Subsections

# 13.3 Aircraft Range: the Breguet Range Equation

Consider an aircraft in steady, level flight, with weight , as shown in Figure 13.1. The rate of change of the gross weight of the vehicle is equal to the fuel weight flow:

For steady, level flight, , , or

The rate of change of aircraft gross weight is thus

Suppose and remain constant along the flight path:

We can integrate this equation for the change in aircraft weight to yield a relation between the weight change and the time of flight:

where is the initial weight. If is the final weight of vehicle and , the relation between vehicle parameters and flight time, , is

The range is the flight time multiplied by the flight speed, or,

The above equation is known as the Breguet range equation. It shows the influence of aircraft, propulsion system, and structural design parameters.

## 13.3.1 Relation of overall efficiency, , and thermal efficiency

Suppose is the heating value (heat of combustion'') of the fuel (i.e., the energy per unit of fuel mass), in J/kg. The rate of energy release is , so

and

Thus

and

 or

Keep in mind that, in general,

## 13.3.2 The Propulsion Energy Conversion Chain

The above concepts are depicted in Figure 13.4 as parts of the propulsion energy conversion train mentioned in Part I, which shows the process from chemical energy contained in the fuel to energy useful to the vehicle.

The combustion efficiency is near unity unless conditions are far off design. We can therefore regard the two main drivers as the thermal and propulsive13.1 efficiencies. The evolution of the overall efficiency of aircraft engines in terms of these quantities was shown in Figure 11.8.

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