It's Rocket Science!

Economics and Rocket Science

I am more of a macro-economics guy, so why should I care about rocket science? Well today when someone talks about Economics, one surely has the term “growth” embedded in their thoughts. Growth, however, may have different meanings to different people or economists – for some, it might be income growth, for some ecological growth while for some it might be social growth. Growth in economics mainly comes from productivity (or total factor productivity). And the major factor which enhances productivity is technological progress. It is this which pushes the technological frontier forward, and rocket science is one such field which has pushed the frontier leaps and bounds. So, whether it be rocket science or any other sciences for that matter, its proper understanding can help grow an economy and making people’s lives better! 

History of Space flight 

One of the earliest mentions of the rocket-like in history come from the writings of Gellius, a Roman. He writes about a Greek individual who uses a wooden pigeon propelled by steam, thus suing Newton’s laws for propulsion for the first time. Interestingly, Newton’s laws would not be developed for about 20 centuries to come since this writing is from 400 BC.

Later, Chinese began experimenting with saltpetre (KNO3), realgar (arsenic sulphide), sulphur and charcoal, three of which are basic ingredients of gun powder. They used it in fireworks in 1-100 AD period.

The earliest record of gunpowder, however, comes from the book written in 850AD, translated as Classified Essentials of the Mysterious Tao of the True Origins of Things. In this book, it is indicated that Taoist alchemists developed gunpowder accidentally while searching for the elixir of immortality, ironic huh!

Near 1000 AD, Chinese began using gunpowder in warfare as incendiary projectiles. Chinese military started using flying fires while using gunpowder as a propellant. They were fired as arrows, grenades and catapults.

Around 1231 AD, the Chinese reportedly used the first true rocket in their fight against Mongols. It is reported that, at the battle of Kai-Kend, the Chinese used a tube, which was capped at one end and contained gunpowder, that was lit from the open end. The ignition of the gunpowder within the capped tube created heat, smoke and other gases that were forced out of the open end of the tube, creating thrust. The tube was controlled by placing a stick along the side that stabilized the solid rocket's flight path in the same way that sticks on a bottle rocket is used. Later, English monk and alchemist Roger Bacom improved the formula for gunpowder for rockets.

During 1300-1600 AD, Frenchman Jean Froissart discovered a way to improve the rocket’s accuracy. He realized that they are more accurate when launched from a tube. There also exists a tale of a Chinese official named Wan-Hu who built a rocket chair and launched himself around this time. In 1591, Johann von Schmidlap wrote a book about the non-military use of rockets. He described the use of sticks to stabilize rockets and also using rockets on top of rockets – rocket staging.

Then, in 1650, the Polish artillery expert, Kasimiez Siemienowicz, published designs for a staged rocket that would offer more destructive capabilities. In 1696, the Englishman Robert Anderson published a document describing the build-up of solid rockets. He described how to mix propellants and pour them into moulds and so on. Then in 1643, Sir Issac Newton was born and in 1687 he published In Principia. Building on Newton’s foundations, and by developing calculus Leibniz brought forward even greater understanding of rocketry in 1700s. Leonhard Euler and Daniel Bernoulli developed fluid dynamics and aerodynamics of rockets.

British Admiral Sir William Congreve had seen rocket used in the conflicts with India in the 1800s and had noted his observations. He also refined the understanding of rockets for British military. In 1806, Frenchman Claude Ruggieri launched rockets containing animals with small parachutes, carrying passengers for the first time. In 1841, a patent was granted in England for the first-ever rocket aeroplane in the name of Charles Golightly. The idea was of the steam-driven rocket, but no prototype was ever constructed.

The late 1800s saw the beginning of modern rocketry with Russian schoolteacher Konstantin Tsiolkovsky, born in 1857 and American Robert Goddard born in 1882.

As a child, Tsiolkovsky contracted scarlet fever and as a result developed hearing impairment, which led him to being homeschooled until the age of 16. He worked as a high school maths teacher until 1920. In 1903, he published what has become known as the first true book on rocket science, The exploration of cosmic space by means of reaction devices. He noted the idea of multistage rockets for rockets and published several papers on the topic. He is known as the father of modern astronautics.

Robert Goddard suffered from stomach problems as a child and resultingly fell two years behind in his schoolwork. He received his PhD and later performed experiments with solid rockets. After his various experiments in 1915, he was convinced that liquid rockets would enable the rocket to carry more payload to higher altitudes. In 1919, he published a book titled A method of reaching extreme altitudes, which is one of the reasons he is known as one of the founders of modern rocketry.

Several scientists during the time believed that rockets to the high altitudes would not be possible because there would be no air to push against. This came from the lack of understanding of rocketry and physics, however, Tsiolkovsky and Oberth, in two separate countries, understood Newton’s laws and were convinced that high altitudes and space flights are possible. Hermann Oberth was a Romanian scientist who published The rocket into Planetary Space, which discussed the effects of space flights on humans. He also showed using Newtonian mechanics on how to put the satellites into space. As a result of his writings, many space clubs were formed, of which Verein fur Raumshiffarhrt (VfR) was a notable one.

In 1930, American Rocket Society was founded by David Lasswe, G. Edward Pendray and 10 others. The aim was to promote the public interest. Meanwhile, Goddard launched a rocket that reached over 800 km/hr and over 600 m altitude. A year later in 1931, Lasser published his book in the United States, and the Austrians launched a mail-carrying rocket. In Germany, the VfR launched a liquid-fuel rocket. Another of the noted rocket scientists, Wernher von Braun, was involved with the experiments of the VfR where he assisted Oberth with his liquid-fuel rocket tests. In 1933, Soviets fired off a rocket using both solid and liquid engines, and it reached over 400m. In 1933, Wernher von Braun was awarded Grant from the German Army Ordnance Department to study rocketry and was later awarded PhD. However, his thesis remained classified until the 1960s. As an outcome of his work, his team launched two rockets in 1934 which reached altitudes of 2.2 and 3.5 km. In 1935, California Institute of Technology began testing rockets near Pasadena, California. Later this became the Jet Propulsion Laboratory.

In 1937, under Nazis, the German rocket scientists were concentrated to make weapons for Hitler. The Germans, including Oberth, were led by von Braun to develop most advanced rockets known to human. Up until 9139, von Braun had Goddard’s publications and plans to design the line of rockets, the most famous being V1 and V2. Throughout the early 1940s, the German rockets V1 and V2 developed continuously. After the war was over the scientists were captured by Russia and the States, with von Braun taken to States. Through the late 1940s, the US made some progress developing liquid hydrogen and liquid oxygen-based rockets. Also, Soviets were launching on a steady basis and remained very much in the competition, trying to reach space and some day intercontinental ballistic missiles (ICBMs)

The space race started between Soviets and the US when the Soviets launched Sputnik 1 into the orbit on October 4, 1957. Sputnik the first vehicle to be launched into space by mankind. Sergie Korolev was the chief designer and the spark of the Soviet Space program. Later in November 1957, Sputnik 2 was launched carrying Laika, a dog to space. The US, however, started late. In 1958, the US launched its first satellite Alpha, dubbed explorer 1, developed by Army Ballistic Missile agency (ABMA). The satellite was developed by William Pickering from JPL, James Allen from the University of Iowa and von Braun from AMBA. It is this satellite which discovered the van allen belt of radiation enveloping the Earth. In 1958, the United States launched the first successful Vanguard rocket. It is the oldest artificial satellite orbiting the Earth. The same year, 1958, Congress approved the Space Act creating the National Aeronautics and Space Administration (NASA). In 1959, the Soviets launched Luna 1, the first aircraft to reach the escape velocity of the Earth. Then Luna-2, which crash-landed on the moon. Luna-3 orbited the moon and sent back the first images from the far side.

1960 witnessed the launch of first television weather satellite Tiros 1, followed by the first communications satellite Echo 1. The Soviets launched 2 doges, Strelka and Belka into space and brought them back safely to the Earth. On April 12, 1961, Yuri Gagarin became the first human to travel in Space. He was launched atop a Vostok 1 with the call sign “Cedar”. The flight time was 60 minutes. On May 3, 1961, Alan Shepard became the first American in space with a sub orbital flight. Then on August 6, the Soviets orbited Gherman Thov for more than 25h around the Earth, making him the first human to orbit for a longer than a day.

From 1961, the rivalry intensified. Flight after flight and experiments after experiments were performed with the objective to set foot on the moon. On July 16, 1969, a Saturn 5 spacecraft launched Neil Armstrong, Edwin Aldrin and Michael Collins into the space and on 20 July 1969, they became the first humans to set foot on a celestial body than the Earth.

The developments of rocket science and engineering during the Apollo missions were refined before being handed over to the world in making new machines like calculators, smartphones and laptops.

At the end of the cold war, Russia and the States had spent way too much to try another moon mission. The humanity would then not return to the moon for at least until the second decade of the 21^st century.

The time period between the mid-1970s to 2000s saw space shuttle program of NASA and at the same time development of the manned space program by China. On October 15, 2003, Shenzhou 5 propelled by the family of rockets called the Long March rockets carried Yang Liwei into the orbit.

Currently, the European Space Agency (ESA) has their own Ariane 5 and Russian purchased Soyuz launch vehicles. ESA is also developing a launch vehicle Vega with cooperation with Italian Space Agency and it is expected to have three solid stages and one upper liquid stage. ISRO, the Indian Space Agency has PSLV and GSLV rockets to launch satellites into the low earth orbit (LEO) and to geosynchronous earth orbit (GEO). ISA, the Iranian Space Agency has been developing the satellite launch vehicle based on North Koreas Taepodong 2 missile system. People’s Republic of China has been using long march rockets, which uses liquid propellants such as unsymmetrical dimethylhydrazine (UDMH) and a tetroxide (dinitrogen teroxide) oxidiser. The National Space Agency of Ukraine (NSAU) and the Russian Agency RKA is in cooperative programs. They have rockets to launch as small as 2 tons for LEO using Rokot, to interplanetary orbit capability using Proton which is comparable to Delta IV or Atlas 5. The Soyuz rocket was originally based on R-7 ICBM and is liquid-based three-stage launch vehicle. It is the most successful launch vehicle in the world. The States have Delta IV rockets which use liquid hydrogen and liquid oxygen for propellant. Delta 1, 3 and Atlas rockets use refined petroleum (RP-1) and liquid oxygen for propellant for their main stage boosters. Several interplanetary probes have been launched on the Atlas 5. The company SpaceX has developed its own family of rockets known as Falcon rockets. In August 2006, NASA gave a contract to SpaceX to develop the Falcon 9 to deliver a manned capsule, called Dragon, to the ISS. A company created by Richard Branson of Virgin group and by the X Prize-winning team Tier One known as Virgin Galactic is currently developing a SpaceShipTwo to launch paying customers into suborbital flights. On January 14, 2004, President Bush announced his vision for space exploration. Following this NASA started the “Constellation Program” searching for vehicle designs, firstly the aircraft looking vehicles such as the Space Shuttle and other X vehicles, and then later the familiar old rocket methods. NASA then finalized the typical rocket system which carries a space capsule atop. The Ares 1 vehicle was developed to be used to launch the Orion space capsule to LRO carrying astronauts. The Area V was to be the heavy-lift capable vehicle that world carry cargo or, for moon missions, the Earth Departure Stage (EDS) and Lunar Surface Access Module (LSAM). The EDS would dock with the Orion spacecraft in LEO and then travel to the moon. In February 2010, President Obama cancelled the constellation program and suggested developing a new program, the Space Launch System (SLS). The SLS combines Ares 1 and Ares 5 and combines them into one rocket. Although it would be capable of heavy-lifting into the space, but would not be good enough to take us to the moon.

Russian launch vehicles

 Atlas and Delta launch vehicles

Chinese launch vehicles 

Falcon launch vehicles

Ares 5 and Ares 1

Saturn V

Rocket Physics and Components

The major components of the rockets have been described.

The same can be understood through the famous V2 rocket was designed as a ballistic missile and so lacks a landing system. In the case of V2, the payload was a warhead. It used a mixture of alcohol and water for fuel and LOX for the oxidizer and had a burn time of 65 seconds.

Rockets work on the 3rd principle of Newton (or conservation of momentum), that is, every action has an equal an opposite reaction. The fuel-oxidizer is combusted in the combustion chamber which generates high-pressure gases. These gases are forced to pass through a nozzle where the velocity of exhaust gases increase and escapes through the bottom of the rocket. In this way, it generates thrust (force), which propels the rocket to the destination trajectory. Mathematically, thrust is the net external force acting on an object that can be calculated as the rate of change of momentum of the body. The average force on the mass, therefore, is

The first term of the equation can be replaced by the following equation, 

Which says that the force generated by the exhaust gases equals the pressure difference between the exhaust gases and the atmospheric pressure multiplied by the exit surface area of the nozzle. This gives us the rocket thrust equation, an important one for rocket design. The exhaust velocity and pressure is determined by the fuel-oxidizer combination, throat and nozzle design. Therefore, the equation can be used to design rockets of the desired thrust  

The impulse-momentum theorem shown below tells us that the force applied over a period of time may change its momentum by imparting “impulse”.

Replacing the force with the obtained equation of thrust and redefining the new parameter called the equivalent velocity or effective exhaust velocity, C, we get the relation that the total impulse imparted divided by the mass ejected is equal to the equivalent velocity. We can tweak this and use it as a metric for rocket performance. The parameter, therefore, is called the specific impulse, I(sp), which tells us the total number of seconds that the rocket can deliver thrust equal to the weight of the total propellant mass under acceleration due to one standard Earth gravity, g. This is an efficiency number that can be used to describe rocket engines. 

The thermodynamic properties of the engine (combustion, gas dynamics and nozzle design) will determine the specific impulse, I(sp). The overall weight of the spacecraft and the rocket will determine the thrust requirement. Thus now using the equation below one can calculate the weight flow rate of propellant mass required, which will lead to design knowledge about how big the nozzle throat of the rocket must be.

As we had discussed, Tsiolkovsky, the father of rocket science, published a path-breaking paper in 1903 for rocket scientists, which shows us the basics of the rocket propulsion. 

Which upon solving and rearranging gives us the required burn time to achieve the required velocity. Note that many times scientists use the term mass ratio or MR synonymous to the ratio of initial to full mass of the rocket. 

Common sense suggests that carrying un-necessary weights is undesirable when energy is so limited. This introduces the concept of staging, where the empty fuel and oxidizer tanks are thrown away ex-post using its contents. There are two types of staging – serial (Apollo missions) and parallel (Space Shuttle program). Serial rocket staging is a system that stacks stages on top of one another, whereas parallel staging strap boosters beside each other.

 

Since after every stage the propellant mass is thrown away, therefore for Nth stage the MR for the rocket would be, 

Thus, using this and the Tsiolkovsky equation, engineers can determine the number of stages required to achieve the final desired velocity.  

Ignition Sequence – Saturn V

About 10 minutes before launch the upper valves open to let fuel and oxidizer flow into the engine. However, the main fuel and oxidizer valves remain closed and so they do not enter the combustion chamber. The next critical moment is 9 seconds before lift-off. Some metal alloys are allowed to burn in the gas chamber and exhaust. They burn through the metal wire, which is connected through the circuit. When all the circuits break then the main oxygen valves open, allowing oxidizer to fall into the nozzle. However, because no fuel is present, no combustion occurs. The falling oxidizer under gravity exerts some force on the turbine and takes the system into motion. Next, the fuel and oxidizer valves leading into the gas generator are opened up, where they burn and turbine and the pumps pick up speed. The gases are released, however, they are not energetic enough and do not generate adequate thrust. At the same time since pumps had picked up speed, this starts building pressure in the fuel line as well. When adequate pressure is built up then the hypergolic cartridge line opens up, which allows some hypergolic propellants to flow into the combustion chamber. A hypergolic propellant is one whose components ignite when they come into contact with each other. The main advantage of hypergolic propellants is that they can be stored as liquids at the room temperature and that engines which are powered by them are easy to ignite reliably. The most commonly used combination is dinitrogen tetroxide plus hydrazine and/or its relative's monomethylhydrazine and unsymmetrical dimethylhydrazine. This combustion then signals the main fuel valve to open, which then ramps up the engine to full power. 

 

Liftoff

The centre of gravity (cg) and centre of pressure (cp) of the rocket is calculated as shown, 

When engines are thrusting, if external forces in the form of wind gusts, shear forces etc wobbles the vehicle, then such a perturbation may displace the rocket from its stable configuration to powered or coasting configuration. Thus, the vehicle would not be aligned in the optimum aerodynamic configuration and lift and drag forces would increase, creating a torque about cg. Therefore, it is a must that cp is below cg. If this is so then the torque created by the perturbing forces during both powered and coasting fight will be in the directions that self-correct the perturbation and place the rocket back into a stable configuration. 

Further, there exist four basic types of attitude control systems for rockets. They are movable aerodynamic structures, such as fins, gimbaled thrust, Vernier rockets and thrust vanes. Fins can only be used in the atmosphere, but the other three methods are all variations on the same technique known as TVC. TVC works by actually redirecting the thrust vector by swivelling the main engine nozzles, using smaller Vernier rockets to thrust with the desired vector, or moving a vane in front of the main engines to redirect its thrust.

Rocket dynamics includes studying all the dynamic forces acting on the rockets. These forces include (1) aerodynamic drag (2) aerodynamic lift (3) weight and (4) engine thrust. Note that the lift and drag act on the centre of pressure whereas weight acts on the centre of gravity. This concept is utilized for guidance and control systems. The aerodynamic lift (L) and drag (D) forces depend upon the size, shape and the angle of attack with respect to the direction of motion. 

Lift force

Drag force

The noteworthy thing here is the term of dynamic pressure (that is, 0.5*rho*v*v). As we move up the atmosphere, its density decreases, while the spacecraft speed keeps on increasing with the altitude. Thus, their shuttle passes through a point called “max-Q”, the point where the spacecraft pushes through the maximum dynamic pressure it meets throughout its flight. It is only after Max-Q, that the rockets are allowed to throttle up, otherwise, the Max-Q would be too large. Max-Q generally occurs around 60s after lift-off.

The rocket motion has 8 degree’s of freedom, that is, positive roll, negative roll, positive pitch, negative pitch, positive yaw, negative yaw, forward thrust and negative thrust (drag)

We have already discussed all of them except roll. Propellant sloshing can create a significant wobble in the rocket which must be corrected for. In fact, slosh was one of the problems in the second flight test of the Space-X Falcon 1 launch vehicle. Similar to sloshing, propellant vorticity is also another issue. Like a big tub, the propellant tank is a large reservoir filled with liquid and has a drain at the bottom. When the drain is opened, the fluid flows down and out of the tank in a swirl. Thus, a vortex is created. Therefore, to conserve the angular momentum, the rocket itself will react by spinning in the opposite direction. However, the rockets mainly roll in order to correct its azimuthal coordinates. Post-roll correction is done, the navigation systems then have to just solve for two variables than three which simplifies the computation efforts. 

Rocket Fuel, Oxidizers and Propellants

Petroleum derivatives encompass a large variety of different hydrocarbon chemicals, most of which can be used as a rocket fuel. A specific type of refined petroleum which can be used as rocket fuel is called as RP-1. A few years ago, RP-2 substituted RP-1 in US rockets. Other options include methane, liquid hydrogen, hydrazine, unsymmetrical dimethylhydrazine, monomethyl hydrazine. For inter-planetary operations of SpaceX, methane seems to be the most suitable fuel as can be observed from table below, and therefore has been adopted. 

The most energetic oxidizer with the highest specific impulse is liquid fluorine. It has high density and is extremely corrosive and toxic. Thus, it has been discarded. Oxidizer liquids that have been used in experimental liquid rocket engines include mixtures of liquid oxygen and liquid fluorine, oxygen difluoride, chlorine trifluoride or chlorine pentafluoride. 

Availability in quantity and a low cost are very important considerations in the selection of a propellant. It is usually more expensive to use a cryogenic propellant than a storable, nontoxic one. For high performance a high content of chemical energy per unit of propellant mixture is desirable. A low molecular mass of the product gases of the propellant combination is also desirable. If very small metallic fuel particles of beryllium or aluminium are suspended in the liquid fuel, it is theoretically possible to increase the specific impulse by 9 and 18% respectively. Further, the desirable conditions are low freezing point, high specific gravity, good chemical stability, good heat transfer properties, low vapor pressure, low viscosity, spontaneously ignitable. 

Rocket Engines

Click here to watch a very interesting video showing launch into orbit and staging of Saturn V, Space shuttle, Falcon Heavy and Space launch system and demonstrating the burn as if rockets were transparent!

1.     Solid Rocket Engines: 

The most widely understood and well-known rocket engine is the solid rocket engine. They are also referred to as solid boosters or solid rocket motors. Its key advantage is its simple mechanics and thereby cheap cost. This rocket consists mainly of the solid propellant, also known as the grain and it makes up around 85% of its mass. The top of the motor contains an igniter, which is used to ignite the engine. Therefore, once this rocket starts, it cannot be switched off. The grain is arranged in different geometrical configurations which allows the formation of different thrust profiles and performance capabilities. Exterior to the grain contains some sort of insulation barrier to protect the motor from extreme temperature and pressures. 

The grain of the solid rocket motor consists of fuel, oxidizer, catalyst, binder compound, plasticizer and some other additives. The two most common binders are HTPB (hydroxyl-terminated polybutadiene) and PBAN (polybutadiene acrylonitrile). This most commonly used oxidizer is PACP (ammonium perchlorate composite propellant). The rate at which a solid propellant is burnt inside the motor is a function of chamber pressure and follows the Saint-Robert’s law, 

2.     Liquid Propellant Rocket Engines: 

Like the solid rocket engine is also called as a solid motor, the liquid-fuelled rocket engine is mostly called as a rocket engine. It mainly consists of fuel, oxidizer tanks, a gas generator, pumping systems, combustion chamber and nozzle. Some engines use the cryogenic propellants and some do not. This type of propellants requires special tanks to store them at such low temperatures. Cryogenic propellants cool the tank wall temperature far below the ambient air temperature. This causes condensation of moisture from the air on the outside of the tank and formation of ice prior to the launch. This extra weight is undesirable and during lift-off it falls of which might damage the vehicle. 

Liquid rocket engines consist of different types of cycles which have developed over the years to become more reliable, reusable and efficient. 

A. Pressure fed cycle: We feed the propellants using the into the thrust chambers using the high pressure of the inert gas. This cycle is inefficient since the extra gas and tanks are heavy. But at the same time this cycle is quite cheap and easy to start. 

The pressure fed cycles have been used in the space shuttles orbital manoeuvring systems and the RCS. 

B.  Gas generator cycle: To have higher chamber pressures and subsequently higher thrust, we use gas generator cycle than the pressure fed cycle. What is done is, small quantities of fuel and oxidizer are burnt in the gas generator, and the hot gases thus generated are used to run the turbine. This turbine is connected to the pump (centrifugal pump) via a shaft. This system is known as turbopump (pump driven by the turbine). The turbopump system is used to pressurize the fuel and oxidizer system which are being fed into the thrust chamber. 

Now, the hot gases which are released from the gas generator, post running the turbine, they are allowed to the outlet, the process is called as the open gas generator cycle. These are relatively less efficient since the exhaust gases coming out from the turbine do not contribute much to thrust generation. However, we can also feed these gases into the thrust chamber, thereby increasing the chamber pressure, with the process being called as the closed gas generator cycle. The closed generator cycle, however, is difficult since the pressure in the turbine then needs to be higher than the thrust chamber pressure, and the pressure in the gas generator (pre-burner) needs to be even larger. 

The hot gases are used to heat some amount of oxidizer, which when turned into gas is fed into the oxidizing tank to generate pressure in the tanks and push the cryogenics in zero gravity. The inert gas like Helium is used to pressurize fuel tanks. The complicated and expensive nature of this cycle is offset by its efficiency. However, these cycles are relatively difficult to start. 

The gas generator cycle has been used in V-2 rocket engine and Saturn-5’s F1 engine.

C. Staged combustion cycle: Now large quantities of fuel are allowed to burn with a limited oxidizer in the gas generator (fuel rich pre burner). As before, the gases run the turbopump system, which is used to pressurize the oxidizer and fuel into the thrust chamber. In this case, however, the limited agent is oxidizer and the pre-burn (gas generator burn) is fuel rich. Now, this fuel-rich gas, post rotating the turbine is allowed to flow into the thrust chamber. Here it mixes with the pressurized oxidizer and the fuel and burns to produce higher thrust than the open gas generator cycles. 

The cycle is very efficient and closed. But the turbines have to suffer harsh conditions and it is difficult to design. This cycle was used by Space Shuttle Main Engine. 

Now there’s another problem with fuel-rich propellant in the pre-burner, that is, the problem of coking. The fuel-rich gas, when burnt, leads to the production of polymers of unburnt carbon particles. The coke thus produced can block the nozzles, turbine components or another important part of the rocket systems and thus pose a threat. The US decided to deal with this problem by using hydrogen as a rocket fuel instead of RP-1. The Soviets, on the other hand, decided to use an oxidizer rich environment In the pre-burner. The problem with the oxidizer rich environment is that it will easily corrode everything it passes through. However, Soviets developed an especial alloy which can withstand such drastic environments which the US engineers had though Impossible. 

Coming back to the US engineers. Despite changing the fuels they had to face another problem with such a cycle. Firstly, because of the very low density of hydrogen, it required a complicated pump to ensure appropriate delivery of hydrogen into the combustion chamber. The hydrogen pump developed was quite different from the oxygen pump. Since RP-1 and oxygen pumps were similar, they could be operated using a single shaft. However, hydrogen pump now required the creation of two shafts (or two turbines) and also two pre burners.  Do remember though that both the pre burners run fuel-rich. Having said that, the two-shaft system created the second problem, that is, the high-pressure gaseous hydrogen was also used to drive the oxidizer pump. Thus, if these get mixed it can lead to quite an explosion. Also because hydrogen is very lightweight it has a tendency to leak through cracks and so extremely good sealants are required to avoid such accidents. 

D. Combustion tap off cycle: In this cycle, a fraction of the exhaust gases released from the thrust chamber are collected and fed into the turbine or the turbopump system, before letting them off. The cycle is simple and efficient, however, the extremely hot gases which are fed into the turbine calls for robust turbines. At the same time, this cycle is even harder than gas-gen cycle to start. 

It was used in the J2 rocket, which powered the second stage of Saturn-5. 

E. Expander cycle: In this cycle, thermal gradient between the exhaust gases and atmosphere is utilized unlike in the combustion tap off cycle which utilizes pressure gradient between the thrust chamber and the atmosphere. The majority of fuel, however, flows through the tubes wrapped around the converging-diverging nozzle. The cryogenic fuel upon passing through these tube expands (flashes) to form fuel vapour, which is used to run the turbopump system. The fuel rich gas then is dumped into the thrust chamber. Like the combustion tap-off cycle, there is no requirement for a gas generator here as well. 

Since the cycle is closed, the cycle is efficient and also simple. Since the gas powering the turbines are at room temperatures, they are great for reusability. This cycle was used by the RL-10 engine. 

F. Electric pump-fed cycle: In this cycle, batteries are used to power the turbine. The DC from the battery is converted into AC to run the turbine. The cycle, however, is simple and relatively new. This cycle was used by the Electron rocket.

G. Full flow Staged combustion cycle: It is similar to staged combustion cycle, with two pre burners two turbines, but here one pre-burner runs fuel rich energizing the fuel pump while the other pre-burner runs oxidizer rich energizing the oxidizer pump. This cycle won’t work with the RP-1 fuel owing to the coking problems. Also, this cycle also required the development of metal alloys that can withstand under such a corrosive environment. The temperature and pressure are less harsh because of the amount of propellant being flown through them. Also, since the fuel and oxidizer now flow through different pre burners there is no problem of sealants. This makes them reliable and decent for reusability. 

This cycle is very reliable. Additionally, all the propellants entering the combustion chamber are gaseous and so the engines perform efficiently. This cycle generates high thrust, are highly efficient and reusable. At the same time, they are very difficult to design.

This cycle is used by Space X Raptor engine. Owing to the difficulty of this cycle, Raptor is the only engine in the history to move out of the test stage into the working environment. 

In this type of rocket engine the fuel is solidified but the oxidizer is allowed to flow through the perforation. 

3. Hybrid Rocket Engine:

In this type of rocket engine the fuel is solidified but the oxidizer is allowed to flow through the perforation. The oxidizer flows through the burning surface of the solid fuel where it is ignited and due to this it will only burn if the oxidizer is present. In this way, it is possible to cut off the rocket by restricting oxidizer flow, even if solid is combusted.  

In a recent example, SpaceShipOne used a four-port perforated, solid fuel motor (HTPB) and nitrous oxide (N20) as an oxidizer. 

References:

Everyday Astronaut. 2019. Is SpaceX's Raptor engine the king of rocket egines? 26 May .

Manley, Scott. 2019. how to start the massive f-1 rocket engine. 18 Jul.

Spaceflight Science. 2014. Liquid Rocket Engine Cycles. 17 March.

Sutton, George P., and Oscar Biblarz. 2010. Rocket propulsion elements. Wiley.

Taylor, Travis S. 2017. Introduction to rocket science and engineering. Taylor & Francis.

Willocx, Olaf. 2017. Combustion cycles. 28 August .