[**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:

C specific fuel consumption, pounds of
fuel per brake horsepower per hour
c 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
P 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

_{P}
_{T}
_{e}

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

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

The overall propulsion-system efficiency is then given by

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:

since

Expressed as a percentage, equation (F4) becomes

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

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:

where the constant 550 converts the power P_{e}
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:

or

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

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

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