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Analytic Approximations of Projectile Motion with Quadratic Air Resistance
Department of Administrative Sciences, Metropolitan College, Boston University, Boston, USA
Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, USA
Institute for Theoretical Physics, Vienna University of Technology, Vienna, Austria
- 1 Department of Administrative Sciences, Metropolitan College, Boston University, Boston, USA
- 2 Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, USA
- 3 Institute for Theoretical Physics, Vienna University of Technology, Vienna, Austria
Journal of Service Science and Management·Volume 03 (2010)·Pages 98–105·Published 26 March 2010·DOI10.4236/jssm.2010.31012
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Abstract
We study projectile motion with air resistance quadratic in speed. We consider three regimes of approximation: low-angle trajectory where the horizontal velocity, u, is assumed to be much larger than the vertical velocity w; high-angle trajectory where ; and split-angle trajectory where . Closed form solutions for the range in the first regime are obtained in terms of the Lambert W function. The approximation is simple and accurate for low angle ballistics problems when compared to measured data. In addition, we find a surprising behavior that the range in this approximation is symmetric about , although the trajectories are asymmetric. We also give simple and practical formulas for accurate evaluations of the Lambert W function.
KeywordsProjectile MotionAir Resistance Quadratic
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