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Analytic Approximations of Projectile Motion with Quadratic Air Resistance

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DOI: 10.4236/jssm.2010.31012    9,439 Downloads   20,166 Views   Citations

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.

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R. Warburton, J. Wang and J. Burgdörfer, "Analytic Approximations of Projectile Motion with Quadratic Air Resistance," Journal of Service Science and Management, Vol. 3 No. 1, 2010, pp. 98-105. doi: 10.4236/jssm.2010.31012.

References

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