et al. 2024] [Christiansen and Lear 2015] [Chu et al. 2015] [Cinquegrana et al. 2017] [Clarke 2008] [Covington and Vojvodich 1971] [Cui et al. 2017] [Curtin 2026] [D’Souza et al. 2022b] [Dang et al. 2021] [Peterson and Hagen 1975] [De Prisco et al. 2026] [Dec and Mitcheltree 2002] [Duston et al. 2004] [Fan 2015] [Feng et al. 2024] [Gage et al. 2019] [Ghosh et al. 2023] [Gong et al. 2018] [Grabow et al. 1976] [Gramola et al. 2022] [Green et al. 1984] [Green and Davy 1981] [Gudhenia and Chakrabarty 2025] [Gulli and Maddalena 2015] [Gupta and Ramkumar 2015] [Hao et al. 2020] [Hasan et al. 2018] [Hassan et al. 2024] [Hays et al. 2020] [He et al. 2025] [Heisler et al. 2017] [Henline et al. 1996] [Herbell and Eckel 1993] [Hetmaniok et al. 2024] [Hiltz et al. 1968] [Hopkins and Rutledge 2024] [Hoter et al. 2026] [Hou et al. 2021] [Hou et al. 2025b] [Hou et al. 2025a] [Hovey 1964] [Hovey 1965] [Huang and Dai 2023] [Huang et al. 2018b] [Hunt 1976] [Hunt et al. 1976] [Hussein 2025] [Hwang et al. 2016b] [Ikenson 2025] [Ivanchenko et al. 2021] [Brown 2006] [Ji 2017] [Ji et al. 2027] [Jiang et al. 2020] [Johnston 1974] [Jumper et al. 1993] [Kammer et al. 1963] [Khan and Chakraborty 2023] [Kim 2017] [Kim and Choi 2026] [Koch et al. 2025] [Kolodziej and Rasky 2002] [Koo 2022] [Korabelnikov and Kuranov 2002] [Kourtides et al. 1997] [Krishna and Ricklick 2017] [Kubota and Uchida 1999] [Kumar and Mahulikar 2016b] [Kumar and Mahulikar 2016a] [Kumar and Mahulikar 2017] [Kundu 2013] [Kurth et al. 2015] [La Sorsa et al. 2026] [Lakatos 2016] [Lakatos 2019] [Lakatos 2025] [Lakatos et al. 2021] [Lane and Kirlin 1978] [Le et al. 2023] [Lee 1984] [Lehman and Christensen 1973] [Leiser et al. 2002] [Li et al. 2021a] [Li et al. 2026d] [Li et al. 2026a] [Liu et al. 2019a] [Lu 1996] [Luo and Han 2026] [Luo et al. 2026] [Lv et al. 2026] [Maiorova et al. 2016] [Mathieu et al. 1990] [McAfee et al. 2025] [McGuire et al. 2004] [McGuire 2011] [Medvedev et al. 2025] [Mehta et al. 2022] [Menees 1983] [Milos and Arnold 2001] [Milos et al. 2012] [Morgan and Williams 2025] [Mungiguerra et al. 2021] [Myers et al. 1999] [Myers et al. 2000] [Nabi and Najafi 2024] [Nagabandi et al. 2020] [Nakhod 2026] [Nestler 1985] [Nikpourian and Bahramian 2020] [Noel et al. 2026] [Ohtake 1998] [Olds and Cowart 2001] [Olds and Izon 2002] [Pallix et al. 2000] [Palmer et al. 1997] [Panerai and Mansour 2016] [Penide-Fernandez and Sansoz 2019] [Prabhu et al. 2012] [Price et al. 2025] [Pronina et al. 2022] [Prosuntsov et al. 2017] [Qu et al. 2026] [DiviaHarshaVardini et al. 2023] [Raghunandan et al. 2021] [Rasky 1995] [Ren et al. 2021] [Rezin et al. 2001] [Robinson et al. 1995] [Rossman and Braun 2016] [Rossman and Braun 2017] [Rufolo et al. 2024] [Sanson et al. 2017] [Sawant et al. 2019] [Schiavazzi and Juliano 2020] [Seif et al. 2018] [Sepka and Samareh 2015] [Shao et al. 2017] [Shao et al. 2026] [Shen and Liu 2020] [Shih et al. 1988] [Shilav et al. 2021] [Sirmalla et al. 2022] [Skolnik and Putnam 2020] [Skolnik and Putnam 2022b] [Skolnik and Putnam 2022a] [Stewart et al. 1985] [Stoll et al. 1975] [Structural Design Aspects 1972] [Sun et al. 2019] [Sun et al. 2024] [Tanchuk et al. 2001] [Thermal Design of Composite 1972] [Tianyang 2025] [Tikhy et al. 2015] [Tobin and Dec 2015] [Tsukahara et al. 2001] [Turner et al. 1985] [Vakhitov and Klygach 2016] [Valentine and Gradl 2019] [Violette 2024] [Visnov 1966] [Vozar et al. 2015] [Wang et al. 2022h] [Wang et al. 2025f] [Williamson et al. 2025] [Woollard et al. 2016] [Wurster 1981] [Xu et al. 2023b] [Yan et al. 2015] [Yang et al. 1990] [Yang et al. 2003b] [Yang et al. 2003a] [Yee et al. 2023] [Yuan et al. 2024] [Yue et al. 2025] [Zhang et al. 2024c] [Zhao et al. 2015] [Zhukov 2019] [Zuccarini 2024]

Propellant tanks and cryogenic storage

Propellant tanks, cryogenic storage, pressurisation, sloshing and propellant management.

146 records. [Ambur et al. 1996] [Angirasa 2015] [Avila et al. 2016] [Bailey et al. 1986] [Baillif et al. 1995] [Baralle and Fournier 1989] [Benton and Debreceni 2004] [Bershadskyi et al. 2022] [Carden et al. 1967] [Chandler 1948] [Cheng et al. 2025a] [Chowdhury et al. 2023] [Colquitt 1969] [Colquitt 1968] [Алєксєєнко and Бучарський 2024] [Crisan et al. 2026] [Dahlene et al. 1969] [Debreceni et al. 1995] [Debreceni et al. 1996] [Debreceni et al. 2004] [Der and Stevens 1987] [Ducret et al. 1996] [Dudley et al. 1992] [Engberg 2005] [Скандаков and Яценко 2021] [Estey et al. 1983] [Fairall 1967] [Frank and Drikakis 2017] [Gallo et al. 2023] [Ge et al. 2022] [Gilliland et al. 1966] [Gonçalves et al. 2024] [Greenberg 1994a] [Greenberg 1994b] [Guan et al. 2024b] [Guan et al. 2024a] [Gyftos et al. 2026] [Heathman et al. 1970] [Heilemann et al. 2021] [Himeno et al. 1999] [Himeno et al. 2001] [Hughes 2025] [Hv et al. 2017] [Imai and Wada 2025] [Imai et al. 2020] [Jan and Aaron 1990] [Jayaseelan et al. 2022] [Jha et al. 2003] [Johnson et al. 2004] [Johnson et al. 1998] [Johnson et al. 2005] [Ju and Zhang 2025] [Kana and Gormley 1967] [Karahan and Cadirci 2024] [Kartuzova and Kassemi 2019] [Kassemi et al. 2018] [Kavalli et al. 2026] [Kerebel and Dugat 1986] [Kumazawa et al. 2003] [L’Heureux 1987] [Lapilli 2015] [柳 2023] [Lee et al. 2024c] [Li et al. 2019a] [Liang et al. 2022b] [Liu et al. 2021c] [Logan 1985] [Lopez and RajKumar 2025] [Lu et al. 2024] [Macconochie et al. 1988] [Macés-Hernández 2026] [Majumdar and Steadman 2001] [Majumdar et al. 2016] [Manko et al. 2026] [Manokaran et al. 2025] [Mazurkivich et al. 2005] [Michihara et al. 2018] [Mitikov and Shynkarenko 2022] [Moghadasi et al. 2018] [Morino et al. 2001] [Morita 1964] [Moser and Keith 1992] [Murashko 2026] [Nair S. et al. 2024] [Nandi 2001] [Netter et al. 1999] [Nosseir et al. 2024] [Olsson et al. 2024] [Ashwath 2023] [Park et al. 2023a] [Pasley 1972a] [Pasley 1972b] [Pazhani et al. 2024] [Pei and Rothhaar 2015] [Pharokhipanah and Bouckenooghe 2024] [Pietrzyk et al. 1993] [Price et al. 1992] [Sundharesan and Jv 2024] [Rankin et al. 1969] [Reske and Brodnick 2024] [Rhee et al. 2025] [Robertson and turnbow 1966] [Robinson 1994] [Rollins et al. 1983] [Rollins et al. 1984] [Rollins et al. 1986] [Rollins et al. 1988] [Prasanraj 2019] [Saha et al. 2025] [Sakai et al. 2025] [Sakowski et al. 2019] [Sato et al. 2020] [Schmidt 1991] [Scholz et al. 1992] [Sidoruk et al. 2020] [Skleznev 2023] [Smeltzer and Bowman 2002] [Solomon and Tamiru 2026] [Spier et al. 1966] [Sreeyesunath and Sugathan 1994] [Streetman and Graves 1963] [Structural Arrangement Trade Study. 1995b] [Structural Arrangement Trade Study. 1995a] [Su 2017] [The Flight of Rocket 1934] [Torre 1986] [Torre et al. 1986] [Trushlyakov and Urbansky 2023] [Trushlyakov et al. 2024] [Tzoumakis et al. 2024] [Utsumi 1997] [Vamsi et al. 2019] [Wang et al. 2016e] [Wei et al. 2025] [Werlink and Pena 2015] [Woodsum and Rowland 1968] [Yang et al. 2023b] [Yang et al. 2025c] [Ye et al. 2025b] [Yoon 2025] [Yoon et al. 2024] [Zhao et al. 2021b] [Zhao et al. 2025b] [Ziglar 2025] [Ziglar and Elsperman 2026] [Zimmerman et al. 2015]

Composite structures and flight vehicle materials

Composite and metallic structures and the materials of flight vehicles, their loads, fatigue and aeroelasticity.

186 records. [Akimov 2026] [Aksoy et al. 2019] [Alexander et al. 1996] [Allen et al. 1983] [Allen et al. 1984] [Ambrus and Herman 1988] [American Institute of Aeronautics and Astronautics 1993] [Anooj et al. 2023] [Askins et al. 2008] [Bai et al. 2017] [Balageas 2002] [Bendix Field Engineering Corp Columbia Md 1974] [Bennaceur and Xu 2019] [Janicki Industries et al. 2025] [Briskman 2000] [Burkhard 1973] [Burrows and Allaire 2019] [Case and Reifsnider 2003] [Cenko and Madson 1993] [Chaloff et al. 1974] [Chilles et al. 2015] [Clausing 1969] [Clinton et al. 1999] [Cohn et al. 1963] [Corvi 1990] [Cox et al. 2022] [Dai et al. 2025] [Dash et al. 2025] [De Leon et al. 2022] [De Luca et al. 2026] [Demirel and Demirci 2026] [Diodati et al. 2023] [Dion 1992] [Dotson and Tiwari 1996] [Dziopa and Koruba 2015] [Fischer et al. 2015] [Flanigan 1989] [Gade and Inman 1998] [Ganilova et al. 2022] [Gourab et al. 2021b] [Goyal et al. 2021] [Goyal et al. 2026] [Guo et al. 2019] [Gupta and Mishra 2024] [Guratzsch and Mahadevan 2004] [Hadjria and D’Almeida 2019] [Hafizuddin Baderillah and Fadhli Zulkafli 2025] [Hartung 1963] [Holladay et al. 2019] [Honchar 2026] [Howard and Hansen 2006] [Howdyshell et al. 1998] [Huangpeng et al. 2021] [Hwang 1963] [Hwang et al. 1979] [Hwang et al. 2025] [Inada 2004] [Ireman et al. 1994] [Ivanco et al. 2020] [Ivanco et al. 2021] [Ivanco et al. 2024] [Jadhav and Sridharan 2001] [Jaiswal et al. 2024b] [Janney and Rogers 1986] [Jayanthi and Jain 2019] [Joint DoD/NASA Advanced Launch 1990] [Jones 1976] [Kashefinishaburi and Hoa 2022] [Kayran 2004b] [Kayran 2004a] [Kemp et al. 1972] [Khamlak 2026] [Khan and Chakraborty 2021] [Kieffer 2006] [Kim et al. 2013] [Kim et al. 2026c] [Kirikera et al. 2003] [Koley et al. 2026] [Koliada 2026] [Krishna 2022] [Krishna et al. 2019] [Kumar 2001] [Kumar 2002] [Kumari and Kumar 2022] [Kunal and Chakraborty 2026] [Lemke et al. 2008] [Liu et al. 2016] [Loesch and Pawlowski 1973] [Lu et al. 2025] [Lutz et al. 2022] [Ma et al. 2024b] [Mahdi et al. 2024] [Manwatkar et al. 2016a] [Manwatkar et al. 2016b] [Mayank et al. 2022] [McGehee et al. 1978] [Mehta 2016] [Mehta 2022] [Miller and Breslau 1956] [Muin and Miah 2025] [Murugesan et al. 2018] [Naval Air Systems Command Patuxent River MD 1999] [Naval Air Systems Command Patuxent River MD 2000] [Nettles and Ratcliffe 2006] [Noll and Huttsell 1978] [Norton 1990] [Oliver et al. 2004] [Orsatelli et al. 2023] [Osama et al. 2025] [Osuna and Adibi 2024] [Paek and Lee 1996] [Paulini 2019] [Pavanasam et al. 2024] [Pawar et al. 2026] [Phelan and Niemann 1998] [Piatak and Sekula 2019] [Piatak et al. 2019] [Podliesnyi 2026] [Poursartip et al. 2024] [Primer on Composite Materials 1985] [Proroka and Lypovskyi 2019] [Puertolas and Perraud 2019] [Pulford and Lake 2023] [Purushotham and Yathin 2018] [Rafla 2019] [Rainey 1964] [Raouf and Pourtakdoust 2017] [Ratnayake et al. 2020] [Richards et al. 2013] [Riley and McNamara 2016] [Riley and McNamara 2017] [Rochefort and Yorra 1976] [Roma Rubi et al. 2025] [Schpey 1980] [Shimizu et al. 2024] [Silva Guimaraes and d’Andrade Souto 2021] [Sioutis and Tserpes 2023] [Skelly 1989] [Sleight et al. 2019] [Song et al. 2021] [Srinivasan et al. 2023] [Srivastava and Jain 2023] [Stamatelos and Labeas 2025] [Strganac 2007] [Stuber et al. 2012] [Tamma and Yurko 1988] [Tang and Dowell 1998] [Tanner 1997] [Tao et al. 2023] [Tate 1969] [Tekin and Kapan 2016] [Thedy and Liao 2023] [Theoretical Analysis on Large-Stroke 2026] [Toda et al. 2000] [Torres et al. 2019] [Triplett 1972] [Tuma et al. 2008] [Turner 1982] [Vagins 1972] [Vargas Venegas and Huang 2022] [Vargas Venegas and Huang 2023] [Vaughn 1999] [Veyret et al. 1993] [Wang 2025] [Wang et al. 2021b] [Weitz et al. 2025] [Wells 1999] [White et al. 2005] [DIVISION OF REACTOR DEVELOPMENT (AEC), WASHINGTON, D. C. and Whitman 1962] [Wignall and Houlden 2020] [Wild et al. 2021] [Wire Mesh-Plastic Composite Material 1981] [Wood 1991] [Wrenn et al. 2001] [Xie et al. 2025] [Xing et al. 2024] [Yadav et al. 2020] [Yang et al. 2015a] [Yu et al. 2025b] [Yue et al. 2018] [Zaitsev et al. 2020] [Zeiler et al. 1999] [Zhang et al. 2024d] [Zhao and Bao 2023] [Zheng et al. 2026] [Ziglar 2026]

Aerodynamics, aerothermodynamics and hypersonic flow

Aerodynamics and aerothermodynamics of launch and entry vehicles, hypersonic flow, boundary-layer transition and aerodynamic heating.

256 records. [A Supersonic/Hypersonic Aerodynamic Investigation 1966] [Aero-Heating Prediction Model 2025] [André et al. 2015] [Aogaki et al. 2017] [Arabshahi 2021] [Areias et al. 2023] [Atay et al. 2026] [Balakumar and Chou 2016] [Balakumar and Chou 2018] [Beck et al. 2019] [Bender et al. 1992] [Blanco 2024] [Brice et al. 1966] [Buzuluk et al. 2020] [Byczkowski and Rao 2023] [Candler 2015] [Chan et al. 2016] [Chavez and Schmidt 1994] [Chen 2020] [Chen and Gibbons 2022] [Chen and He 2025] [Chen et al. 2022b] [Chen et al. 2022a] [Chen et al. 2023c] [Chen et al. 2023a] [Chen et al. 2025d] [Chen et al. 2026b] [Cheng et al. 2023] [Ching et al. 2017] [Ching et al. 2024] [Cooper and Martin 2023] [Corke and Bowersox 2018] [Danehy et al. 2019] [Dias et al. 2026] [Ding and Ziviani 2026] [Direct Numerical Simulations 2023] [Dong and Li 2021] [Donohue and Fletcher 1996] [Dreus et al. 2021] [Duan et al. 2026b] [Duan et al. 2026a] [Dwivedi and Sidharth 2026] [Edquist 2006] [Gorfad Vijaykumar Devraj 2016] [Effects of Mass Transfer 1972] [Erickson 2020] [Esposito and Lappa 2026] [Favaregh et al. 2016] [Fidkowski 2022] [Fievet et al. 2020] [Fine 1979] [French et al. 2021] [Fu et al. 2021c] [Fujio and Taguchi 2026] [Gai and Cao 2025] [Gajoni et al. 2026] [Garbeff et al. 2017] [Gee et al. 2025] [Gnoffo and Inger 1999] [Gokcen 2018] [Gokcen and Skokova 2017] [Gros 1963] [Grossir et al. 2015] [Gui et al. 2023] [Guo et al. 2024b] [Hader and Fasel 2021] [Hader and Fasel 2024] [Hader et al. 2020] [Hahne 1997] [Han and Cao 2019] [He et al. 2026] [Heaney et al. 2021] [Hill and Borg 2024] [Holifield and Tufts 2024] [Hollis 2024] [Hoskin et al. 2024] [Hu et al. 2015] [Huynh and Kriz 2009] [Ifergan et al. 2021] [Inatomi et al. 2019] [Iqbal and Akbar 2026] [Ishimoto 1995] [Jaffrezic et al. 2015] [Jameson et al. 2024] [Jeong and Jo 2026] [Jeong et al. 2026] [Ji et al. 2025] [Jia et al. 2020] [Jiang et al. 2016] [Jiang et al. 2017] [Jo 2026] [Johnston et al. 2026] [Joseph et al. 2026] [Kelly and Cruz 2009] [Kiehn 2020] [Kikuchi et al. 2016] [Kim and Lee 2025] [Kim et al. 2025e] [Kim et al. 2026b] [Kim et al. 2026d] [Klaproth and Hornung 2022] [Koike and Babinsky 2019] [Kumar et al. 2023] [Lawrence and Mills 2002] [Lee and Chen 2018] [Lei et al. 2017] [Li and Zhang 2021] [Li et al. 2019c] [Li et al. 2020b] [Li et al. 2022a] [Li et al. 2025h] [Li et al. 2025d] [Li et al. 2026c] [Lin and Miller 2025] [Lindsay and Fikes 1976] [Liu et al. 2021b] [Liu et al. 2023d] [Liu et al. 2025a] [Liu et al. 2025e] [Liu et al. 2025d] [Lüdeke et al. 2015] [Makhnun et al. 2024] [Marineau 2016] [Mathavaraj and Padhi 2020] [Matsunaga et al. 2017] [Matsuyama 2024] [Mazzone et al. 2024] [Meersman et al. 2022] [Mehta 2015] [Mehta 2021] [Melander and Candler 2024] [Menon et al. 2025] [Miró Miró and Pinna 2018] [Miró Miró and Pinna 2020] [Murray and Lewis 1978] [Narayanan et al. 2026] [Nguyen et al. 2023] [Niu and Su 2023] [Olejnik et al. 2022b] [Ort and Dosch 2019] [Oyama et al. 2021] [Ozawa and Bruce 2025] [Palmer et al. 2015] [Paredes et al. 2018] [Paredes et al. 2019] [Paredes et al. 2021] [Parent and Hanquist 2021] [Patrick 2019] [Paxton et al. 2020] [Pei et al. 2025] [Peng and Wang 2026] [Peng et al. 2018] [Perry 2024] [Poggie 2015] [Pollock et al. 2023] [Prabhu 2012] [Pu and Jiang 2019] [Qi et al. 2021a] [Qiu et al. 2024] [Quan et al. 2026] [Mehta 2023] [Raghunathan et al. 2026] [Rana and Chudoba 2016] [Ransom and Srinivasan 2024] [Rao and Chimata 2024] [Rat et al. 2015] [Reusable Reentry Satellite RRS 1990] [Rich et al. 2001] [Roschke 1955] [Roussos et al. 2025] [Ryu et al. 2024] [Sakamoto et al. 2023] [Santos et al. 2020] [Santos et al. 2021] [Schrage 2025] [Sekula et al. 2015] [Selvakumar and Palanisamy 2020] [Selvam and George 2026] [Sha et al. 2026] [Shimmy 2026] [Shrestha and Candler 2018] [Shrestha et al. 2017] [Shukla 2025] [Sidharth and Dwivedi 2026] [Signorelli et al. 2024] [Singh et al. 2024] [Sippel et al. 2017] [Smith 2021] [Spanelis and Walker 2022] [Striz and Jang 1987] [Su and Liu 2025b] [Su et al. 2025] [Sudarshan et al. 2021] [Sun et al. 2018] [Sun et al. 2020] [Swanson and Daniel 2016] [Takahashi et al. 2018] [Tao and Sun 2019] [Tauber et al. 1999] [Tewell 1984] [Tian et al. 2025a] [Türkoğlu et al. 2026] [Ullah et al. 2024] [Unnikrishnan and Gaitonde 2018] [Uzun et al. 2019] [Vargas Venegas and Huang 2021] [Vo et al. 1993] [Vohra et al. 2026] [Vu and Candler 2026] [Walker et al. 1993] [Wan et al. 2025] [Wang and Josyula 2016] [Wang et al. 2016b] [Wang et al. 2016f] [Wang et al. 2024e] [Wang et al. 2024c] [Wang et al. 2025e] [Wang et al. 2026b] [Welker and Maynes 2026] [Wilcox et al. 2016] [Winski et al. 2019] [Wolverton 2018] [Wu and Yu 2018] [Wu et al. 2026] [Xinguo et al. 2024] [Xu and Wang 2023] [Xu et al. 2022] [Xu et al. 2026] [Yakubayev et al. 2026] [Yamin and Hadi 2026] [Yan et al. 2019] [Yang et al. 2022a] [Yang et al. 2025a] [Yang et al. 2026b] [Yang et al. 2026a] [Ye et al. 2017] [Yin et al. 2023] [Yu and Yuan 2016] [Yu et al. 2025a] [Zeng et al. 2026] [Zhang and Li 2019] [Zhang et al. 2023b] [Zhang et al. 2026a] [Zhang et al. 2026b] [Zhao et al. 2019] [Zheng et al. 2025b] [Zhou et al. 2015c] [Zhou et al. 2016b] [Zhou et al. 2018] [Zhou et al. 2023a] [Zhu 2022] [Zhu et al. 2020] [Ziegler 1963] [Zou et al. 2015] [Zugaj 2017] [Zuppardi and Esposito 2016]

Automatic and autonomous landing

Automatic and autonomous landing of aircraft, unmanned aircraft, reusable rocket stages and planetary landers, and the approach and touchdown problem they share.

Unmanned aircraft and rocket stages now carry the subject. Of the 323 records, 72 name an unmanned aircraft, a drone or a rotorcraft, 65 name a rocket, a launch vehicle, a reusable vehicle or a stage, and 130 date from 2001 or earlier.

323 records. [180 Fault Tolerant Navigation 1994] [Ahmed 2021] [Ahmed 2023] [Ahmed and Wyatt 2024] [Akash and Anbarasu 2025] [Al-Bakri et al. 2020] [Alijani and Osman 2020] [Shuai et al. 2021] [Anderson and Schmidt 1987] [Aoki and Ishigami 2022] [K.А. 2025] [Automatic Landing 1964] [Automatic Landing 1969] [Ayyasamy et al. 2023] [Baca et al. 2017] [Balanis and Cheng 1975] [Banerjee et al. 2016] [Bhargavapuri et al. 2019] [Bicer et al. 2019] [Bischoff et al. 1974] [Boriotti and Maali 1993] [Borowczyk et al. 2017] [Botelho et al. 2022] [Broglio 1961] [Brown 1996] [Bryson et al. 1970] [Bu et al. 2016] [Burrous et al. 1974] [Burton 1981] [Carson et al. 2015] [Chamitoff 1994] [Chen et al. 2025e] [Chen et al. 2026a] [Chessman 2022] [Chester 1995] [Childers et al. 2001] [Chitrakaran et al. 2005] [Chowdhury et al. 2026] [Cockburn 1965] [Colwell 1966] [Cook 1985] [Costache and Stoica 2026] [Crassidis and Mook 1991] [Crassidis et al. 1993] [D’Souza and D’Souza 1997] [Danjun et al. 2015] [Davies 1938] [Davison and Schroeder 1994] [de Lafontaine 1992] [De Oliveira and Lavagna 2024] [CHjen 2022] [National Bureau of Standards 1960] [Digges 1971] [Doehler and Korn 2004] [Doherr et al. 1997] [Dong et al. 2023] [Doniger 1967] [Dougherty and Lee 2016] [Douglas Aircraft Co Long Beach Ca 1963] [Epp et al. 2015] [Evaluation of the Navigation 1979] [Fazeli and Narayan 2017] [Federici et al. 2026] [Fenwick 1966] [Fenwick 1967] [Ferguson and Radke 1993] [Fischer 1981] [Flying Controls and Automatic 1963] [Fortenbaugh 1972] [Foster 1972] [Franklin 1995] [Fujimori et al. 2000] [Gai and Curry 1977] [Garcia-Pardo et al. 2001] [Garcia-Pardo et al. 2002] [Gardinier and Taylor 1999] [Gautam et al. 2017] [Guadagnini et al. 2023] [Guo et al. 2022b] [Guo et al. 2025b] [Günsel et al. 2025] [Hameed and Bindu 2019] [Hara et al. 2024] [Harris 1961] [Hayashi et al. 2025] [He et al. 2019b] [Helliwell 1952] [Hendrick and Horn 2024] [Hess and Judd 1976] [Horn et al. 2014] [Horn et al. 2015] [Hornbuckle 2015] [Hsu et al. 2022] [Hu et al. 2022b] [Huan et al. 2015] [Huang and Zhang 2026] [Huang et al. 2018a] [Huang et al. 2020b] [Huang et al. 2020a] [Igreja and Lemos 2022] [Ilango and Ramanathan 2020] [Jin et al. 2016] [Jung et al. 2015] [Jung et al. 2025a] [Jung et al. 2025b] [Senthil Kumar and Shanmugam 2023] [Kaneko and Yamato 2025] [Ke and Feng 2015] [Kerr et al. 1995] [Kidwell 1963] [Kim et al. 2017] [Kim et al. 2023] [Kluever 2004] [Kluever and Neal 2015] [Klumpp 1966] [Knopp et al. 1992] [Kock et al. 1972] [Koester and Vaillancourt 1992] [Koryanov 2021] [Krishnan and Sajikumar 2023] [Kubota et al. 2003] [Kuhn 1979] [Kulumani and Lee 2022] [Kumar and Padhi 2024b] [Kumar and Padhi 2024a] [Lambregts 1982] [Landy and Kim 1984] [Lawrence et al. 2001b] [Lee and Chiou 1994] [Lee and Mesbahi 2017] [Lee and Park 2025] [Lee and Davidson 1973] [Lee et al. 1998] [Lee et al. 2025a] [Leeman et al. 2022] [Lehman 1964] [Lei et al. 2022] [Li and Hu 2018] [Li et al. 2024d] [Li et al. 2025b] [Li et al. 2025c] [Li et al. 2026e] [Li et al. 2026b] [Lighthill 1963] [Lin et al. 2026] [Ling 1970] [Littell 2019] [Liu and Zhang 2022] [Liu et al. 2017a] [Liu et al. 2023b] [Liu et al. 2024b] [Lowrance and Smith 1996] [Lunghi et al. 2015] [Lunghi et al. 2022] [Lungu and Lungu 2018] [Lykken and Shah 1971] [Lykken and Shah 1972] [Ma and Zhao 2019] [Ma et al. 2019] [Ma et al. 2025a] [Maass et al. 2020] [Maces-Hernandez et al. 2017] [Mackay et al. 2016] [MACKlNNON and Madden 1972] [Maiuzzo 1970] [Mann 1987] [Martin et al. 1995] [McDonald 1980] [McGee 1977] [McGee et al. 1981] [McGee et al. 1984] [Miele et al. 1989] [Miso et al. 1999] [K.А. 2022] [Miyazawa et al. 1993] [Miyazawa et al. 1999] [Shoukun et al. 2024] [Modali et al. 2020] [Mohan et al. 2025] [Moore et al. 1979] [Mu et al. 2025] [Mukhopadhyay 1969] [Muskardin et al. 2016] [Nagarjuna and Suresh 2015] [Negre 1975] [Negre 1977] [Nho and Agarwal 1998] [Ni et al. 2023] [Nugroho et al. 2024] [Numerical Optimization on Approach 2016] [Oakes 2021] [Ohara et al. 2001] [Papadopoulos 1998] [Parker and Templeman 1967] [Parkinson and Fitzgibbon 1989] [Parks and Tubb 1970] [Patrick 1972] [Perez and Benner 1973] [Persson and Wahlberg 2019] [Pessanha Santos et al. 2023] [Phillips et al. 1983] [Pierson 1985] [Pogust and Taylor 1972] [Poritzky 1970] [Poritzky 1971] [Poulose 1992] [Pozzi and Mugnuolo 1998] [Pulk and Stolarik 1977] [Qu et al. 2016] [Qu et al. 2018] [Raei et al. 2022] [Rankin 1994] [Recker et al. 2018] [Reitan and Saib 1976] [Reusable Launch Vehicle Landing 2026] [Riley et al. 1994] [Rimer and Sperling 1965] [Rimer and Sperling 1966] [Robaglia et al. 2018] [Rohan et al. 2023] [Roy and Davison 1986] [Hameed and Bindu 2021] [Sachan and Padhi 2016] [Sagliano et al. 2021] [Sagliano et al. 2024] [Sagliano et al. 2025] [Salt 1995] [Sanchez et al. 2018] [Sanuki 1965] [Sarrafian 1986] [Schmidt 1985] [Schmitt and Burchett 2004] [Schoenman and Doniger 1965] [Shayler 1961] [Shen et al. 2020b] [Shivam et al. 2023] [Silva et al. 2017] [Simplício et al. 2019] [Smith and Meyer 1981] [Smith et al. 1972] [Smith et al. 1973] [Sotirakos and Prazenica 2025] [Steinberg 1992] [Strozecki and Mammar 2021] [Su and Wang 2015] [Su et al. 2022a] [Sullings and Waller 1967] [Suresh and Ratnoo 2019] [Tanaka and Matsumoto 2019] [Tariq et al. 2026] [Templeman and Parker 1968] [The Algorithm 2020] [Thies 2022] [Thompson 1965] [Tiana and Pond 1997] [Trajectory Shaping Guidance 2025] [Tripathi and Padhi 2016] [Tripathi and Patel 2019] [Tripathi et al. 2025] [Tsitses et al. 2024] [Tsoukalas et al. 2026] [Tsuyuki et al. 2005] [K.А. 2023] [van Slagmaat 1992] [Velasco et al. 2017] [Volkov et al. 2022] [Vredevoogd and Thompson 2021] [Wagdi 1984] [Walker 1960] [Walker 1961] [Wang and Carl 1999] [Wang and Song 2018] [Wang and Song 2019] [Wang et al. 2015b] [Wang et al. 2020c] [Wang et al. 2020a] [Wang et al. 2022b] [Wang et al. 2022c] [Wang et al. 2022g] [Wang et al. 2023] [Wang et al. 2026a] [Wasserman and Mitchell 1973] [Watson et al. 2020] [Webber and Page 1963] [Wei and Shao 2021] [Wei et al. 2024] [Weichelt et al. 1986] [Elke et al] [Williamson 1963] [Wilz and Johnson 1975] [Woestemeyer 1964] [Wong et al. 2002] [Wu et al. 2018b] [Wu et al. 2018a] [Wu et al. 2024c] [Wygle 1965] [Wynn and McLain 2019] [Xiangyu et al. 2004] [Xiao 2026] [Xu and Lan 2018] [Xu et al. 2017] [Xu et al. 2018] [Xu et al. 2025b] [Yan et al. 2023a] [Yanagihara et al. 1999] [Yang 2025] [Yao and Xin 2023] [Yelin Zhang et al. 2016] [Yue et al. 2019] [Yue et al. 2022b] [Yue et al. 2022a] [Zeh et al. 1989] [Zhang et al. 2017b] [Zhang et al. 2017a] [Zhang et al. 2019c] [Zhang et al. 2021b] [Zhang et al. 2025f] [Zhang et al. 2025a] [Zhao et al. 2020] [Zhou et al. 2024b] [Zhou et al. 2026b] [Zhu et al. 2026] [Çelik and Demirezen 2024]

Guidance, control, avionics and trajectories

Guidance, navigation and control, avionics, flight software and trajectory design and optimisation for launch, entry and unmanned vehicles.

444 records. [Aamer et al. 2023] [Abbas et al. 2023] [Abdi-Moradi 1988] [Abdo et al. 2021] [Abdullah 2024] [Adaptive Fault Tolerant Servo 2025] [Adimurthy 1987] [Agarwal and Gupta 2004] [Akiyama et al. 2024] [Aktas et al. 2016] [Alexander 1978] [Algorithm for Evaluation 2020] [Alizo Ewald et al. 2026] [Allen 2005] [An et al. 2020] [Ancel et al. 2019] [Andrews 2000] [Ansari and Bajodah 2015] [Ansari and Bajodah 2016a] [Ansari and Bajodah 2016b] [Army Aviation School Fort Rucker Al 1961] [Asamura et al. 2024] [Ashraf et al. 2022] [Attia et al. 2025] [Autonomous Flight Control 2018] [Autonomous Flight Safety System 2008] [Averyanov et al. 2021] [Bail 1968] [Bakirci 2023] [Balesdent et al. 2022] [Batory et al. 1995] [Bauer 1996] [Beaudoin et al. 2018b] [Beaudoin et al. 2018a] [Best et al. 1988] [Bi et al. 2020] [Bielaszka 2026] [Boersma et al. 1970] [Boglis and Stoica 2019] [Bolton 2016] [Boskovic et al. 2017] [Boydston et al. 2015] [Brehm and Goettge 1995] [Briese et al. 2018] [Briese et al. 2020] [Brodecki and Subbarao 2015] [Bull and Martel 2000] [Bull and Lanzi 2007] [Burchett 2003] [Burkhard et al. 1974] [Cai et al. 2024a] [Calamoneri et al. 2024] [Calhoun 2000] [Canepa et al. 2022] [Carter et al. 1993] [Castaldi et al. 2023] [Cato 1964] [Cato 1965] [Chen et al. 2021b] [Chen Liu et al. 2016] [Cheng et al. 2021] [Childers and Condon 2004] [Chin et al. 2016] [Cho et al. 2021a] [Cho et al. 2021b] [Choi and Li 2026] [Civek and Özgören 2017] [Cole et al. 2007] [Corban et al. 2004] [Cotton 1974] [Cowling 2011] [Craig and Russell 1978] [Crawford and Wallace 1998] [Cronin 2013] [Crook and Meyer 1981] [Cruz et al. 2022] [Culp and Bickley 1993] [Czuchry et al. 1979b] [Czuchry et al. 1979a] [D’Andrea 2008] [Dai et al. 2017] [Dana-Bashian et al. 2001] [Davis 1988a] [Dees et al. 2015] [Deets et al. 1988] [Demidovich 2017] [Denton et al. 2022] [Design and Optimization 2023] [孙 et al. 2022] [Determination of External Power 2019] [Dhief et al. 2025] [Diamant et al. 1979] [Dinelli et al. 2019] [Dire et al. 1986] [Drozd 2026] [Du et al. 2019a] [Duan and Luo 2016] [Edwards 2019] [Elliott et al. 2025] [Emma and Pernicka 2003] [Estimating Trajectory Correction Requirements 1972] [ETE Model and High 2022] [Ferrell et al. 2004] [Fielding and Vaziry-Z 1995] [Filippoli 2026] [Fisher et al. 2002] [Fu et al. 2019a] [Fu et al. 2021b] [Fuchs 1980] [Gadhvi and Shankar 2023] [Gainer 1963] [Gamble and Jenkins 2001] [Garg et al. 2022] [Gates and Shipp 1978] [Gebman 1989] [General Electric Co Schenectady Ny 1952] [Gente et al. 2024] [Ghori et al. 2022] [Ghosh and Chattopadhyay 2015] [Gourab et al. 2021a] [Gourab et al. 2023b] [Gourab et al. 2023a] [Green et al. 1993] [Grigoriev and Proskuryakov 2024] [Guiliano 1999] [Guo et al. 2017] [Guo et al. 2025a] [Hajiyev and Cilden–Guler 2023] [Hale 2018] [Han et al. 2019] [Hanc et al. 2022] [Hanlon 2016] [Hanson et al. 2015] [Hao and Zhang 2021] [Hao et al. 2017b] [Harris and Howell 1988] [Hart 1956] [Hasani et al. 2017] [Haswell and Murray 2025] [Havey et al. 1998] [Hayre et al. 1992] [He and Wu 2022] [Heatwole and Lanzi 2010] [Rediess 1976] [Hiroi et al. 2020] [Hitt and Brim 1977] [Holibaugh 1992] [Hu et al. 2022a] [Huang 2016] [Huang 2026] [Huang et al. 2024] [Hussein and de Weck 2025] [Hwang et al. 2016a] [Ossai 2020] [Govers 2024] [Ishkov et al. 2019] [Jakeman 2024] [Jang et al. 2010] [Jang et al. 2014] [Jarvis 1974] [Ji et al. 2016] [Jia et al. 2025] [Jiang and Tan 2023] [Jianguo et al. 2016] [Jo and Ahn 2020] [Johnson and Schrage 2004] [Johnson et al. 2011] [Jones 2001] [Jones et al. 2001] [Joshi et al. 2023a] [Ju et al. 2022] [Junaid R and Beebi M 2015] [Jutty K et al. 2000] [Kabashkin and Filippov 2020] [Karali et al. 2024] [Karas 1990] [Keaton 1986] [Keaton 1987] [Keith and Rothschild 1999] [Khamvilai et al. 2022] [Kim 2016] [Kim and Lim 2020] [Kim et al. 2022b] [Kinsey et al. 1987] [Klion 1977] [Kluever 2022] [Knox-Seith 1963] [Kose et al. 2023] [Kotikalpudi et al. 2020] [Kovalenko 2021] [Krause et al. 2024] [Krishnan et al. 2023] [Krivenko 2026] [Kumar 2024] [Kumar et al. 2024] [Kumar et al. 2025b] [Kumar V V and Beebi M 2015] [Kumari et al. 2023] [Kurz 1963] [Lala and Adams 1987] [Langston 1967] [Launch Vehicle Booster Avionics 2000] [Laurence et al. 2015] [Lee 2026b] [Lee et al. 1993] [Lee et al. 2020a] [Lee et al. 2024b] [Lee et al. 2025b] [Lewis 2016] [Li and Ru 2019] [Li et al. 2017a] [Li et al. 2020c] [Liu et al. 2017b] [Liu et al. 2025c] [Liubimov 2025] [Llinas and Bowman 2001] [Logan et al. 2015] [Lombaerts et al. 2020] [Lu 1997] [Lu et al. 2016] [Lu et al. 2022] [Lu 1999] [Lugo et al. 2019] [Lungu et al. 2018] [Luton 1963] [Lytovchenko 2026] [Ma and Li 2020] [Ma et al. 2018] [Ma et al. 2023] [Ma et al. 2024c] [Martin 1963] [Martin 2007] [Marzioli and Frezza 2021] [MascareÑAs et al. 2019] [Mase et al. 2000] [Masjukov and Konovalov 2022] [Kwon and Hwang 2020] [Mathur and Avižienis 1970] [Mayorga-Macías et al. 2020] [McCormick and Compton 1986] [McKinney 1986] [McLaughlin and Perhinschi 2020] [Melliar-Smith and Schwartz 1981] [Melliar-Smith and Schwartz 1982] [Mendez 1975] [Menon and Lehman 1986] [Strickland and Palumbo 1988] [Migneault 1980] [Millar and Smrcek 2001] [Miotto and LePome 2003] [Miquel Parra et al. 2024] [Mittal 2025] [Mo et al. 2024] [Modular Avionics Systems Architecture 1988] [Mohan and Kishore 2021] [Mooij 2020] [Moon et al. 2015] [Moore 1969] [Morando et al. 2024] [Morgan 1970] [Morgan and Barton 2022] [Muda et al. 2023] [Mukundan et al. 2022] [Muthukumar et al. 2020] [Myung 2022] [Nagarajan and Karthikeyan 2017] [Naigle 2025] [Nair et al. 2016] [Naji and Stoica 2023] [National Research Council Washington DC 2001] [Naval Air Systems Command Arlington VA 1993] [Nedresky 1996] [Ness et al. 1983] [Nguyen et al. 2021] [Nikolaou et al. 2026] [Novack et al. 2018] [Oh and Han 2021] [Oka et al. 2025] [Orsagh et al. 2005] [Ostroff and Wood 1977] [Venkataramana et al. 2023] [Panda et al. 2015] [Panda et al. 2016] [Panda et al. 2017] [Papakonstantinou et al. 2022] [Park et al. 2023b] [Pasciuti et al. 2025] [Patapoff 1961] [Paterson 1991] [Patterson and Arena 2015] [Pei et al. 2017] [Peng et al. 2025] [Perhinschi 1999] [Perhinschi and Perhinschi 1997] [Đức et al. 2026] [Filyakov 2025] [Priyadarshini et al. 2023] [Provost et al. 2017] [Pullen 1973] [Qi et al. 2015] [Qiao 2024] [Qu et al. 2023] [Radhakrishnan et al. 2023] [Radhakrishnan et al. 2024a] [Rahnamai et al. 2018] [Rajendran and Smith 2018] [Navidad et al. 2024] [Guliyev 2025] [Redondo Gutierrez et al. 2022] [Reed 1977] [CHulin 2023] [Sinke 2022] [Resemini and De Souza Costa 2018] [Rice and McCorkle 1979] [Rice et al. 2022] [Rico and Turkoglu 2016] [Risko 1999] [Zardashti et al. 2022] [Robust Super-Twisting Sliding-Mode Controller 2025] [Rogers et al. 2017] [Rosenfeld and Davis 1986] [Ryan and Cummings 2015] [Ryan and Granger 2023] [Saju et al. 2025] [Fosch et al. 2024] [Sahani et al. 2017] [Salahudden 2025] [Salehi et al. 1995] [Satterthwaite 1994] [Savuran and Karakaya 2015] [Schierman et al. 2001b] [Schierman et al. 2001a] [Schlatt 2004] [Schoettle and Hillesheimer 1991] [Schultz and Grefenstette 1992] [Scott 2003] [Seltzer 1970b] [Seltzer 1981] [Settanni et al. 2015] [Shan et al. 2023] [Shen et al. 2019] [Shepperd and Staugler 1999] [Shi et al. 2024] [Shishkin and Khachumov 2025] [Shivers 2010] [Shtessel et al. 2000] [Shukla and Woolsey 2018] [Simms et al. 2014] [Simpson 2010] [Simpson 2005] [Simpson et al. 2005] [Sinha and Kumar 2024] [Sobel and Joshi 2002] [Sobocinski 1981] [Song and Choi 2018] [Sorensen 1962] [Sorgenfrei et al. 2017] [Sruthi S et al. 2015] [Stolarik 2007] [Su and Liu 2025a] [Su et al. 2021] [Sun and van Kampen 2020] [Sun et al. 2026] [Surender et al. 2021] [Surkova and Neusypin 2026] [Szabolcsi 2018] [Taghizadeh et al. 2022] [Tai and Jang 2017] [Taranto and Abdulrahim 2023] [Tatsuya et al. 2018] [Tauke-Pedretti 2016] [Teofilatto and De Pasquale 1998] [Thuillier et al. 2024] [Tian et al. 2015] [Tomczyk 2003] [Tong and Fen 2016] [Tony and Arun Kishore W. C. 2015] [Toso and Maddock 2017] [Tournes and Johnson 2001] [Trotta et al. 2021] [Tullino et al. 2023] [Ukigai et al. 2017] [Using Cell-DEVS for Prototyping 2017] [Usmonov and Kretov 2020] [Vaheed et al. 2024] [Vidan 2016] [Vijayan and Suresh Babu 2015] [Vittal and Bhat 1993] [Walter 1988] [Wang et al. 2015c] [Wang et al. 2015a] [Wang et al. 2018a] [Wang et al. 2024a] [Wang et al. 2025c] [Wang Pei et al. 2017] [Weinert and Meyer 1984] [Wenxuan 1991] [White 1989] [White and Clark 1980a] [White and Clark 1979] [White and Clark 1980b] [Wigginton et al. 2015] [Wilcox 1963] [Wilson 2019] [Wilson and Storey 2016] [Wu et al. 2020a] [Xiang et al. 2025] [Xingjun 2023] [Xu and Zhang 2018] [Xu et al. 2016] [Xu et al. 2023c] [Xu et al. 2024a] [Xu et al. 2025a] [Xue et al. 2024] [Xuefei et al. 2023] [Yan et al. 2016] [Yang et al. 2024a] [Ye et al. 2021] [Yesilbas 2025] [Yeşilbaş 2025] [Yin and Zhu 2018] [Yin et al. 2021] [Ying Xiong 2015] [Yue 2024] [Zanatta et al. 2017] [Zhang 2023a] [Zhang 2023b] [Zhang et al. 2017c] [Zhang et al. 2019b] [Zhang et al. 2019a] [Zhang et al. 2020a] [Zhang et al. 2022a] [Zhang et al. 2023c] [zhang et al 2023] [Zhao et al. 2023] [Zhao et al. 2025c] [Zhao et al. 2026b] [Zheng et al. 2020a] [Zhi et al. 2015] [Zhiqiang et al. 2015a] [Zhou and Tan 2024] [Zhou et al. 2020b] [Zhou et al. 2024a] [Zurera et al. 2025]

Risk, reliability, safety and health management

Risk, reliability, redundancy, safety and health management, with probabilistic risk assessment as a method.

192 records. [5132663 Vehicle Safety System 1993] [Abbott 2003] [Aerospace Corp El Segundo Ca 1963] [Air Force Space Command Space Missile SYS CTR 2014] [Alkhatib et al. 2025] [Alsafadi and Martinez 1993] [Alvord et al. 2024] [An et al. 2021] [Anderson and McWilliams 2003] [Anderson et al. 2015a] [Aras et al. 2023b] [Aras et al. 2023a] [Aras et al. 2025] [Arisandi 2017] [Atamuradov and Camci 2020] [Atamuradov et al. 2020] [Bae et al. 2018] [Ballard 2006] [Ballard and Brown 2005] [Barlow 1982] [Barmin et al. 2018] [Baroth et al. 1999] [Berkowitz and Titulaer 2024] [Bhatt and Singh 2025] [Bibhorr and Anand 2021] [Bird 2020] [Bird and Shao 2020] [Bird et al. 2020] [Bishop et al. 2018] [Bougacha and Varnier 2021] [Bougacha et al. 2021] [Bouhadra and Forest 2024] [Boyd et al. 1988] [Brevault et al. 2016] [Bridges 1988] [Buzzatto 2015] [Cao 2017] [Cao 2024] [Casel and Bickford 2026] [Chang et al. 2018] [Chen and Sakurahara 2025] [Cheng et al. 2025b] [Christian et al. 2023] [Coble et al. 2020] [Corbetta 2020] [Cross and Vesely 2018] [Iverson et al. 2009] [Dawaare et al. 2026] [Decadi and Dias 2022] [Decker and Barbré 2015] [Der Kiureghian 2001] [Desmedt 2002] [Detar et al. 2023] [Dong et al. 2025b] [Ebner and Koops 2022] [Ekimogloy et al. 2026] [Dyakov 2025] [Erickson 1993] [Everline et al. 2008] [Ezhilarasu et al. 2019] [Farag et al. 2025] [Fayssal and Weldon 2008] [Fei 2021] [Fernando 2017] [Fulton 1963] [Gao and Wang 2021] [Gaverina et al. 2026] [Gee and Lawrence 2010] [Geisinger 1970] [Genet and Giugliarelli 2025] [Glaser 1996] [Goebel 2024] [Goebel and Rajamani 2021] [Goebel et al. 2019] [Gomes and Beck 2016] [Gourab et al. 2023c] [Grile and Bettinger 2024] [Guikema and Pate-Cornell 2003] [Guikema and Paté-Cornell 2004] [Gujral and Emdee 2016] [Hamza et al. 2023] [Harper 1988] [Harris et al. 2022a] [Ho et al. 1998] [Hong et al. 2025] [Ireland and Gonzales 2020] [Iverson et al. 2010] [Johnson 1988] [Kahle 2000] [Khan et al. 2015] [Kim 2026] [Kothakonda et al. 2018] [Kouri et al. 2022] [Lane et al. 2026] [Lanzi and Simpson 2010] [Lechniak et al. 2015] [Lee 2019] [Lee 2026c] [Leong 2017] [Leuschen et al. 1999] [Levine 1964] [Lewis 1985] [Lewis 1989] [Li et al. 2016b] [Li et al. 2020e] [Li et al. 2025f] [Liao 2017] [Liu et al. 2017c] [Liu et al. 2023a] [Manwatkar et al. 2017] [Maul et al. 2024] [McCoy et al. 2021] [Meade 2004] [Merriam 2000] [Murthy 2016] [Mustafa et al. 2025] [Najarkolaie et al. 2023] [Lindsey 2016] [Nasiri et al. 2025] [Newman et al. 1961] [Nichols et al. 2022] [Nick and Buchaillot 2024] [Nishino et al. 2015] [Norris et al. 2025] [O’Leary et al. 2025] [Ofsthun 2002] [Pan et al. 2022] [Pandit et al. 2025] [PHM for Aerospace 2017] [Poissant et al. 2020] [Probabilistic Risk Assessment 2023] [Qing et al. 2016] [Racicot 1973] [Randelovic et al. 2023] [Rauzy 2018] [Reinhart 2001] [Reliability Analysis Center Griffiss AFB NY 1981] [Richardson 2024] [Riley et al. 2023] [Rosello et al. 1996] [Roy et al. 2024] [Sabán-Fosch et al. 2025] [Safie et al. 2015] [Safie and Fuller 2011] [Samson 2024] [Sanchez and Liscouët-Hanke 2020] [Sankararaman and Goebel 2020] [Sarotte et al. 2019] [Satoh et al. 2020] [Schreiner et al. 2016] [Shang and Wang 2024] [Shishko and Matijevic 2000] [Shuo and Yi 2017] [Sindoni et al. 2016] [Solanyk 1993] [Sonawane and Daniel Otero 2024] [Sood 2018] [Stenger et al. 2020] [Suhir 2026] [Tak and Jung 2018] [Tatry et al. 1997] [Thornton 1977] [Trevino et al. 2016] [Tuckman 1965] [Turkmen et al. 2023] [Uckun 2005] [Unal et al. 2000] [Unal et al. 2004] [Wang et al. 2022d] [Wangu and Mouyos 1998] [Weglian and Brinsfield 2023] [Weiss and Brundage 2021] [Welch 2023] [Werner et al. 2018] [Wheeler et al. 2021] [Wishart et al. 2023] [Wood 2020] [Xiao et al. 2023] [Xie et al. 2015] [Xue et al. 2017] [Yang 1981] [Yang et al. 2022c] [Yau et al. 2002] [Yerkes and Scofield 2016] [Yu 2017] [Yusuf and Musa 2021] [Zemoura and Farago 2025] [Zhang and Ma 2020] [Zhang et al. 2015b] [Zhang et al. 2017d] [Zhang et al. 2025d] [Zhu et al. 2023]

Design optimisation, uncertainty and computation

Design optimisation, uncertainty quantification, surrogate modelling and computational method.

117 records. [6 DoF Aircraft Simulation 2016] [Abu El-Wafa et al. 2022] [Adelmann 2019] [Alexanderian et al. 2021] [Azis et al. 2025] [Bahrami and Ommi 2022] [Beck and Guillas 2016] [Benek and Luckring 2017a] [Benek and Luckring 2017b] [Bennich and Lindsey 1967] [Bertoni et al. 2018] [Bhattacharya and Jung 2020] [Blanchard and Sapsis 2021] [Branets 2020] [Brevault and Balesdent 2021] [Brevault et al. 2017] [Brevault et al. 2019] [Brevault et al. 2020] [Chen 2025] [Chen et al. 2018] [Coons and Huan 2025] [Cusick and Kontis 2019] [Cusick et al. 2020] [Dababneh et al. 2025] [Dalle et al. 2016] [Dalle et al. 2023] [Iverson et al. 2012] [Davidson 2021] [Dpc 2016] [Dupont et al. 2019] [Fajraoui et al. 2017] [Fekhari et al. 2021] [Findenig et al. 2025] [Fohring and Haber 2016] [Dhanush et al. 2019] [Garcia-Cardona et al. 2021] [Gerling et al. 2024] [Gettatelli et al. 2023] [Gong and Pan 2024] [Gorodetsky and Marzouk 2016] [Graziani and Ngom 2024] [Gruhlke et al. 2026] [Gu et al. 2021b] [Głębocki and Jacewicz 2020] [Han et al. 2026a] [Herold and Boelts 2025] [Hoang et al. 2025] [Howe and Bowers 1991] [Hu and Ludkovski 2017] [Ifenna Okoli et al. 2021] [Jiahe 2020] [Kamilis and Polydorides 2018] [Kim et al. 2026a] [Kitaygorsky 2020] [Lartaud et al. 2023] [Lenggana et al. 2025] [Li et al. 2018] [Li et al. 2024c] [Liu et al. 2015b] [Luo and Strait 2024] [Marino 2001] [Matushin and Makhalov 2020] [Miller et al. 2026] [Ming and Guillas 2021] [Mueller and Kochenderfer 2016] [Murashko and Tkachov 2025] [Nielsen et al. 2015] [Noel et al. 2003] [Novack et al. 2016] [Oh et al. 2015] [Oh et al. 2017] [Prasad 2022] [Pronzato and Zhigljavsky 2020] [Qi et al. 2024] [Rahn and Schottle 1996] [Rheaume and Lents 2018] [Romano et al. 2024] [Rosić and Diekmann 2015] [Shahmirzaee Jeshvaghani et al. 2015] [Shi et al. 2025a] [Shulkind et al. 2018] [Sinsbeck and Nowak 2017] [Sinsbeck et al. 2021] [Smith 1969] [Steffens et al. 2016] [Steppert et al. 2018] [Sun et al. 2021a] [Tekin et al. 2026] [Tetlow et al. 2000] [Thorbergsson and Hooker 2018] [Tobbe et al. 2009] [Travelletti et al. 2023] [Tuohy 1998] [Uma Sankari et al. 2017] [Urschel and Cox 2003] [Villanueva 2022] [Wang et al. 2020b] [Xiangjun et al. 2019] [Xie et al. 2021] [Xiong et al. 2021] [Xu et al. 2020b] [Xue et al. 2018] [Yan et al. 2025] [Yancosek et al. 2025] [Yang et al. 2016a] [Yang Liu and Wanchun Chen 2016] [Yenigelen and Morris 2020] [Yin et al. 2017] [Yu et al. 2024] [Yu et al. 2025c] [Zeeshan et al. 2021] [Zhang et al. 2019d] [Zhang et al. 2024e] [Zhao and Li 2025] [Zhao et al. 2021a] [Zheng et al. 2020b] [Zolla et al. 2025]

Launch vehicle design, staging and operations

Launch vehicle and spacecraft design, staging and separation, recovery and reuse, and launch operations.

305 records. [Tharun et al. 2025] [Aarnio et al. 1991] [Abbott and Matzenauer 1990] [Abrahamm and Valsa 2018] [Adams 1968] [Advanced Transportation System Studies 1995] [Africano 1935] [Air Force Space Command Space Missile SYS CTR 2013] [Allard 2024] [Allen et al. 1994] [Antares 1991] [Ashish and Chandrasekaran 2026] [Argonne National Lab., Ill. 1967] [Bacchetti et al. 2015] [Rifà et al. 2022] [Balaji and Jerry Alexander 2015] [Baumgartner et al. 1979] [Bergman 1973] [Biertümpfel et al. 2023] [Біляєв et al. 2024] [Birkeland and Meuser 1999] [Blanchet et al. 2001] [Boliubash 2025] [Bolster 1967] [Bondar’ et al. 2018] [Borello 2024] [Borio et al. 2025] [Brinton et al. 1994] [Broadfoot 2000] [Brooks 2022] [Buehrle et al. 2010c] [Buehrle et al. 2010b] [Buehrle et al. 2010a] [Burgess 1946] [Cai and Xu 2015] [Cai et al. 2024b] [Campbell and Thomas 2025] [Carson et al. 1986] [Cenkci 1991] [Chalfant 1992] [Chamberlain 1979] [Chandramoul et al. 2020] [Chase 1979] [Chelaru et al. 2022] [China Achieves First Reusable 2026] [Cockrell 2008] [Cockrell et al. 2007] [Cohen and Wasel 1969] [Coleman 2000] [Coley et al. 2018] [Cook 1995] [Cook and Hueter 2003] [Cozzi et al. 2024] [Cremaschi et al. 2017] [Dahlem et al. 1991] [Dalle and Rogers 2015] [Dandappanavar et al. 2026] [Dannenberg 2024] [Davis and Greenberg 1988] [Dees and Stockard 2023] [Environmental Impact Analysis Process. 1988a] [Environmental Impact Analysis Process. 1988b] [Dorrington 1987] [Effect of Design Parameters 2018] [Elkins and Galati 1996] [Elvin 1996] [Endicott 1999] [Erickson 1984] [Escartí-Guillem et al. 2022] [Faulkner and Lyles 2001] [Feng et al. 2019] [Feng et al. 2020] [Firsyuk et al. 2025] [Fischer and Fasoulas 2024] [Fiske et al. 2006] [Flittie and McFarlane 1991] [Flittie et al. 1992] [Francine and Stewart 1995] [Freeman et al. 1996a] [Freeman et al. 1997] [Freeman et al. 1996b] [French 1987] [Fuchs et al. 2018] [Szatkowski and Levin 1991] [Gage and Vander Kam 2003] [Garegnani et al. 2024] [General Dynamics Corp San Diego Ca 1992] [Godai 1986] [Godai 1987] [Golubek and Dron’ 2020] [Gong et al. 2022] [Gonzalez and Marks 1977] [Guruprasad and Mayilvaganan 2023] [Gülgönül and Sözbir 2018] [Hadley 1963] [Hagopian 2002] [Hale 1963a] [Hale 1997] [Hardy et al. 1993] [Hattis 1981] [Hellman et al. 2011] [Hendrickson et al. 2020] [Herdy 2026] [Hinckel 1995] [Hoegenauer and Koelle 1989] [Hoerr 2005] [Holguin and Labbee 1988] [Hong and Ahn 2015] [Honkawa and Yoozbashizadeh 2019] [Hudson and Hunter 1987] [Huether and Otto 1995] [Hwang and Ahn 2024] [Hyland 1971] [Imoto 2016] [Integrated Operations/payloads/fleet Analysis. Volume 1971] [IPAD 1980] [Isaev 2025] [Ito et al. 2020b] [Jacobson 1952] [Jaffe 1988] [Jayan et al. 2024] [Jeyakumar and Biswas 2023] [Jones 2024] [Jung et al. 2023] [Kam and Gage 2004] [Kaplan 2002] [Karel 1967] [Karuntzos 2015] [Kawashima et al. 2025] [Keba and Kulabukhov 2024] [Keith 1991] [Kendrick 1969] [Ketchum 1986] [Kim et al. 2025b] [Ko and Cho 2016] [Koelle 1986] [Koelle and Koelle 1979] [Kong 2025] [Kravchenko et al. 2021] [Krishnaswamy and Mohandas 2025] [Kroncke 1985] [Kruger et al. 2019] [Kumar et al. 2025a] [Kuznetsov 2023] [Johnson and Vaughan 2020] [Lanaman et al. 1965] [Lane et al. 1982] [Lang et al. 2001] [Lang et al. 2002] [Lang et al. 2003] [Lee 1977] [Lee et al. 2026a] [Lewis and Donahoe 2023] [Li et al. 2024a] [Liao et al. 2023b] [Liever and Habchi 2004] [Lim et al. 2024] [Logsdon and Williamson 1997] [Lohse and Lauler 1963] [Lou et al. 2025] [Low-Cost Expendable Launch Vehicles 1992] [Low-Cost Satellites and Satellite 1990] [Lubert 2017] [Lyles and Griner 1998] [Macpherson 1962] [Madhavan Nair 2023] [Magistro et al. 2025] [Makarenko et al. 2015] [Malisuwan and Kanchanarat 2022] [Manwatkar et al. 2024] [Martin Co Baltimore Md 1963] [Martin Co Denver Co 1966] [Martin et al. 1998] [Martin et al. 2024] [Martindale 2006] [Matsuo and Kawaguchi 1995] [Meyers 1991] [Mihaila-Andres et al. 2015] [Mikhalev et al. 2022] [Miller 1963] [Miller et al. 1973] [Milliken 1963] [Mirzabayova and Rustamov 2024] [Mocio 2001] [Morgenthaler and Montoya 1991] [Mori and Maruyama 2016] [Mori et al. 2016] [Moser 1965] [Mosley 1970] [Mueller 1964] [Mueser and Irvine 1950] [Murty et al. 2016] [Naftel and Powell 1983] [Newman and Stahmann 1963] [Ngo et al. 2017] [Nizhnik 2012] [Noneman 2002] [Obermann and Williamson 1998] [Obermann and Williamson 2003] [Oconnor 1966] [Oh et al. 2018b] [Otte et al. 2008] [Peet 2021] [Perumal 2023] [Pinier 2024] [Polsgrove and Thomas 2016] [Portanova et al. 1992] [Poston 1995] [Powell 1962] [Powell et al. 1991a] [Powell et al. 1991b] [Powell et al. 1998] [Puzanov et al. 2024] [Qiang Wu and Wei Wang 2016] [Quest and Waganer 1970] [Ragab and Cheatwood 2015] [Ralph 1965] [Ravindran et al. 2024] [Raymer 2006] [Reed et al. 2016] [刘 2017] [Rey 2000] [Rhisat and Molki 2023] [Rice 1970] [Roback et al. 1981a] [Roback et al. 1981b] [Rocket on Rails 1948] [Rooney 2003] [Rucker 2015] [Ryan and Verderaime 1993] [Vinoth 2017] [Sackheim and Dergarabedian 1996] [Saha et al. 2020] [Samokhvalova and Shlyakhtenkova 2019] [Sanford et al. 2003] [Schumann et al. 2011] [Scully 2015] [Sekula et al. 2016] [Seltzer 1970a] [Shaw and Womack 1984] [Shibato 1995] [Sholes et al. 1994] [Shulepov and Popov 2018] [Shulga and Shcheglov 2021] [Silva Oliveira et al. 2017] [Simon and Chudoba 2021] [Sinclair et al. 2025] [Sithara and Shenil 2022] [Smith and Philips 2003] [Smith and Phillips 2002] [Spencer 1999] [Spiridonov et al. 2022] [Staniszewski 2001] [Steffens and Mavris 2015] [Stower 2024] [Stower 2025] [Straub 2018] [Sudol et al. 2018] [Swaim 1968] [Swan 2026] [Szatkowski and Schultz 1988] [Szedula 1996] [Takahashi et al. 1997] [Tan et al. 2024] [Tanck and Steadman 1998] [Taniguchi 2000] [Taylor et al. 2008] [Tetik and Das 2017] [The Launch Loop 1985] [Thivent 2024] [Thomas et al. 2002] [Timofeev 2020] [Trollheden and Streifinger 1993] [Tuma and Chenevert 2010] [Tumino 2025] [Vivekanand 2024] [Veracka et al. 2005] [Von Chorus et al. 2025] [Wang et al. 2024d] [Wente 1982] [White et al. 1985] [Whitehead 1990] [Wilhite 1981] [Williams 1971] [Williams and Thompson 1967] [Winchell 1992] [Wolfe 1966] [Worlund 1992] [Wu and Zhang 2023] [Xiao et al. 2019] [Yang 2023] [Yang et al. 2022d] [Yarimbatman and Cengiz 2024] [Yedhu U. Krishnan and Saidalavi P 2015] [Yu et al. 2021] [Yuan et al. 2025] [Yun et al. 2023] [Yuwei et al. 2021] [Zaidi and van Zyl 2017] [Zhang et al. 2018a] [Zhang et al. 2022b] [Zhao and Jiang 2018] [Zhiqiang et al. 2015b] [Zhou et al. 2015b] [Zhou et al. 2015a]

Flight test, instrumentation and range operations

Flight test management, instrumentation and range operations.

18 records. [Air Force Test Pilot School Edwards Afb Ca 1990a] [Air Force Test Pilot School Edwards Afb Ca 1990b] [Air Force Test Pilot School Edwards Afb Ca 1993] [American Institute of Aeronautics and Astronautics 1992] [Bowers and Pratt 1985] [Carico 1998] [Chappell 1984] [Development and Implementation 1990] [General Dynamics/Astronautics San Diego Ca 1961] [General Dynamics/Astronautics San Diego Ca 1962] [General Dynamics/Astronautics San Diegoca 1961] [Lux-Baumann and Burkes 2005] [Jones 1970] [Lux and Burkes 2008] [Lux-Baumann and Burkes 2006] [Martin 1978] [Morelli 1994] [Vehicle Performance Monitoring System 1991]

Where the Framing Breaks Down

Cost Is Not an Engineering Quantity and This Article Treats It as One

The analysis above prices simplifications in seconds, kilograms and newtons, and then sets the result beside dollars. Those are not commensurable. A gas generator that costs at most 11.46 seconds of specific impulse, the upper bound the schematic’s flows give, is a fact. Whether that trade was worth making depends on a price never published for a chamber never built in quantity.

This article can compute what simplification cost in physics and cannot compute what it saved in money, and every conclusion about the trade is therefore one-sided.

The Cost Comparison Has a Denominator Problem

Dividing programme cost by vehicle mass is a crude instrument and the numbers move a great deal with the choice. Dividing by the number of airframes built gives a different answer. Dividing by flights achieved gives infinity for both. The mass denominator was chosen because both programmes published a mass, and no denominator would have made the comparison rigorous.

The Review Might Simply Have Been Right

This article has treated the 305 percent growth computed in The Review That Ended It as the price of restoring what low-cost planning removed. There is a less flattering reading and it deserves stating. The original estimate may have been wrong on its own terms rather than deliberately thin, and a programme that underestimates by a factor of four has a competence problem instead of a philosophy.

The record does not distinguish these, and the two readings differ in what they imply. Under the first, low-cost demonstration is a coherent strategy that must budget for eventual rigour. Under the second, the X-34 is a badly estimated project and there is no general lesson at all.

The Comparison With the X-33 Flatters the X-34

The two vehicles were not trying to do the same thing and the per-pound comparison quietly assumes they were. The X-33 was attempting a mass fraction no vehicle had achieved, with technologies never before built. The X-34 was attempting a flight profile within reach of existing practice. A programme attempting something harder should cost more, and some of the ratio is that rather than efficiency.

Behind that caution lies the cluster on cost estimation, cost growth and acquisition, which includes the estimation of weapon system cost growth in Asher and Maggelet 1980 and the evidence on acquisition policy and the cost growth of major programmes in McNicol and Wu 2014.

The Source Base

This article rests on 2,066 research records published through 2001, when the programme was cancelled, and 2,880 published from 2015 onward.

The research survey holds 5,367 research records drawn from the NASA Technical Reports Server, the Defense Technical Information Center and the journal literature indexed by Crossref, of which 965 are report primaries, being 18.0 percent, by the identifier rule set out under The Definition of Primary. The median publication year is 2015. Of the 5,364 dated records, 2,066 were published through 2001, being 38.5 percent, and 2,880 were published in 2015 or later, being 53.7 percent. The survey gathers the literature of the programme’s own period and the contemporary literature, so the 416 records dated 2002 to 2014 do not represent the literature of those years.

A second primary base sits well before 1996. Ablative chamber and nozzle materials were characterised from the late 1950s onward, largely for solid rocket motors, and a 1960s report on throat erosion is a primary source for this article’s recession estimate in a way that a 2020 planetary entry study is not.

The cost of a Fastrac combustion chamber in production is not in the public record, and it is the single number that would decide whether the ablative choice was economically right. The article computes everything around that hole and says where the hole is.

The Definition of Primary

Primacy is a property of the document, and this survey derives it from the identifier. A record is a report primary when its address is on the NASA Technical Reports Server or it carries a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. The vehicle’s own record is primary almost entirely under that rule. Of the 39 titles that name the X-34, 34 are report primaries, and the other 5 are papers of the American Institute of Aeronautics and Astronautics. The rule does not reach the journal papers among the foundational sources, so 18.0 percent is a lower bound on how much of the survey is first-hand.

The programme window is 1996 to 2001 and it is short. Within it the primary record is the engine’s development literature, which is substantial because a government laboratory built the engine and published, and the airframe literature, which is thinner because a company built the airframe and did not.

That asymmetry is the same one the X-32 article found and it points the other way here. The engine is documented like a research project because it was one. The vehicle is documented like a contract deliverable because it was one. Two halves of a single programme, and the half a research agency owned is the half that left a literature.

Thin Subjects

Six subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with a hyphen read as a space. 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 rocket equation and the ascent loss budget rocket equation, Tsiolkovsky, gravity loss, ascent loss, velocity budget, steering loss, drag loss 1
the effective heat of ablation heat of ablation 2
propellant bulk density bulk density, propellant density, propellant densities 2
the gas generator cycle by name gas generator cycle, turbine exhaust 5
the cost of an ablative chamber cost, price, affordable, affordability together with ablative, ablation, ablator 1
the turnaround of a reusable vehicle turnaround 1

No research record takes the rocket equation or the ascent loss budget as its subject. The one title that names the rocket equation describes a software tool built on it, and none names a gravity, drag or steering loss. Both are thin headings over subjects nobody writes papers about, because both live in every textbook and in no journal article.

The effective heat of ablation names two records, a 1964 study of graphite and a 1987 laser experiment on graphite, which is the same phenomenon in a milder form, since the quantity is discussed throughout the ablation literature under the vocabulary of char layers, blowing parameters and surface energy balances rather than under its own name.

Propellant density, on which the comparison with the X-33 turns, names two titles, a 1952 study of variable propellant density and a 2009 study of a microwave thermal rocket, so the ratio of 2.945 rests on tabulated densities rather than on a literature of its own.

The gas generator cycle is named in five titles, all of them design or operating studies of engines or of their components, and none names the turbine exhaust, so the identity between the cycle’s flow and impulse penalties rests on the derivation above.

The cost of an ablative chamber, the number the Epistemic State calls the hinge of the trade, appears in one title, a 1995 programme of ablative material testing for low-pressure, low-cost rocket engines, which names low cost as a design goal.

Turnaround, the one quantity that would have tested the cost argument, names one title, a 2004 turnaround time model for conceptual rocket engines.

A subject can be thin because the work was never done, because the heading is wrong, or because the knowledge is so settled that it stopped generating papers. The rocket equation and the heat of ablation are the third kind, and the third kind is invisible to a count. The cost of an ablative chamber and the turnaround of a reusable vehicle are the first, because no vehicle of the kind was built in quantity or flown often.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject. Its records come from the report servers and from the journal literature. Many words this subject depends on also name something else, and a record that shares only such a word is excluded. Tile also names the ceramic tile industry and the tiles of computer memory and maps, reusable also names the revenue management of reusable resources, ablation also names laser machining and laser deposition, recession also names the retreat of Niagara Falls and of glaciers, vehicle and landing also name road, rail, marine and underwater craft and ground robots, and kerosene and combustion also name the piston engine, including kerosene engines described between 1898 and 1905. The programme’s own names are homonyms too. Fastrac also names a tractor, a road traffic control system, a video rate control algorithm and a resin infusion process for composites, MC-1 also names a partial pressure suit, and Pegasus also names a spoken-language travel interface and an airborne assault concept. Faster, better, cheaper is also a slogan of genotyping, drug manufacture and car assembly. Air launch also names the release of missiles, sonobuoys, windsondes and balloons from aircraft, and carrier aircraft also names the aircraft of naval carriers, so weapons, oceanography and naval aviation are excluded. Correction, erratum, retraction and withdrawal notices, figure, table and supplementary-material records, editorials, conference welcomes, recordings, peer-review reports, journal front matter and news items, signed or unsigned, are excluded as well, because they are parts of works or editorial events and not research works. Reviews of books, dictionary and other reference entries of two pages or fewer, puzzles, and the abstracts of papers, patents and reports reprinted in the abstract sections of other journals are excluded on the same ground, while an authored encyclopedia article of more than two pages and a textbook chapter are research works and stay. A document deposited twice under two identifiers is counted once. No residual cluster remains. Every admitted record belongs to one of the named clusters, because a title that shares only a word with the subject, such as launch, vehicle or turnaround, or that belongs to a distant domain, such as satellite payloads, electric propulsion or gun-launched micro air vehicles, is excluded rather than gathered as other literature.

Some classes of doubtful relevance are kept rather than excluded. They are piston engine studies of combustion chamber wall heat transfer and wall coatings, kept because the article uses gas-side heat transfer, probabilistic risk assessment and health management outside aerospace, kept as method, generic heat transfer and gas turbine film cooling studies, whose physics is that of the rocket chamber, fire science on the charring of wood and of flame-retardant polymers, additive manufacturing process studies with no named product, Bayesian experimental design and uncertainty quantification on non-aerospace examples, autonomous landing of unmanned aircraft on moving platforms, and signed trade-press articles on rockets and launches. A reader who rules any of those classes out will find the survey that much smaller.

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

Epistemic State

Historical Fact

The X-34 contract was awarded to Orbital Sciences in August 1996 as a fixed-price award of 49.5 million dollars, and the vehicle and engine projects were budgeted at about 86 million dollars. The Fastrac engine, also designated MC-1, was developed by the agency’s Marshall centre, used a gas generator cycle and an ablatively cooled chamber and nozzle, and was fired for up to 159.03 seconds. The first airframe rolled out in 1999 and made three captive flights beneath the carrier aircraft that year, the first on 29 June. Two airframes of the three planned were completed. No free flight, powered or unpowered, was ever made. A joint review in 2000 identified inadequate system testing, single-string avionics and unvalidated automatic landing among the risks, and an estimate drawn from the restructure plan put the total requirement near 348 million dollars. The programme ended on 31 March 2001, after a funding decision announced together with the X-33’s. The two airframes passed through storage and a private yard and reached a scrapyard by April

  1. The spending of just under 112 million dollars rests on a secondary compilation alone.

Engineering Analysis

The 5.69 percent gap in the usually quoted engine figures is this article’s arithmetic, and its resolution as a pairing of the 15:1 nozzle’s thrust with the 30:1 nozzle’s impulse rests on the development status report’s schematic. The 91.90 kilogram per second flow, the gas generator fraction of 3.50 percent and the 11.46 second upper bound on the impulse the cycle costs are arithmetic on that schematic’s flows and thrust, and the identity that the fractional impulse penalty equals the fractional flow diversion is exact. The 148 second burn time and its 1.075 margin against the longest published test are arithmetic on published masses and flow. The throat diameter is published, and the characteristic velocity and thrust coefficient derived from it depend on taking the requirement table’s 652 pounds per square inch rather than the schematic’s 633 as the chamber pressure. The liner recession figures depend on an assumed recession rate and are presented as a range. The air-launch energy donation of 531.9 metres per second and the 29.3 percent thrust recovery depend on an approximate published release altitude, an assumed release Mach number and the published area ratio, and the thrust recovery overstates the sea-level case. The bulk densities and the 2.945 ratio are arithmetic on published densities, with the RP-1 density taken at the middle of a published range. The result that the gauge-limited tank fraction goes as one over the radius is derived here, and the finding that the ratio between two propellant systems is exactly the inverse of their bulk density ratio is an identity rather than a coincidence.

Inference

That the 305 percent growth measures the price of restoring what low-cost planning removed is an inference, and the competing reading, that the original estimate was simply wrong, is set out in the Where the Framing Breaks Down section and is not excluded by anything in the record.

That the X-34’s ablative chamber was a defensible economic choice is not asserted, because the number that would decide it was never published.

That a small demonstrator cannot stand in for a large vehicle’s tank fraction is an inference from the minimum gauge argument, and it assumes the X-34’s tanks were built to the same minimum gauge as the previous article’s, which the record does not state.

What the Record Does Not Settle

Whether the X-34 would have flown successfully is not settled. Nothing on the vehicle had failed. Nothing had been demonstrated either.

Whether rapid turnaround was achievable is not settled and could only have been settled by flying.

The production cost of the engine’s consumable chamber is not settled, and it is the hinge of the entire ablative trade.

The tank radius used in the scaling comparison is assumed rather than published, and the comparison moves with it, though the direction of the conclusion does not.

Out of Scope

The detailed thermochemistry of ablation. The carrier aircraft and its modification. The Pegasus booster from which the operating method descends. The X-33, treated in the previous article. The Space Launch Initiative that absorbed both programmes. The disposal history of the airframes beyond the fact of it. The commercial position of the contractor.

Conclusion

The X-34 was cancelled because somebody finally priced the risk.

Nothing on the vehicle broke. No structure failed a test, the engine’s development problems were found and corrected on the ground, and no aerodynamic surprise appeared. What happened is that a programme built to be cheap was asked what it would cost to fly safely, and the answer was four times what it had been given.

The things that made it cheap and the things that made it unflyable were the same things. Single-string avionics, thin system testing and an unvalidated automatic landing are exactly what a low-cost demonstrator deletes and what must be restored before anyone drops a rocket aeroplane over inhabited ground. The cost was never removed. It was deferred, and the deferral carried interest of 305 percent.

Set beside the previous article the pair is exact and inverted. The X-33’s binding quantity was mass, which obeys a conservation law, and its demonstrator returned a reading that did not close. The X-34’s binding quantity was cost, which obeys nothing, and its demonstrator returned a revised estimate. One programme was killed by a number it measured. The other was killed by a number it recalculated.

The physics the cost argument left behind does compute, and it mostly finds the choices sound. The gas generator costs 3.50 percent of the propellant and exactly 3.50 percent of the impulse. The kerosene the vehicle burned is 2.945 times denser than the hydrogen the X-33 carried, which rescues a small vehicle from the minimum-gauge penalty that its size imposes. Air launch donates under six percent of an orbital energy budget and recovers 29.3 percent of the engine’s thrust, so the benefit usually claimed for it is the smaller one. And the ablative chamber, the emblem of the whole approach, made a reusable vehicle that consumed a combustion chamber every flight.

This series has now met a designation marking an absence of demand in the X-27, an absence of knowledge in the X-30, an answer nobody wanted in the X-33, and here a vehicle that was finished, was never asked a question it could fail, and was scrapped. Of the four it is the only one that was ready.

Equations

This section collects the 50 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 50, 32 are established and 18 are bespoke. Weights are quoted in pounds and evaluated in kilograms, every relation is worked in the International System with specific impulse in seconds, and several letters are reused, so $m_f$ is the burnout mass in the rocket equation but the fuel mass in the mixture ratio relation, $t$ is a wall thickness while $t_b$ is the burn time, $e$ is a specific energy, $\mu$ is the gas viscosity in the Bartz correlation, and $\varepsilon$ is the nozzle area ratio.

Equation 1, Definition of Specific Impulse. The specific impulse is the thrust divided by the propellant mass flow and standard gravity. the definition of specific impulse Sutton sets out for propulsion analysis

\[I_{sp} = \frac{F}{\dot{m} \, g_0} \tag{1}\]

Equation 2, Specific Impulse Implied by the Usually Quoted Figures. Putting the usually quoted thrust and mass flow through the definition gives 296.14 seconds, 5.69 percent below the quoted 314. Fastrac engine

\[I_{sp} = \frac{266{,}893}{91.90 \times 9.80665} = 296.14 \ \text{s} \tag{2}\]

Equation 3, Total Engine Mass Flow. The main chamber and gas generator flows published in the engine schematic sum to 202.6 pounds per second, which is the quoted 91.90 kilograms per second. Ballard, Olive and Turner

\[\dot{m} = \left(195.5 + 7.10\right) \times 0.45359237 = 202.6 \times 0.45359237 = 91.90 \ \text{kg/s} \tag{3}\]

Equation 4, Specific Impulse of Each Nozzle on Its Own Thrust. Each nozzle’s published thrust over the total flow closes on its own published impulse to within half a percent, so the quoted set paired the ground nozzle’s thrust with the flight nozzle’s impulse. Ballard, Olive and Turner

\[I_{sp}^{30} = \frac{284{,}415}{91.90 \times 9.80665} = 315.6 \ \text{s} \qquad I_{sp}^{15} = \frac{266{,}698}{91.90 \times 9.80665} = 295.9 \ \text{s} \tag{4}\]

Equation 5, Gas Generator Share of the Flow. The published gas generator flow is 3.50 percent of the total, inside the range of three to seven percent that the cycle typically spends. Ballard, Olive and Turner Huzel and Huang’s design text on liquid propellant rocket engines

\[\frac{\dot{m}_{gg}}{\dot{m}} = \frac{7.10}{202.6} = 0.0350 \tag{5}\]

Equation 6, Bespoke Chamber Specific Impulse With No Turbine Thrust. The flight thrust is divided by the chamber flow alone on the assumption that the turbine exhaust contributes no thrust. Huzel and Huang’s design text on liquid propellant rocket engines

\[I_{sp,c} = \frac{F}{\dot{m}_c \, g_0} = \frac{284{,}415}{88.68 \times 9.80665} = 327.05 \ \text{s} \tag{6}\]

Equation 7, Bespoke Impulse Cost of the Gas Generator Cycle. The difference between the chamber and engine impulses rests on the same assumption of a thrustless turbine exhaust and is therefore an upper bound.

\[\Delta I_{sp} = 327.05 - 315.59 = 11.46 \ \text{s} \tag{7}\]

Equation 8, Burn Time of the Propellant Load. The published propellant load divided by the engine flow gives a burn time of 148.0 seconds.

\[t_b = \frac{m_p}{\dot{m}} = \frac{13{,}600}{91.90} = 148.0 \ \text{s} \tag{8}\]

Equation 9, Margin of the Longest Test Over the Mission Burn. The longest recorded hot fire of 159.03 seconds exceeds the mission burn by about seven and a half percent. Ballard, Olive and Turner

\[\frac{t_{\text{test}}}{t_b} = \frac{159.03}{148.0} = 1.075 \tag{9}\]

Equation 10, Effective Exhaust Velocity. The published flight impulse times standard gravity gives an effective exhaust velocity of 3,079.3 metres per second.

\[v_e = I_{sp} \, g_0 = 314 \times 9.80665 = 3{,}079.3 \ \text{m/s} \tag{10}\]

Equation 11, Mass Ratio From the Published Masses. The release mass over the empty mass taken as the burnout mass gives a mass ratio of 2.6585.

\[\frac{m_0}{m_f} = \frac{21{,}800}{8{,}200} = 2.6585 \tag{11}\]

Equation 12, Tsiolkovsky Rocket Equation Evaluated for the X-34. The effective exhaust velocity times the logarithm of the mass ratio gives an ideal velocity increment of 3,010.9 metres per second.

\[\Delta v = v_e \ln\!\left(\frac{m_0}{m_f}\right) = 3{,}010.9 \ \text{m/s} \tag{12}\]

Equation 13, Bespoke Allowance Left for Losses. The ideal increment plus the carrier contribution at an assumed release Mach number of 0.8 is set against a Mach 8 objective taken as about 2,400 metres per second, leaving 847.0 metres per second for losses.

\[3{,}247.0 - 2{,}400 = 847.0 \ \text{m/s} \tag{13}\]

Equation 14, Thrust to Weight at Release. The flight nozzle’s vacuum thrust over the release weight gives a thrust to weight ratio of 1.330.

\[\frac{F}{m_0 g_0} = \frac{284{,}415}{21{,}800 \times 9.80665} = 1.330 \tag{14}\]

Equation 15, Propellant Mass Fraction. The propellant load over the release mass gives a propellant mass fraction of 62.4 percent.

\[\zeta = \frac{13{,}600}{21{,}800} = 0.6239 \tag{15}\]

Equation 16, Throat Area From the Characteristic Velocity. The throat area is the chamber flow times the characteristic velocity divided by the chamber pressure. characteristic velocity

\[A_t = \frac{\dot{m}_c \, c^{\ast}}{p_c} \tag{16}\]

Equation 17, Area of the Published Throat. The published throat diameter of 8.25 inches gives a throat area of 0.034488 square metres. the nozzle design report

\[A_t = \frac{\pi D_t^2}{4} = \frac{\pi \times 0.20955^2}{4} = 0.034488 \ \text{m}^2 \tag{17}\]

Equation 18, Characteristic Velocity From Published Chamber Figures. The definition run in reverse with the published chamber pressure requirement, throat area and chamber flow gives a characteristic velocity of 1,748 metres per second. Ballard, Olive and Turner

\[c^{\ast} = \frac{p_c A_t}{\dot{m}_c} = \frac{4.495 \times 10^6 \times 0.034488}{88.68} = 1{,}748 \ \text{m/s} \tag{18}\]

Equation 19, Vacuum Thrust Coefficient. The thrust coefficient is the flight thrust divided by the chamber pressure and the throat area, here 1.8345.

\[C_F = \frac{F}{p_c A_t} = \frac{284{,}415}{4.495 \times 10^6 \times 0.034488} = 1.8345 \tag{19}\]

Equation 20, Specific Impulse as Thrust Coefficient Times Characteristic Velocity. The specific impulse factors into the thrust coefficient, which describes the nozzle, and the characteristic velocity, which describes the chamber, divided by standard gravity.

\[I_{sp} = \frac{C_F \, c^{\ast}}{g_0} \tag{20}\]

Equation 21, Exit Area From the Area Ratio. The published area ratio of about 30 times the throat area gives an exit area of 1.0346 square metres.

\[A_e = \varepsilon A_t = 30 \times 0.034488 = 1.0346 \ \text{m}^2 \tag{21}\]

Equation 22, Bartz Correlation for Gas-Side Heat Transfer. The Bartz correlation gives the gas-side heat transfer coefficient at the throat from the gas properties, the chamber pressure, the characteristic velocity and the throat geometry.

\[h_g = \frac{0.026}{D_t^{0.2}}\left(\frac{\mu^{0.2} c_p}{\mathrm{Pr}^{0.6}}\right)\left(\frac{p_c}{c^{\ast}}\right)^{0.8}\left(\frac{D_t}{R_c}\right)^{0.1} \tag{22}\]

Equation 23, Bespoke Throat Heat Flux. The convective flux is evaluated with a coefficient from typical kerosene and oxygen gas properties and a throat curvature radius equal to its diameter, a recovery temperature of 3,150 kelvin and an ablating surface at 1,900 kelvin, all values the article assumes.

\[q = h_g \left(T_{aw} - T_w\right) = 8{,}674 \times \left(3{,}150 - 1{,}900\right) = 10.84 \ \text{MW/m}^2 \tag{23}\]

Equation 24, Steady Recession Rate From an Ablation Energy Balance. The recession rate is the arriving heat flux divided by the material density and the effective heat of ablation.

\[\dot{s} = \frac{q}{\rho_a H_{\text{eff}}} \tag{24}\]

Equation 25, Bespoke Forward Recession Rate From Absorbed Energy. The recession rate is computed on representative property values for silica phenolic that the article assumes, an absorbed energy of 13.76 megajoules per kilogram, and gives an implausible 0.463 millimetres per second.

\[H_{\text{absorb}} = 13.76 \ \text{MJ/kg} \qquad \Rightarrow \qquad \dot{s} = 0.463 \ \text{mm/s} \tag{25}\]

Equation 26, Bespoke Effective Heat of Ablation Implied by the Recession Rate. The balance is inverted with an assumed upper recession rate of a tenth of a millimetre per second and an assumed density of 1,700 kilograms per cubic metre, giving 63.8 megajoules per kilogram. the nozzle design report

\[H_{\text{eff}} = \frac{q}{\rho_a \dot{s}} = \frac{10.84 \times 10^6}{1{,}700 \times 10^{-4}} = 63.8 \ \text{MJ/kg} \tag{26}\]

Equation 27, Bespoke Liner Consumed Over One Burn. The assumed upper recession rate of a tenth of a millimetre per second over the 148 second burn removes 14.8 millimetres of liner.

\[\Delta s = \dot{s} \, t_b = 10^{-4} \times 148.0 = 14.8 \ \text{mm} \tag{27}\]

Equation 28, Specific Energy. The specific energy is the potential energy per unit mass plus the kinetic energy per unit mass.

\[e = g_0 h + \frac{v^2}{2} \tag{28}\]

Equation 29, Bespoke Specific Energy Donated by the Carrier. The specific energy is evaluated at the published release altitude of 38,000 feet and an assumed Mach 0.8. Ballard, Olive and Turner

\[e = 9.80665 \times 11{,}582 + \frac{236.1^2}{2} = 141{,}446 \ \text{J/kg} \tag{29}\]

Equation 30, Bespoke Velocity Equivalent of the Carrier’s Energy. The specific energy at the assumed release speed is converted to the velocity increment that would supply it, 531.9 metres per second.

\[\Delta v_{\text{equiv}} = \sqrt{2e} = 531.9 \ \text{m/s} \tag{30}\]

Equation 31, Thrust Corrected for Ambient Pressure. The thrust falls below its vacuum value by the ambient pressure acting over the nozzle exit area.

\[F = F_{vac} - p_a A_e \tag{31}\]

Equation 32, Thrust Recovered by Launching at Altitude. The difference in standard atmosphere pressure between sea level and the release altitude, acting over the exit area, recovers 83,470 newtons.

\[\left(101{,}325 - 20{,}646\right) \times 1.0346 = 83{,}470 \ \text{N} \tag{32}\]

Equation 33, Bulk Density of a Propellant Combination. The bulk density is the reciprocal of the mass-weighted mean of the reciprocal fuel and oxidiser densities at a given mixture ratio. Huzel and Huang’s design text on liquid propellant rocket engines

\[\rho_{\text{bulk}} = \left[\frac{1}{1+r}\frac{1}{\rho_f} + \frac{r}{1+r}\frac{1}{\rho_o}\right]^{-1} \tag{33}\]

Equation 34, Bespoke Propellant Densities at the Midpoint of the Kerosene Range. The liquid oxygen density is the tabulated value, while the kerosene density is the midpoint of the stated range of 800 to 820 kilograms per cubic metre. Huzel and Huang’s design text on liquid propellant rocket engines

\[\rho_o = 1{,}142 \ \text{kg/m}^3 \qquad \rho_f = \frac{800 + 820}{2} = 810 \ \text{kg/m}^3 \tag{34}\]

Equation 35, Bespoke Bulk Density of Kerosene and Oxygen. The bulk density at the published mixture ratio of 2.17 uses the midpoint kerosene density, giving 1,011.2 kilograms per cubic metre.

\[\rho_{\text{bulk}} = \left[\frac{1}{3.17}\frac{1}{810} + \frac{2.17}{3.17}\frac{1}{1{,}142}\right]^{-1} = 1{,}011.2 \ \text{kg/m}^3 \tag{35}\]

Equation 36, Fuel Share of the Propellant Mass. At the published mixture ratio of 2.17 the fuel is one part in 3.17 of the propellant mass.

\[\frac{m_f}{m_p} = \frac{1}{1+r} = \frac{1}{3.17} = 0.3155 \tag{36}\]

Equation 37, Bespoke Volume of the Load Under Two Propellant Choices. The propellant load is divided by the midpoint kerosene bulk density and by a hydrogen and oxygen bulk density at an assumed mixture ratio of 5.5. X-33

\[\frac{13{,}600}{1{,}011.2} = 13.45 \ \text{m}^3 \qquad \text{against} \qquad \frac{13{,}600}{343.4} = 39.61 \ \text{m}^3 \tag{37}\]

Equation 38, Tank to Propellant Mass Ratio of an Ideal Vessel. For a thin pressure vessel sized by stress the tank mass over the propellant mass contains no length, so the ratio is independent of size.

\[\frac{m_{\text{tank}}}{m_{\text{prop}}} = \frac{k \, \rho_w \, p}{\sigma \, \rho_p} \tag{38}\]

Equation 39, Membrane Thickness of a Cylindrical Wall. The wall thickness that a pressure demands is the pressure times the radius divided by the allowable stress. Bruhn sets out for flight vehicle structures

\[t = \frac{pR}{\sigma} \tag{39}\]

Equation 40, Bespoke Wall and Propellant Mass per Unit Length at Minimum Gauge. The wall is taken as two facesheets each at the minimum gauge, a construction the article assumes, so the wall mass grows with the radius while the propellant mass grows with its square.

\[m'_{\text{wall}} = \rho_w \left(2 \pi R\right) \left(2 t_{\text{gauge}}\right) \qquad m'_{\text{prop}} = \rho_p \pi R^2 \tag{40}\]

Equation 41, Bespoke Gauge-Limited Tank Fraction. Under the minimum gauge assumption the tank to propellant mass ratio falls as one over the radius instead of being independent of it.

\[\frac{m_{\text{tank}}}{m_{\text{prop}}} = \frac{4 \rho_w t_{\text{gauge}}}{\rho_p R} \tag{41}\]

Equation 42, Bespoke Gauge-Limited Tank Fractions for Two Propellants. The gauge-limited fraction is evaluated at an assumed tank radius of 0.75 metres with the laminate density and minimum gauge of the previous article and the two bulk densities above.

\[\frac{4 \times 1{,}570 \times 0.001}{343.4 \times 0.75} = 0.0244 \qquad \text{against} \qquad \frac{4 \times 1{,}570 \times 0.001}{1{,}011.2 \times 0.75} = 0.0083 \tag{42}\]

Equation 43, Length and Span in Metres. The published length and span are converted from feet to metres. The agency’s fact sheet

\[L = 58.3 \times 0.3048 = 17.77 \ \text{m} \qquad b = 27.7 \times 0.3048 = 8.44 \ \text{m} \tag{43}\]

Equation 44, Empty and Propellant Masses in Kilograms. The published unfuelled weight and propellant weight are converted from pounds to kilograms.

\[m_e = 18{,}000 \times 0.45359237 = 8{,}165 \ \text{kg} \qquad m_p = 30{,}000 \times 0.45359237 = 13{,}608 \ \text{kg} \tag{44}\]

Equation 45, Release Mass. The release mass is the sum of the empty and propellant masses, 48,000 pounds or 21,772 kilograms.

\[m_0 = m_e + m_p = 48{,}000 \ \text{lb} = 21{,}772 \ \text{kg} \tag{45}\]

Equation 46, Projected Growth of the Programme Cost. The estimated requirement of 348 million dollars against 86 million budgeted is a growth of 305 percent on the rounded figures. the General Accounting Office

\[\frac{348 - 86}{86} = 3.05 \tag{46}\]

Equation 47, Bespoke Spend per Pound of the X-34. The figure of merit the article defines divides the reported spending of 112 million dollars by the release weight of 48,000 pounds. Orbital Sciences X-34

\[\frac{112 \times 10^6}{48{,}000} = 2{,}333 \ \text{dollars per pound} \tag{47}\]

Equation 48, Bespoke Spend per Pound of the X-33. The same figure of merit divides about 1,280 million dollars of combined spending by the X-33 gross weight of 285,000 pounds. the X-33

\[\frac{1{,}280 \times 10^6}{285{,}000} = 4{,}491 \ \text{dollars per pound} \tag{48}\]

Equation 49, Bespoke Projected Cost per Pound to Finish the X-34. The figure of merit is evaluated with the estimated total requirement of 348 million dollars in place of the money spent.

\[\frac{348 \times 10^6}{48{,}000} = 7{,}250 \ \text{dollars per pound} \tag{49}\]

Equation 50, Price per Kilogram of the Air-Launched Booster. A price of about forty million dollars for some 450 kilograms to low orbit is about 89,000 dollars per kilogram. an air-launched satellite booster

\[\frac{40{,}000{,}000}{450} \approx 89{,}000 \ \text{dollars per kilogram} \tag{50}\]

Notation

  • $I_{sp}$, the specific impulse in seconds, with $I_{sp,c}$ the impulse of the chamber flow alone
  • $F$, the thrust, with $F_{vac}$ the vacuum thrust
  • $\dot{m}$, the total propellant mass flow, with $\dot{m}_c$ the chamber flow and $\dot{m}_{gg}$ the gas generator flow
  • $g_0$, standard gravity
  • $t_b$, the burn time, with $t_{\text{test}}$ the longest test duration
  • $v_e$, the effective exhaust velocity
  • $m_0$, the release mass, with $m_e$ the empty mass and $m_p$ the propellant mass
  • $\Delta v$, the ideal velocity increment
  • $\zeta$, the propellant mass fraction
  • $A_t$, the throat area, with $A_e$ the exit area and $D_t$ the throat diameter
  • $c^{\ast}$, the characteristic velocity
  • $p_c$, the chamber pressure, with $p_a$ the ambient pressure
  • $C_F$, the thrust coefficient
  • $\varepsilon$, the nozzle area ratio
  • $h_g$, the gas-side heat transfer coefficient
  • $R_c$, the radius of curvature of the throat
  • $\mathrm{Pr}$, the Prandtl number of the combustion gas
  • $T_{aw}$, the recovery temperature, with $T_w$ the temperature of the ablating surface
  • $\dot{s}$, the recession rate, with $\Delta s$ the depth removed over a burn
  • $\rho_a$, the density of the ablative material
  • $H_{\text{eff}}$, the effective heat of ablation, with $H_{\text{absorb}}$ the energy the material can absorb
  • $e$, the specific energy supplied by the carrier aircraft
  • $\rho_{\text{bulk}}$, the bulk density of the propellant combination
  • $\rho_f$, the fuel density, with $\rho_o$ the oxidiser density
  • $r$, the mixture ratio
  • $\rho_w$, the wall material density
  • $\rho_p$, the propellant bulk density in the tank relations
  • $\sigma$, the allowable stress of the wall
  • $t_{\text{gauge}}$, the minimum gauge of one facesheet
  • $R$, the tank radius

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