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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
16.100 2002                                                                     1
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

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Brequet range equation

  • 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 16.100 2002 1
  • 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