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What is the most effective rocket propellant to achieve a geosynchronous orbit from the surface of the earth?

By Sean PickThis is a dissertation on comparing the advantages and disadvantages of multiple types of rocket fuel such as: liquid cryogenic, solid rocket fuel and nuclear propulsion to eventually determine that the best rocket fuel is the cryogenic fuel liquid oxygen with liquid hydrogen. To attain this goal fuels will be examined on their ability to achieve a stable geosynchronous orbit at 42,164km by doing specific impulse calculations and also considering the physical implications certain fuels have on the ability to achieve orbit using only one fuel on a single stage spacecraft. During the course of this dissertation the many types of rocket propellant will be evaluated. This will mainly consist of solid fuel boosters and the 3 types of liquid fuel; cryogenic, semi-cryogenic and hypergolic. The main attributes of these fuels that will be examined will be: specific impulse and thrust, while these two values appear to be similar they will have different implications on the very nature of the propellant. To elaborate; the specific impulse of propellant is the force (measured in newtons) produced per unit of fuel in comparison to thrust which is just the force that an accelerated object exerts in the opposite direction to the force produced due to Newton's Third Law of Motion. All specific impulse calculations are taken from sea level due to the affect of pressure on the efficiency of the engine. Higher altitudes yield higher specific impulses. Other special qualities of such propellants will also be evaluated if they aid in the process of a spacecraft achieving a geosynchronous orbit.

A geosynchronous orbit is when an orbiting body has the same orbital period (time taken for the object to make a complete orbit) as it takes for the earth complete one period of rotation around its axis which is 23 hours, 56 minutes and 4 seconds. A variation of a geosynchronous orbit is a geostationary orbit that involves the orbiting body having an orbital inclination of 0 degrees, meaning the satellite will appear to remain at the same point in the sky at all times. Modelling the earth as a completely spherical particle the radius for a geosynchronous orbit is 42,164km with an orbital inclination of 0 degrees. (David A. 2007)

When coming to a conclusion on the most powerful propellant used to achieve a geosynchronous orbit it is important to take into consideration limiting factors such as the inability of solid fuel boosters to be vectored. Vectoring is the ability for the nozzle on the exit of the combustion chamber where the hot gas is released to change shape to alter the rocket's trajectory. This is important when accomplishing a gravity burn which reduces the amount of fuel needed to achieve a geosynchronous orbit. Oxidisers are also needed due to the absence of molecular oxygen in the uppermost parts of the atmosphere such as the ionosphere which is needed for combustion. Cryogenic FuelCryogenic rocket engines use fuel that is at extremely low temperature, the use of an oxidiser such as liquid oxygen is often needed due to the lack of oxygen for combustion in a vacuum. Liquid oxygen is often misrepresented as the fuel itself however this is a misnomer. When the fuel undergoes combustion in the chamber the gas escapes out of the exhaust pipe and is propelled at high velocity. This propels the rocket vertically due to Newtons 3rd Law of Motion because the gas leaving the exhaust pushes the rocket away with an equal amount of force accelerating the rocket forwards. Using this propellant also allows for engines to be vectored, because of this it is easier to accomplish a gravity burn to achieve orbit using less fuel (George P. Sutton et al 2004).

Cryogenic fuels are at a high risk of performing a hard start otherwise known as catastrophic disassembly of the spacecraft. This is when the fuel to oxidiser ratio in the engine is incorrect leading to a large build up of one or the other. When the propellants react together there is a huge increase in pressure inside the combustion chamber that effectively blows the spacecraft apart in a violent explosion.

The first cryogenic to be examined is liquid oxygen (referred to as LOX) and kerosene. This is viewed by some as the most practical way of achieving orbit from take off at ground level (M.D Black 2010). This mixture was used in the most powerful rocket engines ever built; the Rocketdyne F-1, the same engine used in Saturn V rocket. These engines using LOX and kerosene supplied a thrust of 6.77 MN with a specific impulse of 339.3Ns-1 in an oxidiser to fuel ratio of 2.27:1. Considering this engine would have a maximum burn time of 230 seconds this is an unrelenting amount of thrust (George C. Marshall 1968). This is more thrust in one engine than the 3 main Space Shuttle engines combined making this an extremely powerful propellant, so powerful that the Saturn V had to be insulated from the inordinate amplitude of sound it produced, without which would cause the main stage of the rocket to shake apart. For perspective the amplitude of sound produced was so immense it could set fire to foliage a mile away and is the loudest. Taking this into consideration the extraordinary thrust produced by this fuel appears to be excessive when the target is to achieve a geosynchronous orbit when this fuel was used to reach the moon in the main stage, however these were only used in the first lift-off stage so could still possibly be used if the payload to be delivered was unusually massive (David A. 2007).

A more powerful alternative to using LOX and kerosene is to replace the kerosene with liquid hydrogen. This combination is used in the now obsolete space shuttle main engines to produce a specific impulse of 391Ns-1 (Ponomarenko, 2016). This mixture is considered to be the most efficient and powerful of any cryogenic fuel. Having a higher specific impulse than kerosene and liquid oxygen also supports this view. However it has many drawbacks due to both oxidiser and propellant needing to be kept at sub zero temperatures. This causes major design issues on the spacecraft itself, firstly the fuselage of the rocket must be insulated from any sources of heat including the extremely hot exhaust fumes of the rocket itself and heat produced from the friction between the rocket and the air. The technical issues do not end in the atmosphere with the spacecraft having to be protected from solar radiation from the sun that can warm the low density fuel. When it is heated both gases expand within the confined space of the fuselage which results in an increase in pressure and potentially an explosion. To prevent this the rockets must be vented to release excess pressure and welds must be done with meticulous precision to prevent the gases escaping (Derek Lowe 2008). Hypergolic FuelHypergolic fuels are fuels that ignite instantly when the two substances (almost always the oxidiser and propellant) come into contact with each other. This has the added benefit that it makes the ignition sequence at take off extremely simple and easy compromising on the fact they usually produce less thrust and have a lower specific impulse than their cryogenic and semi-cryogenic counterparts resulting in an increase in the amount of fuel needed compared and thus a more massive spacecraft. This ease of the ignition is also safer reducing the risk of a hard start, in larger spacecraft helium is pumped into the propellant tank through safety valves and then into the combustion chamber where the inert noble gas prevents the oxidiser and propellant mixing and instantly igniting. This system has a much higher safety record than other propellants (George P. Sutton et al 2004). Another advantage however is that they can be stored as a liquid at room temperature making the movement and safety of these otherwise extremely toxic and corrosive nature. This is an advantage that cryogenic fuels lack as they can only be used in launch vehicles where they are stored briefly. Hypergolic fuels on the other hand are not limited to launch vehicles and are in fact extremely useful in the upper stages of a spacecraft where spacecraft must manoeuvre into the correct orientation for a geosynchronous orbit by doing correct retrograde burns to modify its speed and thus reducing its orbital radius (John Clark 1972).

A popular and most frequently used hypergolic fuel mixture is unsymmetrical dimethylhydrazine (N2H4) mixed with dinitrogen tetroxide (N2O4). This has an excellent fuel to weight ratio and is also shock resistant increasing its safety rating. It has a specific impulse of 230Ns-1, although this is significantly less than the kerosene and liquid oxygen the excellent fuel to weight ratio results in a less massive spacecraft so less thrust is needed to achieve a geosynchronous orbit velocity (W. G Andrews 1991).

Comparatively the hypergolic fuel chlorine triflouride with hydrazine has a specific impulse of 270Ns-1(Paul M. Ordin et al 1949). This is significantly higher than the specific impulse of hydrazine with other oxidisers, however this substance developed by Nazi scientists is only stable in quartz containers at 180 degrees Celsius due to the fact is more oxidising than oxygen making this an extremely difficult and dangerous substance to store. It initiates combustion with materials otherwise classified as non-flammable such as TeflonTM or asbestos. Quartz has very strong intermolecular forces and bonds making it unlikely for chlorine triflouride to form potentially explosive oxides with it. All equipment that comes into contact with the oxidiser must be emphatically cleaned making this oxidiser extremely unlikely to be used. A case study in 1950 exemplifies this fact when one ton of the substance was spilled and it burnt through 0.3m of concrete and 1m of sand and gravel beneath (Derek Lowe 2008)Solid FuelSolid fuels are exclusively used during the 1st stage of space flight at lift-off where the vessel needs the maximum amount of thrust possible to become airborne with all the rockets mass. They achieve this by being used immediately and then when the fuel supply has been used in its entirety the tanks that stored the fuel are jettisoned increasing the momentum and efficiency of the spacecraft (M.D Black 2010). A huge advantage to using a solid rocket booster (SRB) is that they are easy to store and the mechanism by which they achieve thrust is relatively simple in comparison to other propellants. This decreases the risk of catastrophic disassembly of the vessel with a failure rate of only 1% (M.D Black 2010). By being cheaply manufactured they are extremely useful for budget spacecraft especially in the commercial space flight industry with Space X and Virgin Galactic adopting solid fuel boosters in their launch sequence.

However, there are some negative qualities involving solid rocket fuel boosters, firstly it is notoriously hard to terminate the exothermic reaction occurring in the combustion chamber of a solid rocket fuel booster. This can be overcome at the expense of destroying the tank that would normally be reused after splashing down in the ocean reducing manufacture cost by negating the expense of remaking the system (George P. Sutton et al 2004). Most solid fuel boosters use a self destruct mechanism to stop the reaction by having an explosive charge to separate the nozzle from the combustion chamber, this works by reducing the overall pressure in the combustion chamber and slowing down the rate of reaction, however the reaction still continues.

In the past black powder has been used for very primitive solid fuel booster designed however due to the explosive nature of gunpowder its range is limited to very low thrust motors; never exceeding 40N of thrust (M.D Black 2010). The current solid fuel booster being used by NASA involves a mixture of ammonium perchlorate and aluminium powder. This has an average specific impulse at sea level of 285.6Ns-1(A. Ponomarenko 2016). This is less than the specific impulse of any bipropellant liquid fuel engines, in addition to this they also cannot be used outside the atmosphere, including their uncontrollable burn rate they cannot be used for manoeuvring in orbit for fine adjustments meaning they're limited only to the lift-off stage of flight and nothing else (George P. Sutton et al 2004).

Using this mix of solid fuel and catalyst can also be self detrimental to the efficiency of the solid rocket fuel motor. The products of the reaction between aluminium and ammonium perchlorate results in a residue that can block the nozzle of the solid fuel booster decreasing efficiency of the motor.Hybrid FuelHybrid fuels overcome the issues of solid fuels such as an ammonium perchlorate booster by using a liquid oxidiser with the solid fuel. This allows the engine to be throttled up or down which solid fuel boosters alone cannot perform, in addition to this the motor can also be restarted because the supply of oxidiser can sealed stopping the reaction in an emergency such as a structural failure or if the spacecraft is moving too fast in the atmosphere and wasting fuel because it has reached the terminal speed for its design.

An example of a hybrid fuel is hydroxyl-terminated polybutadiene (HTPB) and nitrous oxide. The HTPB binds the nitrous oxide (which is the oxidiser) into an elastic solid which can also be mixed with traditional ammonium perchlorate fuel and aluminium powder in the ratio 3:17:5 allowing the hybrid fuel to produce a specific impulse of 210Ns-1. This combination is used by the Japanese Space Agency (JAXA) in the M-5 rockets' 2nd 3rd and 4th stage however this is still a lower specific impulse than that of the cryogenic fuel LOX and therefore has a lower efficiency (M.D Black 2010). This hybrid fuel however also negates the limitations of other hybrid fuels due to the fact that the vessel containing the fuel does not have to be as strong as others if they were housing other hybrid fuel such as ammonium perchlorate and thiokol. This problem is overcome because the combustion chamber when using HTPB does not have to be as large as others because the amount of the fuel needed is less because it has a relatively high specific impulse. In other hybrid fuel systems the combustion chamber must be able to endure the full force of combustion and very high temperatures created by the alternative hybrid fuel (M.D Black 2010).

The reason that the specific impulse is generally lower than that of the hybrid fuels' counter parts is due to the mechanism in which the fuel is used. In traditional liquid motors the oxidiser and fuel are mixed at the uppermost point of the combustion chamber whereby controlled streams of the mixture ignite. On the other hand in a hybrid motor the combustion occurs along the evaporation gradient of the fuel and therefore large swathes of fuel is un-combusted and therefore decreases the specific impulse. Because of this hybrid fuels are not usually used for stages requiring large amounts of thrust such as lift-off or boost stages. One method of counteracting this problem involves increasing the surface area for the evaporation to occur on because this will increase the rate of combustion so there is a lower probability for fuel to be left unburned. This can be achieved by allowing the fuel to enter the combustion chamber through multiple entry points but by doing this will increase the size of the combustion chamber, increasing the total mass of the spacecraft, something that is needed to be kept to a minimum. There is an upper bound to how much you can increase the area of evaporation though; too higher a surface area will result in local flameouts along the evaporation gradient decreasing the efficiency of the motor yet again by leaving unburned fuel.

Due to many factors such as: limited funding for development, the fact that solid fuel has much better attributes, especially when tasked with a similar task like lift-off due to higher efficiency and specific impulse. Including the fact that solid fuel is easier to store and handle, it is definitive that hybrid fuels are not a strong contender to be a good propellant to achieve a geosynchronous orbit. Nuclear PropulsionThere are many different types of nuclear propulsion that have been proposed and some have even been developed such as Project Orion which takes advantage of a series of nuclear explosions at a set frequency behind the spacecraft to propel it. If the problems of nuclear propulsion are overcome they will be significantly more powerful than traditional chemical rocket fuel and will enable for manned deep space missions (C. J Everret et al 1955). The problems engineers face depends on the type of nuclear propulsion. A fusion rocket will produce the highest specific impulse of any rocket but achieving nuclear fusion on a fast moving platform is currently far beyond any current technology. Nuclear fusion is only just being developed as a means of generating electricity for the public. A nuclear propelled rocket that undergoes catastrophic disassembly would spread radioactive material across a large area contaminating the surroundings.

Fusion rockets are spacecraft that are propelled through the energy released by the combining of light nuclei to produce a specific impulse in abundant excess of 6000Ns-1 and specific impulses in a vacuum theoretically possible in the magnitude of 100,000Ns-1 (R.B Adams et al 2003). This huge specific impulse would allow a geosynchronous orbit to be achieved using very little fuel and would be extremely efficient; fusion rocketry would also produce less radiation than fission propelled rockets resulting in less mass being constrained by shielding the rocket from the ionising effects of the radiation. The mass of the fusion reactor must be considered, current fusion reactors would weigh more than the fuel needed to accelerate the spacecraft to escape velocity.

Fusion rockets can be split into two categories: direct propulsion or ion propulsion. Direct propulsion is not currently being developed due to the Partial Test Ban Treaty signed in the 1963 that prohibits the detonation of nuclear bombs in the earths atmosphere. Some studies suggest radioactive fallout from each launch could harm one in ten people however other studies state a rather more conservative number (R.B Adams et al 2003). Even so detonation of nuclear bombs in the upper atmosphere such as in the ionosphere where there is a high concentration of charged particles from the sun can be seen as undoubtedly worse. Due to the lack of oxygen to support combustion and a lack of a medium for heat to transfer into, all energy from the blast is converted to more charge particles, otherwise known as an electromagnetic pulse (EMP) that would disable electronic devices such as satellites, a similar affect to that of a solar flare.

Ion propulsion is now more viable; one concept is the magneto-inertial fusion driven rocket or MSNW. Its mechanism of operation would involve large metal rings made from an alkaline metal such as lithium due to its likelihood to donate its one s shell electron to become more stable being exposed to a powerful magnetic field. A consequence of this would be the collapse of these metal rings around a low density plasma which would increase the pressure such that it enters a fusion state. As a result this volatile scorching metal would be propelled out of the vessel to produce specific impulses in the range of 1600Ns-1 to 5770Ns-1 depending on whether in the spacecraft is in a gravity assist or not. The process would be repeated every set interval of time, approximately 1 minute to continue accelerating the rocket (R.B Adams et al 2003). The MSNW is also not sustainable; requiring electrical energy to start the fusion process which means electrical energy must be attained from other sources such as solar panels. ConclusionDue to the unlikelihood of nuclear propulsion technology being developed extensively in the not so distant future I do not think they are the best propulsion method to achieve a geosynchronous orbit however if there was a high probability of this being achieved soon they would be classified without a doubt as the most effective way to achieve said orbit. Solid fuel boosters while being extremely cheap relative to cryogenic and hypergolic fuels present themselves with a number of disadvantages when compared to their counterparts. Firstly their inability to effectively stop the exothermic reaction posses the problem that if the spacecraft in the atmosphere is already going its terminal speed trying to accelerate it more would waste a lot of fuel energy in the form of thermal energy. This lack of control does not end in the atmosphere; the fine control needed to achieve a geosynchronous orbit would not be possible with a solid fuel booster because, waiting for the spacecraft to reach its apoapsis before starting its retro burn would not be a possibility. For this reason solid fuel boosters are not the most effective means to achieve a geosynchronous orbit.

The inefficiency of hybrid fuels and the engineering challenges faced to overcome them can be said to be too complicated for the fuel's benefits. While hypergolic fuels do have their advantages over cryogenic fuels taking into consideration data alone cryogenic fuels almost always have a higher specific impulse. This is especially true if super high energy bipropellants are being used for propulsion. A huge advantage of hypergolic fuels though is there storage conditions. Large amounts of energy is used to ensure that the cryogenic fuels remain liquid, this also increases the complexity of the rocket motor and spacecraft design to avoid catastrophic failure of the vessel. This complexity makes cryogenic rocket motors a lot more prone to failure and human life is something that cannot be compared with specific impulse. This factor compared with the relatively primitive design of hypergolic engines would suggest hypergolic fuels are the best; however the advantages of cryogenic fuels far outweigh the advantages of hypergolic fuels.

Using cryogenic fuels have been determined as the best rocket propulsion method to achieve a geosynchronous orbit but there are many cryogenic fuels. Liquid oxygen and kerosene was used in the most powerful rocket engines ever made by man on the Apollo missions but technology has advanced since then and a combination of liquid hydrogen and liquid oxygen always supports a higher specific impulse and therefore using the cryogenic fuel liquid oxygen with liquid hydrogen is the best method to achieve a geosynchronous orbit. Liquid hydrogen and fluorine and other such more reactive reagents produce a higher specific impulse but, due to their high toxicity and huge issues storing them because of their instability and tendency to explode this means they are not suitable as fuels to use when attempting a geosynchronous orbit. It must be taken into consideration however that all modern spacecraft use a plethora of these fuels during different stages of their journey to achieve maximum possible thrust and to use fuels flourish in the environment that they are performing in. During lift-off for example large amounts of thrust are needed to accelerate a very heavy object to escape velocity so solid rocket boosters are used in conjunction with the first stage cryogenic engines. Due to all mass adding to the force needed to attain escape velocity once the solid rocket boosters have expired they are jettisoned. When in orbit though fine adjustments are needed to ensure they are at the correct attitude and eccentricity. To make these corrections a less powerful fuel such as a cryogenic monopropellant or hypergolic mixture are used. All rockets have their purpose but choosing the correct fuel for the mission is paramount. ReferencesMARSHALL C. BURROWS (June 1968). Mixing and reaction studies of hydrazine and nitrogen tetroxide using photographic and spectral techniques p. 6-18.

GEORGE C. MARSHALL (April 1968) Saturn V Flight Manuel p. 21-31

R.B. ADAMS, R.A. ALEXANDER, J.M. CHAPMAN, S.S. FINCHER, R.C. HOPKINS, A.D. PHILIPS, T.T. POLSGROVE, R.J. LITCHFORD, AND B.W. PATTON (November 2003) Conceptual Design of In-Space Vehicles for Human Exploration of the Outer Planets p. 6-19

C. J. EVERETT AND S. M. ULAM (August 1955) A method of propulsion of projectiles by means of external nuclear explosions part I p. 14GEORGE P. SUTTON (2003). History of liquid propellant rocket engines in the united states".Journal of Propulsion and Power. p. 9781007.

ANDREW PONOMARENKO (2016). RPA Standard Edition. Rocket Propulsion Analysis.

M. D. BLACK (2012).The Evolution of ROCKET TECHNOLOGY, p. 90-101

PAUL M. ORDIN, JOHN M. DIEHL AND RILEY O. MILLER (1948). NACA: Preliminary Investigation of Hydrazine as a Rocket Fuel (NACA Research Memorandum)D. LOWE (2008). Sand Won't Save You This Time. [Blog] Available at: http://blogs.sciencemag.org/pipeline/archives/2008/02/26/sand_wont_save_you_this_time [Accessed 8 Feb. 2016].

DAVID A. VALLADO (2007). Fundamentals of Astrodynamics and Applications. p. 31. JOHN CLARK (1972). Ignition! An Informal History of Liquid Rocket Propellants. p. 6

C. JONES, D. MASSE, C. WILHITE AND M. WALKER (2010). PHARO: Propellant harvesting of atmospheric resources in orbitGEOFFERY A. LANDIS AND DIANNE L. LINNE (October 2001). Mars rocket fuel using in situ propellants Propellant combinationsIsp Range(Ns-1)

Low-energy monopropellants:-Hydrazine- Ethylene oxide-Hydrogen peroxide160 to 190

High-energy monopropellants:- Nitromethane190 to 230

Low-energy bipropellants:-Perchloryl fluoride-Analine-Acid-JP-4-Acid-Hydrogenperoxide-JP-4200 to 230

Medium-energy bipropellants:-Hydrazine-Acid- Ammonia-Nitrogen tetroxide230 to 260

High-energy bipropellants:- Liquid oxygen-JP-4- Liquid oxygen-Alcohol- Hydrazine-Chlorine trifluoride250 to 270

Very high-energy bipropellants:

- Liquid oxygen and fluorine-JP-4 -Liquid oxygen and ozone-JP-4-Liquid oxygen-Hydrazine270 to 330

Super high-energy bipropellants:- Fluorine-Hydrogen- Fluorine-Ammonia- Ozone-Hydrogen- Fluorine-Diborane300 to 385

Rocketdyne F-1 engine from the Saturn V first stage (NASA, (n.d.). Saturn V News Reference.) [image] Available at: http://history.msfc.nasa.gov/saturn_apollo/documents/F-1_Engine.pdf [Accessed 9 Feb. 2016].