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| Fig. 1: Test firing of the RS-25 engine at John C. Stennis Space Center. (Source: Wikimedia Commons) |
Space propulsion systems have been studied and fielded extensively over the past century, with the most common thrust-producing mechanism being a reactionary inertial force produced by expelling mass from the spacecraft. This type of propulsion system is commonly termed a reaction engine. Among other examples, reaction engines are used on launch vehicles to deliver payloads to space, on orbital satellites for orbit transfers or orbit corrections, and on deep-space satellites for exploring the bounds of the solar system.
One of the most important mission requirements is the total change in speed the spacecraft needs to achieve the mission, also known as the Δ of the mission. For example, the total Δv required to take a vehicle from Earth's surface to low earth orbit (LEO) is approximately 9.4 km/s; the total Δv required to make orbital corrections in a geosynchronous orbit is between 10 and 50 m/s per year. [1] Every vehicle-transport space mission has a specific Δv that is required to perform the maneuver. For a single-stage engine producing constant thrust, the total Δv that a spacecraft can achieve with a finite amount of propellant onboard is known as the Δv budget of the spacecraft. The Tsiolkovsky Rocket Equation relates the Δv budget of the spacecraft to exhaust velocity and propellant mass fraction: [2]
where ve is the exhaust velocity of the engine and ζ is the propellant mass fraction of the vehicle, defined as the mass-fraction of the vehicle that the propellant accounts for. Thus, to meet the mission requirement of a large Δv with a low propellant mass-fraction, it is strictly necessary to maximize the exhaust velocity of the expelled propellant. The following sections discuss the fundamental limitations on exhaust velocity.
Chemical propulsion systems produce thrust by converting chemical energy, derived from the propellant, into kinetic energy of the exhaust gas. The chemical energy is extracted from the propellant itself and so the amount of available energy is limited by the amount of propellant onboard. Chemical propulsion systems convert the available chemical energy into kinetic energy by combusting propellant and allowing the gaseous combustion products to thermodynamically expand through a nozzle. An example of an engine used in the chemical propulsion system aboard National Aeronautics and Space Administrations (NASA's) Space Shuttle is the RS-25 engine, as shown in Fig. 1.
An ideal chemical propulsion system would convert all available chemical energy into kinetic energy of the exhaust gas, thus maximizing exhaust velocity and, in turn, the Δv budget of the rocket. The kinetic energy of the exhaust gas is bounded by the specific heat of combustion of the fuel, given in units of energy per mass-fuel. Consider the fuel with the largest specific heat of combustion, hydrogen (H2), with a specific heat of combustion of 285.9 kJ/mol. [3] Hydrogen combusts with oxygen (O2) to form water (H2O), with the chemical formula for the stoichiometric combustion reaction being:
The heat of combustion for the stoichiometric reaction is 285.9 kJ/mol H2 or, equivalently, 15.8 MJ/kg reacted propellant (H2 plus O2). Therefore, approximately 15.8 MJ/kg propellant is the theoretical upper limit for the specific kinetic energy of the exhaust gas ek of chemical propulsion systems, which equates to a theoretical maximum exhaust velocity ve of:
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| Fig. 2: Test firing of ion engine aboard NASA's Deep Space 1 mission. (Source: Wikimedia Commons) |
Electric propulsion systems were invented to surpass the exhaust velocity limit of chemical propulsion systems. [2] This enables missions that require a large Δv budget and a limited amount of propellant mass. The fundamental ideas behind electric propulsion are the following: use an energy source that is not tied to propellant mass and supply the propellent with enough energy from the energy source to achieve the desired exhaust velocity. The way the energy is transferred from the source to the propellent is through electrostatic or electromagnetic fields, hence the name "electric propulsion". An example of an ion engine used in the electric propulsion system that powered NASA's Deep Space 1 mission is shown in Fig. 2.
The energy source should not be derived from chemical bonds, such as an electric battery or fuel cell. This is because the system would still be constrained by the same fundamental energy limits imposed by chemical propulsion systems, equal to the H2−O2 reaction specific heat of combustion of 15.8 MJ per kilogram of reaction mass. However, even if the energy source is chemical, an electric propulsion system can exceed the 5,600 m/s theoretical exhaust velocity limit imposed by chemical propulsion systems since the energy source is separated from the propellant, but at the cost of having an impractical amount of reactant mass onboard the spacecraft. For example, if an electric propulsion system was powered by a H2−O2 fuel cell and the desired specific kinetic energy of the exhaust gas is 31.6 MJ per kilogram propellant or, equivalently, an exhaust velocity of 7,950 m/s then an idealized system would require 31.6/15.8 = 2 kg of reactant mass for every 1 kg of propellant mass. Thus, using a chemical energy source to fuel an electric propulsion system quickly becomes impractical in terms of mass-cost.
Instead, electric propulsion systems have historically relied on solar energy because solar energy does not need to be supplied from onboard mass. While there are some cases of nuclear fission reactors being used as an energy source for electric propulsion systems that are worth mentioning, such as the United States Air Force's (USAF's) Systems for Nuclear Auxiliary Power (SNAP-10A) project, they are not discussed any further here. [4] Of course, there is still a mass-cost associated with converting the available solar energy into usable electricity. This is because the vehicle must deploy a solar array to convert the solar energy into electricity.
For example, consider the roll-out solar arrays (ROSAs) used on NASA's Double Asteroid Redirection Test (DART) mission vehicle. The mass of the ROSAs on the DART mission is not publicly accessible, so some assumptions are made as follows. The company Redwire Space lists their 8.6 meter ROSA at a mass of 36 kg, so it is assumed the total mass of the ROSAs aboard the DART vehicle is roughly the same. [5] The solar array on the DART mission supplied enough energy to power the NASA Evolutionary Xenon Thrust (NEXT) ion engine aboard the spacecraft, about 7.4 kW. [6] The NEXT ion engine can achieve a maximum exhaust velocity of about 40 km/s, which equates to an exhaust gas specific kinetic energy of about 800 MJ per kg propellant. [6] If, instead, the NEXT engine was powered by a H2-O2 fuel cell, achieving an exhaust gas specific kinetic energy of 800 MJ per kg propellant would require an additional 800/15.8 ≈ 50 kg reaction mass per kg propellant. The DART vehicle had a tank capable of carrying about 140 kg of xenon propellant. [7] Assuming the NEXT engine was supplied with enough reaction mass so it could operate at maximum exhaust velocity until it ran out of fuel, the spacecraft would have had to carry 140×50 = 7,000 kg of extra reaction mass to achieve the same exhaust velocity as the roughly 36 kg solar array. Clearly, the deployment of a solar array is a far lower mass-cost than using a chemical energy source.
For an electric propulsion system, the exhaust velocity can essentially be "selected" as an engineering design parameter based on the mission requirements. This is because, in contrast to chemical propulsion systems which typically burn propellant on the order of minutes, electric propulsion systems typically "burn" propellant on the order of years. Thus, chemical propulsion systems can be thought of as "energy-limited" systems because the exhaust velocity is limited by the total chemical energy supplied by the propellant-mass during the short burn; electric propulsion systems can be thought of as "power-limited" systems because the exhaust velocity is not limited by a set amount of stored energy aboard the spacecraft, but the system is limited by the radiant power supplied from the sun at any given moment. The power limitation of an electric propulsion system manifests itself as an immediate trade-off between exhaust velocity and thrust. Considering an ideal electric propulsion system where the system is 100% efficient at converting available power into useful kinetic power, it can be shown that thrust T is proportional to available power Pe but inversely proportional to exhaust velocity ve: [2]
Thus, thrust decreases as exhaust velocity increases. If thrust is too small then the mission will take an impractically long amount of time or, if there are motion-opposing forces on the vehicle such as aerodynamic drag or gravity, the mission can become impossible.
Chemical propulsion systems are fundamentally constrained by the energy supplied in the chemical bonds of its propellant. This puts a strict physical limit on the maximum exhaust velocity that a chemical propulsion system can theoretically achieve, about 5,600 m/s. Electric propulsion systems surpass this physical limit by separating the energy source from the propellant, enabling a separate domain of space missions that require large Δv budgets with strictly limited amounts of propellant.
© Adam Tuckey. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] G. P. Sutton and O. Biblarz, Rocket Propulsion Elements, 9th Ed (Wiley, 2016).
[2] D. M. Goebel, I. Katz, and I. G. Mikellides, Fundamentals of Electric Propulsion, 2nd Ed. (Wiley, 2023).
[3] D. R. Burgess, Jr. and A. P.Hamins, "Heats of Combustion and Related Properties of Pure Substances," U.S. National Institute of Standards and Technology, NIST Technical Note NIST TN 2125, December 2023.
[4] R. A. Johnson, W. T. Morgan, and S. R. Rocklin, "Design, Ground Test and Flight Test of SNAP 10A, First Reactor in Space," Nucl. Eng. Des. 5, 7 (1967).
[5] "ROSA (Roll-Out Solar Array)," Redwire Space, October 2025.
[6] C. Tolbert, "NASA's Evolutionary Xenon Thruster - Commercial (NEXTC)," U.S. National Aeronautics and Space Administration, November 2017.
[7] E. Adams et al., "Double Asteroid Redirection Test (DART) Mission," U.S. National Aeronautics and Space Administration, Octtober 2023.
