Inside the Barrel

During the firing process there is two main forces at work inside the Barrel of the gun.
The first force is from the expanding gases which create the movement of the paintball.
The second force is the friction between the ball and the barrel. Many manufacturers
aim to produce a maximum velocity of 300 fps at the muzzle. Many laws and regulations are
based on the 300 fps velocity.

Gas Force

Paintball markers have various stages of gas regulation, professionals have multiple stages
to ensure constant pressure and velocity. For my example I'll base off a single stage marker
that is more common for regular players.

(Photo courtesy of www.paintballforum.com)
Using 300 fps, 12 inch barrel, and no friction in the barrel we can find the average pressure as the ball moves through the barrel.

m=3.2g (Gary Dyrkacz and Neal Dyrkac)        1 g=6.85217x10^-5 slug

Frictional Force

The Friction inside the barrel can be found similar to the friction of the bolt/slide from the previous page.

F=μ (N)

F=Friction Force, μ=coefficient of Friction, N=Normal Force

Just like before to maximize the performance we need to decrease the coefficient of friction this can also be done with a lubricant

Normally if you hold the barrel of your marker vertical without adding lubricant a paintball won't fall though the barrel.
This means
μ(N)>mg

After adding lubricant most barrels will pass a paintball which then reverses the equation.
μ(N)<mg

Assuming a lubricated barrel where μ(N)=mg we can solve for how much velocity is lost from barrel friction.

Here we see that barrel friction causes a very small percent of velocity to be lost.

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