The thrust-specific fuel consumption, TSFC, for a jet engine is defined in Sec. 6.13. Engi...

The thrust-specific fuel consumption, TSFC, for a jet engine is defined in Sec. 6.13. Engine manufacturers are constantly trying to reduce TSFC in order to reduce the weight of fuel consumed for a given flight of given time duration. By reducing the fuel weight, the payload weight can be correspondingly increased. However, design changes that result in reductions in TSFC also frequently result in slight increases in the engine weight itself, which will then reduce the payload weight. The break even point is where the decrease in fuel weight is exactly cancelled out by the increase in engine weight, giving no increase in the payload weight. Designating the new reduced thrust-specific fuel consumption by (TSFC)new = (TSFC) (1 − εf) and the new weight of the airplane increased by the increase in engine weight by Wnew − W(1 + εW), where εf and εW are small fractional values, prove that the break even point for changes in engine weight and TSFC are given by

where W and W_f  are the average weight of the airplane during, cruise and the weight of fuel used during cruise, respectively, both before any design perturbation in engine weight or TSFC, and t is the total cruising time of flight.