Atmospheric reentry: Encyclopedia - Atmospheric reentry

Atmospheric reentry

Atmospheric reentry - Introduction

The technology of atmospheric reentry was a consequence of the Cold War. Ballistic missiles and nuclear weapons were legacies of World War II left to both the Soviet Union and the United States. Both nations initiated massive research and development programs to further the military capability of those technologies. However before a missile delivered nuclear weapon could be practical there lacked an essential ingredient: an atmospheric reentry technology. In theory, the nation first developing a reentry technology had a decisive military advantage. At first glance, it was not even certain that such a technology was physically possible. It was a simple calculation to show the kinetic energy of a nuclear warhead returning from orbit was more than sufficient to completely vaporize the warhead. However despite this calculation, the military stakes were so high that simply assuming atmospheric reentry's impossibility was unacceptable. Consequently a crash program was initiated to develop such a technology that in many ways was comparable to the Cold War's nuclear research and development programs. Huge amounts of money along with mankind's greatest minds were allocated towards the task. Of course, atmospheric reentry was possible and the nightmare of world wide thermonuclear destruction became real.

The history of atmospheric reentry might have ended on this dreary note had it not been for another consequence of the Cold War. The Soviet Union saw a propaganda and military advantage in pursuing Space Exploration. To the extreme embarrassment of the United States, the Soviet Union orbited an artificial satellite, followed by a series of other technological firsts that culminated with a Soviet soldier orbiting the Earth and returning safely to Earth. Many of these achievements were enabled through atmospheric reentry technology. The United States saw the Soviet Union's achievements as a challenge to its national pride as well as a threat to national security. Consequently the United States followed the Soviet Union's initiative and began its own Space Program.

Like hope escaping Pandora's Box, Space Exploration became the Cold War's apology. This new hope opened the scope of atmospheric entry technology towards spacecraft exploring other planets, humans traveling to the Moon and the promise of people someday living on worlds beyond our own.

Atmospheric reentry - Terminology definitions and jargon

Over the decades since the 1950s, a rich technical jargon has grown around the engineering of vehicles designed to enter planetary atmospheres. Definition of the jargon is prerequisite to meaningful discussion about atmospheric reentry.

Atmospheric entry is the transition from the vacuum of space to the atmosphere of any planet or other celestial body. The term is not used for landing on bodies which have no atmosphere such as the Moon.

Atmospheric reentry refers to the return to an atmosphere previously left for space. Often the word "atmospheric" is dropped and the term reentry (or re-entry) is taken to mean atmospheric reentry in context.

An entry vehicle is typically a non-military vehicle travelling from the near vacuum of space into the atmospere of a planet. An entry vehicle is used by National Aeronautics and Space Administration (NASA) and civilian space agencies for purposes of Space Exploration.

A Reentry Vehicle (RV) is a munition delivered by an Intercontinental Ballistic Missile (ICBM) of the United States Air Force (USAF) or the military of another country. The photographic film return capsule (now obsolete) for a low earth orbit satellite or military reconnaissance satellite was also called an "RV" for "Recovery Vehicle". It is a common error to call a non-military entry vehicle a "reentry vehicle".

A Reentry Body (RB) is a munition delivered by a Submarine Launched Ballistic Missile (SLBM) of the United States Navy (USN).

An RB or RV could in theory be the same device but never are (the USAF and USN never use the same design). The container inside an RB or RV holding the military payload (thermonuclear explosive) is called a bomb can or a physics package.

The outer structure of an entry vehicle, RV or RB that defines its aerodynamics is called an aeroshell.

An entry vehicle, RV or RB is hypersonic when it has a supersonic free-stream velocity that creates a shock wave processing atmospheric gas into chemical dissociation, e.g. molecular nitrogen breaks down into atomic nitrogen. The gas layer processed by the shock wave located between the shock wave and aeroshell is called the shock layer.

The term hypersonics can have a special meaning refering to the engineering of vehicles that cruise or glide at hypersonic velocity or employ a supersonic combusion ramjet or scramjet.

Entry, Descent and Landing (EDL) is the process of getting an entry vehicle from orbit to a planet's surface. EDL includes parachute deployment (descent) and planet surface landing, e.g. braking rockets, air bags, etc.

Dynamic pressure is one half of the local density of the atmosphere times the atmosphere relative velocity squared. Dynamic pressure is typically referred to as "q".

A sphere-cone is a conical aeroshell with a spherical nose. The outer surfaces are tangential along the line of contact (ring) connecting the spherical nose to the cone or frustum. The outer surface is also called the outer mold line. The angle from the sphere-cone's axis of symmetry to the frustum is called the half-angle. The half-angle of a modern RV or RB is typically around 11 degrees. The half-angle of a non-military entry vehicle is typically 45 degrees or greater but never greater than 70 degrees.

The bluntness ratio of a sphere-cone is the ratio of the nose radius divided by the base radius. Most American interplanetary entry vehicles and the Mk-6 RV have a bluntness ratio of 1:2. The Mk-6 had a half-angle of 20.5°. The Mk-6 carried the largest nuclear warhead of any ICBM RV, i.e. the W-53. The Mk-6 RV was also the design ancestor of almost all American interplanetary entry vehicles, e.g. Pioneer Venus, Galileo Probe, etc.

A Thermal Protection System (TPS) is the atmospheric entry system or material used to protect an aeroshell's payload from heating due to hypersonic entry into the atmosphere. The outer layer of material on the aeroshell is also called TPS, TPS material or TPS layer. A famous TPS material is Teflon which was originally developed by the DuPont Corp. and used on RVs.

TPS failure occurs when the temperature of the material bonding the TPS layer to the aeroshell's structure exceeds the maximum allowed for the bonding material. A typical bondline material is RTV-560 (room-temperature vulcanizing adhesives were originally developed by General Electric for use on RVs). A typical maximum allowed bondline temperature is 250 °C. TPS failure can be exacerbated if spallation occurs. Spallation is where chunks of TPS material are torn away from the outer wall of the TPS. This can happen if the maximum allowed dynamic pressure is exceeded. After EDL or TPS failure, the entry vehicle is said to have augered in. This expression for undesired high speed surface impact dates back to World War II fighter pilots and was also used by test pilots at Edwards Air Force Base, the most well known being Brigadier General Chuck Yeager.

Angle-of-attack is the angle between an entry vehicle's principle axis (axis-of-symmetry) and the free stream velocity vector. There are two forms of angle-of-attack. The more common form used with aircraft restricts angle-of-attack to the aircraft's pitch plane. Side slip angle is used with this common form of angle-of-attack. The other form of angle-of-attack (typically used with entry vehicles) is not restricted to the pitch plane and is called total angle-of-attack. The parameter used with total angle-of-attack is aerodynamic roll angle. Angle-of-attack is often called "alpha". Side slip angle is normally called "beta". An aircraft or entry vehicle is at its trim angle-of-attack when its pitching moment is equal to zero, e.g. a pilot could let go of the control stick and the aircraft's attitude would remain unchanged.

Ballistic entry occurs when an entry vehicle has only drag with no apparent lift. An axisymmetric entry vehicle would have no apparent lift if its angle-of-attack time averaged out to zero, e.g. sinusoid angle-of-attack centered or trimmed about zero lift.

Lifting entry occurs when an entry-vehicle has lift and drag. A manned entry vehicle almost always uses lifting entry to reduce decelleration loading on the crew and improve cross range.

Ballistic coefficient is defined for an entry vehicle as its entry mass divided by the product of its aerodynamic area times its drag coefficient. For an RV or RB, the ballistic coefficient is the entry weight divided by the product of its aerodynamic area times its drag coefficient. Ballistic coefficient is sometimes called "beta".

Lift-over-drag ratio (L/D) is the ratio of the coefficient-of-lift divided by the coefficient-of-drag. The L/D of an entry vehicle undergoing ballistic entry is by definition zero.

The Mach number of an entry vehicle is a dimensionless number derived from the free stream relative velocity divided by the free stream speed-of-sound. Speed-of-sound is proportional to the square root of the absolute temperature of the gas. An extremely hot gas at high velocity could have a relatively low Mach number, e.g. the gas from a commercial plasma cutter flowing at orbital velocity (7.8 km/s) could have a Mach number less than three. An entry vehicle is probably hypersonic if its Mach number is greater than 6 and certainly hypersonic if the the Mach number is greater than 9 (being hypersonic depends upon whether the shock layer has undergone chemical dissociation).

Entry angle, flight-path angle or velocity angle are different names for the angle of the velocity vector to the local horizon. Entry angle is typically referred to as "gamma". There are two types of gamma, i.e. relative gamma and inertial gamma. If no distinction is made then assume the gamma is relative.

A gas so tenuous that it can be modelled as a collection of tiny particles is called free molecular. The transition from a free molecular gas to a continuum gas can be determined by its Knudsen number.

Heat flux is the thermal power per unit area experienced by a TPS. The preferred units for heat flux are watts per square centimeter (W/cm²). Heat load is time integrated heat flux. Heat soak is the component of heat load that actually penetrates the TPS and entry vehicle structure.

The interval along the trajectory where the heat flux rises from insignificance, reaches its peak value and then descends back into insignificant is called the heat pulse. Heat pulse plotted as a function of time typically has a bell curve shape. The heat pulse for Mars Pathfinder lasted about 100 seconds. For the Galileo Probe, the heat pulse lasted about 70 seconds.

The total heat flux experienced by an aeroshell undergoing hypersonic entry can have up to three components, i.e convective heat flux, catalytic heat flux and radiative heat flux. Convective heat flux is simply heat convected from the hot shock layer gas to the cooler aeroshell wall. Catalytic heat flux is produced by dissociated gas species in the shocklayer gas recombining into less reactive molecules on the aeroshell wall thus releasing heat. Radiative heat flux comes from the intense light radiating from the shock layer which is in a state of chemical non-equilibrium due to passing through the shock wave. As a function of time from entry, radiative heat flux always reaches its peak value before the convective heat flux reaches its peak value (this can be used as a simple test of a heating model's validity).

The stagnation point is a region of stagnant flow on the leading edge of an aeroshell (there is also an unimportant stagnation point in the vehicle's wake). For a sphere-cone undergoing ballistic entry, the main stagnation point is on the outer surface of the spherical nose that intersects with the sphere-cone's axis-of-symmetry. The region of high temperature, subsonic flow near the stagnation point is called the subsonic cap. For an aeroshell undergoing hypersonic heating due to a convection dominated heat flux from a laminar flow, the stagnation point is almost always the hottest point on the entry vehicle's outer wall. Therefore conservative design for a TPS is normally based upon conditions at the stagnation point. However, for a radiation dominated heat flux or a turbulent flow, the stagnation point might not be the hottest point on the entry vehicle (this situation can occur during high speed return from the Moon or Mars and is difficult to model).

The Fay-Riddell equation is a relatively compact closed form equation used to model the convective and catalytic heat flux at the stagnation point of an aeroshell. This equation was published in February 1958 by J. A. Fay and F. R. Riddell in the "Journal of the Aeronautical Sciences", Vol. 25, No. 2, page 73. The Fay-Riddell equation is remarkably accurate and sometimes used to validate modern computational fluid dynamics (CFD) solutions. Though virtually unknown outside the aerospace profession, the Fay-Riddell equation is amongst the most brilliant mathematical derivations in the history of science (comparable in mathematical sophistication to the solution of the Schrodinger equation for atomic hydrogen).

Newtonian impact theory is a method for modelling the aerodynamics of blunt entry vehicles at Mach numbers that are normally hypersonic. Newtonian impact theory enables closed form solutions for simple aeroshell geometries and was a preferred modelling method prior to the development of CFD. Newtonian impact theory is still extremely useful for the preliminary design of entry vehicles.

Aerobraking occurs when the free molecular gas of a planet's upper atmosphere is used to reshape the orbit of a spacecraft. Heating due to aerobraking is normally insignificant thus requiring no special thermal protection. The term "aerobraking" is often used incorrectly by people outside the aerospace profession.

Aerocapture occurs when the continuum gas of a planet's atmosphere is used to dissipate the kinetic energy of a spacecraft entering from a heliocentric hyperbolic trajectory and then skipping out of the atmosphere into an elliptical orbit centered around the capturing planet. Aerocapture is an enabling technology for Mars exploration. Protecting against heat soak resulting from aerocapture is technically challenging and maybe insolvable for aerocapture to a gas giant planet such as Neptune. Contrary to science fiction, it is more energy efficient to rocket brake into Jupiter orbit rather than aerocapture (this is an exceptional case and due to Jupiter's very strong gravitational field).

Skip reentry is aerocapture to a suborbital ellipse having an apoapsis (maximum orbital altitude) that is just outside of the atmosphere.

The maximum allowed entry angle for an entry-vehicle is called the overshoot angle. The minimum allowed entry angle for an entry-vehicle is called the undershoot angle. The angular range between the overshoot and undershoot angles defines the entry corridor.

A well posed aerocapture trajectory has two possible trajectory solutions to one capture orbit apoapsis. The "lift-down" trajectory (the bank angle points the lift vector towards the ground) is also called an overshoot trajectory. The "lift-up" trajectory (the bank angle points the lift vector towards the zenith) is also called an undershoot trajectory.

A reaction control system (RCS) is the system of small rocket thrusters that reorient a spacecraft with respect to the inertial frame of reference. Control of an RCS is based upon an inertial measurement unit (IMU).

A three Degree of Freedom (3-DoF) trajectory simulation is a model of an entry vehicle's center-of-mass trajectory based upon three spatial coordinates, e.g. X,Y,Z and their corresponding velocities. A six Degree of Freedom (6-DoF) trajectory simulation is a 3-DoF simulation augmented by a model of the vehicle's orientation based upon pitch, yaw and roll angles along with Euler angles. A 3-DoF simulation treats angle-of-attack and bank angle as user input parameters. A 6-DoF simulation includes angle-of-attack and bank angle within the model (control surface orientation and RCS are the user input parameters). 6-DoF simulation of a hypersonic entry vehicle is much more complicated than classical 6-DoF simulation of a low speed, low flying airplane.

The aerodynamic stability of an aeroshell has two aspects, i.e. static stability and dynamic stability. An aeroshell has static stability when its center of mass is upstream from its aerodynamic center. An aeroshell with static stability can still be unstable if it lacks dynamic stability. Dynamic stability is determined through 6-DoF trajectory simulation.

Atmospheric reentry - Blunt body entry vehicles

These four shadowgraph images represent early re-entry vehicle concepts. A shadowgraph is a process that makes visible the disturbances that occur in a fluid flow at high velocity, in which light passing through a flowing fluid is refracted by the density gradients in the fluid resulting in bright and dark areas on a screen placed behind the fluid.

H. Julian Allen and A. J. Eggers, Jr. of the National Advisory Committee for Aeronautics (NACA) made the counter-intuitive discovery in 1952 that a blunt shape (high drag) made the most effective heat shield. From simple engineering principles, Allen and Eggers showed that the heat load experience by an entry vehicle was inversely proportional to the drag coefficient, i.e. the greater the drag, the less the heat load. Their discovery was initially treated as a military secret but eventually published in 1958 as "A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth's Atmosphere at High Supersonic Speeds," NACA Report 1381. The Blunt Body Theory made possible the heat shield designs that were embodied in the Mercury, Gemini and Apollo space capsules, enabling astronauts to survive the fiery re-entry into Earth's atmosphere.

Atmospheric reentry - Entry vehicle shapes

There are several basic shapes used in designing entry vehicles:

The simplist axisymmetric shape is the spherical section. The spherical section's aerodynamics are easy to model analytically using Newtonian impact theory. Likewise, the spherical section's heat flux can be accurately modelled with the Fay-Riddell equation. The static stability of a spherical section is assured if the vehicle's center-of-mass is upstream from the center-of-curvature (dynamic stability is more problematic). By flying at an angle-of-attack, a spherical section has modest aerodynamic lift thus providing some cross-range capability and widening its entry corridor. In the late 1950s and early 1960s, high speed computers were not yet available and CFD was still embryonic. Because the spherical section was susceptible to closed form analysis, that geometry became the default for conservative design. Consequently, manned capsules of that era were based upon the spherical section. The most famous example of a spherical section entry vehicle was the Apollo Command Module (Apollo-CM). Other examples of spherical section entry vehicles as manned capsules are Soyuz/Zond, Vostok, Gemini and Mercury.

The sphere-cone is a spherical section with a frustum attached. The sphere-cone's dynamic stability is typically better than a spherical section. With a sufficiently small half-angle and properly placed center-of-mass, a sphere-cone can provide aerodynamic stability from atmospheric entry to surface impact. The sphere-cone shape was developed early in the evolution of ICBM RV design, e.g. the Mk-6. The sphere-cone is the preferred geometry for modern ICBM RVs. Reconnaissance satellite RVs also used a sphere-cone shape and were the first example of a non-munition entry vehicle (Discoverer-I, launched on 28 February 1959). The sphere-cone was latter used for space exploration missions to other celestial bodies or for return from open space, e.g. Stardust probe. Space exploration entry vehicles based upon the sphere-cone have landed on the surface or entered the atmospheres of Mars, Venus, Jupiter and Titan.

The biconic is a sphere-cone with an additional frustum attached. The biconic offers a significantly improved L/D ratio. A biconic designed for Mars aerocapture typically has an L/D of approximately 1.0 compared to an L/D of 0.37 for the Apollo-CM. The higher L/D makes a biconic shape better suited for transporting people to Mars due to the lower peak deceleration. Arguably, the most significant biconic ever flown was the Advanced Maneuverable Reentry Vehicle (AMaRV). Four AMaRVs were made by the McDonnell-Douglas Corp and represented a quantum leap in RV sophistication. Three of the AMaRVs were launched by Minuteman-1 ICBMs on 20 December 1979, 8 October 1980 and 4 October 1981. AMaRV had an entry mass of approximately 470 kg, a nose radius of 2.34 cm, a forward frustum half-angle of 10.4°, an inter-frustum radius of 14.6 cm, aft frustum half angle of 6°, and an axial length of 2.079 meters. No accurate diagram or picture of AMaRV has ever appeared in the open literature. A schematic sketch does appear in "Dynamics of Atmospheric Re-Entry" by Regan and Anadakrishnan along with trajectory plots showing hairpin turns. AMaRV's attitude was controlled through a split body flap (also called a "split-windward flap") along with two yaw flaps mounted on the vehicle's sides. Hydraulic actuation was used for controlling the flaps. AMaRV was guided by a fully autonomous navigation system designed for evading anti-ballistic missile (ABM) interception. The McDonnell Douglas DC-X (also a biconic) was essentially a scaled up version of AMaRV. AMaRV and the DC-X also served as the basis for an unsuccessful proposal for what eventually became the Lockheed Martin X-33. Amongst aerospace engineers, AMaRV has achieved legendary status along side such technological marvels as the SR-71 Blackbird and the N-1 rocket.

Non-axisymmetric shapes have been used for manned entry vehicles. One example is the winged orbit vehicle that uses a delta wing for maneuvering during descent much like a conventional glider. This approach has been used by the American Space Shuttle and the Soviet Buran. The lifting body is another entry vehicle geometry and was used with the X-23 PRIME (Precision Recovery Including Manoeuvring Entry) vehicle.

The proposed MOOSE system would have used a one-man inflatable ballistic capsule as an emergency astronaut entry vehicle.

Atmospheric reentry - Shock layer gas physics

An approximate rule-of-thumb used by heat shield designers for estimating peak shock layer temperature is to assume the air temperature in kelvins to be equal to the entry speed in meters per second. For example, a spacecraft entering the atmosphere at 7.8 km/s would experience a peak shock layer temperature of 7800 K. This method of estimation is a mathematical accident and a consequence of peak heat flux for terrestrial entry typically occuring around 60 km altitude.

It is clear that 7800 K is incredibly hot (it is above the boiling point of tungsten at 5828 K). For such high temperatures, the air in the shock layer will break down chemically (dissociate) and also become ionized. This chemical dissociation necessitates various physical models to describe the air's thermal and chemical properties. There are four basic physical models of a gas that are important to aeronautical engineers who design heat shields:

1. Perfect (ideal) gas model
2. Real gas equilibrium model
3. Real gas non-equilibrium model
4. Frozen gas model

Almost all aeronautical engineers are taught the perfect gas model during their undergraduate education. Excerpts from NACA Report 1135 titled "Equation, Tables, and Charts for Compressible Flow" often appear in the appendices of thermodynamics textbooks and is familiar to most aeronautical engineers who design supersonic aircraft. Almost all of the important perfect gas equations along with their corresponding tables and graphs are shown in NACA Report 1135. Perfect gas theory is elegant and extremely useful for designing aircraft but assumes the gas is chemically inert. From the standpoint of aircraft design, air can be assumed to be inert for temperatures less than 550 K at one atmosphere pressure. Perfect gas theory begins to break down at 550 K and is not usable at temperatures greater than 2000 K. For temperatures greater than 2000 K, a heat shield designer must use a real gas model.

The equilibrium real gas model is normally taught to aeronautical engineers studying towards a masters degree. Not surprising, it's a common error for a bachelor's level engineer to incorrectly use perfect gas theory on a hypersonic design. An entry vehicle's pitching moment can be significantly influenced by real gas effects. Both the Apollo-CM and the Space Shuttle were designed using incorrect pitching moments determined through inaccurate real gas modelling. The Apollo-CM's trim angle angle-of-attack was higher than originally estimated, resulting in a narrower lunar return entry corridor. The actual aerodynamic-center of the Space Shuttle Columbia was upstream from the calculated value due to real gas effects. On Columbia's maiden flight (STS-1), astronauts John W. Young and Robert Crippen had some anxious moments during reentry when there was concern about losing control of the vehicle.

An equilibrium real gas model assumes that a gas is chemically reactive but also assumes all chemical reactions have had time to complete and all components of the gas have the same temperature (this is called thermodynamic equilibrium). When air is processed by a shock wave, it is superheated by compression and chemically dissociates through many different reactions (contrary to myth, friction is not the main cause of shock layer heating). The distance from the shockwave to the stagnation point on the entry vehicle's leading edge is called shock wave stand off. An approximate rule-of-thumb for shock wave standoff distance is one-tenth the nose radius. One can estimate the time of travel for a gas molecule from the shock wave to the stagnation point by assuming a free stream velocity of 10 km/s and a nose radius of 1 meter, i.e. time of travel is about 10 microseconds. Ten microseconds is roughly the time required for shock wave initiated chemical dissociation to approach chemical equilibrium. Consequently, as air approaches an entry vehicle's stagnation point, the air effectively reaches chemical equilibrium thus enabling an equilibrium model to be usable. However, most of the shock layer between the shock wave and leading edge of an entry vehicle is chemically reacting and NOT in a state of equilibrium. The Fay-Riddell equation, which is of extreme importance towards modelling heat flux, owes its validity to the stagnation point being in chemical equilibrium.

Determining the thermodynamic state of the stagnation point is more difficult under an equilibrium gas model than a perfect gas model. Under a perfect gas model, the ratio of specific heats (also called "isentropic exponent", adiabatic index, "gamma" or "kappa") is assumed to be constant along with the gas constant. For a real gas, the ratio of specific heats can wildly oscillate as a function of temperature. Under a perfect gas model there is an elegant set of equations for determining thermodynamic state along a constant entropy stream line called the isentropic chain. For a real gas, the isentropic chain is unusable and a Mollier diagram would be used instead for manual calculation. However graphical solution with a Mollier diagram is now considered obsolete with modern heat shield designers using computer programs based upon a digital lookup table (another form of Mollier diagram) or a chemistry based thermodynamics program. The chemical composition of a gas in equilibrium with fixed pressure and temperature can be determined through the Gibbs free energy method. Gibbs free energy is simply the total enthalpy of the gas minus its total entropy times temperature. A chemical equilibrium program normally does not require chemical formulas or reaction rate equations. The program works by preserving the original elemental abundances specified for the gas and varying the different molecular combinations of the elements through numerical iteration until the lowest possible Gibbs free energy is calculated (a Newton-Raphson method is the usual numerical scheme). The data base for a Gibbs free energy program comes from spectroscopic data used in defining partition functions. Among the best equilibrium codes in existence is the program Chemical Equilibrium with Applications (CEA) which was written by Bonnie J. McBride and Sanford Gordon at NASA Lewis (now renamed "NASA Glenn Research Center"). Other names for CEA are the "Gordon and McBride Code" and the "Lewis Code". CEA can be downloaded from the Internet along with full documentation and will compile on Linux under the G77 Fortran compiler.

A non-equilibrium real gas model is the most accurate model of a shock layer's gas physics but is more difficult to solve than an equilibrium model. The simplest non-equilibrium model is the Lighthill-Freeman model (Lighthill, M.J., 1957, "Dynamics of a Dissociating Gas. Part I. Equilibrium Flow," Journal of Fluid Mechanics, vol. 2, pt. 1. p. 1; Freeman, N.C., 1958 "Non-equilibrium Flow of an Ideal Dissociating Gas." Journal of Fluid Mechanics, vol. 4, pt. 4, p. 407). The Lighthill-Freeman model initially assumes a gas made up of a single diatomic species susceptible to only one chemical formula and its reverse, e.g. N₂ → N + N and N + N → N₂ (dissociation and recombination). Because of its simplicity, the Lighthill-Freeman model is a useful pedagogical tool but is unfortunately too simple for modeling non-equilibrium air. Air is typically assumed to have a mole fraction composition of 0.7812 molecular nitrogen, 0.2095 molecular oxygen and 0.0093 argon. The simplist real gas model for air is the five species model which is based upon N₂, O₂, NO, N and O. The five species model assumes no ionization and ignores trace species like carbon dioxide.

When running a Gibbs free energy equilibrium program, the iterative process from the originally specified molecular composition to the final calculated equilibrium composition is essentialy random and not time accurate. With a non-equilibrium program, the computation process is time accurate and follows a solution path dictated by chemical and reaction rate formulas. The five species model has 17 chemical formulas (34 when counting reverse formulas). The Lighthill-Freeman model is based upon a single ordinary differential equation and one algebraic equation. The five species model is based upon 5 ordinary differential equations and 17 algebraic equations. Because the 5 ordinary differential equations are loosely coupled, the system is numerically "stiff" and difficult to solve. The five species model is only usable for entry from low Earth orbit where entry velocity is approximately 7.8 km/s. For lunar return entry of 11 km/s, the shock layer contains a significant amount of ionized nitrogen and oxygen. The five species model is no longer accurate and a twelve species model must be used instead. High speed Mars entry which involves a carbon dioxide, nitrogen and argon atmosphere is even more complex requiring a 19 species model.

The frozen gas model describes a special case of a gas that is not in equilibrium. The name "frozen gas" is misleading. A frozen gas is not "frozen" like ice is frozen water. Rather a frozen gas is "frozen" in time (all chemical reactions are assumed to have stopped). Chemical reactions are normally driven by collisions between molecules. If gas density is slowly reduced such that chemical reactions can continue then the gas can remain in equilibrium. However it is possible for gas density to be so suddenly reduced that almost all chemical reactions stop. For that situation the gas is considered frozen.

The distinction between equilbrium and frozen is important because it is possible for a gas such as air to have significantly different properties (speed-of-sound, viscosity, etc.) for the same thermodynamic state, e.g. pressure and temperature. Frozen gas can be a significant issue in the wake behind an entry vehicle. During reentry, free stream air is compressed to high temperature and pressure by the entry vehicle's shock wave. Non-equilibrium air in the shock layer is then transported past the entry vehicle's leading side into a region of rapidly expanding flow that causes freezing. The frozen air can then be entrained into a trailing vortex behind the entry vehicle. Correctly modelling the flow in the wake of an entry vehicle is very difficult. TPS heating in the vehicle's afterbody is usually not very high but the geometry and unsteadiness of the vehicle's wake can significantly influence aerodynamics (pitching moment) and particularly dynamic stability.

Atmospheric reentry - Ablative heat shields

The type of heat shield that best protects against high heat flux is the ablative heat shield. The ablative heat shield functions by lifting the hot shock layer gas away from the heat shield's outer wall (creating a cooler boundary layer) through blowing. The overall process of reducing the heat flux experienced by the heat shield's outer wall is called blockage. Ablation causes the TPS layer to char, melt, and sublimate through the process of pyrolysis. The gas produced by pyrolysis is what drives blowing and causes blockage of convective and catalytic heat flux. Ablation can also provide blockage against radiative heat flux by introducing carbon into the shock layer thus making it optically opaque. Radiative heat flux blockage was the primary thermal protection mechanism of the Galileo Probe TPS material (carbon phenolic). Thermal protection can also be enhanced in some TPS materials through coking. Coking is the process of forming solid carbon on the outer char layer of the TPS. TPS coking was discovered accidently during development of the Apollo-CM TPS material (Avcoat 5026-39).

The thermal conductivity of a TPS material is proportional to the material's density. Carbon phenolic is a very effective ablative material but also has high density which is undesirable. If the heat flux experienced by an entry vehicle is insufficient to cause pyrolysis then the TPS material's conductivity could allow heat flux conduction into the TPS bondline material thus leading to TPS failure. Consequently for entry trajectories causing lower heat flux, carbon phenolic is inappropriate and lower density TPS materials like SLA-561V or SIRCA are better design choices. SLA stands for "Super Light weight Ablator". All of the 70 degree sphere-cone entry vehicles sent by NASA to Mars used SLA-561V as their primary TPS material. SLA-561V begins significant ablation at a heat flux of approximately 80 W/cm² but will fail for heat fluxes greater than 300 W/cm². SLA-561V would be unusable as an Apollo-CM TPS material for lunar return where the peak heat flux is around 497 W/cm². The peak heat flux experienced by the Viking-1 aeroshell which landed on Mars was 21 W/cm². For Viking-1, the TPS acted as a pure thermal insulator and never experienced significant ablation (an inappropriate design choice). However for the Mars Pathfinder aeroshell, the peak heat flux was 106 W/cm². SLA-561V was an appropriate design choice for Mars Pathfinder.

Atmospheric reentry - Thermal soak heat shields

Thermal soak is a part of almost all TPS schemes. For example, an ablative heat shield loses most of its thermal protection effectiveness when the outer wall temperature drops below the minimum necessary for pyrolysis. From that time to the end of the heat pulse, heat from the shock layer soaks into the heat shield's outer wall and would eventually convect to the payload. This outcome is prevented by ejecting the heat shield (with its heat soak) prior to the heat convecting to the inner wall.

Thermal soak TPS is intended to shield mainly against heat load and not against a high peak heat flux (a long duration heat pulse of low intensity is assumed for the TPS design). The Space Shuttle orbit vehicle was designed with a reusable heat shield based upon a thermal soak TPS. A Space Shuttle's underside is coated with thousands of tiles made of silica foam that are intended to survive multiple reentries with only minor repairs between missions. When a Space Shuttle lands, there is a significant amount of heat stored in the TPS. Shortly after landing, a ground support cooling unit connects to the Space Shuttle's internal freon coolant loop to remove heat soaked in the TPS and orbiter structure.

Typical Space Shuttle's TPS tiles (LI-900) have remarkable thermal protection properties but are relatively brittle and break easily. An LI-900 tile could be exposed to a temperature of a 1000 K on one side, but merely warm to the touch on the other side. An impressive stunt that can be performed with a cube of LI-900 is to remove it glowing white hot from a furnace and then hold it with one's bare fingers without discomfort along the cube's edges (the author has done this).

Atmospheric reentry - Passively cooled heat shields

In some early ballistic missile RVs, e.g. the Mk-2 and the sub-orbital Mercury spacecraft, radiatively cooled TPS were used to initially store heat flux during the heat pulse and then latter radiate the heat away from the vehicle. However the technique required a considerable quantity of metal TPS (e.g. beryllium), adding greatly to the vehicle's mass. Consequently ablative and thermal soak TPS have been more common.

Some high-velocity aircraft, such as the SR-71 Blackbird and Concorde, had to deal with heating similar to that experienced by spacecraft but at much lower intensity. Studies of the SR-71's titanium skin revealed the metal structure was restored to its original strength through annealing due to aerodynamic heating. In the case of Concorde the nose was permitted to reach a maximum operating temperature of 260 degrees Fahrenheit (127 degrees Celsius), typically 180 degrees Celsius (325 degrees Fahrenheit) warmer than the ambient air.

A radiatively cooled TPS for an entry vehicle is often called a hot metal TPS. Early TPS designs for the Space Shuttle called for a hot metal TPS based upon titanium shingles. Unfortunately the earlier Shuttle TPS concept was rejected because it was incorrectly believed a silica tile based TPS offered less expensive development and manufacturing costs. A titanium shingle TPS was again proposed for the unsuccessful X-33 Single-Stage to Orbit (SSTO) prototype.

Atmospheric reentry - Actively cooled heat shields

Various advanced reusable spacecraft and hypersonic aircraft designs have been proposed to employ heat shields made from temperature-resistant metal alloys that incorporated a refrigerant or cryogenic fuel circulating through them. Such a TPS concept was proposed for the X-30 National Aerospace Plane (NASP). The NASP was supposed to have been a scramjet powered hypersonic aircraft but failed in development.

In the early 1960s various TPS systems were proposed to use water or other cooling liquid sprayed into the shock layer. Such concepts never got past the proposal phase since ordinary ablative TPS is much more reliable and mass efficient.

Atmospheric reentry - Feathered reentry

In 2004, aircraft designer Burt Rutan demonstrated the feasibility of an alternative or complementary approach to atmospheric reentry with the suborbital SpaceShipOne.

SpaceShipOne has what has been described as a pair of flipping wings; the spacecraft itself changes shape for reentry.

This increases drag, as the craft is now less streamlined. This results in more atmospheric gas particles hitting the spacecraft at higher altitudes than otherwise. The aircraft thus slows down more in higher atmospheric layers (which is the very key to efficient reentry, see above). It should also be noted that SpaceShipOne, in its "wings flipped" configuration, will automatically orient itself to a high drag attitude. Rutan has compared this to a falling shuttlecock.

However, it is important to realise that the velocity obtained by SpaceShipOne prior to reentry is much lower than of an orbital spacecraft, and most engineers (including Rutan) do not consider the shuttlecock reentry technique viable for return from orbit.

Atmospheric reentry - Entry vehicle design considerations

There are four critical parameters considered when designing a vehicle for atmospheric entry:

1. Peak heat flux
2. Heat load
3. Peak deceleration
4. Peak dynamic pressure

Peak heat flux selects the TPS material. Heat load selects the thickness of the TPS material stack. Peak deceleration is of major importance for manned missions. The upper limit for manned return to Earth from Low Earth Orbit (LEO) or lunar return is 10 G. For martian atmospheric entry after long exposure to zero gravity, the upper limit is 4 G. Peak dynamic pressure can also influence the selection of the outermost TPS material if spallation is an issue.

The designer typically considers two worst case trajectories, the undershoot and overshoot trajectories. The overshoot trajectory is typically defined as the shallowest allowable entry velocity angle prior to atmospheric skip-off. The overshoot trajectory has the highest heat load and sets the TPS thickness. The undershoot trajectory is defined by the steepest allowable trajectory. For manned missions the steepest entry angle is limited by the peak deceleration. The undershoot trajectory has the highest heat flux and therefore defines selection of the TPS material.

Based upon Allen and Eggers discovery, maximum aeroshell bluntness (maximum drag) yields minimum TPS mass. Maximum bluntness (minimum ballistic coefficient) also yields a minimal terminal velocity at maximum altitude (very important for Mars EDL). However there is an upper limit to bluntness imposed by aerodynamic stability considerations based upon shock wave detachment. A shock wave will remain attached to the tip of a sharp cone if the cone's half-angle is below a critical value. This critical half-angle can be estimated using perfect gas theory (this specific aerodynamic instability occurs below hypersonic speeds). For a nitrogen atmosphere (Earth or Titan), the maximum allowed half-angle is approximately 60 degrees. For a carbon dioxide atmosphere (Mars or Venus), the maximum allowed half-angle is approximately 70 degrees. After shock wave detachment, an entry vehicle must carry significantly more shocklayer gas around the leading edge stagnation point (the subsonic cap). Consequently, the aerodynamic center moves upstream thus causing aerodynamic instability. It is incorrect to reapply an aeroshell design intended for Titan entry (Huygens probe in a nitrogen atmosphere) for Mars entry (Beagle-2 in a carbon dioxide atmosphere). After being abandoned, the Soviet Mars lander program achieved no successful landings (no useful data returned) after multiple attempts. The Soviet Mars landers were based upon a 60 degree half-angle aeroshell design. In the early 1960s, it was incorrectly believed the Martian atmosphere was mostly nitrogen, (actual Martian atmospheric mole fractions are carbon dioxide 0.9550, nitrogen 0.0270 and argon 0.0160). The Soviet aeroshells were probably(?) based upon an incorrect Martian atmospheric model and then not revised when new data became available.

A 45 degree half-angle sphere-cone is typically used for atmospheric probes (surface landing not intended) even though TPS mass is not minimized. The rationale for a 45 degree half-angle is either aerodynamic stability from entry-to-impact (the heat shield is not jettisoned) or a short-and-sharp heat pulse followed by prompt heat shield jettison. A 45 degree sphere-cone was used with the Deep Space 2 (DS/2) Mars landers but that design was not successful.

Atmospheric reentry - History's most difficult atmospheric entry

The highest speed controlled entry so far achieved was by the Galileo Probe. The Galileo Probe was a sphere-cone that entered Jupiter's atmosphere at 47.4 km/s (atmosphere relative speed at 450 km above the 1 bar reference altitude). The peak (blocked) total heat flux for the Galileo Probe was 16900 W/cm². By way of comparison, the peak total heat flux experienced by a Martian entry vehicle (Mars Pathfinder) was 106 W/cm². The Apollo-4 (AS-501) command module which reentered the Earth's atmosphere at a velocity of 10.77 km/s (atmosphere relative speed at 121.9 km altitude) experienced a peak total heat flux of 497 W/cm². Carbon phenolic was the TPS material used for the Galileo Probe. Carbon phenolic was earlier used for the Pioneer Venus Probes which were the design ancestors to the Galileo Probe. Carbon phenolic was originally developed as a rocket nozzle throat material and then latter used for RV nose tips. The Galileo Probe experienced far greater TPS recession near the base of its frustum than expected. Despite a factor of two safety factor in TPS thickness, the Galileo Probe's heatshield almost failed. The two conflicting theories describing this near failure were higher than expected spallation due to hypersonic turbulence and/or radiative heat flux. The precise mechanism for this higher TPS recession is unknown and currently beyond definitive theoretical analysis.

Atmospheric reentry - Notable atmospheric entry mishaps

Successful atmospheric entry is difficult to achieve. Fortunately we learn from our mistakes:

• Vostok 1 - The service module failed to detach for 10 minutes, but fortunately the courageous Yuri Gagarin survived.
• Mercury 6 - Instrument readings show that the heat shield and landing bag were not locked. It is decided to left the retrorocket in position during reentry. Astronaut John Glenn survived.
• Voskhod 2 - The service module failed to detach for some time, but the crew survived.
• Soyuz 1 - Different accounts exist. Either the attitude control system failed while still in orbit and/or parachutes got entangled during the landing sequence (EDL failure). Cosmonaut Vladimir Mikhailovich Komarov died.
• Soyuz 5 - The service module failed to detach, but crew survived.
• Soyuz 11 - The crew perished due to early depressurization.
• Space Shuttle Columbia - The failure of a Reinforced Carbon-Carbon (RCC) tile on a wing leading edge led to breakup of the orbit vehicle at hypersonic speed resulting in the loss of all seven crew members.
• Mars Polar Lander (MPL) - Failed during EDL. The failure was believed to be the consequence of a software error. The precise cause is unknown due to lack of real time telemetry.
• Genesis - The parachute failed to deploy due to a G-switch being installed backwards (a similar error delayed parachute deployment for the Galileo Probe). Consequently, the Genesis entry vehicle augered into the desert floor. The payload was damaged but it was later claimed that some science data was recoverable.

Atmospheric reentry - Uncontrolled reentry

More than 100 metric tons of man-made objects reenter in an uncontrolled fashion each year. The vast majority burn up before reaching earth's surface. On average, about one cataloged object reenters per day. Approximately one-fourth of all objects are of U.S. origin. Due to the Earth's surface being primarily water, most objects that survive re-entry land in one of the world's oceans.

Atmospheric reentry - Reference books

Martin, John J., "Atmospheric Entry - An Introduction to Its Science ane Engineering," Prentice-Hall, Old Tappan, NJ, (1966).

Regan, Frank J., "Re-Entry Vehicle Dynamics," AIAA Education Series, American Institute of Aeronautics and Astronautics, Inc., New York, ISBN 0-915928-78-7, (1984).

Regan, Frank J. and Anadakrishnan, Satya M., "Dynamics of Atmospheric Re-Entry," AIAA Education Series, American Institute of Aeronautics and Astronautics, Inc., New York, ISBN 1-56347-048-9, (1993).

Etkin, Bernard, "Dynamics of Atmospheric Flight," John Wiley & Sons, Inc., New York, ISBN 0-471-24620-4, (1972).

Vincenti, Walter G. and Kruger, Jr., Charles H., "Introduction to Physical Gas Dynamics," Robert E.Krieger Publishing Co., Malabar, Forida, ISBN 0-88275-309-6, (1986).

Hansen, C. Frederick, "Molecular Physics of Equilibrium Gases, A Handbook for Engineers," NASA SP-3096, NASA (1976).

Atmospheric reentry - Commentary about the reference books

John J. Martin's book was the first and arguably the best in the open literature about designing reentry vehicles. In his book, Martin showed an incredible depth and breadth of knowledge. Unfortunately, this book has been out-of-print for decades but can still be easily acquired second hand through the Internet and is not overly expensive.

John J. Martin was educated as a mechanical engineer, receiving a Ph.D. from Purdue University in 1951. He joined North American Aviation in 1951 and moved to the Bendix Corp. in 1953. In 1960 he joined the Institute for Defense Analyses. While on sabbatical at the Royal Aircraft Establishment in Farnborough, England, Martin wrote "Atmospheric Entry". Sir Michael James Lighthill, who was Martin's host at the Royal Aircraft Establishment, wrote the Foreward to Martin's book. In 1969, Martin served as a science advisor to the US President. During 1973-1974 Martin served as an Associate Deputy Director at the Central Intelligence Agency and later as Deputy Assistant Secretary of the US Air Force. In 1984, Martin became an Associate Administrator at NASA.

"Dynamics of Atmospheric Re-Entry" by Frank J. Regan and Satya M. Anandakrishnan is a revision of Regan's earlier book, "Re-Entry Vehicle Dynamics". Unfortunately Chapter 10 of "Re-Entry Vehicle Dyanmics" was deleted when the book was revised into the newer version. Chapter 10, titled "Moment Equations in Constant Density Atmosphere" concerned the subjects of entry vehicle roll resonance and tricyclic theory. "Re-Entry Vehicle Dynamics" has been out-of-print for years and currently no used copies are listed on the Internet. If you find a second-hand copy of "Re-Entry Vehicle Dynamics", buy it (it's a very rare book). Should you find "Re-Entry Vehicle Dynamics" in a library, photocopy Chapter 10. Despite the omissions from the earlier version, "Dynamics of Atmospheric Re-Entry" is a very useful book and still in print, though very expensive (current list price of $105.95).

Bernard Etkin is the world recognized authority on aircraft guidance and control. Classical 6-DoF theory for aircraft assumes a flat earth with constant atmospheric density in an inertial frame. Consequently classical 6-DoF theory should not be used for simulating hypersonic atmospheric flight that lasts for several minutes. Clasical 6-DoF for hypersonic flight is approximately correct only for a few seconds, e.g. stability analysis for a time discrete event. Etkin's treatment of 6-DoF theory in "Dynamics of Atmospheric Flight" was unusual in being sufficiently general that it touched upon hypersonic flight.

"Introduction to Physical Gas Dynamics" by Vincenti and Kruger is widely used for graduate course work in real gas physics. The book provides an excellent introduction into non-equilibrium gas physics and describes the Lighthill-Freeman model in detail. Most university bookstores offer Vincenti and Kruger for sale (it's a very common book).

Frederick Hansen's NASA SP-3096 is arguably one of the best introductory texts on equilibrium thermodynamics and was written specifically for aeronautical engineers doing entry vehicle work. The partition functions listed in NASA SP-3096 are inaccurate (use the polynomial fits from the Gordon and McBride code, CEA). NASA SP-3096 can sometimes be found used and is in US government document libraries. NASA SP-3096 is worth the trouble of photocopying (it's in the public domain).

A basic dilemma with aerospace technological information is its intrinsic dual use, i.e. aerospace technology can be used towards the extreme benefit of humanity or towards its utter detriment. The technology of atmospheric entry owes its origins to the development of ballistic missiles during the Cold War. Given the enormous expense required in developing atmospheric entry technology, it is doubtful this technology could ever have appeared without the military incentive. It is profoundly ironic that the same techology enabling the annihilation of modern civilization also enabled the exploration and development of outer space. Mankind's survival beyond its planet of origin is dependent upon atmospheric entry technology. Therein lies the fundamental dilemma, aerospace technology must remain open to enable mankind's access to outer space while also remaining restricted to prevent proliferation of weapons of mass destruction (WMD). This basic dilemma is present throughout the literature on atmospheric entry. There is a glass wall between pedagogical and practical information. For example, in the text books listed above, a topic thread will proceed as long as the information is nonspecific but almost always stops at the point of practical application. To go beyond pedagogical information, one must search the technical literature (NACA/NASA Technical Reports, declassified technical reports and peer reviewed archive literature). Declassified technical reports are a frustrating information source since many of the reports were destroyed prior to going through the legally required declassification process. It is almost always true that significant documents referred to in declassified technical reports no longer exist (technical information that cost many millions of dollars to develop has vanished without a trace).

See also

• Shock heating
• skip reentry
• mid-air retrieval

Adapted from the Wikipedia article "Atmospheric reentry", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki