Energy height method for flight path optimisation. Addendum A: numerical method suitable for rapid use on IBM PC compatible computers.
Abstract:ESDU 91016 suggests a method of speeding up the calculation of the optimum flight path by the energy height method of ESDU 90012. Although programming the graphical methods used there is possible, it is quicker to apply a simple linear search routine to seek df/dHe (where f is the parameter to be minimised, for example, time or fuel, and He is energy height) along contours of constant energy height. A feasible flight envelope for the search is first established (taking account of, for example, maximum design speed and altitude, buffet boundary, the requirement that thrust must exceed drag, etc). Then a choice of initial velocity increment is made to establish the region of the minimum and the increment is then progressively reduced as smaller and smaller regions are searched to locate the minimum with a required accuracy. The use of a linear search technique is only necessary because two minima may exist; if it is known there is only one minimum the use of a Fibonacci search routine is recommended and explained. The method is illustrated using the worked examples of ESDU 90012; one is minimum time to a given speed and height for a supersonic combat aircraft and the other is minimum fuel to a given speed and height for a subsonic transport aircraft.
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