Need help writing a joke equation

[1MileCrash]

This is all done really fast for fun, may be some mistakes.

I'm a paintball player, and there seems to be a very prevalent misconception that certain paintball markers shoot paintballs greater distances than others.

This isn't true because before actually playing, your marker must be chronographed to be shooting 300 fps. Obviously if these two paintballs are roughly spherical, and are both traveling at similar velocities, physics doesn't care how expensive the paintball marker is.

Changing 300 fps to 100 m/s for simplicities sake, and assuming the paintball is shot from a height of 1.5 meters:

(I'm getting really frustrated with the math functions, so I'm typing it)

( 100 m/s ) √ (3 m / 9.8 m/s²)

Shows the distance, which comes out to about 55 meters. That seems close enough.

But I want to incorporate a new factor into the equation, the price of the marker.

We will say that anything below a value P of 600 will reduce the range given above, and anything above 600 will increase the range given above.

However at P = 100 the value should stop decreasing, and should decrease by no more than 30 meters. After P = 1600 the value should stop increasing, and should increase by no more than 50 meters.

Can anyone think of a simplistic and clean way to implement this? Perhaps modifying the 100 m/s?

 

[CompuChip]

How about something like an arctangent?

Just start with 600 + arctan(x) and scale such that it gives you the properties you want.