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Excel Workbooks

Projectile Motion with Air Resistance Using 4th Order Runge-Kutta

UPDATED: 03/14/2018

This Excel workbook computes the trajectory of a spherical projectile with fluid drag included. It also demonstrates some additional things that one can do with the Excel/VBA combination. The calculation is actually clearing the screen and replotting at every time step, but on a reasonably fast computer you won’t even notice the refresh. For certain combinations of input parameters (e.g., a very light projectile launched in a very heavy fluid – like a beach ball released from under water) the calculation will go unstable unless you reduce the timestep below the default value. Eventually we will implement an automatic time step control in the Runge-Kutta procedure used to integrate Newton’s Laws of Motion.

Trajectory of a spherical object including fluid drag

Since this calculation done numerically, the drag coefficient is computed as a function of the instantaneous Reynolds number of the sphere, and not restricted to a simple linear or quadratic form.   Of course, if there is no fluid drag at all considered, then this problem can be solved using only pencil and paper.   Complete documentation of this implementation is included in this workbook.

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