X-Planes: ABL Space Systems X-63
Filed under: aerospace, history, engineering
This is the sixty-fourth article in the X-Planes series, following the X-1, the X-2, the X-3, the X-4, the X-5, the X-6, the X-7, the X-8, the X-9, the X-10, the X-11, the X-12, the X-13, the X-14, the X-15, the X-16, the X-17, the X-18, the X-19, the X-20, the X-21, the X-22, the X-23, the X-24, the X-25, the X-26, the X-27, the X-28, the X-29, the X-30, the X-31, the X-32, the X-33, the X-34, the X-35, the X-36, the X-37, the X-38, the X-39, the X-40, the X-41, the X-42, the X-43, the X-44, the X-45, the X-46, the X-47, the X-48, the X-49, the X-50, the X-51, the X-52, the X-53, the X-54, the X-55, the X-56, the X-57, the X-58, the X-59, the X-60, the X-61, and the X-62.
On 20 April 2022 the register gave out two X numbers with the same description, and the description is identical to the byte.
The X-63A went to ABL Space Systems. The X-64A went to a team of Invocon, KT Engineering and Troy7. Both rows carry the same allocation date, the same sponsor, the same engines cell, and the same 101 characters of description [Parsch, DOD 4120.15-L Addendum].
Demonstrator rocket for AFRL’s ARISE (Aerospike Rocket Integration and Suborbital Experiment) program
Eleven descriptions repeat somewhere in the 539 rows of that register, in the copy the compiler last updated on 23 August 2026. Ten of them are munitions, targets and a ground station, being a laser-guided seventy millimetre rocket that appears four times, a ground control station for an unmanned air vehicle that appears three times, an evolved sea sparrow missile that also appears three times, and then seven that appear twice each, which are an air superiority target replacing a retired fighter, captive missile training, a thrust vector control interface to a vertical launching system, an air defence artillery weapon, a multi-stage supersonic target, a generic sub-scale aerial target and a long range standoff cruise missile prototype. The eleventh is this pair, the only duplicated description among the thirty-one rows of the X- series, which are not the only rows whose designation begins with the letter X [Parsch, DOD 4120.15-L Addendum].
Two X numbers were issued for one programme on one day, and the only thing the register uses to tell them apart is the name of the company building each one.
| Designation | Allocated | Contractor | Engines cell | Sponsor |
|---|---|---|---|---|
| X-60A | 07-Sep-18 | Generation Orbit Launch Services | empty |
USAF |
| X-61A | 06-Jun-19 | Dynetics | 1 F107-WR-105 |
DARPA |
| X-62A | 14-Jun-21 | Lockheed Martin | 1 Pratt & Whitney F100 |
USAF |
| X-63A | 20-Apr-22 | ABL Space Systems | 1 rocket engine |
USAF/USSF |
| X-64A | 20-Apr-22 | Invocon, KT Engineering, Troy7 | 1 rocket engine |
USAF/USSF |
| X-65A | 24-Apr-23 | Aurora Flight Sciences | 1 Williams FJ44-3A |
DARPA |
| X-66A | 03-May-23 | Boeing | 2 Pratt & Whitney |
NASA |
| X-68A | 20-Aug-25 | General Atomics | 1 Williams WJ38-15 |
DARPA |
This article is about the ABL vehicle and about the nozzle both vehicles exist to fly. The X-64A is a separate article and a separate machine, built by a different team to answer the measurement half of the same question. A programme that holds two designations does not divide itself neatly at the seam the register draws, so what follows takes the nozzle and the engine, and leaves the instrumentation and the recovery gear to the other number.
The Research Question
A rocket nozzle has one design altitude and flies through all of them.
The exhaust leaves a bell nozzle at whatever pressure the geometry dictates, and the atmosphere outside is at whatever pressure the altitude dictates, and those two numbers agree at exactly one point on the ascent. Everywhere below that point the jet is over-expanded and the atmosphere pushes back on the nozzle wall. Everywhere above it the jet is under-expanded and energy that could have been thrust leaves as pressure. The mismatch is no defect of manufacture. A fixed exit area entails it.
An aerospike inverts the geometry. Instead of expanding the gas inside a bell, it expands the gas along the outside of a central body, so the outer boundary of the plume is the atmosphere itself. The expansion ends where the ambient pressure ends it, and that pressure differs at every altitude. The idea is old, the hardware has been built several times, small aerospike engines have flown on research and university rockets, and no aerospike engine has flown a trajectory representative of a launch to orbit [ARISE and Fly].
So the questions are these. How much is altitude compensation worth, stated as a quantity rather than as an advantage? What does a fixed nozzle lose, and does that loss make the whole case? What does the fixed nozzle’s optimum look like, and can it be built? And what does it mean to assemble one engine out of many small ones, the other half of what this programme bought?
The answers turn out to be sharper than the subject’s reputation suggests. The loss of a fixed nozzle is an exact geometric object. The optimal fixed nozzle obeys a rule that can be written in one line and that mentions neither the gas nor the engine. And on the trajectory this vehicle’s manufacturer publishes, that rule places the optimum within about a tenth of the largest exit area the nozzle can carry without its flow separating, on one side of that limit or the other depending on a chamber pressure nobody has published.
Programme Origin
The programme’s origin is recorded in three places, and none of them is a contract that can be read. The register allocated both numbers on 20 April 2022 with one description, one sponsor cell and one engines cell [Parsch, DOD 4120.15-L Addendum]. The fact sheet of the Air Force Research Laboratory, AFRL, set out two objectives, an altitude-compensating nozzle and an engine built from many modules [ARISE and Fly]. And the award announcement records two three-year agreements made in December 2019 under an other transaction agreement, which a search of the federal award record does not find [AFRL awards agreements under ARISE]. The register is taken first and the programme second.
The Register and Its Unofficial Wording
The register is compiled by Andreas Parsch from Department of Defense data obtained under the Freedom of Information Act, and it is not itself a Department of Defense publication. The compiler notes that for allocations after October 2018 the official description is no longer releasable to the public, and prints the descriptions of those entries in blue to indicate that they are not official wording [Parsch, DOD 4120.15-L Addendum]. At that point the register stops being a primary source, as the X-61 article also finds. Both rows of this pair carry the marking.
The markup has three states and not two. A row may be wholly official. Its description cell may be marked in full. Or a fragment of the description may be marked while the rest is not. Across the whole register those three states divide 539 rows into 436 unmarked, 86 wholly unofficial and 17 partly unofficial, and across the thirty-one X rows they divide into 21 unmarked, 9 wholly unofficial and 1 partly unofficial [Parsch, DOD 4120.15-L Addendum]. Every count in this article is taken from every row of the copy that the compiler last updated on 23 August 2026, which holds 539 rows, five of them dated 2026 and none of those an X row. That copy is later than this article’s date. The version current on that date, the compiler’s update of 11 August 2025 as captured by the Internet Archive on 6 and 10 December 2025, held 526 rows, twenty-nine of them X rows, and lacked fifteen later rows that include the X-68A and the X-76A [Parsch, DOD 4120.15-L Addendum, 11 August 2025]. Under that version the three states divide the register into 432, 82 and 12 rows and the X rows into 21, 8 and none, eight rows are grey, 435 rows and twenty-five X rows carry an engines cell, twenty-five engines cells use the word rocket, and the Defense Advanced Research Projects Agency sponsors two X rows. Every finding about this pair holds in both versions, being the eleven duplicated descriptions, the two USAF/USSF rows, the seven rows naming the Space Force, the two rows reading 1 rocket engine and the 101-character description. The 436 unmarked rows include eleven that the compiler shows in grey, as designations in use but not confirmed as official allocations, so an unmarked description is not the same thing as an official allocation.
A two-number summary of that split loses a row, and the row it loses is the one whose markup is most easily misread. Counting it unofficial discards the official wording it carries, and counting it official contradicts the compiler’s own markup, which states that part of its wording is a reconstruction. The figures above classify each row by the markup it carries. No other accounting gives every row exactly one place.
| Classification | Whole register | Rows of the X- series |
|---|---|---|
| No part of the description marked as a reconstruction | 436 | 21 |
| Description wholly marked as a reconstruction | 86 | 9 |
| Description partly marked as a reconstruction | 17 | 1 |
| Total | 539 | 31 |
Where the Space Force Appears
The sponsor cell of both rows reads USAF/USSF [Parsch, DOD 4120.15-L Addendum].
Those are the only two rows in the entire register that read exactly that, and among the thirty-one X rows they are the only two that mention the Space Force at all. Seven rows in the whole register name the United States Space Force anywhere in the sponsor cell, and two of the seven are these [Parsch, DOD 4120.15-L Addendum].
The X sponsor column otherwise names the Air Force alone eight times, seven of them as USAF and once spelled out, the National Aeronautics and Space Administration, NASA, six times, the Navy four, the Defense Advanced Research Projects Agency four, the Department of Defense once, and a scattering of joint pairs [Parsch, DOD 4120.15-L Addendum]. A service that did not exist when most of this register was written appears in its experimental aircraft series twice, on the same day, for two halves of one rocket programme [United States Space Force].
An Engines Cell That Names a Class
Both rows say 1 rocket engine [Parsch, DOD 4120.15-L Addendum].
Four hundred and forty-five of the 539 rows carry an engines cell at all, and twenty-seven of the thirty-one X rows do. Those cells almost always name a model. The X-62A of the previous article reads 1 Pratt & Whitney F100. The X-65A reads 1 Williams FJ44-3A. The X-66A reads 2 Pratt & Whitney [Parsch, DOD 4120.15-L Addendum]. Exactly two rows in the register say 1 rocket engine, and they are this pair.
Twenty-six rows of the register use the word rocket in an engines cell somewhere, and only two of them are X rows. The third rocket among the X numbers is the X-60A, whose engines cell is empty [Parsch, DOD 4120.15-L Addendum]. That article found a register calling a rocket an aircraft while the Air Force called it a rocket twelve times. Here the register calls it a rocket in its description and then declines to name the engine, which is defensible, because at the moment of allocation the engine did not have a model name and arguably did not yet exist.
The Programme’s Stated Objectives
The Air Force Research Laboratory runs a portfolio called the Affordable Responsive Modular Rocket, or ARMR. ARISE is the most ambitious thing in it, and it has two objectives [ARISE and Fly].
The first objective is the nozzle. The fact sheet is explicit about what a bell does and why that is a problem.
Since the bell exhaust area is fixed, this optimizes the bell-nozzle for a single altitude. Inversely, an aerospike nozzle expands the exhaust gas on the exterior surface. Thus, the ambient atmosphere controls the exhaust expansion and acceleration.
The second objective is modularity, and the fact sheet insists it is separable from the first.
While modular engines do not require an arrangement via the aerospike nozzle, AFRL’s ARMR portfolio research highlights the inherent advantages of a modular-aerospike configuration for a production engine.
The propulsion system is described as multiple thrusters and turbomachinery units working in concert as a single engine, with multiple propellant pumps and multiple gas generators, manifolded so that the propellant divides evenly among them [ARISE and Fly]. The claim concerns how a large engine might be built out of small ones, and its subject is cost and schedule rather than performance.
The fact sheet also names the three flow regimes the flight is meant to visit, and those regimes are why a flight is needed at all.
Aerospike nozzles operate in three modes (open wake, wake transition, and closed wake) at specific altitudes depending on the engine design, flight trajectory, and ambient atmospheric conditions.
It also states why a test stand cannot substitute.
Realistic flight conditions have not validated in this behavior, since wind tunnel and ground testing cannot provide a truly representative flight environment.
That sentence is missing a word in the original and the meaning survives anyway. What a ground test cannot supply is a falling ambient pressure applied to a full-scale plume for the duration of a real ascent, and altitude compensation is by definition a response to a falling ambient pressure.
One tension in the document needs to be named. The programme is called a suborbital experiment, the fact sheet calls the flight a proof-of-principle test gathering data in the relevant environment of suborbital space, and the same page then says ARISE will fly a launch-to-orbit trajectory to reach all three regimes [ARISE and Fly]. This article reads the phrase as a trajectory representative of a launch to orbit rather than a flight that reaches orbit. That reading agrees with the programme’s name and with every other sentence on the page. It is an inference about wording, marked as one.
The clearance line at the foot of the fact sheet reads 88ABW-2020-0773. The document was cleared for public release in 2020, about two years before either designation was allocated, and it names its two flight-test vehicles as abl and Invocon in a figure caption. Neither X number appears anywhere in it [AFRL ARISE fact sheet].
The Instrument That Bought It
A search of the federal award record finds no trace of this programme under the names it is known by.
A search of the public award database for ABL Space Systems returns no result under procurement contracts, indefinite delivery vehicles, grants or the other financial assistance families. Searches for ARISE aerospike, for Aerospike Rocket Integration and Suborbital Experiment and for Affordable Responsive Modular Rocket return nothing at all [USAspending].
This absence needs no interpretation, because the announcement explains it.
The awards were made using the Space Enterprise Consortium Other Transaction Agreement, executed at Space and Missile Systems Center, Development Corp., at Los Angeles Air Force Base, Calif. The OTA acquisition allows for traditional as well as non-traditional contractors to submit proposals, leveraging unique capabilities from companies that may not be able to participate in a standard FAR based contract acquisition process.
An other transaction agreement is a procurement instrument other than a contract, to which many of the laws and regulations governing federal contracts do not apply, and it exists to reach companies, especially non-traditional ones, that would not otherwise compete for the work. An award made through a consortium is administered by the consortium’s manager under a base agreement [Other Transaction Authority], so a search under the name of the company doing the work need not find it. The previous article found a government that spent twenty-nine million dollars on an aeroplane across seventy-three transactions without once writing the aeroplane’s designation down. This is the same silence, with its instrument named in advance.
The announcement gives the terms it does give. Both awards were made in December 2019, each for three years, and each is for the design, test, manufacture, and launch of a sub-orbital flight of a rocket using a highly instrumented modular aerospike liquid rocket engine [AFRL awards agreements under ARISE]. No dollar figure is stated for either. Three years from December 2019 puts first flight at the end of 2022, and the designations were allocated on 20 April 2022, eight months before that deadline and with no vehicle yet flown.
The announcement also states, in a sentence that decides what this article has to compute, that thrust vector control for the aerospike will be demonstrated.
Three people are quoted. Jade Pomerleau, the programme manager, states that the investigation of a revolutionary, promising, yet unproven architecture is the heart of what AFRL does. Harry O’Hanley, the chief executive of ABL, argues that fast-paced engineering is necessary to maintain the superiority of the U.S industrial base. And Karl Kiefer, the president of Invocon, offers the sentence that sets this article’s historical scale [AFRL awards agreements under ARISE].
The Invocon Team feels that this a great opportunity to accomplish what has eluded the rocket community for nearly 60 years.
Nearly sixty years before December 2019 is about 1960, and the remark, whatever its rhetoric, makes a checkable claim about a literature. It is checked later in this article against the dates of the literature itself.
The Sponsor Spells Its Own Programme Two Ways
One small thing falls out of holding all the primary documents at once. The laboratory’s award announcement writes the programme’s name Sub-orbital, and its fact sheet and programme page write Suborbital.
| Source | Sub-orbital |
Suborbital |
|---|---|---|
| AFRL programme page | 0 | 2 |
| AFRL fact sheet, cleared 2020 | 0 | 2 |
| the award announcement as reprinted | 3 | 1 |
| the X-63A encyclopedia entry | 2 | 1 |
| the X-64A encyclopedia entry | 1 | 1 |
| the register | 0 | 1 |
The two web documents the laboratory publishes are internally consistent and use the unhyphenated form, and so does the register [ARISE and Fly] [AFRL ARISE fact sheet] [Parsch, DOD 4120.15-L Addendum]. The announcement uses the hyphenated form three times, including in its title, and the unhyphenated form once, in a phrase that is not the programme’s name [AFRL awards agreements under ARISE]. The expansion itself never varies. Everyone agrees what the letters mean and the sponsor cannot decide where the hyphen goes.
Sizing From First Principles
No dimension of the X-63A engine is public, so this article sizes the nozzle from the physics and the trajectory instead of from a drawing [ABL Space Systems X-63]. The chamber pressure and area ratio of the aerospike as designed are both unknown, and what follows works in thrust coefficients, which do not depend on how large the engine is. The derivation establishes that thrust is affine in ambient pressure, that the ideal altitude-compensating nozzle is the envelope of all fixed nozzles, that the best fixed nozzle expands to the burn-averaged ambient pressure of its flight, that on the manufacturer’s published ascent [ABL Payload User’s Guide] an ideal spike would deliver between 5.3 and 8.5 percent more first-stage impulse than that nozzle by the gain $\eta$ defined below, and that flow separation rather than performance bounds the fixed nozzle the trajectory wants. The last subsection names the wake regimes that separate the ideal spike from a truncated one.
The Claim, Stated Exactly
What follows depends on one elementary fact about a rocket nozzle, and this subsection writes it down before using it.
Let $F$ be the thrust in newton, $\dot{m}$ the mass flow of propellant in kilogram per second, $v_e$ the exhaust velocity at the exit plane in metre per second, $p_e$ the static pressure of the exhaust at that plane in pascal, $p_a$ the ambient atmospheric pressure in pascal, and $A_e$ the area of the exit plane in square metre. Then
\[F = \dot{m} v_e + \left( p_e - p_a \right) A_e \tag{1}\]which is the momentum flux out of the nozzle plus the net pressure force on its exit plane. Group the terms that do not mention the atmosphere and write $F_{\mathrm{vac}}$ for the thrust the same nozzle would produce against a perfect vacuum, in newton.
\[F_{\mathrm{vac}} = \dot{m} v_e + p_e A_e, \qquad F = F_{\mathrm{vac}} - p_a A_e \tag{2}\]Thrust is an affine function of ambient pressure, and the slope is minus the exit area. Nothing else in the nozzle appears in that slope. A fixed nozzle therefore traces one straight line as it climbs, and two numbers fix its behaviour in the atmosphere, being where the line starts and how steeply it falls.
The Same Statement Without the Engine in It
Coefficients are easier to work with than newtons, because they are independent of the engine’s size.
Let $p_c$ be the chamber pressure in pascal, $A_t$ the area of the throat in square metre, $\varepsilon$ the ratio of exit area to throat area, dimensionless, and $C_F$ the thrust coefficient, also dimensionless. The definitions are these.
\[C_F \equiv \frac{F}{p_c A_t}, \qquad \varepsilon \equiv \frac{A_e}{A_t} \tag{3}\]Dividing the affine law by $p_c A_t$ carries it across unchanged, and the slope becomes the area ratio.
\[C_F\left( \varepsilon, p_a \right) = C_{F,\mathrm{vac}}\left( \varepsilon \right) - \varepsilon \frac{p_a}{p_c} \tag{4}\]Two numbers still describe the nozzle and neither is a length. A fixed nozzle is a point on the vertical axis and a slope, and the rest of the argument concerns which straight line to choose.
Where the Vacuum Coefficient Comes From
The vacuum coefficient is not a free parameter. For a calorically perfect gas expanding isentropically it is fixed by the ratio of specific heats and the area ratio alone.
Let $\gamma$ be the ratio of specific heats, dimensionless, let $M$ be the local Mach number, dimensionless, and let $\Gamma$ be the Vandenkerckhove constant, dimensionless, which collects the throat conditions.
\[\Gamma\left( \gamma \right) = \sqrt{\gamma} \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2\left( \gamma - 1 \right)}} \tag{5}\]The area ratio and the pressure ratio at any station follow from the Mach number there.
\[\frac{A}{A_t} = \frac{1}{M}\left[ \frac{2}{\gamma + 1}\left( 1 + \frac{\gamma - 1}{2} M^2 \right) \right]^{\frac{\gamma + 1}{2\left( \gamma - 1 \right)}}, \qquad \frac{p}{p_c} = \left( 1 + \frac{\gamma - 1}{2} M^2 \right)^{-\frac{\gamma}{\gamma - 1}} \tag{6}\]The first of those is monotone on the supersonic branch, so an area ratio fixes a Mach number, a Mach number fixes an exit pressure ratio, and the vacuum coefficient follows.
\[C_{F,\mathrm{vac}}\left( \varepsilon \right) = \Gamma \sqrt{ \frac{2 \gamma}{\gamma - 1} \left[ 1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right] } + \varepsilon \frac{p_e}{p_c} \tag{7}\]Every number this article computes about nozzles comes out of those four relations and nothing else [Huzel and Huang 1967] [NASA SP-8120]. The first term is momentum and the second the exit plane pushing on a vacuum. Written the other way, with the constant absorbed, the momentum term is the form most texts print, and the two agree to thirteen decimal places in the cases checked.
The Symbols This Article Uses
Fifty-five relations need a table, and this is it. Two letters carry two meanings each, and the table records both, since $L$ is a thrust loss in the nozzle sections and a moment arm in the sections about steering, and $k$ indexes a module in one place and is a separation threshold in another.
| Symbol | Meaning | Unit |
|---|---|---|
| $ \alpha $ | equivalent gimbal angle | radian |
| $ \alpha_{1T} $ | first stationary point of the Bessel function of order one | dimensionless |
| $ \bar{M} $ | mean molar mass of the combustion products | kilogram per kilomole |
| $ \bar{p}_a $ | burn-averaged ambient pressure | pascal |
| $ \Delta m_p $ | payload mass bought by a gain in first-stage velocity increment | kilogram |
| $ \Delta v_1 $ | ideal velocity increment of the first stage | metre per second |
| $ \Delta v_2 $ | ideal velocity increment of the second stage | metre per second |
| $ \delta $ | available throttle depth | dimensionless |
| $ \dot{m} $ | mass flow of propellant | kilogram per second |
| $ \eta $ | fractional impulse gain of the ideal spike | dimensionless |
| $ \Gamma $ | Vandenkerckhove constant | dimensionless |
| $ \gamma $ | ratio of specific heats | dimensionless |
| $ \lambda $ | temperature lapse rate of an atmospheric layer | kelvin per metre |
| $ \mu $ | margin in area ratio of the trajectory-optimal nozzle below the separation limit | dimensionless |
| $ \phi $ | direction of the commanded moment | radian |
| $ \rho $ | fraction of guaranteed steering authority retained after one module fails | dimensionless |
| $ \sigma $ | contraction ratio, chamber area over throat area | dimensionless |
| $ \tau_k $ | throttle fraction of module k | dimensionless |
| $ \theta_k $ | angular position of module k on the ring | radian |
| $ \varepsilon $ | ratio of exit area to throat area | dimensionless |
| $ \varepsilon^{\star} $ | area ratio the mean-in-time rule selects | dimensionless |
| $ \varepsilon_{\mathrm{sep}} $ | largest area ratio that avoids separation at sea level | dimensionless |
| $ A $ | cross-sectional area at a station in the nozzle | square metre |
| $ A_b $ | area of the exposed base of a truncated plug | square metre |
| $ A_d $ | exit area of a fixed nozzle at its own design point | square metre |
| $ A_e $ | area of the nozzle exit plane | square metre |
| $ A_t $ | area of the nozzle throat | square metre |
| $ c $ | speed of sound in the combustion products | metre per second |
| $ c_{e,2} $ | effective exhaust velocity of the second stage | metre per second |
| $ c^{\star} $ | characteristic velocity | metre per second |
| $ C_F $ | thrust coefficient | dimensionless |
| $ C_F^{\star} $ | thrust coefficient of the ideal altitude-compensating nozzle | dimensionless |
| $ C_{F,\mathrm{vac}} $ | thrust coefficient in vacuum | dimensionless |
| $ D $ | chamber diameter | metre |
| $ F $ | thrust | newton |
| $ F^{\star} $ | upper envelope of the thrust of all fixed nozzles | newton |
| $ F_w $ | axial force on the wetted surface of a plug | newton |
| $ f_{1T} $ | frequency of the first tangential acoustic mode | hertz |
| $ F_{\mathrm{vac}} $ | thrust the same nozzle would produce against a vacuum | newton |
| $ G $ | vacuum thrust regarded as a function of exit area | newton |
| $ g_0 $ | standard gravity | metre per second squared |
| $ H $ | pressure scale height of the atmosphere | metre |
| $ h $ | geometric altitude | metre |
| $ h_0 $ | altitude at the base of an atmospheric layer | metre |
| $ h_b $ | altitude at main engine cut-off | metre |
| $ I $ | delivered impulse in units of chamber pressure times throat area | second |
| $ I_{sp} $ | specific impulse | second |
| $ J $ | time integral of ambient pressure over the burn | pascal second |
| $ j $ | index of the module that failed | dimensionless |
| $ k $ | index over modules, and elsewhere the separation threshold ratio | dimensionless |
| $ L $ | loss of a fixed nozzle against the envelope, and elsewhere the distance from the engine plane to the centre of mass | newton, and metre |
| $ M $ | Mach number | dimensionless |
| $ m $ | number of sides of the achievable moment polygon | dimensionless |
| $ m_0 $ | mass of the second stage with its payload at ignition | kilogram |
| $ m_f $ | mass of the second stage with its payload at burnout | kilogram |
| $ m_p $ | payload mass | kilogram |
| $ M_s $ | Mach number at the point where the flow separates from the wall | dimensionless |
| $ M_{\mathrm{out}} $ | unbalanced moment left by the loss of one module | newton metre |
| $ N $ | number of thruster modules on the ring | dimensionless |
| $ n $ | shape exponent of the ascent profile, and elsewhere a count of trials | dimensionless |
| $ p $ | static pressure at a station | pascal |
| $ p_0 $ | pressure at the base of an atmospheric layer | pascal |
| $ p_a $ | ambient atmospheric pressure | pascal |
| $ p_b $ | pressure acting on the exposed base of a truncated plug | pascal |
| $ p_c $ | chamber pressure | pascal |
| $ p_d $ | ambient pressure at which a fixed nozzle is matched | pascal |
| $ p_e $ | static pressure of the exhaust at the exit plane | pascal |
| $ p_s $ | wall pressure at the point where the flow separates | pascal |
| $ p_{\mathrm{SL}} $ | sea-level pressure of the standard atmosphere | pascal |
| $ q $ | dummy variable of integration over ambient pressure | pascal |
| $ R $ | specific gas constant of air | joule per kilogram kelvin |
| $ r $ | radius of the ring of thruster modules | metre |
| $ R_u $ | universal gas constant | joule per kilomole kelvin |
| $ T $ | temperature | kelvin |
| $ t $ | time from liftoff | second |
| $ T_0 $ | temperature at the base of an atmospheric layer | kelvin |
| $ t_b $ | burn duration of the first stage | second |
| $ T_c $ | chamber temperature | kelvin |
| $ u $ | dummy variable of integration over angle | radian |
| $ v $ | climb rate | metre per second |
| $ v_e $ | exhaust velocity at the exit plane | metre per second |
| $ w $ | gain in the first-stage velocity increment | metre per second |
| $ X $ | number of engines suffering the instability | dimensionless |
Every symbol above appears in the mathematics and every symbol in the mathematics appears above.
From Coefficient to Seconds
One conversion is needed, because specific impulse is the currency this subject is argued in.
Let $\dot{m}$ be the mass flow as before, $c^{\star}$ the characteristic velocity in metre per second, $T_c$ the chamber temperature in kelvin, $\bar{M}$ the mean molar mass of the combustion products in kilogram per kilomole, $R_u$ the universal gas constant in joule per kilomole kelvin, $g_0$ the standard gravity in metre per second squared, and $I_{sp}$ the specific impulse in second.
\[c^{\star} = \frac{p_c A_t}{\dot{m}} = \frac{1}{\Gamma}\sqrt{\frac{R_u T_c}{\bar{M}}}, \qquad I_{sp} = \frac{C_F \, c^{\star}}{g_0} \tag{8}\]The split is clean, and it lets this article work in coefficients. The characteristic velocity carries everything about the propellant and the chamber, the thrust coefficient carries everything about the nozzle and the atmosphere, and they multiply. A claim about altitude compensation concerns the second factor only.
That is already enough to say something the subject’s usual presentation obscures. The entire atmospheric penalty of a fixed nozzle over a burn is its exit area multiplied by the time integral of the ambient pressure. Let $t_b$ be the burn duration in second, and let $J$ be that integral in pascal second.
\[J = \int_{0}^{t_b} p_a(t) \, \mathrm{d}t, \qquad \int_{0}^{t_b} F \, \mathrm{d}t = F_{\mathrm{vac}} t_b - A_e J \tag{9}\]One number describes the nozzle. One number describes the flight. They multiply.
The Identity That Makes Ambient Pressure and Exit Area Conjugate
Now vary the exit area and ask what happens to the vacuum thrust.
For steady one-dimensional flow the momentum equation along the nozzle reads $\dot{m} \, \mathrm{d}v = -A \, \mathrm{d}p$, where $A$ is the local cross-sectional area in square metre and $p$ the local static pressure in pascal. Differentiate $F_{\mathrm{vac}} = \dot{m} v_e + p_e A_e$ with respect to the exit area, holding the chamber conditions fixed, and the first and third terms cancel exactly.
\[\frac{\mathrm{d} F_{\mathrm{vac}}}{\mathrm{d} A_e} = \dot{m} \frac{\mathrm{d} v_e}{\mathrm{d} A_e} + p_e + A_e \frac{\mathrm{d} p_e}{\mathrm{d} A_e} = -A_e \frac{\mathrm{d} p_e}{\mathrm{d} A_e} + p_e + A_e \frac{\mathrm{d} p_e}{\mathrm{d} A_e} = p_e \tag{10}\]The incremental vacuum thrust bought by an increment of exit area is the exit pressure acting on that increment, and nothing else survives. The result is exact, it holds for any gas obeying the one-dimensional equations, and it takes one line.
It also settles the structure of the problem. Write $G$ for the vacuum thrust regarded as a function of exit area, in newton, so that $G(A_e) = F_{\mathrm{vac}}$. Then $G’(A_e) = p_e$, and the thrust against an atmosphere is
\[F(p_a; A_e) = G(A_e) - p_a A_e \tag{11}\]which is $G$ minus a linear term, in the pairing that defines a Legendre transform. Ambient pressure is the variable conjugate to exit area. The correspondence is no analogy. It is the same pairing with the same stationarity condition, which the next paragraph states.
Maximising the thrust over the exit area at a fixed ambient pressure requires $G’(A_e) = p_a$, and $G’(A_e)$ is $p_e$. So the optimum is $p_e = p_a$, the matched-expansion condition that texts commonly state as a separate fact. Far from separate, it is the first-order condition of the transform.
In coefficients the same statement is a derivative with respect to the area ratio, and the later sections use this form.
\[\frac{\partial C_F}{\partial \varepsilon} = \frac{p_e - p_a}{p_c} \tag{12}\]The derivative of the thrust coefficient with respect to area ratio is the pressure difference across the exit plane. Lengthening the nozzle helps while the exhaust is still pushing harder than the atmosphere and hurts once it is not. That one line holds the entire design trade. Central differences confirm the relation in twenty-seven cases to five parts in ten million, which is the step size, and its vacuum case, the conjugacy identity, in twelve cases to 2.1 parts in a hundred thousand million.
The Envelope of All Fixed Nozzles
Every fixed nozzle is one straight line. The family of all fixed nozzles is a family of straight lines, one for each exit area, and the best achievable thrust at any given ambient pressure is the upper envelope of that family. Write $F^{\star}$ for that envelope, in newton.
\[F^{\star}(p_a) = \max_{A_e} \left\{ G(A_e) - p_a A_e \right\} \tag{13}\]The envelope is the Legendre transform of the vacuum thrust and the thrust curve of an ideal altitude-compensating nozzle [Legendre transformation] [convex conjugate]. An aerospike is an attempt to build a machine that sits on the envelope rather than on one of its tangent lines, and the mechanism by which its plume follows the atmosphere down is studied in a separate literature [Ruf et al. 1997b].
Two consequences follow immediately and neither needs any hardware.
First, the envelope is convex in ambient pressure, because a maximum of affine functions is always convex. So the ideal spike’s thrust curve bends one way and only one way as the vehicle climbs.
Second, every fixed nozzle touches the envelope at exactly one point and lies strictly below it everywhere else. That one point is its design altitude. This tangency is the entire altitude-compensation argument, and gas dynamics plays no part in it.
That second consequence has a name and an exact statement in the Fenchel-Young inequality.
\[G\left( A_e \right) \le F^{\star}\left( p_a \right) + p_a A_e \quad \text{for every } A_e \text{ and every } p_a \tag{14}\]Equality holds if and only if the nozzle is matched to that ambient pressure. Rearranged, the inequality states that the thrust of any fixed nozzle at any altitude is at most the envelope’s, restating the sentence above with a condition attached to the one case where it is tight. At three area ratios against three ambient pressures each, the gap is positive in every case away from the design point and zero to twelve decimal places at it.
The transform also runs backwards, so the envelope loses nothing.
\[G\left( A_e \right) = \min_{p_a} \left\{ F^{\star}\left( p_a \right) + p_a A_e \right\} \tag{15}\]The family of fixed nozzles and the envelope carry the same information. Knowing the ideal spike’s thrust at every altitude is knowing the vacuum thrust of every bell, and conversely. An aerospike is not a new capability so much as a different point on a structure that was already there.
Two derivatives of the envelope fix its shape between them. Let $A_e(p_a)$ denote the exit area the envelope selects at ambient pressure $p_a$, in square metre.
\[\frac{\mathrm{d} F^{\star}}{\mathrm{d} p_a} = -A_e\left( p_a \right), \qquad \frac{\mathrm{d}^2 F^{\star}}{\mathrm{d} p_a^2} = -\frac{\mathrm{d} A_e}{\mathrm{d} p_a} \ge 0 \tag{16}\]The first is the envelope theorem, which says the slope of the envelope is minus the exit area of whichever nozzle is optimal there. Convexity is the other, and it holds for a physical reason rather than a formal one. A higher ambient pressure selects a shorter nozzle, so the exit area falls as the ambient rises, so its negative is non-negative. The envelope bends upward because the optimal nozzle shrinks as the air thickens.
The gap between the envelope and the tangent line has a name. Let $p_d$ be the ambient pressure at which a particular fixed nozzle is matched, in pascal, and let $A_d$ be its exit area in square metre, so that $F^{\star\prime}(p_d) = -A_d$. The loss of that nozzle at some other ambient pressure is
\[L(p_a) = F^{\star}(p_a) - \left[ G(A_d) - p_a A_d \right] = F^{\star}(p_a) - F^{\star}(p_d) - F^{\star\prime}(p_d)\left( p_a - p_d \right) \tag{17}\]That is the Bregman divergence of the convex function $F^{\star}$ generated at the design point [Bregman divergence] [envelope theorem]. It is zero at the design altitude, positive everywhere else, and it grows faster than linearly in the mismatch because the envelope is convex. The performance penalty of a fixed nozzle is not merely analogous to a Bregman divergence. It is one.
Substituting the first derivative above turns that difference into an integral, and the integral is the form that can be read off a picture.
\[L\left( p_a \right) = \int_{p_d}^{p_a} \left[ A_d - A_e\left( q \right) \right] \mathrm{d}q \tag{18}\]The loss is the area between a horizontal line at the fixed nozzle’s exit area and the curve of the exit area the envelope would have chosen. Above the design point the envelope wants a smaller nozzle than the one fitted and the integrand is positive. Below it the envelope wants a larger one and the integrand is negative, but so is the direction of travel, so the loss is positive on both sides and for the same reason.
The order of that subtraction is not free. Written the other way round the same expression is the negative of the loss, so the integrand has to be the fitted nozzle’s exit area minus the one the envelope would have chosen and not the reverse.
A Fixed Nozzle Chosen by a Mean in Time
If a designer must choose one exit area for a whole ascent, what should it be?
One line answers it. The rule appears first as an invariant, the same number coming out of nine separate numerical optimisations that have no reason to agree, and it can then be derived.
Delivered impulse over the burn, in units of chamber pressure times throat area, is the integral of the thrust coefficient. Let $C_F$ be the thrust coefficient, dimensionless, let $C_{F,\mathrm{vac}}$ be its vacuum value, let $p_c$ be the chamber pressure in pascal, and let $\varepsilon$ be the ratio of exit area to throat area, dimensionless. Because $C_F$ is affine in ambient pressure with slope $-\varepsilon$,
\[I(\varepsilon) = \int_{0}^{t_b} C_F \, \mathrm{d}t = t_b \, C_{F,\mathrm{vac}}(\varepsilon) - \frac{\varepsilon}{p_c} \int_{0}^{t_b} p_a(t)\, \mathrm{d}t \tag{19}\]Differentiate with respect to $\varepsilon$ and set the derivative to zero. The derivative of the vacuum thrust coefficient with respect to the area ratio is the exit pressure ratio, by the conjugacy identity above, so
\[t_b \frac{p_e}{p_c} = \frac{J}{p_c} \qquad \Longrightarrow \qquad p_e = \frac{J}{t_b} = \frac{1}{t_b}\int_{0}^{t_b} p_a(t)\, \mathrm{d}t \tag{20}\]The optimal fixed nozzle expands to the time-averaged ambient pressure of its own flight.
Writing $\bar{p}_a$ for that burn-averaged ambient pressure in pascal, and $\varepsilon^{\star}$ for the area ratio the rule selects, dimensionless, the statement constrains the exit pressure alone.
\[\bar{p}_a \equiv \frac{1}{t_b}\int_{0}^{t_b} p_a(t)\, \mathrm{d}t, \qquad p_e\left( \varepsilon^{\star} \right) = \bar{p}_a \tag{21}\]The gas does not appear, and neither do the chamber pressure and the vehicle. The rule is a mean, taken in time and not in altitude, and exact. The question it answers has been asked of other vehicles by other routes [Hiers and Knapke 2019].
The rule also holds numerically. Over four trajectory shapes, five ratios of specific heats and five chamber pressures, one hundred independent searches in all, the exit pressure of each optimum can be set against the burn-averaged ambient pressure computed separately. The optimal area ratios across that grid range from 4.985 to 84.093, a factor of seventeen, and every one of them produces an exit pressure equal to the mean ambient pressure of its own trajectory. The worst relative disagreement across the hundred cases is 4.2 parts in ten million, which is the tolerance of the search rather than an error in the identity.
A mean in time is a strange thing to design a nozzle around, and the strangeness is the point. The atmosphere thins exponentially with altitude but a rocket does not climb at constant speed, so the burn-averaged pressure depends on how quickly the vehicle leaves the dense air rather than on how high it eventually goes. Two vehicles reaching the same altitude on the same burn time, one accelerating hard early and one accelerating hard late, want different nozzles.
The Manufacturer’s Published Ascent
The X-63A was to be a single-stage aerospike variant of the RS1, called the RS1A by its builder, sharing the parent vehicle’s turbopumps, thrusters and injectors [AFRL awards agreements under ARISE]. The parent vehicle’s reference mission is published in the company’s payload user’s guide, which gives the first-stage trajectory as a sequence of timed points [ABL Payload User’s Guide].
Liftoff is at zero. Main engine cut-off and stage separation occur at 160 seconds, at 75 kilometres altitude and 2.6 kilometres per second. Second-stage ignition follows at 163 seconds and 80 kilometres, fairing separation at 200 seconds and 125 kilometres, second-stage cut-off at 508 seconds at 200 kilometres and 7.8 kilometres per second, and payload separation ten seconds after that [ABL Payload User’s Guide].
| Event | Time | Altitude | Speed |
|---|---|---|---|
| Liftoff | 0 seconds | 0 kilometres | 0 kilometres per second |
| Main engine cut-off and stage separation | 160 seconds | 75 kilometres | 2.6 kilometres per second |
| Second-stage start | 163 seconds | 80 kilometres | 2.6 kilometres per second |
| Fairing separation | 200 seconds | 125 kilometres | 2.65 kilometres per second |
| Second-stage cut-off | 508 seconds | 200 kilometres | 7.8 kilometres per second |
| Payload separation | 518 seconds | 200 kilometres | 7.8 kilometres per second |
Those points already say something about the shape of the climb. The mean vertical speed over the first stage is 469 metres per second against a speed at cut-off of 2,600, so the vertical component is about eighteen percent of the total and the trajectory has turned most of the way over by the time the first stage finishes. A first stage is not a lift.
Two published points and a zero initial rate do not determine a trajectory, so the pressure-time integral was computed over a family of monotone profiles. Let $h$ be geometric altitude in metre, $h_b$ the cut-off altitude in metre and $n$ a shape exponent, dimensionless.
\[h(t) = h_b \left( \frac{t}{t_b} \right)^{n}, \qquad 1.5 \le n \le 3.0 \tag{22}\]The exponent is a guess and the sweep keeps it honest. A value of 2 is constant acceleration, below 2 is a vehicle that climbs steeply and then pitches over, and above 2 is one that lingers low.
Ambient pressure comes from the 1976 United States Standard Atmosphere, implemented as its seven layers from the defining constants of the standard [U.S. Standard Atmosphere 1976 1976] [defining constants and abbreviated tables]. Let $\lambda$ be the temperature lapse rate of a layer in kelvin per metre, $T_0$ and $p_0$ the temperature and pressure at its base in kelvin and pascal, $h_0$ its base altitude in metre, $g_0$ the standard gravity and $R$ the specific gas constant of air in joule per kilogram kelvin. A layer with a lapse rate and an isothermal layer take different forms.
\[p(h) = p_0 \left( 1 + \frac{\lambda \left( h - h_0 \right)}{T_0} \right)^{-\frac{g_0}{R \lambda}}, \qquad p(h) = p_0 \exp\left( -\frac{g_0 \left( h - h_0 \right)}{R T_0} \right) \tag{23}\]The isothermal form is the limit of the other as the lapse rate goes to zero. The two forms reproduce the published table values at geopotential altitudes of 5, 11, 15, 20, 32 and 47 kilometres to better than two parts in a hundred thousand. The layers are defined in geopotential altitude and the calculation applies them to the trajectory’s altitude without conversion, which places each pressure slightly low and lowers the burn-averaged pressure below by 0.05 to 0.12 percent across the profiles. The figures below are computed without the conversion, and no conclusion drawn from them depends on a difference of that size. The lineage of the standard is documented as well [the 1976 standard and its predecessors].
The natural length in that expression is the scale height, in metre, and it sets how quickly the question answers itself.
\[H \equiv -\frac{p}{\mathrm{d}p / \mathrm{d}h} = \frac{R T}{g_0} \tag{24}\]At sea level that is 8,434.5 metres, and the lapse rate does not change it there, because the hydrostatic relation makes the local scale height equal to $R T / g_0$ at every altitude, in a layer with a lapse rate as in an isothermal one. What the lapse rate changes is how the scale height varies with altitude, since it varies as the temperature does.
Across that family the burn-averaged ambient pressure runs from 19.4 to 41.6 percent of sea-level pressure, and the value for the constant-acceleration case is 28.06 percent. The unknown shape of the trajectory produces that spread, and the table below gives it in full.
| Profile exponent | Burn-averaged ambient pressure | As a fraction of sea level | Half the integral collected by |
|---|---|---|---|
| 1.5 | 19,620 pascal | 19.4 percent | 17.6 seconds |
| 2.0 | 28,436 pascal | 28.1 percent | 24.0 seconds |
| 2.5 | 35,916 pascal | 35.4 percent | 29.4 seconds |
| 3.0 | 42,178 pascal | 41.6 percent | 34.0 seconds |
A closed form beside the numbers shows what the integral depends on. For an isothermal atmosphere climbed at a constant rate $v$ in metre per second,
\[J = \frac{p_0 H}{v}\left[ 1 - \exp\left( -\frac{v t_b}{H} \right) \right] \;\longrightarrow\; \frac{p_0 H}{v} \quad \text{as } v t_b \gg H \tag{25}\]The atmospheric penalty of a long burn does not depend on how long the burn is. Once the vehicle is several scale heights up, the integral has stopped growing, and what remains is sea-level pressure times the scale height divided by the climb rate. A rocket does not pay for the atmosphere by the second. It pays once, and the bill is set by how fast it left.
The more useful number is where the integral is accumulated. Half of the pressure-time integral of a 160 second burn is collected in the first 17.6 to 34.0 seconds, depending on the profile. The altitude-compensation question is settled in the first 11 to 21 percent of the burn and the remainder barely votes. Ambient pressure is at half of its sea-level value by 5.48 kilometres, at a tenth by 16.1 kilometres, at a hundredth by 31.0 kilometres of geopotential altitude, which is 31.1 kilometres geometric, and at cut-off altitude it is two parts in a hundred thousand of sea level. Ambient pressure is below a tenth of sea level for the last 40 to 64 percent of the burn and below a hundredth for the last 25 to 44 percent, depending on the profile, and the nozzle still has to carry the exit area it chose for the denser air before that.
The Gain of an Ideal Spike on This Trajectory
With the trajectory in hand the gain of ideal altitude compensation can be computed. The comparison is a ratio of two integrals of thrust coefficients, so it requires no dimension of the engine at all, which is fortunate, because none is public.
Writing $\eta$ for the fractional gain, dimensionless,
\[\eta = \frac{\displaystyle\int_{0}^{t_b} C_F^{\star}\left( p_a(t) \right) \mathrm{d}t}{\displaystyle\int_{0}^{t_b} C_F\left( \varepsilon^{\star}, p_a(t) \right) \mathrm{d}t} - 1 \tag{26}\]The throat area cancels, the chamber pressure cancels and the mass flow cancels, so a figure can be quoted at all for a vehicle whose engine is not public.
Against the best possible fixed nozzle for this trajectory, chosen by the rule derived above, an ideal altitude-compensating nozzle delivers between 5.3 and 8.5 percent more first-stage impulse, across ratios of specific heats from 1.20 to 1.24 and chamber pressures from 3 to 10 megapascal. Against the naive choice, a fixed nozzle matched at sea level, the gain is between 7.8 and 12.5 percent.
Two remarks keep those numbers honest.
The first is that this is an upper bound and a generous one. An ideal spike has no truncation loss, no base drag, no wake, no cooling penalty and no extra mass. A real one has all five. What the calculation bounds is the size of the prize and not the size of the win.
The second is the shape of the optimum, which is more interesting than its value. The best fixed area ratio for this trajectory is between 2.5 and 2.7 times the sea-level-matched ratio. At a chamber pressure of 6 megapascal and a ratio of specific heats of 1.20, the sea-level-matched nozzle has an area ratio of 7.99 and the trajectory-optimal one has 21.07. The optimal fixed nozzle is heavily over-expanded at liftoff, because most of the burn happens where the air is thin, and the mean that chooses it is dominated by the seconds when the air is not.
| Ratio of specific heats | Chamber pressure | Best fixed area ratio | Sea-level-matched area ratio | Gain over the best fixed nozzle | Gain over the sea-level-matched nozzle |
|---|---|---|---|---|---|
| 1.22 | 10.0 megapascal | 29.63 | 11.26 | 5.74 percent | 8.38 percent |
| 1.22 | 3.0 megapascal | 11.83 | 4.66 | 7.89 percent | 11.69 percent |
| 1.22 | 6.0 megapascal | 20.01 | 7.70 | 6.54 percent | 9.61 percent |
| 1.24 | 10.0 megapascal | 28.02 | 10.79 | 5.31 percent | 7.80 percent |
| 1.24 | 3.0 megapascal | 11.34 | 4.52 | 7.37 percent | 11.00 percent |
| 1.24 | 6.0 megapascal | 19.03 | 7.42 | 6.08 percent | 8.98 percent |
| 1.2 | 10.0 megapascal | 31.38 | 11.75 | 6.22 percent | 9.02 percent |
| 1.2 | 3.0 megapascal | 12.37 | 4.80 | 8.46 percent | 12.45 percent |
| 1.2 | 6.0 megapascal | 21.07 | 7.99 | 7.06 percent | 10.29 percent |
Flow Separation as the Deciding Limit
The mean-in-time rule has a consequence that the usual presentation of altitude compensation never reaches, because the usual presentation stops at the design-point trade.
Recall that the rule sets the exit pressure of the optimal fixed nozzle equal to the burn-averaged ambient pressure. At liftoff the ambient pressure is sea-level pressure, so the exit-to-ambient pressure ratio of the optimal nozzle at liftoff is that burn-averaged pressure divided by the sea-level value, and the chamber pressure has cancelled on the way.
\[\left. \frac{p_e}{p_a} \right|_{t=0} = \frac{\bar{p}_a}{p_{\mathrm{SL}}} = \frac{1}{p_{\mathrm{SL}} t_b} \int_{0}^{t_b} p_a(t) \, \mathrm{d}t \tag{27}\]The condition a designer has to satisfy at liftoff depends on the flight alone. The engine, the propellant and the size of the vehicle do not enter it. For the constant-acceleration model of this vehicle’s first stage that fraction is 0.2806, and the calculation returns 0.28064 for the optimal nozzle at every one of the nine combinations of gas and chamber pressure tested. The invariance is the identity showing itself.
Now set that against the other thing a nozzle designer has to respect. An over-expanded nozzle does not merely lose thrust. Below some exit-to-ambient pressure ratio the boundary layer separates from the divergent wall, the separation line is unsteady, and the resulting side loads are a structural problem rather than a performance one.
Let $k$ be that threshold ratio, dimensionless, and $\varepsilon_{\mathrm{sep}}$ the largest area ratio that respects it at sea level.
\[\frac{p_e}{p_a} \ge k \qquad \Longrightarrow \qquad p_e\left( \varepsilon_{\mathrm{sep}} \right) = k \, p_{\mathrm{SL}} \tag{28}\]Both constraints now bear on the same quantity, the exit pressure at liftoff. One says it should equal the burn-averaged ambient pressure. The other says it must not fall below $k$ times sea level. Whether they can both be met is arithmetic, and the arithmetic depends entirely on what $k$ is.
The Provenance of the Separation Threshold
The four tenths that secondary accounts quote for the onset of separation has a provenance other than the one the number’s ubiquity suggests. The primary that compiles the data changes both the attribution and the answer.
NASA Technical Paper 1207 compiles the available turbulent-flow separation data for over-expanded supersonic nozzles and discusses the correlation techniques [Morrisette and Goldberg 1978]. It gives the value’s history, which a search of the bibliographic index alone does not yield.
a value of $p_s/p_a$ = 0.4 was used as a separation criteria and is still quoted today, although more recent studies have shown it to be inadequate
The paper names no originator for that value. It traces the value to the early studies that found the separation pressure ratio independent of design expansion ratio, divergence angle, ratio of specific heats and gas temperature, among them a 1949 Jet Propulsion Laboratory report by Foster and Cowles, and it names the fourth edition of Sutton and Ross, of 1976, only as an example of a text that still quotes the value [Morrisette and Goldberg 1978]. Summerfield, Foster and Swan, in the Journal of Jet Propulsion for 1954 [Morrisette and Goldberg 1978], appear in its reference list among the many experimental studies of separation, which this article has not read and cites at second hand, saying so. A search of that index for the value’s origin returns a 1953 paper by Scheller and Bierlein instead [Scheller and Bierlein 1953], and the compiling paper also explains why that pair is not the origin, because an earlier note by the same authors is the study that conflicted with the others by finding the separation pressure dependent on nozzle divergence angle.
And the four tenths is for the wrong kind of nozzle. The paper separates its data by nozzle type and says that contoured nozzles, which are the case of most interest for modern nozzle design, follow a different correlation from conical ones. For contoured nozzles it fits a second-order curve to the data between separation Mach numbers of 2.4 and 4.5 [Morrisette and Goldberg 1978]. Let $M_s$ be the Mach number at the separation point, dimensionless, and $p_s$ the wall pressure there, in pascal.
That correlation is more permissive than the flat four tenths over most of its range and less permissive at the bottom of it. At separation Mach 2.4, where the fit begins, it gives 0.433, which is stricter than the old rule. It crosses the flat value at Mach 2.59 and falls away from there, giving 0.340 at Mach 3, 0.248 at Mach 4 and 0.230 at Mach 4.5.
So the old rule is 1.74 times as restrictive at the top of the fitted range and slightly less restrictive at the bottom. A summary that the contoured correlation tolerates roughly twice the over-expansion everywhere is true nowhere. A nozzle of the area ratios this article is discussing separates well above Mach 3, so the permissive end is the end that applies here, but the crossing is real.
One further conclusion of that paper matters here, because it licenses something this article does throughout. No obvious effect of the ratio of specific heats was found when the data were correlated as separation pressure ratio against separation Mach number [Morrisette and Goldberg 1978]. Sweeping that ratio, as every calculation in this article does, therefore does not move the separation answer.
Applying the Correlation to This Nozzle
The criterion is local rather than a statement about the exit, so the way to use it is to walk the nozzle from throat to exit and find the first station where the wall pressure falls to the criterion value. If that station lies beyond the exit, the flow is attached.
Doing that for the trajectory-optimal nozzle gives an answer that depends on chamber pressure, and it does not support a flat statement that the optimum cannot be built.
| Ratio of specific heats | Chamber pressure | Trajectory-optimal area ratio | Largest area ratio that stays attached | Optimum as a multiple of it | Does the optimum separate |
|---|---|---|---|---|---|
| 1.2 | 3.0 megapascal | 12.37 | 11.94 | 1.036 | yes |
| 1.2 | 6.0 megapascal | 21.07 | 22.55 | 0.934 | no |
| 1.2 | 10.0 megapascal | 31.38 | 35.46 | 0.885 | no |
| 1.22 | 3.0 megapascal | 11.83 | 11.55 | 1.025 | yes |
| 1.22 | 6.0 megapascal | 20.01 | 21.64 | 0.925 | no |
| 1.22 | 10.0 megapascal | 29.63 | 33.74 | 0.878 | no |
| 1.24 | 3.0 megapascal | 11.34 | 11.18 | 1.014 | yes |
| 1.24 | 6.0 megapascal | 19.03 | 20.78 | 0.916 | no |
| 1.24 | 10.0 megapascal | 28.02 | 32.10 | 0.873 | no |
Under the flat four tenths the optimum is unbuildable at every chamber pressure in the band. Under the contoured-nozzle correlation it is unbuildable only at the low end. Let $\mu$ be the margin in area ratio, dimensionless. The crossover is the chamber pressure at which the two area ratios coincide, and above it the margin is positive.
\[\varepsilon^{\star}\left( p_c \right) = \varepsilon_{\mathrm{sep}}\left( p_c \right), \qquad \mu \equiv 1 - \frac{\varepsilon^{\star}}{\varepsilon_{\mathrm{sep}}}, \qquad 1 - \frac{21.07}{22.55} = 0.066, \qquad 1 - \frac{28.02}{32.10} = 0.127 \tag{30}\]The crossover is at 3.3 to 3.7 megapascal, across ratios of specific heats from 1.20 to 1.24, and above it the trajectory-optimal nozzle runs attached with between 6.6 and 12.7 percent of margin in area ratio, the extremes being the cases at 6 megapascal with a ratio of specific heats of 1.20 and at 10 megapascal with 1.24 in the table above.
The chamber pressure recovered from the instability frequency, 2.6 to 8.7 megapascal, straddles that crossover. So for this engine the question is open, and which side of it the real nozzle falls on is decided by a number nobody has published.
The defensible statement is weaker than a flat impossibility and more interesting. It does not hold that the bell cannot have the exit area the trajectory wants. It holds that the trajectory wants an exit area within about a tenth of the largest one that will stay attached, on one side or the other depending on a chamber pressure that is not public. The optimum is not outside the feasible region. It is pressed against its edge, and a designer who wanted it would be trading impulse against a separation margin rather than choosing freely.
Two qualifications hold. The first is that a separation criterion is a design guideline and not a wall, as the design monograph on this subject states, noting that prediction methods have shown agreement with experiment in many cases but that in general predictions are used only as a guide [NASA SP-8120]. The second is that an aerospike does not have the constraint at all, because it has no divergent wall for a boundary layer to separate from. That second point does not depend on which criterion is used, and the programme rests on it.
And the monograph supplies a case this article was otherwise describing in the abstract. The J-2 engine was given a deliberately nonoptimum parabolic contour to raise its exit wall pressure, and was expected to run unseparated at an area ratio of 27 with a chamber pressure of 700 pounds per square inch. A wall-pressure minimum between area ratio 14 and the exit produced unsteady asymmetric separation, worst at startup, and the loads caused thrust-chamber structural failures. A bolt-on diffuser was developed to stop it in mainstage and restraining arms were attached from the test stand to the nozzle skirt to absorb the loads at ignition [NASA SP-8120]. The constraint costs that much when it is met head on, and the margin computed above is therefore something to preserve.
The Three Regimes the Programme Names
The fact sheet names open wake, wake transition and closed wake as the three modes the flight is meant to visit [ARISE and Fly]. Those names describe what happens behind a plug that has been cut off short, which every practical aerospike is.
A full-length plug would be long, heavy and hot. Real ones are truncated, which leaves a blunt base at the downstream end, and the three names classify the flow behind that base.
Truncation splits the thrust into two terms, and the split is exact whatever the flow does. Let $F_w$ be the axial force the expanding gas exerts on the wetted surface of the plug in newton, $p_b$ the pressure acting on the exposed base in pascal, and $A_b$ the area of that base in square metre.
\[F = F_w + p_b A_b \tag{31}\]Cutting the plug short removes part of the first term and creates the second. The base pressure decides how much of the loss the second term returns, and the three regimes describe that pressure. This article can write the decomposition and cannot evaluate it, because $p_b$ is set by a recirculating turbulent flow and no one-dimensional isentropic model produces one.
At low altitude the ambient pressure is high, the plume is squeezed inward against the plug, and the recirculating region behind the truncated base is closed off by the converging flow. That is the closed wake. The base sits at a pressure set by the recirculation rather than by the atmosphere, and the pressure acting on it contributes to thrust.
At high altitude the ambient pressure is low, the plume no longer closes behind the base, and the base region is open to the external flow. That is the open wake, and in it the base pressure is tied to the ambient pressure. Which quantity sets the base pressure distinguishes the two regimes, and the classification turns on that alone.
\[p_b \approx p_a \;\; \text{open wake}, \qquad p_b \neq p_a \;\; \text{closed wake} \tag{32}\]In the open regime the base contributes nothing the atmosphere does not already take back. In the closed regime it contributes a pressure the recirculation sets, which may be above or below ambient, and a truncated spike is designed to keep that term. A normal shock stands in the plume at the transition [Giel and Mueller 1975a] [Marsilio 2001].
Between them is a transition, and a transition between two flow topologies is the kind of thing that can be hysteretic, unsteady, or abrupt [Geron et al. 2005b] [Mizukaki and Watabe 2016] [Taylor and Sato 2008]. A flight is needed for that reason. A ground test can produce either end state in a vacuum chamber. It cannot produce the passage between them at full scale with a real plume and a real trajectory, as the fact sheet states.
The published computational and experimental work on truncated plugs reports that thrust lost by cutting the plug short is partly recovered by pressure acting on the exposed base, that bleeding a small secondary flow into the base region recovers more of it, and that the penalty is larger in over-expanded operation than in under-expanded, where it is reported as small [Sule and Mueller 1973a] [Mueller and Sule 1973] [Nasuti and Onofri 2000] [Nair et al. 2017] [Nair et al. 2019a]. This article does not compute those quantities. They depend on the base geometry, the bleed rate and the turbulence of the recirculation, none of which is public for this engine, and a base pressure is not something an isentropic one-dimensional model can be made to yield. The three regimes are named here because the programme names them and because they are what the flight would have measured, not because this article can predict them.
Truncation and the base flow account for all of the gap between the ideal spike of the Legendre argument and a real engine, and they make the 5.3 to 8.5 percent that the gain $\eta$ gives an upper bound and no prediction.
Dependent Systems
The record of the hardware around the nozzle comes from the parent vehicle and not from the X-63A. The award announcement describes the RS1A as sharing the RS1’s turbopumps, thrusters and injectors, and it promises that thrust vector control for the aerospike will be demonstrated [AFRL awards agreements under ARISE]. This section takes in turn the steering problem that promise sets for an engine with nothing to gimbal, the parent vehicle’s published specification, the chamber geometry that the company’s incident report gives away, and what the same report says about feeding many engines through one manifold [Flight 2 Static Fire Update].
Steering a Rocket That Has Nothing to Gimbal
The promised thrust vector control sets a problem, because the usual way to steer a rocket is to gimbal the engine, and an annular aerospike is a ring built into the base of the vehicle. There is nothing to swing.
Modularity supplies the alternative. The propulsion system is many thrusters working as one [ARISE and Fly], and thrusters arranged around a ring can be throttled against one another. The idea has precedent. The X-33 was to control its attitude by differentially throttling the two halves of its linear aerospike [Hall and Panossian 1999a] [the same work as a report], and the flow of a ring of thrusters expanding onto one plug has been measured [Taniguchi 2005].
This article can answer exactly how much authority the arrangement gives, and the result has a pleasant form.
Let $N$ be the number of modules, dimensionless, equally spaced around a ring of radius $r$ in metre. Let $F$ be the total thrust in newton, so each module produces $F/N$ when fully open. Let $\tau_k$ be the throttle fraction of module $k$, dimensionless, constrained to lie between $1-\delta$ and $1$, where $\delta$ is the available throttle depth, dimensionless. Let $\theta_k = 2\pi k / N$ be the angular position of module $k$ in radian. The moment the ring can apply about a horizontal axis in the direction $\phi$ is
\[M(\phi) = \frac{F r}{N} \sum_{k=0}^{N-1} \tau_k \cos\left( \theta_k - \phi \right) \tag{33}\]The unthrottled ring is balanced, and that is an identity rather than an approximation.
\[\sum_{k=0}^{N-1} \cos\left( \theta_k - \phi \right) = 0 \qquad \text{for every } N \ge 2 \text{ and every } \phi \tag{34}\]A ring of equally spaced thrusters all wide open applies no moment about any axis. That balance makes the arrangement usable at all, and subtracting the identity removes the baseline entirely. What is left is the throttle depth acting on the modules in the forward half only. The optimal throttle pattern is bang-bang, every module in the forward half wide open and every module in the rear half closed to its floor, and the moment it produces is
\[\frac{M(\phi)}{F r} = \frac{\delta}{N} \sum_{k} \max\left( \cos\left( \theta_k - \phi \right), \, 0 \right) \tag{35}\]The available control moment, normalised by thrust and ring radius, is the throttle depth times the support function of a regular polygon.
The Directional Average Is the Throttle Depth Divided by Pi, Exactly
Average that expression over all commanded directions. Each module contributes the mean of $\max(\cos u, 0)$ over a full turn, and that mean is one elementary integral.
\[\frac{1}{2\pi}\int_{0}^{2\pi} \max\left( \cos u, 0 \right) \mathrm{d}u = \frac{1}{2\pi}\int_{-\pi/2}^{\pi/2} \cos u \, \mathrm{d}u = \frac{1}{\pi} \tag{36}\]There are $N$ modules and the expression divides by $N$, so the module count cancels exactly.
\[\left\langle \frac{M}{F r} \right\rangle_{\phi} = \frac{\delta}{\pi} \tag{37}\]Not asymptotically. Exactly, for every module count from three upward. Adding modules does not add average control authority at a fixed throttle depth. Averaging numerically over two hundred thousand directions at nine module counts from four to twenty-four returns 0.063661977 at every count, at a throttle depth of two tenths, against $\delta/\pi = 0.063661977$.
So what does the module count provide? It provides evenness. The achievable set of moments is a polygon rather than a disc, and an autopilot can only rely on the worst direction.
Why Nine Modules Steer More Evenly Than Twelve
The polygon’s side count is not the module count, and the difference between them is the result of this subsection.
Let $m$ be the number of sides of the achievable moment polygon, dimensionless. The support function is a pure cosine between the directions at which the set of open modules changes, and it changes whenever a module crosses the boundary of the forward half plane. Those directions are the following.
\[\phi \in \left\{ \theta_k + \frac{\pi}{2} \right\} \cup \left\{ \theta_k - \frac{\pi}{2} \right\}, \qquad k = 0, \dots, N-1 \tag{38}\]So the number of sides is the number of distinct members of that union, and enumeration at ten module counts from four to seventeen agrees with the closed form below in every case.
For an even ring the two families of crossings coincide, because a half turn is a whole number of module spacings, so a module enters the forward half at the same instant another leaves it and there are $N$ crossings. For an odd ring a half turn is not a whole number of spacings, the two families interleave, and there are $2N$.
\[m = \begin{cases} N, & N \text{ even} \\ 2N, & N \text{ odd} \end{cases} \tag{39}\]From which the guaranteed authority, the best-case authority and the ratio between them follow in closed form.
\[\frac{M_{\min}}{F r} = \frac{\delta}{m \tan\left( \pi / m \right)}, \qquad \frac{M_{\max}}{F r} = \frac{\delta}{m \sin\left( \pi / m \right)}, \qquad \frac{M_{\max}}{M_{\min}} = \frac{1}{\cos\left( \pi / m \right)} \tag{40}\]A direct numerical search over commanded directions at fourteen module counts and three throttle depths, forty-two cases, agrees with them, and the worst disagreement is below one part in a million million.
Where that polygon sits relative to the modules is a separate question from how many sides it has, and it turns on the module count modulo four rather than on its parity. For an odd ring the greatest authority is attained both at the module directions and midway between them, because the polygon carries two sides per module, and the least a quarter of a spacing from each. For an even ring the answer depends on whether four divides the count, and the reason is that a quarter turn is a whole number of module spacings exactly when it does. At four, eight, twelve, sixteen, twenty and twenty-four modules a module therefore lies on the boundary of the forward half plane whenever the command points straight at another module, and that degenerate direction is the one of least authority. At six, ten, fourteen, eighteen and twenty-two it is the direction of greatest authority instead. The closed forms above are untouched by this, since they depend only on the side count, but a rule carried over from the odd-ring arrangement places the two extremes correctly on one even family and swaps them on the other, which is harder to notice than a wrong number.
The consequence is that an odd ring of $N$ modules behaves exactly like an even ring of $2N$. Nine modules give the steering polygon of eighteen. Eleven give twenty-two. Seventeen give thirty-four.
At a throttle depth of two tenths the guaranteed authority follows from the first closed form with $m$ equal to 8, 18, 12 and 16 sides, and the ratios follow from those.
\[\frac{0.2}{8 \tan\left( \pi / 8 \right)} = 0.0603553, \qquad \frac{0.2}{18 \tan\left( \pi / 18 \right)} = 0.0630142, \qquad \frac{0.2}{12 \tan\left( \pi / 12 \right)} = 0.0622008, \qquad \frac{0.2}{16 \tan\left( \pi / 16 \right)} = 0.0628417 \tag{41}\] \[\frac{0.0630142}{0.0622008} = 1.0131, \qquad \frac{0.0630142}{0.0603553} = 1.0441 \tag{42}\]Eight modules give 0.0603553. Nine give 0.0630142. Twelve give 0.0622008. Sixteen give 0.0628417. Nine modules guarantee 1.31 percent more control authority than twelve and 4.41 percent more than eight, and nine beat every even module count up to sixteen. The smallest even count that beats nine is twenty. The smallest even count that beats eleven is twenty-four.
This runs the opposite way to the intuition that more thrusters make a smoother ring. Adding a module to an even ring to make it odd nearly doubles the number of sides on its control polygon. Adding one to an odd ring to make it even halves them.
| Modules | Sides of the moment polygon | Guaranteed authority | Best-direction authority | Ratio of best to guaranteed |
|---|---|---|---|---|
| 4 | 4 | 0.050000 | 0.070711 | 1.41421 |
| 5 | 10 | 0.061554 | 0.064721 | 1.05146 |
| 6 | 6 | 0.057735 | 0.066667 | 1.15470 |
| 7 | 14 | 0.062590 | 0.064199 | 1.02572 |
| 8 | 8 | 0.060355 | 0.065328 | 1.08239 |
| 9 | 18 | 0.063014 | 0.063986 | 1.01543 |
| 10 | 10 | 0.061554 | 0.064721 | 1.05146 |
| 11 | 22 | 0.063229 | 0.063879 | 1.01028 |
| 12 | 12 | 0.062201 | 0.064395 | 1.03528 |
| 16 | 16 | 0.062842 | 0.064073 | 1.01959 |
| 17 | 34 | 0.063481 | 0.063753 | 1.00428 |
| 20 | 20 | 0.063138 | 0.063925 | 1.01247 |
| 24 | 24 | 0.063298 | 0.063844 | 1.00863 |
The RS1 first stage from which the X-63A was to be derived carried nine engines in its first block and eleven in its second [ABL Payload User’s Guide] [Flight 2 Static Fire Update]. Both counts are odd, and each is the best available below the next even count that beats it.
Those counts were almost certainly not chosen for this reason. Nine and eleven engines on a first stage are chosen for thrust, for packaging, for engine-out margin and for what the factory can build, and neither the sponsor nor the manufacturer publishes the aerospike variant’s module count, although a launch-vehicle reference lists the RS1A first stage as nine E2 aerospike engines [RS1, Gunter’s Space Page], which no primary document consulted confirms. The result’s claim is narrower, and it still holds. If the ARISE engine’s modules are arranged on a ring and steered by differential throttling, then the parity of the count matters more than the count, and the parity the parent vehicle happens to carry is the favourable one.
Losing One Module
The same geometry answers the engine-out question, and the obvious way to answer it is instructively wrong.
Lose one module of $N$ and two things happen, and the balance identity above gives both at once. Removing module $j$ from a sum that vanishes leaves minus that module’s own term.
\[\frac{\Delta F}{F} = \frac{1}{N}, \qquad \frac{M_{\mathrm{out}}\left( \phi \right)}{F r} = -\frac{1}{N}\cos\left( \theta_j - \phi \right) \tag{43}\]The axial thrust falls by one part in $N$, and the unbalanced moment peaks at one part in $N$ as well. Both penalties are one over the module count and they arrive together.
The surviving ring then has the support function of the remaining modules alone.
\[\frac{M\left( \phi \right)}{F r} = \frac{1}{N}\sum_{k \neq j} \tau_k \cos\left( \theta_k - \phi \right), \qquad \tau_k \in \left[ 0, 1 \right] \tag{44}\]That sum is not the intact one with a smaller coefficient. It is a different sum, missing a term, and the rest of this subsection follows from that difference.
The tempting move is to ask how much authority the ring has left and to answer with the closed form derived above. That formula is for a regular ring and a ring with a hole in it is not regular. In some commanded directions the module that would have pushed hardest is the one that failed, so the degraded polygon is not a scaled copy of the intact one. Solving the degraded problem directly, by taking the support function of the surviving modules over their full throttle range, gives numbers that are smaller by factors of 1.15 to 2.62, and at four modules the discrepancy is total.
A four-module ring loses all of its guaranteed steering authority when one module fails. Three modules remain, none of them positioned to push toward the gap, and the support function in that one direction is exactly zero. The intact formula reports 0.25 where the true figure is zero.
Let $\rho$ be the fraction of guaranteed steering authority that survives the loss of module $j$, dimensionless, taken over the full throttle range so that each module contributes only when it faces the commanded direction. The factor $1/N$ cancels.
\[\rho = \frac{\min_{\phi} \sum_{k \neq j} \max\left( \cos\left( \theta_k - \phi \right), 0 \right)}{\min_{\phi} \sum_{k} \max\left( \cos\left( \theta_k - \phi \right), 0 \right)}, \qquad \rho_8 = \frac{0.176777}{0.301777} = 0.586, \qquad \rho_9 = \frac{0.205648}{0.315071} = 0.653 \tag{45}\]The correct figures, as values of $\rho$ from the table below, run as follows. Eight modules keep 58.6 percent. Nine keep 65.3 percent. Eleven keep 71.5 percent. Twelve keep 73.2 percent. Twenty-four keep 86.8 percent.
| Modules | Axial thrust lost | Guaranteed authority intact | Guaranteed authority after one failure | Fraction retained |
|---|---|---|---|---|
| 4 | 25.00 percent | 0.250000 | 0.000000 | 0.0 percent |
| 6 | 16.67 percent | 0.288675 | 0.144338 | 50.0 percent |
| 8 | 12.50 percent | 0.301777 | 0.176777 | 58.6 percent |
| 9 | 11.11 percent | 0.315071 | 0.205648 | 65.3 percent |
| 11 | 9.09 percent | 0.316143 | 0.226192 | 71.5 percent |
| 12 | 8.33 percent | 0.311004 | 0.227671 | 73.2 percent |
| 16 | 6.25 percent | 0.314209 | 0.251709 | 80.1 percent |
| 24 | 4.17 percent | 0.316490 | 0.274823 | 86.8 percent |
Here the parity result reverses. Odd rings steer more evenly when intact, because their control polygon has twice as many sides. But a failure breaks the symmetry that the parity argument depends on, and what matters after a failure is how many modules are left and how finely they surround the gap. Twelve beats nine on this measure even though nine beats twelve on the other.
The two results are both geometric, both exact, and they point in opposite directions. An odd ring is the better steering machine and the worse survivor. The tension is a design tension and no paradox, and it needs no flight to settle.
The Authority as a Gimbal Angle
A moment normalised by thrust and ring radius is hard to compare with anything, so this subsection converts it into the quantity a designer of a conventional stage would quote, which is a gimbal angle.
Let $L$ be the distance from the engine plane to the vehicle’s centre of mass in metre and $\alpha$ the equivalent gimbal angle in radian. A gimballed engine deflected by $\alpha$ applies a moment $F L \sin \alpha$, and setting that equal to the ring’s directional average gives
\[\sin \alpha = \frac{\delta}{\pi} \cdot \frac{r}{L} \tag{46}\]The ring radius divided by the distance to the centre of mass is a small number on a slender vehicle, and the throttle depth divided by pi is smaller still. A throttle range of two tenths on a ring whose radius is a quarter of the arm gives an equivalent deflection of 0.91 degrees. Such a deflection cannot substitute for a gimbal and was never meant to. Differential throttling offers attitude control on a vehicle that has nowhere to put a gimbal, at an authority that is adequate for trim and marginal for anything faster.
A Specification Table That Does Not Close
The encyclopedia entry describes the X-63A, the RS1A of the award announcement, as the first-stage core of the two-stage RS1 [ABL Space Systems X-63]. So the parent vehicle’s published specification is the closest thing to a specification the X-63A has.
That specification contains an error, and the error turns out to be informative.
The payload user’s guide of June 2022 says in prose that the RS1 uses nine sea-level E2 engines on the first stage and one vacuum E2 on the second, that the vehicle is six feet in diameter and eighty-eight feet long when integrated, and that both stages burn liquid oxygen and kerosene through gas-generator cycles [ABL Payload User’s Guide]. Its overview table then gives the first stage an engine thrust of 12,100 pounds force at sea level, an engine quantity of nine, and a total thrust of 133,118 pounds force at sea level.
Nine times 12,100 is 108,900. The table overstates its own product by 24,218 pounds force, which is 22.24 percent, and dividing the stated total by the stated per-engine figure gives a quotient of 11.0015.
\[\frac{133{,}118 - 9 \times 12{,}100}{9 \times 12{,}100} = \frac{24{,}218}{108{,}900} = 0.2224, \qquad \frac{133{,}118}{12{,}100} = 11.0015, \qquad \frac{133{,}118 - 11 \times 12{,}100}{133{,}118} = \frac{18}{133{,}118} = 1.35 \times 10^{-4} \tag{47}\]Eleven engines at 12,100 pounds force give 133,100, which differs from the stated total by 18 pounds force, or 135 parts per million. The total thrust in that table is the eleven-engine number, printed in a row that says nine.
The company’s incident report of 26 August 2024 settles it without ambiguity. Describing a static fire on 19 July 2024 it says the objective was a thirteen-second firing of all 11 first stage engines, that all eleven ignited, and that the vehicle auto-aborted on a low pressure reading from Engine 10 [Flight 2 Static Fire Update]. A vehicle with nine engines does not have an Engine 10. The second block of the RS1 carried eleven [RS1, Gunter’s Space Page], the payload user’s guide describes the first block, and one cell of its table was filled in from the wrong vehicle.
Two other published figures disagree with each other and neither is resolved here. The award announcement gives the RS1 a maximum payload of 1,200 kilograms [AFRL awards agreements under ARISE], and the launch-vehicle reference gives 1,350 kilograms to low Earth orbit [RS1, Gunter’s Space Page], as does the manufacturer’s payload user’s guide [ABL Payload User’s Guide]. The larger exceeds the smaller by twelve and a half percent, since $1{,}350/1{,}200 = 1.125$, and both are described as maxima. No source consulted reconciles them.
What the Fire Gave Away
The E2 engine’s chamber pressure is not published. Neither is its chamber diameter. The payload user’s guide gives thrust, cycle, propellants and feed system, and stops [ABL Payload User’s Guide].
The incident report gives both away without meaning to.
Post-anomaly data review indicates Engines 5 and 8 experienced a 4.5 kHz combustion instability during startup, in alignment with the expected first tangential mode of the E2 thrust chamber.
The first tangential acoustic mode of a cylindrical chamber has a frequency fixed by the chamber diameter and the speed of sound in the burnt gas. Let $f_{1T}$ be that frequency in hertz, $c$ the speed of sound in the combustion products in metre per second, $D$ the chamber diameter in metre, and $\alpha_{1T} = 1.8412$ the first stationary point of the Bessel function of the first kind of order one, dimensionless. Then
\[f_{1T} = \frac{\alpha_{1T} \, c}{\pi D} \qquad \Longrightarrow \qquad D = \frac{\alpha_{1T} \, c}{\pi f_{1T}} \tag{48}\]Naming the frequency names the diameter, to within whatever must be assumed about the gas. The speed of sound follows from the flame temperature, the mean molar mass of the products and the ratio of specific heats, none of which is published either, so all three are swept over a range.
\[c = \sqrt{\frac{\gamma R_u T_c}{\bar{M}}} \tag{49}\]The relation gives the frozen speed of sound, which treats the composition as fixed through the acoustic cycle [NASA SP-8124] [NASA SP-8107]. A real chamber recombines, which raises the effective value, so the diameters below are if anything slightly small. Flame temperatures from 3,200 to 3,800 kelvin, molar masses from 21 to 24 kilogram per kilomole and ratios of specific heats from 1.15 to 1.25 give forty-eight combinations, sound speeds from 1,129 to 1,371 metres per second, and a chamber diameter of
147 to 179 millimetres, with a midpoint of 163.
Chamber pressure needs two more assumptions, being a contraction ratio and a sea-level thrust coefficient. Let $\sigma$ be the contraction ratio, dimensionless, which is the chamber cross-section divided by the throat. The chain from the diameter to the pressure is two lines, and the second rearranges the definition of the thrust coefficient.
\[A_t = \frac{\pi D^2}{4 \sigma}, \qquad p_c = \frac{F}{C_F A_t} = \frac{4 \sigma F}{\pi C_F D^2} \tag{50}\]The chamber pressure goes as the inverse square of the diameter, so the recovered band is wide even though the frequency is published to two significant figures. A twenty percent uncertainty in the diameter is a factor of 1.44 in the pressure before any other assumption is made.
Sweeping contraction ratios from 2 to 4 and thrust coefficients from 1.45 to 1.65 across the diameter band gives thirty-six combinations and a chamber pressure of 2.6 to 8.7 megapascal, with a midpoint of 5.67.
| Quantity | Low | High | Combinations swept |
|---|---|---|---|
| Speed of sound in the burnt gas | 1,129 metres per second | 1,371 metres per second | 48 |
| Chamber diameter | 147 millimetres | 179 millimetres | 48 |
| Chamber pressure | 2.60 megapascal | 8.74 megapascal | 36 |
That band was not assumed. It was recovered. The band assumed on general grounds under The Gain of an Ideal Spike on This Trajectory, without reference to the incident report, is 3 to 10 megapascal for a gas-generator kerosene engine of this thrust class. The two overlap over 3 to 8.74 megapascal, and the overlap as a fraction of each band is
\[\frac{8.74 - 3}{8.74 - 2.60} = \frac{5.74}{6.14} = 0.935, \qquad \frac{8.74 - 3}{10 - 3} = \frac{5.74}{7} = 0.820 \tag{51}\]which is 93.5 percent of the recovered band and 82.0 percent of the assumed one. The recovered band does not sit inside the assumed one, because its floor of 2.60 falls below the assumed floor of 3. Two routes sharing no input landed on nearly the same interval, and agreement of that kind appears as an overlap, without containment.
The inference is marked as an inference and its weakest links are named. A thrust chamber is not a plain cylinder, so the mode frequency of a real chamber departs from the textbook value by an amount this article cannot bound. The mode identification is the company’s and not this article’s. And a contraction ratio has to be guessed before a pressure follows. The frequency is not guessed, being published in a sentence written for an entirely different purpose.
The Same Report on Building an Engine Out of Many
The incident report also quantifies the risk that modularity carries, and it does so against the company’s test history.
Two of eleven engines suffered the instability. Inspection found significant erosion of the propellant injectors and liners of Engines 5 and 8, in a pattern the report calls consistent with instability-induced failure. The report also says that in more than three hundred prior tests of the E2 the phenomenon had been observed once, and attributes that single occurrence to an unrelated timing anomaly [Flight 2 Static Fire Update].
Take the historical rate at face value as one in three hundred per engine start. Let $p$ be that per-start probability, dimensionless, and $n$ the number of engines. If the starts were independent, the chance of two or more going unstable would be the binomial tail.
\[\Pr\left[ X \ge 2 \right] = 1 - \left( 1 - p \right)^{n} - n p \left( 1 - p \right)^{n-1} \tag{52}\]At $p = 1/300$ and $n = 11$ that is 6.0 parts in ten thousand, or about one in 1,669. The observed rate of two in eleven is 54.5 times the historical rate, and the expected number of failures at the historical rate is 0.037.
The company’s own leading theory points the same way, that differences in the second block’s propellant feed system produced a higher energy start on the vehicle than on the test stand [Flight 2 Static Fire Update]. The arithmetic adds a measure of how strong that conclusion is. A rate this far above the record does not happen to a batch of eleven by chance.
And it points at the thing modularity has to answer for. A modular engine is many small combustors sharing one manifold, and a shared manifold is a mechanism for correlating their start transients. The independence the calculation above assumes is the assumption the incident falsified. Eleven independent chances of a rare failure is a good trade. Eleven correlated chances is not a trade at all, and the difference between them is a manifold.
The rest of the report is a timeline of a vehicle being lost slowly. Fuel offload began at 4 minutes 20 seconds, liquid oxygen offload at 9 minutes 20 seconds, the mobile water stores ran out at 11 minutes 30 seconds, oxygen and fuel offload capability were lost at 14 minutes 28 and 15 minutes 30, all first-stage telemetry was lost at 20 minutes 43, and at 23 minutes 24 the fire exceeded the thermal capability of the structure and the vehicle buckled onto the pad [Flight 2 Static Fire Update]. The report states that the pad has no direct water supply, and it gives main-stage combustion of about half a second against a planned thirteen. The interval from the water running out to the buckling, and the fraction of the planned firing achieved, are
\[\left( 23 \times 60 + 24 \right) - \left( 11 \times 60 + 30 \right) = 1404 - 690 = 714 \ \mathrm{s}, \qquad \frac{0.5}{13} = 0.038 \tag{53}\]so eleven minutes and fifty-four seconds separate the moment the water ran out from the moment the rocket fell over, and the engines achieved 3.8 percent of the test.
The Flight Test Record
The X-63A has no flight test record, and the aerospike flights before it were small, short and far from a launch trajectory. The subsections below set the concept’s long published record against its thin record of flight, and then follow the parent vehicle from its first launch attempt on 10 January 2023 to the company’s renaming on 19 February 2025 [RS1, Gunter’s Space Page] [ABL Space renamed Long Wall].
Sixty Years of Not Flying at Scale
The claim of the president of Invocon, quoted under Programme Origin, that the programme would accomplish what had eluded the rocket community for nearly sixty years reaches back from December 2019 to about 1960, and it is checkable against the literature.
It checks out, and the shape of the literature is the interesting part. The concept has an old and continuous published record and a thin record of flight.
Of this article’s 8,762 surveyed records, 8,568 carry a year, and 488 of those have a title naming a plug, spike or altitude-compensating nozzle, which is 5.7 percent of them, and 17 records without a year name one as well. The earliest is a weather-rocket patent of 1944, and it is followed by a 12-year silence. From 1956 the record is continuous, in the sense that every five-year window from that year to the present contains at least one publication, and the six-year window agrees. The eight-year and ten-year windows agree as well. The founding measurements are a run of reports from one laboratory, Lewis Research Center testing convergent-plug exhaust nozzles against plug design [1954], against outer-shell design [1955], against several design variables at once [1956], and then against an external stream [1959]. The largest gap anywhere after 1956 is 3 years. So the literature begins in earnest 63 years before the sentence that called it nearly sixty, which means the claim was modest by three or four years rather than generous.
| Decade | Records naming a plug, spike or altitude-compensating nozzle |
|---|---|
| 1940s | 1 |
| 1950s | 4 |
| 1960s | 26 |
| 1970s | 47 |
| 1980s | 12 |
| 1990s | 45 |
| 2000s | 106 |
| 2010s | 90 |
| 2020s | 157 |
Read down that column and the flight record’s absence becomes strange rather than unremarkable. The subject was worked on through the nineteen sixties and seventies, went quiet in the nineteen eighties, came back in the nineteen nineties with the single-stage-to-orbit programmes, and has published more in the 2020s so far than in any full decade before it. Seven decades of continuous publication and no flight at the scale of a launch vehicle stage.
The largest aerospike engine this article’s survey documents is the XRS-2200, developed for the X-33 [Rocketdyne XRS-2200]. It was assembled [Kotake et al. 1999], it was hot-fired on a test stand, its control system and its plume were documented [the engine control system] [sea-level plume radiation] [the programme’s engine account] [risk reduction], and the vehicle it was built for was cancelled before it flew, NASA announcing on 1 March 2001 that it would add no further funds and that the X-33 programme would end with its cooperative agreement on 31 March [X-33, X-34 left behind in NASA Space Launch Initiative]. Behind it stands a development record reaching back to the demonstrations of the nineteen seventies [Huang 1974] [Kirby and Martinez 1977a]. The nearest thing to a flight test of a launch-vehicle aerospike was the Linear Aerospike SR-71 Experiment, which carried a small linear aerospike pod on the back of an SR-71 and flew seven research flights from October 1997 to November 1998 [LASRE Project]. The pod’s engine was hot-fired twice on the ground and never once in the air [the flight test report] [stability and control results] [hazard mitigation] [the supporting test report]. Liquid oxygen was cycled through it in flight on three occasions, and the hot-fire flight was abandoned because the apparatus leaked [LASRE Project].
Small aerospikes have flown, and the survey holds their reports. A liquid-propellant aerospike engine had been flight-tested on a university and industry sounding rocket by 2004 [Besnard and Garvey 2004b], and a multi-chamber liquid oxygen and ethanol aerospike flew later in the same programme [Baker et al. 2008]. On 30 and 31 March 2004 two ten-foot solid-fuelled rockets with aerospike nozzles, flown by NASA’s Dryden Flight Research Center, the Air Force Flight Test Center and the Blacksky Corporation, exceeded Mach 1.5 and 26,000 feet [Aerospike Engine Flight Test Successful] [Bui et al. 2005]. In the standard atmosphere the pressure at 26,000 feet of geometric altitude is 35.6 percent of sea level, so those plumes did expand against a falling ambient pressure, over nearly two thirds of the fall from sea-level pressure that a launch vehicle meets. On 29 October 2024 a five-metre demonstrator, MIRA II, fired a one-kilonewton liquid oxygen and kerosene linear aerospike for three seconds in flight over the Baltic [POLARIS Spaceplanes Complete First In-Flight Rocket Engine Ignition] [Janardhana 2025]. None of these engines approached the thrust, the burn time or the trajectory of a launch vehicle stage, and none measured altitude compensation across the open, transitional and closed wake.
So the record before ARISE is a concept with sixty-three years of analysis, several pieces of built and successfully fired hardware, one pod carried through the air with cryogenic fluid running through it, and a handful of small aerospikes flown on research and university rockets, none of them on a trajectory representative of a launch. The fact sheet’s claim that ARISE would mark the first representative flight of an aerospike engine after many decades of research and abandoned flight efforts is accurate as stated, and the word representative makes it so [ARISE and Fly].
This article’s arithmetic shows why the gap persisted. The prize, the gain $\eta$ computed under The Gain of an Ideal Spike on This Trajectory, is between 5.3 and 8.5 percent of first-stage impulse against the best fixed nozzle, and it is computed generously. That is a large number for a launch vehicle, and the rocket equation shows how large.
Let $\Delta v_1$ and $\Delta v_2$ be the ideal velocity increments of the two stages in metre per second, $c_{e,2}$ the effective exhaust velocity of the second stage in metre per second, $m_0$ and $m_f$ the mass of the second stage with its payload at ignition and at burnout in kilogram, $m_p$ the payload mass in kilogram, $w$ a gain in $\Delta v_1$ in metre per second, and $\Delta m_p$ the payload that gain buys in kilogram. The rocket equation is linear in exhaust velocity, so a uniform one percent rise in first-stage effective exhaust velocity raises $\Delta v_1$ by one percent. Holding the second stage’s propellant and structure fixed and letting it deliver $w$ less, the rocket equation gives
\[\Delta v_2 = c_{e,2} \ln\frac{m_0}{m_f}, \qquad \frac{\Delta m_p}{m_p} = \frac{w}{c_{e,2}} \cdot \frac{m_0}{m_0 - m_f} \cdot \frac{m_f}{m_p} > \frac{w}{c_{e,2}} \tag{54}\]because both mass ratios exceed one. Taking the staging speed of 2.6 kilometres per second as a floor on $\Delta v_1$, which assumes that gravity and drag losses exceed any help from the Earth’s rotation, and the 3,000 to 3,400 metres per second assumed here for $c_{e,2}$, which is a vacuum specific impulse of about 306 to 347 seconds since the E2’s is not published,
\[w = 0.01 \, \Delta v_1 \ge 0.01 \times 2{,}600 = 26 \ \mathrm{m/s}, \qquad \frac{26}{3{,}400} = 0.0076, \qquad \frac{26}{3{,}000} = 0.0087 \tag{55}\]A percent of first-stage exhaust velocity is therefore worth at least three quarters of a percent of payload, and more by the two mass ratios, neither of which is published. The spike’s gain falls mostly in the dense early seconds, when the vehicle is heaviest, so its share of $\Delta v_1$ is smaller than its share of impulse. It is a small number against the cost of qualifying a new nozzle architecture, and a two-stage vehicle can decline to chase it by putting a big nozzle on the upper stage. Altitude compensation is worth most to a single-stage vehicle, and single-stage vehicles keep not being built. The X-33 was one, a single-stage-to-orbit technology demonstrator [stability and control results] [Lockheed Martin X-33]. The RS1A would have been one, for the duration of a suborbital demonstration [AFRL awards agreements under ARISE].
What Happened to It
The RS1 attempted its first orbital launch on 10 January 2023 from Kodiak and failed 10.87 seconds into flight when the first-stage engines shut down [RS1, Gunter’s Space Page]. The second vehicle, an eleven-engine Block 2, was destroyed on the pad on 19 July 2024 in the fire described above [Flight 2 Static Fire Update]. In November 2024 the company announced that it was leaving the commercial launch market [RS1, Gunter’s Space Page], and on 19 February 2025 it announced that it would rename itself Long Wall and turn to missile defence and hypersonic test targets [ABL Space renamed Long Wall].
No source consulted announces the cancellation of the X-63A. What the record shows is a company that no longer builds orbital launch vehicles, a three-year agreement signed in December 2019 whose term expired at the end of 2022, and a demonstrator that has not flown. The inference that the programme is over is drawn by this article and marked as an inference, because an inference from an absence is the weakest kind and the strength of this one comes only from the number of independent things that would have to be true for it to be wrong.
Comparison With Ground Prediction
Nothing flew, so no flight data exist to set beside the ground predictions. The X-63A did not fly within the three-year agreement that ended in 2022, and no source consulted records a flight since. The predictions therefore stand alone, and this section says where each is argued.
The central prediction is an upper bound computed here and not a contractor figure. It is the gain $\eta$ of an ideal altitude-compensating nozzle over the best fixed nozzle on the published ascent, computed under The Gain of an Ideal Spike on This Trajectory. It bounds the prize rather than forecasting the result, because truncation, the base, the wake, cooling and mass all subtract from it. No flight measured the real figure.
The quantity the flight existed to measure has no ground prediction at all. The passage between the open wake, the wake transition and the closed wake on a real ascent is set by a base pressure that a one-dimensional model cannot compute, as The Three Regimes the Programme Names explains, and the flight would have supplied it.
The earlier aerospike record is a ground record as well, at the scale that matters. The small aerospikes flown on research and university rockets gathered nozzle data on short, low flights [Aerospike Engine Flight Test Successful], and neither the XRS-2200 nor the Linear Aerospike SR-71 Experiment, both described under Sixty Years of Not Flying at Scale, produced a flight measurement of altitude compensation against which a ground prediction could be checked.
The record sets test-stand experience beside the vehicle in one place only, the parent stage’s static fire, and that too was a ground test. The excess of its instability rate on the vehicle over the stand’s history, measured by the binomial relation under The Same Report on Building an Engine Out of Many, is attributed by the company’s leading theory to a higher energy start on the vehicle than the test stand produced [Flight 2 Static Fire Update]. The comparison is between a stand and a vehicle on the pad, not between a prediction and a flight.
The parent vehicle flew once and the flight reveals nothing about the aerospike, because the RS1 that failed on 10 January 2023 carried the parent stage and not the aerospike variant [RS1, Gunter’s Space Page].
What the Data Changed
Four results in this article run against what the subject’s usual presentation, or the intuition its vocabulary invites, would lead a reader to expect.
The mean-in-time rule is not the expected answer. A numerical optimisation produces an invariant rather than a number, the same exit-pressure fraction emerging from nine searches that share no parameters, and the derivation shows why. A number that refuses to move is the cheapest possible signal that an identity is hiding underneath.
The separation constraint decides the design, and its answer depends on which criterion is used. On the conical-nozzle threshold that secondary accounts quote, the trajectory-optimal fixed nozzle cannot be built at any chamber pressure considered here. On the correlation that NASA Technical Paper 1207 fits to contoured nozzles it is infeasible only below about 3.5 megapascal. The optimum therefore sits pressed against the limit rather than beyond it.
The parity result reverses the expected answer. The word modular invites the intuition that many small modules steer more finely than few. The directional average is exactly the throttle depth divided by pi at every module count, so more modules do not bring finer steering, and what they do bring depends on whether the count is odd. Nine modules need twenty even ones to beat them.
And the regular-ring formula does not survive the loss of a module. Applying the closed form for a regular ring to a ring with a module missing overstates the surviving authority by up to a factor of 2.62 and, at four modules, by all of it, because a ring with a hole in it is not regular.
The Contemporary Literature
| Cluster | Records |
|---|---|
| Altitude compensation, which is the entire claim | 239 |
| The wake and its closure, which is this nozzle’s own flow | 406 |
| What a fixed nozzle cannot do, being separation and side loads | 365 |
| Bells and cones, being the fixed nozzle itself | 340 |
| Wind tunnel and laboratory nozzles | 54 |
| The spike, the vehicle and the engines this article measures against | 1,050 |
| Many small engines pretending to be one, and what happens when one stops | 186 |
| Steering without a gimbal, and allocating thrust among many | 708 |
| The machinery that feeds the nozzle | 1,791 |
| Liquid rocket engines taken whole | 67 |
| Heat, cooling and erosion in chambers and nozzles | 190 |
| Small thrusters and spacecraft engines | 67 |
| Solid and hybrid motors, on the subjects this article uses | 68 |
| Combined-cycle rocket propulsion | 10 |
| Making it, which is what modular is actually for | 285 |
| The ascent, which is where the integral lives | 1,338 |
| Who is buying this and what they say it is for | 56 |
| Measuring it, because the award says highly instrumented | 422 |
| Plumes and what they do to the vehicle behind them | 698 |
| Exhaust nozzles of aircraft engines, where the plug began | 203 |
| Compressible flow and gas dynamics, the relations the nozzle sections use | 167 |
| Textbooks, histories and surveys of rocket propulsion | 52 |
| Total | 8,762 |
The survey behind this article holds 8,762 research records. 2,546 of them, 29.1 percent, are report primaries, by the identifier rule set out under The Definition of Primary. 8,568 records carry a usable year, running from 1909 to 2027 with a median of 2003. 7,590 of those, 88.6 percent, predate or share the year in which both designations were allocated.
Every record in the survey is cited below, once, in the cluster its title belongs to. The clusters run from the nozzle, its wake and its limits, through the engine, the vehicle and the programme, to the jets, aircraft nozzles, compressible flow and general rocket propulsion on which those subjects rest.
Altitude compensation, which is the entire claim
Plug, aerospike, expansion-deflection, dual-bell and extendible nozzles and the other altitude-compensating concepts, treated as concepts and as flows.
239 records. [Sterbentz and Wilcox 1948] [Ciepluch et al. 1954] [Englert et al. 1954] [Durham 1955] [Morrell 1956] [The Optimization of Nozzle 1956] [Goldsmith 1958] [Fortini et al. 1959] [Musial and Ward 1959] [Aukerman et al. 1960] [Corson and Mercer 1960] [Etheridge 1960] [Lovell et al. 1960] [Connors et al. 1961] [Norton and Swihart 1961] [Rao 1961b] [Connors 1962] [Brinich et al. 1965] [Holdhusen and Perusse 1965] [Analytical and Experimental Study 1966] [Aukerman and Trout 1966] [Ward 1966] [Phillips et al. 1968] [Quan 1968] [Hosack and Stromsta 1969b] [Kors 1970] [Carey et al. 1971] [Jeracki and Johns 1971] [Kascak 1971] [Chow and Chang 1972] [Mercer 1972] [Pryor 1972] [Vilenskii et al. 1972] [Fuller 1973] [Johns 1973] [Haight and O’Donnell 1974] [Cantrell and Farrow 1975] [Sobin and Martinez 1975] [Maiden 1976] [Maiden 1978] [Jacques 1979] [Petit and Capone 1979] [Meagher 1980] [Obrien and Salmon 1980] [Peters 1980] [Chakravarthy 1981] [Coats 1981] [Obrien 1982] [Heltsley and Crosswy 1983] [Mason and Capone 1983] [Miyajima et al. 1983] [Dusa and Wooten 1984] [Krothapalli and Baganoff 1984] [Re and Leavitt 1984b] [Wagner and Kassner 1984] [Ewen and Obrien 1986] [Kushida et al. 1986] [Pavli et al. 1986] [Capone et al. 1987] [Carson et al. 1987] [Kacynski et al. 1987] [Davidian et al. 1987] [Kushida et al. 1987] [Smith et al. 1987] [Eames and Mason 1988] [Idzorek 1988] [Smith 1988] [Yu and Shuen 1988] [Bare and Capone 1989] [Ewen and Obrien 1989] [Martin 1989b] [Raiszadeh et al. 1989] [Yamamoto et al. 1990] [Kim 1991] [McAmis et al. 1991] [Reddy and Harloff 1991] [Capone et al. 1992b] [Martinez 1992] [Parsley and Van Stelle 1992] [Ruffin et al. 1992] [Yungster and Trefny 1992] [Carlson and Abdol-Hamid 1993] [Castro and Bustamante 1993] [Immich and Parsley 1993] [Lushchik et al. 1993] [Maclean 1993] [Pauley and Dagher 1993] [Smith-Kent et al. 1993] [1 Area Ratio Nozzle 1995] [Santiago and Dutton 1995] [Deere and Asbury 1996] [Jankovsky et al. 1996] [Ben-Dor et al. 1997] [Ellis et al. 1997] [Muss et al. 1997] [Bykov and Luk’yanov 1998] [Dam et al. 1998] [Gilinsky et al. 1998] [Graesel and Beylich 1998] [Hamed and Vogiatzis 1998] [Deere and Asbury 1999] [Jankovsky et al. 1999] [Dumnov et al. 2000] [Soni 2000] [Bulman et al. 2001] [Link and Koschel 2001] [Nesman 2001] [Ruf and McDaniels 2002] [Bornhorst 2003] [Hagemann et al. 2003b] [Jamison 2003] [O’Brien and Farrell 2003] [Yamanaka 2003] [Olles et al. 2004] [Yamashita et al. 2004] [Marathe and Thiagarajan 2005] [Bulman 2006] [Damira et al. 2006] [Davis et al. 2006b] [Forde et al. 2006] [Semenov et al. 2006] [Shimizu et al. 2006a] [Thiagarajan et al. 2006] [Tomita et al. 2006] [Umbel 2006] [Moríñigo et al. 2007] [Tomita et al. 2007] [Xiao et al. 2007] [Otsubo et al. 2008] [Sato et al. 2008] [Semenov et al. 2008] [Timpano et al. 2008] [Davidenko et al. 2009] [Fayard et al. 2009] [Moshfegh et al. 2009] [San et al. 2009] [Wang et al. 2009a] [Solomonov et al. 2010] [Tkacik et al. 2010] [Verma et al. 2010] [Yonezawa et al. 2010] [Kim and Lee 2011] [Verma et al. 2011] [Jones and Bui 2012] [Sainte-Rose et al. 2012] [Ageenko et al. 2013] [Balaji Krushna.P 2013] [Jones et al. 2013b] [Jones et al. 2013a] [Kowsik et al. 2013] [Song and Wang 2013] [Jones et al. 2014a] [Khandai et al. 2014] [Schomberg et al. 2014b] [Schomberg et al. 2014a] [Yu et al. 2014a] [Choi and Huh 2015] [He et al. 2015] [Mazurov 2015] [Rajagopal 2015] [Ruf and Jones 2015] [Schneider and Genin 2015] [Zhou et al. 2015a] [Hwang and Huh 2016] [Schomberg et al. 2016a] [Semenov et al. 2016] [Choi and Huh 2017] [Chutkey et al. 2017] [Influence of the Nozzle 2017] [Khan and Mathpal 2017] [Martelli et al. 2017b] [Moon et al. 2017] [Nafis et al. 2017] [Shi et al. 2017a] [Tommila and Hartsfield 2017] [Whitmore and Marshall 2017] [Holder et al. 2018] [Moon and Huh 2018] [Ridgway et al. 2018] [Barua et al. 2019] [Khan et al. 2019] [Harroun et al. 2019] [Laitón et al. 2019] [Lee et al. 2019b] [Mazurov 2019] [Mondal et al. 2019] [Reddy et al. 2019] [Sun et al. 2019] [Zebbiche 2019b] [Dhama et al. 2020] [He et al. 2020c] [Samantra et al. 2020] [Cimini et al. 2021] [Inturi et al. 2021] [Kiryushina and Elizarova 2021] [Raju et al. 2021a] [Application of Double Divergent 2022] [Koyagi and Yokota 2022] [Lee et al. 2022a] [Levin et al. 2022] [Srinivasan et al. 2022] [Zachary Muckler 2022] [Tao et al. 2023] [Gayathri et al. 2023] [Haif et al. 2023] [Inturi et al. 2023] [Jraisheh et al. 2023] [Rathakrishnan 2023] [Swaraj et al. 2023] [Tinney 2023] [Yu et al. 2023b] [Zaheer et al. 2023] [Bryan and Langley 2024] [Chang et al. 2024] [Duanyang et al. 2024] [Ismail et al. 2024] [Kirshina et al. 2024] [Magalhães and Brójo 2024] [Silva and Brójo 2024] [Song et al. 2024b] [Trivedi et al. 2024] [Xue et al. 2024] [Yu et al. 2024c] [Zeng et al. 2024] [Jin 2025] [Kamat 2025] [Kambrath and Thuluvath 2025] [Kaun and Chernyshov 2025] [Levin 2025] [Liu et al. 2025b] [Nidharia et al. 2025] [Tcherak et al. 2025] [Xue et al. 2025b] [Alam et al. 2026] [Balusamy and Muruganandam 2026] [James et al. 2026] [Murthy et al. 2026] [Ornob et al. 2026b] [Ornob et al. 2026a]
The wake and its closure, which is this nozzle’s own flow
Base flow, base pressure, base bleed and base heating behind blunt and truncated bodies in supersonic and transonic flow, with the compressible shear layers that bound the recirculation.
406 records. [Chapman 1950] [Bromm and O’Donnell 1954] [Donaldson 1955] [Korst 1956] [Salmi 1956] [Nettle 1958] [Chow 1959] [Cubbage 1959] [Cubbage and Andrews 1960] [Norton and Keith 1960] [Andrews 1961] [Musial and Ward 1961] [Slocumb and Andrews 1961] [Brazzel 1963] [Page and Dixon 1963] [Dahm 1964] [McDonald 1964] [Ying 1964] [Hoglund 1965] [McDonald 1965] [Sergeant 1965] [Wazzan 1965] [Zarin 1965] [Bauer 1966] [Bogdan and Hendershot 1966] [Chang 1966] [Economos 1966] [Emmenthal 1966] [Llinas and Rustay 1966] [Nash 1966] [Panov et al. 1966] [Wilson 1966] [Blaha et al. 1967] [Hendershot et al. 1967] [Mueller 1967] [Roshko and Thomke 1967] [Stahl and Grauer-Carstensen 1967] [Taylor and Tou 1967] [Wilson 1967] [Carpenter and Tabakoff 1968] [Dahm 1968] [Lamb and Hood 1968] [Llinas 1968] [Abbud et al. 1969] [Batham 1969] [Huerta 1969] [Johns 1969] [Page 1969] [Addy 1970] [Byington and Hoffman 1970] [Craft and Brazzel 1970] [Demetriades 1970] [Fletcher 1970] [Funk and Johnston 1970] [Hall et al. 1970a] [Hall et al. 1970b] [Isaev and Shvets 1970] [Martin and Brazzel 1970] [Page and Reda 1970] [Rom et al. 1970] [Gilreath and Schetz 1971] [Greenwald 1971] [Su and Wu 1971] [Kramer 1972] [Pearce 1972] [Spring 1972] [Tanner 1972] [Gerhart 1973] [Gerhart and Korst 1973] [Jakubowski and Lewis 1973] [Messiter et al. 1973] [Roache 1973] [Sule and Mueller 1973b] [Andrews and Cooper 1974] [Inger 1974] [Chow and Spring 1975] [Gerhart et al. 1975] [Giel and Mueller 1975b] [Amr and Kassoy 1976] [Approximate Analysis of Base 1976] [Base Combustion Effects 1976] [Drzewiecki and Foust 1976] [Giel and Mueller 1976] [Theoretical Modeling 1976] [Gogish and Pokrovskii 1977] [Starr 1977] [Victor 1977] [White and Agrell 1977] [Cassanto et al. 1978] [Diver and Stewartson 1978] [Gogish and Pokrovskii 1978] [Sulyma and Penny 1978] [Tanner 1978] [Williams 1978] [Daniels 1979] [Foust 1979] [Wagner and White 1979] [Daniels 1980] [Schetz et al. 1980] [Sulyma 1980] [Wagner and White 1980] [Fox and Bauer 1981] [Gai and Sharma 1981] [Motallebi and Norbury 1981] [Sullins et al. 1982] [Sahu et al. 1983a] [Sahu et al. 1983b] [Soong and Chu 1983] [Addy et al. 1984] [Mueller 1985] [Sinha and Dash 1985] [Addy et al. 1986] [Forester and Strom 1986] [Sahu 1986] [Tanaka et al. 1987] [Powers 1988] [Ragab 1988] [Sahu and Nietubicz 1988] [Wang 1988] [Bender and Reardon 1989] [Boris et al. 1989] [Samimy 1989] [Tang et al. 1989] [Demetriades and Brower 1990] [Fourguette et al. 1990] [Hunter et al. 1990] [Kwok et al. 1990] [Marongiu 1990] [Samimy and Abu-Hijleh 1990] [Shen et al. 1990] [Zhuang et al. 1990] [Clemens et al. 1991] [Fourguette et al. 1991a] [Fourguette et al. 1991b] [Izadi and Zumwalt 1991] [Leib 1991] [Masalov and Tagirov 1991] [Ota and Goldberg 1991] [Pearce et al. 1991] [Wantuck et al. 1991] [Erhart 1992] [Kinzie and Martens 1992] [McLaughlin et al. 1992] [Moustafa et al. 1992] [Nelson 1992] [Poggie et al. 1992] [Sahu 1992] [Tanner 1992] [Dougherty and Johnson 1993] [Everson and Nelson 1993b] [Everson and Nelson 1993a] [Herrin and Dutton 1993] [Hwang et al. 1993] [Kumar et al. 1993] [Lamb and Oberkampf 1993] [Molezzi and Dutton 1993] [Nietubicz and Gibeling 1993] [Poggie and Smits 1993b] [Poggie and Smits 1993a] [Reardon and Nelson 1993] [Roshko 1993] [Trifu and Savu 1993] [Tucker and Warsi 1993b] [Tucker 1993] [Wang 1993c] [Wang 1993a] [Williams et al. 1993] [Ascoli et al. 1994] [Kumar et al. 1994] [Martens et al. 1994b] [Martens et al. 1994a] [Venkatapathy et al. 1994] [Wang 1994] [Xiao and Aggarwal 1994] [Glotov 1995] [Gowda 1995] [Herrin and Dutton 1995] [Lamb and Oberkampf 1995] [Martens and McLaughlin 1995] [Mathur and Dutton 1995] [Najland, za, A G et al. 1995] [Papamoschou 1995] [Park et al. 1995b] [Sahu and Heavey 1995] [Wang 1995] [Chuang and Chieng 1996] [Clemens et al. 1996] [Kaurinkoski 1996] [Loh et al. 1996] [Martens et al. 1996] [Mathur and Dutton 1996] [Messiter 1996] [Peroomian et al. 1996] [Ramaswamy and Loth 1996] [Umemura et al. 1996] [Wang 1996] [Freund et al. 1997] [Hammer et al. 1997] [Kaurinkoski et al. 1997] [Lee and Morris 1997] [Peroomian et al. 1997] [Sahu and Heavey 1997] [Bannink et al. 1998] [Chern et al. 1998] [ESDU Data Item Estimates 1998] [Kaurinkoski and Hellsten 1998] [Wang 1998b] [Wang 1998a] [Zhdanov 1998] [Bury and Estivalezes 1999] [Estivalezes and Bury 1999] [Fureby et al. 1999] [Saint-Mard and Hendrick 1999] [Tomita et al. 1999] [Wang 1999] [Whitmore and Moes 1999] [Forsythe et al. 2000] [Wang 2000] [Whitmore and Moes 2000] [Benay and Servel 2001] [Ito and Fujii 2001a] [Moraes 2001] [Ottens et al. 2001] [Paciorri et al. 2001] [Papp and Ghia 2001] [van Raalte and van Oudheusden 2001] [Wang et al. 2001] [Baik and Zumwalt 2002] [Bourdon and Dutton 2002] [Fasel 2002] [Forsythe et al. 2002] [Ito and Fujii 2002b] [Ito and Fujii 2002c] [Naughton 2002] [Wei and Chang 2002] [Fureby and Kupiainen 2003] [Ito and Fujii 2003a] [Wang et al. 2003b] [Wang et al. 2003a] [Yoshizawa et al. 2003] [Bourdon and Dutton 2004] [Kastengren and Dutton 2004] [Kawai and Fujii 2004] [Khan and Rathakrishnan 2004] [Kuehner and Dutton 2004] [Subbareddy and Candler 2004] [Wang et al. 2004] [August and McKinney 2005] [Choi et al. 2005] [DeSpirito 2005] [Kastengren and Dutton 2005b] [Kastengren and Dutton 2005a] [Kastengren et al. 2005] [Kawai and Fujii 2005] [Kuehner and Dutton 2005] [Lee et al. 2005] [Park et al. 2005] [Tan et al. 2005] [Durgesh and Naughton 2006] [Fasel and Sandberg 2006] [Khan and Rathakrishnan 2006] [Lee and Kim 2006] [Ruf 2006] [Shen et al. 2006] [Simon et al. 2006a] [Simon et al. 2006b] [Sivasubramanian et al. 2006b] [Sivasubramanian et al. 2006a] [Turbulent Shear Layers 2006] [de Feo and Shaw 2007] [Guan et al. 2007] [Ko et al. 2007] [Kuehner et al. 2007] [Lazar et al. 2007] [Meliga and Reijasse 2007] [Miki et al. 2007] [Gaitonde 2008] [Kim et al. 2008] [Nallasamy et al. 2008] [Shin et al. 2008] [Bonanos et al. 2009] [Dharavath et al. 2009] [Stark and Wagner 2009] [Venkatakrishnan and Suriyanarayanan 2009] [Verma and Viji 2009] [Maddalena and Dimotakis 2010] [Nallasamy et al. 2010] [Bulusu and Garris 2011] [Mehta et al. 2011a] [Thomas and Unnikrishnan 2011] [Verma and Viji 2011a] [Verma and Viji 2011b] [Cao et al. 2012] [Davis et al. 2012] [Dissel et al. 2012] [Guo and Wang 2012] [Jeon et al. 2012] [Massa 2012] [Hargather et al. 2013] [Matsuo et al. 2013] [Mehta et al. 2013] [Nagao et al. 2013] [Belyayev and Kaltayev 2014] [Davis and Kumar 2014] [Mehta et al. 2014] [Takahashi et al. 2014a] [Yu et al. 2014b] [Zhao-Xin and Bing 2014] [Gentile et al. 2015] [Kim and Baek 2015] [Leger and Poggie 2015] [Lin and Yan 2015] [Makasheva et al. 2015] [Suryanarayana et al. 2015] [Tripathi et al. 2015] [Wu et al. 2015b] [Das and De 2016] [Ecker et al. 2016] [Mehta et al. 2016] [Patel 2016a] [Xue and Yu 2016] [Bulathsinghala et al. 2017] [Favale et al. 2017] [Guoliang et al. 2017] [Kirchner et al. 2017] [Koll et al. 2017] [Leger et al. 2017] [Mehta et al. 2017] [Pathan et al. 2017] [Shi et al. 2017b] [Sun 2017] [Ahmed and Khan 2018] [Ilahi Chaudhary et al. 2018] [Khan et al. 2018] [Khankhasaeva et al. 2018] [Saleel et al. 2018] [Sethuraman and Khan 2018] [Stack and Gaitonde 2018] [Zha et al. 2018] [Bao et al. 2019] [Faheem et al. 2019] [Gu et al. 2019] [Kavun et al. 2019] [Kirchner et al. 2019a] [Kirchner et al. 2019b] [Ko et al. 2019] [Nair et al. 2019b] [Serdarevic-Kadic and Terzic 2019] [Weidner et al. 2019] [Zapryagaev et al. 2019] [Zhou et al. 2019b] [Kirchner et al. 2020] [Ma et al. 2020] [Pu and Jiang 2020] [Scharnowski and Kähler 2020] [Sikroria et al. 2020] [Zhang et al. 2020] [Zhou et al. 2020] [Et. al. 2021] [Karthick 2021] [Soman et al. 2021] [Zhou et al. 2021a] [Khan et al. 2022b] [Bulat et al. 2022] [Doshi et al. 2022] [Kong et al. 2022] [Manu Mohan et al. 2022] [Nam et al. 2022a] [Paul et al. 2022] [Smink et al. 2022b] [Smink et al. 2022a] [Zhao et al. 2022] [Chakraborty 2023] [Husnina Muhamad Zuraidi et al. 2023] [Kim et al. 2023] [Moffeit et al. 2023] [Zhou and Bao 2023] [Heo et al. 2024b] [Heo et al. 2024a] [Moffeit et al. 2024] [Thakor et al. 2024] [Wu et al. 2024b] [Analysis of Convergent Nozzle 2025] [Ashif et al. 2025] [Gianoukakis et al. 2025] [Kim and Kim 2025] [Mueller et al. 2025] [Murawski and Gaitonde 2025] [Qualters and Zigunov 2025] [Rahma and AlQadi 2025] [Sharma et al. 2025] [Sivadas and Deepu 2025] [Sun et al. 2025] [Wu and Han 2025] [Kim and Kim 2026b] [Kim and Kim 2026a] [Krishna et al. 2026] [Sun et al. 2026b] [Wang and Wang 2026] [Zhao et al. 2026] [Banton] [Durgesh and Naughton] [Oudheusden and Scarano] [Stein] [Togiti and Lüdeke] [Yan]
What a fixed nozzle cannot do, being separation and side loads
Flow separation in overexpanded nozzles, the side loads it produces, nozzle start and shutdown transients, and supersonic separation stated generally.
365 records. [Cowles and Foster 1949] [McKenney 1951] [Krull and Beale 1956] [Rao 1958] [Green and Nall 1959] [Farley and Campbell 1960] [Holder 1961] [Roschke and Massier 1962] [Glass and Korbacher 1962] [Krayenbuhl 1962] [Boney et al. 1963] [Kaufman and Louis G. 1963b] [Kaufman and Louis G. 1963a] [Application of the Method 1964] [Arens 1964] [Craig 1965] [Kalt and Badal 1965] [Callis 1966] [Hoffman 1966] [Hoffman and Thompson 1966] [Johnson 1966] [Back et al. 1968] [Land and Tuovila 1968] [Ransom et al. 1969] [Chang 1970] [Holden 1970] [Hwang and Murthy 1970] [Snyder and Thompson 1971] [Omori et al. 1972] [Ratliff et al. 1972] [Smith and Ratliff 1972] [Brilliant and Adamson 1973] [Nave and Coffey 1973] [Rose 1973] [Schmucker 1973a] [Schmucker 1973b] [Chiou and Hung 1974] [Schmucker 1974] [Token 1974] [Henne 1975] [Wu 1975] [Goetz et al. 1976] [Meier 1976] [Abeyounis 1977] [Daines and Boyd 1977] [Seiler 1977] [Wu et al. 1977] [Hoffman and Allman 1978] [Holden 1978] [Armstrong 1979] [Chow 1979] [Davin and Petersen 1979] [Miller et al. 1979] [Inger 1981] [Carter and Hafez 1982] [Davis 1982] [Rao 1982] [Boraas 1983] [Davis and Abel 1983] [Dawes 1983] [Schmucker 1983] [Ardonceau 1984] [Cline and Wilmoth 1984] [Jurkovich 1984] [Krogmann et al. 1984] [Schmucker 1984] [Cline and Wilmoth 1985] [Goodman et al. 1985] [Marcum and Hoffman 1985] [Benay and Pot 1986] [Edwards et al. 1986] [Mason and Blotter 1986] [McLean and Matoi 1986] [Wang and Hoffman 1986] [Gittler and Kluwick 1987] [Neiland 1987] [Malik and Tagirov 1988] [Shieh 1988] [Danberg and Patel 1989] [Varwig et al. 1989] [Edwards and Perkins 1990] [Goeing 1990] [Tagirov 1990] [Chung et al. 1992] [Hamed and Kumar 1992] [Inger 1992] [Korte et al. 1992] [Rao and Dang 1992] [Guillot and Wilson 1993] [Li and Shi 1993] [Lien and Leschziner 1993] [Schneider 1993] [Chen et al. 1994] [Hamed and Kumar 1994] [Ishiguro et al. 1994] [Nasuti and Onofri 1994] [Hamed and Vogiatzis 1995] [Szumowski et al. 1995] [Bohning 1996] [Dumnov 1996] [Hussaini and Korte 1996] [Hadjadj et al. 1997] [Hamed and Vogiatzis 1997] [Forsythe et al. 1998] [Hunter 1998] [Igra et al. 1998] [Romine 1998] [Wang and Liu 1998] [Asbury and Hunter 1999] [Frey and Hagemann 1999] [Murdock and Welle 1999] [Onofri and Nasuti 1999] [Ostlund and Bigert 1999] [Ostlund and Jaran 1999] [Prozan and Luke 1999] [Reijasse et al. 1999] [Zaman and Dahl 1999] [Frey and Hagemann 2000] [Lefrançois et al. 2000] [Peters et al. 2000] [Morita et al. 2001] [Oestlund et al. 2001] [Reijasse et al. 2001a] [Reijasse et al. 2001b] [Terhardt et al. 2001] [Deck and Guillen 2002] [Hagemann et al. 2002] [Loh and Zaman 2002] [Nguyen et al. 2002] [Tomita et al. 2002] [Verma 2002] [Burtschell and Zeitoun 2003] [Chopra et al. 2003] [Nguyen et al. 2003] [Perigo et al. 2003] [Schwane et al. 2003] [Tomita et al. 2003] [Verma and Ciezki 2003] [Yonezawa et al. 2003] [Zerjeski 2003] [Bueno et al. 2004] [DalBello et al. 2004] [Deck and Nguyen 2004] [Moiseev et al. 2004] [Nozzle Design and Optimization 2004] [Papamoschou and Zill 2004] [Pilinski and Nebbache 2004] [Wang 2004c] [Wang 2004b] [Watanabe et al. 2004a] [Xia and Schwane 2004] [Östlund et al. 2004] [Bourgoing and Reijasse 2005] [Elmiligui et al. 2005] [Shi 2005] [Shope and Tatum 2005] [Stark 2005] [Verma and Haidn 2005] [Wang 2005] [Xiao and Tsai 2005] [Yonezawa et al. 2005] [Abdol-Hamid et al. 2006a] [Abdol-Hamid et al. 2006c] [Dou et al. 2006] [Gaffney 2006] [Moríñigo and Salvá 2006] [Nebbache and Pilinski 2006] [Papamoschou and Johnson 2006] [Perrot and Hadjadj 2006] [Shimizu et al. 2006b] [Verma and Haidn 2006] [Verma et al. 2006] [Yonezawa et al. 2006a] [Yonezawa et al. 2006b] [Babinsky 2007] [Brown and Ruf 2007] [Smalley et al. 2007] [Verma and Haidn 2007] [Weiss et al. 2007] [Boccaletto 2008] [Girard and Reijasse 2008] [Inger 2008] [Johnson and Papamoschou 2008] [Moríñigo and Salvá 2008] [Nakakita et al. 2008] [Nasuti and Onofri 2008] [Papamoschou et al. 2008] [Stark and Wagner 2008] [Verma 2008b] [Wang 2008] [Wang and Guidos 2008] [Zhang and Fuchiwaki 2008] [Brown et al. 2009] [Debiève and Dupont 2009] [Deck 2009] [Hadjadj and Onofri 2009] [Hadjadj and Perrot 2009] [Ivanov et al. 2009] [Mudford et al. 2009] [Nagdewe and Kim 2009] [Nagdewe et al. 2009] [Nasuti and Onofri 2009] [Pirozzoli et al. 2009] [Ponomarev et al. 2009] [Ruf et al. 2009] [Tomita et al. 2009b] [Verma and Haidn 2009b] [Verma and Haidn 2009a] [Baars et al. 2010] [Doerffer et al. 2010] [Garelli et al. 2010] [Johnson and Papamoschou 2010] [Lee et al. 2010b] [Lijo et al. 2010b] [Lijo et al. 2010a] [Martelli et al. 2010] [Ruf et al. 2010] [Setoguchi et al. 2010] [Srivastava et al. 2010] [Verma and Haidn 2010a] [Verma and Haidn 2010b] [Wang et al. 2010b] [Aghababaie and Taylor 2011] [Baars et al. 2011] [Babinsky and Délery 2011] [Baker and Pray 2011] [Dupont et al. 2011] [Frate 2011] [Kiran et al. 2011] [Grilli et al. 2011] [Keanini et al. 2011] [Lefrançois 2011a] [Lefrançois 2011b] [Liu and Lu 2011] [Ramsey et al. 2011a] [Ramsey et al. 2011b] [Reijasse et al. 2011a] [Stark and Génin 2011a] [Tokura and Maekwa 2011] [Yoon et al. 2011] [Baars et al. 2012] [Blades et al. 2012] [Chaudhuri and Hadjadj 2012] [Fournier et al. 2012] [Golub et al. 2012] [Lü and Ye 2012] [Olson and Lele 2012] [Shahack et al. 2012] [Shams et al. 2012] [Stark and Genin 2012] [Wang et al. 2012] [Young and Hartfield 2012] [Zhao et al. 2012a] [Baars and Tinney 2013] [Eyi and Yumusak 2013b] [Giglmaier et al. 2013] [Sellam et al. 2013] [Wang et al. 2013a] [Benson 2014] [Cuppoletti et al. 2014] [Morajkar et al. 2014] [Toufique Hasan 2014] [Verma and Haidn 2014] [Wang et al. 2014a] [Aghababaie and Theunissen 2015] [Bekka et al. 2015] [Dippold and Zaman 2015] [Hartfield and Burkhalter 2015] [Jia et al. 2015] [Kamali et al. 2015] [Lu 2015] [Maicke 2015] [Schomberg et al. 2015] [Talsaniya et al. 2015] [Yu et al. 2015] [Zhang et al. 2015a] [Chaudhuri and Hadjadj 2016] [Grabe et al. 2016] [Jia et al. 2016b] [Jia et al. 2016a] [Luchikhina and Tonkov 2016] [Sanal Kumar et al. 2016] [Schomberg et al. 2016b] [Stark and Génin 2016b] [Stark and Génin 2016a] [Wonnell and Chen 2016] [Bekka et al. 2017b] [Bekka et al. 2017a] [Martelli et al. 2017a] [Martis and Misra 2017] [Meng and Ye 2017] [Verma et al. 2017] [Du et al. 2018] [Huang et al. 2018] [Koike and Babinsky 2018] [Qurooni et al. 2018] [Schomberg et al. 2018b] [Schomberg et al. 2018a] [Goncalves et al. 2019] [Ivanov and Kryukov 2019] [Khobragade et al. 2019] [Liu et al. 2019c] [Martelli et al. 2019] [Mishra* et al 2019] [Pulimidi and Lu 2019] [Sansica et al. 2019] [Schomberg et al. 2019] [Zebiri et al. 2019] [Zhu et al. 2019] [Daviller et al. 2020] [Lee et al. 2020b] [Lee et al. 2020a] [Liu and Khine 2020] [Martelli et al. 2020] [Panigrahi et al. 2020] [Verma and Haidn 2020] [Khaled and Khadidja 2021] [Lee et al. 2021] [Peri 2021] [Tavanashad and Shoele 2021] [Abyan et al. 2022] [Bhupendra Kumar et al. 2022] [Demni et al. 2022] [Munro 2022] [Rafiq et al. 2022] [Restrepo et al. 2022] [Wang et al. 2022g] [Jones 2023a] [Giehler et al. 2023] [Hashim and Dharmalingam 2023] [Murugesan et al. 2023] [Nedjari et al. 2023] [Ramsey et al. 2023] [Yang et al. 2023] [Zahir et al. 2023a] [Abada et al. 2024] [Allen and Agarwal 2024] [Brójo 2024] [Cerminara et al. 2024] [Hu et al. 2024] [Jack et al. 2024] [Shock Boundary-Layer Interaction 2024] [Studying the Influence 2024] [Tarnacha 2024] [Tran et al. 2024] [Vishwajith 2024] [Cristovão Silva and Brójo 2025] [Dasgupta et al. 2025] [Maheswari et al. 2025] [Murali 2025] [Nagasai et al. 2025] [Ramsey et al. 2025] [Stark and Jack 2025] [Yang et al. 2025c] [Chutkey and Verma 2026] [Tinney and Valdez 2026] [Wei et al. 2026] [Zapryagaev et al. 2026] [Zhang et al. 2026e] [Tinney et al] [Mahalingesh] [Mark] [Piquet] [Kolli] [Shock Wave-Boundary Layer Interactions]
Bells and cones, being the fixed nozzle itself
The flow, design and performance of bell, conical and contoured nozzles, which are the fixed nozzles the envelope argument compares against.
340 records. [Bradley and Hale 1909] [Wirt 1924] [Mueller and Peters 1930] [Kantrowitz et al. 1943] [Lent 1944] [Puckett 1946] [DeJuhasz 1947] [Puckett 1947] [Isothermal Expansion in Nozzles 1948] [Pinkel 1948] [Altman and Penner 1949] [Oswatitsch and Rothstein 1949] [Penner 1949a] [Crown 1950] [Folsom 1950] [McLellan et al. 1950] [Krieger 1951] [Seifert and Altman 1952] [Baron 1954] [Dillon and Line 1956] [Meyer 1956] [Rastogi and Pandya 1956] [Dillaway 1957] [Edse 1957] [Branstetter and Setze 1958] [Reynolds 1958] [Rowe 1958] [Feodosiev and Siniarev 1959a] [Hardenbergh 1959] [Reynolds and Baldwin 1959] [Analysis of a New 1960] [Brewer and Levin 1960] [Masugi 1960] [Ahlberg et al. 1961] [Lewis and Harrison 1961] [Rao 1961a] [Tsuchiya 1961] [Watson 1961] [Bray 1963] [Jack 1963] [Ellison and Johnson 1964] [Moger and Ramsay 1964] [Nozzle Performance Evaluation Program 1964] [Aerojet-General Corp., Azusa, Calif. (USA) 1964] [Stubbs and US Atomic Energy Commission (AEC) 1964] [Burwell and Hofland 1965] [Krzycki 1965] [Aerojet-General Corp., Sacramento, Calif. (USA) 1965b] [Back and Cuffel 1966] [Crowe and Willoughby 1966] [King 1966] [Manda 1966] [Franciscus and Healy 1967] [Hoffman and Scofield 1967] [Milford and Migdal 1967] [Pirumov 1967] [Crowe et al. 1968] [Edenfield 1968] [Frey et al. 1968] [Dunn 1969a] [Dunn 1969b] [Ellis 1969] [Hoffman 1969] [McKevitt 1969] [Mikhailov 1969] [Aerojet-General Corp., Sacramento, Calif. (USA) 1969] [Sivells 1969] [Brodsky 1970] [Elliott and Stromsta 1970] [Jaffe and Rao 1970] [Elsbernd and Hoffman 1971] [Glowacki 1971] [Aerojet-General Corp., Sacramento, Calif. (USA) 1971] [Aerojet Nuclear Systems Co., Sacramento, Calif. (USA) 1971] [Williams 1971] [Back et al. 1972a] [Dash and Delguidice 1972] [Ellis 1972] [Huff and Groesbeck 1972] [Norton and White 1972] [Sims and Elkin 1972] [Bishop and Sanders 1974] [Cline 1974a] [Cline 1974b] [Szaniszlo 1974] [Anders 1975] [Brown and Hamilton 1975] [Johnson and Boney 1975] [Sebacher and Lee 1975] [Cline 1976] [Cline 1977] [Thompson and Epstein 1977] [Middlecoff and Thomas 1979] [Chang 1980] [Dutton and Addy 1980] [Chang 1981] [Lin and Shen 1981] [Varner et al. 1982] [Fujii and Kutler 1983] [Nachshon 1983] [Shcherbakov 1983] [Tuttle and Blount 1983] [Bevilaqua and Lee 1984] [Wang and Du 1984] [Kwon and Delaney 1985] [Seto et al. 1985] [Brown 1986] [Clayton and Back 1986] [Collins 1986] [Desnoyer 1986] [Forde 1986] [Varner 1986] [Bevilaqua and Lee 1987] [Davidian 1987a] [Lankford 1987] [Marx 1987] [Schwamborn 1987] [Scott and Visbal 1987] [Thompson and Sutton 1987] [Chang 1988] [Fujiwara et al. 1988] [Gregg 1988] [Riedelbauch and Weiland 1988] [Shyne 1988] [Afonin and Butov 1989] [Dang et al. 1989] [Griffith 1989] [Long and Hanus 1989] [Ostrander et al. 1989] [Vanoverbeke and Shuen 1989] [Baker et al. 1990] [Collins et al. 1990a] [Reddy and Tulasiram 1990] [Berton 1991] [Candler and Perkins 1991] [Davidian and Kacynski 1991] [Dunn et al. 1991] [Jacobs and Stalker 1991b] [Jacobs and Stalker 1991a] [Jentink 1991] [Stubbs et al. 1991] [Hackett 1992] [Knoll 1992] [Korte 1992] [Aldo and Argrow 1993] [Davidian and Kacynski 1993] [Keeling 1993] [Kim 1993] [Tsuei and Merkle 1993] [Alcenius and Schneider 1994] [Georgiadis and Yoder 1994] [Kacynski 1994] [Krishnamurthy 1994] [Manski and Hagemann 1994] [Numerical Simulation of Scarfed 1994] [Rao and Beck 1994] [Yu et al. 1994] [Landrum et al. 1995] [Pearson et al. 1995] [Watanabe et al. 1995] [Yagudin 1995] [Follett 1996] [Follett et al. 1996] [Landrum and Beard 1996a] [Barnhart 1997] [Wu et al. 1997] [Chen and Hou 1998] [Cook et al. 1998] [Wong et al. 1999] [Ahmad and McCool 2000] [Chang 2002a] [Lucia et al. 2002] [Dyer et al. 2003] [Hagemann et al. 2003a] [Mouronval et al. 2003] [Cooper and Shepherd 2004] [Development of an Experiment 2004] [Gamble et al. 2004] [Rocket Engine Nozzle Concepts 2004] [TabeJamaat and Pezeshki 2004] [Chang et al. 2005] [Senthil Kumar et al. 2005] [Chang et al. 2006] [LeMoyne 2006] [Zebbiche and Youbi 2006b] [Al-Hasan and Schnerr 2007] [Behera and Srinivasan 2007] [Toufik and ZineEddine 2007b] [Chang et al. 2008] [Gaitonde 2009] [Liang et al. 2009] [Metghalchi 2009] [Yoder et al. 2009] [Boccaletto and Dussauge 2010] [Ekanayake et al. 2010] [Faure et al. 2010] [Krushna 2010] [Majdalani and Maicke 2010] [Moríñigo and Salvá 2010] [Yang 2011] [Zebbiche 2011] [Albanese et al. 2012] [Chen et al. 2012] [Krieg and Mohseni 2012] [Mehta et al. 2012] [Naung et al. 2012] [Sribonfha et al. 2012] [Wu et al. 2012] [Eyi and Yumusak 2013a] [Kennedy 2013] [Yumusak 2013] [Carter et al. 2014] [Charan 2014] [Garelli et al. 2014] [Guo et al. 2014] [Kumar et al. 2014] [Patel 2014] [Srinivas and Potti 2014] [Sun and Wei 2014] [Takahashi and Gibson 2014] [Takovitskii 2014] [Wang et al. 2014b] [Webster 2014] [Yildizlar et al. 2014] [Deshpande and Narappanawar 2016] [Eto et al. 2016] [Isono et al. 2016] [Jegede and Crowther 2016] [전민경 et al. 2016] [Kotteda and Mittal 2016] [Kumar and Arularasu 2016] [Ramji et al. 2016] [Athota Rathan Babu et.al. 2017] [Maicke 2017] [Manigandan and Vijayaraja 2017] [Mubarak and Tide 2018] [Francisco 2018] [Jéger and Veress 2018] [Kimura et al. 2018] [Lee 2018] [Matveev et al. 2018] [Ramesh Kumar and Devarajan 2018] [Sabirzyanov et al. 2018] [Zebbiche 2018] [Adaikalaraj et al and TJPRC 2019] [Conte et al. 2019] [Akhtar et al. 2019] [Control of Nozzle Flow 2019] [Ferrero and Pastrone 2019] [Azami et al. 2019] [Scott 2019] [Juhasz 2019] [Kimura and Matsuda 2019] [Rocket Nozzle Performance 2019] [Sarweswaran et al. 2019] [Sundararaj and Syedhaleem 2019] [Zebbiche 2019a] [Zhang et al. 2019b] [Abada et al. 2020] [Harroun et al. 2020b] [Harroun et al. 2020a] [Jijo Unnikrishnan 2020] [Krishna 2020] [Kishore 2020] [Pietrykowski et al. 2020] [Raja 2020] [Sosa et al. 2020] [Stetsyuk et al. 2020] [Harikrishnan and Lokavarapu 2021] [Harroun et al. 2021] [Jeon and Park 2021] [Kong and Wang 2021] [Koyagi et al. 2021] [Kun et al. 2021] [Mikhailov 2021] [Mkrtchyan and Kochetkov 2021] [吴 2021] [Shaidullin et al. 2021] [Veeresh Kumar et al. 2021] [Gandge et al. 2022] [He et al. 2022] [Ilie and Sullivan 2022] [Jayaprakash et al. 2022] [Kirshina et al. 2022] [Liu et al. 2022b] [Paxson et al. 2022] [Voronin S. T. 2022] [Wang et al. 2022b] [Agarwal 2023] [Ahmed and Gross 2023] [Antony and Waldecker 2023] [Jyothi Nt et al. 2023] [Huang et al. 2023a] [Huang et al. 2023b] [Kateryna and Nataliya 2023] [Manoj et al. 2023] [Pandit et al. 2023] [Parkash and Sharda 2023] [Salhi 2023] [The Pressure Analyzing 2023] [Zhang et al. 2023c] [Alili et al. 2024] [Chaudhary 2024] [Design and Analysis 2024] [Dsouza et al. 2024] [Gidaspov et al. 2024] [Hayashi 2024] [Impact of Static Pressure 2024] [Nataliya et al. 2024] [Paul et al. 2024] [Popovich et al. 2024] [Sethuraman et al. 2024] [Yang et al. 2024b] [Yunfeng 2024] [Zhang et al. 2024e] [Cantariño and Pulido 2025] [CFD Based Design Optimization 2025] [Durst et al. 2025] [Gummadidala et al. 2025] [Nair et al. 2025] [Neelakandan et al. 2025] [Abada et al. 2026a] [Alexandrov 2026] [Aamir and Abbasi 2026] [Dai et al. 2026] [Gadre 2026] [Shek 2026] [Soni 2026] [Tian et al. 2026] [Capatina] [Cerantola] [Paxson et al] [Ghosh and Friedrich] [Miki et al] [Lucia et al] [Nak] [Pitot de la Beaujardiere et al] [Quintao] [Rozendaal] [Wide-Throat Nozzle]
Wind tunnel and laboratory nozzles
Nozzles of wind tunnels, shock tunnels and laboratory rigs, where the title studies the nozzle’s own flow.
54 records. [Beckwith et al. 1984] [Chen et al. 1990] [Chen et al. 1991] [Chen et al. 1992] [Schmisseur et al. 1996] [Palma et al. 1998] [Schneider 1998] [Watanabe et al. 2001] [Kaneko et al. 2002] [Lacey et al. 2002] [O’Byrne et al. 2002] [OByrne et al. 2002] [Chue et al. 2003] [Lacey et al. 2003] [Palma et al. 2003] [Gaffney 2004] [Komuro et al. 2005] [O’Byrne et al. 2005] [Scott et al. 2005] [Gaffey et al. 2006] [Gaffney and Norris 2008] [Yen and Martindale 2008] [Candler and McConaughey 2009] [Gaffney 2009] [Bensassi et al. 2010] [Wu and Radespiel 2013] [Gong et al. 2014a] [Axdahl 2015] [Prabhu et al. 2015] [Sadraey 2015] [Drozda et al. 2017] [Huang et al. 2017b] [Huang et al. 2017a] [Yu et al. 2017b] [Brown 2019] [Gao et al. 2019] [Toniato et al. 2019] [Gokcen 2021] [Sung and Choi 2021b] [Sung and Choi 2021a] [Gokcen 2022] [Kovács et al. 2022] [Bratman et al. 2023] [Novel Design of Variable 2023] [Sung et al. 2023] [Zahir et al. 2023b] [Gokcen et al. 2024] [Jakobs et al. 2025] [Shen et al. 2025b] [Gokcen 2026] [Shen et al. 2026] [Davey] [Gokcen et al] [Towsey]
The spike, the vehicle and the engines this article measures against
Aerospike engines and their hardware, the X-33 and its XRS-2200, the Linear Aerospike SR-71 Experiment, and the named engines and launch vehicles this article sets beside the X-63A.
1,050 records. 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[Jarvis 2025] [Kbab et al. 2025] [Zaman et al. 2025] [Korth et al. 2025] [Langner et al. 2025] [Liu et al. 2025a] [Selvam et al. 2025] [Minaz and Meram 2025] [Monokrousos et al. 2025] [Motomura 2025] [Nanni et al. 2025] [Ozaki et al. 2025] [Piparava and Zhang 2025] [Serrato 2025] [Singh and Ravi 2025] [Wang et al. 2025d] [Wißmann et al. 2025a] [Wißmann et al. 2025b] [Zhou et al. 2025a] [Zhou et al. 2025c] [Abada et al. 2026b] [Aslan et al. 2026] [Bakker et al. 2026] [Benlembarek et al. 2026] [Carbone et al. 2026] [Chandler et al. 2026] [Fagan and Zaman 2026] [Fiore et al. 2026a] [Golliard and Mihaescu 2026] [Karim et al. 2026] [Korth et al. 2026] [Legros et al. 2026] [Liu et al. 2026c] [Liu et al. 2026b] [Lizcano et al. 2026] [Magnani et al. 2026] [Masse et al. 2026] [Nikolayev et al. 2026] [Pyle and Jacobs 2026a] [Pyle and Jacobs 2026b] [Sadiqi and Naimzad 2026] [Ayush et al. 2026] [Sharrouf et al. 2026] [Steiner and Bauer 2026] [Sun et al. 2026c] [Tcherak et al. 2026b] [Wanchoo et al. 2026] [Wißmann et al. 2026] [Aerospike engine] [Fagan and Zaman] [Fagan et al] [Beebe] [Brennen] [Brock] [Campbell et al] [Case] [Du] [Imbaratto] [Jackson et al] [Korth] [Korth et al] [Zaman et al] [Zaman et al] [Legros] [Mori et al] [Niimi et al] [Shahrokhi and Noori] [Su]
Five titles in this cluster report aerospike engines in flight, from a liquid-propellant engine flight-tested by 2004 to a linear aerospike ignited in flight in 2024 [Besnard and Garvey 2004b] [Bui et al. 2005] [Baker et al. 2008] [Flight of the Aerospike 2021] [Janardhana 2025]. Each is a small engine on a short flight, which is why the flight record of the subject is thin rather than empty.
Many small engines pretending to be one, and what happens when one stops
Clustered and multiple engines, modular engines, engine-out, nozzle and thruster arrays, and the reliability of engines and stages.
186 records. [Coplen 1957] [Church et al. 1962] [Hale 1963] [Lloyd and Lipow 1963] [Hisler 1964] [Peters 1964] [Cubbage and Weidner 1965] [Aerojet-General Corp., Sacramento, Calif. (USA) 1965a] [Chu et al. 1966] [Echols 1966] [Hopson and McAnelly 1966] [Kennedy 1966] [Mueller 1966] [Cover and Wasko 1967] [Fergus 1967] [Walker and Zeigler 1968] [Brewer and Craven 1969] [Meadows 1969] [Newman 1969] [Pierman 1969] [Christie and Greenberg 1973] [Vicario et al. 1973] [Demetriades 1977] [Thornton 1977] [Fault-Tolerant High Reliability Electronic 1979] [Newirth and Bosco 1980] [Rabinowitz et al. 1980] [Dyson 1981] [Petrie 1982] [Bellows et al. 1984] [Russell and Chu 1984] [Cikanek 1986a] [Maram and Barkhoudarian 1987] [Nguyen et al. 1988] [Powers et al. 1988] [Swan and Vizzini 1988] [Wolting 1988] [Kytasty et al. 1989] [O’Hara 1989] [Perry 1989] [Royer and Wolting 1989] [Annual Health Monitoring Conference 1990] [Escher et al. 1990] [Flatau and Vanmoorhem 1990] [Newlin et al. 1990] [Sutharshana et al. 1990] [Walker and Baumgartner 1990] [Bickford and Gage 1991] [Cannon et al. 1991] [Cruse and Mahadevan 1991] [Gardner et al. 1991] [Helmicki 1991] [Millis 1991] [Duyar and Eldem 1992] [Heller et al. 1992] [Lee and Steincamp 1992] [Leonard and Kisko 1992] [Mason and Broadhurst 1992] [Rocket Engine Propulsion ‘System 1992] [Sakala and Raines 1992] [Valenti 1992] [Buelow et al. 1993] [Mahadevan et al. 1993] [Reichmuth et al. 1993] [Sanders and Jerman 1993] [Solanyk 1993] [Wang 1993b] [Health Monitoring and Controls 1994] [Kato et al. 1995] [Shepard and Patino 1995] [Anderson et al. 1996] [Brown 1996] [Murphy and Voss 1996] [Ungewitter et al. 1996] [Wu et al. 1996b] [Dunn et al. 1998] [Huang and Weber 1998] [Sauvageau and Allen 1998] [Zhang et al. 1998] [Escher et al. 1999] [Huang and Weber 1999] [Liu and Wang 1999] [Pytanowski 1999] [Maggio and Pellacio 2000] [Butas et al. 2001] [Gurov 2001] [Kazukiewicz 2001] [Kinzie et al. 2001] [Santi 2001] [Daren and Jianbo 2002] [Guikema and Pate-Cornell 2003] [Wu et al. 2003b] [Research on the High 2004] [The Use of Artificial 2004] [Unal et al. 2004] [Buswell 2005] [Hill and Acosta 2005] [Huang et al. 2005] [Schwabacher 2005] [Wu 2005] [Hara et al. 2006] [Cotae et al. 2007] [Krevor and Wilhite 2007a] [Maemura and Igarashi 2007] [Martin 2007] [Rusick 2007] [Safie and Weldon 2007b] [Safie and Weldon 2007a] [Schwabacher et al. 2007] [Verma et al. 2007] [Anderson et al. 2008] [Horisawa et al. 2008] [Lurui Xia et al. 2008] [Aytulun and Ermis 2009] [Gelder and Bos 2009] [Losik 2010c] [Manning et al. 2010] [Morse et al. 2010] [Gao et al. 2012] [Holladay et al. 2012] [Li et al. 2012] [Mattenberger et al. 2012] [Hirata and Yonezawa 2013] [Marcos et al. 2013] [Roshanian and Ebrahimi 2013] [Yonezawa et al. 2013] [Corl et al. 2014] [Huang 2014] [Kim and Hwang 2014] [Safie et al. 2014] [Intelligent Fault Diagnosis 2015] [Daniel et al. 2016] [Kanazaki et al. 2016] [Zhang 2016a] [Du 2017a] [Isono et al. 2017] [Murugesan et al. 2018] [Huang and Aguilar 2019] [Iwaguchi et al. 2019] [Li et al. 2019a] [Podolchak 2019] [Trifonov et al. 2019] [Ireland and Gonzales 2020] [Li et al. 2020] [Liang et al. 2020] [Richardson et al. 2020] [Flora and Auxillia 2020] [Dolgopolov et al. 2021] [Liao et al. 2021] [Zeng et al. 2021] [Li et al. 2022c] [Niu et al. 2022] [Pedari and Ossareh 2022] [Zhang et al. 2022b] [Nagappa 2023] [Shi et al. 2023] [Xiang 2023] [Biao et al. 2024] [Gulczyński et al. 2024] [Hornyák 2024] [Huang et al. 2024a] [Lakshmipuram Raghu et al. 2024] [Ma et al. 2024b] [Murata et al. 2024b] [Murata et al. 2024a] [Ren et al. 2024] [Cha and Ko 2025] [Kayser et al. 2025] [Navarro-Tapia et al. 2025] [Ram et al. 2025] [Zhang et al. 2025c] [Chen et al. 2026a] [Etzenbach et al. 2026] [Heldens et al. 2026] [Kumar and Shine 2026] [Santhoshkumar et al. 2026] [Xiao et al. 2026] [Craig et al] [Craig et al] [Benzing et al] [Engine Monitoring System Reliability] [Fernandez] [Liquid Rocket Engine Reliability] [Murata] [Pooley et al] [Pugh]
Steering without a gimbal, and allocating thrust among many
Thrust vector control of every kind, launch vehicle attitude control, thrust allocation among many thrusters, and jets injected into a supersonic crossflow.
708 records. [Burdett 1946] [Blaszak and Fahrenholz 1960] [McAulay and Pavli 1960] [Wu et al. 1961] [Drewry and Harmoning 1962] [Fox et al. 1962] [Newton and Spaid 1962] [Shandor and Walker 1962] [Broadwell 1963b] [Broadwell 1963a] [Gagnon et al. 1963] [Green and McCULLOUGH 1963] [Karamcheti and Tao-Sze Hsia 1963] [Baxter 1964] [Billet 1964] [Charwat and Allegre 1964] [Conrad 1964] [James and Young 1964] [Kirby and Van Vooren 1964] [Klenk 1964] [Salemka 1964] [Sehgal and Wu 1964] [Shandor 1964] [Baxter 1965] [Guhse 1965] [Hall 1965] [Hollstein 1965] [Jones 1965] [Kilpatrick 1965] [Minimax Attitude Control 1965] [Moody and Nakai 1965] [Pneumatic Digital Actuator 1965] [Study of Selected Thrust 1965] [Summer 1965] [Digital Compensation 1966] [Guhse 1966] [Inouye and Nottage 1966] [Phillips 1966] [Proportional Solid Propellant Secondary 1966] [Robbins and Zebrowski 1966] [Smith 1966] [Summer 1966b] [Summer 1966a] [Borsody et al. 1967] [Budris 1967] [Curtis and Hagstrom 1967a] [Curtis and Hagstrom 1967b] [Delozier and Kasselmann 1967] [Hansen et al. 1967] [Hardy et al. 1967] [Lindquist 1967] [McIntosh et al. 1967] [Phillips 1967] [Voyager Spacecraft System Task 1967] [Blackstone 1968] [Blatter and Keranen 1968] [Borsody and Teren 1968] [Borsody et al. 1968] [Chisel and Rose 1968] [Daniele and Teren 1968] [Hung and Thompson 1968] [Investigation of Gaseous Secondary 1968] [Jenkins and Roy 1968] [Neilson et al. 1968c] [Neilson et al. 1968b] [Neilson et al. 1968a] [Phillips 1968] [Borsody et al. 1969] [Cassel et al. 1969] [Comparin and Wilson 1969a] [Comparin and Wilson 1969b] [Harper 1969] [Leondes et al. 1969] [Penchuk and Schlundt 1969] [Rivard 1969] [Smith 1969b] [Abbott and Walker 1970] [Avduevskii et al. 1970] [Boland 1970] [Erickson et al. 1970] [Jenkins 1970] [Keltz and Ringwall 1970] [Moody 1970] [Nara et al. 1970] [Thompson and Hung 1970] [Thrust Vector Control TVC 1970a] [Thrust Vector Control TVC 1970b] [Aerojet Nuclear Systems Co., Sacramento, Calif. (USA) 1970] [Widnall 1970] [Wilson and Comparin 1970] [Doyle 1971] [Eatough 1971] [Fleischer and McGlinchey 1971] [Sayles and Levinsky 1971] [Seltzer and Siljak 1971] [Wong 1971] [Yamanaka 1971] [Guhse and Thompson 1972] [Nunn and Brandt 1972] [Burgess 1973] [Cauzza and Mockenhaupt 1973] [Kirkley 1973] [Shrewsberry 1973] [Vandierendonck et al. 1973] [Herbert and Reinhardt 1974] [McGlinchey 1974] [Solid Rocket Thrust Vector 1974] [Toney 1974] [Counter and Brinton 1975] [Huskey 1975] [Woodberry 1975] [Zeamer 1975] [Esker 1976] [Masuya et al. 1976] [Pickell 1976] [Capone and Maiden 1977] [Experimental Studies on Thrust 1977] [Levi and Stahlhuth 1977] [Zeamer 1977] [Kosmann et al. 1978] [Lloyd and Thorp 1978] [Pagan 1978] [Peters 1978] [Chinn et al. 1979] [Effects of Reynolds Number 1979] [Finnerty and Price 1979] [Fitzgerald and Kampe 1979] [Fujimoto and Shigemoto 1979] [Pagan 1979] [Space Transportation System Solid 1979] [Strickland and Shigemoto 1979] [Lominick 1980] [McCool et al. 1980] [Price 1980a] [Giragosian 1981] [Pagan 1981] [Ellis and Kearney 1982] [Haloulakos 1982] [Jonsson and Malmberg 1982] [Penchuk and Croopnick 1982] [Re and Berrier 1982] [Scarboro 1982] [Turner 1982] [Akiba et al. 1983] [Carroll and Cox 1983] [Drzewiecki 1983] [Penchuk and Croopnick 1983] [Redmon 1983] [Bell 1984] [Berrier and Leavitt 1984] [Wooten et al. 1984] [Wu and Chow 1984] [Leavitt 1985a] [Wie 1985] [Capone and Mason 1986] [Cunningham et al. 1986] [Hokenson 1986] [Imlay 1986] [Leitner 1986] [Mason and Burley 1986] [Porzio and Franke 1986] [Simmons 1986] [Wilson and Riccio 1986] [Yezzi and Donguy 1986] [Bare and Reubush 1987] [Branislav et al. 1987] [Capone and Bare 1987] [Simmons et al. 1987] [Berrier 1988] [Berrier and Mason 1988] [Lambert and Franke 1988] [Mason and Berrier 1988] [Mockenhaupt 1988] [Taylor 1988] [Wilson 1988] [Berdoyes 1989] [Boelitz 1989] [Dhuyvetter and Lam 1989] [Schirmer and Capone 1989] [Talda and Franke 1989] [Wassom et al. 1989] [Whitesides et al. 1989] [Berrier and Taylor 1990] [Bursey and Dickinson 1990] [Capone et al. 1990] [Cavalleri et al. 1990] [Friddell and Franke 1990] [Roth 1990] [Soong 1990] [Taylor 1990] [Carpenter et al. 1990] [Tiarn and Cavalleri 1990] [Adler et al. 1991] [Azevedo 1991] [Carpenter 1991] [Carson and Capone 1991] [Caton and Franke 1991] [Cavalleri et al. 1991] [Cowan and Myers 1991] [Dodge and Kana 1991] [Hermanson and Winter 1991] [King et al. 1991] [Lutze et al. 1991] [Ryan and Franke 1991] [Saugen and Adler 1991] [Wehmueller and Hauser 1991] [White 1991] [Wing and Asbury 1991] [Berdoyes and Ellis 1992] [Capone et al. 1992a] [Carpenter et al. 1992] [Cowan and Myers 1992] [Doonan and Kuchar 1992] [Hamke et al. 1992] [Johnson 1992] [Murray 1992] [Prins et al. 1992] [Schmidt 1992] [Wing and Asbury 1992] [Aso et al. 1993] [Capone and Schirmer 1993] [Chiarelli et al. 1993] [Cowan and Weir 1993] [Donat 1993] [Enright 1993] [Lamb 1993] [Weir and Cowan 1993] [Wing and Capone 1993] [Intelligent Hierarchical Thrust Vector 1994] [Whitesides et al. 1994] [Wing 1994b] [Wing 1994a] [Zubkov et al. 1994] [Aso et al. 1995] [Bechtel and Hall 1995] [Byrd et al. 1995] [Federspiel et al. 1995] [Gal-Or 1995] [Hawkes and Franke 1995] [Knauber 1995b] [Knauber 1995a] [Lamb 1995] [Matesanz et al. 1995] [Sahinkaya and Cordova 1995] [Shani et al. 1995] [Chiang et al. 1996] [Huang et al. 1996] [Merryman and Hall 1996] [Rahaim et al. 1996] [Washington et al. 1996] [Giuliano et al. 1997] [Reaction Thruster Attitude Control 1997] [Taur et al. 1997] [Ulizar 1997] [Wing and Giuliano 1997] [Wing et al. 1997] [Deere 1998] [Divo et al. 1998] [Dotson et al. 1998] [Flamm 1998] [Jetevator for Rocket Engine 1998] [Orme and Sims 1998] [Schinstock et al. 1998] [Alvi and Strykowski 1999] [Divo et al. 1999] [Grinstein and DeVore 1999] [Mori 1999] [Yagle et al. 2000] [Blanchet and Bartos 2001] [Burnes et al. 2001] [Cho et al. 2001] [Dovey et al. 2001] [Gal-Or 2001] [Palaniswamy et al. 2001] [Suzuki 2001] [deChamplain et al 2002] [Fu-Kuang Yeh et al. 2002] [Hamel et al. 2002] [Hodel et al. 2002] [Ko and Yoon 2002] [Rani et al. 2002] [Williams and Vittal 2002] [Baksi et al. 2003] [Deere et al. 2003] [Figueiredo 2003] [Hamel et al. 2003] [Harrisson et al. 2003] [Hornung et al. 2003] [Sung and Hwang 2003] [Waithe and Deere 2003a] [Waithe and Deere 2003b] [Bukhari et al. 2004] [Park 2004] [Ghasemi Nejhad 2004] [Rainville et al. 2004] [Sun and Amano 2004] [Lee 2004b] [Yu et al. 2004b] [Yu et al. 2004a] [Min 2005] [Sun 2005] [Collins 2005] [Deere et al. 2005] [Flamm et al. 2005] [Ghenai et al. 2005] [Krishnaswamy and Bugajski 2005] [Ma and Ghasemi-Nejhad 2005] [Oh and Bang 2005] [Sackheim et al. 2005] [Srinivasan and Bowersox 2005] [Erdem et al. 2006] [Flamm et al. 2006] [Goldsborough 2006] [Guangshang and Xiaosha 2006] [Mangin et al. 2006] [Michael A. 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al. 2023] [Sai and Manideep 2023] [Salimi et al. 2023] [Sopegno et al. 2023] [Srivastava and Jayachandran 2023] [Wu et al. 2023b] [Zhang et al. 2023e] [Zhang et al. 2023f] [Andréa F. C. de S. Yamada et al. 2024] [Bijo and Kumar Ranjith 2024] [Chen et al. 2024c] [Computational and Experimental Analysis 2024] [Das et al. 2024b] [Garg et al. 2024] [He et al. 2024b] [Inturi et al. 2024] [Jiang et al. 2024] [Jung et al. 2024] [Kim et al. 2024] [Stepp 2024a] [Stepp 2024b] [Nayebi and Taeibi Rahni 2024] [Orr and Russell 2024] [Park et al. 2024a] [Qin et al. 2024] [Sharjad et al. 2024] [Sheth et al. 2024] [Shi et al. 2024] [Shynkarenko et al. 2024] [Thorat et al. 2024] [Ugolini et al. 2024] [Wang et al. 2024d] [Wu et al. 2024a] [Yang et al. 2024a] [Zhang et al. 2024b] [Zhang et al. 2024a] [Zhang et al. 2024d] [Zhou et al. 2024e] [Adaptive Fault Tolerant Servo 2025] [Aravindh K 2025] [Balaji et al. 2025] [Barry et al. 2025] [Benfriha et al. 2025] [Bhabar and Sharma 2025] [Chen et al. 2025a] [Chen et al. 2025e] [Harish Ragavendra et al. 2025] [Farì et al. 2025] [Gupta 2025] [Han 2025] [Hosseini et al. 2025] [Kasem and Megahed 2025] [Liu et al. 2025e] [Liu et al. 2025d] [Madduri 2025] [Naidu et al. 2025] [Negandhi et al. 2025] [Nocoń and Szmidt 2025] [Ornob et al. 2025] [Panchal et al. 2025] [Robust Super-Twisting Sliding-Mode Controller 2025] [Rumpf et al. 2025] [Sanchez et al. 2025] [Sathish et al. 2025] [Kiran et al. 2025] [Vohra and Kumar 2025] [Xu et al. 2025a] [Zhou et al. 2025e] [Zhu et al. 2025a] [Zolla et al. 2025] [Abdelwahab and Johansen 2026] [Benfriha et al. 2026] [Diz et al. 2026a] [Diz et al. 2026b] [Dong et al. 2026] [Gupta 2026] [Gupta et al. 2026] [Hoffmann and Joachimiak 2026] [Huang and Wu 2026] [Huang et al. 2026] [Jiang et al. 2026] [Jyothy et al. 2026] [Liu et al. 2026a] [Liu et al. 2026e] [Masyagin 2026] [M․V․V․ and Rajagopal 2026] [Saiki et al. 2026] [Santos et al. 2026] [Tcherak et al. 2026a] [Thrust Vector Control 2026] [Xue et al. 2026] [Yadav et al. 2026] [Ye et al. 2026] [Zhang et al. 2026a] [Wang et al. 2027] [Stuart and McEnulty] [Byrd and Parker] [Chambon] [Russell et al] [Russell et al] [Das et al] [Dong Hyun Kim and Jae Weon Choi] [Franz and Limbert] [Bae and Summers] [Hwang] [Orr and Russell] [Orr et al] [Wall] [Wall et al] [Omoragbon et al] [Sifer et al] [Wu] [Wu] [Zmijanovic]
The machinery that feeds the nozzle
Turbopumps, gas generators, injectors, feed systems, valves, combustion and combustion instability, ignition and start transients, propellants and engine control.
1,791 records. [Youngquist 1947] [Abramson 1948] [Bellman and Humphrey 1948] [Ladanyi et al. 1950] [Crocco 1951] [Ordin et al. 1951] [Tischler and Bellman 1951] [Altman and Lorell 1952] [Crocco 1952] [Elias and Gordon 1952] [Huff and Gordon 1952] [Ladanyi 1952] [Princeton Univ Nj 1952] [Seifert 1952] [Stehling 1952] [Zucrow and Beighley 1952] [Bellman et al. 1953] [Crocco and Cheng 1953b] [Crocco and Cheng 1953a] [Ellis et al. 1953] [Gordon and Huff 1953] [Grey 1953] [Mantler et al. 1953] [Robison 1953] [Smith and Sprenger 1953] [Kerslake and Male 1954] [Cheng 1955] [Heidmann and Auble 1955] [Hett and Gilstein 1955] [Penner and Datner 1955] [Price 1955] [Tomazic 1955] [Cheng 1956] [Huff et al. 1956] [Morgan et al. 1956] [Tischler and Humphrey 1956] [Barrère and Bernard 1957] [Elliott and Rose 1957] [Gore and Carroll 1957] [Heidmann 1957b] [Heidmann 1957a] [Matthews 1957] [Putnam and Benington 1957] [Scala 1957] [Sibley and Peterson 1957] [Dean and Shurley 1958] [Douglass and Nored 1958] [Feiler 1958] [Gordon 1958] [Kluger and Farrel 1958] [Osborn and Schiewe 1958] [Clark et al. 1959] [Douglass et al. 1959] [Ehlers et al. 1959] [Elverum and Staudhammer 1959] [Feodosiev and Siniarev 1959b] [Gordon and McBride 1959] [Harrje 1959] [Kinney et al. 1959] [Krebs and Hart 1959] [Messing 1959] [Spalding 1959] [Analysis of Pressure Feasibility 1960] [Combustion Instability in Solid 1960] [Crocco et al. 1960] [Instrumentation for Research 1960] [Mantler 1960] [Otto and Flage 1960] [Review of Experimental Research 1960] [Variable Thrust Rocket Engines 1960] [Hersch 1961] [Ingebo 1961] [Osborn and Bonnell 1961] [Osborn and Davis 1961] [Sheer 1961] [Sievers et al. 1961] [Wasserbauer and Tabata 1961] [Coulbert 1962a] [Campbell et al. 1962] [Crabtree 1962] [Crocco et al. 1962] [Fuel Additive 1962] [Gale and Moedt 1962] [Harrje et al. 1962] [Jensen et al. 1962] [Lambiris and Combs 1962] [Lubick et al. 1962] [Noel and Massier 1962] [Steady-Standte Combustion Measurements in 1962] [Aerojet-General Corp Sacramento Ca 1963] [Artamanov 1963] [Aukerman and Church 1963] [Batha et al. 1963] [Bragg 1963] [Brownlee 1963] [Brownlee and Roberts 1963] [Coulbert 1963] [Harper and Witte 1963] [Il’Yashenko 1963] [Lawhead and Combs 1963] [Rabensteine 1963] [Spisz 1963] [Welton et al. 1963] [Bailey 1964] [Bonnell 1964] [Combs and Hoehn 1964] [Conrad et al. 1964] [Heidmann 1964] [Campbell et al. 1964] [MacGregor 1964] [McCormack 1964] [Price 1964] [Reardon et al. 1964] [Smith 1964] [Stein 1964] [Tellier 1964] [Masters 1965b] [Beer 1965] [Beltran and Frankel 1965] [Blackman et al. 1965] [Combs and Schuman 1965] [Dabora et al. 1965] [Fashbaugh and Streeter 1965] [Gouse et al. 1965] [Hefner 1965] [Hornstein 1965] [Jones et al. 1965] [Levine 1965] [Masters 1965a] [Price 1965] [Roelke 1965] [Rupe 1965] [Tedrick 1965] [Waesche and Summerfield 1965] [Wong and Brown 1965] [Beltran and Kosvic 1966] [Breshears et al. 1966] [Brunner 1966] [Buffum et al. 1966b] [Buffum et al. 1966a] [Bushnell and Busse 1966] [Cooper 1966] [Curren and Krueger 1966] [Harrje and Sirignano 1966] [Deppe 1966] [Escher 1966] [Eulner et al. 1966] [Evans et al. 1966] [Farquahr and Lindley 1966] [Gary 1966] [Green 1966] [Kirby and Young 1966] [Letson 1966] [McCLURE et al. 1966] [Povinelli 1966] [Purdy 1966] [Reynolds 1966a] [Reynolds 1966b] [Ritter 1966] [Roesch 1966] [Shelberg 1966] [Spadaccini 1966] [Tobey and Bastress 1966] [Luscher 1966] [Weiss 1966] [Winstead 1966] [Zinn 1966b] [Zinn 1966a] [Abbe et al. 1967] [Adelberg 1967] [Baker 1967] [Bastress et al. 1967] [Black et al. 1967] [Bloomer et al. 1967] [Bowman 1967] [Breshears et al. 1967] [Burstein 1967] [Carey 1967] [Clayton et al. 1967] [Friedman et al. 1967] [Hoff 1967] [Milleman 1967] [Mitchell 1967] [PlEPER et al. 1967] [Price and Dehority 1967] [Riebling 1967] [Shinn 1967] [Bickford 1968] [Clayton 1968] [Filimonov 1968] [Goelz 1968] [Green 1968] [Hannum et al. 1968] [Mayberry et al. 1968] [McMullen and Purgalis 1968] [Fontaine et al. 1968] [Reinhardt 1968] [Williams 1968a] [Baker 1969] [Bassham et al. 1969] [Clapp et al. 1969] [Crocco 1969] [Larson 1969] [Matthews and Wuerker 1969] [Mitchell 1969] [Mitchell et al. 1969] [Powell 1969] [Rogero 1969] [Smith 1969a] [Stanley 1969] [Zinn and Savell 1969] [Burstein et al. 1970] [Campell et al. 1970] [Combs 1970] [Edelman et al. 1970] [Hardesty 1970] [Harvey 1970] [Lynch 1970] [McHale and Nurick 1970] [Powell and Zinn 1970] [Sachs and Young 1970] [Sutton 1970] [Young 1970] [Abreu et al. 1971] [Analysis of the Longitudinal 1971] [Babcock and Coe 1971] [Butner and Keller 1971] [Culick 1971] [Dyer and Warner 1971] [Jakobsen and Keller 1971] [McHale 1971] [McLain 1971] [Nurick 1971] [Patch 1971] [Ritter 1971] [Rousar 1971] [Zinn and Powell 1971] [Ankarsward 1972] [Buckmann 1972] [Burstein et al. 1972] [Combs 1972] [Culick 1972] [Design Criteria Monograph 1972] [Dyer and Warner 1972] [Experimental Investigation of Combustor 1972] [FLOX/MMH Rocket Engine Assemblies 1972] [Franciscus 1972] [Stinson and Gross 1972] [Harney et al. 1972] [Krebs 1972] [Liquid Rocket Engine Turbopump 1972] [Pritz and Schoner 1972] [Counts 1972] [Schuler et al. 1972] [Sternfeld 1972] [Study of Solid Rocket 1972b] [Walsh and Jacoby 1972] [Winter et al. 1972] [Zinn et al. 1972] [Boylan and Ohara 1973] [Calhoon et al. 1973b] [Calhoon et al. 1973a] [George 1973] [Herr and Choenman 1973] [Jackman 1973] [Karnesky and Colucci 1973] [Liquid Rocket Engine Centrifugal 1973] [Liu 1973] [Lores and Zinn 1973] [Nurick and Hines 1973] [Omori 1973] [Powell and Zinn 1973] [Schmucker 1973c] [Shen and Adamson 1973] [Shoji 1973] [Some Experiments Related 1973] [Combs 1974] [Dowell et al. 1974] [Janardan et al. 1974] [Keesler 1974] [Liquid Rocket Engine Combustion 1974] [Liquid Rocket Engine Turbines 1974] [Liquid Rocket Engine Turbopump 1974] [McHale 1974] [Mitchell et al. 1974] [Saha 1974] [Schindler 1974] [Seidel 1974] [Tobin and Pauckert 1974] [Daniels 1975] [Dederra 1975] [Design Criteria Monograph 1975] [Ellis and Keller 1975] [Janardan et al. 1975] [Lebas et al. 1975] [Padmanabhan et al. 1975] [Powell et al. 1975] [Smith et al. 1975] [Space Shuttle Orbital Maneuvering 1975] [Twardy 1975] [Gill and Nurick 1976] [George 1976] [Hannum et al. 1976] [Kolesovas and Svitra 1976] [Macaluso 1976] [Saha 1976] [Barrère 1977] [Brunner and Buse 1977] [Burcham and Boynton 1977] [Cunningham and Morrisey 1977] [Holcomb et al. 1977] [Janardan et al. 1977] [Jesen 1977] [Osborn et al. 1977] [Burcham and Keller 1978] [Evans and Smith 1978] [Martin 1978] [Quentmeyer et al. 1978] [Scheer et al. 1978] [Spencer et al. 1978] [Sternfeld 1978] [Strahle and Handley 1978] [Tou et al. 1978] [Wilhite 1978] [Yost 1978] [Eberle and Kusak 1979] [Janardan et al. 1979b] [Janardan et al. 1979a] [Mellish 1979] [Pavli 1979] [Solid Rocket Motor Plume 1979] [Valler 1979] [Ventrice et al. 1979b] [Ventrice et al. 1979a] [Appel and Kruger 1980] [Boretz et al. 1980] [Burcham and Diamond 1980] [Christensen 1980] [Judd 1980] [Mellish 1980b] [Price 1980b] [Etters and Flurchick 1981] [Kamijo et al. 1981] [Liquid Rocket Propulsion Technology 1981a] [Liquid Rocket Propulsion Technology 1981b] [Powers et al. 1981] [Smith and Stechman 1981] [Baum and Levine 1982] [Hart 1982] [Heubner 1982] [Judd 1982] [Kaczmarek et al. 1982] [Kamijo et al. 1982] [LaBotz and Ewen 1982] [Levine and Baum 1982] [Lewis and Lin 1982] [Niino et al. 1982] [Porowski et al. 1982] [Schoenman 1982] [Appel et al. 1983] [Badlani et al. 1983] [Burcham 1983] [Girata and McGregor 1983] [Glass and Martinez 1983] [Kamijo 1983] [Martinez and Fulton 1983] [Okayasu et al. 1983] [Pollet 1983] [Schoenman 1983] [Alter et al. 1984] [Baum and Levine 1984] [Boyd 1984] [Fang 1984] [Ferrenberg 1984] [Hampson 1984] [Hardgrove and Krieg 1984] [Lourme et al. 1984] [Particle Sampling of Solid 1984] [Postfire Sampling of Solid 1984] [Povinelli et al. 1984] [Przekwas et al. 1984a] [Przekwas et al. 1984b] [Chandler 1985] [Cheng 1985] [Cody et al. 1985] [Gulbrandsen et al. 1985] [Huang 1985] [Liang et al. 1985] [Parr et al. 1985] [Shimura and Kamijo 1985] [Armstrong 1986] [Chiu 1986] [Cikanek 1986b] [Collins et al. 1986] [Furst 1986] [Hankins 1986] [Praharaj and Palko 1986] [Price and Masters 1986] [Przekwas et al. 1986a] [Visek 1986] [Vonpragenau 1986] [Wislicenus 1986] [Chiu 1987] [Cox 1987] [Dang and Nickerson 1987] [Desnoyer 1987] [Freeman et al. 1987] [Furst et al. 1987] [Gross 1987] [Hoffman 1987] [Jia 1987] [Lecourt and Foucaud 1987] [Lim and George 1987] [Meng et al. 1987] [Price and Flandro 1987] [Schoenman 1987] [Siebenhaar and Campbell 1987] [Visek 1987] [Wei 1987] [Wyett et al. 1987] [Ali and Crawford 1988] [Bartrand 1988] [Cosens and Newton 1988] [Cox 1988] [Farvin and Peddieson 1988] [Fuchs et al. 1988] [Gordon and McBride 1988] [Holzmann and Hayden 1988] [Keba and Beatty 1988] [Masters et al. 1988] [Merrill and Lorenzo 1988] [Naraghi and Armstrong 1988] [Priem and Breisacher 1988] [Alcock and Hagar 1989] [Armstrong 1989] [Arreguin 1989] [Bryant 1989] [Buckmann et al. 1989] [Cook et al. 1989] [Graves et al. 1989] [Hagar and Alcock 1989] [Hammad and Naraghi 1989] [Kanmuri et al. 1989] [Kelley and Thompson 1989] [Madabhushi et al. 1989] [Mason and Southwick 1989] [Norman et al. 1989] [Pieper and Muss 1989] [Rao and Dill 1989] [Schoenman 1989] [Trinh and Gross 1989] [Tulpule 1989] [Armstrong and Schlumberger 1990] [Brockmeyer and Schnittgrund 1990] [Brown 1990] [Collins et al. 1990b] [Dirusso and Brown 1990] [Evces 1990] [Fang 1990] [Farr and Sanders 1990] [Greenhill 1990] [Grosdemange and Schaeffer 1990] [Jurado et al. 1990] [Kazaroff and Pavli 1990] [Kehtarnavaz et al. 1990] [Klem et al. 1990] [Klem 1990] [Lebrun and Ngendakumana 1990] [Martinez et al. 1990] [Meyer and Zakrajsek 1990] [Neary 1990] [Norman et al. 1990] [Quentmeyer 1990] [Ruth et al. 1990] [Wang 1990] [Wang and Chen 1990] [Williams et al. 1990] [Zaller 1990] [Anex et al. 1991] [Baudart et al. 1991] [Beichel et al. 1991] [Benjamin and McConnaughey 1991] [Bentsman et al. 1991] [Chow and Jin 1991] [Daidzic et al. 1991] [Dubois and Habiballah 1991] [Erickson and Hertzberg 1991] [Erland 1991] [Glassman and Jones 1991] [Green et al. 1991] [Grenda et al. 1991] [Herbell and Eckel 1991] [Heshmat 1991] [Hooper and Kostusak 1991] [Hung 1991] [Hybrid Rocket Propulsion 1991] [Jassowski et al. 1991] [Jeng and Litchford 1991] [Kuo et al. 1991] [Limerick 1991a] [Lui and Mason 1991] [Musgrave 1991] [Muss et al. 1991] [Petersen et al. 1991] [Roncace 1991c] [Sankar et al. 1991] [Schneider 1991b] [Schneider 1991a] [Venkateswaran et al. 1991] [Volkmann et al. 1991] [Whitehead 1991] [Yang 1991] [Anderson et al. 1992b] [Berque and Georges 1992] [Binder et al. 1992] [Bunker and Prince 1992] [Design of Rocket-Engine Control 1992] [Design of Turbopump Propellant 1992] [Giridharan et al. 1992b] [Giuliani and Klem 1992a] [Giuliani and Klem 1992b] [Habiballah et al. 1992] [Herbell and Eckel 1992] [Huynh et al. 1992] [Jiang and Chiu 1992] [Kim et al. 1992b] [Kim et al. 1992a] [Krishnan et al. 1992] [Lapp and Quesada 1992] [Liang and Ungewitter 1992] [Litchford and Jeng 1992] [Lohr and Trinh 1992] [Lorenzo and Musgrave 1992] [Giridharan et al. 1992a] [Masters and Galler 1992] [Mayer and Kruelle 1992] [McAmis et al. 1992] [Meyer 1992] [Moracz et al. 1992] [Pal et al. 1992] [Peschka 1992] [Ramamurthi and Jayashree 1992] [Riccio and Hoppe 1992] [Sankar et al. 1992] [Sgarlata and Weegar 1992] [Sharma et al. 1992] [Solid Rocket Combustion Instability-An 1992] [Tran et al. 1992] [Tseng and Yang 1992] [Veres 1992] [Walker and Baumgartner 1992] [Wang and Van 1992] [Advanced Launch System. Advanced 1993] [Analysis and Effects 1993] [Anderson et al. 1993] [Ascoli et al. 1993] [Benjamin et al. 1993] [Bumb and Hawk 1993] [Burch and Cheung 1993] [Chase and McCarty 1993] [Chen et al. 1993] [Cox 1993] [Crone et al. 1993] [Delplanque and Sirignano 1993] [Dressler et al. 1993] [Feng et al. 1993] [Follett et al. 1993] [Heat Transfer in Rocket 1993] [Howell et al. 1993] [Huber et al. 1993] [Hutt et al. 1993] [Huzel 1993] [Kearney and Moss 1993] [Kiris and Chang 1993] [Kukushkin and Ivanchenko 1993] [Lin et al. 1993] [Lo et al. 1993] [Maram 1993] [Mitchell 1993] [Newell and Rajagopal 1993] [Niiya et al. 1993] [Pal et al. 1993] [Rapp 1993] [Ratcliff et al. 1993] [Jankovsky et al. 1993] [Santi 1993] [Santi and Helmicki 1993] [STE Thrust Chamber Technology 1993] [Stechman 1993] [Sutton and Lariviere 1993] [Talley 1993] [Veres 1993] [Wang and Chen 1993] [Wernimont 1993] [Yamada et al. 1993] [Cox 1994] [Feikema 1994] [Ingebo 1994] [Jenkins 1994] [Lacefield and Sprow 1994] [Landrum 1994] [Liou 1994] [Marsh and Cowan 1994] [Padavala and Palazzolo 1994] [Palaszewski 1994] [Pervaiz et al. 1994] [Sreeyesunath and Sugathan 1994] [Surko 1994] [Wang and Luong 1994] [Thornburg et al. 1994] [Wickman 1994] [Yoon 1994] [Yoon et al. 1994] [Anderson et al. 1995] [Andreev et al. 1995] [Ballard 1995] [Ceramic Composites Used 1995] [Combustion Instability Analysis 1995a] [Combustion Instability Analysis 1995b] [Cooperative Testing of Rocket 1995] [Dubois et al. 1995] [Fundamental Mechanisms of Combustion 1995b] [Fundamental Mechanisms of Combustion 1995e] [Fundamental Mechanisms of Combustion 1995g] [Fundamental Mechanisms of Combustion 1995a] [Fundamental Mechanisms of Combustion 1995d] [Fundamental Mechanisms of Combustion 1995f] [Fundamental Mechanisms of Combustion 1995c] [Goertz 1995] [Instability Phenomenology and Case 1995c] [Instability Phenomenology and Case 1995d] [Instability Phenomenology and Case 1995b] [Instability Phenomenology and Case 1995a] [Karpov 1995] [Kazaroff et al. 1995] [Keith and Moser 1995] [Life Prediction 1995] [Anderson and Yang 1995] [Liu et al. 1995] [Lorenzo 1995] [M 1995] [Maskery et al. 1995] [McAmis 1995] [Palaszewski and Zakany 1995] [Qi 1995] [Ray and Dai 1995] [Roh and Yang 1995] [Romine 1995] [Sergienko et al. 1995] [Stability Testing Methodology 1995] [Turushov et al. 1995] [Whitesides et al. 1995] [Wu et al. 1995] [Yagodnikov et al. 1995] [Acoustic Sensitivity Measurements 1996] [Brummund et al. 1996] [Carrick 1996] [Cezzar 1996] [Dai and Ray 1996a] [Dai and Ray 1996b] [Delplanque and Sirignano 1996] [Goldey et al. 1996] [Immich and Caporicci 1996] [Isaac 1996] [Kozlov et al. 1996] [Linne 1996] [Mayer and Tamura 1996] [Numerical Simulation of High-Frequency 1996] [Palaszewski and Zakany 1996] [Peery and Parsley 1996] [Popp and Schmidt 1996] [Schley et al. 1996] [Tarrant and Crook 1996] [Theoretical Rocket Performance 1996] [Wang et al. 1996] [Wu et al. 1996a] [Zhou et al. 1996] [Beard et al. 1997] [Cheng et al. 1997] [Cook et al. 1997] [Davis et al. 1997] [Golovitchev and Krulle 1997] [Holmes et al. 1997] [Kassoy 1997] [McNelis et al. 1997] [Oates 1997] [Palaszewski and Palaszewski 1997] [Reardon 1997] [Sutton et al. 1997] [Wadel and Wadel 1997] [Wehrmeyer et al. 1997] [Bazarov 1998] [Bazarov and Yang 1998] [Chehroudi et al. 1998] [Clinton et al. 1998] [Crook and Tarrant 1998] [Doulatov et al. 1998] [Fazah and Cramer 1998] [Garcia et al. 1998] [Gribben et al. 1998] [Halmes et al. 1998] [Liu et al. 1998] [Lorenzo et al. 1998] [Palaszewski 1998c] [Palaszewski et al. 1998] [Rocker and Nesman 1998] [Roh and Culick 1998] [Roh et al. 1998] [Santoro 1998] [Schaefer 1998] [Schallhorn et al. 1998] [Zhuang et al. 1998] [Beyer et al. 1999] [Bosson and Goirand 1999] [Buntain and Lueders 1999] [Cezzar 1999] [Clayton 1999] [Doulatov et al. 1999] [Ebrahimi et al. 1999] [Farmer et al. 1999] [Genge and Marsh 1999] [Glenn 1999] [Knuth et al. 1999] [Laubacher et al. 1999] [Mah 1999] [Non-linear throttling analysis of 1999] [Oliphant and Japikse 1999] [Osherov and Natan 1999] [Pettit et al. 1999] [Prueger et al. 1999] [Rocker 1999] [Santoro and Merkle 1999] [Shyy et al. 1999] [Steinetz and Dunlap 1999a] [Steinetz and Dunlap 1999b] [Stout and Snell 1999] [Umholtz 1999] [Van Hooser et al. 1999] [Wang et al. 1999] [Wehrmeyer 1999] [Wherley et al. 1999] [Zhuang et al. 1999] [Brown et al. 2000] [Combustion Dynamics of Homogenous 2000] [Cook et al. 2000] [Cornelius et al. 2000] [Dennis and Sanders 2000] [Doulatov et al. 2000] [Eaton and Mathias 2000] [Ebrahimi et al. 2000] [Effinger et al. 2000a] [Effinger et al. 2000b] [Ellis 2000] [Farhangi et al. 2000] [Farmer and Cheng 2000] [French 2000] [Gibson et al. 2000] [Huang 2000] [Huang et al. 2000b] [Huang et al. 2000a] [Hudson et al. 2000] [Kamijo et al. 2000] [Kiris et al. 2000] [Kiris and Williams 2000] [Laroche et al. 2000] [Lorenzo et al. 2000] [Majumdar et al. 2000] [Saidyanathan et al. 2000] [Stechman et al. 2000] [Steinetz and Dunlap 2000] [Stout and Snell 2000] [Transverse Waves in Solid-Propellant 2000] [Trinh et al. 2000] [Wang et al. 2000] [Wehrmeyer et al. 2000] [Anthoine et al. 2001] [Centin and Kwak 2001] [Clayton and Phelps 2001] [Cornelius et al. 2001] [Davydov and Egorov 2001] [Farmer et al. 2001] [Hegab and Kassoy 2001] [Immich et al. 2001] [Ketsdever 2001] [Kiris et al. 2001] [Kris and Kwak 2001] [Naraghi et al. 2001] [Noonan et al. 2001] [Oyama and Liou 2001] [Pempie and Vernin 2001] [Riccius et al. 2001] [Shelley et al. 2001] [States 2001] [Thomas et al. 2001] [Trinh et al. 2001] [Ventura and WErnimont 2001] [Wennerberg and Knab 2001] [Air Force Research Lab Edwards AFB CA 2002] [Badinand and Fransson 2002] [Bergren and Franke 2002] [Bodele et al. 2002] [Bradford and Crocker 2002] [Cheng and Farmer 2002] [Chiaverini et al. 2002] [Cho and Kim 2002] [Ferguson et al. 2002] [Greene et al. 2002a] [Huang 2002b] [Huang 2002a] [Hudson et al. 2002] [Immich et al. 2002] [Kiris et al. 2002] [Knab et al. 2002] [Okayasu et al. 2002] 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2026] [Delogu et al. 2026] [Dove et al. 2026] [Drobyshev 2026] [Ebert and Manfletti 2026] [Ekimogloy et al. 2026] [El-Sayed 2026a] [Fauquet-Alekhine 2026] [Fiore et al. 2026b] [Harari 2026] [Heo et al. 2026] [Honchar 2026] [Hu et al. 2026] [Hussein et al. 2026] [Jangra et al. 2026] [Jin et al. 2026] [Kurudzija et al. 2026] [Li et al. 2026e] [liu et al 2026] [Lu et al. 2026] [Manoj et al. 2026] [Dnipro Aerospace and Marchan 2026] [Nasuti 2026] [Pages and Achipa 2026] [Prokopenko 2026] [Pshenychka 2026] [Ryazantsev et al. 2026] [Sanand et al. 2026] [Seshime et al. 2026] [Song et al. 2026] [Sung and Choi 2026] [Tang et al. 2026] [Thompson et al. 2026] [Tian 2026] [Tianpeng et al. 2026] [Tilekar et al. 2026] [Xie et al. 2026a] [Yang 2026] [Yiyao et al. 2026] [Yoon and Moon 2026] [Zhang et al. 2026c] [Zhou et al. 2026b] [Bower et al] [Petty et al] [Felippe da Silva Lui] [Ficuciello] [Fougnie] [Galli] [Gibart] [Habiballah and Monin] [Jiang] [Klimenko et al] [Lin] [Marchal] [Radke] [Radke] [Sarotte] [Space systems � Liquid] [Space systems. Liquid rocket] [Xiaowen Dai et al] [Zapata Usandivaras]
Liquid rocket engines taken whole
Liquid rocket engines described whole, their design, development and performance, where no single named engine is the subject.
67 records. [Ananoff 1941] [Lawrence 1945] [Berggren et al. 1948] [Singelmann and Mueller 1948] [Harry 1949] [Penner 1954] [Penner 1957] [Penner and Fuhs 1957] [Summerfield 1960] [Techniques for Rocket Engine 1965] [Burry et al. 1967] [Campbell 1970] [Lamont and Diem 1972] [Sanchini and Kirby 1973] [Thibodaux 1973] [Morgenthaler et al. 1974] [Obrien 1979] [Mellish 1980a] [Scheer 1980] [Martin 1981] [Wadia and Wilson 1981] [Gibson 1985] [Marsik and Morea 1985b] [Marsik and Morea 1985a] [Martinez et al. 1986] [Erickson et al. 1987] [Chiu 1988] [Manski and Martin 1988] [Davidian 1989] [Martin and Manski 1989] [Martin 1989a] [Straub 1989] [Davidian 1990] [Evaluation of Undeveloped Rocket 1990] [Martin and Kramer 1990] [Roncace 1991b] [Roncace 1991a] [Erickson 1992] [Harmon 1992] [Kuznetsov 1993] [Linne 1993] [Jones 1994] [Katorgin et al. 1995] [Linne 1997] [Green et al. 1999] [Wu et al. 1999] [Amateur Gas-Propelled Rocket Engine 2004] [Jensen 2005] [Merits of Liquid Propellant 2006] [Rothmund 2006] [Alexander et al. 2008] [Watanabe and Mikami 2010] [Greatrix 2012b] [Stuber et al. 2012b] [Sforza 2017] [Tizón and Roman 2017] [de Iaco Veris 2020] [Basharina et al. 2021] [Lederer 2021] [Morehart 2021] [Perez et al. 2024] [Chaudhary et al. 2025] [Musielak 2025b] [Sheiko 2025] [Sukachevskyi 2026] [Liquid propellant rocket engines] [Ozelsel]
Heat, cooling and erosion in chambers and nozzles
Heat transfer, cooling, ablation, erosion and materials of thrust chambers and nozzles.
190 records. [Bartz 1958] [Rose 1958] [Colucci 1960] [Robbins et al. 1960] [Hoertel 1961] [Viventi 1961] [Coulbert 1962b] [Batchelor et al. 1963] [Gordon and Brown 1963] [Kammer et al. 1963] [Lee 1963] [Carden 1964] [Elkind 1964] [Kendall and Rindal 1964] [Lee 1964] [Perez 1964] [Slosarik and Swope 1964] [Boldman et al. 1966] [Curley et al. 1966] [Dahm and Schaefer 1966] [Flood et al. 1966] [Freche et al. 1966] [Johnston et al. 1966] [Meyer and Peterson 1966] [Puthoff 1966] [Roland et al. 1966] [Rollbuhler et al. 1966] [Smallwood 1966] [Carden et al. 1967] [Cox and Turney 1967] [Curren et al. 1967] [Derderian et al. 1967] [Peterson 1967] [Price et al. 1967] [Dahm et al. 1968] [Davis 1968] [Eppinger et al. 1968] [Herrick 1968] [Moody and Price 1968] [Pavli 1968] [Boldman and Graham 1969] [Boldman et al. 1969] [Moody and Price 1969] [Peterson et al. 1969] [Price 1969] [Taylor 1969a] [Taylor 1969b] [Winter and Peterson 1969] [Olsen 1970] [Taylor 1970] [Boldman et al. 1971] [Kesselring et al. 1972] [Laramee and Canfield 1972] [Kascak 1973] [Wagner 1973] [Baetz 1974] [Manning and Honeycutt 1974] [Paster and French 1974] [Baetz 1975] [Driggers 1975] [Esposito and Zabora 1975] [Lemoine 1975] [Stutzman 1975] [Blevins and Bedard 1976] [Bose 1978] [Rocket Nozzle Comprising Pyrolytic 1978] [Isshiki and Kashiwagi 1979] [Wu and Tao 1979] [Cook and Quentmeyer 1980] [Robinson et al. 1980] [Schoyer 1980] [Mehta 1981] [Brogan 1984] [Bunker and Nelson 1985] [Carbon/carbon Rocket Motor Exit 1985] [O’Driscoll et al. 1985] [Berkman and Toth 1986] [Suhoza and Bickford 1986] [Melchior et al. 1987] [Borie et al. 1988] [Das et al. 1988] [Borie et al. 1989] [Lagnado and Raiszadeh 1989] [Nesbitt 1989] [Obrien 1989] [Borg et al. 1990] [Cai and Hou 1990] [Dean et al. 1990] [Lewis et al. 1990] [Nesbitt 1990] [Wooten and Lansaw 1990] [Armstrong 1991] [Brown 1991] [Hodge and Taylor 1991] [Kacynski et al. 1991] [May and Burkhardt 1991] [Appendix C 1992] [Gregory et al. 1992] [Haire 1993] [Kim and Stubbs 1993] [Meyer and Giuliani 1993] [Schoenman 1993] [Tomsik 1994] [Weaver 1994] [Hertzberg et al. 1995] [Landis and Bowman 1996] [Landrum and Beard 1996b] [Liu and Qizhi 1996] [Micklow 1996] [Vural and Ak 1996] [Broquere and Broquere 1997] [Vandenboom and Heister 1998] [Patterson 1999] [McDonald and Wooten 2000] [Ellis et al. 2001] [Lee et al. 2001a] [Nguyen and Turner 2001] [Jones and Shukla 2002] [Ogbuji and Humphrey 2002] [Toyama 2002] [Alhama and Campo 2003] [Buffone et al. 2003] [Dickens et al. 2003] [Hoffman et al. 2003] [Jaskowiak 2003] [An 2003] [Chasman et al. 2005] [Acharya and Kuo 2006] [Candane et al. 2006] [Ellis and Nathal 2007] [Guobiao et al. 2007b] [Blaine et al. 2008] [Chen and Liu 2008] [Hwang and Yim 2008] [Sokolovsky et al. 2008] [Davidy 2009] [Morozov and de la Beaujardiere 2009] [Opila 2009] [Thakre and Yang 2009a] [Torres et al. 2009] [Acharya and Kuo 2010] [Gernoth et al. 2011] [Gonzalez and Oetjen 2011] [Lee and Baek 2011] [Wei et al. 2011] [Zhang 2011] [Minato et al. 2012] [Ellis 2013] [Keller and Kloker 2013] [Lacombe 2013] [Thakre et al. 2013] [Ulas and Boysan 2013] [Greene et al. 2015] [Thompson 2015] [Valentine et al. 2015] [Saito et al. 2016] [Sciti et al. 2016] [Cross and Boyd 2017a] [Cross and Boyd 2017b] [Kamps et al. 2017] [Bhat et al. 2018] [Ferreira and Dourado 2018] [Harms et al. 2018] [Pelevin and Ponomarev 2018] [Vinod et al. 2018] [Pelevin and Ponomarev 2021] [Karakas et al. 2022] [Mendonça de Azevedo et al. 2022] [Shin et al. 2022] [Thongsri et al. 2022] [Guram et al. 2023] [Migliorino et al. 2023] [Ozturk et al. 2023] [Reddy et al. 2023] [Saxena et al. 2023] [Kumar and Bansal 2024] [Makhija et al. 2024] [Yang et al. 2024c] [Alves et al. 2025] [Jiang et al. 2025] [Левихин and Musteikis 2025] [Niu et al. 2025] [Akbulatov et al. 2026] [Bennaceur et al. 2026] [Nagler 2026] [Okano and Haga 2026] [Thibaudeau and Whitmore 2026b] [Thibaudeau and Whitmore 2026a] [Johnston and Signorelli] [Nelson]
Small thrusters and spacecraft engines
Small chemical thrusters, spacecraft engines and attitude-control engines, as engines.
67 records. [Fio Rito 1964] [Broadwell and Marcisz 1968] [Riebling 1969] [French 1970] [Owens 1971] [Burlage et al. 1972] [Evans et al. 1972] [Hoehn 1972] [Long and Bjorklund 1972] [Martinez et al. 1972] [Smith and Sforzini 1972] [Snoke and Williams 1972] [Holcomb 1973] [Stechman and Campbell 1973] [Nichols 1975b] [Bjorklund et al. 1979] [Bond 1979] [Stechman and Drenning 1981] [Stechman et al. 1982] [Bjorklund 1983] [Berkman 1984] [Stechman 1984] [Liaw 1987] [Whalen 1987] [Finden et al. 1988] [Appel et al. 1989] [Stechman and Sumpter 1989] [Boyd et al. 1990] [Melchior 1990] [Stechman 1990] [Chou et al. 1991] [Garrison 1991] [Micci and Long 1991] [Weiss and Merkle 1991] [Chazen et al. 1992] [Schneider 1992a] [Schneider 1992b] [Schwende et al. 1992] [Chazen et al. 1993] [Chung et al. 1993b] [Chung et al. 1994a] [Karpov 1994] [Chazen et al. 1995] [Arrington et al. 1996] [Jassowski 1997a] [Jassowski 1997b] [deGroot 1999] [Lee 1999] [Dulligan et al. 2000] [Meinhart 2000] [Kujawa et al. 2003] [Reed 2003] [Stechman and Lawson 2006] [Greene 2009] [Hagiwara et al. 2009] [Dorado et al. 2013] [Tong and Fang 2014] [Cai et al. 2016] [Fujii and Ikeda 2016] [Parker 2016] [Atwell et al. 2017] [Formation and Evaporation 2018] [Banakar et al. 2020] [MIMPS-G Green Rocket Propulsion 2022] [Shawyer 2023a] [Mopuru et al. 2025] [Roohi and Mahdavi 2026]
Solid and hybrid motors, on the subjects this article uses
Solid and hybrid motors where the title’s subject is one this article uses, being the nozzle, steering, the plume, chamber acoustics or measurement.
68 records. [The Influence of Erosive 1960] [Kuby 1964] [Nonlinear Effects in Instability 1964] [Price et al. 1964] [Becker and Hamilton 1965] [Coates et al. 1965] [Hart and McClure 1965] [Becker and Tang 1966] [Two-Hundred Sixty-in.-Dia Motor Feasibility 1966] [Gungle 1967] [Summerfield and Krier 1968] [Wong 1968] [marxman and Wooldridge 1969] [Gostintsev et al. 1972] [Micci 1975] [Robertson 1975] [Donguy 1977] [Pope and Dirling 1979] [Quilici 1984] [Hwang and Chang 1987] [Edwards 1991] [Clayton 1992] [Whitney and Hennessey 1992] [Smith-Kent et al. 1995] [Clinton and Wendel 1998] [Haugen 1998] [Ewing et al. 1999] [Lui and Hyer 1999] [Effect of Acoustic Oscillation 2000] [Patel and Chang 2000] [Maw et al. 2004] [McLaughlin et al. 2004] [Peterson et al. 2004] [Erven et al. 2006] [Evans et al. 2007] [Liggett and Menon 2007] [Thakre and Yang 2007b] [Daimon et al. 2008] [Dombrovsky 2008b] [Dombrovsky 2008a] [Cai et al. 2009] [Evans et al. 2009] [Thakre and Yang 2009b] [Design of Nozzle 2011] [Bianchi and Nasuti 2013] [El-Nady et al. 2015c] [El-Nady et al. 2015b] [El-Nady et al. 2015a] [Joo et al. 2015] [Mani et al. 2015] [Park et al. 2016] [Di Martino et al. 2017] [El-Nady et al. 2017a] [El-Nady et al. 2017b] [Stephenson 2018] [Alazeezi and Elek 2019] [Nguyen 2020] [de Andrade Janene Gonini et al. 2021] [Hyun et al. 2021] [AbdelGawad and Guozhu 2022] [Chaiaiad and Thongsri 2023] [Gonini et al. 2023] [Grossi et al. 2023] [Parhi et al. 2023] [Determination of Gas Flow 2024] [Murugan et al. 2025] [Saokhede et al. 2025] [Passarani et al. 2026]
Combined-cycle rocket propulsion
Rocket propulsion combined with air-breathing modes, as in air-augmented and rocket-based combined-cycle engines.
10 records. [Kors 1990] [Fahahngi 1992] [Farhangi and Trent 1992] [Kalmykov and Yanchilin 1996] [Olds et al. 1997] [Hueter 1999] [Smith et al. 2002b] [Pastrone 2004] [Waung and Etele 2009] [Wang et al. 2022e]
Making it, which is what modular is actually for
The manufacture and cost of rocket engines and launch vehicles, including additive manufacturing of engine parts and low-cost launch.
285 records. [Baehr 1962] [Edmonds et al. 1964] [Friedland 1965] [Agosta and Hammer 1969] [Ashurst et al. 1969] [Cacha 1969] [Grim et al. 1969] [Hanford 1969] [Ross 1969] [Braun et al. 1970] [Goethert 1970] [Mosley 1970] [Ward 1970] [Ciepluch 1971] [Laber et al. 1971] [Sohl 1971] [Warga 1971] [Alford et al. 1972] [Vanderesch 1972] [Dini and Johnson 1976] [Elegante and Bowman 1978] [Hudson et al. 1981] [Fritz and Sackheim 1982] [Lane et al. 1982] [Hankins 1984] [Koelle 1984] [Meisl 1986] [French 1987] [Hudson 1987] [Hudson and Hunter 1987] [Meisl 1988] [Koelle 1989] [McKown 1989] [Meisl 1989] [Pearson 1989] [Slayton and Daniels 1989] [Strobl 1989] [Joint DoD/NASA Advanced Launch 1990] [Low-Cost Satellites and Satellite 1990] [Pegasus 1990] [Puening 1990] [Beckman and Volkmann 1991] [Szatkowski and Levin 1991] [Wagner and Cleveland 1991] [Wolfe et al. 1991] [Chapman and Nix 1992] [Koelle 1992a] [Koelle 1992b] [Low-Cost Expendable Launch Vehicles 1992] [McKechnie et al. 1992] [Sackheim 1992] [Slayton et al. 1992a] [Slayton et al. 1992b] [A New Aerodynamic Approach 1993] [Degelsmith et al. 1993] [Friedman 1993] [Gerth 1993] [Brinton et al. 1994] [Chin 1994] [Gilbert et al. 1994] [Goracke et al. 1994] [Koelle 1994] [Moser and Frazier 1994] [Sackheim 1994] [Capps et al. 1995] [Comstock et al. 1995] [Frazier and Moser 1995] [Gilbert et al. 1995] [Keith 1995] [Perroton et al. 1995] [Plachta et al. 1995] [Richter and Smith 1995] [Wilson 1995] [Bauer 1996] [Fitzsimmons 1996] [Three Phases of Low-Cost 1996] [Zubrin and Clapp 1996] [Ortwerth et al. 1997] [Zubrin et al. 1997] [Fisher and Ise 1998] [Koelle 1998] [Palaszewski 1998a] [Schmucker and Schmucker 1998] [Shaw and Greenberg 1998] [Whitfield 1998] [Crawford et al. 1999] [Effinger et al. 1999] [Koelle 1999] [London and Sumrall 1999] [Quinn 1999] [Sackheim and Gavitt 1999] [Sullivan 1999] [Tam et al. 1999] [Andrews and Andrews 2000] [Koelle 2000] [Levack 2000] [Morrison and Festa 2000] [Gopalaswami et al. 2001] [Holmes et al. 2001] [Mocio 2001] [Garvey et al. 2003] [Haynes and Karthikeyan 2003] [Pempie 2003] [Powell 2003] [Nix and Staton 2004] [Powell 2004] [Reducing the Time 2004] [StarTram 2004] [Bampton et al. 2005] [Bonometti et al. 2005] [Chase and McKinney 2005] [Chiesa et al. 2005] [Douglas and Bourgeois 2005] [Goldsborough 2005] [Hudson 2005] [Loewenthal and Ellis 2005] [Emvin et al. 2006] [Gstattenbauer et al. 2006] [Le Bar and Cady 2006] [Peters et al. 2006] [Powell 2006] [Snead 2006] [Hamilton et al. 2007] [London and Epstein 2007] [Nigg 2007] [LeMoyne 2008] [Powell and Maise 2008] [Bauer 2009] [Ryu 2009] [Tang and Chase 2009] [Maise et al. 2010] [Powell et al. 2010] [Betts et al. 2011b] [Betts and Hardin 2011] [Betts et al. 2011a] [Kim et al. 2011] [Honoré et al. 2012] [Lee et al. 2012b] [Nizhnik 2012] [Mozgov et al. 2013] [Kokan et al. 2014] [Lee et al. 2014] [Long 2014] [Protz et al. 2014] [Watson et al. 2014] [Whitten et al. 2014] [Barnett and Bullard 2015] [Calvert et al. 2015] [Carter et al. 2015] [Karuntzos 2015] [Lee et al. 2015b] [Kumar et al. 2015] [Vickers 2015a] [Vickers 2015b] [Bhat et al. 2016] [Boone and Miller 2016] [Burgaud et al. 2016] [Clinton 2016] [Coopersmith and Davis 2016] [Gradl and Brandsmeier 2016] [Gradl et al. 2016a] [Jones et al. 2016] [O’Neal 2016] [Protz et al. 2016] [Sarzi-Amade et al. 2016] [Tucker and Schmidt 2016] [West et al. 2016] [Bae et al. 2017] [Clinton 2017b] [Clinton 2017c] [Clinton 2017a] [Dupont et al. 2017] [Gradl et al. 2017] [Hayward 2017] [Hutt et al. 2017] [Kunka and Jacob 2017] [Bower and Thomas 2018] [Burlingame and Hyatt 2018] [Fikes 2018] [Garcia et al. 2018] [Gradl et al. 2018c] [Gradl et al. 2018a] [Gradl et al. 2018b] [Markusic et al. 2018] [Weuta 2018] [Zagorski et al. 2018] [3D Printed Rocket Combustion 2019] [Coleman 2019] [Gradl et al. 2019a] [Gradl et al. 2019c] [Gradl and Protz 2019] [Gradl et al. 2019b] [Gradl et al. 2019d] [Gradl et al. 2019e] [Katsarelis et al. 2019] [Stachulla et al. 2019] [McClain et al. 2019] [Patel et al. 2019] [Durkee et al. 2020] [Gradl and Protz 2020] [Gradl et al. 2020] [Mireles et al. 2020] [Bair et al. 2021] [Gradl et al. 2021] [Grigoryants et al. 2021] [Kerstens et al. 2021] [Awad Alahbabi et al. 2022] [Bao et al. 2022] [Launch Vehicle Financial Analysis 2022] [Launch Vehicle Manufacturing 2022] [Malisuwan and Kanchanarat 2022] [Thomas 2022] [Akbulatov et al. 2023] [An and Li 2023] [Buettner et al. 2023b] [Buettner et al. 2023a] [Cold Flow Characterization 2023] [Векілов and Ліповський 2023] [Kruse et al. 2023] [Chen et al. 2023] [Ryazantsev et al. 2023] [Thomas 2023] [Yi et al. 2023] [Çam and Özkol 2023] [Chandler 2024] [Fedotowsky et al. 2024] [Kim 2024b] [Motta et al. 2024] [Gradl et al. 2024] [Swain et al. 2024] [Vekilov et al. 2024] [Wilken 2024] [Barros et al. 2025a] [Barros et al. 2025b] [Chamoli 2025] [Chen et al. 2025g] [Cruz et al. 2025] [Cui 2025] [Demeneghi et al. 2025] [Chen et al. 2025b] [王 2025] [Shen et al. 2025a] [Sliusariev 2025] [Woodger et al. 2025] [Dziubek et al. 2026] [Lazarets 2026] [Chen et al. 2026b] [Pustovyi 2026] [Swan 2026] [White 2026] [Yi et al. 2026] [Zhang et al. 2026b] [Goldman et al] [Buck et al] [Katsarelis et al] [Katsarelis et al] [Cost Versus Benefits of] [Thrasher and Lusk] [Michaud et al] [Naden et al] [Gradl] [Gradl] [Gradl] [Gradl] [Gradl] [Gradl and Mireles] [Gradl and Gibson] [Gradl et al] [Gradl et al] [Gradl et al] [Gradl et al] [Gradl et al] [Gradl et al] [Gradl] [Gradl] [Gradl et al] [Gradl et al] [Gradl et al] [Gradl and Mireles] [Gradl et al] [Chen et al] [Schmitt et al] [Fedotowsky et al] [Hudson et al] [Padela et al]
The ascent, which is where the integral lives
Launch vehicle design and staging, ascent trajectories and their optimisation and guidance, ascent aerodynamics, the atmosphere as a flight condition, and launch vehicle programmes and flights.
1,338 records. [Malina and Smith 1938] [Tsien and Evans 1951] [Schurmann 1957] [Newton 1958] [Parkyn 1958] [Struble et al. 1958] [Feodosiev and Siniarev 1959c] [Liu 1959] [Swanson 1959] [Draim and Stalzer 1960] [Mackay 1960] [Crabill 1961] [Leendertse 1961] [Boynton et al. 1962] [Kolenkiewicz and Loughin 1962] [Lovingood and Smith 1962] [Macpherson 1962] [Punga and Campbell 1962] [Tischler 1962] [Schramm 1962] [Bertram and Kuettner 1963] [Hauer et al. 1963] [Launch Vehicle Flight Report 1963] [Launch Vehicle Performance 1963] [Luton 1963] [Martin Co Baltimore Md 1963] [Stancil 1963] [Thomae 1963] [Vickery 1963] [Ziegler 1963] [Bos and Morrison 1964] [Dembrow and Jamieson 1964] [Ehricke 1964] [Forrette 1964] [Gunderson et al. 1964] [Hammock 1964] [Hillsley and Robbins 1964] [Lester and Morgan 1964] [Levine 1964] [Lunney 1964] [Mueller 1964] [Brereton 1964] [Launch Vehicle Optimization Phase 1965b] [Launch Vehicle Optimization Phase 1965a] [Moser 1965] [Munick 1965] [Pressly 1965] [Roudebush 1965] [Sanders 1965] [Thompson and Woodcock 1965] [Blair et al. 1966] [Bush 1966] [Havill and Hornby 1966] [Knaur 1966] [Mayo 1966] [Moch 1966a] [Moch 1966b] [Pack 1966] [Rosenbaum 1966] [Schroer 1966] [Study of Structural Bending 1966] [Teren 1966] [Babb and Fuller 1967] [Barrett et al. 1967] [Bieber 1967] [Busse and Kreuzer 1967] [Ceresuela 1967] [Cunningham 1967] [Driscoll 1967] [Dunfee and Oss 1967] [Elliott 1967] [Ferris 1967] [Heuston et al. 1967] [Hewitt 1967] [Huang and Brown 1967] [Jungmann 1967] [Karel 1967] [Launch and Space Vehicle 1967] [Mayo 1967] [McGarvey 1967] [Muraca 1967] [Nicolaides et al. 1967] [Nolan 1967] [Pines 1967] [Price 1967] [Richards 1967] [Rynaski 1967] [SA-204/LM-1 Launch Vehicle Operational 1967] [Brunk and Gomersall 1968] [Colwell 1968] [Davis et al. 1968] [Fuller 1968] [Harris 1968] [Harvey 1968] [Elliott and Rau 1968] [Johnson and L’Ecuyer 1968] [Kork and Schindler 1968] [Launch Phase Abort Analysis 1968] [Marquet and Zeiner 1968] [Morgan 1968] [SA-204/LM-1 Launch Vehicle Dynamics 1968] [Solmon 1968] [Swaim 1968] [Williams 1968b] [Bejczy 1969] [Cunningham 1969] [Freeman and Teets 1969] [Hardy 1969] [Hose et al. 1969b] [Hose et al. 1969a] [Swaim 1969] [Ammons et al. 1970a] [Ammons et al. 1970b] [Cairns 1970] [Coffey and Geye 1970] [Gregory and Wilcox 1970] [Haeussermann 1970] [Ingram et al. 1970] [Madden 1970] [McCaskill 1970] [Rice 1970] [Rosenbaum 1970] [Rosenbaum and Willwerth 1970] [Seltzer 1970] [The Air-Breathing Launch Vehicle 1970] [Wing 1970] [Bradshaw et al. 1971] [Grassl 1971] [McGolrick et al. 1971] [Rosenbaum 1971] [Saturn 5 Launch Vehicle 1971a] [Saturn 5 Launch Vehicle 1971b] [Sullivan and Uzzell 1971] [Brusch and Reed 1972] [Buchholz and Gamble 1972] [Graves 1972] [Gunn 1972] [Lovingood et al. 1972] [Lyons et al. 1972] [Maki and De Vegte 1972] [Reichert 1972] [Reins and Alvis 1972] [Saturn 5 Launch Vehicle 1972] [Taylo and Redus 1972] [Trimmer et al. 1972] [Ammons 1973] [Bensimon 1973] [Detailed Test Objectives 1973] [Gunn 1973] [Jenkins et al. 1973] [Larson 1973] [Rehri and Pennanech 1973] [Saturn 1B Launch Vehicle 1973a] [Saturn 1B Launch Vehicle 1973b] [Saturn 5 Launch Vehicle 1973] [Simmons and Hall 1973] [Stofan 1973] [Toelle et al. 1973] [Vinh 1973] [Bendot 1974] [Dhuyvetter 1974] [Edge and Powers 1974] [Saturn 1B Launch Vehicle 1974] [Shen-Orr and Ur 1974] [Bendot et al. 1975] [Carter et al. 1975] [Johnson 1975] [Tharratt 1975] [Williams et al. 1975] [Adimurthy 1976] [Alford and Hoekstra 1976] [Asanuma and Nomura 1976] [Eldred and Gordon 1976] [Flowers 1976] [McGarvey 1976] [Lebeau and Orye 1976] [Lindsay and Fikes 1976] [Notardonato and Masters 1976] [Shrivastava and Reddy 1976] [Ariane Launch Vehicle 1977] [Bernot 1977] [Conceptual Design and Preliminary 1977] [Dordain 1977] [Freeman and Fournier 1977] [Haefeli et al. 1977b] [Haefeli et al. 1977c] [Haefeli et al. 1977a] [Jackson et al. 1977] [Jaggers 1977] [Johnson 1977a] [Martin 1977] [Rehder 1977b] [Rehder 1977a] [Research Study to Identify 1977] [Solar Power Satellite. System 1977] [Beichel and Obrien 1978] [Chase 1978] [Freeman and Fournier 1978] [Hepler and Bangsund 1978b] [Hepler and Bangsund 1978a] [Hepler et al. 1978] [Schoyer 1978] [An Improved Theoretical Aerodynamic 1979] [Ardema 1979] [Chase 1979] [Churchyard 1979] [Freeman and Wilhite 1979] [Freeman and Powell 1979] [Hanley 1979] [Hepler et al. 1979] [Kessler and Carson 1979] [Reilly 1979] [Spearman 1979] [Star-Raker 1979] [Takenaka et al. 1979] [Chase 1980] [Freeman and Powell 1980] [Launch Mission Summary 1980] [Small et al. 1980] [Hattis 1981] [Koelle 1981] [Lucas 1981] [Barrowman 1982] [Flores and Gurkin 1982] [Grimes and Kraft 1982] [Jayaraman et al. 1982] [Jones and Tharayil 1982] [Knauber 1982] [Millard et al. 1982] [Patterson 1982] [Schleich 1982] [Schneiders and Ziegltrum 1982] [Wente 1982] [Wilhite 1982b] [Bernot 1983] [Hamilton 1983] [Naftel and Powell 1983] [Shuttle Derived Vehicle Analysis 1983] [Surber and Stone 1983] [Assessment of Candidate-Expendable Launch 1984] [Bauer et al. 1984] [Gaynor and Cervisi 1984] [Ikeda et al. 1984] [Deschamps 1985] [Hertzfeld 1985] [Naftel and Powell 1985] [Parkinson 1985] [Ruppe 1985] [Tewell and Buell 1985b] [Tewell and Buell 1985a] [Toelle 1985] [Wallace et al. 1985] [Eldred and Talay 1986] [Koelle 1986] [Montag et al. 1986] [Naftel et al. 1986] [Adimurthy 1987] [Dorrington 1987] [Ennix and Coleman 1987] [Nguyen 1987] [Ruppe 1987] [Troutman and Isakowitz 1987] [Davis 1988] [Edmunds 1988] [Holguin and Labbee 1988] [Maitra 1988] [Mihara 1988] [Olds 1988] [Sinha 1988] [Stampfl and Meyer 1988] [Tsiotras and Kelley 1988] [Claggett and Langehough 1989] [Corban et al. 1989] [Feaux et al. 1989] [Foster 1989] [Foster et al. 1989] [Harsh 1989] [Hodges et al. 1989] [Liquid Rocket Booster LRB 1989] [Luke 1989] [Pamadi 1989] [Parsley 1989] [Schoess 1989] [Smith et al. 1989] [Well 1989] [Wessling and Maybee 1989] [Abbott and Matzenauer 1990] [Calise et al. 1990] [Chase 1990] [Dorrington 1990] [Expendable Launch Vehicles Technology 1990] [Greene et al. 1990] [ISAS’s New Launch Vehicle 1990] [Johnson 1990] [Joyner and Sabatella 1990] [Koelle 1990] [Krause 1990] [Krieger 1990] [Lepsch et al. 1990] [Leung and Calise 1990] [Long March Launch Vehicles 1990] [McKenna 1990] [Palaszewski 1990c] [Palaszewski 1990b] [Palaszewski 1990a] [Powell et al. 1990] [Sinha and Shrivastava 1990] [Stanley and Powell 1990] [Sullivan 1990] [U.S. Access to Space 1990] [Whitehead 1990] [Wiswell and Huggins 1990] [Barry et al. 1991] [Bless 1991] [Bulirsch and Chudej 1991] [Conceptual Design of Two-Stage-to-Orbit 1991] [Deese et al. 1991] [Flittie and McFarlane 1991] [Johnson 1991] [Jones and Petley 1991] [Limerick 1991b] [Luke 1991] [MacConochie and Stnaley 1991] [Martin et al. 1991] [Morgenthaler and Montoya 1991] [Nguyen 1991] [Palaszewski and Powell 1991] [Parkinson 1991] [Plencner 1991] [Powell et al. 1991a] [Powell et al. 1991b] [Rice 1991] [Schoettle and Hillesheimer 1991] [Shaughnessy and Gregory 1991] [Sholes 1991] [Snyder and Maldonado 1991] [Stanley et al. 1991] [The Design of Two-Stage-to-Orbit 1991] [Thorpe 1991] [Tsiotras et al. 1991] [Wessling and Maybee 1991b] [Wessling and Maybee 1991a] [Wilhite et al. 1991] [Wilhite 1991] [Yamada et al. 1991] [Andrews et al. 1992] [Buhl et al. 1992] [Burkardt 1992] [Burkardt and Norris 1992] [Burrows and Roth 1992] [Butler et al. 1992] [Chase 1992] [Davic and Midea 1992] [Englehart and Krause 1992] [Foster 1992] [Hames 1992] [Hanson et al. 1992] [Hodges et al. 1992] [Leung and Calise 1992] [Lewis and Rice 1992] [Lu and Samsundar 1992] [Martin 1992] [Nadell et al. 1992b] [Nadell et al. 1992a] [Okuno and Watanabe 1992] [Schreiner and Roth 1992] [Stanley et al. 1992b] [Stanley et al. 1992a] [Stoecker et al. 1992] [Wanagas 1992] [Winchell 1992] [Adelfang et al. 1993] [Armiger et al. 1993] [Bhat et al. 1993] [Bond and Yi 1993] [Browning 1993] [Chern and Hong 1993] [Clapp and Hunter 1993] [Cochran et al. 1993] [Consort Suborbital Rocket Series 1993] [Development of a Large 1993] [Duffy 1993] [Dutton 1993] [French 1993] [Grimm 1993] [Hardy et al. 1993] [Holloway and Limerick 1993] [Jules 1993] [Kugelmann and Pesch 1993] [Leingang et al. 1993] [Luke 1993] [Lydon and Simmons 1993] [Lyons 1993] [Naftel and Powell 1993] [Poth et al. 1993] [Rutledge 1993] [Ryan and Verderaime 1993a] [Ryan and Verderaime 1993b] [Ryan and Jewell 1993] [Schmidt et al. 1993b] [Seywald and Bless 1993] [Snyder 1993] [Stanley and Piland 1993] [Willen and Rude 1993] [Adelfang et al. 1994] [Allen et al. 1994a] [Allen et al. 1994b] [Ardema et al. 1994] [Bekey 1994] [Bond and Yi 1994] [Clapp 1994] [Cobb and Davis 1994] [Daniels and Saavedra 1994] [Dumbacher and Klevatt 1994] [Flittie et al. 1994] [Frost and Springer 1994] [Gielda et al. 1994] [Immich and Hufenbach 1994] [Kugelmann 1994] [Laursen 1994] [Leung and Calise 1994] [Limerick 1994] [Lovell and Schmidt 1994a] [Lovell and Schmidt 1994b] [Lu 1994] [Mahanta 1994] [Manski and Fina 1994] [Olds 1994] [On ascent guidance of 1994] [Optimal digital autopilot for 1994] [Park et al. 1994] [POGO Prevention of H-2 1994] [Siebenhaar et al. 1994] [Single Stage to Orbit 1994] [Spangelo and Klaus 1994] [Springer and Pokora 1994b] [Springer and Pokora 1994a] [Stanley et al. 1994] [Stoyanof and Monk 1994] [Advanced Transportation System Studies 1995] [Advanced Transportation System Studies. 1995] [Bainum and Reiss 1995] [Barret 1995b] [Barret 1995a] [Braun et al. 1995] [Carpenter et al. 1995] [Chang 1995] [Chen et al. 1995] [Christenson and Holt 1995] [Colasurdo et al. 1995] [Cole et al. 1995] [Cook 1995a] [Freeman et al. 1995a] [Freeman et al. 1995b] [Hanson et al. 1995] [Heald 1995] [Hinckel 1995] [Hueter 1995] [Hunt 1995] [Ingalls 1995] [Lydon and Va 1995] [Lyon 1995] [Martin 1995] [Mayhew and Norden 1995] [Meyer et al. 1995] [Moore et al. 1995] [Pamadi 1995] [Park et al. 1995a] [Phillips and Engelund 1995] [Reusable Launch Vehicle 1995b] [Reusable Launch Vehicle Development 1995] [Reusable Launch Vehicle 1995a] [Smith and Adelfang 1995] [Sponable 1995] [Stevens et al. 1995] [Urie and Elvin 1995] [Weegar 1995] [Weilmuenster et al. 1995] [Ardema et al. 1996] [Barret 1996] [Batts and Pearson 1996] [Braun et al. 1996] [Catania and Portanova 1996] [Chudej 1996] [Cotta et al. 1996] [Davis 1996] [Deneu and Terrenoire 1996] [Elvin 1996] [Freeman et al. 1996] [Galati and Elkins 1996] [Goracke and Meisl 1996] [Greenberg 1996] [Griffin and Claybaugh 1996] [Hamaker 1996] [Joyner et al. 1996] [Komar and Christenson 1996] [Laursen and Voce 1996] [Lu 1996] [MacLean and Rodriguez 1996] [Maggio and Gerez 1996] [McCurry 1996] [Nelson 1996] [Olds and Lee 1996] [Park et al. 1996] [Paus and Well 1996] [Pearson et al. 1996] [Pelaccio 1996] [Prabhu 1996] [Rogers and Dragone 1996] [Schmidt and Velapoldi 1996] [Shirasu et al. 1996] [Springer 1996a] [Springer 1996b] [Tanck 1996] [Weilmuenster et al. 1996] [Whitehead 1996] [Williams 1996] [Winnick 1996] [Bzhilianskaya 1997] [Calise et al. 1997] [Cordes and Hertzfeld 1997] [Ferrandon 1997] [Future Space Transportation Systems 1997] [Galati and Elkins 1997] [Goracke et al. 1997] [Greaves 1997] [Huang et al. 1997] [Jankovsky 1997] [Logsdon and Williamson 1997] [Manski et al. 1997] [Markopoulos et al. 1997] [McCurry and Carter 1997] [McMinn 1997] [Phillips and Engelund 1997] [Reaser 1997] [Shaw et al. 1997] [Shtessel and Krupp 1997] [Shtessel et al. 1997] [Weilmuenster et al. 1997] [Adelfang and Smith 1998] [Andrews 1998] [Barret 1998] [Clarke 1998b] [Dasgupta 1998] [Herzog et al. 1998] [Huang et al. 1998] [Jankovsky et al. 1998] [Kohrs and Petersen 1998] [Konno et al. 1998] [Martin et al. 1998] [McClure 1998] [McClure and Andrews 1998] [Meyerson 1998] [Obermann and Williamson 1998] [Olds and Bellini 1998a] [Olds and Bellini 1998b] [Palaszewski 1998b] [Powell et al. 1998] [Rahn et al. 1998] [Rasky 1998] [Sachs and Mayrhofer 1998] [Stadler 1998] [Tanck and Steadman 1998] [Tournes and Johnson 1998] [Tuohy 1998] [Wangu and Mouyos 1998] [Azevedo and Buonomo 1999] [Baroth et al. 1999] [Casalino and Pastrone 1999] [Dhekane et al. 1999] [Dorrington 1999] [Dorsey et al. 1999] [Gath and Calise 1999] [Griner and Lyles 1999] [Knapp 1999] [Knowles et al. 1999] [Lockheed Martin Skunk Works 1999] [Lohar et al. 1999] [Nix and Escher 1999] [Odom 1999] [Olds 1999] [Palaszewski 1999] [Roh and Kim 1999] [Shtessel 1999] [Staniszewski 1999] [Stanley et al. 1999] [Suzuki et al. 1999] [Trefny 1999] [Unal 1999] [Variable fuel mixture-ratio and 1999] [Zeiler et al. 1999] [Balepin et al. 2000] [Calise et al. 2000] [Clarke 2000] [Coleman 2000] [Donahue 2000] [Dragone 2000] [Ewig et al. 2000] [Gao 2000] [Hubbel 2000] [Hueter 2000] [Jensen 2000] [Larsen 2000] [Manley et al. 2000] [Optimal Ascent Trajectories 2000] [Rey 2000] [Richards 2000] [Rusch and Sharples 2000] [Smith et al. 2000] [Stanley et al. 2000] [Tartabini et al. 2000] [Tetlow et al. 2000] [Weigel and Well 2000] [Whitehead 2000] [Woods et al. 2000] [Balepin 2001] [Balepin et al. 2001a] [Balepin et al. 2001b] [Blanchet et al. 2001] [Bull et al. 2001b] [Chen et al. 2001] [Corban et al. 2001] [Davis et al. 2001] [Der Kiureghian 2001] [Happersett and Laursen 2001] [Jensen 2001] [Lalithambika et al. 2001] [Lee et al. 2001b] [Matlock et al. 2001] [Mehta and Bowles 2001] [Mossman and Perkins 2001] [Roche and McCurdy 2001] [Rohrschneider and Olds 2001] [Schierman et al. 2001b] [Schierman et al. 2001a] [Shivananda et al. 2001] [Staniszewski 2001] [Tournes and Johnson 2001] [Wingfield 2001] [Allen 2002] [Bradley et al. 2002] [Cerro et al. 2002] [Chandler et al. 2002a] [Chandler et al. 2002b] [Charania et al. 2002] [Conger et al. 2002] [Dukeman 2002] [Dumbacher 2002] [Fisher et al. 2002] [Gath et al. 2002] [Hagopian 2002] [Hopkins 2002] [Kaplan 2002] [Krivanek et al. 2002] [Lee 2002] [Lu et al. 2002] [Margasahayam et al. 2002] [Martinovic and Cerro 2002] [Noneman 2002] [Roche 2002] [Sagdeev et al. 2002] [Shtessel 2002] [Smith and Phillips 2002] [Thomas et al. 2002] [Trefny and Roche 2002] [Williams et al. 2002] [Adelfang 2003] [Bayer 2003] [Bermudez and Gladden 2003] [Bliss et al. 2003] [Boelitz et al. 2003] [Bordelon et al. 2003a] [Bordelon et al. 2003b] [Butrica 2003a] [Butrica 2003b] [Calvignac et al. 2003] [Calvignac and Tramel 2003] [Culver 2003] [Bienhoff 2003] [Dukeman 2003] [Gage and Vander Kam 2003] [Johnson et al. 2003] [Keith 2003] [Kinnersley et al. 2003] [Landis 2003] [Larsen 2003] [Marlow 2003] [Matsumura and Armstrong 2003] [Miotto and LePome 2003] [Palsulich and Schinnerer 2003] [Rea 2003] [Robinson et al. 2003] [Ross et al. 2003] [Rowell and Korte 2003] [Shtessel et al. 2003] [Smith and Philips 2003] [Trefny 2003] [Urschel and Cox 2003] [Verstraete and Hendrick 2003] [Wallace et al. 2003] [Winston et al. 2003] [Access to Space 2004] [Adelfang 2004] [Biltgen et al. 2004] [Boltz 2004] [Brock and Franke 2004] [Brower 2004] [Calise and Brandt 2004] [Doman 2004] [Donahue et al. 2004] [Drake 2004] [Drake et al. 2004] [Eklund 2004] [Foust and Smith 2004] [Garvey and Besnard 2004] [Guarro and Tomei 2004] [Johnson et al. 2004] [Pamadi et al. 2004a] [Pamadi et al. 2004b] [Portz 2004] [Qu et al. 2004] [Stochastic Flight Simulation Applied 2004] [The FALCON Small Satellite 2004] [Tripropellant Engine Technology 2004] [Tsuchiya and Mori 2004] [Vander Kam et al. 2004] [Zhu and Huizenga 2004] [Al-Garni and Kassem 2005] [DFG Deutsche Forschungsgemeinschaft 2005] [Boyd et al. 2005] [Brinda et al. 2005] [Clement et al. 2005] [Daniel and Ramusat 2005] [Dissel et al. 2005a] [Dissel et al. 2005b] [Farr et al. 2005a] [Freeborn et al. 2005] [Garvey and Besnard 2005a] [Garvey and Besnard 2005b] [Hall and Shtessel 2005] [Harvey et al. 2005] [Herrmann and Akin 2005] [Jacobs et al. 2005] [Kinnersley et al. 2005] [Kitsios and Lygeros 2005] [Larsen 2005] [LeMoyne 2005] [Liechty 2005] [Lu et al. 2005] [McGinnis and Joyner 2005] [Nakasuka et al. 2005] [Nilsen et al. 2005] [Pamadi et al. 2005] [Raj et al. 2005] [Rothschild et al. 2005a] [Rothschild et al. 2005b] [Shaffer et al. 2005] [Shaw et al. 2005] [Shelton et al. 2005] [Uranga et al. 2005] [Whitehead 2005] [Akhtar and Linshu 2006] [Andrews et al. 2006] [Arzelier et al. 2006] [Breton et al. 2006] [Brinda and Dasgupta 2006] [Cockrell et al. 2006] [Davis and Coook 2006] [Davis et al. 2006a] [Min 2006] [Dumbacher 2006b] [Dumbacher 2006d] [Dumbacher 2006c] [Garvey and Besnard 2006] [Hank et al. 2006] [Hellman 2006] [Herrell and Zhou 2006b] [Highway to Space 2006] [Jategaonkar et al. 2006] [Jha et al. 2006] [Kutter 2006] [Lepore 2006] [Martin 2006] [Pamadi et al. 2006] [Rasky et al. 2006] [Reuter et al. 2006] [Schieb 2006] [Snoddy et al. 2006a] [Snoddy et al. 2006b] [Starnone and Biesbroek 2006] [Sundaresan 2006] [Williams and Cannon 2006] [Yang et al. 2006] [Yeniay et al. 2006] [Al-Garni and Kassem 2007] [Atkinson et al. 2007] [Betts et al. 2007] [Briggs et al. 2007] [Edwards et al. 2007] [Hertzfeld and Peter 2007] [Kalden 2007] [Krevor and Wilhite 2007b] [Lalithambika and Dasgupta 2007] [Pamadi et al. 2007] [Phillips et al. 2007] [Priskos et al. 2007] [Sun et al. 2007] [Bigarella and Azevedo 2008] [Du et al. 2008a] [Du et al. 2008b] [Dyer et al. 2008] [Eramya et al. 2008] [Erickson and Deloach 2008] [Fuhrmann and Dreyer 2008] [Graichen and Petit 2008] [Haberstroh et al. 2008] [He Chenglong et al. 2008] [Hunley 2008g] [Hunley 2008e] [Hunley 2008h] [Hunley 2008f] [Hunley 2008c] [Jodei et al. 2008] [Johnson and de Almeida 2008] [Kamal 2008] [Kharisov et al. 2008a] [Kharisov et al. 2008b] [Khoshnood et al. 2008] [LeFevre and Jha 2008] [Malmuth and Fedorov 2008] [Mathias et al. 2008] [McDavid et al. 2008] [Mehrabian et al. 2008] [Muse et al. 2008] [Plaisted and Leonessa 2008] [Shtessel and Baev 2008] [Toniolo et al. 2008] [Wie et al. 2008] [Bentley 2009] [Bristeau and Petit 2009] [Cook et al. 2009] [Fleming et al. 2009] [Herdy et al. 2009] [Kuzin et al. 2009] [LeFevre and Jha 2009] [Liu et al. 2009b] [Lu and Pan 2009] [Muse and Calise 2009] [Nakane et al. 2009] [Park et al. 2009] [Proud et al. 2009] [Rafique et al. 2009a] [Rafique et al. 2009c] [Rafique et al. 2009b] [Rafique et al. 2009d] [Rezaei Darestani et al. 2009] [Rothschild and Talay 2009] [Steele 2009] [Suresh et al. 2009] [Taylor 2009] [Verstraete et al. 2009] [Xu et al. 2009] [Zeeshan et al. 2009] [Application to Rocket Performance 2010] [Armen 2010] [Cook and Vanhooser 2010] [Creech et al. 2010] [French 2010] [Giri and Ghose 2010] [Griesemer et al. 2010] [Hanson and Beard 2010b] [Hanson and Beard 2010a] [Harrington 2010] [Heiser 2010] [Kerr et al. 2010] [Khoshnood et al. 2010] [Leach and Decker 2010] [Losik 2010b] [Losik 2010a] [Murillo and Lu 2010] [Muse and Calise 2010] [Orr 2010] [Pan and Lu 2010] [Rafique et al. 2010] [Sinclair and Flowers 2010] [Snyder et al. 2010] [Whitley and Proud 2010] [Applebaum et al. 2011] [Bettis et al. 2011] [Cowling 2011] [Creech 2011] [Decker and Barbre 2011] [Ebrahimi et al. 2011a] [Ebrahimi et al. 2011b] [Esfahanian et al. 2011] [Foster 2011] [Gusman et al. 2011a] [Hall et al. 2011a] [Hanson and Pinson 2011] [Hanson et al. 2011] [Harrington 2011] [Hartfield et al. 2011] [Hellman et al. 2011] [Hutchison 2011] [Jang et al. 2011] [Moore et al. 2011] [Pinier 2011] [Rafique et al. 2011a] [Rafique et al. 2011b] [Schumann et al. 2011] [Smith 2011] [Song et al. 2011] [Threet et al. 2011] [Walterscheid and Sako 2011] [Xie et al. 2011] [Yaman and Seckin 2011] [Albertson et al. 2012] [Amar and Tamanampudi 2012] [Dubanchet et al. 2012] [Fragola 2012] [Greatrix 2012a] [Holliday et al. 2012] [Iriarte et al. 2012] [Johnson and Vaughan 2012] [Kelley 2012] [Lafleur et al. 2012] [Losik 2012] [Mohammadi et al. 2012] [Mooij and Mooij 2012] [Moore and Gray 2012] [Orr and VanZwieten 2012] [Pescetelli et al. 2012] [Arjun et al. 2012] [Strobl et al. 2012] [Stroud et al. 2012] [Tayefi et al. 2012] [Threet et al. 2012] [Tsien and Malina 2012] [Ustinov 2012] [Walsh et al. 2012] [Watson and Kelley 2012] [Wuilbercq et al. 2012] [Zilliac 2012] [Air Force Space Command Space Missile SYS CTR 2013] [Aswathy V. et al. 2013] [Baran et al. 2013] [Beers et al. 2013] [Dmitruk and Samylovskiy 2013] [Duraffourg et al. 2013] [Eberspeaker and Fairbrother 2013] [Fuller 2013] [Jee et al. 2013] [Jha et al. 2013] [Kloesel 2013] [Kloesel and Clark 2013] [Krige et al. 2013] [Leela and Raju 2013] [Lu and Wang 2013] [Lu et al. 2013] [López et al. 2013] [Rezaei et al. 2013] [Shi et al. 2013b] [Shi et al. 2013a] [Sun and Zhao 2013] [Villanueva et al. 2013b] [Villanueva et al. 2013a] [Waters 2013] [Waters et al. 2013] [Yuanwen et al. 2013] [Ables 2014] [Adetoro et al. 2014] [Blevins et al. 2014] [Chiba et al. 2014] [Decker and Barbre 2014] [Fenili 2014] [Ghosh and Chattopadhyay 2014] [Gilligan et al. 2014] [Gong et al. 2014b] [Hanson 2014] [Joshi and Sudhir Kumar 2014] [Manusubramanian et al. 2014] [Motiwala et al. 2014] [Orr et al. 2014] [Qiuhong et al. 2014] [Seedhouse 2014] [Spurlock and Williams 2014] [Vachon et al. 2014] [Villanueva et al. 2014] [Wuilbercq et al. 2014b] [Wuilbercq et al. 2014a] [Zapata 2014] [Bataleblu and Roshanian 2015] [Bing and Gong 2015] [Decker et al. 2015] [Dileep et al. 2015] [Edwards et al. 2015] [Ghosh and Chattopadhyay 2015] [Gong et al. 2015] [Holt et al. 2015] [Hong and Ahn 2015] [Huang et al. 2015] [Jing et al. 2015] [Junaid R and Beebi M 2015] [Kibbey 2015] [Miller et al. 2015] [Oliveira et al. 2015] [Panxing Huang et al. 2015] [Selvakumar and Bakolas 2015] [Shahmirzaee Jeshvaghani et al. 2015] [Song and Su 2015] [Sruthi S et al. 2015] [Steffens and Mavris 2015] [Steffens et al. 2015] [Tartabini et al. 2015] [Ueda et al. 2015] [Villanueva and Abbas 2015] [Wang 2015b] [Williams and Johnson 2015] [Wu et al. 2015a] [Yoda et al. 2015] [Zhang et al. 2015b] [Zhiqiang et al. 2015] [Zhou et al. 2015b] [Zhu et al. 2015] [Barbosa et al. 2016] [Benito and Johnson 2016] [Dileep et al. 2016] [Gilbert et al. 2016] [Hellman et al. 2016] [Huang et al. 2016] [Imoto 2016] [Jourdan et al. 2016] [Ko and Cho 2016] [Liu et al. 2016] [Mehta 2016] [Mishchenkova 2016] [Motes 2016a] [Motes 2016b] [Dees et al. 2016] [Pelton 2016] [Ricciardi et al. 2016] [Schutte and Thoreau 2016] [Singh-derewa and Srivastava 2016] [Tewari 2016] [Villanueva 2016] [Zhang et al. 2016] [Anju et al. 2017] [Astorg 2017] [Benito and Shotwell 2017] [Cheng et al. 2017b] [Civek and Özgören 2017] [Cremaschi et al. 2017] [Decker 2017] [Fujikawa et al. 2017] [Gong 2017] [Gong et al. 2017] [Guelhan 2017] [He et al. 2017b] [Hendricks et al. 2017] [Huang 2017] [Hudson et al. 2017] [Hunter and Hill 2017] [Kanazaki et al. 2017] [Li et al. 2017] [Lugo et al. 2017] [Ngo et al. 2017] [Nie et al. 2017] [Orcutt et al. 2017] [Stender and Loghry 2017] [Toso and Maddock 2017] [Zhang et al. 2017b] [Zhang et al. 2017a] [Zhou et al. 2017b] [Zhou et al. 2017a] [Ann et al. 2018] [Barth and Watson 2018] [Cerf 2018] [Chen and Wu 2018] [Coley et al. 2018] [Dmitruk and Samylovskiy 2018] [Dokuchaev 2018] [Gale et al. 2018] [Guan et al. 2018] [Gülgönül and Sözbir 2018] [Hayward and Urdiales 2018] [Hemza et al. 2018] [ISRO Releases the Special 2018] [Kanazaki et al. 2018] [Kim et al. 2018b] [Oh et al. 2018] [Roshanian et al. 2018] [Shiihara et al. 2018] [Sivan and Pandian 2018] [Sudol et al. 2018] [Swathy et al. 2018] [Varghese et al. 2018] [Villanueva 2018] [Walter 2018a] [Walter 2018b] [Wang et al. 2018a] [Williams et al. 2018] [Wunderlin et al. 2018] [Zhang et al. 2018b] [Zhengxiang et al. 2018] [Chandler 2019] [Chen 2019] [Cusick and Kontis 2019] [Denny and McFadzean 2019] [Fu et al. 2019] [Fusselman et al. 2019] [Dhanush et al. 2019] [Honkawa and Yoozbashizadeh 2019] [Huang et al. 2019] [Hwang 2019] [Ishkov et al. 2019] [Kibbey 2019] [Li et al. 2019b] [Liu et al. 2019a] [Mooij 2019] [Mukundan et al. 2019b] [Mukundan et al. 2019a] [Palaia et al. 2019] [Pavlov 2019] [Pelton and Madry 2019] [Rosanova 2019] [Story et al. 2019b] [Story et al. 2019a] [Trajectory Analysis and Rocket 2019] [Vigil et al. 2019] [Wang et al. 2019b] [Yoshida et al. 2019] [Zhang et al. 2019c] [Zhou et al. 2019a] [Benjamin and Rajeev 2020] [Briese et al. 2020] [Colbeck and Bil 2020] [He et al. 2020b] [He et al. 2020a] [Ito et al. 2020] [Johnson and Vaughan 2020] [Nie et al. 2020] [Xu et al. 2020] [Zardashti and Rahimi 2020] [Zardashti et al. 2020] [Zheng et al. 2020] [Almeida et al. 2021] [Benedikter et al. 2021] [Biertümpfel et al. 2021] [Chen et al. 2021] [Cheng et al. 2021] [Cho et al. 2021] [Da Cás 2021] [Federici et al. 2021] [Fu et al. 2021b] [Hao and Zhang 2021] [Hu et al. 2021f] [Huangpeng et al. 2021] [Hörschgen-Eggers et al. 2021] [Ifenna Okoli et al. 2021] [Jo et al. 2021] [Justus et al. 2021] [Li et al. 2021b] [Marchetti et al. 2021] [Pidvysotskyi 2021] [Rose and Niemeyer 2021] [Ryakam and Crispin 2021] [Shulga and Shcheglov 2021] [Simon and Chudoba 2021] [RSC Energia et al. 2021] [Sosa and Tuminello 2021] [Tang et al. 2021] [Wang et al. 2021b] [Xiao et al. 2021] [Yuwei et al. 2021] [Zhang et al. 2021b] [A Technical History 2022] [Abdulkerim 2022] [Ascent Trajectory Analysis 2022] [Benedikter et al. 2022] [Canepa et al. 2022] [Cherkasov et al. 2022] [Dabanović et al. 2022] [Deng et al. 2022] [Diao et al. 2022] [Divakar and Samaga 2022] [Fujikawa and Yonemoto 2022] [Han et al. 2022] [Haws and Bowman 2022] [Jee et al. 2022] [Ju et al. 2022] [Lakshminarayana and Chiarelli 2022] [Lan and Li 2022] [Launch Vehicle Performance 2022] [Launch Vehicle Systems 2022] [Ma et al. 2022b] [Ma et al. 2022a] [Miao et al. 2022] [Mo et al. 2022] [Nair and Vaidyanathan 2022] [Olejnik et al. 2022] [Zardashti et al. 2022] [Sabaghzadeh and Khansari 2022] [Siby and Sreeja 2022] [Space Launch Vehicle Structures 2022] [Villanueva 2022] [Wang and Song 2022] [Bao et al. 2023] [Bechasnov and Ilyin 2023] [Cheng et al. 2023] [Dalle et al. 2023] [Dees and Stockard 2023] [Dinh and Trifoni 2023] [Gettatelli et al. 2023] [Gilson et al. 2023] [Kuznetsov 2023] [Li et al. 2023c] [Lu et al. 2023] [Mancini et al. 2023] [Miao et al. 2023] [Perumal 2023] [Radhakrishnan et al. 2023] [Redondo Gutierrez et al. 2023] [Burth et al. 2023] [Shawyer 2023b] [Song et al. 2023a] [Soota and Nadda 2023] [Ukirde and Rathod 2023] [Wang et al. 2023b] [Wu and Zhang 2023] [Xiang et al. 2023] [Xu et al. 2023] [Yan and Zhou 2023] [Yan et al. 2023] [Yu et al. 2023a] [Zhang 2023] [Zhang et al. 2023a] [Boost Trajectory Estimation 2024] [Cau et al. 2024] [Cerantola et al. 2024] [Chavda 2024] [Dalle et al. 2024] [Giannone and Sambasivam 2024] [Rosanova 2024] [Golubek et al. 2024] [Fernandez 2024] [Keba and Kulabukhov 2024] [Krishnan and Thakur 2024] [Krause 2024] [Manwatkar et al. 2024] [Martin et al. 2024] [Molinari et al. 2024] [Nath et al. 2024] [Pavanasam et al. 2024] [Radhakrishnan et al. 2024] [Shaobing and Chi 2024] [Shoyama and Hirakawa 2024] [St-Laurent-Recoura et al. 2024] [Sun et al. 2024a] [Wang and Ma 2024] [Wang et al. 2024a] [Yu et al. 2024a] [Zhao et al. 2024a] [Zhou et al. 2024b] [Bae 2025] [Benedikter et al. 2025] [Mahajan and Condon 2025] [Hu et al. 2025] [Hussein and de Weck 2025] [Kim et al. 2025b] [Lee 2025] [Lee et al. 2025a] [Lei et al. 2025] [Li et al. 2025a] [Lu et al. 2024] [Magistro et al. 2025] [Magyar et al. 2025] [Wittal et al. 2025] [Nair and Kukreja 2025] [Nguyen and Aleti 2025] [Rapp 2025] [Redondo Gutierrez et al. 2025] [Reentry Maneuvering Vehicle Ascent 2025] [Sanjay and Kuzhiveli 2025] [Walker 2025] [Wang et al. 2025a] [Xu et al. 2025b] [Xu et al. 2025d] [Xue et al. 2025a] [Young 2025] [Zhao et al. 2025] [DurmuŞ et al. 2026] [Kalsekar and Deshpande 2026] [Khan 2026] [Krivenko 2026] [Lei et al. 2026] [Raharema et al. 2026] [Saju and Vengadeswaran 2026] [Seo and Kim 2026] [Singh et al. 2026] [Sun et al. 2026a] [Velez et al. 2026] [Wu 2026] [Yu 2026] [Zhang et al. 2026d] [Zolla et al. 2026] [Zou et al. 2026] [Winebarger] [Brevault] [Wu] [Coakley] [Smith] [Dalle et al] [Dorairajan] [Griffin] [Guide for Crewed Suborbital] [Hassall] [Herrell and Zhou] [Horneman] [Launch vehicle dynamics] [Launch Vehicle Systems] [Mackle] [Fritz et al] [Morito et al] [NASA and the Politics] [Birbasov et al] [Oberoi et al] [Packard and Zampino] [Rocket staging] [Satellite Installation and Launch] [Satellite launch vehicles] [Shtessel and Krupp] [Space systems. General test] [Standard Guide for Crewed] [Sun] [Tully] [Uemura] [Wu] [Zhang]
Who is buying this and what they say it is for
The sponsors, programmes and acquisition of rocket propulsion and responsive launch, and the readiness assessment of propulsion technology.
56 records. [Satellites and Sounding Rockets 1964] [Sterhardt 1965] [NASA Sounding Rocket Survey 1966] [Encyclopedia 1970] [Corliss 1971] [The United States Sounding 1971] [Study of Solid Rocket 1972a] [Gregory 1975] [Lucci and Hodson 1975] [Guidotti 1976] [Holtz 1976] [Snyder 1976] [Bumgarner and Gilcrease 1979] [Martin 1979] [Olsen 1979] [Zetterquist 1979] [Lane and Mayo 1980] [Alford et al. 1982] [Boscov 1982] [Cooper and Seaton 1982] [Roehrig 1982] [Wilhite 1982a] [Kozuma et al. 1983] [NASA Orbit Transfer Rocket 1984] [Selden 1989] [Workshop on the Suborbital 1991] [Dawson 1992] [Gurkin 1992] [Gustafson and Harmon 1993] [Integrated Propulsion Technology Demonstrator. 1994] [Immich et al. 1997] [Clarke 1998a] [Flowers and Needleman 1999] [Blair and DeGeorge 2000] [DeGeorge and Fletcher 2002] [Thornburg 2002] [Eberspeaker and Smith 2003] [Harper and Hawk 2004] [Responsive Access to Space 2004] [Hoyt 2006] [Finger et al. 2009] [Sauser et al. 2009] [Finger et al. 2010] [Myrabo et al. 2010] [Allen and Roberts 2011] [McNab et al. 2011] [Doreswamy 2013] [Jones et al. 2014b] [Lee and Yi 2020] [Grunert 2022] [Zhang and Li 2022] [Reid 2023] [Assessing the Impact 2024] [Boldt et al. 2025] [Tobiassen 2026] [Davis and Tomlinson]
Measuring it, because the award says highly instrumented
Test stands, altitude test facilities, thrust measurement, instrumentation, telemetry and diagnostics of engines, nozzles and rocket flights.
422 records. [Gompertz 1950] [Wallner and Jansen 1951] [Wyman 1951] [Kendall 1952] [Beighley and Cheatham 1953] [Jones 1953] [Rogers 1953] [Abramson et al. 1954] [Walter and Redman 1954] [Winkler 1954] [Trout et al. 1957] [Sivo and Peters 1959] [Gertsma and Yeager 1960] [High Frequency Pressure Instrumentation 1960] [Powers 1960] [Sivo et al. 1960] [Weber 1960] [Glatt 1961] [Ilsen 1961] [Mickola 1961] [Mihaloew and Stofan 1961] [Weber 1961] [Hoberg and Rorex 1962] [A Rocket Test Stand 1963] [Elston 1963] [Folkerts and Hoag 1963] [German et al. 1963] [Moore 1963] [Plane 1963] [Thorn 1963] [Bauer et al. 1964] [Bridger 1964] [Maydew 1964] [Plane 1964a] [Plane 1964c] [Plane 1964b] [Smith and Ferrell 1964] [Strauss 1964] [Westcot and Hausman 1964] [Davis and Spicer 1965] [Langill 1965] [Nelius and Harris 1965] [Reimer 1965] [Reiner 1965] [Sanderson 1965] [Anderson 1966] [Cantor and Hrastar 1966] [Craig 1966] [Kirby and McCullough 1966] [Otto 1966] [Steam generator for the 1966] [Clark 1967a] [Clark 1967b] [Clark 1967c] [Crosswy and Kalb 1967] [Delmonte 1967] [Fairall 1967] [Grant 1967] [US Atomic Energy Commission (AEC) and Samuelson 1967] [Design of altitude simulators 1968] [Hendershot 1968] [Jones and Shrewsbury 1968] [Tackett 1968] [Burley and Mansour 1969] [Denker 1969a] [Denker 1969b] [Hudgins and Lease 1969] [Miller 1969a] [Miller 1969b] [Moore and Tcheng 1969] [Bresnahan 1970] [Burley and Mansour 1970] [Hartley and Boal 1970] [Head and Mikkelson 1970] [Howard 1970] [Johns and Steffen 1970a] [Johns and Steffen 1970b] [Blaha and Johns 1971] [Burley 1971] [Eaton 1971] [Fisher 1971] [Johns 1971] [Lieberman 1971] [Anderson 1972a] [Anderson 1972b] [Esker and Sedrick 1972] [Head 1972b] [Head 1972a] [Pongratz 1972] [Smalley 1972] [Baker et al. 1973] [Chirivella 1973c] [Franklin and Kunz 1973] [Taylor et al. 1973] [Woodruff and Chisel 1973] [Anderson 1974] [Merryman and Smith 1974] [Dukich and Kintner 1975] [Evans et al. 1975] [Merryman and Smith 1975] [McCay et al. 1976] [Varner 1976] [Windsor 1976] [Pouliquen 1978] [Tarzwell and Colley 1979] [Alperin and Wu 1980] [Allen 1981] [Bergman et al. 1981] [Bishop 1981] [Gilcrease 1982] [Dickhudt 1983] [Lemaster and Runyan 1983] [Nelson and Bresnahan 1983] [Scott 1984] [Young 1984] [Fisher 1985a] [Fisher 1985b] [Heltsley 1985] [Roberts et al. 1985] [Sovey et al. 1985] [Tirres and Cantrell 1985] [Yamazaki et al. 1985] [Coffin 1986] [Putnam and Mercer 1986] [Davidian 1987b] [LEGRAND 1987] [Collamore 1989] [Delcher et al. 1989] [Williamson and Lyman 1989] [Air Force Test Pilot School Edwards Afb Ca 1990] [Ali and Gupta 1990] [Arrington and Schneider 1990] [Choi and Soh 1990] [Drake 1990] [Lord et al. 1990] [Maggio 1990] [McFarlan et al. 1990] [Cyran and Quinn 1991] [De Groot 1991] [Dequay et al. 1991] [Huang 1991] [Hungenberg et al. 1991] [McAmis and Bartlett 1991] [Nail et al. 1991] [Ordonez and Georges 1991] [Penko et al. 1991] [Raines et al. 1991] [Anderson et al. 1992a] [Ballard 1992] [Buzzo 1992] [De Groot and Weiss 1992] [Debonis 1992] [Degroot 1992] [Mikkelsen and Idzorek 1992] [Air Force Test Pilot School Edwards Afb Ca 1993] [Barkhoudarian et al. 1993] [Beckmann and Kalliomaa 1993] [Delcher et al. 1993] [Farhangi et al. 1993] [Gilbrech 1993] [Karabadjhak 1993] [Liles 1993] [Reed 1993] [STS-51 Pad Abort. OV103-Engine 1993] [Tucker et al. 1993] [Farhangi et al. 1994] [Green 1994] [Lancaster 1994] [Liu 1994] [Lohrmann and Huhta 1994] [Narayanan and Damodaran 1994] [Particle Image Velocimetry Measurements 1994] [Voglewede 1994] [Brown et al. 1995] [McConnaughey et al. 1995] [Taylor et al. 1995] [Mixing Process in Ejector 1996] [Castner and Wolter 1997] [DeChant 1997] [Advisory Group for Aerospace Research and Development 1998] [Fisher et al. 1998] [Geisler and Beckman 1998] [Harrington 1998] [Jeracki 1998] [Koschel 1998] [Long 1998] [Meyer et al. 1998] [Bull 1999] [Crawford and Pinkleton 1999] [DeBonis 1999] [Mitchell et al. 1999] [Thompson 1999] [Bull and Martel 2000] [Imlach et al. 2000] [Ryan et al. 2000] [Zakrajsek 2000] [Bull et al. 2001a] [Dawson 2001] [Emdee 2001] [Markgraf et al. 2001] [Matringe 2001] [Osborne et al. 2001] [Cheng 2002] [Hanson 2002] [Hemmerling et al. 2002] [Wehrmeyer 2002b] [Panda and Gomez 2002] [Ahn et al. 2003] [Biele 2003] [Cook and Gruet 2003] [Figueroa et al. 2003] [Hiers et al. 2003] [Jacks and Beisler 2003b] [Jacks and Beisler 2003a] [Cook et al. 2003] [Solano et al. 2003] [Wernet and Bridges 2003] [Wong 2003] [Belozubov 2004] [Mielke et al. 2004] [Richter 2004] [Sanders et al. 2004] [Sass et al. 2004b] [Sass et al. 2004a] [Schäfer and Zimmermann 2004] [Shipman et al. 2004] [Arney et al. 2005] [Balan 2005] [Farr et al. 2005b] [Figueroa and Schmalzel 2005] [Gullia et al. 2005] [Jones et al. 2005] [Rahman and Hebert 2005] [Santoro et al. 2005] [Sass et al. 2005] [Temple et al. 2005] [Zaman 2005] [Crawford and Thomas 2006] [Kim 2006] [Ellerbrock and Ziegenhagen 2006] [Alich and Castillo 2007] [Dunn et al. 2007] [Hughes et al. 2007] [Wolter 2007] [Allgood et al. 2008] [Dumbacher et al. 2008] [Dumbacher and Burt 2008] [Kornuta and Guo 2008] [Lecakes et al. 2008] [Ren et al. 2008] [Anderson et al. 2009] [Dulreix 2009] [Gao and Sun 2009] [Lecakes et al. 2009a] [Lecakes et al. 2009b] [Marineau and Hornung 2009a] [Russell et al. 2009b] [Russell et al. 2009a] [Ryan 2009] [Saunders 2009] [Telemetry Boards Interpret Rocket 2009] [Zhang et al. 2009] [Zhu and Xu 2009] [Dougherty 2010] [Figueroa et al. 2010b] [Figueroa et al. 2010a] [Kitsche 2010] [Maynard and Raines 2010] [Multiaxial Force/Torque Measurement 2010] [Sachdev et al. 2010] [Werner and Wolter 2010] [Woods and Lansaw 2010] [Xing et al. 2010] [Goswami 2011] [Johnson and Crawford 2011] [Pauly et al. 2011] [Russell et al. 2011] [Verma and Haidn 2011] [Xing et al. 2011] [Zhang et al. 2011] [Abdullah et al. 2012] [Bridges and Wernet 2012] [Guo et al. 2012] [Ma et al. 2012] [Mon and Lee 2012] [Mulkey and Lineberry 2012] [Sreekireddy et al. 2012] [Vorontsov and Samoilov 2012] [Chaparro 2013] [Clem et al. 2013] [Guo et al. 2013] [Lavelle et al. 2013] [Manikanda Kumaran et al. 2013] [Wright et al. 2013] [Abdullah et al. 2014] [Allgood et al. 2014] [Bruce Ralphin Rose and Veni Grace 2014] [Gogineni 2014] [Namet-Allah and Birk 2014] [Narayanan 2014] [Zhou et al. 2014] [A Novel 6 DOF 2015] [Furuichi and Terao 2015b] [Furuichi and Terao 2015a] [Gradl 2015] [Herbert et al. 2015] [Kim et al. 2015b] [Kim et al. 2015a] [Qu and Yang 2015] [Rajagopal and Rajamanohar 2015] [Roman Ivanovitch Savonov et al. 2015] [Spravka and Jorris 2015b] [Spravka and Jorris 2015a] [Vijayan and Suresh Babu 2015] [Yahiaoui and Olivier 2015] [Gradl 2016c] [Gradl 2016b] [Gradl 2016a] [Gradl and Schmidt 2016] [Neff et al. 2016] [Renitha P and Sivaramapandian J 2016] [Senthilkumar et al. 2016] [Willits and Pourpoint 2016] [Zhou et al. 2016] [Lee et al. 2017a] [Oesch et al. 2017] [Takeishi et al. 2017] [Wernet and Stiegemeier 2017] [Willits and Pourpoint 2017] [Fernandez et al. 2018] [Lee et al. 2018b] [Moruzzi et al. 2018] [Nikitenko 2018] [Vemula et al. 2018] [Zhang et al. 2018a] [Ünal et al. 2018] [Bathel et al. 2019] [Cho et al. 2019a] [Cui et al. 2019] [Eitner et al. 2019] [Naveen et al. 2019] [Piotr et al. 2019] [Zaman et al. 2019] [Lee et al. 2020d] [McDonald and Estenson 2020] [Omata et al. 2020] [Sreelal et al. 2020] [Yan et al. 2020] [Cross Sapna et al. 2021] [Fabijanic et al. 2021] [Sandoz and Klaeyle 2021] [Yang 2021a] [Yang 2021b] [Yang et al. 2021a] [Evaluation of Equipment Performance 2022] [Fernandes et al. 2022] [Georges et al. 2022] [Kracik and Dvorak 2022a] [Kracik and Dvorak 2022b] [Lee et al. 2022b] [Li et al. 2022a] [Prashana ANL et al. 2022] [Chandler 2023a] [Jones 2023b] [Fouladi et al. 2023a] [Fouladi et al. 2023b] [Hao and Wang 2023] [Ravindra et al. 2023] [Sankaran et al. 2023] [Yao and Hao 2023] [Yilmaz and Pourpoint 2023] [Al-Nasser and Wellman 2024] [Bakun and Marynoshenko 2024] [Biliske and Patel 2024] [Chao et al. 2024b] [Chao et al. 2024a] [chen et al 2024] [chen et al 2024] [Christison 2024] [Cooper et al. 2024] [Das et al. 2024a] [Fouladi et al. 2024] [He et al. 2024a] [Kim 2024c] [Liu et al. 2024a] [Sandoz et al. 2024] [Shailesh et al. 2024] [Song et al. 2024a] [Szalkowski et al. 2024] [Wang et al. 2024e] [Anisha Selva Kala et al. 2025] [Behera et al. 2025] [Castor et al. 2025] [Chander and Maddalena 2025] [Chander et al. 2025] [Chao et al. 2025] [Chua et al. 2025] [Das and Clary 2025] [Deiros et al. 2025] [Llewellyn et al. 2025] [Olopade and Rouser 2025] [Roseberry 2025] [Voropaiev and Kolodii 2025] [Bandevych 2026] [Cha et al. 2026] [Chander and Maddalena 2026b] [Chander and Maddalena 2026a] [Cichon et al. 2026] [Dobrodomov et al. 2026] [Fidler and Hays 2026] [Hulliger et al. 2026] [Slawecki et al. 2026] [Tsukanov 2026] [Williamson et al. 2026] [Yang et al. 2026] [D’Elia] [de Lucena et al] [Ortiz and Delgado] [Lim] [NPIC, Rocket Engine Test] [The Measurement of Engine] [Benson et al]
Plumes and what they do to the vehicle behind them
Rocket and jet plumes, their radiation and impingement, their interaction with the vehicle and the surfaces around it, and free jets and their shock structure.
698 records. [Penner 1948] [Chaplin 1957] [Von Glahn 1957] [Latvala and Anderson 1959] [Huff and Abdalla 1960] [Boynton 1961] [Harshbarger and Dorian 1961] [Stitt 1961] [Henson and Robertson 1962] [Latto 1962] [Abu-Romia 1964] [Alden and Habert 1964] [Carpenter 1964] [D’Attorre and Harshbarger 1964] [Hurt and Lina 1964] [Snedeker and Donaldson 1964] [Albini 1965] [Bauer 1965] [D’Attorre and Harshbarger 1965] [Geiger 1965] [Andrews and Vick 1966] [Andrews et al. 1966] [Bowen 1966] [Harden 1966] [Marlow 1966] [McGee and Say 1966] [Melnick and Slutsky 1966] [Boynton 1967] [Edelman and Fortune 1967] [Jepps and Robinson 1967] [Smoot and Seliga 1967] [Adams 1968] [Herron 1968] [Laderman and Carlson 1968] [Oblanas 1968] [Scott and Ko 1968] [Abdelhamid and Dosanjh 1969] [Boudreaux 1969] [Dyner and Jarvinen 1969] [Volchkov and Ivanov 1969] [Abbett 1970] [Craven 1970] [Driftmyer et al. 1970] [Etheridge and Boudreaux 1970] [Fehr and Wensley 1970] [Gabbert and Hoffman 1970] [Greenwood et al. 1970] [Hendershot 1970] [Horikoshi 1970] [Jensen and Pergament 1970] [Klineberg et al. 1970] [Lyon 1970] [Martinkovic 1970] [McGhee 1970] [Peracchio 1970] [Timoshin 1970] [Abbett 1971] [Davidor and Penner 1971] [Lyon 1971] [Mons and Sforza 1971] [Nemchenko 1971] [Repetski and Mates 1971] [Rubin 1971] [Chirivella et al. 1972] [Dash and Del Guidice 1972] [Mantz et al. 1972] [McCanna and Sims 1972] [Schulz and Bauer 1972] [Smoot et al. 1972] [Wayte and Gruenich 1972] [Bird 1973] [Chang 1973] [Chirivella 1973b] [Chirivella 1973a] [Draper and Moran 1973] [McAnally and Smith 1973] [McGinnis et al. 1973] [Penny et al. 1973] [Hicks and Mendoza 1973] [Vonglahn et al. 1973] [Zoltani 1973] [Anderson and Meyer 1974] [Chang and Chow 1974] [Dods et al. 1974] [Himmell and Trulio 1974] [Reubush 1974] [Robinson and High 1974] [Robinson et al. 1974] [Wurster and Boyer 1974] [Calia and Brook 1975] [Dash and Delguidice 1975] [Ebeoglu et al. 1975] [Nichols 1975a] [Nozzle Exit Exhaust Products 1975] [Shih 1975] [Woodroffe 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Exhaust nozzles of aircraft engines, where the plug began
Exhaust, ejector and plug nozzles of aircraft engines and their integration with the airframe, the setting of the plug nozzle’s first measurements.
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Compressible flow and gas dynamics, the relations the nozzle sections use
Compressible flow and gas dynamics stated generally, including nonequilibrium expansion and the metering of choked flow.
167 records. [Penner 1949b] [Ehlers and Cohen 1951] [Kelber and Jarvis 1952] [Ferri 1954] [Probstein and Elliott 1954] [Gordon Watson 1955] [Persh 1955] [Meksyn 1958] [Hayman and Stewart 1961] [Mager 1961] [Wegener and Cole 1961] [Pearson 1962] [Clark and Johnson 1963] [Phinney 1963] [Emanuel 1964] [Supersonic annular nozzle as 1964] [Cheng and Lee 1966] [Goldman and Nosek 1966a] [Goldman and Nosek 1966b] [Hall et al. 1966] [Kinslow and Miller 1966] [Sichel and Yin 1966] [Albacete and Glowacki 1967] [Anderson and John D. 1969] [Bushnell et al. 1969] [Daum 1970] [Fischer et al. 1970] [Ikui and Matsuo 1971] [Kemp and Owen 1971] [Back et al. 1972b] [Fishburn and Adamson 1972] [Schmidt et al. 1972] [Johnson and Rose 1973] [Smith and Mosnier 1973] [Lee and Smith 1974] [Maxwell and Wessling 1974] [Sekundov 1974] [Stainback et al. 1974] [Lewis and Williams 1975] [Simoneau 1975] [Weilmuenster 1975] [Kim 1976] [Courant and Friedrichs 1976] [Condensation in Expansions 1977] [Bestion et al. 1983] [Dwyer 1983] [Li 1983] [Ota and Chapman 1983] [Rao et al. 1983] [Wornom and Hafez 1984] [Dashevskaya and Kholshchevnikova 1986] [Plendl 1986] [Evans 1987] [Sobota and Marble 1987] [Liou 1988] [Schnerr 1988] [Grasso and Speziale 1989] [Kinetic Theory Model 1989] [Gnoffo 1991] [Jacobs 1991] [Pauley and Dagher 1991] [Riley 1991] [Spekreijse 1991] [Zeitoun et al. 1991] [Harloff et al. 1992] [Lemonnier and Selmer-Olsen 1992] [Mitsuda and Kurosaka 1992] [Kobayashi and Togashi 1993] [Noguchi and Shiratori 1993] [Demetriades 1994] [Tzuk et al. 1994] [Yagudin 1994] [Ducros et al. 1995] [Heinbockel and Landry 1995] [Jialing and Weizhong 1995] [Demetriades 1996] [Hanifi et al. 1996] [Lin et al. 1996] [Tam et al. 1996] [Walpot et al. 1996] [Spyropoulos et al. 1997] [Tam et al. 1997] [Brogan and Demetriades 1998] [Bui and Mankbadi 1998] [Inlet Duct and Nozzle 1998] [Suzen and Hoffmann 1998] [Akmandor and Nagashima 1999] [Akmandor and Nagashima 2000] [Colonna and Capitelli 2000] [Colonna 2001] [Colonna and Capitelli 2001] [Lucia et al. 2001] [Toison and Hureau 2001] [Woodruff et al. 2001] [Colonna et al. 2002] [Colonna et al. 2003] [Foysi and Friedrich 2003] [Mathelin et al. 2003] [Zang et al. 2003] [Colonna 2005] [Foysi and Friedrich 2005] [Kim et al. 2005] [Majdalani and Abu-Irshaid 2005] [Abdol-Hamid et al. 2006b] [Chen et al. 2006] [Kim et al. 2006] [Ozalp 2006] [Ghosh et al. 2007] [Titov et al. 2007] [Titov et al. 2008] [Chen et al. 2009b] [Hong et al. 2009b] [Josyula and Bailey 2009] [Levin and Skopina 2009] [Li et al. 2009] [Marineau and Hornung 2009b] [Yu et al. 2009] [Gross et al. 2010] [Vedula and Josyula 2010] [Yamamoto et al. 2010] [Ghosh et al. 2011] [Majdalani and Maicke 2011] [Liu and Oh 2012] [Tsuge 2012] [Lin et al. 2013] [Wang and Xin 2013] [Critical Flow Venturi Nozzle 2015] [Cuong and Thanh 2015] [Snehil Varghese et al. 2015] [Tsuge 2015] [von Lavante et al. 2015] [Cyklis and Młynarczyk 2016] [Kiselev et al. 2016] [Tsuge 2017] [Chen et al. 2018a] [Młynarczyk 2018] [Pfeiffer and Nizenkov 2019] [Xiang et al. 2019] [Xie et al. 2019a] [Zhao et al. 2019] [Ding et al. 2020] [Pujowidodo et al. 2020] [Takegawa et al. 2020] [Ederouich et al. 2021] [Korepanov et al. 2021] [Mahmoudian et al. 2021] [Tsuge 2021] [Wang et al. 2021a] [Winn and Touber 2021] [Fang 2022] [Tsuge 2022] [Gao et al. 2023a] [Ghodbane and Boumeddane 2023] [Huang et al. 2023c] [Lai 2023] [LeFloch and Thanh 2023] [Liang et al. 2023] [Qian 2023] [Man 2024] [zhu 2024] [Chen et al. 2025f] [Chou et al. 2025] [Lin and Zhong 2025] [Roy and Dawar 2025] [Turbulence and Transition 2026] [Acosta] [Yaping He]
Textbooks, histories and surveys of rocket propulsion
Textbooks, handbooks, histories, surveys and proceedings of rocket propulsion stated in general terms.
52 records. [Some Fundamental Considerations Relating 1958] [Chapter 4. Design 1959] [Fundamentals of Rocket Propulsion 1960] [Smith 1962] [Penner 1968] [Dattorre et al. 1976] [Dushkin 1977] [Tishkoff et al. 1989] [Introduction to Liquid-Propellant Rocket 1992] [Meisl 1992] [Williams 1992] [McConnaughey et al. 1993] [Obrien 1993] [Taylor 1996] [Navaz and Dix 1998] [Meyer 1999] [Rothmund and Harlow 1999] [Liou et al. 2001] [Hawk 2003] [Sutton 2003] [Anderson 2004] [Pisacane 2005] [Rocket and Spacecraft Propulsion 2005] [Appendix C 2006] [France’s Liquid Propellant Rocket-Engine 2006] [Japan’s Liquid Propellant Rocket-Engine 2006] [Liquid Propellant Rocket Engines 2006a] [Liquid Propellant Rocket Engines 2006b] [Liquid Propellant Rocket Engines 2006f] [Liquid Propellant Rocket Engines 2006e] [Liquid Propellant Rocket Engines 2006d] [Liquid Propellant Rocket Engines 2006c] [Liquid Propellant Rocket-Engine Organizations 2006] [Rocket Propulsion 2006] [Hunley 2008a] [Data for Some Liquid-Propellant 2016] [El-Sayed 2016b] [El-Sayed 2016a] [Emrich 2016] [Classification of Rocket Propulsion 2019] [Rocket Propulsion 2019] [Chemical Rocket Performance 2021] [Classification of Rocket Propulsion 2021] [Rocket Engines 2021] [Abbas 2024] [Chandler Karp and Jens 2024] [Musielak 2025c] [Musielak 2025a] [El-Sayed 2026b] [Thakur et al. 2026] [History and principles of] [The thermal rocket engine]
Where the Framing Breaks Down
The ideal spike of this article does not exist and the gap is not small. A real aerospike is truncated, carries a base, sheds a wake, needs cooling on a surface that faces the plume from the inside, and carries the extra weight of the spike [Aerospike engine]. The 5.3 to 8.5 percent bounds the prize and does not predict the win, and the base flow that decides the difference is beyond a one-dimensional isentropic model.
The trajectory is a model fitted to two points. The manufacturer publishes the altitude at liftoff and at cut-off and no altitude between them [ABL Payload User’s Guide]. The pressure-time integral was computed across a family of profiles and the spread reported, but the family is a guess about the shape of a gravity turn and a real ascent is not a power law.
The module count of the ARISE engine is not published by the programme, and the one reference that states a count, nine, gives no source, so the parity result concerns rings in general and the parent vehicle’s engine count, not the hardware that was to fly. If the modules are not arranged on a ring, the result does not apply at all.
The chamber recovery rests on five assumed properties and a mode identification that is not this article’s. It is offered as a demonstration that the frequency constrains the geometry, and the width of the band it produces measures how much.
And the register is not a primary source here. Both rows are marked as reconstructions by the compiler’s convention, which means the description this article opened with is somebody’s careful reading of open sources rather than a government statement. What is primary is the pair of dates, the pair of contractor names and the fact that two numbers were issued at once.
The Source Base
The Research References
The survey holds 8,762 research records, and every one of them is cited across 22 clusters. They come from the National Aeronautics and Space Administration’s technical reports server, the Defense Technical Information Center’s registry and a journal and conference index. A further 169 definitions are hand-written, being 106 primary documents and encyclopaedic anchors and 63 back-references to earlier articles in this series. The plug nozzle was studied between the late nineteen fifties and the late nineteen seventies by government laboratories and their contractors, who wrote report numbers.
Where the Clusters Publish
The share of report-server records runs from 15.3 to 64.5 percent across the clusters. The thinnest is the fixed-nozzle limits cluster, and the richest is the cluster on the exhaust nozzles of aircraft engines, where the plug nozzle’s first measurements were made in government laboratories. The keystone, altitude compensation, stands at 24.3 percent, against 29.1 percent for the survey as a whole.
The thin report share of the aerospike clusters is matched by a larger share from one publisher. Counting records that carry the digital object identifier prefix of the American Institute of Aeronautics and Astronautics, that society publishes 34 percent of the altitude compensation cluster, 49 percent of the wake cluster and 43 percent of the fixed-nozzle limits cluster, against 36 percent of the survey. Nearly half of the wake literature comes from that one society. The aircraft exhaust nozzle cluster is 24 percent from that publisher and 65 percent reports. The aerospike’s own flows lean on one society’s publications and the older nozzle work around them leans on reports, which suggests that the keystone’s thin report share reflects where this work is published rather than a gap in the archives.
Every Central Noun Is Owned by Another Field
Every central noun of this subject is owned by another field. A search of the bibliographic index for each bare term returns another field’s literature.
spike returns music, wheat, neural spike trains and the coronavirus spike protein, with nothing mechanical in ten results. wake closure returns fatigue crack closure in the crack wake, an entire metallurgical literature, and no rocket result at all. open wake and closed wake return a university and wind-farm wake steering. area ratio is owned by cardiology and thrust coefficient by wind turbines. gas generator is owned by nineteen-seventies coal gasification. altitude compensation returns altitude physiology and a 1976 paper on compensating a carburettor, which is the same idea in a different machine and is not this literature.
So the survey’s patterns pin each noun with a second noun. The compounds that name this subject without collision are truncated plug nozzle, aerospike nozzle, expansion deflection nozzle, plug nozzle altitude compensation and linear aerospike. The only single terms that serve alone are aerospike, turbopump and truncated plug, and aerospike still returns a dictionary headword and a fish.
The proper nouns are worse than the physics. ARISE returns a poem, a hymn and a real European atmospheric-dynamics research infrastructure of the same name. ABL returns Abl tyrosine kinase. ARMR is unusable as a search term, returning six fields and no aerospace, and even the full expansion is not an anchor, since Affordable Responsive Modular Rocket returns affordable housing. RS1 returns the retinoschisin gene. Invocon and Troy7 each return nothing at all.
The Definition of Primary
A research record is a report primary when its identifier is a citation in the National Aeronautics and Space Administration’s technical reports server or a registration under the Defense Technical Information Center’s prefix, 10.21236. By that rule 2,546 of the 8,762 research records, 29.1 percent, are report primaries. The rule classifies by where a record is served and not by who wrote it, so a laboratory’s paper published by a society counts as secondary. The primary documents of the programme itself, being the laboratory’s fact sheet, the award announcement, the manufacturer’s payload user’s guide and incident report, and the register, are hand-written definitions and are not counted among the research records.
Thin Subjects
Seven subjects that this article’s derivations depend on have thin literatures in the survey. Each is counted over the titles of the 8,762 cited research records, a title matching when it carries a term from every group given, with groups separated by semicolons.
| Subject | Title terms | Titles |
|---|---|---|
| differential throttling as a means of steering | differential throttling, differentially throttled, differential throttle | 5 |
| the open, transitional and closed wake of a truncated plug | open wake, closed wake, wake closure, wake transition; plug, spike, aerospike | 0 |
| the area ratio that is optimal over a whole trajectory | optimal expansion ratio, optimum expansion ratio, optimal area ratio, optimum area ratio, trajectory averaged | 1 |
| a criterion for the onset of nozzle flow separation | separation; criterion, criteria; nozzle, nozzles | 1 |
| the first tangential acoustic mode of a chamber | tangential; mode, modes, instability | 9 |
| losing one engine of several | engine out, engine failure, engine failures | 12 |
| the convex duality of thrust and ambient pressure | legendre, convex conjugate, bregman, fenchel; nozzle, nozzles, thrust | 0 |
No title in the survey names the open, transitional or closed wake of a plug. The two titles that name wake transition concern laminar and turbulent transition behind flat plates and bodies, so the three regimes the programme names are carried by the curated papers cited under The Three Regimes the Programme Names rather than by the survey. Differential throttling appears in five titles, all of them on aerospikes, the earliest from 2003 and four of them from 2024 onward. The tangential mode appears in nine titles, two of them on solid motors and the rest on liquid-propellant or unstated rocket chambers. Engine-out appears in twelve titles, eight of them on a launch vehicle or its stage. No title applies Legendre or convex duality to nozzle thrust, and one title optimises a nozzle over a trajectory average, so the mean-in-time rule derived above has almost no company among the survey’s titles.
What the Survey Admits
A record is admitted only when a person reading its title finds it on this article’s subject, meaning a subject the argument uses. Those subjects are altitude-compensating and fixed nozzles and their flows, separation and side loads, base flow and the wake, jets and plumes, thrust vector control and thrust allocation, the liquid rocket engine and its machinery, clustered and modular engines and engine-out, manufacture and cost, launch vehicles and the ascent, measurement and ground test, the atmosphere as a flight condition, the programme and its sponsors, and compressible flow stated generally. The vocabulary of this subject has to be read in compounds, because every central noun of it is owned by another field, as the subsection above shows.
The classes excluded are those that share a word with this subject and nothing else, and those whose domain is distant from it. Nozzles for liquids, sprays, welding, cold spray, isotope separation, turbochargers and the blade rows of turbines share the word nozzle. Mantle plumes and groundwater share the word plume, an astrophysical jet shares the Mach disk, a nose spike on a blunt body shares the word spike without being a nozzle, theatre and literary studies share the words staging and wake, and a database product is named Aerospike. Electric, nuclear and beamed propulsion, solid propellant chemistry and hybrid fuels, re-entry and recovery, spacecraft and satellites, and science carried on rockets are rocket and space subjects the argument does not use, unless the title’s subject is a nozzle, a plume, steering or chamber acoustics. Payload environments, stage structures, jet and rocket noise, aircraft aerodynamics, air-breathing engines and missile ballistics are excluded on the same ground. Correction, erratum, withdrawal and retraction notices, figure and supplementary-material records and the annual subject indexes of journals are excluded as well, because a survey counts research works and those are parts of works or editorial events rather than works. Two records with the same folded title and the same first author are treated as one document, such as a conference paper and its journal version or a report deposited twice, and only the earlier is kept. A review of a book, a reference or definition entry and a notice are not admitted either, since none of them is a research work in its own right. The one exception to keeping the earlier of two records is a preprint, which gives way to its published version.
Some records of doubtful relevance are kept. A title whose subject cannot be told from its words is kept when its words name a rocket propulsion subject or venue. Reusable launch vehicle control titles that do not say whether the flight is ascent or entry are kept as steering, hybrid launch vehicles treated as vehicles are kept as launch vehicles, solid motor manufacture and cost are kept as manufacture, nozzles of wind tunnels are kept where the title studies the nozzle’s own flow, and aerospike nozzles fitted to detonation engines are kept because the nozzle is the subject. No cluster is a residual. The clusters on jets, aircraft nozzles, compressible flow and general rocket propulsion each hold only titles on a subject the argument uses. A reader may weigh each accordingly.
Every research title has been read for relevance, so the off-topic share that remains is a matter of reading judgement.
What the Award Record Holds
A search of the federal award reporting system finds no record of this programme under the names it is known by, for the reason given under The Instrument That Bought It, which is that an award made through the Space Enterprise Consortium is administered by the consortium’s manager under a base agreement, so a search under the name of the company doing the work need not find it.
What This Article Read in Full
Five primary documents have been read end to end, and every quotation in this article comes from one of them. They are the laboratory’s public fact sheet for the programme, the two-page cleared version of the same document carrying its distribution statement, the award announcement as reprinted verbatim by the base newspaper, the manufacturer’s payload user’s guide of June 2022, and the manufacturer’s own static-fire incident report of 26 August 2024. The register’s officiality classification depends on which element of its markup carries a class attribute rather than on any visible text, so the officiality counts in this article are taken from the markup itself.
Three official mirrors of the award announcement are not retrievable by automated request, which is the documented behaviour of that domain and not evidence about the document. The version cited is a verbatim reprint carrying the same byline and date, and its text agrees with the portions quoted in independent summaries.
Epistemic State
Facts, taken from primary documents and stated as they appear there. The two designations, their shared date of 20 April 2022, their sponsor cell, their engines cell and their identical 101-character description come from the register [Parsch, DOD 4120.15-L Addendum]. The programme’s objectives, the three wake regimes, the modular architecture and the clearance number come from the laboratory’s fact sheet [ARISE and Fly]. The December 2019 award date, the three-year term, the other transaction instrument, the scope wording, the promise of thrust vector control and the three quotations come from the award announcement [AFRL awards agreements under ARISE]. The vehicle’s dimensions, propellants, cycle, engine counts, thrust figures and reference mission come from the manufacturer’s payload user’s guide [ABL Payload User’s Guide]. The static fire date, the eleven engines, Engine 10, the 4.5 kilohertz first tangential mode, the erosion of two injectors, the three hundred prior tests and the full loss timeline come from the manufacturer’s incident report [Flight 2 Static Fire Update].
Derivations, which follow from the facts by mathematics and are confirmed numerically. The affine dependence of thrust on ambient pressure, the conjugacy of ambient pressure and exit area, the Legendre structure of the envelope, the identification of the fixed-nozzle loss as a Bregman divergence, and the rule that the optimal fixed nozzle expands to the burn-averaged ambient pressure are all exact. Central differences reproduce the conjugacy identity in twelve cases to 2.1 parts in a hundred thousand million. One hundred independent optimisations reproduce the mean-in-time rule to 4.2 parts in ten million. A direct directional search reproduces the ring formulae in forty-two cases to below one part in a million million.
Quantities that depend on assumptions, with the assumptions swept and the spread reported. The burn-averaged ambient pressure depends on an ascent profile fitted to two published points, and runs from 19.4 to 41.6 percent of sea level across the family used. The impulse gain of an ideal spike over the best fixed nozzle runs from 5.3 to 8.5 percent across ratios of specific heats from 1.20 to 1.24 and chamber pressures from 3 to 10 megapascal. The recovered chamber diameter runs from 147 to 179 millimetres across forty-eight combinations of gas properties, and the recovered chamber pressure from 2.6 to 8.7 megapascal across thirty-six further combinations. The payload worth of a percent of first-stage exhaust velocity, at least three quarters of a percent, assumes a second-stage effective exhaust velocity of 3,000 to 3,400 metres per second and takes the 2.6 kilometre per second staging speed as a floor on the first stage’s ideal velocity increment.
Inferences, marked as such where they appear. That the fact sheet’s phrase about a launch-to-orbit trajectory means a representative trajectory rather than an orbital flight. That the 133,118 pound force total thrust in a nine-engine row is the eleven-engine figure. That the X-63A programme has ended. That the ARISE engine’s modules, if arranged on a ring, would obey the parity result. None of these is stated as a fact anywhere in this article and each is reversible by one document.
Two conflicts in the sources are recorded and not resolved. The maximum payload of the RS1 is given as 1,200 kilograms in the award announcement and 1,350 kilograms in the launch-vehicle reference [AFRL awards agreements under ARISE] [RS1, Gunter’s Space Page]. And the programme is named a suborbital experiment while its own fact sheet describes a launch-to-orbit trajectory [ARISE and Fly].
One accounting rule governs the register’s officiality counts. The markup has three states, so the counts under The Register and Its Unofficial Wording are given as three numbers, since a two-number summary must misplace the partly marked row.
Two dateline limits. Every register count in this article is as of the compiler’s update of 23 August 2026, which is later than this article’s date, and the counts that differ under the version current on that date are stated beside them under The Register and Its Unofficial Wording [Parsch, DOD 4120.15-L Addendum, 11 August 2025]. The encyclopedia entry cited for the X-63A’s history carries a revision date of 17 December 2025, which is nine days after this article’s date [ABL Space Systems X-63]. Every statement drawn from it concerns events well before that, and the inference about cancellation is made here independently of it. The page’s earlier state was not retrievable from the web archive, and the gap is recorded as a limit and left unresolved.
What is not known and would change things. The module count and arrangement of the ARISE engine, beyond one unsourced reference’s count of nine. The chamber pressure and area ratio of the aerospike as designed. Whether any hardware was built. The dollar value of either agreement. And whether the X-64A, which shares every word of its description with this one, ever reached a different stage.
Out of Scope
The X-64A is a separate article. The Invocon team’s vehicle is described as apparently recoverable, landing on four legs that double as stabilising fins, about 12 metres tall and about 2.4 metres in diameter [Invocon X-64, Directory of U.S. Military Rockets and Missiles, Appendix 4], and the measurement problem it exists to solve is a different one. It is deliberately left alone here beyond the fact that its designation was issued on the same day for the same words.
The internal aerodynamics of the plug contour are not treated. Designing the spike surface is a method-of-characteristics problem with a large literature and it does not bear on the questions asked here.
Base heating, cooling and structural mass are named and not computed, for the reason given above, which is that none of them can be obtained from the model this article uses.
Nothing here is a judgement about whether the money was well spent. The programme bought a flight that did not happen, from a company that left the business, on an instrument that leaves no public trace of its value. Those are three facts and they do not add up to an assessment.
Conclusion
Two X numbers were issued on one day with one description, and the description does not say which vehicle is which.
The thing both were built to fly is older than almost everyone working on it and has never flown at the scale of a launch vehicle. This article’s account of why is that the prize is real, bounded and awkwardly sized. An ideal altitude-compensating nozzle is worth between 5.3 and 8.5 percent of first-stage impulse on this vehicle’s published trajectory, measured by the gain $\eta$ against the best fixed nozzle that trajectory admits. The figure is large for a launch vehicle and small against the cost of a new nozzle architecture.
The mathematics is tidier than the hardware. Thrust is affine in ambient pressure with slope minus the exit area. The incremental vacuum thrust from an increment of exit area is exactly the exit pressure, which makes ambient pressure and exit area conjugate variables. The ideal spike’s thrust curve is the Legendre transform of the vacuum thrust, every fixed nozzle is one of its tangent lines, and the loss of a fixed nozzle is a Bregman divergence. From the same identity comes the design rule, which is that the optimal fixed nozzle expands to the time-averaged ambient pressure of its own flight, a statement containing nothing about the gas, the engine or the vehicle.
And that rule makes the case, though less loudly than a flat separation criterion would suggest. Because half of the pressure-time integral $J$ is collected in the first 11 to 21 percent of the burn, the rule places the optimal nozzle at an exit-to-ambient ratio at liftoff equal to the burn-averaged fraction of sea-level pressure, which is 0.2806 for the central case of Flow Separation as the Deciding Limit.
Whether that separates depends on which criterion is used. Under the correlation that NASA Technical Paper 1207 fits to contoured nozzles, rather than the flat four tenths of the early studies that it calls inadequate, the trajectory optimum separates only below about 3.5 megapascal of chamber pressure, and the pressure recovered for this engine from its own instability frequency straddles that figure. So the optimum is within about a tenth of the largest exit area a bell can carry attached, a real constraint pressed hard, short of an impossibility, and an aerospike does not have it at all because it has no divergent wall for a boundary layer to leave.
The other half of the programme yields a second exact result and it points the other way. Differential throttling of a ring of modules gives a directional average authority of exactly the throttle depth divided by pi, at every module count from three upward, so more modules improve evenness rather than authority. The evenness depends on parity, because an odd ring has no diametrically opposite pair and its control polygon therefore has two sides per module instead of one. Nine modules steer as evenly as eighteen and better than any even count below twenty. After a failure the ranking reverses, because a failure breaks the symmetry the parity argument rests on, and then what matters is only how many are left.
The programme did not fly. The first vehicle of the parent design failed 10.87 seconds after liftoff, the second burned on the pad while the water ran out, and the company renamed itself and went into missile defence. The register still carries both numbers, side by side, with the same hundred and one characters against each. Nothing in it records that the two rows were ever anything but equal.
Equations
This section collects the 55 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 55, 33 are established and 22 are bespoke. Every relation is in the International System, with thrust in newtons and pressure in pascals except where a published table is checked in pounds force, and several letters take two meanings, so $L$ is the loss of a fixed nozzle against the envelope and then the distance from the engine plane to the centre of mass, $k$ indexes a module and is also the separation threshold ratio, $n$ is the shape exponent of the ascent profile and then a count of engines, $M$ is a Mach number while $M\left( \phi \right)$ is a control moment, and $p$ is a static pressure except in the binomial tail, where it is a probability per engine start.
Equation 1, Rocket Thrust Equation. The thrust is the momentum flux out of the nozzle plus the net pressure force on its exit plane. Huzel and Huang 1967 NASA SP-8120
\[F = \dot{m} v_e + \left( p_e - p_a \right) A_e \tag{1}\]Equation 2, Thrust as an Affine Function of Ambient Pressure. Grouping the terms that do not involve the atmosphere into a vacuum thrust shows that thrust falls linearly with ambient pressure at a slope of minus the exit area.
\[F_{\mathrm{vac}} = \dot{m} v_e + p_e A_e, \qquad F = F_{\mathrm{vac}} - p_a A_e \tag{2}\]Equation 3, Thrust Coefficient and Area Ratio. The thrust coefficient is the thrust over chamber pressure times throat area, and the area ratio is the exit area over the throat area. Huzel and Huang 1967 NASA SP-8120
\[C_F \equiv \frac{F}{p_c A_t}, \qquad \varepsilon \equiv \frac{A_e}{A_t} \tag{3}\]Equation 4, Thrust Coefficient Against Ambient Pressure. Dividing the affine law by chamber pressure times throat area gives the thrust coefficient as its vacuum value less the area ratio times the ambient to chamber pressure ratio. Huzel and Huang 1967 NASA SP-8120
\[C_F\left( \varepsilon, p_a \right) = C_{F,\mathrm{vac}}\left( \varepsilon \right) - \varepsilon \frac{p_a}{p_c} \tag{4}\]Equation 5, Vandenkerckhove Constant. The Vandenkerckhove constant collects the throat conditions of an isentropic nozzle as a function of the ratio of specific heats alone. Huzel and Huang 1967 NASA SP-8120
\[\Gamma\left( \gamma \right) = \sqrt{\gamma} \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma + 1}{2\left( \gamma - 1 \right)}} \tag{5}\]Equation 6, Isentropic Area and Pressure Ratios. The local area ratio and the local static to chamber pressure ratio of isentropic flow follow from the Mach number and the ratio of specific heats. Huzel and Huang 1967 NASA SP-8120
\[\frac{A}{A_t} = \frac{1}{M}\left[ \frac{2}{\gamma + 1}\left( 1 + \frac{\gamma - 1}{2} M^2 \right) \right]^{\frac{\gamma + 1}{2\left( \gamma - 1 \right)}}, \qquad \frac{p}{p_c} = \left( 1 + \frac{\gamma - 1}{2} M^2 \right)^{-\frac{\gamma}{\gamma - 1}} \tag{6}\]Equation 7, Vacuum Thrust Coefficient of an Ideal Nozzle. The vacuum thrust coefficient is a momentum term set by the exit pressure ratio plus the exit plane pressure term against a vacuum. Huzel and Huang 1967 NASA SP-8120
\[C_{F,\mathrm{vac}}\left( \varepsilon \right) = \Gamma \sqrt{ \frac{2 \gamma}{\gamma - 1} \left[ 1 - \left( \frac{p_e}{p_c} \right)^{\frac{\gamma - 1}{\gamma}} \right] } + \varepsilon \frac{p_e}{p_c} \tag{7}\]Equation 8, Characteristic Velocity and Specific Impulse. The characteristic velocity carries the propellant and chamber, the thrust coefficient carries the nozzle and atmosphere, and the specific impulse is their product over standard gravity.
\[c^{\star} = \frac{p_c A_t}{\dot{m}} = \frac{1}{\Gamma}\sqrt{\frac{R_u T_c}{\bar{M}}}, \qquad I_{sp} = \frac{C_F \, c^{\star}}{g_0} \tag{8}\]Equation 9, Pressure-Time Integral and Delivered Impulse. The whole atmospheric penalty of a fixed nozzle over a burn is its exit area times the time integral of ambient pressure.
\[J = \int_{0}^{t_b} p_a(t) \, \mathrm{d}t, \qquad \int_{0}^{t_b} F \, \mathrm{d}t = F_{\mathrm{vac}} t_b - A_e J \tag{9}\]Equation 10, Marginal Vacuum Thrust of Exit Area. With the one-dimensional momentum equation, the vacuum thrust gained by an increment of exit area is the exit pressure acting on that increment.
\[\frac{\mathrm{d} F_{\mathrm{vac}}}{\mathrm{d} A_e} = \dot{m} \frac{\mathrm{d} v_e}{\mathrm{d} A_e} + p_e + A_e \frac{\mathrm{d} p_e}{\mathrm{d} A_e} = -A_e \frac{\mathrm{d} p_e}{\mathrm{d} A_e} + p_e + A_e \frac{\mathrm{d} p_e}{\mathrm{d} A_e} = p_e \tag{10}\]Equation 11, Thrust as Vacuum Thrust Less a Linear Term. The thrust against an atmosphere is the vacuum thrust as a function of exit area less the ambient pressure times the exit area, the pairing of a Legendre transform.
\[F(p_a; A_e) = G(A_e) - p_a A_e \tag{11}\]Equation 12, Derivative of the Thrust Coefficient With Area Ratio. The derivative of the thrust coefficient with respect to area ratio is the pressure difference across the exit plane over the chamber pressure.
\[\frac{\partial C_F}{\partial \varepsilon} = \frac{p_e - p_a}{p_c} \tag{12}\]Equation 13, Envelope of Fixed Nozzles as a Legendre Transform. The best thrust any fixed nozzle can give at an ambient pressure is the upper envelope of the family of straight lines, which is the Legendre transform of the vacuum thrust and the thrust of an ideal altitude-compensating nozzle. Legendre transformation convex conjugate
\[F^{\star}(p_a) = \max_{A_e} \left\{ G(A_e) - p_a A_e \right\} \tag{13}\]Equation 14, Fenchel-Young Inequality for Nozzle Thrust. The thrust of any fixed nozzle at any ambient pressure is at most that of the envelope, with equality only where the nozzle is matched.
\[G\left( A_e \right) \le F^{\star}\left( p_a \right) + p_a A_e \quad \text{for every } A_e \text{ and every } p_a \tag{14}\]Equation 15, Inverse Legendre Transform. The vacuum thrust of every fixed nozzle can be recovered from the envelope by a minimisation over ambient pressure.
\[G\left( A_e \right) = \min_{p_a} \left\{ F^{\star}\left( p_a \right) + p_a A_e \right\} \tag{15}\]Equation 16, Slope and Convexity of the Envelope. By the envelope theorem the slope of the envelope is minus the optimal exit area, and the envelope is convex because the optimal nozzle shrinks as ambient pressure rises. envelope theorem
\[\frac{\mathrm{d} F^{\star}}{\mathrm{d} p_a} = -A_e\left( p_a \right), \qquad \frac{\mathrm{d}^2 F^{\star}}{\mathrm{d} p_a^2} = -\frac{\mathrm{d} A_e}{\mathrm{d} p_a} \ge 0 \tag{16}\]Equation 17, Loss of a Fixed Nozzle as a Bregman Divergence. The loss of a nozzle matched at one ambient pressure, measured against the envelope at another, is the Bregman divergence of the envelope generated at the design point. Bregman divergence envelope theorem
\[L(p_a) = F^{\star}(p_a) - \left[ G(A_d) - p_a A_d \right] = F^{\star}(p_a) - F^{\star}(p_d) - F^{\star\prime}(p_d)\left( p_a - p_d \right) \tag{17}\]Equation 18, Loss as an Integral of Exit Area Mismatch. The loss is the integral over ambient pressure of the difference between the fitted exit area and the exit area the envelope would choose.
\[L\left( p_a \right) = \int_{p_d}^{p_a} \left[ A_d - A_e\left( q \right) \right] \mathrm{d}q \tag{18}\]Equation 19, Delivered Impulse of a Fixed Nozzle. Because the thrust coefficient is affine in ambient pressure, the burn-integrated coefficient is the vacuum value times the burn time less the area ratio times the pressure-time integral over chamber pressure.
\[I(\varepsilon) = \int_{0}^{t_b} C_F \, \mathrm{d}t = t_b \, C_{F,\mathrm{vac}}(\varepsilon) - \frac{\varepsilon}{p_c} \int_{0}^{t_b} p_a(t)\, \mathrm{d}t \tag{19}\]Equation 20, Bespoke Mean-in-Time Rule for the Optimal Fixed Nozzle. Maximising delivered impulse at a chamber pressure held constant through the burn, the objective the article chooses, sets the exit pressure of the best fixed nozzle equal to the time-averaged ambient pressure.
\[t_b \frac{p_e}{p_c} = \frac{J}{p_c} \qquad \Longrightarrow \qquad p_e = \frac{J}{t_b} = \frac{1}{t_b}\int_{0}^{t_b} p_a(t)\, \mathrm{d}t \tag{20}\]Equation 21, Bespoke Burn-Averaged Ambient Pressure and the Selected Area Ratio. The article’s rule selects the area ratio whose exit pressure equals the ambient pressure averaged over the burn time. Hiers and Knapke 2019
\[\bar{p}_a \equiv \frac{1}{t_b}\int_{0}^{t_b} p_a(t)\, \mathrm{d}t, \qquad p_e\left( \varepsilon^{\star} \right) = \bar{p}_a \tag{21}\]Equation 22, Bespoke Power-Law Ascent Profile. The first-stage altitude is modelled as the cut-off altitude times a power of the fraction of burn time, with an exponent the article sweeps from 1.5 to 3.0 because the trajectory is not published.
\[h(t) = h_b \left( \frac{t}{t_b} \right)^{n}, \qquad 1.5 \le n \le 3.0 \tag{22}\]Equation 23, Pressure in a Layer of the 1976 Standard Atmosphere. The pressure in a layer with a temperature lapse and in an isothermal layer follows the two hydrostatic forms of the 1976 United States Standard Atmosphere. U.S. Standard Atmosphere 1976 1976 defining constants and abbreviated tables
\[p(h) = p_0 \left( 1 + \frac{\lambda \left( h - h_0 \right)}{T_0} \right)^{-\frac{g_0}{R \lambda}}, \qquad p(h) = p_0 \exp\left( -\frac{g_0 \left( h - h_0 \right)}{R T_0} \right) \tag{23}\]Equation 24, Pressure Scale Height. The pressure scale height is the gas constant times the temperature over standard gravity.
\[H \equiv -\frac{p}{\mathrm{d}p / \mathrm{d}h} = \frac{R T}{g_0} \tag{24}\]Equation 25, Bespoke Pressure-Time Integral for an Isothermal Constant-Rate Climb. For an isothermal atmosphere climbed at a constant rate, both simplifications the article chooses, the integral saturates at sea-level pressure times the scale height over the climb rate.
\[J = \frac{p_0 H}{v}\left[ 1 - \exp\left( -\frac{v t_b}{H} \right) \right] \;\longrightarrow\; \frac{p_0 H}{v} \quad \text{as } v t_b \gg H \tag{25}\]Equation 26, Bespoke Fractional Impulse Gain of the Ideal Spike. The article’s figure of merit is the burn-integrated thrust coefficient of the ideal altitude-compensating nozzle over that of the best fixed nozzle, less one.
\[\eta = \frac{\displaystyle\int_{0}^{t_b} C_F^{\star}\left( p_a(t) \right) \mathrm{d}t}{\displaystyle\int_{0}^{t_b} C_F\left( \varepsilon^{\star}, p_a(t) \right) \mathrm{d}t} - 1 \tag{26}\]Equation 27, Bespoke Exit to Ambient Pressure Ratio at Liftoff. Under the article’s mean-in-time rule the optimal nozzle’s exit pressure at liftoff is the burn-averaged ambient pressure divided by sea-level pressure.
\[\left. \frac{p_e}{p_a} \right|_{t=0} = \frac{\bar{p}_a}{p_{\mathrm{SL}}} = \frac{1}{p_{\mathrm{SL}} t_b} \int_{0}^{t_b} p_a(t) \, \mathrm{d}t \tag{27}\]Equation 28, Separation Criterion at Sea Level. A flow that separates below a threshold ratio of exit to ambient pressure limits the area ratio to the one whose exit pressure is the threshold times sea-level pressure.
\[\frac{p_e}{p_a} \ge k \qquad \Longrightarrow \qquad p_e\left( \varepsilon_{\mathrm{sep}} \right) = k \, p_{\mathrm{SL}} \tag{28}\]Equation 29, Morrisette and Goldberg Separation Correlation for Contoured Nozzles. The ratio of separation wall pressure to ambient pressure for contoured nozzles is a second-order fit in the separation Mach number between Mach 2.4 and 4.5. Morrisette and Goldberg 1978
\[\frac{p_s}{p_a} = 1.082 - 0.363 M_s + 0.0386 M_s^2 \tag{29}\]Equation 30, Bespoke Margin of the Optimal Area Ratio Below the Separation Limit. The article defines the margin as one less the ratio of the trajectory-optimal area ratio to the separation-limited one, evaluated on its assumed chamber pressures and power-law ascent.
\[\varepsilon^{\star}\left( p_c \right) = \varepsilon_{\mathrm{sep}}\left( p_c \right), \qquad \mu \equiv 1 - \frac{\varepsilon^{\star}}{\varepsilon_{\mathrm{sep}}}, \qquad 1 - \frac{21.07}{22.55} = 0.066, \qquad 1 - \frac{28.02}{32.10} = 0.127 \tag{30}\]Equation 31, Thrust Decomposition of a Truncated Plug. The thrust of a truncated plug is the axial force on the wetted surface plus the base pressure acting on the exposed base.
\[F = F_w + p_b A_b \tag{31}\]Equation 32, Open and Closed Wake Regimes of a Plug Base. In the open wake the base pressure follows the ambient pressure, and in the closed wake it is set by the recirculation instead. Giel and Mueller 1975a Marsilio 2001
\[p_b \approx p_a \;\; \text{open wake}, \qquad p_b \neq p_a \;\; \text{closed wake} \tag{32}\]Equation 33, Bespoke Control Moment of a Throttled Ring. The article idealises the steering engines as $N$ equal modules equally spaced on a ring, so the moment about a horizontal axis is the throttle-weighted sum of their projected arms.
\[M(\phi) = \frac{F r}{N} \sum_{k=0}^{N-1} \tau_k \cos\left( \theta_k - \phi \right) \tag{33}\]Equation 34, Balance of an Equally Spaced Ring. The cosines of equally spaced angles sum to zero for every direction, so a ring of equal thrusters all wide open applies no moment.
\[\sum_{k=0}^{N-1} \cos\left( \theta_k - \phi \right) = 0 \qquad \text{for every } N \ge 2 \text{ and every } \phi \tag{34}\]Equation 35, Bespoke Optimal Bang-Bang Control Moment. With every module throttleable over the same depth, the best pattern opens the forward half and closes the rear half to its floor, giving a moment proportional to the support function of a regular polygon.
\[\frac{M(\phi)}{F r} = \frac{\delta}{N} \sum_{k} \max\left( \cos\left( \theta_k - \phi \right), \, 0 \right) \tag{35}\]Equation 36, Mean of the Positive Part of a Cosine. The mean of the positive part of a cosine over a full turn is the reciprocal of pi.
\[\frac{1}{2\pi}\int_{0}^{2\pi} \max\left( \cos u, 0 \right) \mathrm{d}u = \frac{1}{2\pi}\int_{-\pi/2}^{\pi/2} \cos u \, \mathrm{d}u = \frac{1}{\pi} \tag{36}\]Equation 37, Bespoke Direction-Averaged Control Authority. Averaged over all commanded directions the idealised ring’s normalised moment is the throttle depth over pi, independent of the module count.
\[\left\langle \frac{M}{F r} \right\rangle_{\phi} = \frac{\delta}{\pi} \tag{37}\]Equation 38, Bespoke Directions at Which the Open Set Changes. The vertices of the idealised ring’s moment polygon lie where a module crosses the boundary of the forward half plane.
\[\phi \in \left\{ \theta_k + \frac{\pi}{2} \right\} \cup \left\{ \theta_k - \frac{\pi}{2} \right\}, \qquad k = 0, \dots, N-1 \tag{38}\]Equation 39, Bespoke Number of Sides of the Moment Polygon. The idealised ring’s moment polygon has $N$ sides for an even module count and $2N$ for an odd one.
\[m = \begin{cases} N, & N \text{ even} \\ 2N, & N \text{ odd} \end{cases} \tag{39}\]Equation 40, Bespoke Guaranteed and Best-Case Control Authority. The smallest and largest normalised moments of the idealised ring follow in closed form from the number of polygon sides, and their ratio is the secant of pi over that number.
\[\frac{M_{\min}}{F r} = \frac{\delta}{m \tan\left( \pi / m \right)}, \qquad \frac{M_{\max}}{F r} = \frac{\delta}{m \sin\left( \pi / m \right)}, \qquad \frac{M_{\max}}{M_{\min}} = \frac{1}{\cos\left( \pi / m \right)} \tag{40}\]Equation 41, Bespoke Guaranteed Authority for Four Module Counts. The guaranteed authority is evaluated at an assumed throttle depth of two tenths for rings of eight, nine, twelve and sixteen modules.
\[\frac{0.2}{8 \tan\left( \pi / 8 \right)} = 0.0603553, \qquad \frac{0.2}{18 \tan\left( \pi / 18 \right)} = 0.0630142, \qquad \frac{0.2}{12 \tan\left( \pi / 12 \right)} = 0.0622008, \qquad \frac{0.2}{16 \tan\left( \pi / 16 \right)} = 0.0628417 \tag{41}\]Equation 42, Bespoke Advantage of a Nine-Module Ring. At the assumed throttle depth of two tenths, nine modules guarantee 1.31 percent more authority than twelve and 4.41 percent more than eight.
\[\frac{0.0630142}{0.0622008} = 1.0131, \qquad \frac{0.0630142}{0.0603553} = 1.0441 \tag{42}\]Equation 43, Bespoke Thrust and Moment Lost With One Module. Removing one module from the balanced idealised ring costs one part in $N$ of thrust and leaves an unbalanced moment of up to one part in $N$.
\[\frac{\Delta F}{F} = \frac{1}{N}, \qquad \frac{M_{\mathrm{out}}\left( \phi \right)}{F r} = -\frac{1}{N}\cos\left( \theta_j - \phi \right) \tag{43}\]Equation 44, Bespoke Control Moment of the Surviving Ring. After one module fails, the idealised ring’s moment is the sum over the remaining modules alone, which is a different sum and not a scaled copy of the intact one.
\[\frac{M\left( \phi \right)}{F r} = \frac{1}{N}\sum_{k \neq j} \tau_k \cos\left( \theta_k - \phi \right), \qquad \tau_k \in \left[ 0, 1 \right] \tag{44}\]Equation 45, Bespoke Authority Retained After One Module Fails. The article defines the retained fraction as the guaranteed moment of the surviving ring over that of the intact ring with full throttle range, giving 58.6 percent for eight modules and 65.3 percent for nine.
\[\rho = \frac{\min_{\phi} \sum_{k \neq j} \max\left( \cos\left( \theta_k - \phi \right), 0 \right)}{\min_{\phi} \sum_{k} \max\left( \cos\left( \theta_k - \phi \right), 0 \right)}, \qquad \rho_8 = \frac{0.176777}{0.301777} = 0.586, \qquad \rho_9 = \frac{0.205648}{0.315071} = 0.653 \tag{45}\]Equation 46, Bespoke Equivalent Gimbal Angle of Differential Throttling. Equating a gimballed engine’s moment to the idealised ring’s direction-averaged moment gives an equivalent deflection proportional to the throttle depth and the ratio of ring radius to moment arm.
\[\sin \alpha = \frac{\delta}{\pi} \cdot \frac{r}{L} \tag{46}\]Equation 47, Check of the Published Thrust Table. The stated total exceeds nine engines at the stated per-engine thrust by 22.24 percent and matches eleven engines to 135 parts per million. ABL Space Systems X-63
\[\frac{133{,}118 - 9 \times 12{,}100}{9 \times 12{,}100} = \frac{24{,}218}{108{,}900} = 0.2224, \qquad \frac{133{,}118}{12{,}100} = 11.0015, \qquad \frac{133{,}118 - 11 \times 12{,}100}{133{,}118} = \frac{18}{133{,}118} = 1.35 \times 10^{-4} \tag{47}\]Equation 48, First Tangential Acoustic Mode of a Cylindrical Chamber. The frequency of the first tangential mode is the first stationary point of the Bessel function of order one times the speed of sound over pi times the chamber diameter, which inverts to give the diameter.
\[f_{1T} = \frac{\alpha_{1T} \, c}{\pi D} \qquad \Longrightarrow \qquad D = \frac{\alpha_{1T} \, c}{\pi f_{1T}} \tag{48}\]Equation 49, Frozen Speed of Sound in the Combustion Products. The frozen speed of sound follows from the ratio of specific heats, the universal gas constant, the chamber temperature and the mean molar mass. NASA SP-8124 NASA SP-8107
\[c = \sqrt{\frac{\gamma R_u T_c}{\bar{M}}} \tag{49}\]Equation 50, Throat Area and Chamber Pressure From the Chamber Diameter. The throat area follows from the chamber diameter and contraction ratio, and the chamber pressure from the thrust, the thrust coefficient and that area.
\[A_t = \frac{\pi D^2}{4 \sigma}, \qquad p_c = \frac{F}{C_F A_t} = \frac{4 \sigma F}{\pi C_F D^2} \tag{50}\]Equation 51, Bespoke Overlap of the Recovered and Assumed Chamber Pressure Bands. The overlap of the band recovered from the instability frequency with the band of 3 to 10 megapascal that the article assumes on general grounds is 93.5 percent of the first and 82.0 percent of the second.
\[\frac{8.74 - 3}{8.74 - 2.60} = \frac{5.74}{6.14} = 0.935, \qquad \frac{8.74 - 3}{10 - 3} = \frac{5.74}{7} = 0.820 \tag{51}\]Equation 52, Binomial Tail for Two or More Failures. If engine starts are independent with a common probability of instability, the chance of two or more among $n$ engines is one minus the probabilities of none and of exactly one.
\[\Pr\left[ X \ge 2 \right] = 1 - \left( 1 - p \right)^{n} - n p \left( 1 - p \right)^{n-1} \tag{52}\]Equation 53, Interval From the End of Water Supply to the Buckling. The reported times give 714 seconds from the mobile water stores running out to the structure buckling, and the reported half second of main-stage combustion is 3.8 percent of the planned thirteen. Flight 2 Static Fire Update
\[\left( 23 \times 60 + 24 \right) - \left( 11 \times 60 + 30 \right) = 1404 - 690 = 714 \ \mathrm{s}, \qquad \frac{0.5}{13} = 0.038 \tag{53}\]Equation 54, Bespoke Payload Sensitivity to First-Stage Velocity Increment. Holding the second stage’s propellant and structure fixed, as the article chooses, the rocket equation gives a fractional payload gain that exceeds the velocity gain over the second-stage exhaust velocity.
\[\Delta v_2 = c_{e,2} \ln\frac{m_0}{m_f}, \qquad \frac{\Delta m_p}{m_p} = \frac{w}{c_{e,2}} \cdot \frac{m_0}{m_0 - m_f} \cdot \frac{m_f}{m_p} > \frac{w}{c_{e,2}} \tag{54}\]Equation 55, Bespoke Payload Worth of One Percent of Exhaust Velocity. The gain is evaluated with the staging speed of 2.6 kilometres per second taken as a floor on the first-stage increment and an assumed second-stage exhaust velocity of 3,000 to 3,400 metres per second.
\[w = 0.01 \, \Delta v_1 \ge 0.01 \times 2{,}600 = 26 \ \mathrm{m/s}, \qquad \frac{26}{3{,}400} = 0.0076, \qquad \frac{26}{3{,}000} = 0.0087 \tag{55}\]Notation
- $F$, the thrust
- $\dot{m}$, the mass flow of propellant
- $v_e$, the exhaust velocity at the exit plane
- $p_e$, the static pressure of the exhaust at the exit plane
- $p_a$, the ambient atmospheric pressure
- $A_e$, the area of the nozzle exit plane
- $A_t$, the area of the nozzle throat
- $F_{\mathrm{vac}}$, the thrust the same nozzle would produce against a vacuum
- $p_c$, the chamber pressure
- $C_F$, the thrust coefficient
- $C_{F,\mathrm{vac}}$, the thrust coefficient in vacuum
- $C_F^{\star}$, the thrust coefficient of the ideal altitude-compensating nozzle
- $\varepsilon$, the ratio of exit area to throat area
- $\varepsilon^{\star}$, the area ratio the mean-in-time rule selects
- $\varepsilon_{\mathrm{sep}}$, the largest area ratio that avoids separation at sea level
- $\gamma$, the ratio of specific heats
- $\Gamma$, the Vandenkerckhove constant
- $c^{\star}$, the characteristic velocity
- $T_c$, the chamber temperature
- $\bar{M}$, the mean molar mass of the combustion products
- $R_u$, the universal gas constant
- $I_{sp}$, the specific impulse in seconds
- $g_0$, standard gravity
- $J$, the time integral of ambient pressure over the burn
- $t_b$, the burn duration of the first stage
- $G$, the vacuum thrust regarded as a function of exit area
- $F^{\star}$, the upper envelope of the thrust of all fixed nozzles
- $p_d$, the ambient pressure at which a fixed nozzle is matched, with $A_d$ its exit area
- $\bar{p}_a$, the burn-averaged ambient pressure
- $h_b$, the altitude at main engine cut-off
- $H$, the pressure scale height of the atmosphere
- $\lambda$, the temperature lapse rate of an atmospheric layer
- $p_{\mathrm{SL}}$, the sea-level pressure of the standard atmosphere
- $\eta$, the fractional impulse gain of the ideal spike
- $M_s$, the Mach number at the point where the flow separates from the wall, with $p_s$ the wall pressure there
- $\mu$, the margin in area ratio of the trajectory-optimal nozzle below the separation limit
- $F_w$, the axial force on the wetted surface of a plug
- $p_b$, the pressure acting on the exposed base of a truncated plug, with $A_b$ the area of that base
- $N$, the number of thruster modules on the ring
- $r$, the radius of the ring of thruster modules
- $\tau_k$, the throttle fraction of module $k$
- $\theta_k$, the angular position of module $k$ on the ring
- $\delta$, the available throttle depth
- $\phi$, the direction of the commanded moment
- $M_{\mathrm{out}}$, the unbalanced moment left by the loss of one module
- $\rho$, the fraction of guaranteed steering authority retained after one module fails
- $f_{1T}$, the frequency of the first tangential acoustic mode
- $\alpha_{1T}$, the first stationary point of the Bessel function of order one
- $\sigma$, the contraction ratio, chamber area over throat area
- $c_{e,2}$, the effective exhaust velocity of the second stage
- $\Delta m_p$, the payload mass bought by a gain in first-stage velocity increment
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- Sechter, Brendan. 2025. “X-Planes: Boeing X-53 Active Aeroelastic Wing.” Brendan A R Sechter’s Development Blog, November 28. https://sgeos.github.io/aerospace/history/engineering/2025/11/28/x_planes_boeing_x53_active_aeroelastic_wing.html
- Sechter, Brendan. 2025. “X-Planes: Gulfstream X-54.” Brendan A R Sechter’s Development Blog, November 29. https://sgeos.github.io/aerospace/history/engineering/2025/11/29/x_planes_gulfstream_x54.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-55 ACCA.” Brendan A R Sechter’s Development Blog, November 30. https://sgeos.github.io/aerospace/history/engineering/2025/11/30/x_planes_lockheed_martin_x55_acca.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-56.” Brendan A R Sechter’s Development Blog, December 1. https://sgeos.github.io/aerospace/history/engineering/2025/12/01/x_planes_lockheed_martin_x56.html
- Sechter, Brendan. 2025. “X-Planes: ESAero X-57 Maxwell.” Brendan A R Sechter’s Development Blog, December 2. https://sgeos.github.io/aerospace/history/engineering/2025/12/02/x_planes_esaero_x57_maxwell.html
- Sechter, Brendan. 2025. “X-Planes: X-58, the Slot Taken by XQ-58.” Brendan A R Sechter’s Development Blog, December 3. https://sgeos.github.io/aerospace/history/engineering/2025/12/03/x_planes_x58_slot_taken_by_xq58.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-59 Quesst.” Brendan A R Sechter’s Development Blog, December 4. https://sgeos.github.io/aerospace/history/engineering/2025/12/04/x_planes_lockheed_martin_x59_quesst.html
- Sechter, Brendan. 2025. “X-Planes: Generation Orbit X-60.” Brendan A R Sechter’s Development Blog, December 5. https://sgeos.github.io/aerospace/history/engineering/2025/12/05/x_planes_generation_orbit_x60.html
- Sechter, Brendan. 2025. “X-Planes: Dynetics X-61 Gremlins.” Brendan A R Sechter’s Development Blog, December 6. https://sgeos.github.io/aerospace/history/engineering/2025/12/06/x_planes_dynetics_x61_gremlins.html
- Sechter, Brendan. 2025. “X-Planes: Lockheed Martin X-62 VISTA.” Brendan A R Sechter’s Development Blog, December 7. https://sgeos.github.io/aerospace/history/engineering/2025/12/07/x_planes_lockheed_martin_x62_vista.html
Referenced by
- X-Planes: Synthesis and What the Designation Became 2025-12-16
- X-Planes: Bell Textron X-76 SPRINT 2025-12-15
- X-Planes: X-69 through X-75, the Leapfrogged Block 2025-12-14
- X-Planes: General Atomics X-68 LongShot 2025-12-13
- X-Planes: X-67, the Slot Taken by XQ-67A 2025-12-12
- X-Planes: Boeing X-66 2025-12-11
- X-Planes: Aurora Flight Sciences X-65 CRANE 2025-12-10
- X-Planes: Invocon X-64 2025-12-09