Title: A Simple Solution for Maximum Range Flight,
Abstract: Within the standard framework of quasi-steady flight, this paper derives a
speed that realizes the maximal obtainable range per unit of fuel. If this
speed is chosen at each instant of a flight plan $h(x)$ giving altitude $h$ as
a function of distance $x$, a variational problem for finding an optimal $h(x)$
can be formulated and solved. It yields flight plans with maximal range, and
these turn out to consist of mainly three phases using the optimal speed:
starting with a climb at maximal continuous admissible thrust, ending with a
continuous descent at idle thrust, and in between with a transition based on a
solution of the Euler-Lagrange equation for the variational problem. A similar
variational problem is derived and solved for speed-restricted flights, e.g. at
250 KIAS below 10000 ft. In contrast to the literature, the approach of this
paper does not need more than standard ordinary differential equations solving
variational problems to derive range-optimal trajectories. Various numerical
examplesbased on a Standard Business Jet are added for illustration.