The drag work minimization path for a flying object with altitude-dependent drag parameters
Abstract
The work due to drag force for a flying object is considered. The density of the fluid, the drag coefficient, and the velocity are all assumed to be functions of altitude. The differential equation describing the path for minimum drag work is derived using variational calculus. A special form of this equation describing exponentially decaying fluid density is then considered. The equation is cast into a dimensionless form. One of the dimensionless parameters is the final height/final distance and the other is related to the exponential decay of the density. An analytical solution for the path is found by solving the equation. The analytical solution is approximated using Taylor series expansions and contrasted with the perturbation solution. The effect of dimensionless parameters on the path is discussed. © IMechE 2009.
Description
Keywords
Differential equations , Differentiation (calculus) , Variational techniques , Analytical solutions , Dimensionless parameters , Drag forces , Exponential decays , Fluid densities , Flying objects , Optimum path , Perturbation solutions , Perturbations , Special forms , Taylor series expansions , Variational calculus , Variational methods , Drag