Rocket Physics, the Hard Way: Rocket Engine Engineering

Header image: SpaceX Raptor test fire (image source: SpaceX.)

“Anyone who sits on top of the largest hydrogen-oxygen fueled system in the world; knowing they’re going to light the bottom, and doesn’t get a little worried, does not fully understand the situation.”

– Astronaut John Young, first space shuttle commander

What discussion of rocket physics is complete without an overview of rocket engines?

In our first installment, we learned about the Tyranny of the Rocket Equation and how it governs all rocket design. In particular, we learned the importance of specific impulse, a measure of a rocket engine’s efficiency. You may have wondered, how can we maximize that?

This week, we will delve into the inner workings of liquid-fueled chemical rocket engines, the workhorses of space exploration, and the likeliest propulsion system to be used for the first human expedition to Mars. While the average rocket engine is less complex than the average car engine, the difficulty of its engineering lies in the extreme conditions it must endure while remaining lightweight.

The SpaceX Raptor is designed to supply its spacecraft with kinetic energy at a rate of 11 million horsepower1 – the equivalent of four Hoover Dams, generated by an engine weighing approximately 1.5 tonnes. By comparison, one of the most powerful sports cars ever made, the Bugatti Veyron, has an engine weighing 0.5 tonnes (one-third as much), but can only generate a meager 1,200 horsepower.

Within a Raptor’s combustion chamber, methane and oxygen burn at temperatures hot enough to melt its walls (if it were not for regenerative cooling)2, at pressures exceeding those in SCUBA cylinders. The exhaust is expelled at over ten times the speed of sound. Why are such extreme conditions necessary?

SpaceX Raptor Engine
Test of the vacuum version of the SpaceX Raptor engine (image source: SpaceX.)

Full of Hot Air

At the heart of all chemical – or more generally, all thermal – rocket engines is a simple and familiar thermodynamic principle: when a gas is heated, it expands. Chemical rockets burn fuel and oxidizer inside a combustion chamber. This imparts an enormous amount of heat to the gases, causing them to expand rapidly – in other words, an explosion occurs. In a rocket engine, this explosion is occurring continuously as fuel and oxidizer are pumped in.

Rocket Combustion Chamber
The pressure of the hot gases pushing against the inside of the combustion chamber and nozzle generates thrust (image source: Wikimedia Commons.)

The hot gases are then forced through a constriction (thus converging), accelerating them to the speed of sound. Then, they continue into the nozzle which expands it (thus diverging), accelerating them further to hypersonic velocities3. As it expands and pushes the rocket forward, the pressure and temperature of the gas both fall. In exchange, its velocity increases. The pressure of the escaping gases pushing against the walls of the engine drives the rocket forward. This converging-diverging nozzle arrangement is known as a de Laval nozzle, which is found in all rocket engines ranging from model rockets to the Saturn V’s mighty F-1 engines.

Essentially, a rocket is an efficient way of converting the fuel’s chemical energy into kinetic energy. When the propellant is combusted, propellant energy is converted into thermal energy. Because the engine resists the explosion, the gas reaches high pressures. As the gas flows through the nozzle, it exchanges thermal and pressure energy for kinetic energy.

In other words, the explosion pushes back against the combustion chamber and nozzle, forcing the rocket forward.

To increase the thrust of the rocket, one can add more engines or increase the rate of propellant consumption. However, this will not improve the rocket’s delta-V. In a nutshell, delta-V is the ability of a rocket to change its velocity, which in turn determines how difficult of a mission it can perform.

In fact, adding engines actually decreases delta-V due to their added mass. Recall from our previous installment on the Rocket Equation that there are only two ways to improve delta-V: carry more fuel or improve specific impulse. Specific impulse is how efficiently each kilogram of fuel drives the rocket forward; to improve this efficiency, we need to design and optimize our engines carefully.

Here are the four most common strategies to improve performance:

First, we can choose fuel-oxidizer combinations that result in an exhaust with lightweight molecules. The lighter the molecules of the exhaust, the faster they will go at a given temperature, increasing the engine’s exhaust velocity – and consequently, its specific impulse. Accordingly, high-performing chemical fuels tend to have large amounts of hydrogen, as hydrogen is the lightest known element.

Rocket Physics
A comparison showing that exhaust velocity is higher with light molecules than with heavy molecules (image by author, CC BY 4.0.)

The best-performing combination in use is hydrogen and oxygen4, which burns to produce hot steam. Burning heavier, hydrocarbon fuels like methane or kerosene produces not only steam, but also carbon dioxide and some other messy compounds. The higher mass of carbon dioxide molecules reduces the engine’s exhaust velocity, lowering its specific impulse.

Given these caveats, why do rockets use any fuel besides hydrogen and oxygen?

While having excellent performance, liquid hydrogen causes numerous headaches when it comes to storage. This is because it must be kept at an extremely cold -253 °C, it causes metals to become brittle, it easily leaks through the smallest seams and cracks, and leaks are difficult to detect (just to name a few). Furthermore, it has only 7% the density of water, meaning that large, heavy tanks are required to store it (which partially cancels out the efficiency gains.)

The extremely low boiling point of hydrogen is perhaps the worst of these problems. -253 °C is a mere twenty degrees above absolute zero, with helium being the only known substance with a lower boiling point. The walls of the Space Shuttle’s external fuel tank were just over six millimetres thick, and they had to insulate against a temperature difference of over 270 degrees. This is a very hard thing to do, to put it mildly.

The fragile insulating foam required frequently broke off in flight, damaging the orbiter’s heat shield. This damage led to the near-destruction of STS-27 Atlantis during reentry. NASA evidently did not learn their lesson; STS-107 Columbia was actually destroyed on reentry for the same reason, fifteen years later. There were no survivors.

While kerosene has poorer performance and tends to leave messy carbon deposits in the engine, it is much denser and easier to store. This is why kerosene and other less efficient fuels tend to be more commonly used than hydrogen.

The next time you watch a rocket launch, observe the colors of the engine exhaust plumes. You may be able to identify the fuel. As an example, kerosene engines tend to produce soot. The incandescent glow of this soot is why the Saturn V’s first stage, fueled by kerosene and oxygen, had a brilliant fiery exhaust flame. On the other hand, the Space Shuttle’s RS-25 engines, burning hydrogen and oxygen, had near-transparent exhaust.

Rocket engine exhaust
A comparison of exhaust flames. The Saturn V F-1 engine’s incandescent kerosene-oxygen flame (left) and the Space Shuttle RS-25 engine’s transparent hydrogen-oxygen flame (right) (image credit: NASA.)

Other fuel combinations such as Aerozine 50 and dinitrogen tetroxide may also produce transparent exhaust plumes. This combination was used by the Apollo lunar ascent modules, for instance, which is why the flame is invisible:

Secondly, we can increase the combustion temperature. This will increase the amount of energy available to the gases, causing their molecules to move faster, improving the engine’s exhaust velocity (and by extension, specific impulse.) High temperatures can generally be achieved by using a more energetic fuel-oxidizer combination. However, high temperatures also require tougher materials and more powerful cooling systems to keep the engine from burning away.

Rocket Physics
A comparison showing that exhaust velocity is higher at higher combustion chamber temperatures (image by author, CC BY 4.0.)

Generally, higher temperatures result in higher efficiencies, and the highest possible temperature usually occurs when the fuel and oxidizer are mixed in the perfect ratio, known as the stoichiometric ratio in chemistry.

However, the fuel-oxidizer ratio that results in the best possible specific impulse may actually be slightly off from the stoichiometric ratio. Recall that lowering the mass of the molecules in the exhaust also helps improve the engine’s performance. Fuels tend to have lower molecular weights than oxidizers, so adding an excess of fuel can actually improve performance up to a point, by lowering the average mass of the exhaust molecules. This is known as ‘fuel-rich combustion’ or ‘burning rich’.

For example, the hydrogen-oxygen combination gets its high performance by both burning energetically and having lightweight exhaust molecules. A hydrogen molecule is only one-sixteenth the mass of an oxygen molecule, meaning that having some excess, unburned hydrogen in the exhaust can significantly improve performance.

There is also another reason to burn rich: corrosion. The infernal temperatures (over 3,000 °C) and pressures (hundreds of atmospheres) found inside a rocket engine make the combusting gases far more reactive than they are at normal conditions.

Corrosion is an especially serious problem with oxygen. Oxygen is already highly reactive in normal conditions (if you don’t believe me, try setting your hair on fire.) At the temperatures and pressures found inside a rocket engine, it will enthusiastically combust with almost anything, including a wide variety of metals. An excess of fuel helps reduce the concentration of oxygen, protecting the engine from corrosion. This is why most rocket engines burn rich, with some notable exceptions.

If the combustion mixture has an excess of oxygen (whether by design or by accident), it is known as ‘oxidizer-rich combustion’ or ‘burning lean’. If the engine alloys aren’t designed to resist the ensuing oxidation, the oxygen will begin combusting with the engine itself.

This occurred during the Starship SN8 test – due to low pressure in the header fuel tank (a small auxiliary fuel tank meant exclusively for landing), the combustion chambers were starved of fuel. This meant that there was too much oxygen in the engine. The hot, oxygen-rich gases began reacting with copper in the engine’s alloys, producing the brilliant green flame that was observed during the landing burn:

SpaceX SN8
Green exhaust flames from the Starship SN8’s Raptor engines, indicating that the oxygen-rich combustion mixture was burning away the inside of the engine (image credit: SpaceX.)

This is a condition half-jokingly known as ‘engine-rich combustion’.

Clearly, optimizing a rocket engine is a tricky problem. High combustion temperatures give high performance, but adding an excess of fuel may help improve it even further, with the added advantage of protecting one’s engine from corrosion.

Another strategy we can use is increasing the pressure in the combustion chamber. This will force gases out at even higher velocities. While higher combustion temperatures can help achieve this, the main strategy used is to inject the fuel and oxidizer at higher pressures.

Rocket Physics
A comparison showing that exhaust velocity is higher at higher combustion chamber pressures (image by author, CC BY 4.0.)

Rocket propellant tanks are pressurized – usually with helium gas or vaporized propellant – for a number of reasons. Firstly, they have to be pressurized to keep the contents liquid. Secondly, because the structure of the rocket must be as light as possible, some designs rely on this internal pressure to maintain rigidity.

For example, because the tanks of the Atlas ICBM (which was later adapted into an orbital launch vehicle) were a fraction of a millimetre thick, they had to be kept pressurized at all times or they would crumple under their own weight. The SpaceX Falcon boosters use ‘flight pressure stabilization’; this means that while their structures can maintain integrity without pressurization on the ground, they rely on tank pressurization during flight to avoid collapsing under aerodynamic and thrust forces.

The third reason is that pressurizing the propellants increases the pressures that can be achieved in the combustion chamber.

The simplest method is known as a ‘pressure-fed’ combustion cycle. The propellants are piped directly to the combustion chamber, relying on tank pressurization to maintain pressure. This makes for an extremely simple engine design, as it is no more than some valves and plumbing. Unfortunately, it also limits the maximum achievable pressures to what the propellant tanks can withstand before getting too heavy.

When higher performance is required, the pressure can be stepped up using pumps. The Rocket Lab Rutherford engines, designed for small orbital rockets like the Electron, use pumps powered by lithium-ion batteries. More powerful engines like the Merlin, RS-25, or F-1 engines use more complex combustion cycles that siphon off some of the combustion’s energy to power the pumps. While these designs can achieve much higher pressures, they are also more complex and failure-prone.

Driving up the pressure in the combustion chamber, either by pressurizing the propellants or by using powerful pumps, is one way to increase an engine’s efficiency – however, high pressures require high material strengths, which limits how far an engine designer can take this strategy.

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We can also increase the size of the nozzle. This will increase the area available for the exhaust gases to push upon, increasing the thrust produced for a given mass of fuel (i.e. specific impulse.) Larger nozzles use the exhaust’s energy more efficiently.

Rocket Physics
A comparison showing that exhaust velocity is higher for larger nozzles (image by author, CC BY 4.0.)

However, as with the other three strategies, there are limits.

The larger a nozzle, the heavier it is. Eventually, the mass penalty will become so great that it begins to cancel out the gains in efficiency.

Bonus: We can reduce the ambient pressure. There is another important factor in the performance of a rocket engine that we have ignored until now – the pressure of the atmosphere trying to force the exhaust back into the engine. In the vacuum of space, this is not a concern. However, at sea level, where the pressure of air is approximately ten tonnes per square meter, atmospheric pressure causes serious efficiency losses and even exhaust jet instabilities.

Rocket Physics
A comparison showing that exhaust velocity is higher in a vacuum than in an atmosphere (image by author, CC BY 4.0.)

As the nozzle expands the exhaust, its temperature and pressure fall – this is because it is exchanging its pressure and temperature for velocity as it expands. The ambient pressure of the atmosphere resists this expansion, reducing the engine’s thrust.

Rocket engine design
Comparison of various rocket engine nozzle expansion ratios and their impact on the exhaust jet. The further you go down, the more fully expanded the jet is. The second engine from the top is the optimum design (image source: Wikimedia Commons.)

Usually, the more the exhaust is expanded, the higher the engine’s efficiency becomes. However, there is a limit. If the exhaust is expanded so much that it leaves the engine at a significantly lower pressure than ambient pressure, efficiency will begin going down again. If the exhaust leaves the engine at a much lower pressure than ambient, the jet ‘separates’ from the nozzle walls and can become unstable, causing control issues or even structural damage.

This is visualized in the diagram on the left. The nozzle at the top is underexpanded because the nozzle is too small for the amount of pressure energy the exhaust contains, allowing energy to go to waste.

The second nozzle from the top is just right, because the exhaust leaves the engine at exactly the same pressure as the atmosphere. This design point is rarely reached in real engines.

The two nozzles at the bottom are overexpanded, because the nozzles are too large for the amount of pressure energy the exhaust contains. The exhaust has been expanded so much that it leaves the engine at lower than atmospheric pressure, which is why the jets look pinched; they are being squeezed by the atmosphere.

Because space is a vacuum, all rocket nozzles are underexpanded in space; the exhaust pressure will always be greater than ambient. As a result, rocket engine nozzles designed for use in a vacuum should be as large as is practical.

This is why rocket engines designed to work within the atmosphere and in space have different nozzle sizes. For example, compare the SpaceX Raptor sea level and vacuum engines:

SpaceX Raptor
The SpaceX Raptor sea level and vacuum engines (image source: SpaceX.)

The two variants are very similar, except that the vacuum variant has a nozzle ‘skirt’ extension, making it bigger. This skirt gives it better efficiency in the vacuum of space over the sea level variant. This is why rocket engines have different specific impulse and thrust numbers quoted for sea level and vacuum conditions.

Consequently, the engines designed for the lower stages of a rocket tend to expand their exhaust less than the engines designed for the upper stages of a rocket, because they have to operate deeper in the atmosphere.

As is the case with mission planning, something as simple as choosing the size of a rocket engine’s nozzle is a complex game of tradeoffs between multiple competing design priorities. The design of a rocket engine is a system of fiendishly complex problems, relying on fields as diverse as fluid dynamics, mechanical engineering, thermodynamics, chemical engineering, and even acoustics. Nevertheless, they are important ones to solve. As the Rocket Equation will tell you, the engine’s efficiency is everything.

Until the recent advances made by private companies such as SpaceX and Rocket Lab, engine technology had remained relatively stagnant since the 1960s. Some of the problems mentioned here could be overcome using techniques such as aerospike engines, but such technologies are still in their infancy.

If you find these difficult and important problems fascinating, consider pursuing a career in rocket engineering. The next great advance may come from you.

Footnotes and further reading

1 Calculated by multiplying the thrust of 2,200,000 N by vacuum exhaust velocity of 3,700 m/s, resulting in a thrust power of 8.14 gigawatts.

2 How is it possible for the engine to burn hotter its melting point without violently exploding? Two reasons: Firstly, the hottest part of the flame is kept far away from the engine walls by clever manipulation of the gas flows. Secondly, the walls are kept cool by pumping super-cold fuel through them. For an excellent explanation of how this works, check out the episode of Richard Hammond’s Engineering Connections on the Space Shuttle:

3 If converging ducts accelerate gases below the speed of sound, why do diverging nozzles accelerate them above the speed of sound? These are due to complex gas dynamics effects that I do not understand.

4 The highest-performing rocket fuel combination ever tested burned lithium, fluorine, and hydrogen. While it had an astounding specific impulse of 542 seconds (compared to ~450 seconds for hydrogen-oxygen), fluorine is called “The Element from Hell” for a reason. If you ever plan to build a fluorine-powered rocket, please inform me immediately so that I can move somewhere safe, like the next continent over.

For explanations of the various engine combustion cycles, the Wikipedia pages are strongly recommended (in order of approximately increasing complexity):

To calculate the performance of a rocket engine, learn more about the relevant thermodynamics and fluid mechanics of a de Laval nozzle here.

If all this talk of structural mechanics, pressurization, fluid mechanics, thermodynamics, combustion, and pumps fascinates you, you should consider pursuing a degree in mechanical or aerospace engineering!

If you are looking to do research in Canada, there is ongoing research and development in rocket propulsion systems at the University of Toronto, the University of Waterloo, Ryerson University, Carleton University, and others. Canada has exciting space initiatives brewing, and we need talent.

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