golfpro
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Realistic Ballflight
Hello All,
This is a math \ geometry problem, but don't let that put you off. If we have any number crunchers in our midst, perhaps they'll like to play with this...
I am looking for a formula which will create a realistic ballflight using parameters of DistanceX and TakeOff Trajectory. I am currently using "y = (X * (dist - X)) / (dist * Trajectory)" and find this creates a symmetrical
path over which I have sufficient control.
However, this formula does not, of course, allow me to create a path in which the zenith is not absolutely central to the Xdisplacement. Ideally, this would occur somewhere around 2/3(?) of the distance.
I have considered using 2 formulae to derive the path, with the calculation being processed by the secondary routine after the xdisplacement reaches 2/3 total distance, but can't make it work properly.
I am convinced (but in no way informed) that I need the formula for an 'egg' shape, cut through at an offset angle.
If anyone has any knowledge of parabolas, trajectories, ballistics or amateur golf I would love to hear your ideas.
I think we can treat the mass of the ball as a constant, and ignore any wind effect, but it would be nice to add a parameter which modifies take off velocity.
Thanks in advance.
This is a math \ geometry problem, but don't let that put you off. If we have any number crunchers in our midst, perhaps they'll like to play with this...
I am looking for a formula which will create a realistic ballflight using parameters of DistanceX and TakeOff Trajectory. I am currently using "y = (X * (dist - X)) / (dist * Trajectory)" and find this creates a symmetrical
path over which I have sufficient control.
However, this formula does not, of course, allow me to create a path in which the zenith is not absolutely central to the Xdisplacement. Ideally, this would occur somewhere around 2/3(?) of the distance.
I have considered using 2 formulae to derive the path, with the calculation being processed by the secondary routine after the xdisplacement reaches 2/3 total distance, but can't make it work properly.
I am convinced (but in no way informed) that I need the formula for an 'egg' shape, cut through at an offset angle.
If anyone has any knowledge of parabolas, trajectories, ballistics or amateur golf I would love to hear your ideas.
I think we can treat the mass of the ball as a constant, and ignore any wind effect, but it would be nice to add a parameter which modifies take off velocity.
Thanks in advance.
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jstolan, you're absolutely right. The problem is that this would end up in solving a multidimensional differential equation of at least degree 2 (as the acceleration is a vector of the components g and Acc, and V - also vectorial now - depends on the acceleration vector ... &%$§$ can't type integral signs here ;-), so it'd be better to assume a constant wind velocity....
Acc = - K * V;
Where K is a constant and V the instantaneous velocity. So the faster the object is going the greater the decelleration.