Specific impulse (usually abbreviated as ) is a physical quantity defined as the ratio of change in momentum (impulse) to the mass used, usually fuel. It typically uses units of metres per second (a SI unit) or feet per second (in imperial units). It is equivalent to thrust (a force, in newtons or pounds) per mass flow rate (in kg/s or lbm/s).
It serves as a measure of how efficiently an engine, such as a rocket or jet engine, generates thrust from propellant. is the effective exhaust velocity used in the Tsiolkovsky rocket equation which calculates how much a vehicle's velocity can be changed with a given quantity of fuel.
Normalized specific impulse is the ratio of specific impulse to Earth's standard acceleration of gravity, g (in m/s2 or ft/s2). It is measured in seconds, and conveniently is the same number in both SI and imperial units. It can be understood as the time that one kilogram of fuel can produce one kilogram-force of thrust, which is equal to the time that one pound-mass of fuel can produce one pound-force of thrust.
Overview
Reaction engines, such as rockets and jet engines propel a vehicle by expelling mass in one direction, which pushes the vehicle in the other direction according to Newton's third law of motion. This expelled mass is called the reaction mass. An engine can push harder if it expels the reaction mass at a higher exhaust velocity , or expels mass at a faster rate, .
Assuming that the engine expels mass at a constant exhaust velocity , the thrust is
If this is integrated over time, the result is the total change in momentum. Dividing by the mass shows that the specific impulse is equal to the exhaust velocity. In practice, the specific impulse is usually lower than the actual physical exhaust velocity due to inefficiencies in the rocket, and thus corresponds to an "effective" exhaust velocity.
The specific impulse in units of velocity is defined by where is the average thrust.
Types of engines The practical meaning of the measurement varies with different types of engines. Car engines consume onboard fuel, breathe environmental air to burn the fuel, and push against the ground beneath them. There is no reaction mass. In this case, is momentum per fuel burned.
Chemical rocket engines, by contrast, carry their fuel, oxidizer, and reaction mass with them, so is momentum per reaction mass.
Airplane engines are in the middle, as they only push against airflow through the engine. Some of this reaction mass is carried with them, and some is breathed from the air. Therefore, "specific impulse" could be taken to mean either "per reaction mass", as with a rocket, or "per fuel burned" as with cars. The latter is the traditional and more common choice. Because of these differences, specific impulse is not directly comparable between different types of engines.
Specific impulse can be taken as a measure of efficiency. In cars and planes, it typically corresponds with fuel efficiency, i.e. the distance travelled per unit mass or volume of fuel. In rocketry, it corresponds to the achievable delta-v, which is the typical way to measure changes between orbits, via the Tsiolkovsky rocket equation
where is the specific impulse measured in units of velocity, and are the initial and final masses of the rocket. The difference between and is the reaction mass that was expelled.
Propulsion systems
Rockets For any chemical rocket engine, the momentum transfer efficiency depends heavily on the effectiveness of the nozzle. The nozzle is the primary means of converting reactant energy (e.g. thermal or pressure energy) into a flow of momentum moving the same direction. Nozzle shape and effectiveness have a great impact on total momentum transfer from the reaction mass to the rocket.
The efficiency of the conversion of input energy to reactant energy also affects , either thermal energy in combustion engines or electrical energy in ion engines. This efficiency determines the amount of delta-v a rocket can perform with a given load of fuel. Optimizing the tradeoffs between fuel quantity and specific impulse is one of the fundamental engineering challenges in rocketry.
Although the specific impulse has units of velocity, it almost never corresponds to an actual physical velocity. In chemical and cold gas rockets, the shape of the nozzle has a high impact on the energy-to-momentum conversion. There are other sources of losses and inefficiencies as well, such as the details of the chemical combustion in such engines. The physical exhaust velocity is higher than the "effective exhaust velocity", which is the "velocity" of the specific impulse. The momentum exchanged and the mass used to generate it are physically real measurements. Typically, rocket nozzles work better when the ambient pressure is lower, such as in space versus in the atmosphere. Engines are typically described by a sea-level , and a vacuum , which is higher. Ion engines, however, do not use a nozzle, although they have other sources of losses so that the momentum transferred is lower than the physical exhaust velocity of their reaction mass.
It is common to express specific impulse as the product of two numbers: a characteristic velocity , which summarizes combustion-chamber performance into a quantity with units of speed, and a thrust coefficient , which is a dimensionless quantity that summarizes nozzle performance. An additional factor of is a units conversion.
Units of seconds In rocketry, the specific impulse is often reported in seconds instead of effective exhaust velocity of an engine (m/s), by dividing through standard gravity :
This is convenient when using gravitational force units (kgf or lbf), since then expresses the amount of thrust per unit propellant flow (kg/s or lb/s). Representing specific impulse in units of time also has the advantage of being agnostic between imperial and SI units:
Physically, measured in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant whose weight (under g) is equal to the engine's thrust. It is the length of time that the engine can produce 1 kgf (or 1 lbf) of thrust from 1 kg (or 1 lb) of propellant.
Cars Although the car industry almost never uses specific impulse on any practical level, the measure can be defined, and makes good contrast against other engine types. Car engines breathe external air to combust their fuel, and (via the wheels) react against the ground. The only meaningful way to interpret "specific impulse" is as "thrust per fuelflow", although one must also specify if the force is measured at the crankshaft or at the wheels, since there are transmission losses. Such a measure corresponds to fuel mileage.
Airplanes In an aerodynamic context, there are similarities to both cars and rockets. Like cars, airplane engines breathe outside air; unlike cars they react only against fluids flowing through the engine (including the propellers as applicable). There are several possible ways to interpret "specific impulse": as thrust per fuel flow, as thrust per breathing-flow, or as thrust per "turbine-flow" (i.e. excluding air though the propeller/bypass fan). Since the air breathed is not a direct cost, with wide engineering leeway on how much to breathe, the industry traditionally chooses the "thrust per fuel flow" interpretation with its focus on cost efficiency. In this interpretation, the resulting specific impulse numbers are much higher than for rocket engines, although this comparison is quite different — one is with and the other is without reaction mass. It exemplifies the advantage an airplane engine has over a rocket due to not having to carry the air it uses.
As with all kinds of engines, there are many engineering choices and tradeoffs that affect specific impulse. Nonlinear air resistance and the engine's inability to keep a high specific impulse at a fast burn rate are limiting factors to the fuel consumption rate.
As with rocket engines, the interpretation of specific impulse as a "velocity" does not actually correspond to the physical exhaust velocity. Since the usual interpretation excludes much of the reaction mass, the physical velocity of the reactants downstream is much lower than the effective exhaust velocity suggested from the I.
General considerations Specific impulse should not be confused with energy efficiency, which can decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so.
Specific impulse should not be confused with total thrust. Thrust is the force supplied by the engine and depends on the propellant mass flow through the engine. Specific impulse measures the thrust per propellant mass flow. Thrust and specific impulse are related by the design and propellants of the engine in question, but this relationship is tenuous: in most cases, high thrust and high specific impulse are mutually exclusive engineering goals. For example, LH2/LO bipropellant produces higher (due to higher chemical energy and lower exhaust molecular mass) but lower thrust than RP-1/LO (due to higher density and propellant flow). In many cases, propulsion systems with very high specific impulse—some ion thrusters reach 25–35 times better than chemical engines—produce correspondingly low thrust.
When calculating specific impulse, only propellant carried with the vehicle before use is counted, in the standard interpretation. This usage best corresponds to the cost of operating the vehicle. For a chemical rocket, unlike a plane or car, the propellant mass therefore would include both fuel and oxidizer. For any vehicle, optimizing for specific impulse is generally not the same as optimizing for total performance or total cost. In rocketry, a heavier engine with a higher specific impulse may not be as effective in gaining altitude, distance, or velocity as a lighter engine with a lower specific impulse, especially if the latter engine possesses a higher thrust-to-weight ratio. This is a significant reason for most rocket designs having multiple stages. The first stage can optimized for high thrust to effectively fight gravity drag and air drag, while the later stages operating strictly in orbit and in vacuum can be more easily optimized for higher specific impulse, especially for high delta-v orbits.
Propellant quantity units The amount of propellant could be defined either in units of mass or weight. If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to be equivalent to units of speed; this interpretation is commonly labeled the effective exhaust velocity. If a force-based unit system is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time. The problem with weight, as a measure of quantity, is that it depends on the acceleration applied to the propellant, which is arbitrary with no relation to the design of the engine. Historically, standard gravity was the reference conversion between weight and mass. But since technology has progressed to the point that we can measure Earth gravity's variation across the surface, and where such differences can cause differences in practical engineering projects (not to mention science projects on other solar bodies), modern science and engineering focus on mass as the measure of quantity, so as to remove the acceleration dependence. Measuring specific impulse by propellant mass gives it the same meaning for a car at sea level, an airplane at cruising altitude, or a helicopter on Mars.