Quest for Performance: The Evolution of Modern Aircraft

Appendix F

Estimation of Overall Propulsion-System Efficiency

[517] The overall propulsion-system efficiency discussed in chapter 10 is the ratio of the power usefully expended in propelling the aircraft to the heating value of the fuel consumed per unit time. The overall propulsion-system efficiency is the product of the cycle efficiency and the propulsive efficiency . A simple method for estimating the overall propulsion-system efficiency is developed in the following for aircraft powered with either jet, turboprop, or reciprocating engines. The symbols used in appendix F are defined as follows:

 CP specific fuel consumption, pounds of fuel per brake horsepower per hour cT specific fuel consumption, pounds of fuel per pound of thrust per hour H heating value of fuel, British thermal units per pound h fuel-flow rate, pounds per hour J Joule's constant, 778 foot-pounds per British thermal unit M Mach number P power usefully expended in propelling the aircraft, foot-pounds per second Pe power developed by engine, horsepower Q heat added by fuel per unit time, British thermal units per second T thrust, pounds V velocity, feet per second

The jet propulsion system is considered first. In such a system the heat added per unit time is given by the following expression:

(F1)

[518] and the power usefully expended in propelling the aircraft is

P=TV (F2)

The overall propulsion-system efficiency is then given by

(F3)

If the heating value of the fuel is taken as 18 500 British thermal units per pound, the overall propulsion-system efficiency is given by the following simple expression:

>(F4)

since

(F5)

Expressed as a percentage, equation (F4) becomes

(F6)

Equation (F6) may also be expressed in terms of the Mach number as

(F7)

where the speed of sound has been taken as 971 feet per second (this value being for altitudes above the tropopause).

An expression for the overall propulsion-system efficiency of propeller-driven aircraft, powered with either reciprocating or turboprop engines, will now be developed. The capability of these types of engines is usually expressed in terms of the power that they develop rather than their thrust. Consequently, the expression for the overall propulsion-system efficiency is developed in a slightly different way [519] than that used for jet-propelled aircraft. The amount of power developed by the engine will first be related to the engine cycle efficiency. The amount of heat added to the engine per unit time, given by equation (F1), is also applicable to propeller-driven aircraft and is used in forming the following relationship:

(F8)

where the constant 550 converts the power Pe from horsepower to foot-pounds per second. If the specific fuel consumption cp is defined as the amount of fuel used per brake horsepower per hour, the cycle efficiency may then be expressed as follows:

(F9)

or

(F 10)

Expressed as a percentage, equation (F10) for the cycle efficiency becomes

(F11)

If the propulsive efficiency is taken as 86 percent, a reasonable average value, the overall propulsion-system efficiency becomes

(F12)

Equations (F7) and (F12) were used in the construction of figure 10.2.