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[edit] An Overview of Atmospheric Entry

Abstract: This Technical Report provides a broad overview of the process of atmospheric entry. It discusses the various considerations which should be taken into account when choosing an entry trajectory for a particular spacecraft, the different varieties of entry trajectory available and their characterisations in terms of the considerations introduced earlier, and the factors which must be controlled to achieve a particular entry trajectory. Mathematical models appropriate for simulating atmospheric entry are developed. A survey of techniques and technologies relating to atmospheric entry is given.

[edit] Introduction

Atmospheric entry is the process by which a spacecraft enters a planet or other body's atmosphere. The most familiar example is Earth atmosphere reentry, when a spacecraft launched from Earth returns to the ground (such as a landing of a manned spacecraft), although the term also encompasses the entry by interplanetary probes (such as Mars landers or rovers) of atmospheres other than that of Earth. The process of atmospheric entry can be quite punishing of spacecraft, subjecting them to very high acceleration, dynamic pressure and temperature, making it one of the highest risk parts of any spaceflight, and designing a spacecraft to survive entry one of the most demanding tasks a spacecraft designer faces: the dynamic and thermal loads which a spacecraft is subject due during atmospheric entry are influenced by the vehicle's size, mass, shape and flight plan, and these loads can in turn influence the choice of materials for a spacecraft's construction (which feeds back into the spacecraft mass).

The primary reference for this report is ^[1].

[edit] Considerations in choosing an entry trajectory

The details of a spacecraft's entry trajectory can have a very significant impact on the conditions the spacecraft is subject to during entry. In this section we discuss some of the most important considerations which need to be taken into account in choosing an entry trajectory for a space mission.

[edit] Dynamic loads

Different entry trajectories submit spacecraft to different so-called dynamic loads. This term refers to things such as levels of acceleration (colloquially called "g forces"), dynamic pressure, vibration, etc. Dynamic loads have the potential to damage or even destroy spacecraft, parts of spacecraft, or spacecraft payloads if these are not designed to endure them. This point is particularly salient for manned spacecraft, where the maximum acceleration experienced during entry must be carefully considered. Accelerations beyond particular thresholds can cause loss of consciousness and even death in humans.

[edit] Thermal loads

Perhaps the most well known detail of atmospheric entry is the extremely high temperatures which a spacecraft may have to endure during entry. Contrary to popular belief, this heating is primarily not caused by friction between the spacecraft and the atmosphere, but rather by the compression of the atmospheric gases in a "shock layer". Heat is transferred from the hot compressed gases to the spacecraft primarily through conduction, although at very high entry speeds radiative heating can also become significant. A spacecraft's thermal protection system, designed to protect the spacecraft against these temperatures, is of vital importance, and TPS failures have dramatic consequences (e.g. the 2003 destruction of the Space Shuttle Columbia). There are two important factors to consider with regard to thermal loads: the total heat load, which is the total quantity of heat energy (in, e.g., kilojoules) transferred to the spacecraft during entry, and the instantaneous heating rate, which is the rate at which this energy is transferred (in, e.g, kilowatts), which varies with time as well as over the surface area of the spacecraft.

[edit] Landing footprint

If a spacecraft is to be recovered shortly after landing, as is typically the case with manned spacecraft, it is important to have in advance an accurate estimate of the spacecraft's landing site. Different entry trajectories can lead to variations in both the inherent accuracy with which an entry can be aimed, and the extent to which a spacecraft can control its descent to aim for a designated landing site.

[edit] Types of entry trajectory

While all atmospheric entry trajectories are dictated by the same physical forces, there are meaningful distinctions to be made between different classes or types of trajectory. In this section we discuss some common or significant trajectory types, and briefly discuss the types in terms of typical dynamic and thermal loads and landing footprints.

[edit] Ballistic entry

A ballistic entry is, by definition, an entry during which the spacecraft does not generate any aerodynamic lift, and thus the only forces acting on spacecraft are gravitational attraction to the planet or other body whose atmosphere is being entered, and aerodynamic drag resulting from movement through the atmosphere. Ballistic entry occurs when a spacecraft is symmetric about the entry velocity vector, as is always the case for spherical spacecraft (such as the Vostok and Voskhod capsules from early Soviet human spaceflight), and for conical spacecraft (such as the US Mercury, Gemini and Apollo spacecraft) flown with zero angle of attack. In practice, a zero angle of attack is rare for a conical spacecraft (since the spacecraft's centre of mass usually does not lie along a line of symmetry - and this was the case for the three aforementioned US spacecraft), however if the spacecraft is rolled constantly during entry, the direction of the lifting force generated by the non-zero angle of attack is "spread around" uniformly, resulting in a roughly ballistic trajectory. This technique was used by the Mercury spacecraft.

Generally speaking, ballistic entry trajectories are associated with higher levels of acceleration (no less than 8 g when entering Earth's atmosphere, which is survivable by humans but very uncomfortable) than other entry trajectories. They feature a lower total heat load than non-ballistic trajectories, but higher instantaneous heating rates. Ballistic trajectories do not allow any control (or "steering") of the spacecraft during reentry, resulting in large landing footprints. Some of these disadvantages explain why spherical spacecraft (which must necessarily undergo ballistic entry) have not been used for manned spaceflight since its earliest days, despite their other advantages (such as general simplicity and optimal internal volume to structural mass ratios).

[edit] Gliding or lifting entry

A gliding entry, or lifting entry, is the logical opposite of a ballistic entry, i.e. an entry in which the spacecraft does generate aerodynamic lift. This occurs with conical or otherwise radially symmetric spacecraft flown with a non-zero angle of attack (as seen in the Gemini, Apollo and Soyuz spacecraft), and more significantly with winged spacecraft such as the US Space Shuttle.

Even quite modest magnitudes of lifting force are sufficient to significantly reduce both the maximum acceleration and the instantaneous heating rate experienced during reentry, making lifting trajectories more desirable than ballistic trajectories in many cases, and especially manned spacecraft, where the lower acceleration leads to greater comfort and safety for occupants. It is important to note that, while lifting entries experience lower instantaneous heating rates than ballistic entires, the typically longer duration of lifting entries results in a higher total heat load. Thus the difference between ballistic and lifting entries from a thermal loading point of view can be characterised as a choice between a small amount of heat energy absorbed quickly or a large amount of heat energy absorbed gradually (where "small" and "large", and "quickly" and "gradually" are understood to be relative terms).

[edit] Skip entry

A skip entry is a particular class of lifting entry in which the magnitude of the lifting force and the angle of reentry are such that after initially entering the atmosphere, the spacecraft then lifts itself back out of the atmosphere into open space, completing a brief suborbital flight before entering the atmosphere a second time, at significantly reduced velocity to the first entry.

While skip entries are generally more complicated than other lifting entries or ballistic entries (requiring more precise control over the various factors affecting entry trajectories), they are extremely useful in some situations. For instance, when entry velocities are very high (such as when returning to Earth from the moon), skip entries permit lower thermal loads than "direct" entries, since much of the kinetic energy associated with the spacecraft is removed during the first "skip". Also, skip entries can allow landing in areas which could not be reached from the same entry conditions using non-skip entries, which can be useful when astrodynamical considerations prohibit a "direct" descent to a desired landing site.

Skip entries are relatively rare in practice, but were used successfully as part of the Soviet Zond program.

[edit] Factors affecting entry trajectories and associated phenomena

Having discussed various significant types of entry trajectories and their characteristics, we now turn our attention to the various factors which affect a spacecraft's entry trajectory. These are the factors which must be considered, designed or controlled in order to achieve a particular choice of trajectory.

[edit] Factors related to the spacecraft and its flight

Many of the factors affecting entry trajectory pertain to either the spacecraft itself or the manner in which it is flown. These are the factors of greatest interest to the spacecraft designer or space mission planner, since they may be directly designed or controlled to achieve the desired trajectory.

Spacecraft shape (since this influences drag and lift)
Spacecraft mass
Spacecraft centre of mass
Spacecraft control program
Entry velocity
Entry angle

[edit] Factors related to the atmosphere and associated body

An entry trajectory is not determined uniquely by particulars of the spacecraft and its flight: the particulars of the atmosphere being entered and the body (most likely a planet or moon) it surrounds are also influential. Obviously, these factors are not under the control of designers or planners.

Atmospheric density
Mass of planet/body (since this influences gravitational acceleration)

[edit] Mathematical models

The descriptions of entry trajectories thus far has been quite generalised and qualitative in nature. Obviously, when designing actual spaceflights, more precise analyses of atmospheric entry are required. Mathematical models can be used to compute actual numerical values of such quantities as maximum acceleration or maximum temperature during atmospheric entry, and these models are indispensable for planning purposes. In this section we develop a mathematical model of atmospheric entry.

The full equations of motion dictating atmospheric entry are non-linear and do not admit an analytic solution. However, they may be solved numerically using algorithms such as the Runge Kutta methods. By making various simplifying assumptions, approximate forms of the equations can be found which are analytically solvable.

[edit] Trajectory models

[edit] Model geometry and notation

Let:

$LaTeX: V =$ inertial velocity
$LaTeX: R =$ planetary radius
$LaTeX: h =$ height above planetary surface
$LaTeX: r = R +h =$ distance from planetary center
$LaTeX: s =$ down-range travel relative to non-rotating planet
$LaTeX: \gamma =$ flight-path angle (positive above local horizon)
$LaTeX: m =$ spacecraft mass
$LaTeX: g(h) =$ gravitational acceleration at height $LaTeX: h$

[edit] Concepts

In addition to basic physics (Newton's laws of motion and constant gravitational acceleration) and basic geometry (including decomposition of vectors into orthogonal components using trigonometric functions), the main components of our mathematical model of atmospheric entry trajectories are the equations for calculating drag and lift.

The drag equation is:

$LaTeX: F_D\, =\, \tfrac12\, \rho\, u^2\, C_D\, A,$

where

F_D is the force of drag, which is by definition the force component in the direction of the flow velocity,

ρ is the mass density of the fluid,

u is the velocity of the object relative to the fluid,

A is the reference area, and

C_D is the drag coefficient

The lift equation is:

$LaTeX: C_L={L \over \frac{1}{2}\rho v^2A} = \frac{L}{q A}$

where

L is the lift force,

ρ is fluid density,

v is true airspeed,

q is dynamic pressure, and

A is planform area.

Both of these equations make reference to the density $LaTeX: \rho$ of the atmosphere. This differs with altitude, and for the purposes of numerical integration of the equations of motion, an atmospheric model must be used. Some available models include:

[edit] Equations of motion

Using the model geometry defined above, and subjecting the model spacecraft to gravitational acceleration, drag and lift (as defined above), we arrive at the equations of motion:

$LaTeX: \frac{dV}{dt} = - \frac{D}{m} - g(h)sin(\gamma)$
$LaTeX: \frac{dr}{dt} = \frac{dh}{dt} = Vsin(\gamma)$
$LaTeX: \frac{Vd\gamma}{dt} = \frac{L}{m} - \left(g(h) - \frac{V^2}{r}\right)cos(\gamma)$
$LaTeX: \frac{ds}{dt} = \left(\frac{R}{r}\right)Vcos(\gamma)$

Solution of these equations allows the computation of the acceleration and dynamic pressure at all times during the entry.

[edit] First order analytic solutions

As has been mentioned, the nonlinear equations of motion do not permit an exact analytic solution. However, by making certain simplifying assumptions, we can develop simplified, so-called "first order" approximations to the equations which are analytically tractable. We do not present these approximations or the means of their solution here, but we present some results of interest.

[edit] Thermal load models

[edit] Atmospheric entry techniques and technology

Having now thoroughly discussed the physics of atmospheric entry, we turn our attention to various techniques and technologies which have been developed to achieve safe and reliable entry in practice.

[edit] Trajectory design

Entry trajectory design is usually performed through the definition of an entry corridor, specified by a range of permissible entry angles.

A typical approach to defining entry corridors is based on the idea of overshoot and undershoot. The overshoot angle is the minimum entry angle such that the spacecraft enters the atmosphere, as opposed to skipping out (without subsequent entry, as seen in a skipping entry trajectory). The undershoot angle is the maximum entry angle such that the spacecraft (and its payload and/or occupants) can survive the dynamic loads induced by the trajectory (in the case of manned spacecraft, the undershoot angle is typically determined by the maximum acceleration the occupants can endure without losing consciousness or suffering injury). The range of entry angles between the overshoot and undershoot angles constitute the entry corridor.

The entry corridor determines the degree of accuracy with which entry angle must be capable of being controlled, which has implications for the minimum required accuracy of navigation and and control systems.

The entry corridor also determines the range of heat load and heating rate which the spacecraft will be subject to, which has implications for the design of thermal protection systems. The overshoot trajectory will have the highest heat load of trajectories within the corridor, while the undershoot trajectory will have the highest heat rate. A TPS must be able to protect a spacecraft from both of these extreme trajectories in order for the entire corridor to be safe.

The overshoot-undershoot approach to entry corridor determination results in the widest possible corridor. If the entry angle can be reliably controlled to a significantly greater degree than this maximum corridor width, there is no reason in principle that a spacecraft could not be designed to only survive entry through a more narrow corridor (which may enable, e.g. lower TPS mass).

[edit] Thermal Protection

Perhaps the most significant practical aspect of atmospheric entry is the requirement for thermal protection systems capable of keeping spacecraft structures, payloads and occupants safe from the extremely high temperatures encountered during reentry. TPS technologies can be largely divided into three separate categories, which we discuss below.

[edit] Heat sinking

Heat sink TPS technology involves positioning a significant mass of material with a very high melting point and a very high specific heat forward of the spacecraft, so that this mass is able to absorb the majority of the entry heat load. Since the conduction of heat energy from this mass to the rest of the spacecraft is proportional to the difference in temperature between the two, not the difference in thermal energy, the high specific heat keeps conductive heating of the rest of the spacecraft quite low.

Heat sink TPSes have a tendency to be very high in mass.

Heat sink TPS was used on early suborbital (but not later orbital) flights in the US Mercury program. The heat sink material used was beryllium.

[edit] Radiative cooling

Radiative cooling TPS technology involves constructing the portion of the outer skin of the spacecraft which is exposed to hot atmospheric gases from a material with a high emissivity, and in such a way that the main structure is extremely well insulated from this outer skin. During atmospheric entry, the outer skin becomes so hot that significant quantities of energy are lost through thermal radiation. If the outer skin material has a sufficiently high emissivity and the instantaneous heating rate is sufficiently low throughout the entry, the outer skin of the spacecraft can achieve thermal equilibrium (losing heat through radiation at the same rate it absorbs it from the atmosphere) at temperatures below the skin's melting point.

Due to the requirement of low instantaneous heating rate, radiative cooling TPS is best suited to long-duration gliding or lifting entries, rather than ballistic entries, which have higher heating rates.

Radiative cooling TPS technology is used by the US Space Shuttle.

[edit] Ablative cooling

Ablative cooling TPS technology involves coating the outer surfaces of the spacecraft which are exposed to hot atmospheric gases with a material which readily vaporises under the heat load of entry. The sweeping away of the gases produced by vaporisation carry heat energy which was absorbed by the ablative material prior to vaporisation away from the vehicle and back into the atmosphere. The layer of vaporised material can also act to push the hot shock layer of gas back from the edge of the heat shield, reducing the instantaneous heating rate.

Ablative cooling TPSes typically offer a lower total TPS mass than heat sink or radiative cooling TPSes suitable for the same entry trajectory, making them quite popular.

Materials suitable for use as ablative heat shielding tend to be fairly exotic, and are often proprietary.

Ablative cooling TPS technology was used on orbital Mercury flights as well as Gemini, Apollo and Soyuz spacecraft.

[edit] Drag control

Typically, spacecraft do not produce sufficient drag by themselves to slow down to safe landing speeds by the time they reach ground level. To ensure soft landings, some device must be used to introduce additional high levels of drag. A variety of drag control devices having been used to lower spacecraft speeds to safe levels, and we review them here.

[edit] Parachutes

The most commonly used drag control technology for atmospheric entry is the familiar parachute.

A significant limitation of parachutes is that they typically cannot be released until late in the entry process, because parachutes will only deploy correctly within certain ranges of vehicle speeds and atmospheric densities. This prevents parachutes from adding drag early in the entry process, at high altitudes, where higher levels of drag act to decrease thermal loads.

[edit] Shuttlecocking spacecraft

[edit] Ballutes

A ballute is, essentially, an inflatable parachute (the word is a combination of "balloon" and "parachute"), typically toroidal in shape. Ballutes have the advantage over parachutes that they can be reliably deployed at extremely high altitudes (or even in deep space), since their deployment depends upon being inflated by gas stored as part of the ballute system, unlike parachutes which deploy using the ambient atmospheric gases. By significantly increasing the drag of a spacecraft at high altitudes during the entry process, the thermal loads can be decreased, reducing the required mass of the spacecraft's TPS.

Ballutes have been proposed for use during spacecraft atmospheric entry, with detailed studies performed for NASA's Constellation project, but never actually used for this purpose. They have been used in other applications, such as slowing the descent of free-falling bombs.

[edit] References

↑ Griffin, Michael D & French, James R. (2004). Space vehicle design, American Institute of Aeronautics and Astronautics.

[0] Griffin, Michael D & French, James R. (2004). Space vehicle design, American Institute of Aeronautics and Astronautics.

[1]

CSTART Technical Report 0001