Analytical Calculation Of Trajectories Using A
Power Law For The Drag Coefficient Variation
With Mach Number
Author(s)
W. Roetzel
Abstract
For hand calculations and for the fast computation of direct fire trajectories two
analytical solutions of the point mass equation of motion in stationary air are
presented, which are based on the power law for the drag coefficient variation
with Mach number cD = CMa-m. The first quadrature solution provides time of
flight τ, horizontal downrange distance x and height y as functions of the angle
of flight ϕ. The second closed from solution yields ϕ (x), τ (x), y (x) and is
applicable to weakly curved trajectories. Using a moving co-ordinate system,
both analytical solutions can also be applied to situations with wind.
Keywords: point mass trajectory, analytical solution, direct fire, drag coefficient,
Mach number, wind.
1 Introduction
For the precise computation of trajectories numerical methods are required and
available, which take the variation of drag coefficient with Mach number into
account as well as the change of air pressure and temperature along the
trajectory. Wind can also be considered in the equation of motion and other side
effects may be accounted for. There seams to exist no longer any need for
analytical solutions. However, for direct fire applications with short distances
and moving targets, highly sophisticated computer programmes are prohibitively
time consuming. Not extremely but sufficiently accurate analytical solutions are
more appropriate in such cases. Also for hand calculations for small arms using a
pocket computer, analytical solutions are very useful. In wide regions of the
Keywords
point mass trajectory, analytical solution, direct fire, drag coefficient,
Mach number, wind.
Related Book
Other papers in this volume
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