DIY Solar Panels

My gun shoots 0.20 gram bb’s at a muzzle velocity of 410 f/s (or 125 m/s). I want to ultimately create a table of distance (m) as the independent variable in increments of 5m, vs. velocity (m/s), so I can see how fast the bb will be traveling upon impact with a target X meters away.

I have a basic understanding of what is happening to the bb. I know that (disregarding gravity and any spin on the bb) wind resistance is the only force acting on the bb once it is fired. To calculate the drag force, I know that you can use this equation:

D = 1/2 * C * A * p * v^2

Where D is the drag force in Newtons, C is the drag coefficient (0.47 for a spherical bb), A is the cross-sectional area of the bb (0.0000281 meters), p is the density of the air (1.293 kg/m^3 at STP), and v is the instantaneous velocity of the bb. When I plug all the known values in to the equation above, it becomes:

D = 0.000008534118 * v^2

So this means that the drag force is dependent on the bb’s velocity at a given time. I just don’t know how to put this all together so I can get a nice Distance vs. Velocity chart. Any ideas/help would be much appreciated. Thanks a lot!

The D is a force which causes a negative acceleration on the bb

Therefore the horizontal velocity changes as the bb moves through the air. It decreases.

To truly solve this you need to apply integral calculus.

using a = dv/dt = D/m

So you have dv/v^2 = (0.000008534118/m)*dt

You integrate to solve this for v as a function of t

Then apply v = dx/dt

So the distance dx = v*dt

Integrate this to find x as a function of t

Now for given a given time you have both velocity and distance

Just set up the table t……..x…….v

for different times

Good Luck