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Punkin Chunkin drag computation error

It was fun to find the articles on determining the flight path of a pumpkin. I found an error in the acceleration-due-to-drag calculations, though.

One cannot calculate the vertical and horizontal drag independently because the drag is based on the velocity of the pumpkin and it goes in the opposite direction of the velocity. The articles tried to say the drag is based on the separate vertical and horizontal velocities. That method fails because drag is based on the square of the velocity, not the velocity itself.

The total speed is the size of the hypotenuse, (vx^2 + vy^2)^0.5

The total drag acceleration is k times the pumpkin's speed squared:
 A=k(vx^2 + vy^2)

The X component is that total drag acceleration times the ration of the speed in the x direction divided by the total speed
 Ax = k(vx^2 + vy^2) * ( x/(vx^2 + vy^2)^0.5 ) = k*vx*(vx^2 + vy^2)^0.5

Similar for the Y component
 Ay = k*vy*(vx^2 + vy^2)^0.5
Look, it gets rid of the ugly abs() call in the code too!

These accelerations are greater than then the original ones. This is expected because of the parabolic nature of the square function.

by Michael Heyman on Jul 21 2011 4:45pm Reply

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