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The drag work minimization path for a flying object with altitude-dependent drag parameters

2009; SAGE Publishing; Volume: 223; Issue: 5 Linguagem: Inglês

10.1243/09544062jmes1346

2041-2983

Mehmet Pakdemi̇rli̇,

Experimental and Theoretical Physics Studies

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.