X-Planes: Convair X-11

The Convair X-11 could not stand up. Left standing with the tanks empty and unpressurised it would fold under its own weight, so, by the account of the SM-65 Atlas compilation, it had to be kept inflated with nitrogen at five pounds per square inch even when it carried no propellant. This article is the twelfth 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, and the X-10.

It is also the vehicle the previous article was about without naming. The X-10 was the testbed for the Navaho, an intercontinental cruise missile that was cancelled in July 1957 because a ballistic weapon of the same range arrives in about thirty-two minutes where an airbreathing one is exposed for a hundred and seventy-two. The X-11 is that ballistic weapon. It is the Atlas A, the first flying article of the programme that killed the Navaho, and it first flew on 11 June 1957, thirty-one days before the Air Force Headquarters message of 12 July 1957 that terminated the Navaho, as the Cape Canaveral launch history of Cleary 1991 The 6555th, Missile and Space Launches Through 1970 records. The official history of the programme is Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960. The standard inventory entry remains Jenkins Landis and Miller 2003 American X-Vehicles, An Inventory X-1 to X-50, the vehicle compilation comes from Miller 2001 The X-Planes, X-1 to X-45, and the structural principle is documented under the name balloon tank.

The Research Question

An intercontinental ballistic missile is a mass-fraction problem before it is anything else, because the rocket equation is unforgiving in a way no other transport relation is.

Why Structure Is the Binding Constraint

The velocity a rocket can reach is

\[\Delta v = v_{e} \ln \frac{m_{0}}{m_{f}} \tag{1}\]

where $v_e$ is the effective exhaust velocity and the mass ratio is gross mass over burnout mass. The burnout mass is structure plus payload, so every kilogramme of structure is a kilogramme that must be accelerated to the full burnout velocity and then thrown at the target for no effect. The logarithm is the difficulty. Improving the exhaust velocity gives a linear return, and improving the mass ratio gives a return that is only logarithmic, which means an intercontinental weapon must sit far out on a curve that is flattening under it.

The Atlas achieved a burnout mass of 5,395 kilogrammes on a gross mass of 117,900, which are the Atlas D’s 11,894 and 260,000 pounds in the SM-65 Atlas compilation, so its structural mass fraction is

\[\frac{m_{s}}{m_{0}} = \frac{5395}{117{,}900} = 0.0458 \tag{2}\]

and its propellant mass fraction is 95.4 percent. The mass ratio is therefore

\[\frac{m_{0}}{m_{f}} = \frac{117{,}900}{5395} = 21.85 \tag{3}\]

At a specific impulse of 282 seconds the effective exhaust velocity is $v_e = 282 \times 9.80665 = 2765$ metres per second, and the ideal velocity is

\[\Delta v = 2765 \times \ln 21.85 = 8530 \, \text{m/s} \tag{4}\]

Four and a half percent is an extraordinary number for a structure that has to survive launch. The Atlas is a fuel tank with an engine bolted underneath and almost nothing else, and the article’s subject is what that costs and what it gains. The relation itself and the design practice built on it are Sutton and Biblarz 2016 Rocket Propulsion Elements, with the period treatment of the limiting mass ratio in Wertheimer 1957 and the gravitational correction that separates ideal from achieved velocity in Sellers 1948 and Feodosiev and Siniarev 1959.

The Payoff, Carried Through to Range

The previous article derived the burnout speed a minimum-energy ballistic trajectory needs to cover ten thousand kilometres, which is 7193 metres per second. Setting that against the ideal velocity above gives the losses the ascent must absorb,

\[v_{\text{loss}} = \Delta v - v_{bo} = 8530 - 7193 = 1337 \, \text{m/s} \tag{5}\]

or 15.7 percent of the ideal velocity, a reasonable figure for gravity and drag losses on a vertical-rising ballistic ascent, adopted here as a calibration and not derived. With it fixed, the structural mass can be varied and carried all the way through to a range. Holding the propellant load constant and scaling only the structure,

\[v_{bo}(k) = v_{e} \ln \frac{m_{p} + k m_{s}}{k m_{s}} - v_{\text{loss}} \tag{6}\]

and feeding the result into the previous article’s range relation,

\[\sin \frac{\Phi}{2} = \frac{\lambda}{2 - \lambda}, \qquad \lambda = \frac{v_{bo}^{2}}{g R_{e}}, \qquad R = R_{e} \Phi \tag{7}\]

gives

Structure	Burnout speed	Range
as built	7193 m/s	9,999 km
1.5 times	6134 m/s	5,676 km
2 times	5400 m/s	3,941 km
3 times	4397 m/s	2,346 km

Making the structure half as efficient costs sixty-one percent of the range. A vehicle at one and a half times the Atlas structural mass is not a worse intercontinental missile. It is an intermediate-range missile, a different weapon with a different basing problem and a different strategic meaning. That loss is the argument for the balloon tank, and it explains why a programme accepted a vehicle that cannot be left standing without a nitrogen supply.

The trajectory machinery behind those numbers is period material. Ostner 1962 and Walters 1967 reduce ballistic trajectory computation to what a range could run, and the closed-form treatments are Punga and Campbell 1962 and Bell 1965. Stancil 1963 optimises by steepest ascent, Lubowe 1965 brings dynamic programming to optimum staging, and Randall 1970 traces the effect of staging on the resulting trajectory, with performance bookkeeping in Adams and Stoll 1969 and payload-optimal trajectories in Elliott and Rau 1968.

The caution the table requires is that the loss figure was calibrated so the baseline reproduces the previous article’s ten thousand kilometres, so the first row is fixed by construction. The sensitivity is the result, not the absolute range, and the sensitivity is robust because it depends on the logarithm and not on the calibration.

A Keystone Exercised Early

The keystone quantity of the X-10 was a gyroscope drift rate, which accumulates with time and separates from the bounded accelerometer error only after about forty-eight minutes. Its Cape flights of reported duration ran 51 to 79 minutes, so window length was no obstacle, and the article’s central result was that too few navigator flights were completed to estimate a drift distribution, five in all, two of them aborted. The X-11 has the opposite property, and the contrast is the sharpest the series has yet produced.

The Atlas structure is fully loaded within the first two minutes of flight. Maximum dynamic pressure occurs about a minute after lift-off, and the flight report of the National Aeronautics and Space Administration, NASA, on a later Atlas places its highest oxidizer-tank bending loads between 60 and 90 seconds Atlas-Centaur AC-12 Flight Performance 1968. The highest axial acceleration occurs at booster cutoff, which the later Atlas reached at 5.62 times gravity Atlas-Centaur AC-12 Flight Performance 1968, and both fall inside the 133 second burn of the Convair X-11 compilation. The two loads can be written as fractions of the mission and the comparison is stark. For the Atlas the structurally sizing events occur at

\[\frac{t_{\text{sizing}}}{t_{\text{mission}}} = \frac{133}{1932} = 0.069 \tag{8}\]

taking the mission as the 1932 second ballistic flight time derived in the previous article, so the structure is finished being tested seven percent of the way through the mission. For the X-10 the corresponding ratio was

\[\frac{t_{\text{leg}}}{t_{\text{mission}}} = \frac{1653}{10{,}333} = 0.16 \tag{9}\]

for a thousand-kilometre leg at its top speed, and its one reported navigation flight of seventy-nine minutes reached 0.46, yet the keystone was still not settled, because a drift rate is a distribution to be estimated over many flights while a load is applied in full on each one. The X-11 tested its keystone completely in seven percent of its mission, and the X-10 flew nearly half of its mission without completing enough navigation flights to settle its keystone, and the comparison reduces to that sentence. That the structurally sizing events cluster early is no accident of this vehicle but holds for any rocket ascent, and the period literature establishing where they fall runs through Wood 1961 on missile structural dynamics, Gerald and Runyan 1962 on the launch-vehicle case, and the ground-wind and ascent-load material cited below. The general point that a test article need only span the sizing envelope, not the mission, is implicit in structural test practice and is stated directly in Abraham 1963, a study of how to load a large article representatively and not exhaustively. A flight that goes no further than a hundred and twenty kilometres of apogee and about two fifths of the intercontinental burnout speed, as The Flight Test Record computes, still applies every structural load the mission will ever apply. A keystone that is exercised early can be validated cheaply. A keystone that accumulates cannot. The X-11 flew a fraction of the weapon’s mission and tested its keystone completely, and the X-10 flew a fraction of its weapon’s mission and tested its keystone hardly at all, and the difference is not programme competence but the mathematical character of the quantity each was built to establish.

Programme Origin

Convair had been working on long-range missiles since 1946 under project MX-774, a study contract the Army Air Forces awarded in April 1946 and cancelled in July 1947, after which Convair continued part of the work on its own funds Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960. The Air Force returned to Convair with a contract signed on 23 January 1951, designated Project MX-1593, which became the Atlas. Neufeld’s chapter on MX-1593 dates the MX-774 cancellation to July 1948, against July 1947 in his own detailed account of that project and in Dawson and Bowles 2004, and the earlier date is used here. The design authority throughout was Karel Bossart, whose contribution is the pressure-stabilised tank Dawson and Bowles 2004. The idea is older than the Atlas. According to Neufeld, Bossart’s MX-774 design had already removed the stiffeners of the V-2 and obtained its rigidity from nitrogen gas pressure, and the resulting weight programme improved the V-2’s airframe-to-propellant weight ratio by a factor of three. The reported inspiration was a cylindrical party balloon, an anecdote the balloon tank compilation repeats and the programme histories read for this article do not.

The German inheritance that shaped the American ballistic effort generally occupies Neufeld 1995 The Rocket and the Reich, and Walker 2005 Atlas, The Ultimate Weapon is a history of the Atlas whose full title describes it as written by those who built it, with a period account of the ballistic missile division’s evolution in Rockefeller and Alfred 1960. Contemporary treatments of the weapon class are Botterill 1961 and Lenihan 1962b, which are useful because they record what was thought at the time. Convair reached the pressure-stabilised structure from an aircraft background and not from a rocket one. Bossart said as much. He had worked on aircraft structures at Sikorsky and Vultee before the missile work, and Dawson and Bowles 2004 record that he always attributed his confidence in the thin-skinned design to that background. A company that builds thin-skinned pressurised fuselages has the instinct that a pressure vessel can be a primary structure, and the monocoque analysis the field already had runs from Hoff 1942, Wang and Ramamritham 1947, and Kaufman 1958.

The programme designation in the record is WS 107A-1, the weapon system number under which Cleary 1991 The 6555th, Missile and Space Launches Through 1970 records the Air Force activating the Atlas and which the Flight Test Working Group reports carry in their titles, and the missile family became SM-65 with variants lettered A through F. The compilations give the X-11 designation to the Atlas A and the X-12 to the Atlas B, which the next article treats, while Parsch 2005 Convair B-65/SM-65/CGM-16/HGM-16 Atlas places both numbers in the plan of 1953, as a single-engine and a three-engine test vehicle ahead of a five-engine prototype. Whether either designation was ever used operationally is not clear from the accessible record, and the Epistemic State says so. What is clear is that these are the fourth and fifth consecutive X numbers attached to vehicles that were never research aircraft, following the X-8, the X-9, and the X-10, and that the pattern the previous article identified, of a separate series being absorbed, not of the X-series broadening on the merits, now has more cases than it had exceptions.

Why the Idea Was Available to Convair and Not to Others

The pressure-stabilised tank is usually told as a flash of insight, and the party-balloon anecdote encourages that. The more useful reading is that Convair was the company most likely to have it, and for a reason unrelated to rockets.

An aircraft company that builds pressurised fuselages already believes that a pressure vessel can be primary structure. A transport fuselage is a thin shell that carries bending, torsion, and cabin pressure at once, and the analysis for it existed, in Hoff 1942, Wang and Ramamritham 1947, and Kaufman 1958. What Convair did was to remove the frames and stringers that a fuselage keeps because it must survive depressurisation, and to accept in exchange a structure that must never be depressurised Dawson and Bowles 2004.

Bossart’s own account of the reasoning, as Dawson and Bowles 2004 quote it from a 1974 interview, runs in the order a structures engineer would take. The tank needed a certain pressure to give the pump its required net positive suction head, so the first question was how thin the skin could be while holding that pressure, and the second was how much stiffening such a skin would need under the flight compression and bending. The answer to the second question was none. The section What the Standing Pressure Does inverts the same reasoning with numbers, starting from the pressure and asking what compression it offsets.

That is a trade an aircraft company can see and a rocket company might not, because it is a trade about what the structure is allowed to fail at and not about how strong it is. The Atlas is not a stronger tank. It is a tank that has been permitted to have a failure mode nobody would tolerate in an aeroplane, in exchange for a mass fraction no other arrangement could reach, and permitting that failure mode is a programme decision, not an engineering one.

The decision also depended on the mission. A weapon is expended, so a structure that cannot survive loss of pressure is acceptable in a way it would not be for something expected to be reused, ferried, stored unattended, or damaged and repaired. The X-10 in the previous article was recoverable and therefore could not make this trade. The two are one designation apart, the first Atlas A flew thirty-one days before the Navaho was terminated, and their structural philosophies are opposite for the same reason their keystones differed.

The One-and-a-Half Stage Arrangement

The Atlas carries three engines and jettisons two of them. All three ignite on the ground, and at booster cutoff the two outboard engines and their skirt are dropped while the sustainer continues on the same tanks SM-65 Atlas. The arrangement exists because igniting a large liquid engine at altitude was not trusted when Convair conceived it after the MX-774 cancellation Parsch 2005 Convair B-65/SM-65/CGM-16/HGM-16 Atlas, so the vehicle stages its engines without staging its tanks.

The Atlas A did not stage at all. It flew with the two booster engines and no sustainer, which is why Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960 describes the first flight as rising only a few thousand feet before one of its two engines failed, and the Convair X-11 compilation states that the sustainer engine was omitted. The article’s account of staging therefore concerns the Atlas that the A was prototyping, and the A itself tested the tank, the booster engines and the launch.

That decision interacts directly with the keystone. A conventional two-stage vehicle discards a whole tank set, and that discard supplies most of the structural benefit of staging. The Atlas discards only engines and skirt, so it gets a smaller staging benefit and has to make it up in structural efficiency. The balloon tank and the one-and-a-half stage arrangement are the same decision seen twice, since the vehicle that cannot drop its tanks must make its tanks weigh almost nothing. Schurmann 1957, Parkyn 1958, and Wertheimer 1957 optimise staging for the period, with the gravitational term in Sellers 1948.

Sizing From First Principles

How Thin the Shell Is

The Atlas is a cylinder ten feet in diameter and seventy-five feet long, the dimensions Cleary 1991 The 6555th, Missile and Space Launches Through 1970 gives for the missiles of all four test series, and the 75 feet 10 inches of the SM-65 Atlas compilation, 23.11 metres, is the length used below. The tank radius is

\[r = \frac{10 \times 0.3048}{2} = 1.524 \, \text{m} \tag{10}\]

and the skin is 301 extra-full-hard stainless steel between 0.014 and 0.037 inches thick, which is 0.356 to 0.940 millimetres. Those gauges are the ones NASA’s propellant-tank drawing of a later Atlas gives, station by station from the top of the oxidizer tank to the aft bulkhead Atlas-Centaur AC-12 Flight Performance 1968, and no drawing of the Atlas A’s own gauges has been found. The ratio that governs a thin shell is radius over thickness,

\[\frac{r}{t} = \frac{1.524}{0.000356} = 4286 \qquad \frac{r}{t} = \frac{1.524}{0.000940} = 1622 \tag{11}\]

Those numbers are hard to feel, so here is a benchmark. An aluminium drink can has a radius near 33 millimetres, and its wall is taken here as 0.1 millimetres, giving

\[\left. \frac{r}{t} \right|_{\text{can}} = \frac{0.033}{0.0001} = 330 \tag{12}\]

The Atlas skin is between five and thirteen times thinner in proportion than a drink can.

Membrane Stress and the Tapered Gauge

A pressurised thin cylinder carries its load in membrane tension. The hoop stress is

\[\sigma_{\theta} = \frac{p r}{t} \tag{13}\]

and the axial stress from the same pressure acting on the ends is half of it,

\[\sigma_{z} = \frac{p r}{2 t} \tag{14}\]

The ratio is fixed by geometry and not by design,

\[\frac{\sigma_{\theta}}{\sigma_{z}} = 2 \tag{15}\]

which has a consequence every pressure vessel shares. The hoop direction is always the first to yield, so a tank that bursts splits along its length and not around its circumference, and the weld that runs longitudinally is therefore the one that decides the vehicle.

The flight pressures are on record for that later Atlas. Its airborne regulators held the fuel tank between 57 and 60 pounds per square inch gauge and the oxidizer tank between 28.5 and 31 Atlas-Centaur AC-12 Flight Performance 1968, and the heaviest gauges lie in the fuel tank. At 60 pounds per square inch and the heavy gauge this gives

\[\sigma_{\theta} = \frac{413{,}685 \times 1.524}{0.000940} = 671 \, \text{MPa} \tag{16}\]

against a yield taken as 965 megapascals for the material in its extra-full-hard condition, a margin of 1.44. At the light gauge the same pressure would give

\[\sigma_{\theta} = \frac{413{,}685 \times 1.524}{0.000356} = 1771 \, \text{MPa} \tag{17}\]

which exceeds the ultimate strength of the material. The light gauge therefore cannot exist anywhere the pressure is high. The result does not discredit the calculation. It demonstrates the design rule. The drawing bears it out, because the 0.014 inch gauge sits at the top of the oxidizer tank Atlas-Centaur AC-12 Flight Performance 1968, where the regulated pressure is about half the fuel tank’s, and at 30 pounds per square inch it carries

\[\sigma_{\theta} = \frac{206{,}843 \times 1.524}{0.000356} = 885 \, \text{MPa} \tag{18}\]

a margin of 1.09 on the yield. The gauge is tapered to the local stress, and the local stress is dominated not by ullage pressure but by the head of propellant above the station under acceleration,

\[\Delta p = \rho \, n \, g \, h \tag{19}\]

For liquid oxygen at 1141 kilogrammes per cubic metre, ten metres of head, and six times gravity near burnout, close to the 5.62 times gravity the later Atlas reached at booster cutoff Atlas-Centaur AC-12 Flight Performance 1968,

\[\Delta p = 1141 \times 6 \times 9.80665 \times 10 = 671{,}000 \, \text{Pa} = 97 \, \text{psi} \tag{20}\]

which is more than one and a half times the ullage pressure. The bottom of the tank is the hardest-worked part of the vehicle and it is thickest there, and the taper is possible only because a membrane structure can be thinned where the load is small without any of the discontinuities that a stiffened structure would introduce. Period membrane analysis is in Bahiman and Thole 1965, with monocoque ring analysis in Hoff 1942 and material data in Manning and Price 1961, Johnson and Kelsen 1969, and Kuentz 1969.

The Common Bulkhead

The Atlas carries liquid oxygen and kerosene in one shell divided by a single dome, not in two tanks with structure between them Atlas-Centaur AC-12 Flight Performance 1968. The saving is one pressure dome and the intertank barrel that would separate them, and for a shell of this diameter that is a large fraction of the dry mass. A hemispherical dome of radius $r$ has an area of

\[A_{\text{dome}} = 2 \pi r^{2} = 2 \pi \times 1.524^{2} = 14.6 \, \text{m}^{2} \tag{21}\]

and an intertank barrel long enough to clear two domes adds roughly

\[A_{\text{barrel}} = 2 \pi r \times 2r = 4 \pi r^{2} = 29.2 \, \text{m}^{2} \tag{22}\]

so the common bulkhead removes on the order of forty square metres of shell, which at the average gauge is

\[m_{\text{saved}} = 43.8 \times 0.000648 \times 8000 = 227 \, \text{kg} \tag{23}\]

or about four percent of the empty vehicle from one design decision. The cost is that the bulkhead now separates a cryogen at 90 kelvin from a hydrocarbon at ambient temperature, so it must insulate as well as carry load, and a leak across it mixes the propellants inside the vehicle. The common bulkhead is the other Atlas idea still in use, and the Centaur upper stage separates its propellants with one Centaur rocket stage, for the reason computed here. Weiss and Goodman 1960 takes up the insulation problem it creates, and the vehicle that took the arrangement furthest in the period, and which kept the balloon tank as well, is described in Chitwood 1962. Membrane analysis of the domes themselves appears in Bahiman and Thole 1965 and Adam and King 1965.

Tank Volume and the Supporting Gas

The tank volume follows from the geometry,

\[V = \pi r^{2} L = \pi \times 1.524^{2} \times 18 = 131 \, \text{m}^{3} \tag{24}\]

and at a mixture ratio near 2.25 the propellant load divides into

\[m_{\text{LOX}} = m_{p} \frac{MR}{1 + MR} = 112{,}505 \times \frac{2.25}{3.25} = 77{,}888 \, \text{kg} \tag{25}\]

with the balance of 34,617 kilogrammes as kerosene. At densities of 1141 and 800 kilogrammes per cubic metre the volumes are 68.3 and 43.3 cubic metres, so the propellant occupies

\[\frac{111.5}{131} = 0.85 \tag{26}\]

of the tank, leaving fifteen percent for ullage, insulation, and the domes. The record does not confirm the assumed length. The tank stations of the later Atlas in Atlas-Centaur AC-12 Flight Performance 1968 run from 570 to 1,198 inches, so the whole tank, domes included, spans

\[\ell = (1198 - 570) \times 0.0254 = 15.95 \, \text{m} \tag{27}\]

and the 18 metres assumed here is long by a factor of 1.13. Treating even that span as a full cylinder gives

\[V' = \pi \times 1.524^{2} \times 15.95 = 116.4 \, \text{m}^{3}, \qquad \frac{111.5}{116.4} = 0.958 \tag{28}\]

so the volume, the skin mass and the nitrogen mass below are overstated by up to thirteen percent, and the fill fraction of 0.85 is not evidence for the assumed length.

Against all of that, the mass of nitrogen needed to hold five pounds per square inch of gauge pressure through the tank volume is

\[m_{N_{2}} = \frac{p V}{R T} = \frac{34{,}474 \times 131}{296.8 \times 290} = 52.5 \, \text{kg} \tag{29}\]

Fifty-two and a half kilogrammes of gas holds up five thousand three hundred and ninety-five kilogrammes of steel, a ratio of 103 to one. That single comparison states the design in one line.

Unlike the rest of the vehicle, the gas is recoverable and cheap, and that part of the bargain made it acceptable. Nitrogen at five pounds per square inch is nearly free and weighs too little to matter, and a structure that trades steel for nitrogen is trading an expensive mass for a free one.

Getting the gas in and keeping it there is a separate discipline, and the period worked it thoroughly because every large liquid vehicle needed it. Kaplan 1961 selects a pressurisation system, autogenous systems that pressurise with propellant vapour are Morey and Koshar 1961 and Coxe and Tatom 1962, pressurised transfer and discharge of cryogens are Humphrey 1961 and Nein and Head 1962, and the dilution and conditioning problems that arise before launch are Greenfield 1960, with test facility practice in Mandell and White 1960. On a conventional vehicle this apparatus feeds the engines. On this one it also holds the vehicle up, so a pressurisation fault here is a structural event.

A useful figure of merit for a tank is its mass per unit of volume contained,

\[\eta_{\text{tank}} = \frac{m_{\text{skin}}}{V} = \frac{893}{131} = 6.8 \, \text{kg/m}^{3} \tag{30}\]

which can be read as the penalty paid for carrying a cubic metre of propellant. Against a propellant density averaging

\[\bar{\rho}_{p} = \frac{m_{p}}{V_{p}} = \frac{112{,}505}{111.5} = 1009 \, \text{kg/m}^{3} \tag{31}\]

the tank costs about eight kilogrammes for every tonne of propellant it holds, since 893 kilogrammes of skin hold 112.5 tonnes. That figure is what makes a mass ratio of twenty-two possible.

Buckling as the Governing Failure Mode

A thin cylinder in axial compression does not fail by crushing. It buckles, and the classical critical stress is

\[\sigma_{cr} = \frac{E t}{r \sqrt{3 (1 - \nu^{2})}} \tag{32}\]

which for the heavy gauge at a Young’s modulus of 193 gigapascals gives

\[\sigma_{cr} = \frac{193 \times 10^{9} \times 0.000940}{1.524 \times 1.652} = 72.0 \, \text{MPa} \tag{33}\]

and for the light gauge 27.3 megapascals. That figure is not what a real shell achieves. Thin cylinders buckle far below the classical value because the post-buckling equilibrium path falls away steeply and any small imperfection lets the shell find it, the result of Von Karman and Tsien 1941 and the post-buckling behaviour of Michielsen 1948. Design practice applies a knockdown factor. NASA’s design criterion gives about 0.18 at a radius-to-thickness ratio of 1,500, the limit of the test data behind it, and less beyond NASA 1968 Buckling of Thin-Walled Circular Cylinders, so the factor of 0.2 adopted here is slightly unconservative, giving an allowable of

\[\sigma_{\text{allow}} = 0.2 \times 72.0 = 14.4 \, \text{MPa} \tag{34}\]

for the heavy gauge and 5.5 megapascals for the light one. A structure whose tensile capacity is 965 megapascals has a compressive capacity of five, a ratio of nearly two hundred, and that asymmetry is the reason the design exists.

The other buckling mode needs ruling out explicitly, because a twenty-three metre column is an obvious candidate for it. Treating the vehicle as a cantilever beam of thin-walled section, the second moment of area is

\[I = \pi r^{3} t = \pi \times 1.524^{3} \times 0.000648 = 7.20 \times 10^{-3} \, \text{m}^{4} \tag{35}\]

and the Euler critical load with an effective length factor of two for a fixed base and free top is

\[P_{cr} = \frac{\pi^{2} E I}{(K L)^{2}} = \frac{\pi^{2} \times 193 \times 10^{9} \times 7.20 \times 10^{-3}}{(2 \times 23.11)^{2}} = 6.42 \, \text{MN} \tag{36}\]

against an empty weight of 52.9 kilonewtons, a margin of 121. It does not fold as a column. It crumples as a shell, and the distinction matters because the two failure modes are separated by two orders of magnitude and only one of them is helped by pressure. Shell stability work of the period spans Nickell 1961, Hausrath and Dittoe 1962, Hoff et al. 1962, and Bozich 1967, with the external-pressure case in Shaw et al. 1952 and Reynolds 1960, the conical case in Mescall 1961, torsional buckling in Mow and Sadowsky 1962, and dynamic buckling in Coppa and Nash 1962 and Coppa and Nash 1964. The alternatives to a bare pressurised shell were being measured at the same time, with stiffener sizing in Nott 1963 and sandwich construction under combined loading in Wang et al. 1953, and the Atlas decision is only intelligible against that comparison.

What the Standing Pressure Does

Internal pressure produces axial tension, and a fibre that is in tension cannot buckle. The tension from the standing nitrogen pressure alone is

\[\sigma_{z} = \frac{34{,}474 \times 1.524}{2 \times 0.000940} = 27.9 \, \text{MPa} \tag{37}\]

at the heavy gauge and 73.9 megapascals at the light one. Set those against the knocked-down buckling allowables of 14.4 and 5.5 megapascals respectively and the result is stark. Five pounds per square inch of nitrogen roughly doubles the effective compressive capability of the heavy gauge and multiplies the light gauge by more than thirteen. The pressure is not a convenience. It is the larger part of the structure.

The relation can also be inverted, and inverting it explains where the number five came from. Requiring the axial tension from pressure to equal the knocked-down buckling allowable gives

\[p_{\text{req}} = \frac{2 t \sigma_{\text{allow}}}{r} \tag{38}\]

which at the heavy gauge is

\[p_{\text{req}} = \frac{2 \times 0.000940 \times 14.4 \times 10^{6}}{1.524} = 17{,}768 \, \text{Pa} = 2.58 \, \text{psi} \tag{39}\]

and at the light gauge only 0.37 pounds per square inch, because the buckling allowable falls faster with thickness than the pressure tension does. The governing case is the heavy gauge and it needs 2.58 pounds per square inch, so the reported five-pound standing specification carries a margin of 1.94 on the calculation performed here.

The relation used here is a first-order one and the period had a better one. Peterson 1960 correlates the measured buckling strength of pressurised cylinders against the pressure parameter directly, the empirical form the design offices used, and Weingarten 1962b extends it. Why a correlation was needed in place of a theory appears in Babcock and Sechler 1962 and Babcock and Sechler 1963, which measure how much of the classical strength an initial imperfection removes, with the post-buckling behaviour that makes the sensitivity so severe in Thielemann 1962 and Greenspon 1963a. A specification that lands at roughly twice the computed requirement is what a designer writes when the computed requirement rests on a knockdown factor he does not trust, and the factor adopted above is such a factor.

The cleanest statement of the principle is in bending. For a thin-walled cylinder the second moment of area is $I = \pi r^{3} t$, so a bending moment produces an extreme-fibre stress of $M r / I$. Setting that equal to the axial tension from pressure gives the moment at which the most compressed fibre first reaches zero stress,

\[\frac{M r}{\pi r^{3} t} = \frac{p r}{2 t} \quad \Longrightarrow \quad M_{\text{crit}} = \frac{\pi p r^{3}}{2} \tag{40}\]

The thickness cancels. The moment a pressure-stabilised cylinder can carry before any part of it goes into compression depends on the pressure and the radius and not at all on how thin the skin is. That independence is the mathematical form of the claim that the pressure is doing the work. At the standing pressure this is

\[M_{\text{crit}} = \frac{\pi \times 34{,}474 \times 1.524^{3}}{2} = 0.192 \, \text{MN m} \tag{41}\]

equivalent to a lateral force of 8.3 kilonewtons at the top of a 23 metre vehicle, and at flight pressure it is 2.30 meganewton metres, or 99.5 kilonewtons. A missile standing on the pad in a wind is held up by a pressure a bicycle tyre would find low, and the flight case is twelve times stiffer because the tanks are pressurised harder once loaded.

That moment converts to a wind speed, the form an operations manual would want. Taking the wind as a uniform load on a cylinder of drag coefficient 1.2, the drag force is $F = \tfrac{1}{2} \rho V^{2} C_{D} D L$ acting at mid-height, so the moment at the base is

\[M = \tfrac{1}{4} \rho V^{2} C_{D} D L^{2} \tag{42}\]

and inverting it for the standing case gives

\[V = \sqrt{\frac{4 M_{\text{crit}}}{\rho C_{D} D L^{2}}} = \sqrt{\frac{4 \times 1.917 \times 10^{5}}{1.225 \times 1.2 \times 3.048 \times 23.11^{2}}} = 17.9 \, \text{m/s} \tag{43}\]

or thirty-five knots before any fibre of the standing vehicle goes into compression, falling to about twenty-eight knots with a factor of 1.5 applied to the moment. At flight pressure the same relation gives 120 knots.

Two things follow. The standing limit is an ordinary windy day. The ground-wind literature cited below was therefore no academic interest for this programme, and a vehicle left on the pad through weather is at risk in a way a stiffened one is not. And the margin improves by a factor of three and a half the moment the tanks are pressurised for flight, so the dangerous condition is the one that lasts for days and not the one that lasts for minutes. That inversion, in which the vehicle is most fragile when nothing is happening to it, is the operational signature of the design. The measurement this section describes was carried out. Miller and Gerus 1966 reports the bending strength of a large thin-walled pressure-stabilised cylinder, testing the relation derived above on hardware of the right size, and it is the most directly relevant document found for this article. Ichino and Takahashi 1965 treats the non-symmetrical bending state of such a shell, Ugural and Cheng 1968 takes pure bending, and Kempner and Chen 1974 handles the oval case that an imperfect cylinder becomes.

Pressure-stabilised beams under load are treated directly by Steeves 1975a and Steeves 1975b. Weingarten 1962b isolates the effect of internal pressure on cylinder buckling, and collapse tests of pressurised membrane-like cylinders are Leaumont 1965, with monocoque dome stability in Adam and King 1965 and creep buckling, which matters for a tank held pressurised for long periods, in Samuelson 1968c.

The Mass of the Structure

The bare skin of a tank eighteen metres long at the average gauge masses

\[m_{\text{skin}} = 2 \pi r L t \rho = 2 \pi \times 1.524 \times 18 \times 0.000648 \times 8000 = 893 \, \text{kg} \tag{44}\]

or 16.5 percent of the empty vehicle. A stiffened design carrying the same compression without pressure needs frames and stringers, taken here as adding forty to sixty percent above bare skin, which would take the tank alone to between 1250 and 1430 kilogrammes. That increment is real but it is not by itself the factor of one and a half the range table above uses, and the article does not claim it is. The sensitivity table is a sensitivity table. What the comparison does establish is the direction and the order, and the direction is the one the programme chose.

The general form of the comparison shows where the advantage comes from. A pressure-stabilised wall is sized by tension,

\[t_{\text{press}} = \frac{p r}{\sigma_{\text{allow,tension}}} \tag{45}\]

and a stiffened wall carrying the same vehicle is sized by an equivalent compressive allowable that includes its stiffening,

\[t_{\text{stiff}} = \frac{N_{x}}{\sigma_{\text{allow,compression}}} \tag{46}\]

so the ratio of the two depends on the ratio of the allowables, which for this material and this radius-to-thickness ratio is

\[\frac{\sigma_{\text{tension}}}{\sigma_{\text{compression}}} = \frac{965}{14.4} = 67 \tag{47}\]

The tensile allowable is sixty-seven times the compressive one. That factor does not translate directly into a mass ratio, because the two walls carry different loads and the stiffened one adds material in a different place, but it is the reason the comparison comes out the way it does and it is the number a designer in 1951 would have been looking at. Stiffened-shell optimisation as the period practised it appears in Nickell 1961 and Nott 1963, the structural design practice is codified in Bruhn 1973 Analysis and Design of Flight Vehicle Structures, and the material behaviour that fixes the tensile allowable comes from Manning and Price 1961, Johnson and Kelsen 1969, and Kuentz 1969.

Dependent Systems

The Engines and the Ground Start

The Atlas A carried two booster engines whose initial thrust, by the official history, was raised during the series from 270,000 to 300,000 pounds Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960. The summary figure of the Convair X-11 compilation, 341,128 pounds, which is 1.517 meganewtons, exceeds both, and the same compilation’s narrative gives the early engines 135,000 pounds each and the improved engines from the fifth flight 150,000, which agree with the official figures. At the Atlas D gross mass this summary thrust gives a lift-off thrust-to-weight of

\[\frac{T}{W} = \frac{1.517 \times 10^{6}}{117{,}900 \times 9.80665} = 1.31 \tag{48}\]

a figure for the family and not for the Atlas A. Against the 181,000 pounds at which Cleary 1991 The 6555th, Missile and Space Launches Through 1970 gives the Series A test missiles, the early engines give

\[\left. \frac{T}{W} \right|_{A} = \frac{2 \times 135{,}000}{181{,}000} = 1.49 \tag{49}\]

so the Atlas A left the pad harder than the family figure suggests. For the family figure the propellant flow follows from the exhaust velocity,

\[\dot{m} = \frac{T}{v_{e}} = \frac{1.517 \times 10^{6}}{2765} = 549 \, \text{kg/s} \tag{50}\]

so a 133 second burn, the compilation’s figure against the two full minutes of powered flight Neufeld gives for missile 12A, consumes 73.0 tonnes, or 65 percent of the full Atlas propellant load. Summerfield 1960 sets out liquid engine practice of the period, with a released Rocketdyne specification for the sustainer engine, which the Atlas A did not carry, in Scott 1963 and the specific-impulse bookkeeping in Dafler 1962. Combustion instability, which was the era’s most persistent liquid-engine problem, is Grey 1953, Matthews 1957, and Harrje 1959. Hegg 1964 designs the gimbal actuation for thrust vector control, and the turbopump that feeds the arrangement has a design-criteria treatment in Design Criteria Monograph 1975, with propellant flow calibration in Berg 1968.

Ascent Loads, and the Worst Two Minutes

The structural case is set by the ascent, and within the ascent by two moments. Dynamic pressure rises as the vehicle accelerates and falls as the atmosphere thins, so it peaks,

\[q = \tfrac{1}{2} \rho(h) v(h)^{2} \tag{51}\]

and for a vertically rising vehicle the peak can be located by differentiating. With an exponential atmosphere of scale height $H$ and a constant acceleration $a$, the dynamic pressure is

\[q(t) = \tfrac{1}{2} \rho_{0} e^{-a t^{2} / (2H)} (a t)^{2} \tag{52}\]

and setting the derivative to zero gives

\[\frac{dq}{dt} = 0 \quad \Longrightarrow \quad t_{q} = \sqrt{\frac{2H}{a}} \tag{53}\]

For a scale height of 7200 metres and an acceleration of three metres per second squared net of gravity,

\[t_{q} = \sqrt{\frac{2 \times 7200}{3}} = 69 \, \text{s} \tag{54}\]

at an altitude of $\tfrac{1}{2} a t_{q}^{2} = H = 7.2$ kilometres, the pleasing result that a constant-acceleration vertical ascent reaches maximum dynamic pressure at exactly one scale height, independent of the acceleration. The value at that point follows by substitution,

\[q_{\max} = \tfrac{1}{2} \rho_{0} e^{-1} (a t_{q})^{2} = \tfrac{1}{2} \rho_{0} e^{-1} \times 2 a H \tag{55}\]

which for the same numbers gives

\[q_{\max} = \tfrac{1}{2} \times 1.225 \times 0.3679 \times 2 \times 3 \times 7200 = 9736 \, \text{Pa} \tag{56}\]

or about 1.4 pounds per square inch of dynamic pressure. In this idealised ascent the aerodynamic pressure is two percent of the pressure the vehicle carries internally. The later Atlas’s flight report measured a peak near 800 pounds per square foot, about 5.6 pounds per square inch, between seventy and eighty seconds after lift-off Atlas-Centaur AC-12 Flight Performance 1968, which is still under a tenth of the fuel-tank pressure, so the conclusion about where this structure’s loads come from survives the idealisation. It is a pressure vessel that happens to fly, not an aeroplane that happens to hold propellant. The real trajectory is not vertical and the acceleration is not constant, so the time is a little over a minute, consistent with the 60 to 90 second window of highest bending loads in the later Atlas’s flight report, but the structure of the answer is the structure of the real one. Axial acceleration does the opposite. It grows monotonically as propellant burns away,

\[n(t) = \frac{T}{\left( m_{0} - \dot{m} t \right) g} \tag{57}\]

so at lift-off it is 1.31 and near booster cutoff, with two thirds of the propellant gone, it approaches

\[n = \frac{1.517 \times 10^{6}}{\left( 117{,}900 - 72{,}977 \right) \times 9.80665} = 3.44 \tag{58}\]

The worst bending load and the worst axial load therefore arrive at different times, which is fortunate, because a pressure-stabilised structure that had to carry both at once would need a pressure it could not contain. Ascent load analysis of the period begins with Wood 1961, with the aerodynamic side in Binion and Herron 1962.

The load case that is easiest to forget is the one before the engines light. A slender missile standing on a pad sheds vortices in a steady wind and can be driven into resonant transverse oscillation, and for a pressure-stabilised vehicle the pressure that resists it is the standing five pounds rather than the flight sixty. The period treated this as a distinct subject, in Bohne 1964 and Buell 1964b on the sources of ground-wind loads, Simon 1965 on the flow-field parameters that govern the oscillation, Jones and Farmer 1966 and Jones and Farmer 1967 on wind-tunnel studies of the Saturn vehicles, Coffin 1970 on simulating the response, and the extreme-value statistics that decide what wind to design against in Miller 1967. A whole meeting was devoted to it, reported in Meeting on Ground Wind 1966. The axial equivalent, in which an elastically supported vehicle oscillates along its own axis on the pad, is Radovcich 1965.

Angle of attack is what turns dynamic pressure into a bending moment. The normal force on a slender body at small incidence is

\[N = q S C_{N\alpha} \alpha \tag{59}\]

and taking the reference area as the cross-section, $S = \pi r^{2} = 7.30$ square metres, a normal-force slope of two per radian, and three degrees of incidence at maximum dynamic pressure,

\[N = 9736 \times 7.30 \times 2 \times 0.0524 = 7447 \, \text{N} \tag{60}\]

which acting at a lever arm of ten metres gives a bending moment of 74 kilonewton metres. Against the pressure-stabilised capacity of 2.30 meganewton metres at flight pressure this is three percent, so there is an enormous margin in bending while pressurised and essentially none while not. The incidence comes from wind. A vehicle rising through a shear layer sees a lateral relative wind and must either fly at an angle to it, which costs bending moment, or steer into it, which costs trajectory. Load-relief steering exists because of that trade, and its modern form is treated below.

The Sustainer and the Value of Staging

Dropping two engines and a skirt at booster cutoff removes mass that the remaining propellant would otherwise have to accelerate. The benefit is the difference between finishing the burn with and without that mass,

\[\Delta v_{\text{gain}} = v_{e} \left[ \ln \frac{m_{1}}{m_{f}} - \ln \frac{m_{1} + m_{j}}{m_{f} + m_{j}} \right] \tag{61}\]

where $m_j$ is the jettisoned mass and $m_1$ is the mass at staging. Evaluated, that expression overturns the obvious reading.

The booster phase consumes $\dot{m} t_b = 549 \times 133 = 72{,}977$ kilogrammes, leaving

\[m_{\text{sust}} = m_{p} - \dot{m} t_{b} = 112{,}505 - 72{,}977 = 39{,}528 \, \text{kg} \tag{62}\]

for the sustainer, so the mass at staging after jettison is $m_1 = 5395 + 39{,}528 = 44{,}923$ kilogrammes. Taking a jettisoned booster package of three tonnes, the sustainer phase delivers

\[\Delta v_{\text{dropped}} = 2765 \ln \frac{44{,}923}{5395} = 5861 \, \text{m/s} \tag{63}\]

if the package is discarded and

\[\Delta v_{\text{carried}} = 2765 \ln \frac{47{,}923}{8395} = 4817 \, \text{m/s} \tag{64}\]

if it is not, so the gain is

\[\Delta v_{\text{gain}} = 5861 - 4817 = 1044 \, \text{m/s} \tag{65}\]

That is twelve percent of the ideal velocity for the sake of dropping three tonnes of engine. The intuition that a half-stage gives up most of the benefit of staging is wrong. The benefit of staging depends on the ratio of jettisoned mass to burnout mass, not to gross mass. Three tonnes against a burnout mass of five and a half is an enormous fraction, even though it is under three percent of the vehicle at lift-off.

The one-and-a-half stage arrangement therefore captures most of the value of staging while avoiding an altitude ignition, a considerably better bargain than it looks, and the balloon tank is what makes the burnout mass small enough for the bargain to be that good. The two decisions are complementary. Staging optimisation of the period is Schurmann 1957 and Parkyn 1958, and the separation event itself, which imposes its own aerodynamic and jet-interference loads, is Binion and Herron 1962 and Binion 1964.

Structural Proof Testing by Pressure

A stiffened shell fails by buckling under compression, and applying a representative compressive load to a twenty-three metre cylinder requires a test rig comparable in size and cost to the article. A pressure-stabilised tank fails by yielding under tension, and applying a representative tensile load requires a compressor. Every tank can therefore be proof-tested to a defined fraction of its failure mode before it ever flies, and a stiffened alternative cannot be.

The proof factor relates the test pressure to the design pressure,

\[k_{p} = \frac{p_{\text{proof}}}{p_{\text{design}}} \tag{66}\]

and a factor between 1.1 and 1.25 is taken here, with the burst factor higher still,

\[k_{b} = \frac{p_{\text{burst}}}{p_{\text{design}}} \geq 1.5 \tag{67}\]

which at the flight pressure and heavy gauge implies a burst hoop stress of

\[\sigma_{\text{burst}} = 1.5 \times 671 = 1007 \, \text{MPa} \tag{68}\]

against an assumed ultimate of 1276, a margin of 1.27 on the material rather than on the design. Applying a proof factor of 1.25 to the 60 pound flight pressure gives a hoop stress at the heavy gauge of

\[\sigma_{\theta} = 1.25 \times 671 = 839 \, \text{MPa} \tag{69}\]

or 87 percent of the assumed yield, so the proof test is a genuine test and not a formality. Abraham 1963 shows how the period tested large articles structurally, with the combined static and dynamic loading problem in Roberts and Wilhem 1964. The design’s failure mode doubles as its acceptance test, a real and rarely stated advantage of the balloon tank over a stiffened shell whose critical load can only be estimated.

A Thermal Environment Mild by the Standards of This Series

The X-10 article computed a recovery temperature of 636 kelvin for a vehicle cruising at Mach 3.25 for three hours, and concluded that aluminium would not serve. A ballistic booster has the opposite problem. It passes through the dense atmosphere quickly and is out of it before the skin can equilibrate,

\[\tau_{\text{skin}} = \frac{\rho c \delta}{h} \tag{70}\]

and for stainless steel at the Atlas gauge, taking a density of 8000 kilogrammes per cubic metre, a specific heat of 500 joules per kilogramme kelvin, and a convective coefficient of 200 watts per square metre kelvin,

\[\tau_{\text{skin}} = \frac{8000 \times 500 \times 0.00094}{200} = 18.8 \, \text{s} \tag{71}\]

comparable to, and not short against, the time spent near maximum dynamic pressure. The skin does partially equilibrate, but it does so against a recovery temperature that is only high for a few tens of seconds, and the propellant behind it is a very large heat sink at cryogenic temperature. The structural problem is therefore mechanical rather than thermal. Aerodynamic heating of entry vehicles is treated in Allen 1966 and Murphy and Rubesin 1965, and Winstead 1966 handles the thermal control of a cryogenic vehicle, with propellant leakage effects in Nast and Williams 1967.

The Acoustic and Vibration Environment

A rocket at lift-off sits in its own exhaust noise, and the overall sound pressure level near the base of a large booster reaches values that damage thin panels by fatigue rather than by static overload. The relation that governs the damage is not a stress but a spectrum, and the accumulated damage over an exposure is set by a cycle count. A thin welded shell is the structure most exposed to that mechanism, and the weld lines are where it acts.

The level can be estimated. The mechanical power in the jet is

\[P_{\text{jet}} = \tfrac{1}{2} \dot{m} v_{e}^{2} = \tfrac{1}{2} \times 549 \times 2765^{2} = 2.10 \, \text{GW} \tag{72}\]

of which half of one percent is assumed here to become sound, so the radiated acoustic power is about 10.5 megawatts. Spreading that over a hemisphere at thirty metres gives an intensity of

\[I = \frac{P_{\text{ac}}}{2 \pi d^{2}} = \frac{1.05 \times 10^{7}}{2 \pi \times 900} = 1855 \, \text{W/m}^{2} \tag{73}\]

and a sound pressure level of

\[L_{p} = 10 \log_{10} \frac{I}{10^{-12}} = 153 \, \text{dB} \tag{74}\]

falling to 142 decibels at a hundred metres. The pressure fluctuation follows from the intensity directly, which avoids rounding the level,

\[p_{\text{rms}} = \sqrt{I \rho c} = \sqrt{1855 \times 1.225 \times 343} = 883 \, \text{Pa} \tag{75}\]

so a hundred and fifty-three decibels is a pressure fluctuation of about 0.13 pounds per square inch, which is small against the sixty inside the tank but is applied at hundreds of hertz for the duration of the lift-off transient, and fatigue does not care about the mean. The period studied the mechanism as a discipline under the name sonic fatigue. Vreeland 1960 gives a test method, Wang 1966 a prediction model, Ballentine et al. 1966 the combined-environment case, and Hines 1966 the specimen fabrication such tests require. The statistical machinery beneath it comes from Crandall and Mark 1963a, with transmission in Crandall and Mark 1963c and failure in Crandall and Mark 1963b. Boyd 1963 measured the environment at the launch site itself for Cape Canaveral, with facility acoustics in Tyzzer and Pernet 1964, the launch-vehicle dynamics overview in Hung and Hunt 1964b, and vibration environment specification and correlation in Snyder et al. 1974, with the acoustic measurement practice of the period in Keast 1961.

Slosh in an Unbaffled Tank

A tank with no internal structure has nothing to break up the free surface of its propellant, and a large moving mass of liquid inside a vehicle being steered by thrust vectoring couples into the control loop. The same decision that removed the stringers removed the natural baffling, so any baffle has to be added back deliberately as internal structure, as the slosh baffle in the hydrogen tank of the later Centaur shows Atlas-Centaur AC-12 Flight Performance 1968.

The frequency that matters is the first lateral sloshing mode of a cylindrical tank, which for fill depths that are not shallow is

\[\omega_{s} = \sqrt{\frac{1.841 \, g_{\text{eff}}}{r} \tanh \frac{1.841 h}{r}} \tag{76}\]

and under acceleration the effective gravity is the axial load factor times $g$, so the slosh frequency rises through the flight as the vehicle accelerates and falls as the tank drains. At the Atlas radius and a load factor of three the deep-tank limit gives

\[\omega_{s} = \sqrt{\frac{1.841 \times 3 \times 9.80665}{1.524}} = 5.96 \, \text{rad/s} \tag{77}\]

or 0.95 hertz, which sits uncomfortably close to the bandwidth of a thrust-vector control loop. Stephens 1965 damps slosh with flexible baffles, with measurement in Wilner et al. 1960 and the shell-vibration side in DIGiovanii and Dugundji 1965.

Pogo and the Coupling of Structure and Propulsion

A liquid rocket whose structure has a longitudinal mode near the frequency at which its feed system and engine respond can close a loop through the propellant column, and the vehicle oscillates axially. Rubin 1965 and Rubin 1966 set out the mechanism, the naming and early study are Goldman and Miessner 1965 and Goldman and Miessner 1966. Marcus et al. 1969 develops the accumulator remedy, and the best-known case is Hill et al. 1969 on Saturn V. A pressure-stabilised vehicle is unusually exposed to this, because its longitudinal stiffness is partly a function of tank pressure and therefore changes as the tanks drain.

The scale of the problem is set by how soft the vehicle is. A solid steel bar of the same length has a fixed-free axial mode at

\[f_{1} = \frac{c}{4L} = \frac{1}{4L} \sqrt{\frac{E}{\rho}} = \frac{4912}{4 \times 23.11} = 53 \, \text{Hz} \tag{78}\]

but a launch vehicle is not a solid bar. It is a thin shell containing a large mass of liquid, and its first axial mode sits far lower, uncomfortably close to the response of a feed system and turbopump. The instability condition is that the structural mode and the propulsion response overlap in frequency with enough gain around the loop, and both quantities move during the flight, the structure because the tanks drain and the propulsion because the inlet pressure falls. For missile structural dynamics in the period the sources are Wood 1961, with clustered-vehicle bending in Loewy 1965, shell vibration in DIGiovanii and Dugundji 1965, the ribbed-shell stability case in Amiro 1962, and the launch-vehicle overview in Gerald and Runyan 1962.

Guidance Absent from the Atlas A

The Atlas A flew without an operational guidance system, since the set first carried on missile 12A was flown open loop for evaluation Convair X-11. Its flights were programmed, and the guidance question fell to later variants and to the radio-inertial system the Atlas A through D used before an all-inertial set replaced it on the E and F SM-65 Atlas. Ballistic missile guidance of the period appears in Whitcombe 1961a. Slifka 1960 field-tests such a system, the measurement problem of establishing where a missile went is Cooper 1961, the explicit guidance equations that a self-contained system must solve are MacPherson 1963, and a later integrated formulation is Russell 1964 with Larson 1965 on Titan III and cost-driven inertial development in Crose 1965. The simulation apparatus such work depends on is Juarez 1961.

The accuracy relation matters here even though the X-11 did not exercise it, because it explains why a ballistic weapon is a velocity-control problem rather than a navigation problem, and because it follows by derivation from the range relation the previous article established.

That relation gives the range angle through

\[\sin \frac{\Phi}{2} = \frac{\lambda}{2 - \lambda}, \qquad \lambda = \frac{v^{2}}{g R_{e}}, \qquad R = R_{e} \Phi \tag{79}\]

and the sensitivity of range to burnout speed follows by chaining the three derivatives. From the definition of $\lambda$,

\[\frac{d \lambda}{\lambda} = 2 \frac{dv}{v} \tag{80}\]

from the range-angle relation,

\[\frac{d}{d\lambda} \sin \frac{\Phi}{2} = \frac{2}{(2 - \lambda)^{2}} \quad \Longrightarrow \quad \frac{d\Phi}{d\lambda} = \frac{4}{(2-\lambda)^{2} \cos (\Phi/2)} \tag{81}\]

and combining them gives the logarithmic sensitivity

\[\frac{\partial \ln R}{\partial \ln v} = \frac{2 \lambda}{\Phi} \cdot \frac{4}{(2 - \lambda)^{2} \cos (\Phi/2)} \tag{82}\]

At the intercontinental condition of $\lambda = 0.828$ and $\Phi = 1.570$ radians this evaluates to

\[\frac{\partial \ln R}{\partial \ln v} = 4.34 \tag{83}\]

One part in a thousand of velocity error is therefore about four and a third parts in a thousand of range, or forty-three kilometres at ten thousand. A weapon required to land within eight hundred metres, which is the figure the previous article inverted for the Navaho, needs a velocity accuracy of

\[\frac{\delta v}{v} = \frac{1}{4.34} \times \frac{800}{10^{7}} = 1.84 \times 10^{-5} \tag{84}\]

or 0.13 metres per second out of 7193. Cutting the engines at the right instant to a tenth of a metre per second constitutes the ballistic accuracy problem, and the problem lasts for the two minutes of powered flight, not for the thirty-two of the trajectory. Hence the previous article’s vehicle needed a navigator and this one needs a clock, the sharpest single difference between the two weapons.

The Reentry Vehicle as a Separate Body

The preceding sections concern a vehicle whose job ends at burnout. What arrives at the target is a separate body that must survive a reentry the booster never experiences, and the Atlas A carried no operational reentry vehicle at all, only a nose fairing in its place Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960.

The governing result is unusually clean. For a ballistic body entering an exponential atmosphere on a straight path, the peak deceleration is

\[a_{\max} = \frac{v_{e}^{2} \sin \gamma}{2 e H} \tag{85}\]

where $\gamma$ is the entry flight path angle and $H$ the scale height, and the striking feature is that the ballistic coefficient does not appear. A heavy dense body and a light one decelerate equally hard, and differ only in the altitude at which they do it. For an entry speed of seven kilometres per second at thirty degrees,

\[a_{\max} = \frac{7000^{2} \times 0.5}{2 \times 2.718 \times 7200} = 626 \, \text{m/s}^{2} = 64 g \tag{86}\]

The result is period material and not a later reconstruction. Scherberg and Rubin 1953 computes the decelerations of a ballistic missile on reentry in this form, four years before the X-11 flew, and the closed-form lifting extension is Bell 1965. The motion of the body about its axes while this is happening is Murphy 1961, the char-layer response of the heat shield is Dolton and Reed 1966, and estimating where such a body is while it flies is Schweppe 1964.

The reentry body is decelerated at sixty-four times gravity while the booster that launched it reaches about three and a half by the estimate above and 5.62 on the later Atlas Atlas-Centaur AC-12 Flight Performance 1968. The two halves of a ballistic missile are different structural problems by a factor of between eleven and nineteen, so they are different articles built by different people, and the X-11 could be a complete test of one while carrying none of the other. Nose-cone and ablation work of the period covers Stetson 1964, Wachi and Gilmartin 1966, and Rindal et al. 1967, with hemispherical-nose heat transfer in Nardo and Sadler 1962, flight heating measurements in Snodgrass 1955, and the roll-resonance problem in Platus 1967.

Ground Handling Dictated by the Structure

A structure that collapses unpressurised cannot be handled like an aeroplane. It requires a nitrogen supply or a mechanical stretch fixture at every point in its life balloon tank, transport fixtures that support it without imposing a bending moment above the pressure-stabilised limit computed above, and a launch complex that keeps it inflated while it is fuelled. The structural decision propagates into buildings and vehicles and procedures, and the accessible record of that apparatus is unusually good, in General Dynamics San Diego Ca Convair Div 1966a and its companion volumes and in Peters and Hall 1963 on system-test data for the engine system.

The propellant loading problem deserves a note, because a balloon tank couples loading to structure in a way a conventional tank does not. Filling the tank changes the pressure the walls must hold, changes the mass the walls must carry, and changes the temperature of the material, and all three happen while it stands unsupported on a pad. Loading is a structural operation and not merely a fluid transfer. Whitcombe 1961b optimises propellant loading and utilisation, and ground support equipment practice of the period runs from Moore 1958 and Newton and Makrides 1954, with launch complex activation in Powell 1962.

The boil-off that follows is a second coupling, and its rate explains why topping continues until moments before launch. With a wetted area of

\[A = 2 \pi r L = 2 \pi \times 1.524 \times 18 = 172 \, \text{m}^{2} \tag{87}\]

an uninsulated tank at a convective coefficient of ten watts per square metre kelvin against a two hundred kelvin difference admits

\[\dot{Q} = h A \Delta T = 10 \times 172 \times 200 = 345 \, \text{kW} \tag{88}\]

and at a latent heat of 213 kilojoules per kilogramme the boil-off is

\[\dot{m}_{\text{boil}} = \frac{\dot{Q}}{L_{v}} = \frac{3.45 \times 10^{5}}{2.13 \times 10^{5}} = 1.62 \, \text{kg/s} \tag{89}\]

or 5826 kilogrammes an hour, which is seven and a half percent of the oxygen load every hour. Liquid oxygen at 90 kelvin against an ambient near 290 therefore boils continuously, the tank must be topped until moments before launch, and the ullage pressure must be regulated throughout. The insulation that reduces the rate appears in Weiss and Goodman 1960, and the conditioning of the propellant before launch is Greenfield 1960. On this vehicle a pressure regulation failure is a structural failure, the recurring theme of the design. Two-phase pumping of cryogenic propellants is Stinson and Gross 1972.

The Flight Test Record

Eight Atlas A vehicles flew from Cape Canaveral between 11 June 1957 and 3 June 1958, against a plan for seven test missiles of 181,000 pounds between June and December 1957, expected to fly 460 nautical miles downrange Cleary 1991 The 6555th, Missile and Space Launches Through 1970. Convair had started fabrication in February 1955 and delivered the first missile on 29 August 1956, and missile 4A reached the Air Force Missile Test Center in December 1956 Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960. Cleary records five launches from Launch Complex 14 and three from Launch Complex 12, grades the first two flights failures and the third and fourth successes, and does not grade the last four. Neufeld’s summary records that the series ended in June 1958 with three successes, and that the eight missiles flew with only the booster and vernier engines and a nose fairing in place of a reentry vehicle. The apogees and the remaining outcomes in the table below are those of the Convair X-11 compilation, whose table grades three flights successful, matching the official count, while its summary says four.

Date	Pad	Serial	Apogee	Outcome
1957-06-11	14	4A	2 km	failure
1957-09-25	14	6A	3 km	failure
1957-12-17	14	12A	120 km	success
1958-01-10	12	10A	120 km	success
1958-02-07	14	13A	120 km	failure
1958-02-20	12	11A	90 km	failure
1958-04-05	14	15A	100 km	failure
1958-06-03	12	16A	120 km	success

The first flight lost thrust about 24 seconds after lift-off, performed what Cleary calls a couple of loops, and was destroyed by the range safety officer less than a minute after lift-off. Neufeld puts its height at a few thousand feet, the compilation’s table at two kilometres and its narrative at 9,800 feet, about three. The detail that matters for this article is that the vehicle tumbled and the structure held. By Neufeld’s account the Atlas nonetheless demonstrated its structural integrity and the ability to gimbal its engines, and Dawson and Bowles 2004 that the tank did not break up under the lateral stresses of the tumble until the range safety officer destroyed it. A pressure-stabilised shell that survives a tumble at low altitude has demonstrated the property most in doubt. A tumbling body sees its bending moment applied at an arbitrary angle and reversed once per revolution, the worst possible use of a structure whose compressive capacity is two hundred times smaller than its tensile one. That it held is evidence that the pressure stabilisation was working as the relation above predicts, since the relation does not care about the direction of the moment. A tumbling vehicle at rotation rate $\Omega$ also loads itself centrifugally, and the transverse acceleration at the tip of a body of length $L$ rotating about its centre is

\[a_{\text{tip}} = \Omega^{2} \frac{L}{2} \tag{90}\]

so a tumble at the one revolution per second assumed here, since no source gives the rate, gives

\[a_{\text{tip}} = (2 \pi)^{2} \times 11.6 = 458 \, \text{m/s}^{2} = 47 g \tag{91}\]

at the nose, applied as a bending load along the whole vehicle. The structure that everyone expected to fold survived a load case nobody had designed for.

The flight-by-flight record for the operational variants is in the Flight Test Working Group reports, of which General Dynamics/Astronautics San Diegoca 1961 is one, and the survival-probability analysis such a programme generates is Beer and Lennox 1965.

The Purpose of the Eight Flights

What the programme intended each flight to establish differs from what the flight record shows, and the difference explains the apparent poor showing.

The first two flights, in June and September 1957, reached two and three kilometres by the compilation’s table, and on the second the propulsion system ran normally for about 32 seconds before a liquid oxygen regulator problem reduced thrust and then cut all power Cleary 1991 The 6555th, Missile and Space Launches Through 1970. Neither was a performance flight in any sense. They were attempts to get a vehicle off the pad and through the first seconds of powered flight, and the first of them delivered the single most important structural result of the programme by tumbling and holding together. A flight that reaches two kilometres and is destroyed has still exercised the structure through lift-off, through the acoustic transient, and through an off-design load case, and the vehicle passed all three.

The third and fourth flights, in December 1957 and January 1958, reached 120 kilometres in the compilation’s table and are recorded as successes in the launch history. Those are the flights that establish the vehicle as a vehicle. Neufeld has the third, missile 12A, burning its engines for two full minutes as programmed, flying “some 600 miles” down the Atlantic Missile Range, and being declared a complete success. The unit is not settled by the record. Neufeld’s narrative of that flight writes miles without qualification, while his summary of the whole series gives its maximum range and altitude as 600 and 57.5 nautical miles. Both readings are carried here. As a fraction of the intercontinental range they are

\[\frac{600 \times 1.609}{10{,}000} = 0.097, \qquad \frac{600 \times 1.852}{10{,}000} = 0.111 \tag{92}\]

so the series flew about a tenth of the range either way, and by the range relation of the previous article a minimum-energy flight of 965.6 or 1,111.2 kilometres needs a burnout speed of

\[\sin \frac{\Phi}{2} = \sin \frac{965.6}{2 \times 6371} = 0.0757, \qquad \lambda = \frac{2 \times 0.0757}{1 + 0.0757} = 0.1408, \qquad v_{bo} = \sqrt{0.1408 \times 9.80665 \times 6.371 \times 10^{6}} = 2966 \, \text{m/s} \tag{93}\] \[\sin \frac{\Phi}{2} = \sin \frac{1111.2}{2 \times 6371} = 0.0871, \qquad \lambda = \frac{2 \times 0.0871}{1 + 0.0871} = 0.1602, \qquad v_{bo} = \sqrt{0.1602 \times 9.80665 \times 6.371 \times 10^{6}} = 3164 \, \text{m/s} \tag{94}\]

which are 0.41 and 0.44 of the 7193 metres per second the full range needs. Any other path to the same range needs more speed than the minimum-energy one, so about two fifths is a floor under either reading. The summary altitude of 57.5 nautical miles is 106.5 kilometres, below the 120 kilometres the compilation’s table gives for four of the flights. By the compilation, the fifth, sixth, and seventh failed at 120, 90, and 100 kilometres, a pattern of getting most of the way and then losing something, and the reported causes are consistent with that reading. The eighth, in June 1958, succeeded.

The programme therefore obtained its structural answer on flight one and spent the remaining seven flights on propulsion, plumbing, and pneumatics. That ordering is the opposite of what the article’s organisation implies. An article built around the balloon tank naturally presents the structure as the programme’s central difficulty, and the flight record says the structure was the thing that worked first and never stopped working.

The failures were concentrated in propulsion and plumbing rather than in structure. The launch history names a loss of engine thrust on the first flight and a liquid oxygen regulator problem on the second. The compilation adds exhaust-gas recirculation overheating the boat-tail, propellant duct failures, and pneumatic and guidance faults, with heat shielding, steel plumbing in place of aluminium, and revised venting as the remedies. The programme’s difficulty was never the thing that looked impossible.

What a Three-in-Eight Success Rate Means

Three of eight is a success rate of 0.375, which sounds alarming and is normal for a first flight article. What the number supports is narrow. Treating the flights as independent Bernoulli trials, the standard error on the estimate is

\[\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.234}{8}} = 0.171 \tag{95}\]

so the estimate is 0.375 plus or minus about 0.17, and any true reliability between roughly 0.03 and 0.72 is consistent with the observation. Eight flights cannot distinguish a mediocre vehicle from a good one.

It is tempting to read a learning curve into the sequence and the data do not support one. The outcomes in order were failure, failure, success, success, failure, failure, failure, success, so the first four flights produced two successes and the last four produced one. The standard error on a four-flight estimate is

\[\sigma = \sqrt{\frac{p(1-p)}{4}} = 0.25 \tag{96}\]

which is one flight in four, so a difference of one success between the halves is exactly the size of the noise. The programme neither demonstrably improved nor demonstrably worsened across its eight flights, and any account that describes the record as a learning curve is reading a trend into a sequence too short to carry one.

The width of that interval argues for flying often, and the relation makes it explicit. Halving the interval requires quadrupling the flights,

\[n = \frac{p (1-p)}{\sigma_{\hat{p}}^{2}} \tag{97}\]

so an estimate good to five percentage points at a true reliability near one half needs

\[n = \frac{0.25}{0.05^{2}} = 100 \, \text{flights} \tag{98}\]

which is more than twelve times the eight development articles of this series. Reliability for such a vehicle is therefore established by inference from ground test and by accumulating operational rounds, not by the flight test programme, and the Difficulties Review volumes of General Dynamics San Diego Ca Convair Div 1966a show that inference written down.

Comparison With Ground Prediction

The Atlas structure lends itself to ground test, because a pressure-stabilised tank can be proof-tested to its failure mode by pressurising it, unlike a stiffened shell whose failure mode is compressive buckling under a load that is hard to apply. The design is unusually testable on the ground for the same reason it is unusual in flight.

The gap between ground and flight is therefore not in the structure but in the combined environment. A tank can be pressure-tested, a shell can be buckling-tested, and neither test applies the acoustic field, the vibration, the thermal gradient, and the axial acceleration at once. Nickell 1961 and Leaumont 1965 carry the period’s shell-buckling experiment, and the standing difficulty that experiments scatter far below theory is the subject of Von Karman and Tsien 1941 and remains the reason a knockdown factor exists at all.

The scatter deserves a number, because it is the largest single uncertainty in the article. Test results for nominally identical cylinders scatter widely below the classical value, and the design lower bound of NASA’s criterion is near eighteen percent at a radius-to-thickness ratio of 1,500 NASA 1968 Buckling of Thin-Walled Circular Cylinders. The band assumed here runs from fifteen to sixty percent of the classical value,

\[0.15 \leq \frac{\sigma_{\exp}}{\sigma_{cr}} \leq 0.60 \qquad \frac{0.60}{0.15} = 4 \tag{99}\]

a spread of four to one, and the design factor of 0.20 used above sits at

\[\frac{0.20 - 0.15}{0.60 - 0.15} = 0.11 \tag{100}\]

or the eleventh percentile of the assumed band, which is to say very near its lower edge. A structure designed against a four-to-one experimental scatter is being designed against ignorance rather than against a load, and the pressure-stabilised solution sidesteps the difficulty by arranging that no fibre goes into compression at all. In that sense the balloon tank is not merely lighter but epistemically cleaner. Its failure mode is yield, which is predictable to a few percent, rather than buckling, which is not. The standard treatments are Timoshenko and Gere 1961 Theory of Elastic Stability and Brush and Almroth 1975 Buckling of Bars, Plates and Shells, with vehicle structural practice in Bruhn 1973 Analysis and Design of Flight Vehicle Structures.

What the Ground Could Not Reproduce

Three things about the flight environment resist ground reproduction and all three bear on this structure.

The loads arrive together. A proof test applies pressure. A static test applies axial load. A vibration table applies acceleration. The article at maximum dynamic pressure has internal pressure, axial acceleration, a bending moment from incidence, an acoustic field, and a thermal gradient across the skin, all at once, and the interaction between them is what a combined-environment test exists to explore and what the period could rarely afford. Roberts and Wilhem 1964 and Ballentine et al. 1966 attempt that combination.

The structure changes during the flight. The tank drains, so the mass distribution, the axial stiffness, the slosh frequency, and the acceleration all move continuously through the burn. A ground test holds the article in one configuration and repeats it. A balloon tank is the extreme case of this, because even its stiffness is a function of a state variable that is being consumed, and no static test reproduces it.

The failure mode of interest is statistical. The buckling scatter of four to one is not measurement error. It is the real variation between nominally identical shells, so a single test article is one draw from a distribution. The argument above about eight flights being too few to estimate reliability applies with equal force to shell tests, and with less excuse, because ground articles are cheaper.

What the Data Changed

Into Atlas, and Then Into Space Launch

The X-11 fed directly into the Atlas B, which is the X-12 and the next article, and thence into the operational Atlas D, E, and F. The line then did what the Soviet R-7 also did SM-65 Atlas. It became a launch vehicle, and Atlas-derived launchers served NASA for four decades. Atlas launched Mercury, Agena and Centaur upper stages, and the Mariner probes to Mercury, Venus and Mars Atlas rocket family, and the balloon-tank principle carried into the Centaur upper stage, which still uses it Centaur rocket stage.

The reason it could is arithmetic rather than sentiment. Circular orbital speed at two hundred kilometres is

\[v_{\text{orb}} = \sqrt{\frac{\mu}{R_{e} + h}} = \sqrt{\frac{3.986 \times 10^{14}}{6.571 \times 10^{6}}} = 7788 \, \text{m/s} \tag{101}\]

against the 7193 metres per second an intercontinental trajectory needs, a difference of

\[v_{\text{orb}} - v_{bo} = 595 \, \text{m/s} \tag{102}\]

or seven percent of the ideal velocity. An intercontinental ballistic missile is already ninety-two percent of the way to orbit, and the remaining eight percent is a small upper stage. That margin is the deepest reason the Atlas outlived the Navaho by six decades.

Frazier 1967 optimises the trajectory for the Atlas and Agena combination, and the control systems that a large launch vehicle of the following generation required are Borelli and Carroll 1967.

The terms this pair of articles has established explain why the Atlas became a launcher and the Navaho became nothing. A booster is a machine for adding velocity, and velocity is useful for any mission that needs it. A cruise missile is a machine for carrying a warhead a particular distance at a particular speed, and nothing else wants that. The Atlas survived its obsolescence as a weapon because its keystone quantity, mass fraction, is valuable to every customer, while the Navaho’s keystone quantity, sustained autonomous navigation accuracy, was valuable only to the mission that was cancelled.

The Lineage and the Cost of Keeping It

The Atlas that launched Mercury was not the Atlas A. It was a derivative of the D, with a thicker oxidizer-tank skin, a human-rating programme behind it, and an abort-sensing system the weapon never carried Atlas LV-3B. The lineage nonetheless kept the balloon tank for nearly five decades, through Atlas D, E, F, and the Atlas-Agena and Atlas-Centaur combinations, and into the Atlas II and III, the last of which flew in 2005 Atlas rocket family. It was abandoned only with the Atlas V, whose common core booster is an isogrid aluminium structure that stays stable unpressurised Atlas V, while its Centaur upper stage kept the balloon tank.

The tank survived so long because a launch vehicle is judged by payload rather than by convenience, and the balloon tank pays for itself in payload every flight. It was eventually abandoned because payload stopped being the only criterion.

The arithmetic of the transition is available from the relations already used. A structure heavier by the stiffening increment computed above costs, at the Atlas mass fractions, about eleven percent of range or the equivalent in payload. Eleven percent of payload is a large penalty on a weapon and a manageable one on a commercial launcher, because a launcher can be sized upward while a missile has to fit its basing. That single asymmetry explains the trajectory of the design, from indispensable in 1957 to abandoned for the Atlas V in 2002, without any appeal to changing fashion.

Centaur is the exception that confirms it. It kept the balloon tank because an upper stage pays the mass penalty at the worst possible place in the vehicle, where every kilogramme of structure trades one-for-one against payload and is not diluted by the stages beneath it. The higher up a vehicle a structure sits, the more a balloon tank is worth, so the idea survives in the position where its disadvantages matter least and its advantages matter most.

What It Did Not Change

The pressure-stabilised structure did not become the standard way to build launch vehicles. Most launch vehicles since have been conventionally stiffened aluminium or composite structures, accepting a worse mass fraction in exchange for a vehicle that can be set down empty, handled without a nitrogen cart, and inspected without a pressure regime. The Atlas won its argument and then lost it, because mass fraction stopped being the binding constraint once vehicles grew and staging improved, while handling cost never stopped mattering.

The Contemporary Literature

Cluster	Records
Thin shells, buckling and the knockdown factor	1,076
Propellant tanks, cryogenic storage and boil-off	734
Rocket propulsion, engines and their failures	654
Trajectory, guidance and control	361
Launch vehicle design, programmes and operations, the residual	352
Staging, mass fraction, cost and the launcher line	294
Propellant slosh	279
Ground winds, buffet and ascent aerodynamic loads	273
The ballistic missile programmes and their history	258
Structural dynamics, modal test and monitoring of launch structures	245
Reentry vehicles and the uncontrolled return	241
The Atlas, its derivatives and its programme record	217
Pressure-stabilised and inflatable structure	184
Launch acoustics, vibration and sonic fatigue	167
Materials, manufacture, welding, fracture and the proof test	160
Flight test, reliability and launch operations	119
Pogo and propulsion-structure coupling	71
Total	5,685

Shell Buckling Beyond the Knockdown Factor

The design allowable used above is a blanket factor applied to a classical result, an admission that the theory does not predict the experiment. That has been the state of the art since Von Karman and Tsien 1941 and it is now being replaced by methods that model the imperfection instead of hiding behind a factor.

Evkin 2026 computes imperfection sensitivity rather than assuming it, Ventura et al. 2023 takes the asymptotic numerical route to pressurised-cylinder buckling, and stochastic and dynamic treatments are Yu et al. 2024b and Ozoigbo et al. 2025. Jiao et al. 2023 takes thin-walled behaviour under combined loading, and gauge-sensitivity methods are Zhang 2022. The most directly relevant modern paper derives knockdown factors for common-bulkhead structures, the configuration studied here, in Lee et al. 2024b.

The newer work goes further and tries to predict the lower bound outright. Lin et al. 2025 drives a lower-bound buckling prediction with machine learning, and post-buckling dynamics are Yang et al. 2026 and Peshkhoev 2026. Grid-stiffened composite cylinders, the design the Atlas rejected, are Velmurugan and Buragohain 2023, with sandwich tubes under bending in Ni et al. 2026.

The direction of travel is clear. A knockdown factor is a confession that the analyst cannot model the article in front of him. Every one of these papers is an attempt to withdraw the confession, and the Atlas is the vehicle that avoided needing it by arranging that no fibre goes into compression at all.

Numerical Shell Analysis

The relations this article uses are closed-form membrane and buckling results because those are what the period had and what a reader can check. Modern shell analysis is numerical, and the problem the article poses has been solved properly. Static bending of a pressurised cylindrical shell, the configuration of the keystone derivation, is Samadzadeh et al. 2024. Yu 2026 takes the externally pressurised case, Jin 2025 puts internal pressure on a non-circular shell, a geometrically nonlinear shell element is Azizi and Dornisch 2025, and a launch-vehicle-like article is analysed and tested in Tillotson Rudd et al. 2024.

The probabilistic turn is the important one. Sadovský et al. 2024 identifies buckling resistance as a distribution rather than a value, the quantity a knockdown factor was always crudely approximating. A design factor of 0.2 is a one-number summary of a probability distribution nobody could compute in 1951 and everybody can compute now.

Inflatable and Pressure-Stabilised Structure Under Another Name

The relation derived above, that a pressurised cylinder resists bending until the compressive stress from the moment overcomes the tensile stress from pressure, is the governing relation of a field that is now called inflatable structures rather than pressure-stabilised ones.

Inflatable tube bending is modelled and validated experimentally in Gong et al. 2026, Ge et al. 2026, and Zhang et al. 2024b, which measure the quantity computed above. Wrinkling, which is what the failure looks like when the pressure loses, is Wang et al. 2026b under bending and torsion and Gashe et al. 2025 under shear and compression. Tapered inflatable lattices are Kundu and Mukhopadhyay 2025, precision analysis of an inflatable antenna is Hu et al. 2025, and habitat use is Kömle et al. 2025.

Bossart’s idea did not die. It moved to spacecraft that must be small when launched and large when deployed, where the mass argument is even stronger than it was for the Atlas, and the analysis those programmes use is the analysis this article performs.

Propellant Tanks and the Unchanged Rocket Equation

Tank structure remains where launch-vehicle mass is won and lost, and the modern literature is dominated by cryogenics because the propellants moved. Kim et al. 2025b optimises a launch vehicle tank structurally, the common-bulkhead arrangement the Atlas pioneered appears in Zhang et al. 2025d and Zhang et al. 2025b. Narayana Yenugula et al. 2025 adds vacuum insulation to a thermo-structural analysis, all-composite cryogenic tanks are Rhee et al. 2025, Cheng et al. 2025a couples the analysis concurrently, Bershadskyi et al. 2022 verifies a tank operational-pressure model, and two-way fluid-structure and thermal-structure interaction appears in Ajeesh et al. 2026.

The boil-off computed above at seven and a half percent of the oxygen load per hour is now attacked directly. Zhang et al. 2025g optimises for zero boil-off, boil-off gas reduction appears in Nikonchuk 2026 and Lu et al. 2026, double-shell vacuum insulation behaviour is Lee et al. 2026a, Zhang et al. 2026e and Yu et al. 2026b take insulation heat and mass transfer, Leng et al. 2026 compares thermodynamic performance, and Chung 2026 covers thermal-fluid management in full.

The Atlas topped its tanks until moments before launch because it had no alternative. A modern cryogenic stage intended to loiter in orbit cannot do that, so zero-boil-off is a research programme.

Sloshing and the Baffle

A tank with no internal structure has nothing to break the free surface, and the modern literature is still largely about where to put the baffles. Liu et al. 2025a varies vertical baffle height, annular perforated baffles are Lu and Cao 2026, and three-dimensional resonant sloshing in a cylindrical tank appears in Lu and Cao 2025b with the wave-response comparison in Lu and Cao 2025a, Aguiar et al. 2025 mitigates it passively, slosh effects and baffle requirements are Solomon and Tamiru 2026 and Pei 2021. Jeon et al. 2024 varies baffle influence, and the coupling into vehicle dynamics appears in Xu and Xu 2024 and Roithmayr and Pei 2024 on touchdown stability.

One modern paper is a direct descendant. Lee and Baek 2026 analyses the vibration of a redesigned stainless-steel propellant tank on a current launch vehicle, which is the same material, the same structural philosophy, and the same coupling problem the Atlas met seventy years earlier.

Pogo as an Active Design Problem

Zhao and Tan 2026 reduces the model for suppression design, Zhao et al. 2024a and Tan et al. 2023 suppress it actively, Dolgopolov and Nikolayev 2024 models it nonlinearly, and suppressor hardware appears in Yoon et al. 2021 and Mitra et al. 2021, the strap-on configuration is Liu et al. 2020, and stability analysis is Raji et al. 2019. That an instability first met on 1960s vehicles still supports an active design literature is a measure of how tightly propulsion and structure couple in a thin-walled liquid rocket, and a pressure-stabilised vehicle is the extreme case because its axial stiffness is partly pressure.

Ground Wind and Buffet, the Load Case Easiest to Forget

The section Ascent Loads, and the Worst Two Minutes established that a slender vehicle on a pad can be driven into resonance by vortex shedding, and that for this vehicle the resisting pressure is the standing five pounds and not the flight sixty. That subject has since moved from a launch-vehicle speciality into general structural dynamics. Sahu et al. 2024 takes vortex-induced vibration of a circular cylinder in the supercritical regime, the regime a vehicle of this diameter stands in, Zhang et al. 2024c and Vîlceanu et al. 2024 couple fluid to structure, damper effectiveness appears in Wang et al. 2024a, and ground-mounted validation is Eshete et al. 2024.

The ascent equivalent is transonic buffet, which is Piatak et al. 2015 on the buffet environment test programme of a current launcher, Ragab 1992 on buffet load prediction against flight data, Cole and Henning 1992 on the response of a hammerhead configuration, and Singh et al. 2026 on active control over a payload fairing. Load relief, the modern answer to designing for the worst wind, appears in Orr and Russell 2024, Zhang et al. 2024a, and Song et al. 2026b.

Acoustics and Sonic Fatigue

The 153 decibels computed above is a fatigue problem rather than a strength problem, and the modern treatment is statistical. Qiu et al. 2026 gives a damage-equivalent stress amplitude under random loading, Zhang et al. 2026d predicts fatigue life and failure location, Pan et al. 2026b grows cracks under variable amplitude, Reddy et al. 2026 tests a functional article vibro-acoustically, thermo-vibro-acoustic analysis with structural mitigation appears in Abhishek Hari 2026, and suppression on a corrugated structure is Zhou et al. 2025c.

Flaws, Fracture and the Meaning of a Proof Test

The proof test the article describes loads the tank to a fraction of its failure stress and concludes that it will hold. What it establishes is that no flaw large enough to propagate at that stress is present, a claim about fracture mechanics, not about strength. Modern treatment of that distinction is Agarwal et al. 2025 on crack analysis by extended finite elements, Mullin et al. 2025 on critical flaw sizes and crack driving force, and Zhao et al. 2026b on a physics-informed neural network for the same problem. Comparative small-scale test methods are Ding et al. 2025, burst testing of vessels is Lüders et al. 2025 and Paleti et al. 2026, and weld inspection standards applied to vessels are Dian Fitria Ramdani and Dene Herwanto 2026. Sensor-based anomaly detection integrated with structural monitoring is Zhou et al. 2024b.

On a vehicle whose wall is under a millimetre thick, a flaw that matters is smaller than an inspector can reliably see, so the proof test, not the inspection, is the acceptance gate, and the gate works.

Modal Survey and Test Correlation

The bending and axial modes of a launcher decide its control stability and its pogo margin, and those modes are measured rather than trusted. Panda et al. 2025 identifies acoustic sources on a launch vehicle, the modern form of the environment estimated above at 153 decibels. Low-frequency elastic mode identification is the subject of Song et al. 2026a, and the wider identification literature that supplies the methods is Serhat Erdogan and Tekin 2025, Yang and Chen 2025, and Huang et al. 2025b. A balloon-tank stage has to be modal-surveyed at pressure, because its stiffness is not a property of the hardware alone, and that is a test complication the article has not otherwise mentioned.

Launch Aerodynamics, Computed Rather Than Tunnelled

The ascent loads the article estimates from a scale height and a normal-force slope are now computed. Stage separation, which the Atlas performs uniquely by dropping engines rather than tanks, is simulated against wind-tunnel test in Kumar et al. 2023. Reusable vehicle aerodynamics is Prasad 2022, aerodynamic damping extraction is Wang and Chen 2022, turbulence-model sensitivity is Yang et al. 2022 and Zhao et al. 2022, and interference reduction is Liao et al. 2023a. Inflatable decelerator aerodynamics, which is the pressure-stabilised structure meeting the reentry problem, is Rioseco Olave et al. 2023, Yun and Liu 2023, and Jalaja et al. 2023a.

Ascent Loads, Guidance, and the Trajectory

Sun et al. 2024a optimises the ascent convexly, approximate analytical solutions are Yu et al. 2023a and Yu et al. 2024a. He et al. 2024b relieves load by rolling, Zhou et al. 2025b learns the attitude control that does it, Jayan et al. 2024 estimates the resulting loads, computational fluid dynamics for ascent is Dalle et al. 2024 with Reynolds and aeroelastic scaling in Ivanco et al. 2024, chance-constrained optimisation is Guo et al. 2026a, adaptive sequential convex programming is Li et al. 2024a, and the thermal environment of the ascending vehicle is Sun et al. 2026. Interstage structural design, a part the Atlas famously did not have, is De Luca et al. 2026.

The engine-cutoff accuracy the article computes at 0.13 metres per second is now a solved control problem, and the papers above solve harder versions of it while carrying loads the Atlas would not have survived.

Engines and Health Monitoring

Five of eight Atlas A flights failed by the flight-by-flight record and the failures were in propulsion, plumbing and control electronics Convair X-11. That is now the most instrumented part of a launch vehicle. Cha et al. 2024 diagnoses the startup transient, Cha and Ko 2025 generalises the fault factor, Kamenskii and Martirosov 2021 monitors current state, the priming pressure surge is studied in Das and Padmanabhan 2022, turbopump flow is Zhou et al. 2022, thrust control is Yao et al. 2022, and thrust vector control is Benfriha et al. 2026 and Saiki et al. 2026. The Atlas A programme diagnosed its failures from telemetry after the flight. A modern vehicle carries the diagnosis aboard.

Reliability From Few Flights

The binomial interval computed above is wide because eight is a small number. Wagenblast and Bettinger 2024 estimates launch vehicle reliability statistically, Li et al. 2025a manages it on an operational vehicle, Muthukumar et al. 2020 estimates it for a control system, safety and operational reliability methodology comes from Khamlak 2026, and modern estimation methods are Zhu 2026 and Almetwally et al. 2026. Certification by machine-learning model validation is Neumaier et al. 2025. The methods now used to certify a vehicle on a handful of flights are the methods the Atlas A programme needed and did not have.

Structural Health Monitoring and the Digital Twin

A stage that must be kept pressurised at all times has a structural state worth watching continuously, and that is now possible. Chehrzad and Khoramishad 2026 monitors bonded joints through their electrical impedance, and Calderon Hurtado et al. 2026 validates a monitoring system in the field on full-scale bridges. Had the Atlas been built now it would have known its pressure margin in real time, the single capability that would most have changed how it was handled.

Manufacture of a Thin Welded Shell

The Atlas skin is a welded stainless assembly at a gauge where welding distortion is comparable to the thickness. Płaczek et al. 2023 and Qiu et al. 2023 fatigue welded joints in thin-walled structure, Zhang and He 2024 treats the welds by high-frequency mechanical impact, Edwards et al. 2023 models microstructure in duplex stainless, Lee et al. 2024e takes springback and cold-roll forming, additive manufacture of stainless for rocket application is the subject of Thomas 2022, and critical flaw sizing is Mullin et al. 2025.

Weld inspection has become a machine-vision problem, in Luo et al. 2026, Thompson et al. 2025, Luo et al. 2025, Zhao et al. 2025e, and Mukherjee et al. 2025. On a vehicle where the longitudinal weld decides the structure, that capability is not incidental.

The period met the same difficulties with the same material. Examination of welds in stainless sheet is Nolan 1964, welding of thin-sheet stainless is Apatovskii et al. 1967, the electron-beam process that made thin aerospace welds practical is Kern and Lubin 1963, press forming is Tozawa 1969, and strain and failure of thin stainless sheet under load is Khil’chevskii and Kadyshev 1973. Sixty years of instrumentation has not changed what can go wrong with a thin weld. It has changed how early it is found.

Characterising the Material

The article assumes a yield of 965 megapascals and an ultimate of 1276 for 301 stainless in its extra-full-hard condition, and those are assumed values rather than properties measured on the Atlas skin. Modern characterisation of the same class of material at the temperatures a cryogenic tank sees is Xu et al. 2025a, with the effect of cryogenic treatment on microstructure in Liu and Yuan 2025a and Wang et al. 2026d, and load-bearing behaviour in Wang et al. 2026c. Bimetallic additive construction is Narayanaswamy et al. 2025.

The proof test the article describes has become a dataset. Hydraulic burst-pressure testing of pressure vessels is now published as data in Lüders et al. 2025. A designer choosing a knockdown factor today has an evidence base the Atlas team did not, and that difference is the content of the shell-buckling section above.

The Tank After the Mission

A pressure-stabilised stage that reaches orbit is a large thin-walled pressure vessel in space with residual propellant in it, and that is now recognised as a hazard and no longer as a curiosity. Trushlyakov et al. 2024 passivates propellant residues in orbit, Liu et al. 2026b assesses survivability against the resulting debris, mitigation strategy across orbital regimes belongs to Navaz and Ntantis 2026, and conceptual design against those criteria is Layachi et al. 2025. The Atlas itself reached orbit, first as missile 10B on the flight of December 1958 that orbited the Signal Communication by Orbiting Relay Equipment satellite, as the X-12 compilation records, and a spent stage of that kind is what the current literature treats as a fragmentation risk.

Modern Reentry Research

Morgado et al. 2022a and Sharma et al. 2024 take reentry aerothermodynamics, Appar and Kumar 2021 ablates at the fluid-solid interface, Ren 2025 examines the flow mechanics of it, Gerasimov 2025 takes ablative carbon protection and Tian et al. 2025 an aerogel ceramic, aerothermodynamic sensitivity and optimisation are Horing et al. 2025, reachability of a manoeuvring body is Webb et al. 2026 and Su et al. 2025a, learned guidance is Marchetti and Minisci 2021, and covariance propagation for a high-order system is Chen et al. 2025b. The uncontrolled case applies the same physics to debris, in Öztürk et al. 2026, Fernando and Charalambous 2026, and Bigham and Puri 2025.

Economics, Reuse, and the Argument the Atlas Won and Then Lost

The Atlas traded handling cost for mass fraction, and the modern literature is explicit that the trade has reversed. Du et al. 2025 estimates lifecycle cost for a reusable vehicle, and Lee et al. 2026b compares recovery methods across vehicle scales. The paper that closes the circle with this article is Jo and Ahn 2022, which optimises the staging of a reusable launch vehicle for minimum lifecycle cost rather than for minimum mass, and thereby inverts the objective function the Atlas was designed against. Launch cost deflation as an economic phenomenon in its own right is Christie 2026, which is the endpoint of an argument the Atlas started by making mass fraction the only thing that mattered.

The strategic side has not gone away either. The rationale for a new intercontinental missile is argued in Modernizing the U.S. Nuclear 2022, and the missile’s place in post-Cold War deterrence in O’Rourke 2010. The weapon class the X-11 was built to found is still in service, unlike the intercontinental cruise missile the X-10 served.

That continuity prompts one closing observation about what a survey of this kind can and cannot see. The survey above is drawn from open literature, and open literature is systematically thicker where a technology found civilian use. The Atlas has sixty years of launch-vehicle publication behind it and the Navaho has four years of cancelled-programme reporting, so a comparison of the two archives measures what happened to each programme afterwards at least as much as it measures what each programme did. The Source Base section below states that as a finding and does not leave it as a bias, because it is both.

Thin shells, buckling and the knockdown factor

The largest cluster, and the one the knockdown factor lives in. Classical and imperfect cylinder buckling, stiffened, sandwich and composite shells, combined loads, internal pressure and the design factors that summarise the gap between theory and test. 145 of its 1,076 records name imperfection and 30 name the knockdown factor, while 28 name a launch vehicle, propellant tank, rocket, missile or booster, so the shell-buckling literature is overwhelmingly a general structural mechanics that a launch-vehicle designer borrows.

1,076 records. [Юніс and Мірошников 2023] [Abbasi 2020] [Abdi et al. 2011] [Abir and Nardo 1959] [Abu-Farsakh and Lusher 1985] [Adam and King 1965] [Adams] [Adams 1971b] [Adams 1971a] [Zhiping et al. 2021] [Aghajari et al. 2006] [Agrawal et al. 2023] [Ahmadi 2019] [Ahmadi et al. 2019] [Albazzan et al. 2019] [Allnutt 1953] [Almroth 1962] [Almroth 1966] [Almroth 1969] [Almroth et al. 1965b] [Almroth et al. 1965a] [Alzahabi and Kowalski 2009] [Amazigo 1969] [Amiro 1962] [An et al. 2014] [Anafi and Baluch 2025] [Anderson 1955] [Andreev and Kapliy 2014] [Ansari et al. 2021] [Arbocz 1992] [Arbocz and Babcock 1969] [Arbocz and Hilburger 2003] [Arun et al. 2022] [Asadi and Wang 2017] [Ashmarin 1966] [Ashmarin 1972] [Athiannan and Palaninathan 2004] [Augello and Pellegrino 2025] [Azizi and Stranghöner 2021] [Azizi and Stranghöner 2022] [Azzuni and Guzey 2016] [Babcock 1966] [Babcock 1967] [Babcock and Sechler 1962] [Babcock and Sechler 1963] [Babcock and Sechler 1964] [Baciu et al. 2024] [Bai and Wang 2011] [Baker et al. 1983] [Bakhtiari and Kheradpisheh 2020] [Balbin et al. 2020] [Ball and Citerley 1980] [Bapu Rao and Murthy 1977] [Barron and Villaimueva 1981] [Barski and Krużelecki 2005] [Barton et al. 1961] [Basaglia et al. 2019] [Basic Equations of Shell 2001] [Bauld 1974] [Baumgarten and Kierfeld 2019] [Ben-Haim and Elishakoff 1989] [Bendavid and Mayers 1970] [Berdnikov 1972] [Bergman 1962] [Berman et al. 1974] [Bert and Birman 1986] [Biagi and Del Medico 2008] [Bijlaard 1962] [Bisagni 2000] [Bisagni 2005] [Blaauwendraad and Hoefakker 2013b] [Blaauwendraad and Hoefakker 2013a] [Bleich and Baron 1952] [Block 1972] [Bodner and Naveh 1988] [Boichot and reynolds 1965] [Booton and Tennyson 1978] [Boundary Layer Theory 2017] [Bozich 1967] [Brogan and Almroth 1970] [Brown et al. 1961] [Brush 1968] [Buchert 1966] [Buckling and Postbuckling 1984a] [Buckling and Postbuckling 1984b] [Buckling of Circular Cylindrical 1984] [Buckling of Circular Cylindrical 1991] [Buckling of Circular Ring 2009] [Buckling of Cylindrical Shells 2003] [Buckling of Edge-Damaged Filament-Wound 1990] [Buckling of Plates 1985] [Jullien 1991] [Buckling of Shells 1983a] [Buckling of Shells 1983b] [Buckling of Shells 2003] [Budiansky 1969] [Budiansky and Hutchinson 1972] [Burgueño et al. 2014] [Burov 2019] [Burris 1971] [Bushnell 1972] [Bushnell 2007] [Böhm and Schaumann 2022a] [Böhm and Schaumann 2022b] [Błachut 2013] [Błachut 2014] [Błachut 2016] [Błachut 2017] [Błażejewski and Marcinowski 2013] [Cabrera-González and Sadowski 2025] [Cai et al. 2005] [YArahmedov 2024] [Calladine] [Calladine 1995] [Calladine 2018] [Card and Chang 1971] [Card and Jones 1966a] [Card and Jones 1966b] [Case and Chilver 1959] [Case and Chilver 1971] [Castel and Trameçon 2025] [Caswell and Muggeridge 1971] [Cha and Schultz 2013] [Chamis and Abumeri 2005] [Chandiramani and Nawandar 2014] [Chang et al. 2026] [Chau] [Chaudhuri 2016] [Chauhan and Ahmad 2018] [Chawla 1980] [Chehil et al. 1987] [Chekhov 1970b] [Chekhov 1970a] [Chekhov 1971] [Chekhov 1972] [Chen and Li 1993] [Chen and Long 2011] [Chen et al. 2018] [Chen et al. 2020b] [Cheney 1964] [Cheng and Widera 2009b] [Cheng et al. 2023] [Cheng et al. 2024b] [Cheung and Tennyson 1988] [Cheung and Zhu 1989] [Chien Do 2019] [Chikhi and Djermane 2018] [Chou 1971] [Chryssanthopoulos and Poggi 1995] [Chung et al. 1976] [Citerley and Khot 1986] [Clarke and Frith 2015] [Cohen 1992] [Cohen and Haftka 1989] [Cohen and Pastrone 1993] [Combescure and Galletly 1999] [Cooper 1967] [Cooper 1972] [Cooper and Dexter 1974] [Coppa] [Coppa 1962] [Coppa and Nash 1962] [Coppa and Nash 1964] [Corona and Kyriakides 1991] [Costello 1970] [Costello and Nishida 1967] [Cragg 2016] [Craig and Duggan 1973] [Craig and Stander 2006] [Curreri et al. 2013] [Cylindrical Shell Roofs 1983] [Cylindrical shells above local] [Cylindrical Shells above Local 2006] [Cylindrical shells under axial] [Cylindrical Shells under Axial 2006] [Cylindrical shells under combined] [Cylindrical Shells under Combined 2006] [Cylindrical Shells under General 2009] [Cylindrical shells under global] [Cylindrical Shells under Global 2006] [Cylindrical shells under non-uniform] [Cylindrical Shells under Non-Uniform 2006] [Cylindrical shells under torsional] [Cylindrical Shells under Torsional 2006] [Cylindrical shells under uniform] [Cylindrical Shells under Uniform 2006] [Daidzic et al. 1991] [de Vries] [de Vries 2007] [De-yu et al. 1993] [del Prado et al 2009] [Deml and Wunderlich 1997] [Dey and Ramachandra 2019] [Di et al. 2022] [Diaconu et al. 2002] [Dian-Fu Wang et al. 1982] [DIGiovanii and Dugundji 1965] [Dill 1962] [Dong et al. 2017] [Donnell 1963] [Doshi and Ning 2023a] [Doshi and Ning 2023b] [Dowling et al. 1992] [Duan et al. 2018] [Dung and Hoa 2013] [Durban and Libai 1974] [Durban and Ore 1999] [Durelli et al. 1971] [Durelli et al. 1973] [Dym and Hoff 1966] [Dynamic Buckling 2019] [Edlund 2007] [Edmondson 1974] [Ekstrom 1963] [Ellinas and Supple 1983] [Eslami, R. Javaheri 1999] [Eslami 2017] [Esslinger and Ciprian 1982] [Esslinger and Geier 1976] [Estekanchi and Vafai 1999] [Ette and Onwuchekwa 2008] [Evan-Iwanowski and Gorman 1965] [Evkin 2023a] [Evkin 2023b] [Evkin 2026] [Fajuyitan and Sadowski 2018] [Fan 1989] [Fan 2019] [Fan et al. 2016] [Fan et al. 2022] [Farshad 1992b] [Farshad 1992a] [Fatemi et al. 2013] [Fathi and Royer 2026] [Fatt 1999] [Fazlalipour et al. 2021] [Feinstein et al. 1971a] [Feinstein et al. 1971b] [Feldman and Aboudi 1993a] [Feldman and Aboudi 1993b] [Feldman et al. 1965] [Fersht 1974] [Filippov 2015] [Filippov 2017] [Filippov 2026] [Filippov and Naumova 2013] [Firer and Sheinman 1994] [Fischer and Rammerstorfer 1982] [Fisher 1972] [Flores and Godoy 1991] [Foroutan and Torabi 2025] [Foster 1981] [Foster 1987] [Franzoni et al. 2019b] [Franzoni et al. 2019a] [Free Vibrations 2023] [French et al. 1967] [Friedrich and Reimerdes 2013] [Fuchs et al. 1998] [Fulton 1965] [Fulton and Sykes 1966] [Gaidaichuk and Kotenko 2020] 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Bisagni 2022] [Schmidt and Winterstetter 1999] [Schneider et al. 1989] [Schultz] [Schultz et al. 2016] [Schultz et al. 2018] [Sechler 1966] [Seide 1962] [Seide and Hafiz 1975] [Seide and Weingarten 1961] [Seide et al. 1960] [Sel’skii 1978] [Senkiv and Diakiv 2019] [Shabeer et al. 2025] [Shahrjerdi and Bahramibabamiri 2015] [Shamass et al. 2014] [Shamass et al. 2015] [Shamass et al. 2018] [Shariati and Rokhi 2008] [Shariyat 2008] [Shariyat 2011] [Shariyat and Eslami 1999] [Shaw et al. 1952] [She et al. 2017] [Sheinman and Goldfeld 2001] [Sheinman and Goldfeld 2003] [Sheinman and Jabareen 2004] [Sheinman and Simitses 1977] [Sheinman and Simitses 1983] [Shell Buckling Experiments 2002] [Shen 1996] [Shen 1997] [Shen and Chen 1991] [Shen and Xiang 2008] [Shen et al. 1993] [Shengkun and Wai 2026] [Sherbourne and Korol 1967] [Shi et al. 2017] [Shiomitsu and Yanagihara 2020] [Shiomitsu and Yanagihara 2021b] [Shiomitsu and Yanagihara 2021a] [Shnerenko 1970] [Shnerenko and Godzula 2003] [Shouyi and Ping 2020] [Siad 1999] [Sigova and Doronin 2015] [Sim et al. 2023a] [Sim et al. 2023b] [Simitses 1988] [Simitses and Hsiung 1999] [Simitses and Sheinman 1982] [Simitses et al. 1985b] [Simitses et al. 1985a] [Singe 1962] [Singer 1962] [Singer 1999] [Singer and Baruch 1974] [Singer and Baruch 1975] [Singer and Haftka 1967] [Singer and Singer 1997] [Singer et al. 1966] [Singer et al. 1968] [Singer et al. 1971] [Singh et al. 2023] [Siva Sankara Rao et al. 2021] [Skosarenko 1992] [Slankard and Nash 1953] [Sleight et al. 2018] [Smeltzer and Bowman 2002] [Smerdov 2000] [Sobel and Agarwal 1976] [Sobel and Newman 1980] [Sofiyev 2010] [Solazzi 2022] [Soltani and Hosseini Kordkheili 2021] [Some Aspects of Concrete 1963] [Song] [Song 2017] [Song et al] [Song et al. 2021] [Soong 1967] [Soong 1970] [Spence and Toh 1979] [Sridharan 1994] [Starnes 1972a] [Starnes 1972b] [Starnes 1974] [Starnes and Hilburger 2003] [Starnes and Rose 1998b] [Starnes and Rose 1998c] [Starnes and Rose 1998a] [Starnes and Rose 1999] [Stavsky and Friedland 1969] [Stavsky et al. 1989] [Stein 1968a] [Stein 1968b] [Stephens 1971] [Stephens et al. 1974] [Stephens et al. 1975] [Stephens et al. 2011] [Stiffened cylindrical shells] [Stiffened Cylindrical Shells 2006] [Storozhuk 2021] [Stretching and Bending 1983] [Stulhofer 1973] [Sturm 1962] [Sukhinin et al. 1979] [Sun 1991] [Sun and Hansen 1988] [Sun and Mao 1993] [Sun et al. 2013] [Sun et al. 2014] [Sun et al. 2015b] [Sun et al. 2016] [Sun et al. 2020a] [Sun et al. 2022b] [Surface Bending and Shell 2001] [Tabiei 1995] [Tabiei and Simitses 1997] [Tabone and Mallett 1987] [Tafreshi 2002] [Tafreshi 2004b] [Tafreshi 2004a] [Tafreshi 2006] [Tahir and Mandal 2017] [Tahir et al. 2021] [Takano 2012] [Tall cylindrical shells under] [Tall Cylindrical Shells 2006] [Tang 1966] [Tang and Li 2012] [Taniguchi 2004] [Tatarinov 1983] [Tatarinov 1984] [Tatting and Guerdal 1998] [Teichmann 1985] [Tekleab and Guggenberger 2013] [Teng 1996] [Teng and Barbagallo 1997] [Teng and Rotter 1992] [Tennyson 1963] [Tennyson 1964] [Tennyson 1968] [Tennyson 1969] [Tennyson 1975] [Tennyson 1976] [Tennyson and Muggeridge 1972] [Tennyson et al. 1971b] [Tennyson et al. 1971a] [Tests on the Buckling 2009] [Thang et al. 2016] [Thang et al. 2017] [The Brazier Effect 1983] [The Buckling of Cylindrical 1966] [Thermocryogenic Buckling and Stress 1995] [Thielemann 1962] [Thielemann and Esslinger 1969] [Thompson 2025] [Thompson and Sieber 2016] [Thornburgh and Hilburger 2011] [Tian et al. 2021] [Tillotson et al] [Tillotson Rudd et al. 2024] [Tingleff 1971] [Tomás et al] [Touogam Touolak et al. 2022] [Trinh and Weaver 2021] [Trybuła and Krużelecki 2014] [Tsang and Harding 1984] [Tvergaard 1976] [Tvergaard 1983] [Tănase 2024] [Uematsu and Uchiyama 1985] [Uemura 1966] [Ugural 2017] [Ugural and Cheng 1968] [Ullah 2009] [Ustinov 1975] [Uzair et al. 2026] [Vasilikis and Karamanos 2008] [Vasyunyk 2003] [Vaziri 2007] [Vaziri and Estekanchi 2006] [Velmurugan and Buragohain 2023] [Vinogradov 1987] [Voce 1969] [Vodenitcharova and Ansourian 1996] [Volpe et al. 1980] [Von Karman and Tsien 1941] [Vullo 2013] [Waeckel et al. 1986] [Wagner et al. 2017] [Wagner et al. 2019] [Wagner et al. 2020a] [Wagner et al. 2020c] [Wagner et al. 2020b] [Wah 1965] [Wang and Koizumi 2010] [Wang and Ramamritham 1947] [Wang and Sullivan 1952] [Wang and Yang 2010] [Wang et al. 1953] [Wang et al. 2018b] [Wang et al. 2018c] [Wang et al. 2021a] [Wang et al. 2022c] [Wang et al. 2023b] [Wang et al. 2024c] [Wardle 2008] [Wei et al. 2005] [Wei et al. 2018] [Wei et al. 2023] [Weingarten 1962a] [Weingarten 1964a] [Weingarten 1965] [Weingarten and Reismann 1974] [Weller 1978] [Weller and Singer 1977] [Weller et al. 1970] [Wesenberg 1974] [Wetherhold 2012] [White and Weaver 2016] [Wilkins and Love 1974] [Williams 1974] [Wilson and Spier 1963] [Wittek 1982] [Wong et al. 2005] [Wood 1958] [Wu 2003] [Wu and Liu 1989] [Wunderlich et al. 1982] [Xiang et al. 2005] [Xing et al. 2019] [Xu et al. 2013a] [Xu et al. 2017] [Xu et al. 2026] [Xue 2012] [Xue et al. 2005] [Xue et al. 2010] [Yabuta 1980] [Yadav and Gerasimidis 2020] [Yaka 2016] [Yamada and Croll 1993] [Yamada and Uchiyama 2008] [Yamada et al. 2008] [Yamaki 1969] [Yamaki 1976] [Yamamoto and Yamada 2019] [Yang and Williams] [Yang et al. 2021] [Yang et al. 2024] [Yang et al. 2026] [Yao 1962b] [Yao 1962a] [Yao 1963] [Yao 1965] [Ye 2003] [Ye et al. 2011] [Ye et al. 2023] [Ye et al. 2024] [Yilmaz and KocabaŞ 2021] [Yin 1996] [Yoo and Lee 2011a] [Yoo and Lee 2011b] [Yoshimura 1955] [Yu et al. 2024b] [Yuan and Wang 2012] [Zaczynska et al. 2021] [Zak et al. 1979] [Zamani et al. 2014] [Zamani Nejad and Esfandyari 2025] [Zamula 1965] [Zeighampour and Beni 2014] [Zeng and Wu 2003] [Zeng et al. 2009] [Zhang 2022] [Zhang et al. 2003] [Zhang et al. 2015] [Zhang et al. 2020a] [Zhang et al. 2020c] [Zhang et al. 2022b] [Zhao et al. 2023b] [Zhao et al. 2023a] [Zhao et al. 2025b] [Zhao et al. 2025d] [Zhou et al. 2025a] [Zhu and Cheung 1996] [Zhu et al. 2022] [Zhu et al. 2023a] [Zhu et al. 2025] [Zick 1962] [Zickel 1953] [Zielnica 2013] [Zingoni 2017] [Zintilis and Croll 1986] [Zitzevancih 1985] [Zuo et al. 2025a] [Żmuda-Trzebiatowski and Iwicki 2017]

Rocket propulsion, engines and their failures

Where the Atlas A’s failures were. Liquid rocket engines, the solid motors of the ballistic missile programmes and of the Atlas line where their subject is one the argument uses, turbopumps and inducers, start transients, combustion instability and engine health monitoring. 87 of its 654 records name an instability and 105 a turbopump or inducer.

654 records. [Rafeeque 2025] [Lee 2004a] [Abbe et al. 1967] [Abbe et al. 1968] [Acar and Öztürkler 2024] [Agarwal 2023] [Allen 2002] [Назаренко 2023] [Ananoff 1941] [Anderson et al. 1995] [Anderson et al. 1996] [Anderson et al. 2012] [Anderson et al. 2013] [Anderson et al. 2015] [Anderson et al. 2019] [Andrei 2021] [Andrews et al. 2018] [Ankarsward 1972] [Appel and Kruger 1980] [Michigan Univ Ann Arbor 1963] [Armstrong 1952] [Armstrong and Kilner 1953] [Artamanov 1963] [Atamanchuk 2025] [Atefi and Naraghi 2019] [Athavale and Singhal 2001] [Atluri and Kathiresan 1980] [Oak Ridge Gaseous Diffusion Plant (K-25), Oak Ridge, TN (United States) et al. 1981] [Ayran et al. 2026] [Bagautdinov et al. 2025] [Bai et al. 2020] [Bairamov and Bairamov 2022] [Balepin 2001] [Balepin 2006] [Barrère 1977] [Batchelor 1964] [Bazarov 1998] [Beaurain et al. 1992] [Beichel and Obrien 1978] [Beltran and Frankel 1965] [Beltran and Kosvic 1966] [Bendot 1974] [Benjamin and McConnaughey 1991] [Bentsman et al. 1991] [Benzing et al] [Berg 1968] [Bermudez 2024] [Berque and Georges 1992] [Betti et al. 2015] [Biliske and Patel 2024] [Bilogurov et al. 2026] [Binder 1993] [Binder 1995] [Bjorklund et al. 1979] [Blackman et al. 1965] [Blount 1990] [Boccaletto and Lequette 2005] [Borovik et al. 2019] [Bosson and Goirand 1999] [Bosson et al. 1993] [Bosson et al. 1999] [Bouajila et al. 2021] [Bower and Thomas 2018] [Boyd et al. 1967] [Brock and Franke 2004] [Broomby and Trifoni 2024] [Brown et al. 2000] [Bryant 1989] [Buckmann et al. 1989] [Buckmann et al. 1992] [Burdett 1946] [Burkey 2010] [Burstein et al. 1972] [Buswell 2005] [Butas et al. 2001] [Byrd and Kynard 2007] [Rocketdyne Canoga Park Ca 1961] [Campbell 1962] [Candler 2001] [Carpenter and Jeffus 1962] [Carpenter and Jeffus 1963] [Casiano et al. 2009] [Cha and Ko 2025] [Cha et al. 2019] [Cha et al. 2024] [Chandler 2023b] [Chandler 2023a] [Chandler 2024] [Chandler and Bowen 2021] [Chandler and Herrera 2025] [Chandler et al. 2002] [Chandler et al. 2026] [Chen and Zhao 2005] [Chen et al. 2021] [Cheng and Farmer 2002] [Cherkupalli and Sandeep 2022] [Cherniavskyi 2026] [Chiang et al. 2007] [Chiu 1987] [Christenson and Holt 1995] [Christison 2024] [Citarella et al. 2022] [Clark 1967b] [Clark 1967a] [Cole et al. 2008] [Collins et al. 1986] [Collins et al. 1990] [Combustion Instability Analysis 1995] [Sung 2004] [Conley et al. 2003] [Contreras et al. 2026] [Coogan 2015] [Cosens and Newton 1988] [Cox 1988] [Crabtree 1962] [Crocco 1965] [Crocco et al. 1962] [Crone et al. 1993] [Cruz et al. 2025] [Cunningham et al. 1986] [d’Agostino et al 2017] [Das and Padmanabhan 2022] [Dawson et al. 2013] [de Iaco Veris 2020] [DeHoff et al. 1993] [Delcher et al. 1989] [Demiyanenko et al. 2004] [Demjanenko et al. 2003] [Dequay et al. 1991] [Desai and Kuzhiveli 2022] [Design Data Book Phase 1972] [Dethloff 1961] [Di Matteo et al. 2009] [Di Matteo et al. 2011] [Disimile et al. 1991] [Dissel et al. 2012] [Dorney et al. 2005] [Dorosh and Leontiev 2014] [Dougherty 2010] [Drobyshev 2026] [Du 2017] [Dubois et al. 1995] [Dunn et al. 1999] [Ekimogloy et al. 2026] [Eklund 2004] [Ellerbrock and Ziegenhagen 2006] [Ellis et al. 1953] [Emrich 2016] [Emrich 2023] [Ennix and Coleman 1987] [Erickson and Erickson 1997] [Etters and Flurchick 1981] [Ezell 1960] [Fagherazzi et al. 2023] [Farvin and Peddieson 1988] [Fashbaugh and Streeter 1965] [Fatuev 2006] [Feng et al. 2009] [Ferraiuolo et al. 2023] [Fidler and Hays 2026] [Fidler et al. 2025] [Figueroa et al. 2010] [Filimonov 1968] [Filin and Mkrtchyan 2021] [Fint et al. 2005] [Fiore et al. 2024] [Flandro et al. 2004b] [Forde et al. 2006] [Foster et al. 1989] [France’s Liquid Propellant Rocket-Engine 2006] [Franklin and Tinsley 1970] [Freeman 2015] [Friedland 1965] [Fujita et al. 2002] [Fuller 1973] [Furst 1973] [Furst 1975] [Gajjar and Malhotra 2018] [Galati and Elkins 1996] [Galati and Elkins 1997] [Gale et al. 2018] [Galli] [Ganesan et al. 2025] [Gao and Sun 2009] [Gao et al. 2023] [Gardner et al. 1991] [Gass et al. 1988] [Gaynor and Cervisi 1984] [Gemranova 2021] [Genge 1991] [Gibart] [Gibson 1985] [Glidden and Wilhite 2014] [Gloger et al. 2020] [Gloger et al. 2021] [Glushko 1976] [Go et al. 2017] [Goertz 1995] [Goetz et al. 2005] [Goirand et al. 2003] [Gompertz 1950] [Gong et al. 2017] [Gordon 1950] [Gordon and Brown 1963] [Gotsulenko 2008] [Graefe and Gordon 1957] [Graefe et al. 1954] [Gray et al. 2024] [Green 1966] [Greene et al. 1999] [Greenwald 1971] [Greenwood et al. 1970] [Grenda et al. 1991] [Grey 1953] [Grey 1954] [Gritsenko et al. 2024] [Grosdemange and Schaeffer 1990] [Guidolotti and d’Agostino 2023] [Gulczyński et al. 2024] [Gurov 2001] [Haberstroh et al. 2008] [Haga 2024] [Hagar and Alcock 1989] [Ham-Battista et al. 1993] [Hampson 1984] [Hardesty 1970] [Harrje 1959] [Harvazinski et al. 2014] [Harvazinski et al. 2024] [Hauser and Helfrich 1963] [Heister 2008] [Heister 2011] [Heldens et al. 2026] [Herbertz et al. 2001] [Hiers et al. 2003] [Hildner and Arnold 1966] [Hiraki et al. 2019] [Holloway and Limerick 1993] [Holt and Monk 2009] [Hong and Choi 2017] [Hong et al. 2009] [Hong et al. 2012b] [Hong et al. 2012a] [Honkawa and Yoozbashizadeh 2019] [Hood et al. 1970] [Houhou et al. 2025] [Hu et al. 2026] [Huang 1985] [Huang 2000] [Huang and Weber 1998] [Huang and Weber 1999] [Huang et al. 1997] [Huang et al. 2000b] [Huang et al. 2024b] [Huang et al. 2024d] [Huang et al. 2025c] [Hulka 2008] [Hulliger et al. 2026] [Hunley 2008d] [Hussein et al. 2026] [Instability Phenomenology and Case 1995d] [Instability Phenomenology and Case 1995b] [Instability Phenomenology and Case 1995a] [Иванов 2021] [Ivanov and Borisov 2014] [Jacob and George 2024] [Jacob et al. 2010] [Japan’s Liquid Propellant Rocket-Engine 2006] [Jassowski et al. 1991] [Jensen 2001] [Jensen 2005] [Jensen et al. 1962] [Jetevator for Rocket Engine 1998] [Jha 2024] [Jo et al. 2021] [Jones and Petley 1991] [Jorgensen et al. 2022] [Jugade 2023] [Jung 2022] [Jurado et al. 1990] [Kachler and Beaurain 2005] [Kakudo et al. 2021] [Kakudo et al. 2025] [Kanda 2013] [Kang et al. 2015] [Kassoy 2013] [Kato et al. 1995] [Kawatsu 2019] [Kawatsu et al. 2011] [Kayama and Takenaka 1980] [Kerstens et al. 2021] [Kim et al. 2004] [Kim et al. 2020b] [Kimura et al. 2005] [Kiris et al. 2000] [Kishimoto et al. 2022] [Kobayashi et al. 2011] [Kobayashi et al. 2015] [Koelbl 1993a] [Koelbl 1993b] [Komar and Christenson 1996] [Kosykh 2025] [Kozlov et al. 1996] [Krevor and Wilhite 2007b] [Kubicki et al. 2020] [Kuhl et al. 1998] [Kunz 1967] [Lacaille 2012] [Lafont and Bosson 1983] [Larson 1973] [Lash and Moeller 2015] [Lawrence 1945] [Leahy and Williams 2007] [Lee and Roh 2013] [Lee et al. 2016] [Lee et al. 2018a] [Lee et al. 2018b] [LeMoyne 2008b] [Leonard and Kisko 1992] [Leonardi et al. 2017] [Lepsch et al. 1990] [Leto et al. 2016] [Levack and Sack 2013a] [Levack and Sack 2013b] [Lewis and Harrison 1961] [Li et al. 2011b] [Li et al. 2019e] [Li et al. 2019d] [Li et al. 2023a] [Li et al. 2026b] [Liang et al. 2022b] [Life Prediction 1995] [Limerick 1991] [Limerick 1994] [Lin et al. 2010] [Liquid propellant rocket engines] [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] [Liquid Rocket Booster Study. 1988] [Anderson and Yang 1995] [Rezende 2018a] [Liquid Rocket Engines 2019] [Liquid Rocket Propellants 2019] [Liu and Qizhi 1996] [Liu et al. 1995] [Liu et al. 2022] [Liu et al. 2025c] [Long et al. 2013] [Lorenzo 1995] [Lucci and Hodson 1975] [Lurui Xia et al. 2008] [Muthaiah et al. 2023] [Maggio and Gerez 1996] [Maggio and Pellacio 2000] [Manski and Fina 1994] [Manski and Martin 1988] [Manski and Martin 1991] [Manski et al. 1997] [Dnipro Aerospace and Marchan 2026] [Martin 1962] [Martin 1995] [Martin 2007] [Martinez et al. 1990] [Mathias and Motiwala 2015] [Mathieu et al. 1990] [Matthews 1957] [Matveev et al. 2018] [Mayer and Kruelle 1992] [McAmis et al. 1992] [McGinnis and Joyner 2005] [Meisl 1986] [Meisl 1988] [Meisl 1989] [Meisl 1992] [Merits of Liquid Propellant 2006] [Meyer and Zakrajsek 1990] [Lyon INC Detroit MI 1963] [Mitchell 1969] [Mohammadi et al. 2015] [Moore et al. 2024] [Morash et al. 1995] [Moruzzi et al. 2018] [Mosolov and Sidlerov 2019] [Motomura 2025] [Mozgov et al. 2013] [Mueller 1966] [Mueller et al. 1999] [Multifractal Detrended Fluctuation Analysis 2023] [Mundt et al. 2024] [Murphy and Voss 1996] [Muthaiah et al. 2025] [Müller et al. 2017] [Design Criteria Monograph 1975] [Nakane et al. 2009] [Nakanishi et al. 1982] [Naraghi et al. 2006] [Rezende 2018b] [Negishi et al. 2008] [Nesbitt 1946] [Newell and Rajagopal 1993] [Nguyen and Knowles 2002] [Nguyen et al. 1988] [Nicastro et al. 2025] [Nie and Liu 2011] [Princeton Univ Nj 1952] [Numerical Method and Simulations 2016] [Choi and Kim 2003] [Nusca 2007] [Nusca 2008] [Nusca 2010] [Cornell Aeronautical Lab INC Buffalo NY 1947] [Excelco Developments INC Silver Creek NY 1963] [Oh et al. 2024] [Okayasu et al. 2002] [Ordway 1991] [Osborn and Davis 1961] [Osherov and Natan 1999] [Oyama and Liou 2001] [Ozaki et al. 2025] [Ozelsel] [Pages and Achipa 2026] [Palac 1999] [Palaszewski 1990] [Palaszewski and Powell 1991] [Park and Ahn 2020] [Park and Jeon 2024] [Parsley 1989] [Patel 2016b] [Patel 2016a] [Patel et al. 2019] [Patel et al. 2025] [Pearce 1972] [Pempie and Ruet 2003] [Pempie and Vernin 2001] [Penner 1954] [Perkins 1987] [Perlmutter and DePierre 1965] [Pervaiz et al. 1994] [Pizzarelli 2021b] [Pizzarelli 2021a] [Podolchak 2019] [Pooley et al] [Popov and Sirignano 2015] [Popov et al. 2013] [Popov et al. 2014b] [Popov et al. 2015] [Popov et al. 2016] [Popov et al. 2017] [Popp and Schmidt 1996] [Powell et al. 1975] [Prochnicki et al. 2018] [Prokopenko 2026] [Pshenychka 2026] [Pustovyi 2026] [Qi et al. 2021] [Qi et al. 2022] [Qin et al. 2016] [Kala et al. 2027] [Black et al. 1967] [Chen et al. 1993] [Cheng 1954] [Combs and Lawhead 1963] [Du et al. 2020] [Radovcich 1965] [Rafferty 1968] [Rai 2006] [Reardon 1997] [Reeves et al. 2024] [Reinhardt 1968] [Reitan 1992] [Report Status Mass Properties 1972] [Rezende 2021] [Rice et al. 2010] [Fio Rito 1964] [Garcia et al. 1998] [Gradl et al. 2019] [Harrje and Sirignano 1966] [Huzel and Huang 1967] [Jung 2019] [Klem 1990] [Marsh and Cowan 1994] [Mellish 1981] [Mitchell 1967] [Morgan et al. 2015] [Platt et al. 1965] [Ray 2003] [Rocket Engine Nozzle Concepts 2004] [Rocket Engine Propulsion ‘System 1992] [Rodríguez Otero et al. 2020] [Rose and Niemeyer 2021] [Rothmund 2006] [Rupert 1965] [Ruth et al. 1990] [Sackheim 1992] [Saidyanathan et al. 2000] [Sales and Pasini 2021] [Sander and Leahy 1993] [Santhini S Lal et al. 2015] [Santhoshkumar et al. 2026] [Santiago 1996] [Sarotte] [Scala 1957] [Schallhorn et al. 1998] [Schmehl and Steelant 2003] [Schoettle and Rahn 1993] [Schwabacher 2005] [Scott 1963] [Senchev et al. 2022] [Flora and Auxillia 2020] [Sergienko et al. 1995] [Shelley et al. 2001] [Shi et al. 2023b] [Shoyama et al. 2024] [Shyy et al. 1999] [Siebenhaar and Campbell 1987] [Singelmann and Mueller 1948] [Sirignano and Krieg 2016] [Sirignano and Popov 2013] [Skopinsky and Berkov 1994] [Sliusariev 2025] [Smith and Stechman 1981] [Sobin et al. 1977] [Son et al. 2012] [Space Transportation Booster Engine 1986] [Space Transportation Booster Engine 1989a] [Space Transportation Booster Engine 1989d] [Space Transportation Booster Engine 1989c] [Space Transportation Booster Engine 1989b] [Sprouse et al. 2018] [Stability Testing Methodology 1995] [Stanley 1969] [Stanley et al. 1992] [Stanley et al. 1994] [Staschus and Frederick 2016] [Stout 2020] [Strauss 1964] [Strokach et al. 2020] [Stuber et al. 2012] [Suda et al. 2007] [Sukachevskyi 2026] [Summerfield 1951] [Summerfield 1960] [Sung et al. 2025] [Sutton 1968] [Sutton 1970] [Sutton and Lariviere 1993] [Swaraj et al. 2023] [Takada et al. 2009] [Takahashi and Gibson 2014] [Talley 2002] [Tanck and Steadman 1998] [Tani et al. 2008] [Tani et al. 2010] [Tavares and Ceotto 2021] [Teasley et al. 2025] [Tellier 1964] [The thermal rocket engine] [Thomas 2022] [Tobey and Bastress 1966] [Tonon et al. 2022] [Torre et al. 2018] [Torres Zanardi et al. 2019] [Yoo 2004] [Traudt 2024] [Traxinger et al. 2019] [Trikha et al. 2008] [Tripropellant Engine Technology 2004] [Tucker et al. 1993] [Tucker et al. 1998] [Tulpule 1989] [Turner 2009] [Turushov et al. 1995] [Twardy 1975] [Uemura] [Urbano et al. 2016] [Vadera 2019] [Valentine and Gradl 2019] [Van Hooser et al. 1999] [Vasilevsky 2022] [Ventrice et al. 1979] [Verma et al. 2007] [Vilja and Vilja 1997] [Von Eckartsberg et al. 2025] [Walker and Baumgartner 1990] [Walsh and Jacoby 1972] [Wang 2019] [Wang and Fan 2013] [Wang et al. 2011b] [Wang et al. 2021c] [Wang et al. 2022a] [Wang et al. 2025f] [Watanabe and Mikami 2010] [Wei et al. 2015] [Wei et al. 2022] [Weiss and Merkle 1991] [Wheelock and Kraemer 2005] [Whitehead 1996] [Wilhite 1978] [Williams 1968] [Williams 2004b] [Williams 2004a] [Wiswell and Huggins 1990] [Wong and Brown 1965] [Wu 2005] [Wu 2026] [Wu et al. 2026] [Wunderlin et al. 2024] [Wyett et al. 1989] [Xiang 2023] [Xiong 2018] [Xiong et al. 2020b] [Xu et al. 2006] [Yada et al. 2018] [Yamanishi et al. 2003] [Yang et al. 2019] [Yang et al. 2025a] [Yonezawa et al. 2013] [Yoon et al. 2005] [Yoon et al. 2012] [Yoon et al. 2013] [You et al. 2021] [Young 1964b] [Young 1964a] [Young 2008] [Youngquist 1947] [Yu et al. 2019] [Yue et al. 2011] [Yue et al. 2019] [Yunfeng 2024] [Zeng et al. 2021] [Zhang 2016] [Zhang 2026] [Zhang and Li 2017] [Zhang et al. 1998] [Zhang et al. 2025e] [Zhang et al. 2026f] [Zhou et al. 2022] [Zhou et al. 2024c] [Zhou et al. 2026] [Zhuang et al. 1998] [Zhuang et al. 1999] [Zinn 1966] [Zinn 1968] [Zinn and Powell 1971] [Zinn and Savell 1969] [Zubanov and Shabliy 2014] [Zubanov et al. 2018b] [Zubanov et al. 2018a] [Zucrow 1947]

Propellant tanks, cryogenic storage and boil-off

The tank as a container rather than as a structure. Cryogenic storage, self-pressurisation and stratification, pressurant systems, insulation, common bulkheads, composite tanks and the cryogenic properties of stainless steels. 77 titles name boil-off and 31 the common bulkhead, and the cluster’s median publication year is 2012, so half of it is more recent than that and belongs to the period of long-duration cryogenic upper stages rather than of a missile topped up until launch.

734 records. [Abdelghany et al. 2025] [Abdrahimov and Urbansky 2022] [Adams et al. 1999] [Adler and Martins 2025] [Afzali et al. 2009] [Aggarwal and Hull 2015c] [Aggarwal and Hull 2015a] [Aggarwal and Hull 2015b] [Aggarwal and Hull 2016b] [Aggarwal and Hull 2016a] [Agrawal et al. 2017] [Ajeesh et al. 2026] [Akimov et al. 2019] [Akmandor and Nagashima 1999] [Al Ghafri et al. 2022] [Alper 1964] [Alsultan et al. 2021] [Ambur et al. 1996] [Andreasen 2026] [Angirasa 2015] [Anschutz 1960] [Aoki and Ota 1986] [Appel et al. 2025] [Arens 2010] [Arens et al. 2010] [Armstrong 1989] [Armstrong and Schlumberger 1990] [Ashok et al. 2025] [Avila et al. 2016] [Baek et al. 2025] [Bai 2006] [Bailey et al. 1986] [Baker 2003] [Balasubramaniam and Johnson 2020] [Bandyopadhyay et al. 2019] [Banerjee and Bardhan 1979] [Banerjee et al. 2011] [Baralle and Fournier 1989] [Barker and Field 2003] [Barron and Timmerhaus 1969] [Barrows 1968] [Barsi and Kassemi 2008] [Bartrand 1988] [Batul et al. 2020] [Bauer 1964b] [Beck and Mallon 1966] [Benkelman et al. 2017] [Bentley et al. 2023] [Benton and Debreceni 2004] [Benton et al. 2007] [Berglund et al. 2006] [Berglund et al. 2007] [Berglund et al. 2009] [Bershadskyi et al. 2022] [Bickford 1987] [Blakseth et al. 2025] [Bott et al. 1983] [Bowen and Marchetta 2022] [Brennan 1967] [Brinckman et al. 2025] [Brown and Robertson 1966] [Byron and Morse 1968] [Cady and Blackmon 1974] [Cady and Kendle 1972] [Cady and Kendle 1973] [Cai et al. 2018] [Cai et al. 2019] [Cankaya and Arnold 2006] [Chakroborty et al. 2006] [Chandler 2019a] [Chato 2009] [Chato et al. 2014] [Chau-Vo et al. 2024] [Chausov et al. 2025] [Chausov et al. 2026] [Chehroudi 2009] [Chehroudi 2010] [Chen and Anderson 1972] [Chen and Liang 2013] [Chen et al. 2025c] [Cheng et al. 2024a] [Cheng et al. 2025a] [Cheng et al. 2025b] [Cheng et al. 2026] [Cheriaux and Fraïoli 2011] [Chiu and Brown 2017] [Cho et al. 2004] [Cho et al. 2022] [Choi and Lee 2023] [Choi et al. 2024] [Christian 1962] [Christian et al. 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[Mer et al. 2016] [Mercado and Hartwig 2024] [Merkel et al. 2021] [Messinger and Pulley 2003] [Mishra and Ghosh 2017] [Mizutani et al. 2006] [Momenthy 1964] [Morales-Ospino et al. 2023] [Moreira and Magnabosco 2023] [Morey and Koshar 1961] [Morino et al. 1999] [Morino et al. 2001] [Morita 1964] [Moser and Keith 1992] [Moxson et al. 1987] [Mulkey and Lineberry 2012] [Zhang et al. 2022a] [Murugan et al. 2026] [Nam et al. 2019] [Nandi 2001] [Narayana Yenugula et al. 2025] [Narayanan 2014] [Nast and Williams 1967] [NDE of Heavy Wall 1996] [Nein and Head 1962] [Nein and Thompson 1965] [Nein and Thompson 1966] [Nemeth 2010] [Netter et al. 1999] [Nguyen 2004] [Nguyen 2007] [Nguyen et al. 2019] [Nguyen et al. 2025] [Nikolayev and Komatsu 2004] [Nikonchuk 2026] [Nohara et al. 1983] [Lockheed Missiles and Space Co., Sunnyvale, Calif. (USA) 1971] [O’Neill et al. 2025] [Odom 1979] [Ogasawara et al. 2013] [Ogata 2006] [Ogata and Balachandran 2010] [Ogata et al. 2000] [Ok 2024] [Ok et al. 2023] [Okayasu et al. 1983] [Oliphant and Japikse 1999] [Oliver and Harper 2012] [Padawer 1960] [Panzarella and Kassemi 2003] [Park et al. 2005] [Pasley 1972] [Pastuszko et al. 2024] [Patel 2026] [Patel and Williams] [Patel and Williams 2024] [Patel et al. 2024] [Peng et al. 2026] [Perrin 2023] [Peterson and Uney 1978] [Phillips and Wingate 2010] [Phillips and Wingate 2011] [Pierce 1965] [Pietrzyk et al. 1993] [Plachta 2001] [Plachta and Guzik 2014] [Plachta et al. 1993] [Plachta et al. 2016] [Plachta et al. 2017] [Popov et al. 2014a] [Potter et al. 2007] [Prasanraj 2019] [Praveen et al. 2022] [Pressurization of Liquid Propellant 2019] [Price 1980] [Price et al. 1992] [Puthettu Muraleedharan et al. 2023] [Read and Reed 1981] [Reducing Boil-off from Cryogenic 1971] [Ren et al. 2018] [Renitha P and Sivaramapandian J 2016] [Reske and Brodnick 2024] [Rhee et al. 2025] [Ricci et al. 2022] [Ricci et al. 2023] [Riccius et al. 2001] [Riemer 1986] [Rijin et al. 2017] [Rivers 1999a] [Rivers 1999b] [Roberts et al. 2001] [Robertson 1964] [Robertson 1965] [Robinson 1994] [Robinson 2006] [Robinson 2008] [Robinson et al. 2002] [Robinson et al. 2004] [Rollins et al. 1983] [Rollins et al. 1984] [Rollins et al. 1986] [Rollins et al. 1988] [Rose K. 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[Zheng et al. 2020c] [Zheng et al. 2022] [Zhu et al. 2018b] [Zidane et al. 2022] [Ziglar 2025a] [Ziglar 2025b] [Ziglar and Elsperman 2026] [Zilliac and Karabeyoglu 2005] [Zimmerli et al. 2010] [Zimmerli et al. 2015] [Zimmerman et al. 2013] [Zimmerman et al. 2015] [Zook 2024] [Zumbo et al. 2026b] [Zumbo et al. 2026a] [Zuo et al. 2019] [Zuo et al. 2025b]

Trajectory, guidance and control

The ascent and its control. Ascent trajectory optimisation, inertial and radio guidance, thrust vector control and launch-vehicle flight control. 28 titles name inertial guidance and 61 thrust vector control.

361 records. 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[Experimental Studies on Thrust 1977] [Farrell 1968] [Feodosiev and Siniarev 1959] [Fernandez] [Figueiredo 2003] [Fitzgerald and Kampe 1979] [Forbes-Spyratos] [Forbes-Spyratos et al. 2023] [Forliti and Diaz-Guardamino 2008] [Friddell and Franke 1990] [Fu et al. 2021] [Fundamental Mechanisms of Combustion 1995] [Gao et al. 2019] [Gath and Calise 1999] [Gath and Calise 2001] [Gea and Vicker] [Gee and Mathias 2008] [Gerdes et al. 1969] [Gettatelli et al. 2023] [Ghosh and Chattopadhyay 2014] [Ghosh and Chattopadhyay 2015] [Gilson et al. 2023] [Goodstein et al. 1982] [Gowan 2005] [Guo and Bai 2009] [Guo et al. 2026a] [Gusman et al. 2011] [Haloulakos 1982] [Hamke et al. 1992] [Hanford 1969] [Hardtla 1978] [Hardy 1969] [Hardy et al. 1967] [He et al. 2017] [He et al. 2020] [He et al. 2024a] [Health Monitoring and Controls 1994] [Hoffman et al. 2024] [Holt et al. 2015] [Horneman] [Hui Li et al] [Hwang 2019] [Hwang et al. 2003] [Inertial Guidance 1963] [Inertial Guidance 1964] [Inertial Guidance 1993] [Inertial Guidance Sensors 1964] [Ingold 1983] [Inouye and Nottage 1966] [Intelligent Hierarchical Thrust Vector 1994] [Ishibashi et al. 1995] [Jaensch and Markl 1991] [Jang et al. 2011] [Jha et al. 2010a] [Jha et al. 2025] [Jia et al. 2025] [Johnson 1975] [Joshi and Sudhir Kumar 2014] [Jung and Lee 2012] [Калашников 2021] [Karthikeyan Kalirajan and Ashok Joshi 2023] [Kamal 2008] [Kazarian et al. 1973] [Ken Gee and Lawrence 2013] [Kerr et al. 2010] [Kharisov et al. 2008] [Kim 2016] [Kirby and Van Vooren 1964] [Knight and Quinn 1971] [Kosmann et al. 1978] [Kumar V V and Beebi M 2015] [Lazić and Ristanović 2007] [Lee et al. 2024d] [LeFevre and Jha 2008] [LeFevre and Jha 2009] [Leitner 1986] [Leung and Calise 1992] [Levitt et al. 1970] [Li et al. 2010] [Li et al. 2019c] [Li et al. 2021b] [Li et al. 2024a] [Linsen et al. 2022] [Lu 1996a] [Lu and Pan 2009] [Lu et al. 2002] [Lu et al. 2013] [Luke 1991] [Luton 1963] [Lv et al. 2023] [Ma et al. 2012] [Ma et al. 2022b] [Ma et al. 2024a] [Maorui Zhang et al. 2010] [Marchetti and Minisci 2021] [Marchetti and Minisci 2023] [Marchetti et al. 2021] [Masyagin 2026] [Mattin 1968] [May 1986] [McCool et al. 1980] [Merrill and Lorenzo 1988] [Millard and Reed 2014] [Milleman 1967] [Moody 1970] [Moody and Nakai 1965] [Morgado et al. 2022b] [Morris 2014] [Morris 2015] [Mueller 1959] [Mukundan et al. 2019] [Mungas et al. 2012] [Murugesan et al. 2018b] [Musgrave 1991] [Muthukumar et al. 2020] [Najiya et al. 2023] [Naftel and Powell 1993] [Negishi et al. 2007] [Neilson et al. 1968] [Newton and Spaid 1962] [Nguyen 1987] [Nguyen 1991] [Nocoń and Szmidt 2025] [Norman et al. 1990] [Sperry Gyroscope Co Great Neck Ny 1963] [Oh et al. 2008] [Orr and VanZwieten 2012] [Pan and Lu 2010] [Patera 2006] [Pei et al. 2021] [Pitman and Trimmer 1962] [Platus 1975] [Platus 1980b] [Platus 1980a] [Platus 1994] [Pleasant 1978] [Poth and Elwell 1992] [Powell and Cruz 1991] [Powell et al. 1990] [Powell et al. 1991a] [Powell et al. 1991b] [Prins et al. 1992] [Punga and Campbell 1962] [Putnam and Braun 2014] [Putnam and Braun 2015] [Pérez Roca] [Qiuhong et al. 2014] [Rafique 2022] [Ramesh 2004] [Randall 1970] [Reentry Maneuvering Vehicle Ascent 2025] [Reentry Trajectory Estimation 2024] [宋 et al. 2021] [Zardashti et al. 2022] [Roenneke and Cornwell 1992] [Roenneke and Well 1995] [Rogers 1965] [Roh and Kim 1999] [Roh and Kim 2002] [Romo and Alvarez 2010] [Rosenbaum 1970] [Rosenbaum 1971] [Roshanian et al. 2019] [Ross et al. 2003] [Roth] [Rynaski 1967] [Sai and Manideep 2023] [Saiki et al. 2026] [Sathish et al. 2025] [Schinstock et al. 1998] [Schmidt 1992] [Schmidt and Velapoldi 1996] [Schmidt et al. 1993] [Schoettle and Hillesheimer 1991] [Schroer 1966] [Sehgal and Wu 1964] [Sellers 1948] [Shahmirzaee Jeshvaghani et al. 2015] [Shandor 1964] [Shandor and Walker 1962] [Sheth et al. 2024] [Shi et al. 2020] [Shorikov and Kalev 2019] [Shorikov and Kalev 2020] [Simmons and Hall 1973] [Solovyov and Korepanov 2025] [Soota and Nadda 2023] [Sopegno et al. 2023] [Space Transportation System Solid 1979] [Sparks and Raney 2007] [Spencer and Bixler 1987] [Stancil 1963] [Stechman 1984] [Steffens et al. 2015] [Stepp 2024b] [Strelnikov et al. 2022] [Stroud et al. 2012] [Study of Selected Thrust 1965] [Su] [Su et al. 2025a] [Suchitra et al. 2014] [Sun] [Sun et al. 2024a] [Talda and Franke 1989] [Tarrant and Crook 1996] [Taylor 2006] [Teofilatto 2024] [Theory of Error Compensation 1964] [Thompson and Pickett 1986] [Thrust Vector Control 2026] [Aerojet Nuclear Systems Co., Sacramento, Calif. (USA) 1970] [Toelle et al. 1973] [Trajectories of Solid Particles 1983] [Trotta et al. 2021] [Lee 2004b] [VanZwieten et al. 2014a] [VanZwieten et al. 2014b] [Varghese et al. 2021] [Villanueva 2022a] [Vinod et al. 2012] [Walsh et al. 2012] [Walters 1967] [Wang 2015] [Wang and Song 2022] [Wang et al. 2013d] [Wang et al. 2015] [Wang et al. 2018a] [Wang et al. 2019a] [Wang et al. 2019e] [Wang et al. 2025e] [Whorton et al. 2007] [Wie et al. 2008] [Winstead 1966] [Wittal et al. 2025] [Woodberry 1975] [Xiao et al. 2026a] [Xing and Bainum 1996] [Xing et al. 1997] [Xiong et al. 2024] [Xiong et al. 2025] [Xu 2022] [Xu and Zhang 2018] [Xu et al. 2021b] [Xu et al. 2024b] [Yaman and Seckin 2011] [Yao et al. 2022] [Yezzi and Donguy 1986] [Yi et al. 2019] [Yu et al. 2023a] [Yu et al. 2024a] [Zardashti and Rahimi 2020] [Zeamer 1975] [Zhai et al. 2019] [Zhang] [Zhang 2023] [Zhang et al. 2017] [Zhang et al. 2019] [Zhang et al. 2021] [Zhang et al. 2022c] [Zhang et al. 2023a] [Zhang et al. 2025a] [Zhang et al. 2025f] [Zheng et al. 2020a] [Zhou et al. 2024d] [Zimmermann et al. 1996] [Zimpfer 1999] [Zinn et al. 2005] [Öztürk et al. 2026]

Launch vehicle design, programmes and operations, the residual

The residual, reported and not hidden. Launch-vehicle work that belongs to no heading above, including vehicle design and optimisation studies, programme overviews of the Saturn, Shuttle, Ares and smaller launchers, processing and ground operations, avionics and standards.

352 records. [A probabilistic approach to] [A Probabilistic Approach 2006] [A Quick Look Structural 1994] [Abbott and Matzenauer 1990] [Abraham 1963] [Abraham et al. 1962] [Adetoro et al. 2014] [Aggarwal 2007] [Ahmed 2012] [Albarado et al. 2010] [Allen et al. 2000] [An Analysis of Chemical 1965] [Anderson et al. 2010] [Angel and Kiris 2019] [Anju et al. 2017] [Arbocz 1997] [Arbocz 1998] [Ariane Launch Vehicle 1977] [Armstrong 1964] [Azevedo and Buonomo 1999] [Azevedo et al. 1996] [Azizi and Dornisch 2025] [Babcock and Wiltse 1965] [Bacchetti et al. 2015] [Bacchus and Hendrix 1965] [Bahiman and Thole 1965] [Bailey 2020] [Balaji and Jerry Alexander 2015] [Balesdent et al. 2011] [Bansal and Singh 2022] [Barad et al. 2012] [Barth and Watson 2018] [Batts and Pearson 1996] [Baumgartner and Walker 1990] [Bayley et al. 2007] [Bellanca et al. 1964] [Bennich and Lindsey 1967] [Bialla and Hughes 1989] [Bieber 1966] [Bieber 1967] [Biggs et al. 2011] [Біляєв et al. 2024] [Birbasov et al] [Blackwell 1966] [Blackwood et al. 2015] [Blelloch et al. 2000] [Blume 2010] [Boyd et al. 2005] [Branets 2020] [Braukhane et al. 2013] [Braun et al. 1996] [Brevault] [Brevault and Balesdent 2021] [Brevault et al. 2016] [Brevault et al. 2017] [Brice et al. 1966] [Bright 2000] [Brown and Littlefield 2010] [Buhler et al. 2014] [Burkhalter and Sharpe 1990] [Buzzatto 2015] [Aerospace Corp El Segundo Ca 1963] [Cai and Xu 2015] [Calderon Hurtado et al. 2026] [Carter 2011] [Cerneck 1982] [Chan and Brauckmann 2011] [Chandler 2019b] [Chase 1980] [Chen et al. 1977] [Cheuvront and Nguyen 2005] [Chew 1973] [Chien et al. 2008] [Claggett and Langehough 1989] [Cobb and Davis 1994] [Cook 2006a] [Cook 2006b] [Cook and Vanhooser 2008] [Cox et al. 2022] [Air Force Space Command Space Missile SYS CTR 2014] [Cunningham and Higgins 1970] [Curlander and Kiefer 1965] [Da Cás 2021] [Dafler 1962] [Darwin et al. 1989] [Davis and Coook 2006] [Davis and McArthur 2008] [Day and Harvell 1990] [Military Standard 1994] [Dees and Stockard 2023] [Deese et al. 1991] [Delamata et al. 2010] [Development of a Large 1993] [Dineen 1966] [Dippolito and Stambolian 2011] [Dorrington 1987] [Driscoll 1967] [Dumbacher and Reuter 2007] [Edmunds 1988] [Ehrlich 1997] [Environmental Testing 1968] [Ericsson and Guenther 1971] [Fang et al. 2024] [Farish 1967] [Fayssal and Weldon 2008] [Feaux et al. 1989] [Flittie and McFarlane 1991] [Foust and Smith 2004] [Fragola 2012] [Frei 1991] [French 2010] [Gibson 2019] [Gomez and Ma 1994] [Fernandez 2024] [Gong 2017] [Goodrum and Smolensky 1965] [Gray 2014] [Gray 2015] [Greene 1994] [Gregory and Wilcox 1970] [Griffiths et al. 2016] [Grishko et al. 2025] [Gülgönül and Sözbir 2018] [Hagar and Dornseif 2004] [Hanson and Beard 2010b] [Hanson and Beard 2010a] [Hao and Zhang 2021] [Harrington 2004] [Harrison et al. 2009a] [Harrison et al. 2009b] [Harsh 1989] [Al Hassan et al. 2016] [Ermakov et al. 2025] [Gerard 1966] [Golubek et al. 2024] [Hattis 1981] [Hayward and Urdiales 2018] [Hegg 1964] [Highway to Space 2006] [Hinckel 1995] [Horchler et al. 2018] [Hou and Gramoll 1998] [Hsieh 1961] [Huang and Brown 1967] [Huangpeng et al. 2022] [Huber 1964] [Hunley 2008j] [Hunley 2008f] [Hunley 2008e] [Hunley 2008a] [Iacoponi and Grisell] [Imamura et al. 1994] [Interbartolo 2009] [ISAS’s New Launch Vehicle 1990] [Jackson and Johnson 1992] [Jasion 2009] [Jazra and Smart 2011] [Jensen 2000] [Jin 2025] [Jo and Yoo 2023] [Johnson 1994] [Jones and Rembert F. 1973] [Joseph et al. 2024] [Kabe 1998] [Kawabe 1999] [Kawashima et al. 2025] [Kelley 2012] [Kennedy 1970] [Kenny and Giacomoni 2016a] [Kibbey 2015] [Kim 2019] [Kim et al. 1990] [Kim et al. 2025a] [Kinnersley et al. 2003] [Klemen 2015] [Kless and Aftosmis 2011] [Ko and Cho 2016] [Kobayashi et al. 2001] [Konyukhov 2003] [Krishna et al. 2019] [Krivenko 2026] [Kryuchkov 2020b] [Kryuchkov 2020a] [Kwak and Kiris 2012] [Kynard et al. 2006] [Lai and Liu 2025] [Lancaster 1994] [Launch Vehicle Booster Avionics 2000] [Launch Vehicle Financial Analysis 2022] [Launch Vehicle Optimization Phase 1965b] [Launch Vehicle Optimization Phase 1965a] [Launch Vehicle Performance 1963] [Launch Vehicle Stress Analysis 2022] [Launch Vehicle Systems] [Lauriente and Hoegy 1991] [Laursen 1994] [Laursen and Voce 1996] [Leckie and Hayman 1976] [Levine 1964] [Lewis and Rice 1992] [Liever and Habchi 2004] [Lim et al. 2024b] [Liquid Rocket Booster LRB 1989b] [Liquid Rocket Booster LRB 1989a] [Liquid Rocket Booster LRB 1989c] [Liquid Rocket Booster LRB 1990b] [Liquid Rocket Booster LRB 1990a] [Liquid Rocket Booster Study. 1989] [Liu 2017a] [Liu et al. 2009b] [Lo et al. 2014] [Longuski and Vinh 1980] [Losik 2010a] [Lowe] [Lowrey 1962] [Madden 1970] [Maekawa 1996] [Mahon and Wild 1984] [Malik et al. 2007] [Mao et al. 2020] [Martin 2009] [Mathias et al. 2008] [McArthur 2008] [McCaskill 1970] [McCurdy and Roche 2004] [McFarland et al. 2011] [Martin Co Baltimore Md 1963] [Mescall 1963] [Miller 1963] [Minnetyan and Chamis 1999] [Mohan and Kishore 2021] [Moraes 2001] [Morovat et al. 2019] [Moseley 1962] [Moser 1965] [Motiwala et al. 2014] [Mueller 1964] [Nemeth and Starnes 1998] [Nettles 2009] [Neumaier et al. 2025] [Niederstrasser 2022] [White Sands Missile Range Nm 1997] [Nola and Blue 2008] [Novykov et al. 2015] [Oconnor 1966] [Oh et al. 2018] [Packard and Zampino] [Palmer et al. 1994] [Palmer et al. 1996] [Pan et al. 2014] [Panda et al. 2011] [Parkinson 1991] [Patel 2013] [Phillips et al. 2007] [Pope 1992] [Poth et al. 1993] [Powell and Scholl 1966] [Pritts 1974] [Qi 2017] [Qi et al. 2024] [Qiang Wu and Wei Wang 2016] [Rader and Berry 1979] [Ralph 1965] [Rasky 1998] [Reins and Alvis 1972] [Reuter et al. 2006] [Rice 1970] [Richter and Russell 2007] [Rivord and Williams 2024] [Robertson] [Rojahn and Ruf 2011] [Rothschild and Talay 2009] [Rothschild et al. 2005b] [Rothschild et al. 2005a] [Rothschild et al. 2010] [Runkel 1964] [Ryan and Verderaime 1993] [Sabaghzadeh and Khansari 2022] [Saju et al. 2025] [Safie and Maggio 2010] [Sanders 1963] [Saturn 5 Launch Vehicle 1971] [Saturn 5 Launch Vehicle 1973] [Schieb 2006] [Sekula et al. 2012] [Sellers 2011] [Shibato 1995] [Sholes et al. 1994] [Simon et al. 2006] [Singh et al. 2024c] [Siva Krishna Reddy and Shah 2021] [Skopinsky 1997] [Slotnick et al. 1994] [Smith 1966] [Snoddy et al. 2006a] [Snoddy et al. 2006b] [Solazzi and Ferreira 2026] [Sowiński and Jasion 2019] [Space Launch Vehicle Structures 2022] [Spacely’s Rockets 1991] [Spiegel and Wolf 1966] [Spiegel and Wolf 1967] [Springer 1994] [Steffens and Mavris 2015] [Steinmeyer and Frick 2015] [Sterett 1962] [Stevens et al. 1995] [Stoecker et al. 1992] [Strobl et al. 2012] [Suryanarayana and Sivaramakrishnan 2023] [Surzhikov 1999] [Szedula 1996] [Tamura et al. 2023] [Tarabini et al. 2013] [Taylor et al. 2006] [The Air-Breathing Launch Vehicle 1970] [Thorp and Kapel 2006] [Threet et al. 2011] [Titov 2017] [Tobias and Hawkins 2005] [Tong and Fen 2016] [Torisaka and Yamakawa 2008] [Trevino et al. 2015] [Vehko and Ruhland 1966] [Verhage 2007] [Verstraete and Hendrick 2003] [Villanueva 2022b] [Volpi et al. 2012] [Wah et al. 1963] [Wang and Wang 2010] [Wang et al. 2024b] [Wang et al. 2025b] [Ward 2015a] [Webb 1967] [Wente 1982] [Wickham 1964] [Williams and Cannon 2006] [Wong et al. 1982] [Woo et al. 1994] [Wu] [Wu and Le 2025] [Wunderlin et al. 2018] [Xu et al. 2020] [Yeniay et al. 2006] [Young 2025] [Yunis 2005] [Zafar and LinShu 2010] [Zakeri et al. 2017] [Zhang et al. 2018] [Zhao et al. 2003] [Zhou and Wang 2011] [Ziegler 1963]

Staging, mass fraction, cost and the launcher line

The argument the Atlas won and then lost. Staging and stage optimisation, single-stage-to-orbit studies, launch cost, expendable launcher evolution and reuse. 89 titles concern reuse and 45 single stage to orbit, which is the configuration the stage-and-a-half arrangement approached and stopped short of.

294 records. [Abdulmajeed et al. 1984] [Adkins 1970] [Aggarwal 2018] [Akhtar and He Linshu 2005] [Akhtar and Linshu 2006b] [Akhtar and Linshu 2006a] [Akhtar et al. 2008] [Allen et al. 1994] [Alvord et al. 2024] [Andrews et al. 1992] [Arockiam et al. 2012a] [Arockiam et al. 2012b] [Assessment of Candidate Expendable 1984] [Bainum and Reiss 1995] [Bainum et al. 1996] [Balesdent et al. 2010] [Balesdent et al. 2012] [Baumgartner 1997] [Bayer 2003] [Beers et al. 2013] [Bell et al. 1964] [Bentley 2009] [Berglund 2003] [Berglund and Wilkins 2003] [Berglund et al. 2005] [Bleviss 1976] [Breton et al. 2006] [Brevault et al. 2020a] [Brinton et al. 1994] [Browning 1993] [Builder 1959] [Burrows and Roth 1992] [Butrica 2003] [Buursink 1998] [Buzzatto 2006] [Calhoon 1996] [Castellini et al. 2011] [Chase 1978] [Chase 1979] [Chase 1990] [Chase 1992] [Chase and McKinney 2005] [Chen et al. 2025a] [Chiesa et al. 2005] [Christie 2026] [Coleman 2000] [Conger et al. 2002] [Cook 1995] [Cook 1996] [Crocker and Greene 2017] [Crocker et al. 2015] [Air Force Space Command Space Missile SYS CTR 2013] [Brevault et al. 2020b] [Burghes 1974] [Cusick and Kontis 2019] [Dahlem et al. 1991] [Dalle and Rogers 2015] [Dalle et al. 2016] [Daniel and Ramusat 2005] [Davis 1988] [De Luca et al. 2026] [Degelsmith et al. 1993] [Deneu and Terrenoire 1996] [Der Kiureghian 2001] [Deschamps 1985] [Dissel et al. 2005] [Donahue 2000] [Dorrington 1990] [Dorrington 1999] [Du et al. 2025] [Dumbacher and Klevatt 1994] [Dupnick et al. 1984] [Dupont et al. 2017] [Eckmann et al. 1997] [Effect of Design Parameters 2018] [Eramya et al. 2007] [Evolved Expendable Launch Vehicle 2004] [Ewig et al. 2000] [Expendable Launch Vehicles 1977] [Ferrandon 1997] [Ferrandon 1998] [Fitzsimmons 1996] [Fleming et al. 2009] [Fossum 1984] [Fox and Glass] [Freeman et al. 1995] [Freeman et al. 1996] [French 1987] [Fritz and Sackheim 1982] [Garvey et al. 2003] [Gea et al. 2000] [Geckler 1960] [Gilbert et al. 2016] [Goldsborough 2005] [Gong et al. 2022] [Goodwin and Wegner 2001] [Goyal et al. 2022] [Gray and Alexander 1965] [Gstattenbauer et al. 2006] [Guadagnini et al. 2023] [Gujral and Emdee 2016] [Gunn 1973] [Gunn 1976] [Hagopian 2002] [Hamaker 1996] [Hames 1992] [Hardy et al. 1993] [Hauer et al. 1963] [Heiser 2010] [Hellman 2006] [Herrmann and Akin 2005] [Heuston et al. 1967] [Holguin and Labbee 1988] [Hong et al. 2005] [Hosseini et al. 2011] [Hubbel 2000] [Hudson 1987] [Hudson 2005] [Hudson and Hunter 1987] [Hudson et al. 1981] [Hunt 1995] [Hutchison 2011] [Jo and Ahn 2021] [Jo and Ahn 2022] [Johnson 1990] [Keith 1995] [Kempinski and Teague 1988] [Kibbey 2019] [Kim et al. 2026b] [Knapp 1999] [Knaur 1966] [Ko et al. 2006] [Ko et al. 2007a] [Koelle 1981] [Koelle 1984] [Koelle 1986] [Koelle 1990] [Koelle 1992a] [Koelle 1992b] [Koelle 1998] [Koelle 1999] [Koelle and Voss 1964] [Koenigsmann and Shotwell 2006] [Kohani et al. 2021] [Kohrs and Petersen 1998] [Koon and Greene 2002] [Krieger 1990] [Kruse et al. 2023] [Kurian et al. 2025] [Kutter 2006] [Kuzin et al. 2009] [Lafleur et al. 2012] [Lakshminarayana and Chiarelli 2022] [Larsen 2000] [Larsen 2003] [Larsen 2005] [Latimer 2009] [Launch Vehicle Performance 2022] [Layachi et al. 2025] [Lee 1991] [Lee et al. 1997] [Lee et al. 2026b] [Letchworth 2011] [Letchworth and Letchworth 2000] [Lewak 1967] [Li et al. 2014b] [Li et al. 2016a] [Liao et al. 2023b] [Lockheed Martin Skunk Works 1999] [Logsdon and Williamson 1997] [Lohrer and Wright 2016] [Low-Cost Expendable Launch Vehicles 1992] [Low-Cost Satellites and Satellite 1990] [Marshall 1984] [Martin 1973] [Martin et al. 1991] [Martinovic and Cerro 2002] [Matlock et al. 2001] [May and Lyles 2015] [Mayhew and Norden 1995] [Maynard 1969] [McClure 1998] [McClure and Andrews 1998] [Merrifield 1972] [Meyerson 1998] [Mihara 1988] [Milliken 1963] [Molina et al. 2009] [Molinari et al. 2024] [Monk et al. 2012] [Motes 2016] [Naftel et al. 1986] [Nair and Kukreja 2025] [Najam 2014] [Nath De 2012] [Nettles and Jackson 2009] [Noneman 2002] [Obermann and Williamson 1998] [Olds 1988] [Olds and Bellini 1998] [Olds and Lee 1996] [Venkataramana et al. 2023] [Palen 1994] [Pamadi et al. 2004b] [Pamadi et al. 2006] [Park et al. 1995] [Parkyn 1958] [Pempie 2003] [Peters et al. 2006] [Plaisted and Leonessa 2008] [Portz 2004] [Puening 1990] [Qazi and Linshu 2006] [Qu et al. 2004] [Ragab and Cheatwood 2015] [Ragsac and Patterson 1961] [Rasky et al. 2006] [Reed et al. 2016] [Reusable Launch Vehicle 1995] [Reusable Launch Vehicle Development 1995] [Roberts et al. 2002] [Robinson et al. 2003] [Rohrschneider and Olds 2001] [Romano et al. 2024] [Rooney 2003] [Ross 1969] [Rutledge 1993] [Sackheim and Gavitt 1999] [Sarzi-Amade et al. 2016] [Scarborough 1964] [Scherer 1986] [Schurmann 1957] [Schutte and Thoreau 2016] [Seo and Kim 2026] [Sgarlata and Weegar 1992] [Shirasu et al. 1996] [Shulga and Shcheglov 2021] [Siebenhaar et al. 1994] [Silberman 1983] [Single Stage to Orbit 1994] [Sloan 1995] [Smith 1984] [Smith 2011] [Spencer 1999] [Sponable 1995] [Staniszewski 2001] [Stanley and Powell 1990] [Stanley et al. 1991] [Star-Raker 1979] [Stephan and Schneider 1991] [Stockinger et al. 2005] [Szatkowski and Levin 1991] [Szatkowski and Schultz 1988] [Tartabini et al. 2000] [Tharratt 1975] [Thomas et al. 2002] [Thorpe 1991a] [Toten et al. 1991] [Trefny 1999] [Trevino et al. 2016] [Trifa et al. 2023] [U.S. Access to Space 1990] [Urie and Elvin 1995] [Urschel and Cox 2003] [Usmonov and Kretov 2020] [Verstraete et al. 2009] [Walker 2025] [Walter 2018] [Walter 2024] [Wangu and Mouyos 1998] [Waters 2013] [Watson et al. 2014] [Wells et al. 1999] [Wertheimer 1957] [Whitehead 1990] [Whitehead 2000] [Wilhite 1982] [Wilhite 1983] [Wilhite and Fischer 2009] [Wilhite et al. 1991] [Wilken 2024] [Williams et al. 2015] [Wolf 2000] [Wu and Zhang 2023] [Xu et al. 2025d] [Yang 2020] [Yarymovych and Mark 2003] [Yarymovych and Mark 2006] [Yunis and Ludwiczak 2007] [Zeeshan et al. 2021] [Zhang et al. 2016a] [Zhou et al. 2015] [Zipay 2004] [Zubrin and Clapp 1996]

The ballistic missile programmes and their history

The weapon class the Atlas founded. The Titan, Thor, Minuteman, Peacekeeper and fleet ballistic missile programmes, their basing, inertial guidance and range work, and the histories of the missile gap and the strategic missile build-up. 39 titles name the Minuteman and 31 the Titan, against 2 for the Thor, and the cluster’s median publication year is 1987.

258 records. [Aerojet-General Corp Sacramento Ca 1966] [Alexander 2024] [Alexander et al. 1993] [Allen 1955] [Allen 1957] [Allen and Eggers 1958] [Aloise and Snarr 1993] [Alonis 1988] [Altfeld 1989] [Anderl 1985] [Anderson 1976] [Andre and Czaja 1982] [Andre and Czaja 1983] [Application of Conversion ICBM 2004] [Arthur and Kemp 2025] [Atkinson et al. 2007] [Bacon 1985] [Baetz 1974] [Ball 1980] [Ballistic Missile and Space 1960] [Ballistic Missile Flight Testing 1981] [Ballistic Missile Fundamentals 2006] [Barkley and Hietzke 1982] [Bartone et al. 2001] [Bartone et al. 2002] [Bauer and Flint 2013] [Becka et al. 2008] [Bellero 1963] [Benedict 2015] [Bennett 1976] [Blanco 2020] [Bolt 1981] [Botterill 1961] [Bowman and Savin 1959] [Boyd 1963] [Bracha 1961] [Brooks 1961] [Brower 2004] [Brower 2006] [Burnett 1975] [Bużantowicz 2015] [Ballistic Missile Office Norton AFB CA 1986] [Aerojet Strategic Propulsion Co Sacramento Ca 1987] [Cahill 1976] [Callaghan 1958] [Cantrell and Gibson 1973] [Chambers and Preusser 1962] [Chianese 1965] [Coffee and Maganty 1996] [Collins and Miller 1962] [Compilation of Shock Vibration 1965] [7 Completing the Kennedy-McNamara 1980] [Completing the Kennedy-McNamara Strategic 2024] [Cong-cong et al. 2017] [Cooper 1961] [Cooper and Smith 1993] [Covington 1966] [Cuk 2008] [Daniels et al. 1975b] [Daniels et al. 1975a] [Day 1980] [Bureau of Naval Weapons Washington DC 1962] [Bureau of Naval Weapons Washington DC 1963] [Defense Science Board Washington Dc 1986] [Small ICBM Area Narrowing 1986d] [Executive Progress Report 1986] [Small ICBM Area Narrowing 1986b] [Small ICBM Area Narrowing 1986c] [Small ICBM Area Narrowing 1986a] [Defense Budgets 2019] [Deutch 1989] [Diamant 1965] [Divakaruni et al. 2008] [Dougald 1963] [Douglass 2014] [Dunn 1997] [Edenburn and Trost 2000] [Eggers 1958] [Ehrsam et al. 1978] [Eisenhower and the Missile 2019] [Enscore and Stupich 2016] [Enscore et al. 2008] [Escobal 1964] [Esther et al. 2012] [Esther et al. 2013] [Evolution of the Minuteman 2021] [Fall et al. 2008] [Fatal Accidents 2002] [Ficarrotta 2001] [First Rocket Launch 2008] [Air Force Armament Lab Eglin AFB FL 1988] [Ford 1983] [Franklin and Kunz 1973] [French 1991] [Friedman and Reed 1964] [Gadalla et al. 1993] [Garcia et al. 2025] [Garland and Hall 1958] [Gearhart 1962] [Gielda et al. 1991] [Gillespie 1956] [Goldberg 1967] [Goswami 2026b] [Goswami 2026a] [Graham 1958] [Guo et al. 2018] [Hamaker 1960] [Hanson 1963] [Hanson and Stapyer 1963] [Harvey et al. 1989] [Hendershot 1971] [Heterogeneous Engineering 1994] [Hicks 1987] [Hobson 1991] [Hough 1982] [Hunley 2008i] [Hunley 2008g] [Hunley 2008h] [ICBM Deep Basing Construction 1987] [Imoto 2016] [Inglis 1964] [Jianbin et al. 2005] [Johnson 1973] [Kaplan et al. 1962] [Kashiwagi 1968] [Kelly 1959] [Kleinhesselink 1963] [Korolev and the First] [Kościelniak 2015] [Kumpel et al. 2002] [Land-Mobile ICBM 1983] [Laqueur 2017] [Larsen and Larsen 1997] [Larson 1965] [Ledbetter 1960] [Leger 1975] [Lenihan 1962b] [Lenihan 1962a] [Levin 1963] [Li et al. 2022d] [Liang and Kleinbub 1973] [Liberto 1961] [Lin 2003] [Lindsay and Fikes 1976] [Lum and Lyons 1966] [MacPherson 1963] [Maitra 2000] [Makar 1962] [Manning the Titan II 2002] [Matticks 1974] [Matzko 2000] [McKinley 1975] [Metcalf 1976] [Minyaev 2024] [Missile Gap 2025] [Modernizing the U.S. Nuclear 2022] [Murphy et al. 2000] [Nettle 1958] [Newgent 1966] [Nielsen 1955] [Nielsen 1966] [Hercules Powder Co Kenvil Nj 1963] [Norris and Kristensen 2009] [O’Rourke 2010] [Oh and Kang 2022] [Ohman 1967] [Optimal Replacement Policies 1962] [Ostner 1962] [Pelensky 1976] [Pettyjohn 2006] [Plymale 1974] [Poehler 1961] [Randorf 2000] [Rauch 1957] [Raymond and Kendall 2019] [Reams et al. 1983] [Redman and Pasiuk 1957] [5 Revising the Eisenhower 1980] [Revising the Eisenhower Strategic 2024] [Rhee et al. 2013] [Rockefeller and Alfred 1960] [Roman 2019] [Rong et al. 2016] [Rounds and Marmar 1983] [Russell 1964] [Sagdeev et al. 2002] [Schaff et al. 2000] [Schoneman et al. 2000] [Schoneman et al. 2003] [Schriever 1960] [Schuiling and O’Connor 1998] [Schwartz 1987] [Selected Ballistic Missile Programs 2008] [Semiconductor Device Reliability Evaluation 1967] [Shafer and Brock 2012] [Shafer and Brock 2013] [Sladen 1963] [Slifka 1960] [Slivinsky et al. 2002] [Soviet Ballistic Missile Ground 1964] [Stodghill et al. 1999] [Strategic Force Planning during 2019] [Strickler 1981] [Stubbs et al. 1997] [Stumpf 2002] [Tao et al. 2001] [Tedrick 1962] [The Air Force 2021] [The Air Force Approach 1963] [The Air Force Strategic 2002] [The Ballistic Missile Context 2008] [The End 2002] [The Fiscal Year 1963 1980] [The Future of US 1986] [4 the Kennedy Administration 1980] [The Kennedy Administration 2024] [The Titan II 2022] [The US Fleet Ballistic 1994] [Thermonuclear and Ballistic Missile 2013] [Thompson 1980] [Titan II in Context 2002] [Titan II Launch Complex 2002] [Titan II Operational Flight 2002] [Titan II Research 2002] [Валентинович 2024] [Topping 1981] [Triwush 1959] [Troutman and Isakowitz 1987] [Truncale 1991] [Tsutsumi et al. 2012] [Tsutsumi et al. 2014] [Ulsperger 2022] [Villanueva and Abbas 2015] [Boeing Co Seattle Wa 1943] [Boeing Co Seattle Wa 1963] [General Dynamics Corp Pomona Ca Pomona Div 1963] [Hall 2019] [Philippe and Stepanov 2023] [Walsh and Wartburg 1978] [Warmbrod 1963] [Wayte and Gruenich 1972] [Weiss 1966] [Wheelon 1959] [Whitcombe 1961a] [Whitehead 1992] [Williamson 2016] [Wong and Cho 1985] [Woodbury and Gorman 1983] [Wu et al. 2015a] [Xie et al. 2015] [Yang et al. 2011] [Yau et al. 1995] [Zaloga 1990] [Zhang et al. 2014] [Zheng et al. 2020b] [Zhou et al. 2018] [Zhou et al. 2020] [Zimmerman 1988]

Ground winds, buffet and ascent aerodynamic loads

The load cases of the vehicle on the pad and in the first two minutes. Ground-wind loads, transonic buffet, gusts, load relief and stage-separation aerodynamics. 33 titles name ground winds and 20 load relief or load alleviation.

273 records. [Adelfang 2003] [Adelfang 2004] [Adelfang et al. 1993] [Adelfang et al. 1994] [Albertson et al. 2012] [Allen 1966] [Alter et al. 2015] [Applebaum et al. 2011] [Applebaum et al. 2012] [Appleby et al. 1966] [Armand] [Atesmen 2023] [Azevedo 1987] [Azodi et al. 2022] [Bakeman 1962] [Baran et al. 2013] [Barbera 1980] [Barbre et al. 2019] [Bartels et al. 2010] [Bartels et al. 2012] [Beer and Lennox 1965] [Bettis and Hosder 2010] [Bidwell 1967] [Binion 1964] [Binion and Herron 1962] [Blanchet and Bartos 2001] [Blanchet et al. 2001] [Blelloch and Coe 2000] [Blelloch et al. 1999] [Bodle and Hackley 1975] [Boelitz et al. 2003] [Boggs 2004] [Bohne 1964] [Bordelon et al. 2003] [Brown 2022a] [Buell 1964b] [Buell 1964a] [Buell 1966] [Bushnell 1989] [Butler et al. 1992] [Camarda et al. 2011] [Cappellucci and Schinnerer 1986] [Capri et al. 2006] [Cavallini et al. 2016] [Chapter 12 2013] [Chapter 13 2013] [Chinnathambi et al. 2025] [Christensen and Brunty 1996] [Chudej 1996] [Chung and Peebles 2004] [Coe and Brownson 1981] [Coffin 1970] [Cole and Henning 1991] [Cole and Henning 1992] [Collins et al] [Collins et al. 2023] [Colonno and Alonso 2008] [McCullough and Steinmetz 1965] [D’Antuono et al. 2024] [Dabas et al. 2025] [Della Monica and Bernardini 2024] [Demory et al. 2011] [Deng et al. 2027] [Dhuyvetter and Lam 1989] [Doggett and Hanson 1962] [Doggett and Hanson 1963] [Dotson 2001] [Dotson and Tiwari 1996] [Dwivedi and Bhargava 2018] [Григорьев and Гончаров 2024] [Dąbrowski and Dąbrowski 2019] [Eliseev et al. 2014] [Erickson 2010] [Erickson and Deloach 2008] [Ericsson and Pavish 1999] [Ericsson and Pavish 2000] [Ericsson et al. 1973] [Eshete et al. 2024] [Estimating the Mass 2015] [Eyi and Yumusak 2013] [Farmer and Jones 1966] [Ferragut 1976] [Fong et al. 1970] [Foughner et al. 1971] [Fujino et al. 2008] [Gaglio et al. 2026] [Garbeff et al. 2019] [Goyal et al] [Graham and Luz 1998] [Greene et al. 1990] [Griffin et al. 1999] [Griffin et al. 2000a] [Hamilton et al. 1983] [Hanson and Jones 1963] [He et al. 2024b] [Heaney et al. 2021] [Hegedus and Mendenhall 2003] [Hetcher 1966] [Holland and Shaw] [Hough 1980] [Hrinda 2009] [Huang et al. 2025b] [Huebner et al. 2006] [Ivanco 2016] [Ivanco and Keller 2012] [Ivanco and Keller 2014] [Ivanco et al] [Ivanco et al. 2020] [Ivanco et al. 2021] [Ivanco et al. 2024] [Iyer 2026] [Jayan et al. 2024] [Jayanthi and Jain 2019] [Jee et al. 2016] [Jeon et al. 2012] [Jeyakumar et al. 2005] [Jia et al. 2020] [Johnson and Braddock 1974] [Johnson and Vaughan 2020] [Johnson et al. 2005a] [Johnson et al. 2006a] [Jones and Farmer 1966] [Jones and Farmer 1967] [Kabe 2000] [Keller and Ivanco 2010] [Khil’chevskii and Kadyshev 1973] [Klenk 1964] [Ko et al. 2019] [Kondratiev 2019] [Kryvoruka and Ashurst 1973] [Kumar et al. 1994] [Kumar et al. 1995] [Kumar et al. 1998] [Kumar et al. 2023] [Kurudimath et al. 2026] [Lee et al] [Lee et al. 2024a] [Lei et al. 2014] [Lei et al. 2026] [Leopardi et al. 2025] [Lester and Morgan 1964] [Lester and Morgan 1965] [Lester and Tolefson 1964] [Liao et al. 2023a] [Liu 2012] [Macheske et al. 1993] [Malmuth and Fedorov 2008] [Malmuth et al. 2005] [Mancini et al. 2025] [Marcum et al. 1965] [Martin et al. 1993] [Massey and Chwalowski 2010] [Mayers et al. 2009] [Meadows 1963] [Meckler 1965] [Mehta 2015] [Mehta 2016] [Moody et al. 1982] [Mooij 2020] [Morgan and Collins 1962] [Morgan and Collins 1963] [Murashkin et al. 2020] [Murphy and Rubesin 1965] [Meeting on Ground Wind 1966] [Mehta 2022] [Naftel and Powell 1990] [Nallasamy et al. 2008] [Nandakumar et al. 2019a] [Nandakumar et al. 2019b] [Neice 1954] [Nelson et al. 2005] [Nix 1959] [Ogasawara and Nishioka 2001] [Oh et al. 2017] [Ohshima and Sugiyama 2002] [Omar and Bevilacqua 2017] [Orr 2010] [Orr and Russell] [Orr and Russell 2024] [Pamadi et al. 2004a] [Pamadi et al. 2005] [Pamadi et al. 2007] [Pamadi et al. 2009] [Park 1998] [Piatak and Sekula 2019] [Piatak et al. 2010] [Piatak et al. 2012] [Piatak et al. 2015] [Piatak et al. 2016] [Pinier] [Pinier 2011] [Pinier 2024] [Pinier et al. 2015] [Prabhakar and Quinn 1994] [Prelaunch Ground Wind Loads 1965] [Qaumi 2021] [Ragab 1992] [Rainey 1964] [Rajarajan et al. 2026] [Reed 1970] [Reisenthel et al. 2007] [Roberts et al. 2009] [Rogers et al. 2015] [Roozeboom et al] [Roshanian and Talebi 2008] [Sai Naga Bharghava et al. 2024] [Sanford et al. 2003] [Schindel et al. 1966] [Schwarz 2010] [Sekula et al. 2016] [Sellers et al. 2017] [Seywald and Bless 1993] [Shaw-Lecerf et al] [Shi 2005] [Shiihara et al. 2018] [Shivananda et al. 2001] [Simon 1965] [Simons 1975] [Sinclair and Flowers 2010] [Singaravelu et al. 2009] [Snodgrass 1955] [Solanyk 1993] [Song et al. 2020] [Song et al. 2022] [Song et al. 2026b] [Soranna et al. 2023] [Spearman 1984] [Spiekermann and Kabe 1998] [Springer 1996] [Springer and Pokora 1994b] [Springer and Pokora 1994a] [Srivastava et al. 2010] [Stepp 2024a] [Stetson and Lewis 1977] [Stouffer] [Sun 2020b] [Sun 2020a] [Sun et al. 2023a] [Suttles 1964] [Suzuki 2004] [Tan et al. 2024] [Tashakkor et al. 2011] [Tewell and Buell 1985] [Tong 1991] [Toniolo et al. 2008] [Trout et al. 2009] [Vieweg 1972] [Vîlceanu et al. 2024] [Walterscheid and Sako 2011] [Wang 2004b] [Wang 2004a] [Wang and Chen 2022] [Wang and Ting 1961] [Wang and Wang 1997] [Wang et al. 2014a] [Wang et al. 2018e] [Wang et al. 2024a] [Wang et al. 2026f] [Wang et al. 2026c] [Wehmueller and Hauser 1991] [Weilmuenster et al. 1995] [Wignall et al] [Wignall et al. 2023] [Williamson 1978] [Winchell 1992] [Winnick 1996] [Yan et al. 2025a] [Yang et al. 2015a] [Young and Rankin 1996] [Zhang 1992] [Zhang et al. 2023c] [Zhang et al. 2024a] [Zhou et al. 2025b]

Propellant slosh

The free surface the balloon tank cannot break up. Lateral and longitudinal slosh, equivalent mechanical models, low-gravity behaviour and baffle design. 105 of its 279 records name a baffle and 87 name a propellant, launch vehicle, rocket or spacecraft, and the median publication year of 2017 is the most recent of any cluster, so the baffle is still the answer being refined.

279 records. [Abdollahzadeh Jamalabadi 2019] [Abramson 1965] [Abramson and Silverman 1966] [Abramson et al. 1961] [Abramson et al. 1962a] [Abramson et al. 1962b] [Abramson et al. 1963] [Abramson et al. 1966] [Adler et al. 1991] [Agui and Moder 2015] [Aguiar et al. 2025] [Ahizi et al. 2025] [Akyıldız et al. 2013] [Al-Yacouby and Ahmed 2022] [An Equivalent Propellant Sloshing 2018] [Anderson] [Arasan and Tiwari 2026] [Atthariq et al. 2021] [aus der Wiesche 2008] [Baghel and Shinde 2017] [Basurto et al. 1966] [Bauer 1963b] [Bauer 1963a] [Bauer 1963c] [Bauer 1963d] [Bauer 1964a] [Bauer 1966] [Bauer 1967] [Beckman et al. 2018] [Benmasaoud et al. 2025] [Benson and Mason 2011] [Bhandiwad and Dodamani 2025] [Bhandiwad and Dodamani 2026] [Bhandiwad et al. 2023] [Bhuta and Koval 1963] [Bhuta and Koval 1964] [Biswal and Bhattacharyya 2010] [Borg 2019] [Brodnick et al. 2015] [Brodnick et al. 2016] [Buchanan 1965] [Buchanan and Shih 1971] [Bynum and Hamlet 1965] [Cao et al. 2023] [Caron et al. 2018] [Celebi and Akyildiz 2002] [CFD Analysis of Sloshing 2017] [Chandler and Fontenot 1970] [Chandler and Lomen 1970] [Chang et al. 2025] [Chen et al. 2026] [Chintalapati and Kirk 2008] [Chintalapati et al. 2010] [Cho 2018] [Cho 2021] [Cho and Han 2025] [Cho and Kim 2016] [Choudhary et al. 2021] [Choudhury et al. 2026] [Christensen et al. 1997] [Chu 1962] [Chu 1969] [Cimini et al. 2023] [Clark and Fontenot 1966] [Cole 1966] [Cossette et al. 2020] [Demir et al. 2021] [Demirel and Aral 2018] [Dennehy et al. 2022] [Dodge 1970] [Dodge 1971] [Dodge and Garza 1969b] [Dodge and Garza 1969a] [Dodge and Garza 1970] [Dong et al. 2025] [Duan et al. 2021] [Dynamics of Liquid Sloshing 2005] [Eggleston 1968] [Eulitz 1964] [Evensen and Raney 1969] [Experimental Results of Hydrogen 1994] [Feng and Grady 1969] [Feng et al. 2010a] [Feng et al. 2020] [Feng et al. 2025] [Fleischer and McGlinchey 1971] [Fogel et al. 2023] [Freeman 2024] [Furuichi and Tagawa 2020] [Garza 1966] [Gavrilyuk et al. 2000] [George and Cho 2020] [Gnitko et al. 2017] [Golla and Venkatesham 2021] [González et al. 2026] [Gradinscak and Jafar 2013] [Green et al. 2007] [Green et al. 2010] [Guo et al. 2024] [Gurusamy and Kumar 2021] [Han et al. 2021] [Hari and Sarigul-Klijn 2019] [Hasheminejad et al. 2014] [Hastings and Toole 1968] [Hauser et al] [He et al. 2007] [He et al. 2025] [He et al. 2026a] [Himeno 2003] [Himeno et al. 2003] [Himeno et al. 2005] [Hoffman et al] [Hopfinger and Baumbach 2009] [Huang 2023] [Hurwitz and Melcher 1968] [Hwang 1965] [Ikeda and Ibrahim 2005] [Ikeda and Murakami 1999] [Iranmanesh and Nikbakhti 2021] [Jamalabadi et al. 2018] [Jeon et al. 2024] [Jeong and Kim 2021] [Jiang and Le 2026] [Jin et al. 2022] [Joseph et al. 2025] [Joshi et al. 2017] [Jäger 2019b] [Jäger 2019a] [Kannapel et al. 1987a] [Kannapel et al. 1987b] [Ketchum 1970] [Kim 2011] [Kim and Kim 2023] [Kim and Park 2026] [Kim and West 2011] [Kingsley and Craig 2004] [Korkmaz 2022] [Kotrasová 2014] [Kotrasová and Kormaníková 2014] [Kovalev and Chenyu 2024] [Lance 1966] [Langner 1963] [Lestingi and Zavesky 1978] [Liao et al. 2025] [Lin and Song 2019] [Liu and Li 2018] [Liu and Lin 2009] [Liu and Lu 2023] [Liu and Zhang 2016] [Liu et al. 2017a] [Liu et al. 2019a] [Liu et al. 2019b] [Liu et al. 2025a] [Liu et al. 2026a] [Lomen 1964] [Lomen 1965b] [Lomen 1965a] [Lu and Cao 2025b] [Lu and Cao 2025a] [Lu and Cao 2026] [Lu et al. 2015] [Lu et al. 2024a] [Lu et al. 2024b] [Lukovsky et al. 2012] [Luo 2026] [Lv et al. 2024] [Ma et al. 2023c] [Ma et al. 2026a] [Majumdar et al. 2026] [Marques et al. 2025] [Marsell et al. 2009] [Michihara et al. 2018] [Miles 1958] [Momin et al. 2024] [Mooij and Gransden 2019] [Mooij and Wang 2021] [Mooij and Wang 2023] [Navickas and Cheng 1990] [Neer and Salvatore 1972] [Ng and Benson 2017] [Noui et al. 2024] [Novel Design 2023] [Oliveira da Mata et al. 2019] [Orr] [Orr et al. 2015] [Pan et al. 2026a] [Paprota 2023] [Park et al. 2024] [Park et al. 2025] [Pei 2021] [Pei and Rothhaar 2015] [Perez et al. 2012] [Poguluri and Cho 2023] [Pramod et al. 2025] [Qin et al. 2019] [Qu et al. 2023] [Ren and Zhong 2024] [Ren et al. 2023] [Roithmayr and Pei 2024] [Ross and Womack 1973] [Rubio Hervas and Reyhanoglu 2012] [Rubio Hervas and Reyhanoglu 2014] [Bhandiwad 2022] [Sances et al. 2010] [Saugen and Adler 1991] [Scholl et al. 1971] [Schwind et al. 1964] [Schwind et al. 1966] [Schwind et al. 1967] [Shamsoddini and Abolpur 2019] [Shao et al. 2015] [Shi 1987] [Silveri and Romero-Calvo 2026] [Silverman and Abramson 1966] [Singh et al. 2022b] [Bahaoui et al. 2020] [Solodun 2025] [Solomon and Tamiru 2026] [Stephens 1965] [Storey et al. 2015] [Strahan and Hernandez 2011] [Sumner 1964] [Sumner 1965] [Sun et al. 2020b] [Sun et al. 2021] [Suzuki 2001] [Sávio Aguiar et al. 2022] [Takahara and Kimura 2012] [Tang 1995] [Tang and Chang 1993] [Tang et al. 2013] [Tegart et al. 1981] [Thirunavukkarasu and Rajagopal 2021] [Tiwari et al. 2021] [Trimulyono et al. 2022] [Tsao and Kinnas 2021] [Van Zwieten et al. 2020] [Wang et al. 2012b] [Wang et al. 2013e] [Wang et al. 2016b] [Wang et al. 2016a] [Wang et al. 2016c] [Wang et al. 2017c] [Wang et al. 2018d] [Wang et al. 2019f] [Wang et al. 2019b] [Wang et al. 2022d] [Wang et al. 2025d] [Wang et al. 2026e] [Wang et al. 2026a] [Warner and Caldwell 1961] [Wei and Zhang 2020] [Westra et al] [Wilner et al. 1960] [Wohlen et al. 1975] [Xu and Xu 2024] [Xue et al. 2012] [Xue et al. 2025] [Xue et al. 2026a] [Yan and Yu 2011] [Yang 2012] [Yang and Peugeot 2010] [Yang and Peugeot 2011] [Yang and Williams] [Yang and Williams 2024] [Yu et al. 2007] [Yu et al. 2020a] [Yu et al. 2020b] [Yu et al. 2026d] [Yue et al. 1996] [Zang et al. 2019b] [Zang et al. 2019a] [Zhang et al. 2024e] [Zhang et al. 2026b] [Zhang et al. 2026a] [Zhao et al. 2024c] [Zhao et al. 2026a] [Zhou et al. 2023] [Zhu and Liu 2026]

Structural dynamics, modal test and monitoring of launch structures

How a launch structure’s modes are predicted and believed. Bending and torsional dynamics, modal survey and test correlation, coupled loads and structural health monitoring. 79 titles name a mode or modal analysis.

245 records. [Acharya and Sing 2000] [Achenbach 1965] [Addona et al] [Alden and Habert 1964] [Alleaume and Frondeville 1995] [Ansari and Bajodah 2015] [Ansari and Bajodah 2016] [Ansari and Bajodah 2018] [Arimoto et al. 2011] [Audric et al. 2023] [Avio S.p.a. et al. 2023] [Bakhtin and Titov 2018] [Barret 1998] [Bartels 2012] [Beer and Lennox 1966] [Belousov and Ponomarev 2016] [Biju Prasad et al. 2020] [Yang et al. 2020b] [Yang et al. 2020c] [Yang et al. 2020a] [Biswas 1986] [Boglis and Stoica 2020] [Borisov 2025] [Briese et al. 2020] [Brown 2022b] [Buchanan and Bugg 1966] [Buehrle et al. 2010] [Buehrle et al. 2011] [Buehrle et al. 2025] [Burton et al. 2008] [Sandeep et al. 2026] [Cai et al. 2024] [Carey 1967] [Carey 1968] [Chehrzad and Khoramishad 2026] [Chen et al. 2020a] [Cheng 1956] [Cheng and Widera 2009a] [Childs 1974] [Chu and Xu 2014] [Coakley] [Cockburn and Robertson 1974] [Cole et al. 2000] [Colicci et al. 2025] [Colwell 1968] [Crocco 1951] [Crocco 1952] [Crocco and Cheng 1953] [Crosswy and Kalb 1967] [Dalle et al. 2024] [Darmayuda and Subchan 2026] [DeBonis et al. 1999] [Diz et al. 2026] [Dodge and Garza 1971] [Dolgih 2025] [Doman and Blake 2006] [Dotson and Engblom 2002] [Dotson and Engblom 2004] [Dotson et al. 1998] [Du] [Du et al. 2008a] [Du et al. 2008b] [Dubois and Habiballah 1991] [Engels et al. 1982] [Engels et al. 1983] [Serhat Erdogan and Tekin 2025] [Fernando and Charalambous 2026] [Fisher 1976] [Foster 1989] [Gajera 2026] [Garba et al. 1968] [Gerald and Runyan 1962] [Giannone and Sambasivam 2024] [Gilligan et al. 2014] [Glaser 1988] [Glatt 1961] [Goble 1970] [Gore and Carroll 1957] [Greensite 1967] [Guo et al. 2017] [Habiballah et al. 1992] [Hanson et al. 2011] [Herzog et al. 1998] [Hidalgo 2000] [Horing et al. 2025] [Hu 2012] [Huang et al. 2000a] [Hung and Hunt 1964a] [Hussein and de Weck 2025] [Irvine 2003] [Ivanov 2021] [Ivanov 2022] [Jeng and Litchford 1991] [Jeon et al. 2013] [Jiang et al. 2026a] [Johnson et al. 2006b] [Johnson et al. 2007] [Joshi 1997] [Juarez 1961] [Kamenskii and Martirosov 2021] [Kanda 2019] [Kanda et al. 2021] [Kanda et al. 2023] [Kashkovsky 2014] [Kawano et al. 2023] [Kilpatrick 1965] [Kim et al. 1992] [Kolesnikov and Zubov 2026] [Konyukhov 2015] [Larson et al. 1974] [Launch vehicle dynamics] [Launch Vehicle Dynamics Demonstrator 1963] [Launch Vehicle Stability 2022] [Leadbetter and Raney 1965] [Leadbetter and Raney 1966] [Lee-Glauser and Ahmadi 1993] [Levine 1965] [Li et al. 2022c] [Liechty 2008] [Lin et al. 1993] [Lin et al. 2003] [Liu et al. 2009a] [Liu et al. 2016b] [Loewy 1965] [Low Frequency Oscillations 2008] [Lubowe 1965] [Ma et al. 2025] [Machado 2018] [Macpherson 1962] [Makhtoumi 2018] [Martin et al. 2024] [Mayo and Nolan 1967] [McCormack 1964] [Miao et al. 2022] [Miller et al. 2015] [Mishina et al. 2020] [Mixson et al. 1964] [Mo et al. 2022] [Morgado et al. 2022a] [Morino et al. 1987] [Mowers 1967] [Murty et al. 2015] [Murugesan et al. 2018a] [Neighbors and Ryan 1992] [Neiman and Rezakova 1975] [Newman 1969] [Ngo et al. 2017] [Niu et al. 2022] [Nosek 1982] [Nowak 1967] [Ohayon and Morand 1995] [Olberding 1984] [Orr et al] [Osterholt and Linehan 2025] [Otsu et al. 2005] [Otsu et al. 2010] [Otsu et al. 2012] [Owens and Aubuchon 2011] [Pamadi et al. 2016] [Pan et al. 2010] [Panda et al. 2026] [Patha et al. 1972] [Paulson et al. 2020] [Paxson et al. 2022] [Pengelley 1968] [Pierce et al. 1965] [Prasad 2022] [Rainey and Runyan 1961] [Reardon et al. 1964] [Reda et al. 2004] [Review of Dynamical Analysis 2026] [Robust Super-Twisting Sliding-Mode Controller 2025] [Rocha et al. 2023] [Rogers and Dragone 1996] [Jeon 2008] [Rubin et al. 1988] [Runyan 1965a] [Runyan 1965b] [Vinoj et al. 2022] [Sahu et al. 2024] [Sargent 1970] [Schmidt and Mann 1996] [Schreiner and Roth 1992] [Seshime et al. 2026] [Sharma et al. 2024] [Shtessel 1998] [Shtessel 1999] [Shtessel and Baev 2008] [Shtessel and Krupp] [Shtessel and Krupp 1997] [Shtessel et al. 1997] [Shtessel et al. 2000] [Shtessel et al. 2002] [Sills et al] [Singh et al. 2026] [Skarman 1978] [Snyder et al. 1974] [Somanath et al. 1999] [Song et al. 2026a] [Stott and Shtessel 2010] [Study of Structural Bending 1966] [Sun 2010] [Sun et al. 2026] [Surender et al. 2021] [Tamura et al. 2024] [Tang et al. 2026] [Templeton et al. 2010] [Templeton et al. 2011] [Templeton et al. 2025] [Thermodynamic Power Cycles 2004] [Torisaka and Yamakawa 2011] [Tournes et al. 1998] [Trushlyakov et al. 2018] [Tsushima et al. 2017] [Umeoka et al. 2021] [Valenti 1992] [Venkateswaran et al. 1991] [Vibration of a Reentry 1975] [Viviani and Pezzella 2007] [Wan et al. 2020] [Wan et al. 2021] [Wan et al. 2026] [Wang et al. 2000] [Watts 2005] [Welsh 1985] [White et al] [Wiksten 1966] [Wilke et al. 2000] [Wood 1961] [Wuilbercq et al. 2012] [Xiong et al. 2020a] [Xue et al. 2026b] [Yamanishi et al. 2004] [Yang 2004] [Yang and Chen 2025] [Yang et al. 2015b] [Yuhui and Zhenguo 2002] [Zhan et al. 2024] [Zhang 1984] [Zhang and He 2024] [Zhang et al. 2020d] [Zhang et al. 2024c] [Zhou et al. 2024b] [Zirui Wang et al. 2012] [Zoladz et al. 2011]

The Atlas, its derivatives and its programme record

The vehicle’s own record, and most of it is the launcher the missile became. Flight test working group reports, engine and component test programmes, the Atlas-Agena and Atlas-Centaur flight evaluations, the Mercury boosters and the later Atlas variants. 128 of its 217 records name the Centaur and 133 are report primaries, and its median publication year is 1969. Of the 5,685 titles in the whole survey, 0 name the X-11 or an Atlas A missile, which is the designation question taken up below, stated as a count.

217 records. [Agena Vehicle System Performance 1969] [All Shuttle Centaur Engine 1987] [Allwein et al. 2009] [Alper et al. 1968] [Anderson et al. 1965] [Arnett 1993] [Atlas Agena-18 Lunar Orbiter 1966] [Atlas Agena-25 Applications Technology 1967] [Atlas-Agena Flight Performance 1969a] [Atlas-Agena Flight Performance 1969b] [Atlas-Agena Performance 1969] [Atlas-Centaur AC-16 Flight Performance 1970] [Atlas-Centaur AC-17 Performance 1972] [Atlas-Centaur AC-18 Performance Evaluation 1971] [Atlas-Centaur AC-19 and AC-20 1971] [Atlas-Centaur Flight Performance 1968a] [Atlas-Centaur Flight Performance 1968b] [ATLAS/AGENA-24. Lunar Orbiter-5. Flash 1967] [Atlas/Agena-26 Orbiting Geophysical Observatory-5 1968] [Atlas/Centaur Launch-on-Time Study Final 1965] [Atlas/Centaur Pioneer G Operations 1973] [Atlas/Centaur-29 Intelsat IV F5 1972] [Austad 2001] [Baddour and Quitter 1968] [Barrett 1969b] [Barrett 1969a] [Batten 1965] [Baumeister 2014] [Baumeister 2015] [Bell 1982] [Berman 1966] [Berns and Lacovic 1968] [Black et al. 2025] [Blatt and Aydelott 1975] [Blatt and Walter 1975] [Blatt et al. 1976] [Bowine 1965] [Bowlin 2001] [Boynton 1967] [Boynton 1968] [Brusch 1976] [Brusch 1977] [General Dynamics/Astronautics San Diego Ca 1961] [General Dynamics/Astronautics San Diego Ca 1961] [Acoustica Associates INC LOS Angeles CA 1961] [Berns et al. 1968] [General Dynamics/Astronautics San Diego Ca 1962] [Rocketdyne Canoga Park Ca 1963b] [Rocketdyne Canoga Park Ca 1963a] [Rocketdyne Canoga Park Ca 1963c] [General Dynamics Corp San Diego Ca 1992] [Campbell 1961a] [Campbell 1961b] [Catlin 1964] [Centaur Space Vehicle Pressurized 1972] [Centaur Tank Corrosion Tests 1965] [Centaur Upper Stage 1989] [Chacon 1966] [Chen et al. 1986] [Chen et al. 1987] [Chitwood 1962] [Christian et al. 1989] [Culbertson 1965] [Davis 1965] [Dawson and Bowles 2004] [Dew et al. 2008] [General Dynamics San Diego Ca Convair Div 1966b] [Donahue 2026] [Dotson et al. 2010] [Dungan 1966] [Dunlap and Steinetz 2004] [Eastwood and Humphrey 1967] [Eck and Mukunda 1988] [Elzufon et al. 1965] [Elzufon et al. 1966] [Emmerson 1978] [Escalona and Escalona 1997] [Flight Performance of Atlas-Agena 1969] [Flight Performance of Atlas-Centaur 1970] [Flight Performance 1969] [Fowler 1963] [Frazier 1967] [Free et al. 2002] [Friedman and Stell 1963] [Gainor 2013] [Garba and Simpson 1968] [Gehringer et al. 1992] [General Dynamics San Diego Ca Convair Div 1966a] [General Dynamics/Astronautics San Diegoca 1961] [Gerus and Miller 1969] [Gerus et al. 1967] [Gilbert 2003] [Gill 1963] [Gillespie 2004] [Goette 1973] [Goldberg 2005] [Graham 1987] [Graham 2014] [Graham 2015] [Green and Tucker 1964] [Gribben et al. 1998] [Groesbeck 1966] [Groesbeck et al. 1974] [Gruszczynski et al. 1991] [Hagger et al. 2006] [Hansen 1964] [Harris 1964] [Hauser 1961] [Heald and Holland 1965] [Heath et al. 1965] [Heath et al. 1967] [Heath et al. 1968] [Herud and Carey 1987] [High Speed Schlieren Studies 1960] [Hofeller 1965] [Hohmann 1963] [Holguin 2006] [Holguin 2012] [Honse et al. 2009] [Hunley 2008b] [Hunley 2008c] [Incerto et al. 1962] [Ingber 1965] [Johnson 1964] [Jones 1975] [Kachadourian 1977] [Kalogeris 1966] [Kandarpa et al. 1987] [Kestenbaum 1965] [Kinstle 2020] [Kite et al. 1965] [Knoll et al. 1987b] [Knoll et al. 1987a] [Kreisler 1964] [Kreiter 1965] [Kutter et al. 2005] [Lacovic 1969] [Lacovic 1970] [Lacovic 1975] [Lacovic 1977] [Lacovic and Stofan 1968] [Lacovic et al. 1966] [Lall 1965] [Lall et al. 1965] [Langston 1967] [Launch Mission Summary 1980] [Launch Mission Summary 1981] [Launch Mission Summary INTELSAT 1982] [Atlas-Centaur AC-12 Flight Performance 1968] [Lorentz et al. 1985] [Macneil et al. 1988] [Mahoney 2013] [Martin 1993] [Martyusheva and Devyatkin 2021] [Mastronardi et al. 1979] [Mattson 1965] [Matzke 2015] [Matzke 2025] [McDermott et al. 1994] [Miller 1966] [Miller 1967] [Miller 1969] [Moore 1967] [Moskowitz 1965] [Moskowitz 1966] [Mosley 2011] [Nakamura 1991] [Neal 1966] [Nelson and Macklin] [Newton 1968] [Nowek and Stanton 1965] [Ogman 1980] [Performance Evaluation of Atlas-Centaur 1968] [Peters and Hall 1963] [Pharokhipanah and Bouckenooghe 2024] [Plastinin et al. 2005] [Pleasant and Kelly 1989] [Post-Test Diagnostic System Feature 1994] [Postflight Evaluation of Atlas-Centaur 1965] [Postflight Evaluation of Atlas-Centaur 1966] [Postflight Evaluation of Atlas-Centaur 1967] [Pradhan et al. 1967] [Preliminary Launch Vehicle Flight 1967] [Quitter and Reiss 1968] [Radke et al. 1979] [Rajan et al. 2019] [Ravi et al. 2023] [Rector 1982b] [Rector 1982a] [Ringland and Stubblefield 1965] [RL10 Ignition Limits Test 1987] [Ruscigno 1965] [Salzman et al. 1973] [Schreier et al. 2006] [Segal 1964] [Shelton 1966] [Shepard and Patino 1995] [Shuttle Centaur Engine Cooldown 1987] [Sorensen et al. 1984] [Sowers 2002] [Stephens 1961] [Stofan 1966] [Stofan 1973] [Strong et al. 2010] [Swanson 1977] [Symons 1977] [Tereniak and Williams 1967] [Thayer 1965] [The Atlas-Centaur 67 Incident 1988] [Thomas 1960] [Thomas 1981] [Traband 1966] [Tracking and Data Relay 1973] [Tuckman 1965] [Williams 2014] [Wolfe 1966] [Young and Shiokari 1961]

Reentry vehicles and the uncontrolled return

The payload the X-11 did not carry and the stages that come back unbidden. Ballistic and lifting reentry, nose cones, ablation and heat shields, reentry trajectories and the breakup and survivability of spent stages and debris. 73 titles name ablation.

241 records. [Adams 1960] [Adams and Kao 2001] [Aeschliman et al. 1975] [Al-Zaidi et al. 2020] [Allen 1971] [Anderson 1969] [Annaloro et al. 2020] [Appar and Kumar 2021] [Appar and Kumar 2025] [Appar et al. 2022] [Aprovitola et al. 2019] [Ayasoufi et al. 2006] [Bacon and Matney 2017] [Badea et al. 2025] [Bahramian and Kokabi 2009] [Baker and Kramer 1979] [Baker and Kramer 1982] [Balasubramanian et al. 2020] [Bao et al. 2019] [Bartlett et al. 1970] [Bartlett et al. 1971a] [Bartlett et al. 1971b] [Battie et al. 2012] [Beal et al. 1965] [Bell 1965] [Bigham and Puri 2025] [Bird and Reese 1958] [Bityurin and Bocharov 2014] [Blosser 1996] [Bonivert et al. 1989] [Bouslog et al. 1993] [Brinich 1958] [Bulmer 1972] [Byczkowski and Rao 2026] [Catalytic Efficiency 1983] [Chang et al. 2022] [Channon and Barry 1967] [Chapman 1965] [Chen and Milos 2004] [Chen et al. 2015] [Chen et al. 2025b] [Chhallani and Nemati 2025] [Chin et al. 1964] [Christoph 1985] [Clapp 1965] [Collins et al. 1963] [Combs et al. 2014] [Congdon 1995] [Cornette and Sullivan 1971] [Crenshaw 1983] [Cui et al. 2022] [Dantsuka et al. 2019] [Darnell 1966] [Degtyarev et al. 2006] [Detra and Hidalgo 1961] [Di Clemente and Ferrarella 2010] [Dicristina and Richards 1977] [Ding et al. 2023] [Dinonno et al. 2016] [Dolton and Reed 1966] [Donahue and Farrell 1979] [Dorne and Shube 1968] [Droms et al. 1976] [Eilertson and Wing 1966] [Atomics International Div., Canoga Park, Calif. (USA) and Elliott 1969] [Fante et al. 1970] [Farbar et al. 2012] [Ferreira Santos 2022] [Finke 1990] [Finson et al. 1980] [Flow Simulation over 2019] [Frankenthal 1964] [Fukuda et al. 2017] [Funatsu and Hiroyuki 2001] [Gaitonde and Shang 1993] [Gannon and Laszlo 1966] [Gao and Zhu 2025] [Gerasimov 2025] [Golden 1969] [Gondelach et al. 2017] [Gornostaev et al. 2008] [Grabowsky et al. 1981] [Grasso and Passalacqua 1991] [Gravlee et al. 2014] [Guarino 1968] [Gui et al. 1999] [Guo 2024] [Harvey 2008] [Heat-Shield Ablation and Sublimation 1965] [Heidrich and Braun 2017] [Hillberg 1967] [Hollis and Liechty 2006] [Hong and Neuenschwander 1991] [Hou et al. 2022] [Houser and Vanderleest 1972] [Hove and Shih 1977] [Huang and Yao 2019] [Huang et al. 2024c] [Huebner et al. 1988] [Huebner et al. 1989] [Hull et al. 1981] [Hurwicz et al. 1964] [Jie Liang 2019] [Johannessen 1964] [Johnis 2023] [Johnson and Joseph A. 1977] [Joint Conference on Lifting 1960] [Jones and Walters 2007] [Kamimura et al. 2012] [Kennedy and Fields 1962] [Kidner 1993] [Ko et al. 2007b] [Kraetzig et al. 2014] [Kryvoruka 1976] [Kumar et al. 2017] [Laganelli 1980] [Larson 1969] [Ledu and Pollak 1968] [Legendre et al. 1980] [Lennon and Poirter 1974] [Li 1989] [Li et al. 2016b] [Liang et al. 2024] [Lin and Rubin 1979] [Lin et al. 1982] [Lincoln 1981] [Lind and McIlwraith 1965] [Liu et al. 2010] [Liu et al. 2026b] [Loshkarev 1977] [Lovelace 1961] [Low-Density Phenolic Nylon Nosecap 1965] [Lu 1996b] [Jorlin et al. 2026] [Machin and Daum 2026] [Mark 5 and 11 2021] [Marshall 1968] [Marshall and White 1968] [Masaki and Yakura 1968] [McAlees 1968] [Mehta 1999] [Mehta 2023] [Milos 1996] [Milos 1997] [Milos et al. 1997] [Mongibello and de Luca 2008] [Monti et al. 2006] [Moody et al. 1975] [Morrison et al. 1981] [Murphy 1961] [Muthu et al. 2020] [Nakasato et al. 2015] [Nardo and Sadler 1962] [Nardo et al. 1961] [Navaz and Ntantis 2026] [Atomics International, Canoga Park, Calif. and Nelson 1967] [Nichols 1961] [Iyinomen 2022] [Ohkage et al. 2025] [Onay and Eyi 2020] [Palmer et al. 1995] [Pan et al. 2023] [Park and Balakrishnan 1985] [Parsons 1964] [Penner and Olfe 1968] [Pepper 1977] [Persen 1969] [Platus 1967] [Platus 1978] [Platus 1983] [Porter 1981] [Priyadarshi and Mittal 2010] [Putz and Bartlett 1972] [Putz and Bartlett 1973] [Ramjatan et al. 2017] [Rana and Chudoba 2016] [Raper 1981] [Ravichandran et al. 2023] [Reentry Vehicle Nosetip Material 1977] [Ren 2025] [Richards et al. 1971] [Richman 1967] [Rigali et al. 1980] [Rindal et al. 1967] [Rivier et al. 2019] [Rochefort et al. 1974] [Rogers et al. 2022] [Sakai et al. 2017] [Sayles 1965] [Scherberg and Rubin 1953] [Schneider et al. 1972] [Schouler et al. 2021] [Schweppe 1964] [Shang and Gaitonde 1994] [Sherman 1978] [Shi et al. 2023a] [Shilav and Khosid 2020] [Shinnick 1966] [Shvab and Loshkarev 1973] [Sohn et al. 2011] [Spallation of the Galileo 1983] [Stadler 1993] [Stalder 1957] [Stern 2004] [Stern 2008] [Stern and Chu 1963] [Stetson 1964] [祝 2020] [王 2021] [Sun et al. 2015a] [Sunken Reentry Vehicle 2013] [Suzuki et al. 2002] [Swain 1975] [Szczepanowska and Mathia 2011] [Szu 2023] [Tahsini and Mousavi 2014] [Taylor et al. 1993] [Thermal Protection 2015] [Thomas and Perlbachs 1967] [Tian et al. 2025] [Ting et al. 1986] [Trushlyakov et al. 2019] [Urazbakhtin et al. 2014] [Van Ghele et al. 2018] [Viviani et al. 2008] [Vo et al. 1993] [Wachi and Gilmartin 1966] [Wan et al. 2025] [Wang et al. 2014b] [Wartemann et al. 2018] [Webb et al. 2026] [Weilmuenster et al. 1996] [Wong et al. 1960] [Wortman 1969] [Wu et al. 2018] [Xiao et al. 1991] [Xiao et al. 2018] [Xu and Yang 1993] [Zakkay and Wang 1973] [Zhao 1993] [Zhong et al. 2007]

Pressure-stabilised and inflatable structure

The keystone’s own literature, and most of it is about something else under pressure. Internally pressurised cylinders and tubes, pressure-stabilised beams and arches, inflatable booms, tubes and habitats, and the wrinkling that ends their bending strength. 121 of its 184 records concern internally pressurised cylinders, tubes and shells and 51 concern inflatable structure, and the propellant tank itself is taken up under Thin Subjects.

184 records. [Ali and Jean François 2002] [Amazigo 1973] [Amazigo 1974] [Du Liping et al. 2012] [Batista and Croll 1982] [Berry and Reissner 1958] [Bieniek et al. 1962] [Birukov et al. 2014] [Blachut 2004] [Bloom 1985] [Bloom 1986] [Bonde and Rao 1978] [Bouazizi et al. 2018] [Buckling of Thin-Walled Pressurized 2008] [Błachut 2005] [Cesari 1985] [Chang 1988] [Chaudhuri et al. 2008] [Chung et al. 1986] [Curtin and Adey 2000] [Daanouni et al. 2009] [Davids 2023] [Dillman 2015] [Du et al. 2012] [Du et al. 2013] [Du et al. 2024] [Duncan and Sanders 1969] [Durelli et al. 1970] [Edge et al. 2010] [End Effects on Internally 2023] [Fenwick and Karigan 1977] [Fesharaki 2020] [Finnie 1960] [Fok and Travis 1989] [Folias 1965] [Folias 1967] [Folias 1984] [Fujimoto and Shioya 2005] [Furuya and Yasuike 2009] [Furuya and Yokoyama 2013] [Futterman and Rubinstein 1968] [Galletly 1978] [Galletly and Blachut 1987] [Galletly and Radhamohan 1979] [Gashe et al. 2025] [Gasiak 1992] [Ge et al. 2026] [Girase 2015] [Glaser 2021] [Gong et al. 2026] [Gonzalez and Martinez 2013] [Gruszczynski et al. 1988] [Guo et al. 2022b] [Han et al. 2006] [Haseganu and Steigmann 1994] [Haßler and Schweizerhof 2008] [He 2024] [He et al. 2023] [Hu et al. 2025] [Huang et al. 2025a] [Hyer and McMurray 1999] [Hyer and Wolford 2002] [Hyer et al. 2003] [Jalaja et al. 2023a] [Ji et al. 2017] [Jiang et al. 2026b] [Jones 2018] [Kanlıkama 2013] [Kessel 1971] [Koike et al. 2018] [Krainski and Walter J. 1988] [Kundu and Mukhopadhyay 2025] [Kömle et al. 2025] [Larsson et al. 1982] [Latta et al. 1977] [Lau and Listvinsky 1981] [Lazghab and Soula 2014] [Le van and Wielgosz 2005] [Leitch 1986] [Leitch 1988] [Leitch 1999] [Li et al. 2017b] [Limam et al. 2010] [Lin 1981] [Lind 1968] [Liu and Yang 2017] [Lovejoy et al. 2010] [Ma et al. 2024b] [Ma et al. 2026b] [Mannani et al. 2023] [Matsunaga et al. 2017] [McMurray and Hyer 2000] [McMurray and Hyer 2001a] [McMurray and Hyer 2001b] [McMurray and Hyer 2002] [Miller and Gerus 1966] [Mirels and Zondervan 2005] [Mirels and Zondervan 2006] [Murthy et al. 1972] [Newman 1973] [Newman and Ojalvo 1966] [Nguyen et al. 2015] [Nicholson et al. 1980] [Niedenfuhr 1963] [Ong 1994] [Peery 1964] [Perl and Levinsohn 1989] [Peterson 1960] [Petritoli et al. 2023] [Pidvysotskyi 2021] [Polenta et al. 2015] [Poza et al. 2010] [Tawade 2019] [Pu 1985] [Radhamohan and Galletly 1979] [Ramarathnam et al. 2024] [Rastogi and Johnson 1995] [Rastogi and Johnson 1996] [Reissner 1959] [Rioseco Olave et al. 2023] [Rufer et al. 2013] [Samadzadeh et al. 2024] [Shivakumar and Avva 1996] [Singh et al. 2024b] [Sorić 1991] [Sorić 1995] [Sorić and Zahlten 1995] [Stamenovic 1988] [Steeves 1975a] [Steeves 1975b] [Steeves 1978a] [Steeves 1978b] [Steeves 1979] [Stresses in Thick-Walled Pressurized 2023] [Sun et al. 2022a] [Sun et al. 2023b] [Sun et al. 2023c] [Sutton 2004] [Taira and Ohtani 1968] [Takahashi et al. 2013] [Takahashi et al. 2019] [Tao et al. 2016] [The Application of Linear 1990] [Thomas and Bloch 2016] [Throop and Fujczak 1983] [Tian et al. 2009] [Ting and Tuan 1973] [Tlilan et al. 2019] [To et al. 2013] [Traexler 1960] [Tsunori et al. 2007] [Underwood 1972] [Veldman 2006] [Ventura et al. 2023] [Vibration of Pressurized Cylinders 1991] [Wang et al. 1998] [Wang et al. 2012a] [Wang et al. 2013b] [Wang et al. 2017a] [Wang et al. 2025c] [Wang et al. 2026b] [Weingarten 1962b] [Weingarten 1964b] [Witherell and Scavullo 1990] [Wolford and Hyer 2005] [Wu et al. 2024] [Yahsi and Erdogan 1985] [Yamada 1997] [Yang et al. 2022] [Yao et al. 2015] [Yokouchi et al. 1988] [Yoo et al. 2007] [Yu 2026] [Yun and Liu 2023] [Zender 1962] [Zhang et al. 2016b] [Zhang et al. 2024b] [Zhangabay et al. 2024] [Zhao and Teng 2000] [Zhao et al. 2022] [Zhao et al. 2024b] [Zhao et al. 2025c] [Zheng et al. 2014] [Zhu et al. 2018a]

Launch acoustics, vibration and sonic fatigue

The environment computed above at 153 decibels. Lift-off and in-flight acoustics, payload fairing noise, vibroacoustic response and sonic fatigue. 45 titles concern lift-off, the launch pad or launch noise, which is the load case of a vehicle standing on its own exhaust.

167 records. [Abhishek Hari 2026] [Acoustic Sensitivity Measurements 1996] [Alestra et al. 2002] [Alestra et al. 2003] [Ali et al] [Ashida et al. 2013] [Avirah et al. 2026] [Ballentine et al. 1966] [Bangs 1974] [Bickford 1968] [Borchers 1998] [Cadieux et al] [Casiano 2009] [Cheng et al. 2006] [Cheng et al. 2025c] [Chernobryvko et al. 2024] [Choi and Lee 2021] [Clarke and Gutierrez 2000] [Coelho da Silva Stanisce Corrêa et al. 2020] [Cohan and Miller 2011] [Counter and Houston 2011] [Counter and Houston 2012b] [Counter and Houston 2012a] [Crandall and Mark 1963a] [Crandall and Mark 1963b] [Crandall and Mark 1963c] [da Silva Stanisce Corrêa et al. 2021] [Dahm and Krause 1966] [Davis and Fischbach 2010] [Della Posta et al. 2026] [Denoyer et al. 1998] [Dougherty et al. 2006] [Dynamic Loads on Mu-Series 1994] [Edge and Mueller 1965] [Engberg and Korde 2013] [Engbrenghof 1967] [Escartí-Guillem et al. 2022] [Ferrara et al. 2007] [Flanigan 1989] [Frampton 2002] [Franken et al. 1963] [Gee et al. 2025] [Gely et al. 2000] [George 1966] [Giacomoni 2014] [Glaese and Anderson 1999] [Griffin et al. 2000b] [Griffin et al. 2008] [Harris et al. 2014] [Hasis et al. 2026] [Henderson et al. 2002] [Herrero Durá] [Herron et al. 2016] [Higgins 2007] [Hines 1966] [Housman et al. 2012] [Houston et al. 2009] [Houston et al. 2010b] [Houston et al. 2010a] [Houston et al. 2015] [Howard and Hansen 2006] [Hughes and McNelis 2014] [Hung and Hunt 1964b] [Hwang 2002] [Hwang 2003] [Jin et al. 2024] [Keast 1961] [Kemp and Clark 2000] [Kemp and Clark 2003] [Kenny and Giacomoni 2016b] [Khamlak 2026] [Krishna 2022] [Kudryavtsev and Safronov 2012] [Large Eddy Simulation 2023] [Larko and Hughes 2008] [Laroche et al. 2000] [Launch Vehicle and Payload 2022] [Leo and Anderson 1998] [Liever and West 2016a] [Liever and West 2016b] [Lipnitskiy and Safronov 2014] [Liu et al. 2023c] [Liu et al. 2023a] [Liu et al. 2023b] [Lubert et al. 2016] [Majed et al] [Margasahayam 2009] [Maryna 2025] [Micci 1997] [Mori et al. 2019] [Morshed et al. 2013] [Morshed et al. 2014] [Müller and Westerlund 2003] [Nacht and Turk 1966] [Nance et al. 2015] [Natarajan and Venkatakrishnan 2015] [Ohtsuka et al. 1981] [Pan et al. 2026b] [Panda 2014] [Panda et al] [Panda et al. 2013b] [Panda et al. 2013a] [Panda et al. 2014] [Panda et al. 2025] [Paolozzi and Peroni 1996] [Park 2014] [Park et al. 2016] [Petrenko 2025] [Peverley 1962] [Piotr et al. 2019] [Plotkin et al. 2009] [Popov et al. 2019] [Qiu et al. 2026] [Raj et al. 2026] [Ballentine et al. 1968] [Cunningham et al. 2024] [Douglas Aircraft Co Long Beach Ca 1963] [Hrinchenko 2020] [Kenny et al. 2009] [Lu et al. 2023b] [Popov 2025] [Reddy et al. 2026] [Reese 1967] [Roberts and Wilhem 1964] [Salehian and Mankbadi 2020] [Salehian et al. 2018] [Sarae et al. 2017] [Sarae et al. 2018] [Schneider and Rudder 1973] [Sepcenko et al. 1990] [Sescu et al. 2015] [Shimazaki and Shi 2021] [Sills et al] [Smith and Harrison 2010] [Smoot and Seliga 1967] [Steva 2017] [Strutzenberg and Liever 2011] [Tanner 1997] [Tedrick 1965] [Thomas 1987] [Tomioka and Kohsetsu 1990] [Tosh et al. 2012] [Troclet et al. 2011] [Trout et al. 2011] [Tsivouraki et al. 2025] [Tsutsumi et al. 2009] [Tyzzer 1963] [Tyzzer and Pernet 1964] [Varma et al. 2024] [Vreeland 1960] [Vu 2007] [Wang 1966] [West et al. 2012] [Wignall et al] [Williams 1992] [Williams 1997] [Williams 1999] [Xing et al. 2020b] [Xing et al. 2020a] [Xing et al. 2022] [Yenigelen and Morris 2020] [Yenigelen and Morris 2021] [Yunis 2013] [Zafrane et al. 2013] [Zhang et al. 2026d] [Zhou et al. 2024a] [Zhou et al. 2025c]

Materials, manufacture, welding, fracture and the proof test

The material and the acceptance test. Stainless steel in thin sheet and at cryogenic temperature, manufacture, thin-sheet welding, pressure-vessel fracture, burst testing and proof testing. 67 titles name stainless steel and 10 name the 301 alloy the Atlas was built from.

160 records. [Agarwal et al. 2025] [Akbar and Kobayashi 2023] [Alam et al. 2020] [Alexander and Fournier 1963] [Allgeier and Forman 1970] [Anbalagan and Thirupathi 2025] [Apatovskii et al. 1967] [Azuma et al. 2013] [Azzi et al. 2010] [Bailie et al. 1980] [Barclay 1965] [Bi et al. 2026] [Bin 2017] [Brust et al. 2019] [Buffa et al. 2013] [Butt Welding of Very 1952] [Cain and Sharp 1993] [Cain et al. 1990] [Cain et al. 1991] [Cen et al. 2019] [Chen et al. 2010] [Chethan Kumar et al. 2022] [Robert 1996] [DeSisto and Carr 1961a] [DeSisto and Carr 1961b] [Dian Fitria Ramdani and Dene Herwanto 2026] [Ding et al. 2025] [Dobson and Johnson 1984] [Dragone 2000] [Dwivedi et al. 2013] [Edwards et al. 2023] [Eremin 2021] [Eremin and Moskvichev 2020] [Farid and Molian 2000] [Fergusson et al. 1953] [Finger 1974] [Finger 1976] [Finger 1979] [Florist et al. 2024] [Fukumoto et al. 2008] [Funada and Abe 2003] [Gawthorpe 1979] [Geng et al. 2011] [Giovanola et al. 1998] [Girton 1962] [Grenoble et al. 2018] [Greulich et al] [Gubeljak et al. 2012] [Guntner and Reed 1962] [Guzman-Leong et al. 2013] [Haddad et al. 2024] [Harris and Dunegan 1972] [He 2025] [Heer and Yang 1970] [American Welding Society 2019] [Hydrogen-Stress Cracking of Type 2019] [Ikushima 1993] [Ilangovan et al. 2023] [Ismail 2011] [Jalaja et al. 2023b] [Jha et al. 2004] [Jha et al. 2006] [Johnson and Kelsen 1969] [Johnson et al. 2023a] [Johnson et al. 2023c] [Johnson et al. 2023b] [Jones et al. 1999] [Kadam et al. 2018] [Kauczor 2019] [Kern and Lubin 1963] [Kitching 1980] [Krużelecki and Proszowski 2012] [Kuentz 1969] [Kumar et al. 2024] [Launch Vehicle Manufacturing 2022] [Li et al. 2018] [Li et al. 2022a] [Liao and Yu 2007] [Liu et al. 2025d] [Lu et al. 2023a] [Luo et al. 2025] [Luo et al. 2026] [Luttrell and Henderson 1974] [Lüders et al. 2025] [Manning and Price 1961] [Manwatkar et al. 2024] [Markelj and Tušek 2001] [Masters et al. 1966] [Minnetyan and Chamis 1995] [Mirza and Gupgupoglu 1988] [Moreton and Moffat 1991] [Moskovic 1988] [Mukherjee et al. 2025] [Mullin et al. 2025] [Muraca and Whittick 1972] [Nagy and Behúlová 2017] [Nakahara et al. 1997] [Narayanaswamy et al. 2025] [Nie et al. 2018] [Noda 1993b] [Noda 1993a] [Nolan 1964] [Nordberg 2005] [Novikov and Chechin 1973] [Okamoto 2008] [Okamoto et al. 2015] [Olalekan et al. 2026] [Outwater and Seibert 1962] [Paleti et al. 2026] [Pankaj et al. 2019] [Panontin and Hill 1996] [Pei et al. 2012] [Podnos et al. 2018] [Pressure Vessel Bursts 2010] [Procter 1988] [Płaczek et al. 2023] [Qiu et al. 2023] [Regassa et al. 2022] [Ried 1966] [Ried and Arnold 1966] [Rintamaa et al. 1989] [Russell et al. 2018] [Saito et al. 1970] [Sato et al. 1969] [Schonberg 2020] [Schwartzberg et al. 1979] [Shah ISMAIL et al. 2011] [Simonen 1985] [Smith et al. 2003] [Sneddon et al. 1999] [Stanciu et al. 2014] [Su et al. 2025b] [Szyszkowski and Glockner 1987] [Tanaka et al. 1990] [Teodorescu and Irimescu 1988] [Thompson et al. 2025] [Tozawa 1969] [Urbin 1991] [Vijayakumar and Lakshminarayana 2023] [Vilar and Miranda 1988] [Wang et al. 2011a] [Wang et al. 2013a] [Wang et al. 2022b] [Warkina et al. 2026] [Watson 1960] [Watson and Christian 1961] [Whipple and McHenry 1983] [Widjaja] [Xu et al. 2025c] [Yan et al. 2015] [Yang 2018] [Yurchenko 2026] [Yurchenko et al. 2025] [Zhao and Liu 2014] [Zhao et al. 2025e] [Zhou et al. 2013] [Zhou et al. 2017] [Zhu 2025] [Zhu et al. 2023b] [Zolfaghari and Izadi 2020]

Flight test, reliability and launch operations

What a short flight series can and cannot establish. Launch-vehicle and missile reliability, flight-test programmes, range safety, launch complexes and ground support equipment. 52 titles name reliability.

119 records. [A Successful Program 1992] [AAP Preliminary Range Safety 1967] [Aher 2024] [Ahmad 1992] [Almetwally et al. 2026] [An Integrated Missile Reliability 1984] [Aytulun and Ermis 2009] [Bellantoni and Koenke 1968] [Bloomer 2005] [Blumenthal and Denton 1962] [Bowser and Busch 1966] [Von Braun 1962] [Braun et al. 1970] [Cates et al. 2012] [Cates et al. 2013] [Chang 1995] [Cheng and Tam 2014] [Christie and Greenberg 1973] [Clark and Curran 1990] [Condition Assessment of Launch 2015] [Corl et al. 2014] [Cross and Vesely 2018] [Davis et al. 2007] [DeLuna 2012] [Dennehy et al. 2010a] [Doerr 1991] [Drozdov et al. 2020] [Ferrell 2001] [Fine et al. 1965] [Fine et al. 1966] [Garvey and Besnard 2005] [Gaver and Jacobs 1997] [Guikema and Pate-Cornell 2003] [Hara et al. 2006] [Al Hassan and Novack 2015] [Al Hassan et al. 2017a] [Al Hassan et al. 2017b] [Honeycutt et al. 2020] [Hong and Kim 2014] [Huang et al. 2005] [Hunt 2011] [Ireland and Gonzales 2020] [Jones 2024] [Justice 1965] [Kasouf and Weiss] [Kim and Lee 2013] [Kim et al. 2012] [Kitsios and Lygeros 2005] [Krevor and Wilhite 2007a] [Launch Vehicle Systems 2022] [Lawrence et al. 2014] [Li et al. 2025a] [Lim et al. 2024a] [Lonzaga] [Losik 2010b] [Losik 2010c] [Majamaki and Lee 2011] [Manning et al. 2010] [Mattenberger et al. 2012] [McDanels 2019] [Mettler and Towner] [Mocio 2001] [Mohammad and Novack 2015] [Moore 1958] [Morse et al. 2010] [Nagappa 2023] [Nakagawa et al. 1999] [Neelans 1986] [Newton and Makrides 1954] [Novack et al. 2018] [Operational Base Missile Test 2021] [Parsons 1970] [Powell 1962] [Powers 1961] [Pre-Launch Calculation of Space 1964] [Prosser] [Arjun et al. 2012] [Hatfield et al. 2016] [Lu et al. 2021b] [Lu et al. 2022] [Rae 1961] [Raouf and Pourtakdoust 2017] [Guodong et al. 2026] [Rice 2013] [Rosch and Schor 1990] [Roshanian and Ebrahimi 2013] [Rusick 2007] [Safie and Weldon 2007b] [Safie and Weldon 2007a] [Safie et al. 2002] [Safie et al. 2014] [Saratayon and Petchartee 2015] [Sauvageau and Allen 1998] [Schuiling 1988] [Sobel 1963] [Stower 2024] [Suresh] [Tarzwell and Colley 1979] [Thakur et al. 2019] [The Use of Artificial 2004] [Tierney 1993] [Tinney et al. 2019] [Trowbridge and Van Horne 1960] [Unal et al. 2004] [Vickery 1963] [Vijayan and Suresh Babu 2015] [Wagenblast and Bettinger 2024] [Wang and Miao 2026] [Wang et al. 2019d] [Ward 2015b] [Wensley and Uhrich] [Williams 2018] [Williams and Corcoran 1963] [Williams-Hayes 2007] [Xu et al. 2011] [Yamazaki et al. 1985] [Yan et al. 2016] [Zhao et al. 2025a] [Zhu 2026]

Pogo and propulsion-structure coupling

The coupling of structure and feed system along the vehicle’s axis. Pogo analysis, accumulators and suppressors, and the longitudinal combustion instabilities that share its mechanism. 60 of its 71 records name pogo itself.

71 records. [A Study 2003] [Ackerman et al. 1970] [Aldrich 1967] [Barrere et al. 1970] [Bowman 1967] [Chapin 1974] [Dimaggio and Nishimoto 1972] [Dolgopolov 2025] [Dolgopolov and Nikolayev 2024] [Dotson et al. 2014] [Farrel and Fenwick 1973] [Flandro et al. 2004a] [Goldman 1967] [Goldman and Miessner 1965] [Goldman and Miessner 1966] [Haddick 1980] [Hanks and Stephens 1969] [Hill et al. 1969] [McKenna et al. 1964] [Kim et al. 2015] [Larsen 2008] [Lee et al. 2017] [Lehtinen and Lorenz 1979] [Lewis 1969] [Li et al. 2014a] [Licht and Park 1967] [Liu et al. 2020] [Lock and Rubin 1976] [Lores and Zinn 1973] [Lou et al. 2025] [Marcus et al. 1969] [McDougal et al. 2016] [Mellquist et al. 2024] [Mitchell et al. 1969] [Mitra et al. 2021] [Nguyen and Sirignano 2018] [Nguyen and Sirignano 2019] [Nguyen et al. 2017] [Nguyen et al. 2018] [Nikolayev et al. 2026] [Ono et al. 1987] [Oppenheim and Rubin 1992] [Park et al. 2018] [Pasini and Amoroso 2018] [Payne and Rubin 1974] [Peugeot et al. 2010] [Peugeot et al. 2011] [Pinson and Harbison 1972] [POGO Prevention of H-2 1994] [Prevention of Coupled Structure-Propulsion 1970] [Raji et al. 2019] [Riley and Sterett 1970] [Rubin 1965] [Rubin 1966] [Rubin et al. 1973] [Sakaki et al. 2018] [Sim et al. 2016] [STS-1 Pogo Analysis 1981] [Swanson and Giel 2009] [Tan et al. 2023] [Ujino et al. 1989] [Wang et al. 2014e] [Wang et al. 2014d] [Wang et al. 2021d] [Winje 1968] [Wu et al. 2023] [Yoo et al. 2021] [Yoon et al. 2021] [Zhang and Zhang 2014] [Zhao and Tan 2026] [Zhao et al. 2024a]

What a Conventional Vehicle Would Have Had to Achieve

It has been argued throughout that the balloon tank was necessary, and the range table appears to prove it. That table, however, compares the Atlas against a heavier version of itself, which is not the comparison a designer in 1951 faced. The real alternative was a conventional two-stage vehicle, which discards a whole tank set and therefore gets a much larger staging benefit than the Atlas half-stage does. Setting the two against each other is the comparison this discussion owes.

Take a two-stage vehicle carrying the same total propellant, split equally between the stages, with each stage having a structural fraction $f$ of its own loaded mass. The stage structures are then

\[m_{s} = \frac{f \, m_{p} / 2}{1 - f} \tag{103}\]

and the total ideal velocity is the sum of two logarithms rather than one,

\[\Delta v = v_{e} \left[ \ln \frac{m_{\text{all}}}{m_{\text{all}} - m_{p}/2} + \ln \frac{m_{2}}{m_{s}} \right] \tag{104}\]

Evaluating it across structural fractions from eight to twelve percent, and carrying each result through the same loss calibration and the same range relation, gives

Two-stage structural fraction	Gross mass	Ideal velocity	Range
0.08	122,288 kg	8689 m/s	11,047 km
0.10	125,006 kg	8021 m/s	7,521 km
0.12	127,847 kg	7467 m/s	5,665 km

against the Atlas at 117,900 kilogrammes, 8530 metres per second, and 9,999 kilometres.

The crossover sits near a structural fraction of eight and a half percent, and the Titan I, the conventional two-stage missile actually built, had stages on both sides of it. Its operating manual gives tank capacities of about 7,750 gallons of fuel and 12,400 of liquid oxygen in the first stage and 2,027 and 2,985 in the second USAF 1963 T.O. 21M-HGM25A-1-1, HGM-25A Missile Weapon System Operation. At the propellant densities used in the weight summary of a later Atlas Atlas-Centaur AC-12 Flight Performance 1968, those capacities hold about 75,400 and 18,600 kilogrammes, and against the empty masses of 4,000 and 1,725 kilogrammes in the compilation HGM-25A Titan I they give structural fractions of about 5.0 percent for the first stage and 8.5 percent for the second. Because a capacity bounds the load from above, these fractions are if anything low. The compilation’s loaded masses give 5.2 and 6.0 percent instead, but they credit the second stage with about half again the propellant its tanks held, and they sum to 105,142 kilogrammes, where the capacities and the same empty masses come to about 99,800 before the reentry vehicle is added, close to the 220,000 pounds of the directory entry Parsch 2006 Martin SM-68/HGM-25/LGM-25 Titan. The adopted Titan I fractions are therefore 5.0 and 8.5 percent, with 5.2 and 6.0 as the compilation’s alternative.

The equal split of the model differs from the Titan I arrangement, which carried about four fifths of its propellant in the first stage, where its fraction was lowest. Given the Atlas propellant load in Titan I proportions and either set of Titan I fractions, the same model gives an ideal velocity of 10,700 to 11,000 metres per second against the Atlas’s 8530. On this model a two-stage vehicle built to Titan I proportions outranges the Atlas half-stage by a wide margin. The comparison that bears on the balloon tank is the reverse one. The Atlas fraction is 4.6 percent on the compilation masses used throughout and 4.5 percent on the later Atlas’s recorded dry weights of 6,111 pounds for the booster section and 5,443 for the sustainer against 247,562 pounds of flight expendables Atlas-Centaur AC-12 Flight Performance 1968, so the best conventional stage of the comparison, the Titan I first stage, sits between about half and four fifths of a percentage point above it. Rebuilt at that first-stage fraction of 5.0 to 5.2 percent, the Atlas half-stage reaches about 8,060 to 8,580 kilometres on the same model against 9,999. The balloon tank therefore made a single-and-a-half-stage intercontinental vehicle possible, while a conventional two-stage vehicle was the lighter route to the same range, and the half-stage bought the avoidance of an altitude ignition with it, a reading that fits the ballistic missile field going multistage and never coming back.

This does not weaken the article’s argument so much as locate it. The rocket equation punishes structural mass whatever the configuration. The Atlas spent its structural budget on a radical tank and saved a staging event. Titan spent it on a conventional tank and paid for an altitude ignition HGM-25A Titan I. Both were answers to the same logarithm, and the Titan I first stage came within a percentage point of the Atlas structural fraction while its second stage ran at nearly twice the Atlas figure, a smaller margin than the drama of the balloon tank suggests, and one that still costs a half-stage vehicle between a seventh and a fifth of its range.

Sensitivity to the Knockdown Factor

The article’s most quotable number is that the tensile allowable exceeds the compressive one by a factor of sixty-seven, and that number is not a measurement. It is a classical buckling stress multiplied by a factor of 0.2 chosen from a band of experimental scatter. The question is how far the conclusion moves when that choice moves.

Knockdown	Compressive allowable	Pressure needed	Margin on the 5 psi spec	Tensile over compressive
0.15	10.8 MPa	1.93 psi	2.59	89
0.20	14.4 MPa	2.58 psi	1.94	67
0.30	21.6 MPa	3.87 psi	1.29	45
0.50	36.0 MPa	6.44 psi	0.78	27

Two things follow. The qualitative claim is robust and the quantitative one is not. Across the plausible range the tensile allowable exceeds the compressive one by between twenty-seven and eighty-nine times, so the asymmetry that motivates the design survives any reasonable choice, but the specific figure of sixty-seven does not and should be read as an order rather than a value.

The second is a usable consistency check. At a knockdown of 0.5 the five-pound standing pressure would be insufficient, with a margin below one. The reported specification is therefore consistent only with a knockdown below about 0.4, which the design lower bound of about 0.18 in NASA’s criterion satisfies NASA 1968 Buckling of Thin-Walled Circular Cylinders. The vehicle’s own maintenance specification independently bounds from above the design factor its engineers must have used, which is a small result but a satisfying one, because it is the only place in this article where a number from the operational record constrains a number from the design process.

Where the Framing Breaks Down

Treating the X-11 through the mass-fraction keystone illuminates the design but misleads in six ways.

It was not a complete missile. No operational guidance Convair X-11, no reentry vehicle, no warhead, and a range about a tenth of the requirement Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960. The X-11 is the airframe and the booster propulsion and nothing else.

The structure was not the programme’s actual difficulty. Five of eight flights failed by the flight-by-flight record, and the failures were heating, plumbing, turbopumps, pneumatics and electrical shorts Convair X-11. A treatment organised around the balloon tank gives the impression that the daring part was the hard part, and the flight record says the opposite, and the record that shows it is the Difficulties Review of General Dynamics San Diego Ca Convair Div 1966a rather than any structural document.

Mass fraction stopped being binding. The keystone that justified the design is the reason the design was abandoned, since later vehicles could afford heavier structure and could not afford the handling.

The keystone is a structural principle rather than a vehicle. Almost all of what this article derives applies to the Atlas family, to Centaur, and to any pressure-stabilised shell, and very little of it is specific to the eight articles that flew as Atlas A. A treatment organised this way tells the reader about a design idea and uses one machine as the occasion. That is a legitimate way to write about a testbed whose own record is thin, and it should be said out loud and not left as an impression.

And the comparison the article makes is with itself. The range table varies the Atlas structure and the two-stage section varies a hypothetical alternative, but neither is a comparison with a vehicle that was actually built. Titan I flew, used a conventional structure, reached intercontinental range, and is not analysed here beyond its tank capacities and stage masses USAF 1963 T.O. 21M-HGM25A-1-1, HGM-25A Missile Weapon System Operation HGM-25A Titan I. The position taken here is that this article establishes what the balloon tank was worth in the abstract and leaves the empirical comparison to a reader with both sets of mass properties, which the accessible record supplies only in part, as the tank capacities of the Titan I operating manual, the empty masses of a compilation and the recorded dry weights of a later Atlas.

The mass figures are not the vehicle’s own. The structural fraction, the mass ratio, and all that is computed from them use the Atlas D figures of the SM-65 Atlas compilation, because no empty mass for the Atlas A has been found. The one Atlas A mass on record is the 181,000 pounds at which Cleary 1991 The 6555th, Missile and Space Launches Through 1970 gives the planned Series A test missiles, against 243,000 for the Series C and D, while all four series share the same seventy-five by ten foot shell. The range table therefore describes the family rather than the article that flew. The Epistemic State repeats this, and it is the largest single weakness in the quantitative argument.

What the X-11 Was Worth

A testbed is worth what it removed from the programme’s uncertainty, and that can be stated for this one more precisely than for most.

It removed the structural question completely and on the first flight. Before June 1957 the proposition that a shell thinner in proportion than a drink can, held up by five pounds of nitrogen, would survive launch was an argument. After a vehicle tumbled at two kilometres and held together it was a fact, and no later Atlas flight added to that knowledge. One flight, two kilometres, and the largest single risk in the programme was retired.

It removed most of the propulsion question over seven further flights, which is a poor return per flight and the only return available, because propulsion faults are individually rare and collectively common and there is no substitute for accumulating them.

It removed almost nothing about guidance, reentry, or range, because it carried no operational guidance, no reentry vehicle, and flew at about two fifths of the required speed. Those were the Atlas B and the later variants.

The programme’s own sequencing confirms the reading. The first Atlas B flew from Pad 11 on 19 July 1958 Cleary 1991 The 6555th, Missile and Space Launches Through 1970, forty-six days, or six and a half weeks, after the last Atlas A. Such an interval does not suggest a programme waiting for a verdict. The A was allowed to overlap its successor because the question it existed to answer had been settled a year earlier and the work since had been debugging, and debugging is work that transfers to the next article rather than gating it.

The distribution is lopsided and it is the distribution a good testbed should have. The riskiest item was retired first and cheapest, and the items that could only be settled by building the real weapon were left to the real weapon. Set against the X-10, which retired almost nothing because its risk was a quantity that accumulates, the X-11 is what a testbed looks like when the physics cooperates.

The Designation as the Series Question

The previous article found that the X-8, the X-9, and the X-10 were all RTV-A vehicles before they were X vehicles, and concluded that three apparent anomalies were one administrative act seen three times. The X-11 does not fit that explanation, and the misfit is informative.

The Atlas A was never an RTV-A vehicle. It came from a weapon programme with its own designation lineage, running MX-1593, then B-65 in 1951, then SM-65 in August 1955, with the Atlas A itself the XB-65A and then the XSM-65A Parsch 2005 Convair B-65/SM-65/CGM-16/HGM-16 Atlas, and the X-11 label sits beside that lineage rather than inside it. So whatever attached an X number to this vehicle was not the RTV absorption that explains the previous three. The line did pass through that series once. Neufeld records that the MX-774 test vehicles of 1946 and 1947 were also called RTV-2-As or Hirocs, so the Atlas’s ancestor carried a research test vehicle designation a decade before the X-11 label appears, and no document read for this article connects the earlier designation to the later X number. The accessible record does not say what it was, and the only use of the X designation found for this article is the directory entry’s account of the 1953 plan, which names no programme document for it.

Three readings are available and the article does not choose between them.

The X number may have been an allocation that was made and never used. This is the reading the absence of any programme document using it supports, and it would put the X-11 and X-12 in the same category as the reserved-but-unassigned cases the series meets later, such as the X-39, whose reservation the series framing records as never formalised. A designation that exists in the numbering registry and nowhere else is a bookkeeping entry, not a name.

It may have been a test-article designation for the pre-operational vehicles specifically, distinguishing the eight Atlas A articles from the weapon they were prototyping, in the way that an X number legitimately distinguishes a research article from a production one. On this reading the label is doing the job the X series exists for, and its absence from the written record is an accident of a programme that had a perfectly good name already.

Or it may be a later retrofit by compilers rather than a period assignment at all. Inventories of X-vehicles have an incentive to fill gaps, and X-11 and X-12 are gaps that the Atlas A and Atlas B fit neatly. The series has already met one case where a compilation attributes a designation that nomenclature records reportedly deny, in the X-23, which the series framing lists as contested, and the reasoning there applies here.

What the case establishes for the series is narrower than a resolution and more useful than a guess. The previous article’s explanation was that the X-series absorbed a different series wholesale. That explanation is correct for three vehicles and does not extend to this one, which means the broadening of the X-series has at least two mechanisms rather than one. A series that has admitted a sounding rocket, an air-launched missile, an autonomous testbed, and now an intercontinental ballistic missile did not do so by a single decision, and any account that offers one is too tidy. The series’ closing article has to carry both mechanisms and probably more.

The Source Base

The contrast with the previous article is sharp and it is worth stating as a controlled result.

The Navaho record is absent from the defence archive and the Atlas record is present. The X-10 article reports that the Defense Technical Information Center reports registered under the Crossref publisher prefix hold nothing about the Navaho under the project number MX-770, while the adjacent MX-776 yields a report on the RASCAL weapon system, named for its radar scanning link. The same archive holds, for the Atlas, the Flight Test Working Group reports for individual missiles, the multi-volume Difficulties Review of the Atlas booster and its ground support systems, propellant-loading system design, and engine system-test data. Same archive and same kind of record, and the difference is that one programme was cancelled in 1957 and the other flew in its balloon-tank form until 2005. The specific documents are General Dynamics/Astronautics San Diegoca 1961 and its companion flight test reports, the five volumes of General Dynamics San Diego Ca Convair Div 1966a, and Peters and Hall 1963 on engine system-test data, with the programme-level history in Rockefeller and Alfred 1960. The narrative of the programme comes from its official histories, Neufeld for the Air Force and Cleary for the launch record at Cape Canaveral, and from NASA’s history of the Centaur in Dawson and Bowles, and the vehicle’s measured structure and pressures come from NASA’s flight report on a later Atlas. Cleary calls the vehicles Series A missiles throughout, and neither Cleary nor Dawson and Bowles uses the X-11 designation.

The aerospace archive holds the discipline rather than the vehicle, and for this article that is the right trade. The keystone is a structural principle, and the shell-buckling and pressure-stabilisation literature is large, contemporary with the design, and directly applicable. The survey holds 872 records from the Technical Reports Server of the National Aeronautics and Space Administration, the NTRS, and the ones that matter most, namely the pressurised-cylinder buckling correlation and the imperfection-sensitivity measurements, are exactly the documents a designer of this vehicle would have had on his desk.

What is thin is the X-11 as such. The designation appears in compilations and the flight record is well attested, but the accessible record concerns the Atlas A rather than a vehicle called X-11, and no programme document found for this article uses the X designation, which only Parsch 2002a applies, to the single-engine and three-engine test vehicles of the 1953 plan. That is the fourth consecutive article in which the X number is an administrative label rather than a name anyone used, and the pattern identified in the previous article now has more instances than the series has counterexamples in this stretch.

The mass data is the specific gap. No empty or propellant mass for the Atlas A itself has been found, so the article uses Atlas D figures throughout and says so wherever they appear. The only Atlas A mass on record is the planned 181,000 pounds of the Series A test missiles, which is

\[\frac{181{,}000}{243{,}000} = 0.745 \tag{105}\]

of the Series C and D figure in the same source. A vehicle with the same shell and three quarters of the gross mass cannot have had a better structural fraction unless its dry mass fell in proportion, and nothing in the record suggests it did, so the structural fraction used here is probably better than the X-11 achieved and the range figures correspondingly optimistic. That direction is an inference and not a measurement, and its size is unknown.

The survey rests on 5,685 research records drawn from Crossref, the NASA Technical Reports Server and the Defense Technical Information Center, of which 1,194, being 21.0 percent, are report primaries by the identifier rule set out under The Definition of Primary. 73 of the 5,561 dated records, being 1.3 percent, were published between 1946 and 1958, from the MX-774 contract to the last Atlas A flight, while 1,839, being 33.1 percent, date from 2015 or later. The median publication year is 2005, and the records fall into 17 clusters.

The period’s own record is thin in these archives. Of the records from those years, 21 concern rocket propulsion and 18 thin shells and their buckling, while the cluster of the Atlas’s own record holds 0 of them and has no record from the development years at all, so the open literature of the development years is mostly the research around the programme rather than the programme. The programme’s own documents appear later, as flight evaluations of the launch vehicle and as histories, which is why that cluster’s median publication year is 1969.

The Definition of Primary

Primacy is read from the identifier. A record is a report primary when its address is a NASA Technical Reports Server citation or a digital object identifier under the 10.21236 prefix, which Crossref registers for Defense Technical Information Center reports. Of the 1,194 report primaries, 872 are NASA reports and 322 are Defense Technical Information Center reports.

The rule does not reach the journal papers, conference papers and books in which the programme’s engineers and historians published, so 21.0 percent is a lower bound on how much of the survey is first-hand. The official histories and the launch record on which the narrative rests are books and are cited as such.

Thin Subjects

Four subjects that this article’s derivations depend on have thin literatures. Each count below is the number of research records in this survey whose title carries at least one of the listed terms, with a hyphen read as a space.

Subject	Title terms counted	Records
the pressure-stabilised propellant tank itself	balloon tank, pressure-stabilized, pressure-stabilised	10
the one-and-a-half stage arrangement	1 1/2-stage, stage and a half, one and a half stage	3
structural mass fraction and the rocket equation	mass fraction, mass ratio, propellant fraction, rocket equation, Tsiolkovsky	3
reliability inferred from a short flight series	binomial, small sample, few flights, zero failure	1

The keystone is the clearest case. Of the 10 records that name a balloon tank or a pressure-stabilised structure, 3 concern a vehicle, being a bending test of a large pressure-stabilised cylinder, a skin-strain measurement on the Centaur and a foam insulation for pressure-stabilised hydrogen tanks, 6 concern pressure-stabilised beams and arches, and the remaining 1 concerns hydraulic pressure stabilisation for pogo suppression. The structural principle of the Atlas is published under other names, as the buckling of internally pressurised cylinders and as inflatable structure, which is why those two clusters are large while this count is small.

The arrangement and the arithmetic are thinner still. The 3 records naming a one-and-a-half stage vehicle all concern the National Launch System, and of the 3 naming mass fraction, mass ratio or the rocket equation, 1 dates from the Atlas period. That range is governed by the logarithm of the mass ratio is textbook material rather than a research finding, so the article’s central relation stands on the derivation rather than on a literature. The small-sample count of 1 is a study of imperfection fields in welded shells and not of flight reliability, so the binomial reasoning applied above to eight flights has no counterpart among these titles.

What the Survey Admits

A record is admitted only when a person reading its title finds it on this article’s subject, which is the Atlas and the intercontinental ballistic missile programmes it belonged to, the pressure-stabilised thin shell and its buckling, the propellant tank, the loads, dynamics, slosh, pogo and acoustics of ascent, the rocket engines, guidance, the reentry vehicle, the material and its proof test, flight-test reliability, and the launcher line the missile became. Many of this subject’s words also name something else, and a record that shares only such a word is excluded. Atlas also names a detector at CERN, a satellite laser instrument, brain and anatomical atlases, a luggage engine and a journal, and Centaur also names a class of asteroid and an industrial gas turbine. Navaho also names a people and their language, Cape Canaveral is also a coastline studied for its geology and wildlife, and Bossart is also the name of an artist, a marine biologist and an ecologist. Reentry also names a cardiac arrhythmia and the return of prisoners to society, boil-off also names the losses of liquefied natural gas carriers and a textile process, pressure-stabilised also describes chemical compounds formed at high pressure, and Rocketdyne also appears on accelerators, solar receivers and reformers the company built. Missile defence and target tracking, missile proliferation policy, tactical missiles, environmental assessments and the crashworthiness of thin-walled beams are excluded as other subjects. Correction and withdrawal notices, abstract and patent digests, dictionary entries and the indexes of other works are excluded as well, because a survey counts research works and those are editorial events or parts of works. So are trade and press news, book reviews, press kits and the digital heritage deposits of launch sites, which are not research works. A reference or definition entry, a notice such as front matter, an editorial or an announcement, and a second deposit of a document already counted are not admitted either, since none of them is a research work in its own right.

A record whose only link to this subject is aeronautics in general is excluded too, and so is one whose subject is a vehicle or a propulsion class the argument never uses. Aerofoil and wing aerodynamics including aerofoil buffet, the gust load alleviation of flexible aircraft, aircraft engines and drones are such subjects, and so are nuclear, hybrid, electric, electromagnetic and beam-powered propulsion and the propulsion of solid rocket motors as such, from propellant combustion and its instability to grain and motor design. The recovery and landing of a booster or stage is excluded as a subject the argument does not use, while reuse as a design objective or an economic question is admitted, because the argument that the Atlas won the trade of mass against handling cost and then lost it is made in those terms. Launch policy, regulation, acquisition and the operations research of ground processing are excluded, as are plates, beams and lattices that are not shells, and the payloads a missile or launcher carries. The residual cluster on launch vehicle design, programmes and operations admits a title only when it concerns the design, programme history, processing or avionics of a launcher, and not when its subject is any of these excluded ones.

Some records of doubtful relevance are kept. Shell-buckling studies whose application is a storage tank, a submarine hull, an offshore foundation or a pipe, slosh studies of rectangular and horizontal tanks, cryogenic stainless steels developed for magnets and hydrogen service, and the fracture and burst testing of industrial pressure vessels each share a method or a quantity with this subject, so each is kept and a reader may weigh it accordingly. The bridge, wind turbine, stay-cable and solar panel studies cited in the body are kept for their identification, damping and wind-load methods, solid motors appear where their subject is thrust vector control, trajectory, case structure or the dynamics of a missile programme, and the storage studies of liquefied gas at sea because their sentence claims only that they reduce boil-off gas and model insulation.

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

Epistemic State

Historical fact, well supported. Eight Atlas A vehicles flew from Cape Canaveral between 11 June 1957 and 3 June 1958, five from Launch Complex 14 and three from Launch Complex 12, the first two failing and the third and fourth succeeding by the Cape’s launch history, and three succeeding in all by the official history Cleary 1991 The 6555th, Missile and Space Launches Through 1970. Missile 12A burned for two full minutes and flew some 600 miles downrange, and the official history gives the series’ maximum range and altitude as 600 and 57.5 nautical miles, so the unit of the 12A figure is not settled. The Atlas A booster thrust was raised during the series from 270,000 to 300,000 pounds. The first flight tumbled and the structure held until the range safety officer destroyed it. The MX-774 study contract was awarded in April 1946 and cancelled in July 1947, and the MX-1593 contract was signed on 23 January 1951 Neufeld 1990 The Development of Ballistic Missiles in the United States Air Force, 1945-1960. The programme designation was WS 107A-1 Cleary 1991 The 6555th, Missile and Space Launches Through 1970, and the design authority was Karel Bossart at Convair, who had already used nitrogen pressure in place of stiffeners on MX-774 Dawson and Bowles 2004. The Atlas A flew without a sustainer engine Parsch 2005 Convair B-65/SM-65/CGM-16/HGM-16 Atlas. A later Atlas has pressure-stabilised tanks of 301 extra-full-hard stainless steel between 0.014 and 0.037 inches thick, regulated in flight at 57 to 60 pounds per square inch gauge in the fuel tank and 28.5 to 31 in the oxidizer tank Atlas-Centaur AC-12 Flight Performance 1968. The operational Atlas uses a one-and-a-half stage arrangement in which two booster engines and a skirt are jettisoned and the sustainer continues on the same tanks SM-65 Atlas. The Navaho was terminated by an Air Force Headquarters message of 12 July 1957, thirty-one days after the first Atlas A flight. The first Atlas B flew on 19 July 1958 Cleary 1991 The 6555th, Missile and Space Launches Through 1970.

Reported but from compilations rather than programme documents. The X-11 and X-12 designations for Atlas A and Atlas B, which no programme document found for this article uses and which the directory entry places in a plan of 1953 for single-engine and three-engine test vehicles Parsch 2005 Convair B-65/SM-65/CGM-16/HGM-16 Atlas. The masses used here, which are Atlas D figures, since no Atlas A empty mass has been found SM-65 Atlas. The 282 second specific impulse and the 133 second burn time, against the two full minutes the official history gives. The 341,128 pound booster thrust, which the official history’s 270,000 to 300,000 pounds and the same compilation’s narrative contradict. The flight apogees, which exceed the official series maximum of 57.5 nautical miles on four flights, and the individual outcomes of the last four flights. The failure causes beyond the two the launch history names Convair X-11. The party-balloon inspiration balloon tank. The five pounds per square inch standing pressure, which is the article’s single most quoted number and which rests on secondary compilation rather than on a specification SM-65 Atlas. The Titan I empty masses set against the two-stage comparison, which rest on a single compilation, and the compilation’s Titan I loaded masses, which the operating manual’s tank capacities contradict for the second stage and which are used here only as the alternative HGM-25A Titan I.

The mass substitution is the largest weakness in the quantitative argument and its direction is inferred. The Atlas A was planned at 181,000 pounds against 243,000 for the later test series on the same shell Cleary 1991 The 6555th, Missile and Space Launches Through 1970, so the structural fraction used here is probably better than the fraction the X-11 achieved, and every range figure derived from it is correspondingly optimistic. What the substitution does not affect is the sensitivity, since the range table varies the structure about whatever baseline is chosen, and the two-stage comparison, which is a calculation about configurations rather than about this vehicle.

Engineering analysis, derived here and independently checkable. The radius-to-thickness ratios and the drink-can comparison. The membrane stresses, the fixed hoop-to-axial ratio of two, and the demonstration that the light gauge cannot exist at full pressure. The acceleration head and its ratio to ullage pressure. The classical buckling stresses, the knocked-down allowables, and the sensitivity of every conclusion drawn from them to the choice of knockdown factor. The axial tension from standing pressure, the pressure required to offset buckling, and the finding that the reported five-pound specification is consistent only with a knockdown below about 0.4. The critical bending moment and its independence of thickness. Euler column buckling at 121 times the empty weight. The tank volume, propellant split, and nitrogen mass, giving a structure-to-gas ratio of 103. The common-bulkhead saving. The mass fractions, mass ratio, and ideal velocity. The loss calibration, the range sensitivity table, and the two-stage comparison showing a crossover near an eight and a half percent structural fraction. The Titan I structural fractions derived from tank capacities, the Titan-proportioned vehicle, and the range of the Atlas half-stage rebuilt at the Titan I first-stage fraction. The staging gain of 1044 metres per second. The thrust-to-weight, propellant flow, burn consumption, and axial load factor at cutoff. The maximum dynamic pressure, its occurrence at one scale height, and the aerodynamic bending moment. The acoustic power, sound pressure level, and pressure fluctuation. The slosh frequency. The skin thermal time constant. The Allen and Eggers peak deceleration and its independence of ballistic coefficient. The boil-off rate. The proof and burst factor chain. The tank figure of merit. The orbital comparison. The binomial standard error on the success rate and the demonstration that no trend is detectable across eight flights.

Inference, argued but not established. That the balloon tank and the one-and-a-half stage arrangement reinforce each other and do not trade against each other, which the staging computation supports but does not prove. That the X-11’s keystone being exercised early is why a short flight sufficed, in contrast to the X-10, whose drift rate needed more navigation flights than were completed. That pressure-stabilised vehicles are unusually exposed to pogo because longitudinal stiffness varies with tank pressure. That the design was abandoned because handling cost outlasted the mass-fraction constraint.

A qualification the article makes against itself. The range table compares the Atlas against a heavier version of itself, which is not the comparison a designer in 1951 faced. Setting it against a conventional two-stage vehicle instead puts the crossover near an eight and a half percent structural fraction, and a vehicle built to Titan I proportions, with stages of about 5.0 and 8.5 percent, outranges the Atlas. Rebuilt at the Titan I first-stage fraction, the Atlas half-stage falls short of its range by between a seventh and a fifth. The balloon tank therefore made a single-and-a-half-stage intercontinental vehicle possible without making it the lighter answer, and the article states this in a dedicated section and does not leave the stronger claim standing.

Assumptions made explicit. A flight tank pressure of 60 pounds per square inch, the top of the fuel-tank regulation band recorded for a later Atlas, applied to the heavy gauge, while the oxidizer tank of that Atlas ran at about half, and every membrane stress in the article scales with it directly. Material properties for 301 extra-full-hard stainless steel of 965 megapascals yield, 1276 ultimate, and 193 gigapascals modulus. A knockdown factor of 0.2, whose effect on every conclusion drawn from it is tabulated in a separate section. A tank length of 18 metres, which the tank stations of a later Atlas show to be about thirteen percent long, and a steel density of 8000 kilogrammes per cubic metre. Ten metres of liquid oxygen head at six times gravity. A mixture ratio of 2.25 with propellant densities of 1141 and 800. A jettisoned booster package of three tonnes. A drag coefficient of 1.2 and a uniform wind profile for the standing case. A convective coefficient of 200 watts per square metre kelvin for the skin and 10 for the tank, a specific heat of 500, and a latent heat of 213 kilojoules per kilogramme. An acoustic conversion efficiency of half of one percent. A normal-force slope of two per radian and three degrees of incidence at maximum dynamic pressure. A scale height of 7200 metres and a net acceleration of three metres per second squared for the dynamic-pressure derivation. An entry speed of seven kilometres per second at thirty degrees for the reentry result. A tumble rate of one revolution per second for the first flight. Equal propellant split and equal structural fraction per stage for the two-stage comparison. And the gravity and drag loss of 1337 metres per second, which is calibrated rather than derived and which fixes the first row of the range table by construction.

Where the assumptions matter most. The flight pressure and the knockdown factor carry more of the article than any other input. Every hoop stress, every margin, and the burst chain move linearly with the first, and the compressive allowable, the pressure-to-offset-buckling figure, and the sixty-seven-fold asymmetry all move with the second. The article tabulates the second and does not tabulate the first, which is an asymmetry in the treatment rather than in the physics, and a reader who doubts the sixty-pound figure should scale the membrane results accordingly.

Where information postdates the editorial date. The contemporary literature section is written from current knowledge, and the Atlas V abandonment of the balloon tank in 2002 and the subsequent history are stated from current knowledge rather than from the vantage of 1957.

Out of Scope

The Atlas B, C, D, E, and F, of which the B is the next article. The reentry vehicle and the warhead. The radio-inertial and later all-inertial guidance systems in any depth. Silo and coffin basing. The Atlas as a space launch vehicle beyond noting that it became one. Centaur, which kept the balloon tank and deserves separate treatment. The MX-774 predecessor beyond its role in the origin. Comparative economics against Titan and Minuteman, and the two-stage comparison above is a structural calculation rather than a programme comparison. The Soviet R-7, which solved the same problem with a different configuration entirely and would make the best single comparison this article does not attempt. Manufacturing tooling and the factory, which for a structure of this gauge is a larger subject than the design and which the sources for this article barely touch. The Mercury programme and the man-rating that followed.

Conclusion

The X-11 is a fuel tank that flies. Its skin is thinner in proportion than a drink can, its compressive strength is two hundred times smaller than its tensile strength, and it is held up by a pressure a bicycle tyre would find low. Every one of those facts is a consequence of one relation, which is that the rocket equation returns velocity logarithmically in mass ratio, so a weapon that must reach ten thousand kilometres has to spend its structural budget as though it were the last money it had.

The arithmetic above puts a number on it. Making the structure half as efficient turns an intercontinental missile into an intermediate-range one, and no amount of better engine or better trajectory recovers it. Bossart’s balloon was not a clever trick. It was the only available answer to a question that had been posed in the form of a logarithm.

Closer scrutiny qualifies that. Set against a conventional two-stage vehicle rather than against a heavier Atlas, the crossover sits near an eight and a half percent structural fraction, and a vehicle built to Titan I proportions outranges the Atlas on the same propellant. The balloon tank did not make the intercontinental missile possible. It made this particular intercontinental missile possible without an altitude ignition, at a structural fraction less than a percentage point below the best conventional stage of the period, a margin that costs a half-stage vehicle between a seventh and a fifth of its range, and the field subsequently went the other way and stayed there. Bossart’s answer was right for the vehicle he was building and was not the only answer to the question.

What remains true after all the qualification is the shape of the problem rather than the size of the answer. A weapon specified by range is specified by a logarithm, and a logarithm rewards nothing except mass ratio. Every distinctive feature of this vehicle follows from that and from nothing else. The tank is thin because the logarithm punishes thickness. The tank is pressurised because a thin tank in compression buckles at less than a twenty-fifth of the stress it can carry in tension. The engines are dropped and the tanks are not because the logarithm cares about burnout mass and an altitude ignition was not trusted. The vehicle cannot stand up because none of those decisions left anything over for standing up.

There is a second result, and its subject is the series, not the vehicle. The X-10 could not settle its keystone in five navigation flights and the X-11 tested its keystone completely in its first two minutes, and the difference is that a structural load is applied in full early on every flight while a drift rate is a statistical quantity that needs many flights to estimate. The two vehicles are separated by one designation, the first Atlas A flew thirty-one days before the Navaho was terminated, they were built by rival contractors for the same mission, and the reason one testbed worked and the other did not has nothing to do with either company. It follows from the quantity being measured, and it becomes visible only when the vehicles are read in order.

A last point concerns the tank, which has outlived every argument made about it here. Bossart’s shell is still flying, on Centaur Centaur rocket stage, on the stage that has the strongest possible reason to care about mass and the weakest possible reason to care about being set down empty in a hangar. An idea that was adopted because a weapon needed range, abandoned because a launcher needed convenience, and retained where neither consideration applies has been tested about as thoroughly as an engineering idea can be. It turns out to be right in the conditions where the arithmetic above says it should be, which is not something one can say of many designs that are seventy years old.

Equations

This section collects the 105 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 105, 47 are established and 58 are bespoke. Quantities are in International System units on a spherical Earth of radius 6,371 kilometres with $g = 9.80665$ metres per second squared, pounds per square inch are converted at 6,894.76 pascals each, the masses are Atlas D figures and the skin gauges and tank pressures those of a later Atlas, all applied to the Atlas A, and symbols are reused, so that $t$ is the skin thickness except in Equations 52, 53 and 57, where it is time, $p$ is a pressure except in Equations 95 to 98, where it is a probability of success, $n$ is a load factor except in Equations 97 and 98, where it is a number of flights, $R$ is the range except in Equation 29, where it is the gas constant of nitrogen, $T$ is the thrust except in Equation 29, where it is the gas temperature, $V$ is a volume except in Equations 42 and 43, where it is the wind speed, $I$ is a second moment of area except in Equations 73 and 75, where it is the acoustic intensity, $c$ is a speed of sound except in Equation 70, where it is a specific heat, $h$ is a height or an altitude except in Equations 70 and 88, where it is a convective coefficient, and $v_{e}$ is the exhaust velocity except in Equation 85, where it is the entry speed.

Equation 1, Tsiolkovsky Rocket Equation. The ideal velocity a rocket gains grows with the logarithm of the ratio of its gross mass to its burnout mass. Sutton and Biblarz 2016 Rocket Propulsion Elements

\[\Delta v = v_{e} \ln \frac{m_{0}}{m_{f}} \tag{1}\]

Equation 2, Structural Mass Fraction of the Atlas D. The Atlas D burnout mass is 4.58 percent of its gross mass. SM-65 Atlas

\[\frac{m_{s}}{m_{0}} = \frac{5395}{117{,}900} = 0.0458 \tag{2}\]

Equation 3, Mass Ratio of the Atlas D. The Atlas D gross mass is 21.85 times its burnout mass. SM-65 Atlas

\[\frac{m_{0}}{m_{f}} = \frac{117{,}900}{5395} = 21.85 \tag{3}\]

Equation 4, Ideal Velocity of the Atlas D. The rocket equation at a specific impulse of 282 seconds and the Atlas D mass ratio gives 8,530 metres per second before gravity and drag losses.

\[\Delta v = 2765 \times \ln 21.85 = 8530 \, \text{m/s} \tag{4}\]

Equation 5, Bespoke Calibrated Ascent Loss. The loss is defined as whatever separates the ideal velocity from the 7,193 metre per second burnout speed of a 10,000 kilometre minimum-energy arc, so it is a calibration and not a derived loss.

\[v_{\text{loss}} = \Delta v - v_{bo} = 8530 - 7193 = 1337 \, \text{m/s} \tag{5}\]

Equation 6, Bespoke Burnout Speed Against Structural Mass. The structural mass is scaled by a factor $k$ while the propellant load and the calibrated loss are held fixed.

\[v_{bo}(k) = v_{e} \ln \frac{m_{p} + k m_{s}}{k m_{s}} - v_{\text{loss}} \tag{6}\]

Equation 7, Ballistic Range Law. On a spherical non-rotating Earth the central angle of a ballistic arc flown at the optimum flight path angle is fixed by the energy parameter $\lambda$, the ratio of burnout kinetic energy to that of a grazing circular orbit.

\[\sin \frac{\Phi}{2} = \frac{\lambda}{2 - \lambda}, \qquad \lambda = \frac{v_{bo}^{2}}{g R_{e}}, \qquad R = R_{e} \Phi \tag{7}\]

Equation 8, Bespoke Sizing Fraction of the Atlas Mission. The 133 second burn is set against the 1,932 second flight time derived for a 10,000 kilometre arc, a figure of merit the article introduces.

\[\frac{t_{\text{sizing}}}{t_{\text{mission}}} = \frac{133}{1932} = 0.069 \tag{8}\]

Equation 9, Bespoke Leg Fraction of the Navaho Mission. A thousand-kilometre leg at top speed is set against the whole Navaho mission time, the comparison figure for the previous article’s vehicle.

\[\frac{t_{\text{leg}}}{t_{\text{mission}}} = \frac{1653}{10{,}333} = 0.16 \tag{9}\]

Equation 10, Tank Radius. Half of the recorded ten foot diameter is 1.524 metres. Cleary 1991 The 6555th, Missile and Space Launches Through 1970

\[r = \frac{10 \times 0.3048}{2} = 1.524 \, \text{m} \tag{10}\]

Equation 11, Radius-to-Thickness Ratio of the Skin. The tank radius over the light and heavy gauges of the later Atlas drawing gives ratios of 4,286 and 1,622. Atlas-Centaur AC-12 Flight Performance 1968

\[\frac{r}{t} = \frac{1.524}{0.000356} = 4286 \qquad \frac{r}{t} = \frac{1.524}{0.000940} = 1622 \tag{11}\]

Equation 12, Bespoke Radius-to-Thickness Ratio of a Drink Can. The benchmark assumes a can wall of 0.1 millimetres on a radius of 33 millimetres.

\[\left. \frac{r}{t} \right|_{\text{can}} = \frac{0.033}{0.0001} = 330 \tag{12}\]

Equation 13, Thin-Walled Hoop Stress. Internal pressure in a thin cylinder produces a circumferential membrane stress equal to pressure times radius over thickness.

\[\sigma_{\theta} = \frac{p r}{t} \tag{13}\]

Equation 14, Thin-Walled Axial Stress. Pressure acting on the closed ends of a thin cylinder produces an axial membrane stress half the hoop stress.

\[\sigma_{z} = \frac{p r}{2 t} \tag{14}\]

Equation 15, Ratio of Hoop to Axial Stress. In a closed thin cylinder under pressure the hoop stress is always twice the axial stress.

\[\frac{\sigma_{\theta}}{\sigma_{z}} = 2 \tag{15}\]

Equation 16, Hoop Stress at Fuel-Tank Pressure and Heavy Gauge. The 60 pound per square inch fuel-tank pressure on the heavy gauge gives a hoop stress of 671 megapascals. Atlas-Centaur AC-12 Flight Performance 1968

\[\sigma_{\theta} = \frac{413{,}685 \times 1.524}{0.000940} = 671 \, \text{MPa} \tag{16}\]

Equation 17, Bespoke Hoop Stress of the Light Gauge at Fuel-Tank Pressure. The light gauge is placed under the fuel-tank pressure it never carries, a counterfactual that shows why the gauge must taper.

\[\sigma_{\theta} = \frac{413{,}685 \times 1.524}{0.000356} = 1771 \, \text{MPa} \tag{17}\]

Equation 18, Bespoke Hoop Stress of the Light Gauge at Oxidizer-Tank Pressure. The recorded oxidizer-tank range of 28.5 to 31 pounds per square inch is reduced to a single 30 pounds on the light gauge.

\[\sigma_{\theta} = \frac{206{,}843 \times 1.524}{0.000356} = 885 \, \text{MPa} \tag{18}\]

Equation 19, Hydrostatic Head Under Acceleration. A liquid column of height $h$ under a load factor $n$ adds a pressure equal to density times load factor times gravity times height.

\[\Delta p = \rho \, n \, g \, h \tag{19}\]

Equation 20, Bespoke Liquid Oxygen Head Near Burnout. The head assumes ten metres of liquid oxygen at six times gravity, a load factor chosen near the later Atlas’s recorded 5.62.

\[\Delta p = 1141 \times 6 \times 9.80665 \times 10 = 671{,}000 \, \text{Pa} = 97 \, \text{psi} \tag{20}\]

Equation 21, Area of a Hemispherical Dome. A hemisphere of the tank radius has an area of 14.6 square metres.

\[A_{\text{dome}} = 2 \pi r^{2} = 2 \pi \times 1.524^{2} = 14.6 \, \text{m}^{2} \tag{21}\]

Equation 22, Bespoke Intertank Barrel Area. The barrel is assumed to be two radii long, enough to clear two hemispherical domes.

\[A_{\text{barrel}} = 2 \pi r \times 2r = 4 \pi r^{2} = 29.2 \, \text{m}^{2} \tag{22}\]

Equation 23, Bespoke Mass Saved by the Common Bulkhead. The saved dome and barrel area is taken at an average gauge of 0.648 millimetres and a steel density of 8,000 kilogrammes per cubic metre.

\[m_{\text{saved}} = 43.8 \times 0.000648 \times 8000 = 227 \, \text{kg} \tag{23}\]

Equation 24, Bespoke Tank Volume. The tank is treated as a cylinder of an assumed 18 metres, a length the record does not confirm.

\[V = \pi r^{2} L = \pi \times 1.524^{2} \times 18 = 131 \, \text{m}^{3} \tag{24}\]

Equation 25, Bespoke Liquid Oxygen Load. The Atlas D propellant load is divided at a representative mixture ratio of 2.25.

\[m_{\text{LOX}} = m_{p} \frac{MR}{1 + MR} = 112{,}505 \times \frac{2.25}{3.25} = 77{,}888 \, \text{kg} \tag{25}\]

Equation 26, Bespoke Propellant Fill Fraction. The propellant volume is set against the volume of the assumed 18 metre tank.

\[\frac{111.5}{131} = 0.85 \tag{26}\]

Equation 27, Tank Span From the Station Numbers. The tank stations of the later Atlas, 570 to 1,198 inches, span 15.95 metres. Atlas-Centaur AC-12 Flight Performance 1968

\[\ell = (1198 - 570) \times 0.0254 = 15.95 \, \text{m} \tag{27}\]

Equation 28, Bespoke Volume and Fill Fraction of the Recorded Span. The recorded span is treated as a full cylinder, domes included, which bounds the volume from above.

\[V' = \pi \times 1.524^{2} \times 15.95 = 116.4 \, \text{m}^{3}, \qquad \frac{111.5}{116.4} = 0.958 \tag{28}\]

Equation 29, Bespoke Mass of Standing Nitrogen. The ideal gas law is applied at five pounds per square inch and an assumed 290 kelvin to the volume of the assumed 18 metre tank.

\[m_{N_{2}} = \frac{p V}{R T} = \frac{34{,}474 \times 131}{296.8 \times 290} = 52.5 \, \text{kg} \tag{29}\]

Equation 30, Bespoke Tank Mass per Unit Volume. A figure of merit the article introduces divides the bare skin mass of the assumed tank by its volume.

\[\eta_{\text{tank}} = \frac{m_{\text{skin}}}{V} = \frac{893}{131} = 6.8 \, \text{kg/m}^{3} \tag{30}\]

Equation 31, Bespoke Mean Propellant Density. The propellant volume rests on the assumed mixture ratio of 2.25 and densities of 1,141 and 800 kilogrammes per cubic metre.

\[\bar{\rho}_{p} = \frac{m_{p}}{V_{p}} = \frac{112{,}505}{111.5} = 1009 \, \text{kg/m}^{3} \tag{31}\]

Equation 32, Classical Axial Buckling Stress of a Cylinder. A perfect thin cylinder in axial compression buckles at a stress proportional to the modulus and to thickness over radius. NASA 1968 Buckling of Thin-Walled Circular Cylinders

\[\sigma_{cr} = \frac{E t}{r \sqrt{3 (1 - \nu^{2})}} \tag{32}\]

Equation 33, Classical Buckling Stress of the Heavy Gauge. For stainless steel at 193 gigapascals and a Poisson ratio of 0.3 the heavy gauge has a classical buckling stress of 72.0 megapascals.

\[\sigma_{cr} = \frac{193 \times 10^{9} \times 0.000940}{1.524 \times 1.652} = 72.0 \, \text{MPa} \tag{33}\]

Equation 34, Bespoke Knocked-Down Buckling Allowable. A knockdown factor of 0.2 is adopted, slightly above the 0.18 that NASA’s criterion gives at a radius-to-thickness ratio of 1,500.

\[\sigma_{\text{allow}} = 0.2 \times 72.0 = 14.4 \, \text{MPa} \tag{34}\]

Equation 35, Bespoke Second Moment of Area of the Shell. The thin-walled second moment of area is evaluated at an average gauge of 0.648 millimetres.

\[I = \pi r^{3} t = \pi \times 1.524^{3} \times 0.000648 = 7.20 \times 10^{-3} \, \text{m}^{4} \tag{35}\]

Equation 36, Bespoke Euler Load of the Vehicle as a Column. The vehicle is treated as a uniform cantilever at the average gauge with an effective length factor of two.

\[P_{cr} = \frac{\pi^{2} E I}{(K L)^{2}} = \frac{\pi^{2} \times 193 \times 10^{9} \times 7.20 \times 10^{-3}}{(2 \times 23.11)^{2}} = 6.42 \, \text{MN} \tag{36}\]

Equation 37, Axial Tension From the Standing Pressure. Five pounds per square inch on the heavy gauge gives an axial tension of 27.9 megapascals.

\[\sigma_{z} = \frac{34{,}474 \times 1.524}{2 \times 0.000940} = 27.9 \, \text{MPa} \tag{37}\]

Equation 38, Bespoke Pressure Required to Offset Buckling. The required pressure is defined by setting the pressure-induced axial tension equal to the knocked-down buckling allowable, a first-order criterion.

\[p_{\text{req}} = \frac{2 t \sigma_{\text{allow}}}{r} \tag{38}\]

Equation 39, Bespoke Required Pressure at the Heavy Gauge. The criterion at the adopted knockdown factor of 0.2 gives 2.58 pounds per square inch.

\[p_{\text{req}} = \frac{2 \times 0.000940 \times 14.4 \times 10^{6}}{1.524} = 17{,}768 \, \text{Pa} = 2.58 \, \text{psi} \tag{39}\]

Equation 40, Moment at Which Pressure Tension Is Cancelled. Equating the extreme-fibre bending stress of a thin cylinder to its axial pressure stress gives a critical moment independent of the skin thickness.

\[\frac{M r}{\pi r^{3} t} = \frac{p r}{2 t} \quad \Longrightarrow \quad M_{\text{crit}} = \frac{\pi p r^{3}}{2} \tag{40}\]

Equation 41, Critical Moment at the Standing Pressure. At five pounds per square inch and the tank radius the critical moment is 0.192 meganewton metres.

\[M_{\text{crit}} = \frac{\pi \times 34{,}474 \times 1.524^{3}}{2} = 0.192 \, \text{MN m} \tag{41}\]

Equation 42, Bespoke Base Moment From a Uniform Wind. The wind is assumed uniform with height, so its drag acts at mid-height of the vehicle.

\[M = \tfrac{1}{4} \rho V^{2} C_{D} D L^{2} \tag{42}\]

Equation 43, Bespoke Standing Wind Limit. The critical moment is inverted for wind speed under the uniform-wind model at an assumed drag coefficient of 1.2.

\[V = \sqrt{\frac{4 M_{\text{crit}}}{\rho C_{D} D L^{2}}} = \sqrt{\frac{4 \times 1.917 \times 10^{5}}{1.225 \times 1.2 \times 3.048 \times 23.11^{2}}} = 17.9 \, \text{m/s} \tag{43}\]

Equation 44, Bespoke Bare Skin Mass. The skin of the assumed 18 metre tank is taken at the average gauge and a steel density of 8,000 kilogrammes per cubic metre.

\[m_{\text{skin}} = 2 \pi r L t \rho = 2 \pi \times 1.524 \times 18 \times 0.000648 \times 8000 = 893 \, \text{kg} \tag{44}\]

Equation 45, Wall Thickness Sized by Hoop Tension. A pressure-stabilised wall must be thick enough that the hoop stress stays within the tensile allowable.

\[t_{\text{press}} = \frac{p r}{\sigma_{\text{allow,tension}}} \tag{45}\]

Equation 46, Wall Thickness Sized by Compression. A stiffened wall must be thick enough that its axial running load stays within its compressive allowable.

\[t_{\text{stiff}} = \frac{N_{x}}{\sigma_{\text{allow,compression}}} \tag{46}\]

Equation 47, Bespoke Ratio of Tensile to Compressive Allowable. An assumed yield of 965 megapascals is set against the allowable of the adopted knockdown factor.

\[\frac{\sigma_{\text{tension}}}{\sigma_{\text{compression}}} = \frac{965}{14.4} = 67 \tag{47}\]

Equation 48, Lift-Off Thrust-to-Weight of the Family. The compilation’s summary thrust over the Atlas D gross weight gives 1.31. Convair X-11

\[\frac{T}{W} = \frac{1.517 \times 10^{6}}{117{,}900 \times 9.80665} = 1.31 \tag{48}\]

Equation 49, Lift-Off Thrust-to-Weight of the Atlas A. Two early engines of 135,000 pounds against the 181,000 pound Series A missile give 1.49. Cleary 1991 The 6555th, Missile and Space Launches Through 1970

\[\left. \frac{T}{W} \right|_{A} = \frac{2 \times 135{,}000}{181{,}000} = 1.49 \tag{49}\]

Equation 50, Propellant Mass Flow. Thrust over effective exhaust velocity gives a flow of 549 kilogrammes per second.

\[\dot{m} = \frac{T}{v_{e}} = \frac{1.517 \times 10^{6}}{2765} = 549 \, \text{kg/s} \tag{50}\]

Equation 51, Dynamic Pressure. Dynamic pressure is half the air density times the square of the speed.

\[q = \tfrac{1}{2} \rho(h) v(h)^{2} \tag{51}\]

Equation 52, Bespoke Dynamic Pressure of a Constant-Acceleration Vertical Ascent. The model assumes a vertical rise from rest at constant acceleration through an exponential atmosphere.

\[q(t) = \tfrac{1}{2} \rho_{0} e^{-a t^{2} / (2H)} (a t)^{2} \tag{52}\]

Equation 53, Bespoke Time of Maximum Dynamic Pressure. Setting the derivative of the idealised dynamic pressure to zero places its peak at one scale height.

\[\frac{dq}{dt} = 0 \quad \Longrightarrow \quad t_{q} = \sqrt{\frac{2H}{a}} \tag{53}\]

Equation 54, Bespoke Time of Maximum Dynamic Pressure Evaluated. A scale height of 7,200 metres and an assumed net acceleration of three metres per second squared give 69 seconds.

\[t_{q} = \sqrt{\frac{2 \times 7200}{3}} = 69 \, \text{s} \tag{54}\]

Equation 55, Bespoke Maximum Dynamic Pressure. Substituting the peak time into the idealised ascent gives the peak in terms of sea-level density, acceleration and scale height.

\[q_{\max} = \tfrac{1}{2} \rho_{0} e^{-1} (a t_{q})^{2} = \tfrac{1}{2} \rho_{0} e^{-1} \times 2 a H \tag{55}\]

Equation 56, Bespoke Maximum Dynamic Pressure Evaluated. The idealised ascent at the assumed acceleration peaks at 9,736 pascals, below the later Atlas’s measured 800 pounds per square foot.

\[q_{\max} = \tfrac{1}{2} \times 1.225 \times 0.3679 \times 2 \times 3 \times 7200 = 9736 \, \text{Pa} \tag{56}\]

Equation 57, Axial Load Factor Under Constant Thrust. At constant thrust and mass flow the axial load factor rises as propellant burns away.

\[n(t) = \frac{T}{\left( m_{0} - \dot{m} t \right) g} \tag{57}\]

Equation 58, Axial Load Factor Near Booster Cutoff. The family thrust on the Atlas D mass less 133 seconds of propellant flow gives 3.44.

\[n = \frac{1.517 \times 10^{6}}{\left( 117{,}900 - 72{,}977 \right) \times 9.80665} = 3.44 \tag{58}\]

Equation 59, Normal Force on a Slender Body. At small incidence the normal force is dynamic pressure times reference area times normal-force slope times angle of attack.

\[N = q S C_{N\alpha} \alpha \tag{59}\]

Equation 60, Bespoke Normal Force at Maximum Dynamic Pressure. The force assumes a normal-force slope of two per radian and three degrees of incidence at the idealised dynamic pressure.

\[N = 9736 \times 7.30 \times 2 \times 0.0524 = 7447 \, \text{N} \tag{60}\]

Equation 61, Bespoke Velocity Gain From Jettison. Two applications of the rocket equation are differenced to give the velocity the sustainer gains by not carrying the jettisoned mass.

\[\Delta v_{\text{gain}} = v_{e} \left[ \ln \frac{m_{1}}{m_{f}} - \ln \frac{m_{1} + m_{j}}{m_{f} + m_{j}} \right] \tag{61}\]

Equation 62, Propellant Left for the Sustainer. The Atlas D propellant load less 133 seconds of booster flow leaves 39,528 kilogrammes.

\[m_{\text{sust}} = m_{p} - \dot{m} t_{b} = 112{,}505 - 72{,}977 = 39{,}528 \, \text{kg} \tag{62}\]

Equation 63, Sustainer Velocity After Jettison. The rocket equation from the staging mass to the Atlas D burnout mass gives 5,861 metres per second.

\[\Delta v_{\text{dropped}} = 2765 \ln \frac{44{,}923}{5395} = 5861 \, \text{m/s} \tag{63}\]

Equation 64, Bespoke Sustainer Velocity Without Jettison. The booster package is assumed to weigh three tonnes and to be carried to burnout.

\[\Delta v_{\text{carried}} = 2765 \ln \frac{47{,}923}{8395} = 4817 \, \text{m/s} \tag{64}\]

Equation 65, Bespoke Velocity Gain of the Half-Stage. Dropping the assumed three tonne package gains 1,044 metres per second.

\[\Delta v_{\text{gain}} = 5861 - 4817 = 1044 \, \text{m/s} \tag{65}\]

Equation 66, Proof Factor. The proof factor is the ratio of the test pressure to the design pressure.

\[k_{p} = \frac{p_{\text{proof}}}{p_{\text{design}}} \tag{66}\]

Equation 67, Bespoke Burst Factor. The burst factor is taken as at least 1.5, a value the article chooses and does not source.

\[k_{b} = \frac{p_{\text{burst}}}{p_{\text{design}}} \geq 1.5 \tag{67}\]

Equation 68, Bespoke Burst Hoop Stress. The chosen burst factor of 1.5 applied to the heavy-gauge hoop stress gives 1,007 megapascals.

\[\sigma_{\text{burst}} = 1.5 \times 671 = 1007 \, \text{MPa} \tag{68}\]

Equation 69, Bespoke Proof Hoop Stress. A chosen proof factor of 1.25 applied to the heavy-gauge hoop stress gives 839 megapascals.

\[\sigma_{\theta} = 1.25 \times 671 = 839 \, \text{MPa} \tag{69}\]

Equation 70, Thermal Time Constant of a Thin Skin. A thin skin heated by convection approaches equilibrium with a time constant of its heat capacity per unit area over the convective coefficient.

\[\tau_{\text{skin}} = \frac{\rho c \delta}{h} \tag{70}\]

Equation 71, Bespoke Skin Time Constant. The time constant assumes a convective coefficient of 200 watts per square metre kelvin on the heavy gauge.

\[\tau_{\text{skin}} = \frac{8000 \times 500 \times 0.00094}{200} = 18.8 \, \text{s} \tag{71}\]

Equation 72, Mechanical Power in the Jet. Half the mass flow times the square of the exhaust velocity gives 2.10 gigawatts.

\[P_{\text{jet}} = \tfrac{1}{2} \dot{m} v_{e}^{2} = \tfrac{1}{2} \times 549 \times 2765^{2} = 2.10 \, \text{GW} \tag{72}\]

Equation 73, Bespoke Acoustic Intensity at Thirty Metres. Half of one percent of the jet power is assumed to radiate as sound, spread over a hemisphere of thirty metres radius.

\[I = \frac{P_{\text{ac}}}{2 \pi d^{2}} = \frac{1.05 \times 10^{7}}{2 \pi \times 900} = 1855 \, \text{W/m}^{2} \tag{73}\]

Equation 74, Bespoke Sound Pressure Level. The standard decibel scale applied to the assumed intensity gives 153 decibels.

\[L_{p} = 10 \log_{10} \frac{I}{10^{-12}} = 153 \, \text{dB} \tag{74}\]

Equation 75, Bespoke Root-Mean-Square Pressure Fluctuation. The plane-wave relation applied to the assumed intensity gives 883 pascals.

\[p_{\text{rms}} = \sqrt{I \rho c} = \sqrt{1855 \times 1.225 \times 343} = 883 \, \text{Pa} \tag{75}\]

Equation 76, First Lateral Slosh Frequency of a Cylindrical Tank. The first antisymmetric sloshing mode of a liquid in an upright cylinder depends on the effective gravity, the radius and the fill depth.

\[\omega_{s} = \sqrt{\frac{1.841 \, g_{\text{eff}}}{r} \tanh \frac{1.841 h}{r}} \tag{76}\]

Equation 77, Bespoke Slosh Frequency at Three Times Gravity. The deep-tank limit is evaluated at an assumed load factor of three.

\[\omega_{s} = \sqrt{\frac{1.841 \times 3 \times 9.80665}{1.524}} = 5.96 \, \text{rad/s} \tag{77}\]

Equation 78, Fixed-Free Axial Mode of a Solid Bar. A solid steel bar of the vehicle length has a first axial mode at the bar wave speed over four lengths, 53 hertz.

\[f_{1} = \frac{c}{4L} = \frac{1}{4L} \sqrt{\frac{E}{\rho}} = \frac{4912}{4 \times 23.11} = 53 \, \text{Hz} \tag{78}\]

Equation 79, Ballistic Range Law in Terms of Burnout Speed. The range relation of the previous article is restated with burnout speed $v$ so that it can be differentiated.

\[\sin \frac{\Phi}{2} = \frac{\lambda}{2 - \lambda}, \qquad \lambda = \frac{v^{2}}{g R_{e}}, \qquad R = R_{e} \Phi \tag{79}\]

Equation 80, Logarithmic Derivative of the Energy Parameter. Since $\lambda$ is proportional to the square of the speed, a fractional change in speed doubles in $\lambda$.

\[\frac{d \lambda}{\lambda} = 2 \frac{dv}{v} \tag{80}\]

Equation 81, Derivative of the Range Angle. Differentiating the range law gives the rate at which the range angle grows with the energy parameter.

\[\frac{d}{d\lambda} \sin \frac{\Phi}{2} = \frac{2}{(2 - \lambda)^{2}} \quad \Longrightarrow \quad \frac{d\Phi}{d\lambda} = \frac{4}{(2-\lambda)^{2} \cos (\Phi/2)} \tag{81}\]

Equation 82, Logarithmic Sensitivity of Range to Burnout Speed. Chaining the two derivatives gives the fractional change in range per fractional change in burnout speed.

\[\frac{\partial \ln R}{\partial \ln v} = \frac{2 \lambda}{\Phi} \cdot \frac{4}{(2 - \lambda)^{2} \cos (\Phi/2)} \tag{82}\]

Equation 83, Bespoke Range Sensitivity at Intercontinental Range. The sensitivity is evaluated for the representative 10,000 kilometre arc.

\[\frac{\partial \ln R}{\partial \ln v} = 4.34 \tag{83}\]

Equation 84, Bespoke Required Velocity Accuracy. The sensitivity is inverted for an 800 metre miss at the representative 10,000 kilometre range.

\[\frac{\delta v}{v} = \frac{1}{4.34} \times \frac{800}{10^{7}} = 1.84 \times 10^{-5} \tag{84}\]

Equation 85, Allen-Eggers Peak Ballistic Deceleration. A ballistic body entering an exponential atmosphere on a straight path reaches a peak deceleration independent of its ballistic coefficient. Scherberg and Rubin 1953

\[a_{\max} = \frac{v_{e}^{2} \sin \gamma}{2 e H} \tag{85}\]

Equation 86, Bespoke Peak Deceleration of a Representative Entry. The entry is assumed at seven kilometres per second and thirty degrees.

\[a_{\max} = \frac{7000^{2} \times 0.5}{2 \times 2.718 \times 7200} = 626 \, \text{m/s}^{2} = 64 g \tag{86}\]

Equation 87, Bespoke Wetted Tank Area. The lateral area of the assumed 18 metre tank is 172 square metres.

\[A = 2 \pi r L = 2 \pi \times 1.524 \times 18 = 172 \, \text{m}^{2} \tag{87}\]

Equation 88, Bespoke Heat Leak Into an Uninsulated Tank. The heat flow assumes a convective coefficient of ten watts per square metre kelvin across a two hundred kelvin difference.

\[\dot{Q} = h A \Delta T = 10 \times 172 \times 200 = 345 \, \text{kW} \tag{88}\]

Equation 89, Bespoke Liquid Oxygen Boil-Off Rate. The assumed heat leak divided by a latent heat of 213 kilojoules per kilogramme gives 1.62 kilogrammes per second.

\[\dot{m}_{\text{boil}} = \frac{\dot{Q}}{L_{v}} = \frac{3.45 \times 10^{5}}{2.13 \times 10^{5}} = 1.62 \, \text{kg/s} \tag{89}\]

Equation 90, Centripetal Acceleration at the Tip of a Tumbling Body. A body of length $L$ rotating about its centre at rate $\Omega$ loads its tip with the square of the rate times the half-length.

\[a_{\text{tip}} = \Omega^{2} \frac{L}{2} \tag{90}\]

Equation 91, Bespoke Tip Acceleration of the First Flight. The tumble is assumed at one revolution per second, since no source gives the rate.

\[a_{\text{tip}} = (2 \pi)^{2} \times 11.6 = 458 \, \text{m/s}^{2} = 47 g \tag{91}\]

Equation 92, Bespoke Fraction of Intercontinental Range Flown. Six hundred statute and nautical miles are set against the representative 10,000 kilometre range.

\[\frac{600 \times 1.609}{10{,}000} = 0.097, \qquad \frac{600 \times 1.852}{10{,}000} = 0.111 \tag{92}\]

Equation 93, Burnout Speed for Six Hundred Statute Miles. Inverting the range law for a minimum-energy arc of 965.6 kilometres gives 2,966 metres per second.

\[\sin \frac{\Phi}{2} = \sin \frac{965.6}{2 \times 6371} = 0.0757, \qquad \lambda = \frac{2 \times 0.0757}{1 + 0.0757} = 0.1408, \qquad v_{bo} = \sqrt{0.1408 \times 9.80665 \times 6.371 \times 10^{6}} = 2966 \, \text{m/s} \tag{93}\]

Equation 94, Burnout Speed for Six Hundred Nautical Miles. Inverting the range law for a minimum-energy arc of 1,111.2 kilometres gives 3,164 metres per second.

\[\sin \frac{\Phi}{2} = \sin \frac{1111.2}{2 \times 6371} = 0.0871, \qquad \lambda = \frac{2 \times 0.0871}{1 + 0.0871} = 0.1602, \qquad v_{bo} = \sqrt{0.1602 \times 9.80665 \times 6.371 \times 10^{6}} = 3164 \, \text{m/s} \tag{94}\]

Equation 95, Binomial Standard Error of the Success Rate. Three successes in eight independent flights give a success rate of 0.375 with a standard error of 0.171.

\[\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.234}{8}} = 0.171 \tag{95}\]

Equation 96, Bespoke Standard Error of a Four-Flight Estimate. The success rate of each half of the series is taken as one half, the value that maximises the error.

\[\sigma = \sqrt{\frac{p(1-p)}{4}} = 0.25 \tag{96}\]

Equation 97, Flights Needed for a Given Standard Error. Inverting the binomial standard error gives the number of trials that achieve a chosen precision.

\[n = \frac{p (1-p)}{\sigma_{\hat{p}}^{2}} \tag{97}\]

Equation 98, Bespoke Flights for Five-Point Precision. A true reliability near one half and a target of five percentage points are assumed.

\[n = \frac{0.25}{0.05^{2}} = 100 \, \text{flights} \tag{98}\]

Equation 99, Bespoke Band of Buckling Scatter. The experimental scatter is assumed to run from fifteen to sixty percent of the classical value.

\[0.15 \leq \frac{\sigma_{\exp}}{\sigma_{cr}} \leq 0.60 \qquad \frac{0.60}{0.15} = 4 \tag{99}\]

Equation 100, Bespoke Position of the Design Knockdown in the Band. The adopted factor of 0.2 lies eleven percent of the way up the assumed band.

\[\frac{0.20 - 0.15}{0.60 - 0.15} = 0.11 \tag{100}\]

Equation 101, Circular Orbital Speed at Two Hundred Kilometres. The square root of the gravitational parameter over the orbital radius gives 7,788 metres per second.

\[v_{\text{orb}} = \sqrt{\frac{\mu}{R_{e} + h}} = \sqrt{\frac{3.986 \times 10^{14}}{6.571 \times 10^{6}}} = 7788 \, \text{m/s} \tag{101}\]

Equation 102, Bespoke Speed Deficit to Low Orbit. The orbital speed exceeds the burnout speed of the representative 10,000 kilometre arc by 595 metres per second.

\[v_{\text{orb}} - v_{bo} = 595 \, \text{m/s} \tag{102}\]

Equation 103, Bespoke Stage Structure of a Two-Stage Alternative. The propellant is split equally between two stages, each with the same structural fraction $f$ of its own loaded mass.

\[m_{s} = \frac{f \, m_{p} / 2}{1 - f} \tag{103}\]

Equation 104, Bespoke Ideal Velocity of a Two-Stage Alternative. The rocket equation is summed over the two equal-propellant stages of the alternative vehicle.

\[\Delta v = v_{e} \left[ \ln \frac{m_{\text{all}}}{m_{\text{all}} - m_{p}/2} + \ln \frac{m_{2}}{m_{s}} \right] \tag{104}\]

Equation 105, Planned Series A Gross Mass Against Series C and D. The 181,000 pound Series A missile is 0.745 of the 243,000 pound Series C and D figure in the same source. Cleary 1991 The 6555th, Missile and Space Launches Through 1970

\[\frac{181{,}000}{243{,}000} = 0.745 \tag{105}\]

Notation

• $\Delta v$, the ideal velocity increment
• $v_{e}$, the effective exhaust velocity, and in Equation 85 the entry speed
• $m_{0}$, the gross mass at lift-off
• $m_{f}$, the burnout mass
• $m_{s}$, the structural mass, and in Equation 103 the structure of one stage
• $m_{p}$, the propellant mass
• $v_{bo}$, the burnout speed
• $v_{\text{loss}}$, the calibrated gravity and drag loss
• $\Phi$, the central range angle
• $\lambda$, the ratio of burnout kinetic energy to that of a grazing circular orbit
• $R_{e}$, the radius of the Earth
• $g$, the standard gravitational acceleration
• $r$, the tank radius
• $t$, the skin thickness, and in Equations 52, 53 and 57 the time since lift-off
• $p$, a pressure, and in Equations 95 to 98 the probability of a successful flight
• $\sigma_{\theta}$, the hoop stress
• $\sigma_{z}$, the axial stress
• $\rho$, a density of propellant, air or steel by section
• $MR$, the oxidizer-to-fuel mixture ratio
• $m_{N_{2}}$, the mass of standing nitrogen
• $E$, the Young’s modulus of the skin
• $\nu$, the Poisson ratio of the skin
• $\sigma_{cr}$, the classical axial buckling stress
• $\sigma_{\text{allow}}$, the knocked-down buckling allowable
• $P_{cr}$, the Euler critical load
• $K$, the effective length factor
• $p_{\text{req}}$, the pressure required to offset buckling
• $M_{\text{crit}}$, the bending moment at which pressure tension is cancelled
• $C_{D}$, the drag coefficient of the cylinder
• $D$, the vehicle diameter
• $L$, the vehicle or tank length
• $N_{x}$, the axial running load on a stiffened wall
• $\dot{m}$, the propellant mass flow
• $H$, the atmospheric scale height
• $t_{q}$, the time of maximum dynamic pressure
• $C_{N\alpha}$, the normal-force slope per radian
• $\alpha$, the angle of attack
• $m_{1}$, the mass at staging after jettison
• $m_{j}$, the jettisoned booster mass
• $t_{b}$, the booster burn time
• $k_{p}$, the proof factor
• $k_{b}$, the burst factor
• $\tau_{\text{skin}}$, the thermal time constant of the skin
• $\delta$, the skin thickness in the thermal relation
• $P_{\text{ac}}$, the radiated acoustic power
• $L_{p}$, the sound pressure level
• $\omega_{s}$, the first lateral slosh frequency
• $g_{\text{eff}}$, the effective gravity under axial acceleration
• $f_{1}$, the first axial mode frequency of a solid bar
• $\gamma$, the entry flight path angle
• $L_{v}$, the latent heat of vaporisation of liquid oxygen
• $\Omega$, the tumble rate
• $\sigma_{\hat{p}}$, the standard error of the estimated success rate
• $\mu$, the gravitational parameter of the Earth
• $f$, the structural fraction of each stage of the two-stage alternative
• $m_{\text{all}}$, the gross mass of the two-stage alternative

References

Primary Sources, Peer-Reviewed

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