Propulsive efficiency
In aerospace engineering, concerning aircraft, rocket and spacecraft design, overall propulsion system efficiency
is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity.
The cycle efficiency is expressed as the percentage of the heat energy in the fuel that is converted to mechanical energy in the engine, and the propulsive efficiency is expressed as the proportion of the mechanical energy actually used to propel the aircraft.
The propulsive efficiency is always less than one, because conservation of momentum requires that the exhaust have some of the kinetic energy, and the propulsive mechanism (whether propeller, jet exhaust, or ducted fan) is never perfectly efficient.
It is greatly dependent on exhaust expulsion velocity and airspeed.
In an engine, efficiency is defined as the ratio of useful work done to energy expended.
is negative; in any reversible work-extracting process, entropy is overall not increased, but rather is moved from a hot (high-entropy) system to a cold (low-entropy one), decreasing the entropy of the heat source and increasing that of the heat sink.
In generic terms, the propulsive power can be calculated as follows: The thrust can be computed from intake and exhaust massflows (
): The work done by the engine to the flow, on the other hand, is the change in kinetic energy per time.
This does not take into account the efficiency of the engine used to generate the power, nor of the propeller, fan or other mechanism used to accelerate air.
It merely refers to the work done to the flow, by any means, and can be expressed as the difference between exhausted kinetic energy flux and incoming kinetic energy flux: The propulsive efficiency can therefore be computed as: Depending on the type of propulsion used, this equation can be simplified in different ways, demonstrating some of the peculiarities of different engine types.
The general equation already shows, however, that propulsive efficiency improves when using large massflows and small velocities compared to small mass-flows and large velocities, since the squared terms in the denominator grow faster than the non-squared terms.
The losses modelled by propulsive efficiency are explained by the fact that any mode of aero propulsion leaves behind a jet moving into the opposite direction of the vehicle.
The propulsive efficiency formula for air-breathing engines is given below.
This cancels out the mass-flow and leads to: For pure jet engines, particularly with afterburner, a small amount of accuracy can be gained by not assuming the intake and exhaust massflow to be equal, since the exhaust gas also contains the added mass of the fuel injected.
For turbofan engines, the exhaust massflow may be marginally smaller than the intake massflow because the engine supplies "bleed air" from the compressor to the aircraft.
In most circumstances, this is not taken into account, as it makes no significant difference to the computed propulsive efficiency.
By computing the exhaust velocity from the equation for thrust (while still assuming
), we can also obtain the propulsive efficiency as a function of specific thrust (
It varies slightly with altitude due to changing atmospheric pressure, but can be up to 70%.
Rocket engines have a slightly different propulsive efficiency (
) than air-breathing jet engines, as the lack of intake air changes the form of the equation.
However, in practice, this results in a very low specific impulse, causing much greater losses due to the need for exponentially larger masses of propellant.
Unlike ducted engines, rockets give thrust even when the two speeds are equal.
In 1903, Konstantin Tsiolkovsky discussed the average propulsive efficiency of a rocket, which he called the utilization (utilizatsiya), the "portion of the total work of the explosive material transferred to the rocket" as opposed to the exhaust gas.
[6] The calculation is somewhat different for reciprocating and turboprop engines which rely on a propeller for propulsion since their output is typically expressed in terms of power rather than thrust.
The equation for heat added per unit time, Q, can be adopted as follows: where H = calorific value of the fuel in BTU/lb, h = fuel consumption rate in lb/hr and J = mechanical equivalent of heat = 778.24 ft.lb/BTU, where
is engine output in horsepower, converted to foot-pounds/second by multiplication by 550.
Given that specific fuel consumption is Cp = h/Pe and H = 20 052 BTU/lb for gasoline, the equation is simplified to: expressed as a percentage.
of 86% (for the optimal airspeed and air density conditions for the given propeller design[citation needed]), maximum overall propulsion efficiency is estimated as:
