The document presents the Brequet Range Equation, which is used to calculate an aircraft's range. It defines range as the integral of velocity over time from takeoff to landing. It then derives an equation for the rate of change of an aircraft's weight due to fuel burn. Finally, it shows that assuming the lift-to-drag ratio is constant, this results in the Brequet Range Equation, which calculates range as a function of true airspeed, lift-to-drag ratio, specific fuel consumption, and initial and final weights.

1. Brequet Range Equation
V
t=ti t=tf
W=Wi W=Wf
Range
tf
Range = ∫ Vdt
ti
In level flight at const speed:
L = W , Lift = Weight
T = D , Thrust = Drag
The aircraft weight changes during flight due to use of fuel. Relate weight
change to time change:
dW
dW = dt
dt
fuel weight
=− dt
time
fuel weight T
=− dt
time T
The quantity:
fuel weight 1
time T
is known as the specific fuel consumption or sfc. It has units of:
lb( fuel ) force
sfc units = or
lb − hr force − time
⇒ dW = − sfc iT dt
Wf
V 1
⇒ Range = − ∫ dW
Wi
sfc T
But since T = D and L = W we have:
Wf
V L dW
Range = − ∫
Wi
sfc D W
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2. This is the general form of the range equation. The Breguet range equation is
V L
found by assuming that is constant for the entire flight. In that case:
sfc D
Wf Wf
V L dW V L dW
Range = − ∫ =− ∫
Wi
sfc D W sfc D Wi W
Breguet range equation:
V L Wi
Range = log
sfc D Wf