- #1

TomB

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I am a Physics undergrad degree graduate who is attempting to do a personal project involving the projectile motion of an American football in a 2D space. I want to take into account the drag force that the ball will experience and also take into account the spin of the football (in the same direction of the velocity of the ball) which should have some sort of relationship with the drag. I assume the ball is thrown with no wind and the ball is thrown through air at 20 Celsius.

Let x be the horizontal coordinate and z be the vertical coordinate.

I believe I have two equations to start:

m * a_x = C * v_x

m * a_z = C * v_z - m * g

where

m is mass of football

a_x is acceleration of football in x dimension

C is drag coefficient

v_x is velocity of football in x dimension

a_z is acceleration of football in z dimension

v_z is velocity of football in z dimension

g is acceleration due to gravityFirstly, is it right for me to assume that C will be the same in both directions considering the non spherical shape of an American Football?

Next, I am curious if there is some way to build out the relationship between C (drag coefficient) and w (angular velocity of football in direction of velocity of football) I assume is proportionate to w in some way, but I am unsure how to get started in terms of finding this relationship.

If anyone can give me any tips, papers, textbooks or anything that can get me on the right direction for this project please let me know.