PORTAL_Rocketry - Wikiparency

**Rocketry** is the science and engineering of rockets: vehicles that carry all of their own propellant and fly by throwing mass backwards. This portal is its front door on Wikitube, article face [[Rocket]]. It runs in thirty sections from the first large liquid rockets through the physics of flight, the engine and its nozzle, and the chemistry of the propellants, to where a rocket in orbit can go next. Two of its five parts carry the weight of the page: **Rocketry physics** (Part II) and **Rocket fuel chemistry** (Part IV). ## How to read this page Each section is a short summary of a subject that has its own full article, named in the line under the heading, with the related articles beside it. Every section opens the same microsim, one three.js scene called the Rocket explorer, in that section's state. The explorer has three modes. In **build**, a rocket stands on the page part by part - tanks sized from the real propellant densities, engines sized from their rated thrust and the propellant chemistry - and the reader can change any stage. In **launch**, the build flies: thrust, drag in the 1976 Standard Atmosphere, gravity and the Earth's rotation, step by step, and the flight fails when the physics says it should, with the cause named. In **windows**, the rocket in orbit looks for its launch window to the Moon, the planets and Pluto, from real planet positions. The explorer carries four real vehicles, each built from its own primary source - the Saturn V from its 1968 flight manual, the Space Shuttle from NASA's 1981 News Reference, Falcon 9 from a 2019 FAA environmental assessment and the V-2 from the Smithsonian's record - and a rocket of the reader's own. Values the sources do not give are marked EST in the explorer. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html" data-title="The Rocket explorer"></div> *Try: tick exploded and read the parts of the Saturn V; switch mode to launch and press LAUNCH; then open windows and pick a destination.* ## Part I — The rocket The first four sections look at the rocket as a machine: where the large liquid rocket came from, the smallest rockets, the launch vehicles that carry payloads to orbit, and the engine at the bottom of every stage. Each opens the explorer in its build mode, where every part of a vehicle is labelled with its real numbers. ### History of rockets *Main article: [[History_of_rockets]] · See also: [[Konstantin_Tsiolkovsky]], [[Robert_H._Goddard]], [[Hermann_Oberth]], [[V-2_rocket]], [[Gunpowder]]* The large liquid-propellant rocket begins with the German Army's A-series. Between 1932 and 1934 the Army tested small liquid-oxygen and alcohol rockets, the A-1 and A-2, of 300 kg thrust; the 1,500 kg thrust A-3 followed in 1935-1937, and the A-4 was proposed in 1936 as a 25-tonne-thrust scale-up and designed in detail in 1939-1941.[^nasm] As the V-2 it became the first large-scale liquid-propellant rocket vehicle and the first long-range ballistic missile: liquid oxygen burned with a 75 percent alcohol and water mixture, the water helping to cool the motor, and it carried a one-ton warhead to about 320 km.[^nasm] The museum calls it the ancestor of today's large rockets and launch vehicles.[^nasm] Opened on the V-2, the explorer labels each part of the A-4 with its propellant masses and chamber figures; its default flight climbs to about 165 km, above the 100 km line.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=v-2&explode=1&embed=1" data-title="The V-2 in the Rocket explorer"></div> *Try: press e to close and open the exploded view; switch mode to launch and press LAUNCH to fly the V-2 above 100 km; add 20 t of payload and it cannot leave the pad.* Connects to: [[#Launch vehicle|Launch vehicle]] · [[#Rocket engine|Rocket engine]] · [[#Action and reaction|Action and reaction]] ### Model rocket *Main article: [[Model_rocket]] · See also: [[Sounding_rocket]]* A model rocket is the same machine at the smallest scale: a light airframe, a factory-made solid motor, and a flight whose apogee is set by the motor's total impulse, the rocket's mass and its drag. The physics is the physics of every other section on this page - thrust, specific impulse, the rocket equation and drag in the lower atmosphere - without staging or orbit. The explorer does not fly a model rocket yet: the section's own microsim, a motor thrust curve and a coast to apogee through the 1976 Standard Atmosphere,[^usa76] is on the portal's build list. *Section microsim: on the build list (no explorer state carries this subject yet).* Connects to: [[#Thrust|Thrust]] · [[#Max q|Max q]] · [[#Solid propellants|Solid propellants]] ### Launch vehicle *Main article: [[Launch_vehicle]] · See also: [[Saturn_V]], [[Space_Shuttle]], [[Falcon_9]], [[Reusable_launch_vehicle]]* A launch vehicle is a stack of rockets whose job is to put a payload into orbit or beyond. The explorer carries four, each built from its own source. The Saturn V of the Apollo flight manual weighed 4,792,200 lb at launch in its first stage, 1,034,900 lb in the second and 262,300 lb in the third; five F-1 engines of 1,522,000 lbf each burned the first stage for 150.7 seconds.[^sa503] The Space Shuttle paired two solid rocket boosters of 11,790 kN each with three main engines fed from an External Tank of 719,112 kg of propellant.[^stsnr] Falcon 9 carries nine Merlin engines of 190,000 lbf each at sea level and about 403 tonnes of liquid oxygen and RP-1 in its first stage.[^faa] Built in the explorer, the Saturn V comes to 2,775 t at lift-off with a 45 t spacecraft, a thrust-to-weight ratio of 1.24 and 12.6 km/s of ideal delta-v across its three stages.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&embed=1" data-title="Launch vehicles in the Rocket explorer"></div> *Try: change rocket to Space Shuttle, Falcon 9 and V-2 and compare lift-off mass, thrust-to-weight and total delta-v in the readout; tick exploded to see every stage in parts.* Connects to: [[#Staging|Staging]] · [[#The rocket equation|The rocket equation]] · [[#Reaching orbit|Reaching orbit]] ### Rocket engine *Main article: [[Rocket_engine]] · See also: [[Combustion_chamber]], [[Turbopump]], [[Combustion_instability]]* A liquid rocket engine has three working parts: the thrust chamber, where the injector sprays the propellants into the combustion chamber and the nozzle expands the hot gas; the feed system, which delivers the propellants either from pressurised tanks or through turbopumps; and the controls that start, run and stop it.[^sp125] Huzel and Huang build their NASA design manual around those elements, from thrust-chamber layout and cooling to injectors, gas generators, ignition, combustion instability, turbopumps and valves (chapters 4 to 7).[^sp125] In the explorer every engine is sized from its rated thrust and the chemistry of its propellant: the throat area follows from the thrust, the chamber pressure and the characteristic velocity, and the bell from the nozzle area ratio.[^rk] The engine view opens on the Saturn V's five F-1s with the nozzle, combustion chamber and turbopump pulled apart. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&explode=1&view=engine&embed=1" data-title="The F-1 engine cluster in the Rocket explorer"></div> *Try: drag to turn the cluster and read each label; change the chamber pressure or the nozzle Ae/At and watch the bell and the Isp in the readout change.* Connects to: [[#The nozzle|The nozzle]] · [[#Engine cycles|Engine cycles]] · [[#Cooling|Cooling]] ## Part II — Rocketry physics The next ten sections are the physics of flight: why a rocket moves at all, what thrust and specific impulse measure, how the rocket equation turns propellant into speed, why rockets are staged, and what gravity and the air take away on the way to orbit. They open the explorer in its launch mode, where each flight is computed from the build. ### Action and reaction  *Microsims from the articles this section links:* <div class="wt-simrow"> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Newton's_laws_of_motion.html" data-title="Newton's laws of motion · matter"></div> <div class="wt-sim" data-src="https://editor.p5js.org/sciencenibber/full/ONl3-NO3g" data-title="Newton's laws of motion · p5.js"></div> </div>  *Main article: [[Newton's_laws_of_motion]]* A rocket needs nothing to push against. It throws mass out of its nozzle at high speed, and the reaction to the force that accelerates the exhaust backwards accelerates the rocket forwards: the third law, applied to a body that loses mass as it goes.[^ostax] That is why a rocket works in vacuum, and why it works better there: with no air pressing on the nozzle exit, all of the exhaust's momentum becomes thrust.[^sp125] The explorer's launch mode computes each flight from that balance, step by step, from the pad to burnout.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=launch&vehicle=v-2&rate=10x&go=1&embed=1" data-title="Action and reaction: a V-2 flight in the Rocket explorer"></div> *Try: watch the readout: acceleration climbs as propellant burns away, from under 2 g at lift-off to over 7 g at burnout.* Connects to: [[#Momentum of a variable-mass system|Momentum of a variable-mass system]] · [[#Thrust|Thrust]] ### Momentum of a variable-mass system  *Microsims from the articles this section links:* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Momentum.html" data-title="Momentum"></div>  *Main article: [[Momentum]]* Treat the rocket and the exhaust it ejects as one system and total momentum is conserved. In a short time the rocket loses a mass dm of exhaust at speed ve relative to itself, and its own speed rises by dv = -ve dm/m; summing those steps gives the rocket equation of the section after next.[^ostax] The same bookkeeping explains why the rocket speeds up faster and faster as it lightens: the thrust stays nearly constant while the mass it pushes falls. In the explorer, a Falcon 9 goes from 1.4 g at lift-off to 5.6 g near second-stage burnout.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=launch&vehicle=falcon-9&go=1&embed=1" data-title="A Falcon 9 ascent in the Rocket explorer"></div> *Try: set playback to 1x to follow the mass readout fall tonne by tonne; the flight path is coloured by dynamic pressure.* Connects to: [[#Action and reaction|Action and reaction]] · [[#The rocket equation|The rocket equation]] ### Thrust *Main article: [[Thrust]]* The thrust of a rocket engine is F = mdot ve + (pe - pa) Ae: the momentum flux of the exhaust plus a pressure term, the difference between the nozzle exit pressure and the ambient pressure acting over the exit area.[^sp125] The pressure term is why the same engine gives more thrust in vacuum than at sea level, and why a nozzle can only be exactly right at one altitude. The explorer applies it at every step of the ascent, with the ambient pressure from the 1976 Standard Atmosphere.[^usa76][^rk] For the Merlin, sized from its 190,000 lbf sea-level rating, it shows 290 s of specific impulse at sea level and 320 s in vacuum.[^faa][^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=falcon-9&explode=1&view=engine&embed=1" data-title="Merlin engines: sea-level and vacuum thrust in the Rocket explorer"></div> *Try: select stage 2 to compare the vacuum engine; raise Ae/At on stage 1 and watch the sea-level Isp and the over-expansion warning.* Connects to: [[#Specific impulse|Specific impulse]] · [[#The nozzle|The nozzle]] ### Specific impulse *Main article: [[Specific_impulse]]* Specific impulse, Isp = F/(mdot g0), is the thrust delivered per unit weight flow of propellant, in seconds; multiplied by standard gravity it is the effective exhaust velocity.[^sp125] It is the single best measure of how much a propellant and engine get out of each kilogram. From the NASA equilibrium method, at 100 bar chamber pressure and a nozzle area ratio of 40, the explorer's theoretical vacuum specific impulse at each propellant's best mixture ratio is about 455 s for liquid hydrogen with liquid oxygen, 369 s for methane, 359 s for RP-1, about 340 s for the nitrogen-tetroxide storables and 334 s for the V-2's alcohol and water.[^rp1311][^rk] Real engines deliver a few percent less; the explorer calibrates each preset engine to its source.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&pair=LOX/LH2&explode=1&embed=1" data-title="Specific impulse by propellant in the Rocket explorer"></div> *Try: change the propellant menu and read the vacuum Isp in the readout; the tanks resize with each propellant's density.* Connects to: [[#The rocket equation|The rocket equation]] · [[#Rocket propellant|Rocket propellant]] · [[#c* and C_F|c* and C_F]] ### The rocket equation *Main article: [[Tsiolkovsky_rocket_equation]] · See also: [[Rocket_mass_ratio]], [[Payload_fraction]]* Integrating the momentum balance gives the rocket equation: delta-v = ve ln(m0/mf), the change in speed from the exhaust velocity and the ratio of starting mass to final mass.[^ostax] The logarithm is the hard part: doubling the delta-v needs the mass ratio squared, so a rocket that must reach orbit is mostly propellant. The explorer applies it stage by stage. For the Saturn V it gives 3.77 km/s from the S-IC, 4.67 km/s from the S-II and 4.16 km/s from the S-IVB, 12.6 km/s in total before gravity and drag take their share.[^sa503][^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&embed=1" data-title="Delta-v by stage in the Rocket explorer"></div> *Try: lower the payload and watch every stage's delta-v rise; move propellant mass and see the logarithm at work.* Connects to: [[#Delta-v|Delta-v]] · [[#Staging|Staging]] ### Delta-v *Main article: [[Delta-v]]* Delta-v is the currency of spaceflight: every manoeuvre has a price in change of speed, and a rocket's budget is what the rocket equation gives it. Reaching a 200 km orbit means reaching about 7.8 km/s of orbital speed, plus what gravity and drag take on the way up.[^rk] From orbit, the explorer prices the departure burn for each destination from real planet positions: the November 2026 window to Mars costs 3.63 km/s from a 300 km orbit, a characteristic energy C3 of 9.6 km2/s2, with 278 days to arrival.[^jpl][^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=windows&dest=Mars&embed=1" data-title="The delta-v to Mars in the Rocket explorer"></div> *Try: drag the payload down in build mode and come back: the readout says whether the rocket has the delta-v for the trip.* Connects to: [[#The rocket equation|The rocket equation]] · [[#Reaching orbit|Reaching orbit]] · [[#Other propulsion|Other propulsion]] ### Staging *Main article: [[Multistage_rocket]]* A single stage carries its empty tanks and engines all the way; a multistage rocket drops them when they are spent, so each later stage starts lighter and gets more delta-v out of the same propellant.[^ostax] The Saturn V dropped its S-IC after 150.7 seconds, ran the S-II for 367 seconds and used the S-IVB twice, for 156 and 336 seconds.[^sa503] The flight manual's first-stage thrust history also records the centre engine shutting down before the outer four.[^sa503] In the explorer the S-IC separates at about 81 km and 2.65 km/s.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=launch&vehicle=saturn-v&go=1&embed=1" data-title="Saturn V staging in the Rocket explorer"></div> *Try: watch the caption for each staging event; switch the rocket to Space Shuttle to see boosters drop while the core keeps burning.* Connects to: [[#The rocket equation|The rocket equation]] · [[#Gravity loss|Gravity loss]] ### Gravity loss *Main article: [[Gravity_loss]] · See also: [[Gravity_turn]]* A rocket climbing straight up loses about 9.8 m/s of speed to gravity every second, so the sooner it turns sideways toward orbital speed the less it loses; but turning early keeps it low in thick air, where drag and dynamic pressure grow. The gravity turn is the compromise: a small pitch kick soon after lift-off, then thrust along the flight path while gravity bends it over.[^rk] The explorer flies exactly that programme, and the kick angle and time are the reader's to set: this state uses a gentle 0.3 degree kick. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=launch&vehicle=saturn-v&kick=0.3&go=1&embed=1" data-title="A slow pitch-over in the Rocket explorer"></div> *Try: try kicks of 0.3, 0.8 and 3 degrees: too gentle wastes delta-v climbing, too hard breaks the Saturn V at max q.* Connects to: [[#Max q|Max q]] · [[#Reaching orbit|Reaching orbit]] ### Max q *Main article: [[Max_q]] · See also: [[Dynamic_pressure]]* Dynamic pressure, q = 1/2 rho v2, rises as the rocket speeds up and falls as the air thins; its peak, max q, is the heaviest aerodynamic load of the flight.[^usa76] The Shuttle's main engines could be throttled between 65 and 109 percent: full thrust for lift-off and the first part of the ascent, less later to hold the acceleration to 3 g.[^stsnr] In the explorer the Saturn V peaks at 32 kPa about 72 seconds after lift-off; an empty Falcon 9 accelerates so hard that it passes its airframe limit and breaks up, and the throttle bucket saves it.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=launch&vehicle=falcon-9&payload=0&rate=10x&go=1&embed=1" data-title="Max q in the Rocket explorer"></div> *Try: tick throttle bucket and LAUNCH again: the same empty Falcon 9 now reaches orbit.* Connects to: [[#Gravity loss|Gravity loss]] · [[#Thrust vector control|Thrust vector control]] ### Reaching orbit *Main article: [[Escape_velocity]] · See also: [[Orbital_speed]], [[Hohmann_transfer_orbit]], [[Oberth_effect]], [[Orbital_mechanics]]* Orbit is falling sideways fast enough to keep missing the Earth: at 200 km the circular speed sqrt(GM/r) is about 7.78 km/s, and the escape speed there is sqrt(2) times that.[^rk] A transfer orbit between two circles takes two burns; from a 200 km orbit, the Hohmann transfer to the Moon's distance needs about 3.13 km/s and about five days.[^rk] With a 45 t payload, the explorer's Saturn V leaves 3.20 km/s in its third stage after reaching orbit: enough.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=windows&dest=Moon&embed=1" data-title="From orbit to the Moon in the Rocket explorer"></div> *Try: switch the destination to Mars, Jupiter or Pluto and compare the departure burns.* Connects to: [[#Delta-v|Delta-v]] · [[#Other propulsion|Other propulsion]] ## Part III — Engine and nozzle physics Six sections go inside the engine: the nozzle that turns hot gas into directed speed, the compressible flow that governs it, the split of performance between chemistry and nozzle, the cycles that drive the pumps, the cooling that keeps the chamber intact, and the gimbals that steer. ### The nozzle *Main article: [[Rocket_engine_nozzle]] · See also: [[De_Laval_nozzle]], [[Choked_flow]], [[Shock_diamond]]* The nozzle converges to a throat, where the flow reaches the speed of sound, and then diverges, where the gas expands and speeds up further; the ratio of exit area to throat area sets how far it expands and what pressure it leaves at.[^sp125] A nozzle expanded for vacuum over-expands at sea level: its exit pressure falls below the ambient pressure, and far enough below it the flow separates from the wall.[^sp125] The explorer flags a nozzle whose sea-level exit pressure is under 0.35 of ambient - an illustrative separation threshold - and fails a vacuum nozzle fired from the pad.[^rk] This state opens on Falcon 9's second-stage engine, area ratio 117 in the explorer. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=falcon-9&stage=2&explode=1&view=engine&embed=1" data-title="The vacuum nozzle in the Rocket explorer"></div> *Try: select stage 1 and raise Ae/At until the over-expansion warning appears.* Connects to: [[#Compressible flow|Compressible flow]] · [[#Thrust|Thrust]] · [[#c* and C_F|c* and C_F]] ### Compressible flow *Main article: [[Compressible_flow]] · See also: [[Isentropic_process]]* The flow through a rocket nozzle is compressible: its density changes as fast as its speed, and the one-dimensional isentropic relations tie area, Mach number, pressure and temperature together.[^sp125] Wikitube's compressible-flow microsim from the Thury hydrodynamics set carries this regime already; the framework library's isentropic and normal-shock functions are the ones that size the explorer's nozzles.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Compressible_flow.html" data-title="Compressible flow (Thury Hydrodynamics set)"></div> *Try: work the controls of the Thury compressible-flow sim; then return to the explorer's nozzle states above.* Connects to: [[#The nozzle|The nozzle]] ### c* and C_F *Main article: [[Characteristic_velocity]] · See also: [[Thrust_coefficient]]* Specific impulse splits into two factors: Isp g0 = c* CF. The characteristic velocity c* measures the chamber - the chemistry and the combustion - and the thrust coefficient CF measures the nozzle.[^sp125] The NASA equilibrium program reports both: for liquid hydrogen and oxygen at a mixture ratio of 5.55 and 53.3 bar it gives c* = 2,333.4 m/s and, at a pressure ratio of 100, CF = 1.664.[^rp1311b] The explorer's table reproduces that c* to 0.1 m/s.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&explode=1&embed=1" data-title="c* and the nozzle in the Rocket explorer"></div> *Try: change the propellant and watch c* in the readout; change only Ae/At and c* stays put while Isp moves.* Connects to: [[#Specific impulse|Specific impulse]] · [[#Flame temperature|Flame temperature]] ### Engine cycles *Main article: [[Staged_combustion_cycle]] · See also: [[Gas-generator_cycle]], [[Expander_cycle]], [[Pressure-fed_engine]]* A pump-fed engine has to drive its turbopumps with some of its own propellant. In the Shuttle's main engines the propellants were partially burned in two preburners to make the high-pressure gas that drove the turbopumps, and combustion was completed in the main chamber - the staged-combustion cycle, which wastes none of the turbine gas.[^stsnr] The alternative that Huzel and Huang describe at length burns a small flow in a separate gas generator and dumps its exhaust after the turbine; the simplest engines use no pumps at all and push the propellants out of pressurised tanks.[^sp125] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=shuttle&stage=2&explode=1&embed=1" data-title="Space Shuttle main engines in the Rocket explorer"></div> *Try: select stage 1 to compare the solid boosters, which have no pumps at all.* Connects to: [[#Rocket engine|Rocket engine]] · [[#Cooling|Cooling]] ### Cooling *Main article: [[Regenerative_cooling_(rocketry)]]* The combustion gas is far hotter than any wall material can stand, so the chamber has to be cooled. In regenerative cooling one of the propellants flows through passages in the chamber and nozzle walls before it is injected, carrying the heat back into the combustion; ablative walls instead char and erode away slowly; radiation-cooled walls run hot and shed heat as light.[^sp125] The explorer compares each engine's flame temperature with an illustrative limit for its cooling method. This state runs methane at its stoichiometric mixture in an ablative chamber: 3,612 K against a 3,400 K limit, and the chamber burns through.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&pair=LOX/CH4&of=3.99&cooling=ablative&explode=1&embed=1" data-title="Chamber cooling limits in the Rocket explorer"></div> *Try: switch cooling to regenerative, or lower the O/F toward 3.4, and the warning clears.* Connects to: [[#Flame temperature|Flame temperature]] · [[#Mixture ratio|Mixture ratio]] ### Thrust vector control *Main article: [[Thrust_vectoring]]* A rocket steers by turning its thrust. Liquid engines swing on gimbals at the thrust structure; solid motors move the nozzle.[^sp125] The Shuttle's main engines were gimballed to give pitch, yaw and roll control during ascent, and each Solid Rocket Booster steered with a movable nozzle.[^stsnr] The explorer labels each thrust structure with its gimbal range and flies its pitch programme through them.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&explode=1&view=engine&stage=1&embed=1" data-title="Gimballed engines in the Rocket explorer"></div> *Try: switch the rocket to Space Shuttle and find the movable nozzles on the boosters.* Connects to: [[#Gravity loss|Gravity loss]] · [[#Rocket engine|Rocket engine]] ## Part IV — Rocket fuel chemistry Eight sections are the chemistry of the propellants: what counts as a propellant, which molecule is oxidised and which reduced, why engines run away from the stoichiometric mixture, how hot the flame gets, why the hot gas partly comes apart, and the three families in service: cryogenic, hypergolic and solid. The explorer computes all of them from one equilibrium table baked with the NASA method. ### Rocket propellant  *Microsims from the articles this section links:* <div class="wt-sim" data-src="https://editor.p5js.org/sciencenibber/full/DsIanlgNT" data-title="Rocket propellant"></div>  *Main article: [[Rocket_propellant]] · See also: [[Liquid_rocket_propellant]]* A propellant is judged by more than its specific impulse. Huzel and Huang list the other qualities an engine designer weighs: density, storability, handling hazard, stability, compatibility with materials and cost.[^sp125] Density matters because tanks have mass. Liquid oxygen weighs 1.142 g/cm3 and liquid hydrogen only 0.071, so the Saturn V's S-II needs about 920 cubic metres of tank for its 65 tonnes of hydrogen.[^sp125][^sa503][^rk] The explorer sizes every tank from the propellant mass and the density. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&explode=1&embed=1" data-title="Propellant tanks in the Rocket explorer"></div> *Try: select stage 2 and read the liquid hydrogen tank; set the first stage to LOX/LH2 and watch it stretch.* Connects to: [[#Cryogenic propellants|Cryogenic propellants]] · [[#Specific impulse|Specific impulse]] ### Oxidizer and fuel  *Microsims from the articles this section links:* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Redox.html" data-title="Redox"></div>  *Main article: [[Redox]] · See also: [[Oxidizing_agent]]* Combustion in a rocket is a redox reaction: the fuel is oxidised and the oxidizer reduced. The stoichiometric mixture burns every atom of fuel to carbon dioxide, water and nitrogen. Balancing the atoms gives a stoichiometric oxidizer-to-fuel mass ratio of 7.94 for liquid oxygen with hydrogen, 3.40 for liquid oxygen with RP-1 and 3.06 for nitrogen tetroxide with UDMH.[^rk] Nitrogen tetroxide carries its own oxygen, so the storable propellants need no cryogenic oxidizer at all. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&pair=N2O4/UDMH&explode=1&embed=1" data-title="Oxidizer and fuel in the Rocket explorer"></div> *Try: step the propellant menu through all seven pairs and read the stoichiometric O/F in the readout.* Connects to: [[#Mixture ratio|Mixture ratio]] · [[#Hypergolics|Hypergolics]] ### Mixture ratio *Main article: [[Stoichiometry]] · See also: [[Air–fuel_ratio]]* Engines do not run at the stoichiometric mixture. Burning a little fuel-rich leaves light molecules such as hydrogen and carbon monoxide in the exhaust, and a lighter exhaust leaves the nozzle faster. The Shuttle's main engines ran liquid oxygen and hydrogen at 6 to 1, against a stoichiometric 7.94.[^stsnr][^rk] In the explorer's table for liquid oxygen and RP-1, the flame temperature peaks near 3,710 K at a mixture ratio of about 3.0, while the specific impulse peaks earlier, near 2.6.[^rk] This state sets the Saturn V's F-1 to the stoichiometric 3.4. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&of=3.4&embed=1" data-title="Mixture ratio in the Rocket explorer"></div> *Try: drag O/F from 2.0 to 3.4 and watch Tc, the exhaust molecular mass and Isp in the readout.* Connects to: [[#Flame temperature|Flame temperature]] · [[#Dissociation and equilibrium|Dissociation and equilibrium]] ### Flame temperature  *Microsims from the articles this section links:* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Combustion.html" data-title="Combustion"></div>  *Main article: [[Adiabatic_flame_temperature]] · See also: [[Heat_of_combustion]], [[Standard_enthalpy_of_formation]], [[Combustion]]* With no heat lost to the walls, the chemical energy of the propellants goes into heating the products: the adiabatic flame temperature. The NASA program finds it by combustion at constant pressure and enthalpy, with the reactants entered at their real temperatures and enthalpies - liquid hydrogen at 20.27 K, liquid oxygen at 90.17 K.[^rp1311][^rp1311b] For hydrogen and oxygen at a mixture ratio of 5.55 and 53.3 bar it gives 3,389.27 K; the explorer's table gives 3,388 K.[^rp1311b][^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&pair=LOX/CH4&of=3.4&embed=1" data-title="Flame temperature in the Rocket explorer"></div> *Try: raise the chamber pressure and watch Tc rise slightly: higher pressure holds back dissociation.* Connects to: [[#Dissociation and equilibrium|Dissociation and equilibrium]] · [[#Cooling|Cooling]] ### Dissociation and equilibrium *Main article: [[Chemical_equilibrium]] · See also: [[Gibbs_free_energy]]* At rocket-chamber temperatures the products do not stay as water and carbon dioxide: part of them breaks back into hydrogen and oxygen atoms and hydroxyl radicals, which soaks up energy and caps the temperature. The NASA program finds the composition that minimises the Gibbs energy; in its hydrogen and oxygen example, atomic hydrogen is 3.4 percent of the chamber gas by moles.[^rp1311][^rp1311b] As the gas expands and cools in the nozzle the atoms can recombine and give the energy back; the program computes both limits, shifting equilibrium and frozen composition.[^rp1311] The explorer uses shifting equilibrium throughout.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&pair=LOX/LH2&of=7.9&embed=1" data-title="Dissociation in the Rocket explorer"></div> *Try: drag O/F from 4 up to 7.9 and watch the flame temperature stop rising: dissociation takes the rest.* Connects to: [[#Flame temperature|Flame temperature]] · [[#Mixture ratio|Mixture ratio]] ### Cryogenic propellants *Main article: [[Cryogenic_rocket_engine]] · See also: [[Liquid_hydrogen]], [[Liquid_oxygen]], [[Methane]], [[RP-1]]* Liquid oxygen boils at -297.4 F (90 K) and liquid hydrogen at -422.9 F (20 K); both must be kept cold in insulated tanks.[^sp125] The Shuttle's External Tank held 616,493 kg of liquid oxygen and 102,618 kg of liquid hydrogen; its oxygen tank alone held 541,482 litres.[^stsnr] The explorer's tank for that oxygen comes to 540 cubic metres.[^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=saturn-v&stage=2&explode=1&embed=1" data-title="Liquid hydrogen and oxygen in the Rocket explorer"></div> *Try: switch the rocket to Space Shuttle and read the External Tank labels.* Connects to: [[#Rocket propellant|Rocket propellant]] · [[#Specific impulse|Specific impulse]] ### Hypergolics *Main article: [[Hypergolic_propellant]] · See also: [[Hydrazine]], [[Unsymmetrical_dimethylhydrazine]], [[Dinitrogen_tetroxide]], [[Monopropellant]]* Hypergolic propellants ignite on contact, so an engine needs no igniter; the common pairs are also storable at ordinary temperatures.[^sp125] The Shuttle orbiter's orbital manoeuvring engines, 26,688 N each, burned hypergolic propellants.[^stsnr] The NASA program's example 12 is the classic pair: monomethylhydrazine and nitrogen tetroxide at a mixture ratio of 2.5 and 1,000 psia, with c* = 1,708.6 m/s; the explorer's table gives 1,708.3.[^rp1311b][^rk] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=custom&pair=N2O4/MMH&explode=1&embed=1" data-title="Hypergolic propellants in the Rocket explorer"></div> *Try: compare the three storable pairs in the propellant menu: UDMH, MMH and hydrazine with nitrogen tetroxide.* Connects to: [[#Oxidizer and fuel|Oxidizer and fuel]] · [[#Other propulsion|Other propulsion]] ### Solid propellants *Main article: [[Solid-propellant_rocket]] · See also: [[Ammonium_perchlorate_composite_propellant]], [[Ammonium_perchlorate]], [[Hybrid-propellant_rocket]]* A solid motor carries fuel and oxidizer premixed in a rubbery grain cast inside the case. Each Shuttle booster held 502,125 kg of propellant: 69.83 percent ammonium perchlorate as oxidizer, 16 percent aluminium powder as fuel, 12 percent polymer binder, 2 percent epoxy curing agent and 0.17 percent iron oxide to set the burning rate.[^stsnr] It gave 11,790 kN at lift-off and burned for about two minutes.[^stsnr] Aluminium burns to aluminium oxide, which condenses in the flame; the NASA program's solid-propellant example finds the liquid oxide and a flame temperature of 2,724 K.[^rp1311b] <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?vehicle=shuttle&explode=1&embed=1" data-title="Solid rocket boosters in the Rocket explorer"></div> *Try: select stage 2 to compare the liquid core; press e to put the boosters back on the tank.* Connects to: [[#Staging|Staging]] · [[#Oxidizer and fuel|Oxidizer and fuel]] ## Part V — Beyond chemical, and back down The last two sections leave the launch pad: where a rocket in orbit can go next, and how it comes back through the air. ### Other propulsion *Main article: [[Spacecraft_propulsion]] · See also: [[Spacecraft_electric_propulsion]], [[Ion_thruster]], [[Nuclear_thermal_rocket]], [[Solar_sail]]* Beyond the Moon the delta-v bill grows quickly. The explorer finds the cheapest direct departures from real planet positions: 6.8 km/s from low orbit to Jupiter, 7.4 km/s to Saturn, and for Pluto about 12 km/s.[^jpl][^rk] Pluto is expensive for a reason the explorer shows: it lies about 4 degrees below the plane of Earth's orbit now, so a direct arc must tilt its whole plane. Moved into that plane, the best direct transfer would need half the energy.[^rk] That gap is what flybys, electric thrusters and other propulsion exist to close; the explorer's flyby option is on the build list. <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/rocketry/Rocket.html?mode=windows&dest=Pluto&embed=1" data-title="The launch window to Pluto in the Rocket explorer"></div> *Try: click the launch-window chart to pick other departure dates and flight times; green is the cheapest.* Connects to: [[#Delta-v|Delta-v]] · [[#Reaching orbit|Reaching orbit]] ### Atmospheric entry *Main article: [[Atmospheric_entry]] · See also: [[Heat_shield]], [[Kármán_line]]* Coming back, a spacecraft trades its orbital speed for heat in the upper atmosphere. The same 1976 Standard Atmosphere that sets the drag on the way up sets the heating on the way down, from the 100 km line into the dense air below 50 km.[^usa76] The explorer does not fly entry yet: the section's own microsim, an entry corridor of heating and deceleration against flight-path angle, is on the portal's build list. *Section microsim: on the build list (no explorer state carries this subject yet).* Connects to: [[#Reaching orbit|Reaching orbit]] · [[#Max q|Max q]] ## Spine | # | Section | Main article | See also | State | Status | |---|---|---|---|---|---| | 1 | History of rockets | [[History_of_rockets]] | [[Konstantin_Tsiolkovsky]], [[Robert_H._Goddard]], [[Hermann_Oberth]], [[V-2_rocket]], [[Gunpowder]] | `?vehicle=v-2&explode=1` | live · rocketry/Rocket.html?vehicle=v-2&explode=1&embed=1 | | 2 | Model rocket | [[Model_rocket]] | [[Sounding_rocket]] | — | section sim on the build list | | 3 | Launch vehicle | [[Launch_vehicle]] | [[Saturn_V]], [[Space_Shuttle]], [[Falcon_9]], [[Reusable_launch_vehicle]] | `?vehicle=saturn-v` | live · rocketry/Rocket.html?vehicle=saturn-v&embed=1 | | 4 | Rocket engine | [[Rocket_engine]] | [[Combustion_chamber]], [[Turbopump]], [[Combustion_instability]] | `?vehicle=saturn-v&explode=1&view=engine` | live · rocketry/Rocket.html?vehicle=saturn-v&explode=1&view=engine&embed=1 | | 5 | Action and reaction | [[Newton's_laws_of_motion]] | — | `?mode=launch&vehicle=v-2&rate=10x&go=1` | live · rocketry/Rocket.html?mode=launch&vehicle=v-2&rate=10x&go=1&embed=1 | | 6 | Momentum of a variable-mass system | [[Momentum]] | — | `?mode=launch&vehicle=falcon-9&go=1` | live · rocketry/Rocket.html?mode=launch&vehicle=falcon-9&go=1&embed=1 | | 7 | Thrust | [[Thrust]] | — | `?vehicle=falcon-9&explode=1&view=engine` | live · rocketry/Rocket.html?vehicle=falcon-9&explode=1&view=engine&embed=1 | | 8 | Specific impulse | [[Specific_impulse]] | — | `?vehicle=custom&pair=LOX/LH2&explode=1` | live · rocketry/Rocket.html?vehicle=custom&pair=LOX/LH2&explode=1&embed=1 | | 9 | The rocket equation | [[Tsiolkovsky_rocket_equation]] | [[Rocket_mass_ratio]], [[Payload_fraction]] | `?vehicle=saturn-v` | live · rocketry/Rocket.html?vehicle=saturn-v&embed=1 | | 10 | Delta-v | [[Delta-v]] | — | `?mode=windows&dest=Mars` | live · rocketry/Rocket.html?mode=windows&dest=Mars&embed=1 | | 11 | Staging | [[Multistage_rocket]] | — | `?mode=launch&vehicle=saturn-v&go=1` | live · rocketry/Rocket.html?mode=launch&vehicle=saturn-v&go=1&embed=1 | | 12 | Gravity loss | [[Gravity_loss]] | [[Gravity_turn]] | `?mode=launch&vehicle=saturn-v&kick=0.3&go=1` | live · rocketry/Rocket.html?mode=launch&vehicle=saturn-v&kick=0.3&go=1&embed=1 | | 13 | Max q | [[Max_q]] | [[Dynamic_pressure]] | `?mode=launch&vehicle=falcon-9&payload=0&rate=10x&go=1` | live · rocketry/Rocket.html?mode=launch&vehicle=falcon-9&payload=0&rate=10x&go=1&embed=1 | | 14 | Reaching orbit | [[Escape_velocity]] | [[Orbital_speed]], [[Hohmann_transfer_orbit]], [[Oberth_effect]], [[Orbital_mechanics]] | `?mode=windows&dest=Moon` | live · rocketry/Rocket.html?mode=windows&dest=Moon&embed=1 | | 15 | The nozzle | [[Rocket_engine_nozzle]] | [[De_Laval_nozzle]], [[Choked_flow]], [[Shock_diamond]] | `?vehicle=falcon-9&stage=2&explode=1&view=engine` | live · rocketry/Rocket.html?vehicle=falcon-9&stage=2&explode=1&view=engine&embed=1 | | 16 | Compressible flow | [[Compressible_flow]] | [[Isentropic_process]] | Thury `Compressible_flow` | live · thury/Compressible_flow.html | | 17 | c* and C_F | [[Characteristic_velocity]] | [[Thrust_coefficient]] | `?vehicle=custom&explode=1` | live · rocketry/Rocket.html?vehicle=custom&explode=1&embed=1 | | 18 | Engine cycles | [[Staged_combustion_cycle]] | [[Gas-generator_cycle]], [[Expander_cycle]], [[Pressure-fed_engine]] | `?vehicle=shuttle&stage=2&explode=1` | live · rocketry/Rocket.html?vehicle=shuttle&stage=2&explode=1&embed=1 | | 19 | Cooling | [[Regenerative_cooling_(rocketry)]] | — | `?vehicle=custom&pair=LOX/CH4&of=3.99&cooling=ablative&explode=1` | live · rocketry/Rocket.html?vehicle=custom&pair=LOX/CH4&of=3.99&cooling=ablative&explode=1&embed=1 | | 20 | Thrust vector control | [[Thrust_vectoring]] | — | `?vehicle=saturn-v&explode=1&view=engine&stage=1` | live · rocketry/Rocket.html?vehicle=saturn-v&explode=1&view=engine&stage=1&embed=1 | | 21 | Rocket propellant | [[Rocket_propellant]] | [[Liquid_rocket_propellant]] | `?vehicle=saturn-v&explode=1` | live · rocketry/Rocket.html?vehicle=saturn-v&explode=1&embed=1 | | 22 | Oxidizer and fuel | [[Redox]] | [[Oxidizing_agent]] | `?vehicle=custom&pair=N2O4/UDMH&explode=1` | live · rocketry/Rocket.html?vehicle=custom&pair=N2O4/UDMH&explode=1&embed=1 | | 23 | Mixture ratio | [[Stoichiometry]] | [[Air–fuel_ratio]] | `?vehicle=saturn-v&of=3.4` | live · rocketry/Rocket.html?vehicle=saturn-v&of=3.4&embed=1 | | 24 | Flame temperature | [[Adiabatic_flame_temperature]] | [[Heat_of_combustion]], [[Standard_enthalpy_of_formation]], [[Combustion]] | `?vehicle=custom&pair=LOX/CH4&of=3.4` | live · rocketry/Rocket.html?vehicle=custom&pair=LOX/CH4&of=3.4&embed=1 | | 25 | Dissociation and equilibrium | [[Chemical_equilibrium]] | [[Gibbs_free_energy]] | `?vehicle=custom&pair=LOX/LH2&of=7.9` | live · rocketry/Rocket.html?vehicle=custom&pair=LOX/LH2&of=7.9&embed=1 | | 26 | Cryogenic propellants | [[Cryogenic_rocket_engine]] | [[Liquid_hydrogen]], [[Liquid_oxygen]], [[Methane]], [[RP-1]] | `?vehicle=saturn-v&stage=2&explode=1` | live · rocketry/Rocket.html?vehicle=saturn-v&stage=2&explode=1&embed=1 | | 27 | Hypergolics | [[Hypergolic_propellant]] | [[Hydrazine]], [[Unsymmetrical_dimethylhydrazine]], [[Dinitrogen_tetroxide]], [[Monopropellant]] | `?vehicle=custom&pair=N2O4/MMH&explode=1` | live · rocketry/Rocket.html?vehicle=custom&pair=N2O4/MMH&explode=1&embed=1 | | 28 | Solid propellants | [[Solid-propellant_rocket]] | [[Ammonium_perchlorate_composite_propellant]], [[Ammonium_perchlorate]], [[Hybrid-propellant_rocket]] | `?vehicle=shuttle&explode=1` | live · rocketry/Rocket.html?vehicle=shuttle&explode=1&embed=1 | | 29 | Other propulsion | [[Spacecraft_propulsion]] | [[Spacecraft_electric_propulsion]], [[Ion_thruster]], [[Nuclear_thermal_rocket]], [[Solar_sail]] | `?mode=windows&dest=Pluto` | live · rocketry/Rocket.html?mode=windows&dest=Pluto&embed=1 | | 30 | Atmospheric entry | [[Atmospheric_entry]] | [[Heat_shield]], [[Kármán_line]] | — | section sim on the build list | ## The book shelf | # | Title | Where it serves this page | Where it is | |---|---|---|---| | 1 | Design of Liquid Propellant Rocket Engines, 2nd ed. (Huzel & Huang, NASA SP-125, 1967) | engines, nozzles, cycles, cooling, propellant properties: sections 4, 7, 8, 15, 18-21, 26-27 | `Portal Books/PORTAL_Rocketry/` (NASA, public domain) | | 2 | Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, I and II (Gordon & McBride, NASA RP-1311, 1994/1996) | the propellant chemistry: sections 8, 17, 23-25, 27-28 | `Portal Books/PORTAL_Rocketry/` (NASA, public domain) | | 3 | University Physics Volume 1 (OpenStax, 2016), sec. 9.7 Rocket Propulsion | momentum, the rocket equation, staging: sections 5, 6, 9, 11 | [open.umn.edu](https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-1) | | 4 | Chemistry: Atoms First 2e (OpenStax, 2019), ch. 9 Thermochemistry | enthalpy and flame temperature for the chemistry articles: sections 22-25 | [open.umn.edu](https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first-2e) | The vehicle sources sit beside the shelf rather than on it: the Saturn V Flight Manual SA-503 (1968), NASA's Space Shuttle News Reference (1981), the FAA's 2019 Falcon 9 environmental assessment and the Smithsonian's V-2 record, with the U.S. Standard Atmosphere, 1976 and the JPL planetary elements for the flight and the windows. ## Crosslinks - Anchor article: [[Rocket]] (the pair whose outline this page follows: History, Design › Propellant, Physics). - Sibling rooms: [[PORTAL_Solar_System]] for where the rockets go, [[PORTAL_Physics]] for momentum and gravitation, [[PORTAL_Chemistry]] for redox, stoichiometry and equilibrium, [[PORTAL_Aviation]] for flight in the atmosphere. - The explorer: one page, `rocketry/Rocket.html` on the Wikitube three.js host; its libraries are `wt/wt-rocket.js` (engines, vehicles, ascent, failures, windows), with the 1976 atmosphere in `wt/wt-flight.js` and the Lambert solver in `wt/wt-mech.js`. A child article embeds its own state, for example `?vehicle=shuttle&explode=1&embed=1`. - The build queue: [[PORTAL_Rocketry.worklist]] (30 Main and 53 See-also articles). - Index: [[PORTAL_INDEX]] · all rooms: [[portals]]. ## Notes [^sa503]: NASA Marshall Space Flight Center (1968). *Saturn V Flight Manual SA-503* (MSFC-MAN-503). Stage weights and engine data, p. 1-3; propellant weight summaries, Figs. 2-21 to 2-23. NTRS 19750063889, https://ntrs.nasa.gov/citations/19750063889 [^stsnr]: NASA (1981). *Space Shuttle News Reference*. Solid Rocket Booster statistics, p. 2-18; External Tank, pp. 2-33 to 2-35; main engines, p. 2-6; Orbiter, p. 1-8. NTRS 19810022734, https://ntrs.nasa.gov/citations/19810022734 [^faa]: Federal Aviation Administration (2019). *Draft Environmental Assessment for Issuing SpaceX a Launch License for an In-Flight Dragon Abort Test*, sec. 2.1.3 (Falcon 9) and sec. 2.2 (propellant loads). [^nasm]: Smithsonian National Air and Space Museum. "Missile, Surface-to-Surface, V-2 (A-4)", inventory A19600342000, https://airandspace.si.edu/collection-objects/missile-surface-surface-v-2-4/nasm_A19600342000 [^sp125]: Huzel, D. K.; Huang, D. H. (1967). *Design of Liquid Propellant Rocket Engines*, 2nd ed. NASA SP-125. NTRS 19710019929, https://ntrs.nasa.gov/citations/19710019929 [^rp1311]: Gordon, S.; McBride, B. J. (1994). *Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, I. Analysis*. NASA RP-1311. NTRS 19950013764, https://ntrs.nasa.gov/citations/19950013764 [^rp1311b]: McBride, B. J.; Gordon, S. (1996). *... II. Users Manual and Program Description*. NASA RP-1311-P2, Examples 5, 8 and 12 (appendix G). NTRS 19960044559, https://ntrs.nasa.gov/citations/19960044559 [^ostax]: Ling, S. J.; Sanny, J.; Moebs, W. et al. (2016). *University Physics Volume 1*. OpenStax, sec. 9.7 "Rocket Propulsion", pp. 446-450. https://openstax.org/details/books/university-physics-volume-1 [^usa76]: NOAA, NASA, USAF (1976). *U.S. Standard Atmosphere, 1976*. NASA-TM-X-74335. [^jpl]: JPL Solar System Dynamics, *Approximate Positions of the Planets*, Table 1 (Keplerian elements, valid 1800-2050), https://ssd.jpl.nasa.gov/planets/approx_pos.html, and the JPL Small-Body Database for Pluto - the ephemeris of the Solar System explorer. [^rk]: Computed by the Rocket explorer (wt-rocket.js, 2026-09-18) from the cited inputs: propellant performance from an equilibrium table baked with the RP-1311 method (it reproduces RP-1311 Examples 8 and 12 within 0.1 %), ascent over a rotating Earth in the 1976 Standard Atmosphere, transfers by Lambert's problem over the JPL elements. Values the sources do not give (chamber pressures, nozzle ratios, Falcon 9 and V-2 masses) are marked EST in the explorer. --- *Created 2026-09-18 · wt-portal run (Rocketry) · explorer-first build · 30 sections · 0 deletions* --- *Repopulated 2026-09-19 · append-only · source: _tools/generate/g34_portal_section_sims.py@00a28cb2 (players of the linked articles, each URL 200-checked) · 217 added · 0 deletions*