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Abstract: In this paper we examine the detailed theory of the American football inflight, with spin and air resistance included. We find the theory has much incommon with the theory of a gyroscope and also rocket trajectory with amisaligned thruster. Unfortunately most of the air resistance data, forrocketry and ballistics, is for speeds of Mach 1 or higher, where the airresistance increases dramatically. We shall approximate a realistic airresistance, at the slower speeds of football flight, with a drag forceproportional to cross sectional area and either $v$ or $v^2$, depending onspeed, where $v$ is velocity of the football. We begin with a discussion of themotion, giving as much detail as possible without the use of complex analyticcalculations. We point out the previous errors made with moments of inertia andmake the necessary corrections for more accurate results. We show that theshape of an American football closely resembles a parabola of revolution.



Author: Curtis Horn, Heidi Fearn

Source: https://arxiv.org/



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