Rocket Physics, the Hard Way: Re-entry and Hypersonic Flight

Header image: Artist’s impression of an Apollo capsule re-entry (image source: NASA.)

“That was a real fireball, boy. I had great chunks of that retropack breaking off all the way through…”

NASA astronaut John Glenn, reporting to mission control shortly after the fiery re-entry of his spacecraft, Friendship 7

One of the most harrowing parts of a spacecraft’s journey is atmospheric entry. When it collides with the air at thousands of kilometres per hour, the gasses heat up to extreme temperatures. Anything without a heat shield quickly disintegrates.

Why does this heating occur? The answer is NOT friction! The truth is much more complicated. In this installment, we will delve into a realm of physics known as gas dynamics and learn how it applies to space travel.

Compressibility and Sound

In our last installment, we covered Bernoulli’s principle and the concept of dynamic pressure. When a gas is disturbed by a force (such as a spacecraft moving through it), the disturbance propagates as sound, which is composed of waves of alternating high and low pressure. For example, consider this uniformly vibrating sphere:

Sound waves
A vibrating sphere sending sound waves through still air (image source: Wikimedia Commons.)

Notice that the regions of high pressure compress the gas (make it more dense), while the regions of low pressure rarefy the gas (make it less dense.) The compressibility (or squishiness, if you prefer) of fluids is what makes sounds, shockwaves, and rocket engines possible.

Disturbances in a gas generally propagate at the speed of sound. The speed of sound depends on many properties, but is mainly determined by the density and compressibility1 of the medium in which it is traveling. These are in turn affected by the gas’s temperature and molecular properties.

In air, the speed of sound is about 343 metres per second at average sea-level conditions. By comparison, water is much more difficult to compress than air (being a liquid), and so has a higher speed of sound of about 1,480 metres per second. Sound tends to travel more slowly in more compressible media.

Consider a car driving on the highway. As it moves, it disturbs the air around it, creating a pocket of high-pressure air in front of the car and a pocket of low-pressure air in its wake. Cars travel much slower than the speed of sound, meaning that the air has time to get out of its way as it drives. A car driving on the highway at 120 km/h is traveling at about Mach 0.1, or 10% the speed of sound. At such low speeds, the flow is gentle and the compressibility of air isn’t very noticeable.

Airflow car
Airflow around a toy car (image source: Rob Bulmahn, CC BY 2.0.)

A simple rule of thumb is that for Mach numbers below 0.3, we can pretend the fluid is incompressible and still get fairly accurate calculations, simplifying the mathematical models used. However, in rocket engines and high-speed aerodynamics, the flow is so violent that gas compressibility can no longer be ignored.

Unfortunately, this also means that the flows become much more difficult to model.

Shocks and Booms

When a vehicle moves through air at high Mach numbers, the air has less time to get out of the object’s way. This means that it gets compressed by the vehicle’s motion more strongly.

Soundwaves pressure
The propagation of disturbances from a vehicle moving slower than sound (modified from graphic made by Rchisena92 on Wikimedia Commons, CC BY-SA 3.0.)

When the object starts moving faster than the speed of sound (at supersonic speed), the real fun begins. Because the disturbances caused by the vehicle’s motion cannot keep up with the vehicle, the soundwaves ‘pile up’ in front of it and form a shock. Shocks are less than one micron thick.

Supersonic sound waves
The propagation of disturbances from a vehicle moving faster than sound – the shock is indicated by the dotted lines (modified from graphic made by Rchisena92 on Wikimedia Commons, CC BY-SA 3.0.)

Immediately in front of the shock, the air is undisturbed, blissfully unaware of the vehicle’s approach. The shock forms because the oncoming air suddenly encounters the vehicle’s surface without warning and does not have time to get out of the way. The air gets violently compressed as it passes through the shock, causing its pressure, density, and temperature to jump almost instantaneously. Watch this video by Eugene Khutoryansky for a visualization of how shocks work:

When a supersonic aircraft flies past an observer on the ground, the observer hears a ‘sonic boom’ because of the shock passing by. Shocks can come in many different shapes shapes depending on the flow and the vehicle’s geometry, but here are some common examples:

Bullet shock wave
The conical shocks created by a bullet travelling at Mach 1.9 (image by Settles1 on Wikimedia Commons, CC BY-SA 3.0.)
Shock wave
A ‘bow shock’ created by a blunt body at re-entry velocities (image source: NASA.)
Jet shockwave
A false-color image of the shock patterns made by two supersonic aircraft flying close to each other – notice that the shocks interact with each other in complex ways, which is an active area of research (image source: NASA.)

Understanding shock physics and geometry is crucial to aircraft and rocket design. At the speeds rockets fly through the atmosphere, shocks can cause parts of the rocket to overheat from the high temperatures or to suffer structural failure from the increased pressures. They also increase the drag generated by the vehicle, meaning that the engines have to work harder to push the rocket through the atmosphere. Rocket nozzles themselves rely on the formation of a ‘normal shock’ inside them to accelerate the exhaust to supersonic speeds.

These considerations shape the design decisions made in the vehicle’s design. Complicating this process is the fact that the best vehicle design varies drastically depending on the speed at which it is designed to travel. We will go over these in the next section.

Regimes

When flying through an atmosphere, different design considerations are required depending on airspeed. To understand these varying considerations, NASA divides atmospheric flight into six speed regimes. We’ll begin with the slowest regime and work our way up.

Subsonic speeds are anything much slower than Mach 1. Here, shocks do not form because disturbances can still propagate faster than the gas flows, making aerodynamic control relatively easy. Launch vehicles accelerate so rapidly that they don’t spend much time here.

Transonic speeds are around Mach 1. In this regime, some parts of the airflow are supersonic, while others are still subsonic. The reason for this is that the shape of the vehicle’s body may accelerate subsonic airflows to supersonic speeds, while other parts may decelerate supersonic airflows to subsonic speeds. Most commercial airliners fly at these speeds.

Transonic effects are most commonly seen on the wings of the aircraft. The curvature accelerates the airflow to supersonic speeds, then a shock forms when the air loses enough energy to become subsonic again:

transonic
A diagram showing the formation of shocks over a wing at various transonic Mach numbers (image source: Federal Aviation Administration.)

Because the properties of the airflow change so drastically when it passes through a shock, shock formation can cause serious problems. In the transonic regime, the sudden jump in air pressure and density can cause control instabilities, increase drag, and reduce lift. Here, the normal laws of aerodynamics begin to break down.

These issues are what made the sound barrier so difficult to break. Nevertheless, it was broken in 1947 by Chuck Yeager. As told in the famous Tom Wolfe book, The Right Stuff, Yeager accomplished this feat using a rocket-powered aircraft that was specifically designed to overcome these obstacles. Today, advancements in aerodynamics and engineering allow aircraft to fly at and faster than the transonic regime.

Supersonic speeds occur between Mach 1 and 3. In this regime, the airflow is faster than sound everywhere on the vehicle’s body. Because of this, vehicles are generally easier to control in the supersonic regime than in the transonic one. However, special considerations are still required in designing the airframe – for example, sharp noses and very thin wings become optimal, which is opposite to what is best for the subsonic regime.

Concorde  plane
The Concorde supersonic aircraft, exhibiting delta wings and a sharp nose for flight in the supersonic regime (image credit: Eduard Marmet, via Wikimedia Commons, CC BY-SA 3.0.)

Supersonic aircraft create shocks as they pass through the air. At such high speeds, the shock-compression of the air begins to heat it up significantly; a phenomenon known as shock-heating. The Concorde’s nose could reach 127 °C while cruising at Mach 2, which required the use of special materials and cooling measures to withstand the heat. This also limited how much time it could spend at top speed.

High supersonic speeds occur between Mach 3 and 5. Mach 3 is approximately the limit for conventional jet engines. Beyond this point, the air starts to become too hot when it enters the engine. This causes efficiency losses2 and is harsher on moving parts. Engines that chill incoming air like the SABRE (Synergetic Air Breathing Rocket Engine) can extend this range up to Mach 5.5, but not much further.

Perhaps the most famous high supersonic aircraft is the SR-71 Blackbird, which had a blistering top speed of Mach 3.2. To help combat the low efficiency of jet engines at such speeds, it used a special kind of engine called a turbo-ramjet.

SR-17 Blackbird
The SR-71 Blackbird – need I say more? (image credit: US Air Force)

The temperatures reached in the high supersonic regime cause aluminum alloy airframes to weaken too much. As a result, high supersonic aircraft like the SR-71 must be built from more exotic materials that maintain their strengths at high temperatures, like titanium.

However, launch vehicles the Space Shuttle or Falcon 9 still use lightweight aluminum-lithium alloy despite travelling much faster than the SR-71 in the atmosphere. Why?

Aircraft need to fly (relatively) low in the atmosphere to supply their engines with oxygen, requiring them to fly through denser air for long periods of time. Dense air means stronger shocks and stronger aerothermal heating.

On the other hand, launch vehicles, powered by rocket engines, don’t need the atmosphere. In fact, they try to get out of the atmosphere as quickly as possible to minimize drag losses. As a result, by the time they reach high supersonic speeds during ascent, their altitude is so high that aerothermal heating is relatively mild.


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Hypersonic speeds occur between Mach 5 and 10. This is where things start to get interesting. Even exotic air-breathing engines with no moving parts like ramjets become inefficient. Accordingly, most hypersonic vehicles are powered by rocket engines. The sharp-tipped noses used at supersonic speeds start to become impractical because they heat up too much (for complex aerodynamic reasons). Blunt noses become optimal again.

What makes the hypersonic regime unique is that the temperatures reached by the gas become so high – several hundreds to over one thousand degrees Celsius – that engineers need to consider chemical and quantum effects. Aircraft flying at this speed may need to use special cooling systems for their airframes. This introduces several new engineering headaches. To understand what goes on at hypersonic speeds, we need to understand what it means for a gas to be hot.

The Earth’s atmosphere is composed primarily of molecules of nitrogen and oxygen. These do not naturally exist as individual atoms (or as chemists call it, as a monatomic gas) but rather, they come in bound pairs; N2 and O2 (a diatomic gas.) This is because for most gases, the diatomic form is more stable.

When a volume of air is heated, its molecules bounce around randomly at higher speeds. Temperature is simply a measure of the average random kinetic energy these molecules have. However, not all the heat supplied goes into making the molecules whiz about faster.

Heating a molecule also causes its bonds to begin spinning and vibrating like tuning forks. Normally, this isn’t much of a concern. However, at the temperatures encountered in hypersonic flight, the various different ways the molecule’s bonds can vibrate start to strongly affect the gas’s ability to absorb heat (or its heat capacity.) Because thermodynamics becomes so important at these speeds, both to keep the vehicle from overheating and to predict the gas’s fluid properties, designers must account for this.

At higher speeds and temperatures, the heat can begin breaking molecules apart. Diatomic nitrogen and oxygen begin breaking up into single atoms: a phenomenon known as dissociation. Dissociation further complexifies the gas’s thermodynamic, fluid, and even chemical properties. These single atoms, known in chemistry as free radicals, are extremely reactive. Hot oxygen free radicals are especially reactive and can corrode the vehicle’s skin, requiring special material choices to withstand the thermal and chemical onslaught.

molecular dissociation
The dissociation of molecular oxygen into reactive monatomic oxygen (image by author, CC-BY 4.0.)

As the temperature rises, the gas continues to behave in even more alien ways. At high enough temperatures, air becomes so energetic that electrons may jump between quantum states. Some electrons may have so much energy that they escape the atom altogether – a phenomenon known as ionization.

When a gas is ionized, it transitions into the so-called ‘fourth state of matter’: plasma. Plasma is found in many places in nature, from the Sun to lightning bolts to the insides of neon lights. Because it conducts electricity3, the ionization of gas around a hypersonic vehicle can interfere with radio communications. This is why spacecraft often experience communications blackouts during their return to Earth.

The coup de grâce of these design and modelling headaches is that even the fundamental mechanisms by which heat is transferred within the gas changes. In everyday life and in normal flight, a gas disperses heat through convection (by molecules moving in bulk) and conduction (by molecules transmitting their vibrations to each other.) At hypersonic speeds, the air is so hot that it begins to become incandescent, transferring heat by radiation. This radiation is the reason that spacecraft and meteors trail brilliantly glowing plasma when they reenter the atmosphere.

All in all, the hypersonic regime is an extremely difficult regime to fly in; not just because most air-breathing engines become useless or because the thrust required to maintain these speeds is so enormous, but also because the air itself begins to break down (along with the conventional laws of aerodynamics). Sustained powered hypersonic flight is rare; ascending rockets are usually in the near-vacuum upper regions of the atmosphere by the time they reach these speeds. However, spacecraft reentering the atmosphere must contend with hypersonic aerodynamics during their return to Earth.

Re-entry speeds occur above Mach 10, such as when spacecraft reenter the Earth’s atmosphere at Mach 25. At such extreme speeds, the vehicle’s design is at the mercy of shock heating due to the extreme temperatures reached. Temperatures easily reach thousands of degrees Celsius, weakening and melting most conventional aircraft materials.

Notice that spacecraft designed to survive re-entry feature non-aerodynamic, blunt designs, which generate a lot of drag:

Crew Dragon atmosphere
An artist’s impression of a Crew Dragon capsule reentering the Earth’s atmosphere (image source: SpaceX.)

Alternatively, spaceplanes like the Space Shuttle are designed to enter the atmosphere at a steep angle, which also cause a large amount of drag:

Space Shuttle atmosphere
An artist’s impression of the Space Shuttle reentering the Earth’s atmosphere (image source: NASA.)

While generating drag is needed to slow down from orbital velocities, the bluntness of the spacecraft’s aerodynamic profile also helps reduce heating. Recall how the shapes of the shocks in front of the vehicle vary according to its geometry:

Shock wave geometry
The evolution of re-entry capsule design for crewed spaceflight (image source: NASA.)

Notice that the arrow-shaped body on the top-left has a shock that is attached to it. Because the shock is where the air is heated, an attached shock could overheat the vehicle at hypersonic and re-entry speeds. On the other hand, all the other blunt-shaped bodies have detached shocks, which are separated from them by a small distance. This reduces the amount of heat transferred to them, although it drastically increases the drag generated. Hence, spacecraft tend to enter the atmosphere with their blunt ends forward, reducing the heat the spacecraft must withstand and improving braking.

Taking the heat

Despite these aerodynamic tricks, the hull of the spacecraft may still reach thousands of degrees Celsius. The Space Shuttle’s hull reached 1,650 °C while reentering from low-Earth orbit, for example, which would melt titanium. It is not sufficient for a material to simply remain solid at these temperatures – it must also maintain its structural strength, which means that the real maximum temperature has to be well below its melting point. So, to withstand these temperatures, the Space Shuttle’s hull was made from special TPS (Thermal Protection System) tiles.

space shuttle tiles
Space Shuttle STS-114 Discovery approaches the International Space Station, sporting its thermal protection blankets and tiles (image source: NASA.)

The underside of the hull, which hit the atmosphere first, was made from ceramic tiles containing low-density silica fiber with a black borosilicate outer shell:

Shape shuttle tps
A space shuttle TPS tile (image source: Wikimedia Commons.)

Silica fibers can withstand high temperatures, and their low density makes them excellent insulators. These properties allowed the TPS tiles to absorb enormous amounts of heat while insulating the shuttle’s aluminum frame, keeping it from reaching high temperatures. After re-entry, the black coating helped to dissipate heat by radiation. However, these tiles are fragile and break easily, as was tragically demonstrated with the Columbia disaster.

The nose of the shuttle experienced the strongest shock heating during re-entry, and so was made from reinforced carbon-carbon. This was only used in small parts of the vehicle because it is heavy and especially brittle.

The Space Shuttle could glide, allowing it to spread the deceleration over a long period of time, keeping the re-entry heating relatively gentle. Furthermore, it returned from low orbits, where the amount of energy that had to be dissipated was moderate.

Just how high can the temperature get, and what do we do when ceramic tiles can’t survive them?

The Apollo capsule’s heat shield faced temperatures of up to 2,760 °C on its high-speed return from the Moon. Titanium, by comparison, melts at approximately 1,760 °C.

When the Soviet Venera 10 lander entered Venus’s dense atmosphere at interplanetary velocities, temperatures reached 12,000 °C – the surface of the Sun is a relatively cool 5,600 °C.

However, the crown for the most treacherous atmospheric entry ever attempted undoubtedly belongs to the Galileo atmospheric probe. On December 7, 1995, the probe slammed into the Jovian atmosphere at Mach 50, creating a shock that heated the air to an infernal 15,500 °C.

Galileo probe
An artist’s impression of the Galileo atmospheric probe falling through Jupiter’s atmosphere (image credit: NASA.)

On a clear day at sea level, the Sun delivers heat to the Earth’s surface at a rate of approximately 1 kilowatt per square metre of area.

The incandescent glow of the plasma and the hot gases rushing past the Galileo atmospheric probe’s heat shield delivered heat to it at a rate of 35 kilowatts…

…per square centimetre.

That is 350,000 times the intensity of the Sun at the Earth’s surface.

No known material can survive these temperatures for long – which is why most types of heat shields are instead designed to gradually vaporize, layer by layer, throughout entry. These are known as ablative heat shields.

The idea for an ablative heat shield goes at least as far back as 1920, when American rocket engineer Robert Goddard observed that even though meteors entered the Earth’s atmosphere at extremely high velocities, their insides remained cold. This was because the outer layers of the meteor would crack and fall away as it flew through the atmosphere, taking away their heat with them.

Modern ablative heat shields are usually made from a type of plastic resin. When exposed to high temperatures, it vaporizes and chemically decomposes into gases. These processes consume thermal energy, causing a thin boundary of cooler gas to form on the heat shield. The gas is blown away by the oncoming airflow, taking its heat away with it. The shield absorbs the remaining thermal energy that still manages to leak through, preventing the spacecraft from heating up.

While ablative heat shields can withstand extreme reentries and are much tougher than the fragile TPS tiles used by the Space Shuttle, they can only be used once. Nevertheless, all modern crewed space capsules, from Soyuz to Dragon, use ablative heat shields.

Looking forward

Hypersonic flight will continue to be an increasingly important problem as humanity continues to expand into space. For spacecraft that land on other worlds, such as the planned aerobraking maneuvers that the SpaceX Starship will execute at Mars, effectively withstanding the heat and controlling the vehicle’s flight path become even more crucial. New re-entry technologies are on the horizon, such as shaping the re-entry plasma with magnetic fields3 or actively cooling the hull by pumping ultracold fuel through it, eliminating the need for traditional heat shields. On the other side of the equation, sending payloads into orbit may become cheaper by using space planes that can operate at hypersonic speed. For these reasons, understanding hypersonic physics is essential for leaving the Earth’s atmosphere – and returning safely.

Footnotes and further reading

1 Alternatively, one may use the bulk modulus, which is the reciprocal of compressibility.

2 This is because a jet engine is a subclass of the family of heat engines. They produce power by taking a relatively cold fluid and heating it up to high temperatures. However, as the intake air reaches very high temperatures, the combustion process struggles to add more energy to it because it’s already hot.

3 Physicists have explored exploiting the electrical conductivity of plasma to improve the handling of spacecraft reentering the Earth’s atmosphere. By generating a powerful magnetic field around the spacecraft during re-entry, electrical currents are induced in the plasma as it flows past (much like how generators generate electricity by moving magnets over coils.) The electrical current causes the plasma to generate its own magnetic field, which repels the spacecraft’s original magnetic field. This improves the braking performance, controllability, and thermal loading on the spacecraft during re-entry. This technique is known as magnetohydrodynamic (MHD) flow control, which at the time of writing has not yet been flight-tested. MHD effects can also be used in the exact opposite way to accelerate any electrically-conductive fluid, such as in magnetoplasmadynamic (MPD) thrusters and rarely, in marine propulsion systems. The eponymous fictional Soviet submarine in the 1980 thriller film The Hunt for Red October is depicted as using an MHD drive.

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