User:Richard.f.long/Aircraft path performance

Aircraft Path Performance is a measure of an aircraft's performance characteristics over a finite trajectory. It deals with end point conditions such as flight time and fuel burned, as well as establishing relationships between 4D trajectory variables. In general, path performance problems cannot be solved analytically due to the nature of the relationships between variables and numerical methods are thus required.

General Path Performance Problem
A trajectory, $$ T $$ may be defined over a finite space and divided into differential segments $$ \delta s $$ of sufficient size so as to allow point performance calculations to be performed. The trajectory may be defined as

$$ T = \int_{s_1}^{s_2}\delta s $$

Where $$ s_1 $$ and $$ s_2 $$ are, respectively, the initial and final endpoints of the trajectory.