Why is the barrel size important for the muzzle velocity and the range?
In: Engineering
The longer the barrel, the faster the muzzle velocity.
The reason muzzle velocity is useful is because it’s the fastest point in the bullet’s flight.
When you fire a round, the propellant is ignited and it rapidly reacts in the chamber to form hot gasses. As more gas forms, the pressure increases since there’s not much room for it to escape.
This pressure exerts a force on the bullet, pushing it along the barrel. As long as the gas cannot escape any other way, it continues to push on the bullet.
The more time and distance that the bullet is being pushed, the higher its velocity will increase.
Once the bullet exits the muzzle, the gas is free to expand in all directions. It’s now done pushing on the bullet, and the only forces on the bullet are friction, so it starts to slow down. This makes muzzle velocity the highest velocity in a bullet’s flight.
If you’re familiar with physics and energy, you can recall the equations of kinetic energy and work.
Ek = (1/2)*m*v^2
The final velocity is related to the amount of energy given to the bullet. The bullet gains energy from the work done on it by the force of the gas pushing on it.
W = F x d (cross product)
In this case F and d are co-linear so
W = F*d
F is highest immediately after the ignition and drops slightly as the gas expands through the volume of the barrel and decreases in pressure, but the pressure is still very high until the end of the barrel, so F is positive the entire length of the barrel.
d is the distance that the force is applied over, or in this case the length of the barrel.
Since W is proportional to d, a longer barrel corresponds to higher kinetic energy in the bullet and therefor higher velocity.
The only way that a longer barrel wouldn’t increase muzzle velocity is if the force exerted by the gas got lower than the friction and drag forces before the bullet traveled the full length of the barrel.
If you imagined a perfect long chamber and barrel where gas could not escape except through the muzzle, then as the bullet moved along the barrel the volume behind the bullet increases and the pressure would decrease. If the barrel is long enough, then eventually the volume would be so large that the pressure fell below the external pressure and actually started “pulling” back on the bullet. This would reverse the force vector and cause a longer barrel to be detrimental.
I’m not perfectly familiar with gun design, but I believe gas can escape through other gaps or vents in the chamber as well. That means the pressure will decreases more quickly and stop pushing on the bullet sooner. I’m sure this is taken into account when designing a firearm and its ammunition so as not to be detrimental to its performance.
Lastly, rifling is a useful design in the barrel. It causes the bullet to rotate in the barrel so that it will have an axial rotation in flight. In a rifled barrel, the longer it is more time and length it’ll have to start a rotation. If it’s rotating in the air, it helps to reduce drag by “spinning” the air away from it and increase accuracy by helping to balance the drag forces on each side of it. You can think of it like a football (American). If you throw a football and don’t spin it just right it wobbles all over the place, and might even turn end over end.
If a bullet wobbles at all, it drastically increases its drag and reduces accuracy and range.
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