L W dw F W=L-D(LD=F(D) The rate of change of aircraft gross weight is thus dw Suppose L/D and Isp remain constant along flight path dw We can integrate this equation for the change in aircraft weight to yield a relation between the weight change and the time of flight W W Dl, where w is the initial weight If w is the final weight of vehicle and initia 0, the relation between vehicle parameters and flight The range is the flight time multiplied by the flight speed, or, W Range= cot aircraft designer propulsion system structural designer 2A-92A-9 L D F W g dW dt F Isp f m˙ =− =− WLD L D F L D = = ( ) = ( ) The rate of change of aircraft gross weight is thus dW dt W L D Isp = − ( ) . Suppose L/D and Isp remain constant along flight path: dW W dt L D Isp = − ( ) . We can integrate this equation for the change in aircraft weight to yield a relation between the weight change and the time of flight: ln W W t L D i Isp = − ( ) , where Wi is the initial weight. If Wf is the final weight of vehicle and tinitial=0, the relation between vehicle parameters and flight time, t f , is L D I W W t sp i f f ln = . The range is the flight time multiplied by the flight speed, or, Range c t L D c I W W f sp i f = =     × × ( ) ×      0 0  aircraft designer propulsion system designer structural designer ln { { 123