# Calculation of Engine Fuel Consumption

At this point of the calculation the total power required of the engine(s), for the given weight and flight condition, is known. We now use this information to determine the fuel consumption.

In most instances, engine fuel consumption data are given in terms of the specific fuel consumption (sfc) (kg/h/kW) for a corresponding power setting (P). A small adjustment of the data permits a simple method to be used to calculate the fuel consumption of a gas-turbine engine from the specified amount of power.

The concept of fuel flow of an engine (Wf) (kg/h) is now introduced. It is readily seen that it is obtained from the product of the sfc and the power. By plotting the resulting fuel flow against power, a variation very close to linear can be seen and, hence, can be specified by a straight line equation which can be determined by linear regression (least squares). The resulting linear variation makes the fuel consumption calculation very straightforward.

To make the method even more useful, the operating altitude and temperature will need to be incorporated into the calculation. If the fuel flow v power variation is plotted for each atmospheric condition, a series of straight line fits will result. However, these straight line
fits will collapse close to one single straight line if the fuel flow and engine power are normalized by the factor:

(A. 22)

where d is the pressure ratio and в is the absolute temperature ratio (both relative to ISA sea – level atmosphere conditions).

We can thus define the engine fuel consumption law for any atmospheric condition as:

This gives the ability to incorporate different atmospheric conditions into the calculation method. As with the rest of the methods described in this appendix, its simplicity requires that for this fuel consumption calculation, it is assumed that the engine(s) is(are) not operating close to a limit.

The resulting straight line fit has a positive intercept on the fuel-flow axis, defined by the term Ae. This has an important influence on the optimization of fuel consumption for a multi­engined helicopter. If we have a helicopter which has N engines, each combining to give a total power production of P, then it follows that each engine must generate a power of P/N whereupon the total fuel consumption for all N engines combined is given by:

Wf

=TE+Be

that is:

Wf = N • Ae • §V

The result of the first term on the right-hand side of (A.24) means that, from (A.25), it can be seen that for a given power requirement, the smaller the number of engines, the lower the fuel consumption. In consequence, as a helicopter design develops, if the optimizing for fuel consumption is paramount, a minimum number of engines capable of providing sufficient power should be the choice. This may be in direct conflict with the other requirements, particularly with the performance of the helicopter having sustained an engine failure when the design will tend to move in the opposite direction – that is, to have a maximum number of engines. As can be seen, the selection of the engine provision for a multi-engine helicopter is therefore not so simple.