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Unread 11-01-2012, 10:23
Dan.Tyler Dan.Tyler is offline
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Re: Drag coefficient of 2012 Game Piece

Quote:
Originally Posted by dellagd View Post
Here is a good sim for checks on your calculations: http://phet.colorado.edu/en/simulati...jectile-motion

Just plug in your air resistance, though I wish someone could tell me the equations behind it.
I will try to remember to put them up later. This is using some of the fairly simple ones... and almost all of it is already included in this thread, actually.

But, if you want to look them up yourself:

Without air resistance:
  • Basic projectile trajectory (horizontal speed is constant, accelerated downward at rate of G until impact)
  • Assumes no lift is generated (lift can't exist without drag )
With air resistance:
  • Still assumes no lift is generated
  • Drag is calculated using the basic drag formula (the one found on wikipedia), from your input of C_D
  • The air density/viscosity (yes, they're linked) is calculated using the standard atmosphere model (that's why altitude is a required input).
  • Air is assumed to be calorically perfect and molecules are assumed to be point-masses with no individual volume (this is why these simple equations are never going to be right).

And, to put them all together, you need to use a touch of vector calculus (sounds a lot more scary than it is) to find the instantaneous (and therefore all) velocities... the overall velocity will be reduced by your drag force. This will reduce both the horizontal and vertical components, and your vertical component will still be constantly affected by gravity.

To get CD, use the magnus effect stuff to first find your CL based on your spin rate (a hint, spinning at 2*Pi radians/second will give you the most lift from magnus effects), then use that CL to calculate the second term of your CD, use the chart/equations posted that included the roughness and talked of the unfortunate asymptote in the chart to find your first term, sum them to get your total CD, and then use that in the equations. Or assume no spin and just use the first term... that's all you can do in the sims I've seen posted so far. I might be feeling very generous and make a matlab code with all this in it if anyone would be interested. (And then it's up to you to add it into whatever programming methods you are using... I'm not doing all the work, after all...).

Oh yeah, don't forget... even if you include all of this stuff, it will still be wrong. Significantly. Your best bet is to try and simulate a simple trajectory for calculations; and to add in a scaling factor that will allow you to adjust it. Usually, a linear factor will handle most of the errors assuming you're using the same projectile and not changing your altitude by more than 50m during flight.

And, if this seems overwhelming... just remember... this IS rocket science. Very basic rocket science... but still in the ballpark.

Last edited by Dan.Tyler : 11-01-2012 at 10:33.