# Projectile acceleration in barrel

• cheekibreeki
In summary, the individual is trying to determine the necessary pressure and barrel length for a pneumatic airgun to achieve a muzzle velocity of 300m/s with a 0.2 gram 6mm bb. They have done some calculations but are coming up with impractical barrel lengths. Others suggest considering fluid flow and using energy instead of acceleration and time. It is also mentioned that there may be no legal limit for air guns in the Netherlands, and that the speed of the projectile may be visible to the naked eye.
cheekibreeki
Another gun-related question:

I'm building a pneumatic airgun and I'm trying to find out what pressure/barrel length I have to use for a given muzzle velocity. I've done a bit of number crunching but I keep coming up with insane barrel lenghts, and that's not even considering any friction. Here's what I did:

I want to accelerate a 0.2 gram 6mm bb to a velocity of 300m/s using compressed air.

I take a pressure difference of 30 bar (3,0 * 10^6 Pa) so a total pressure of 31 bar and a surface area of 2.83 * 10^ -4 m^2. P = F/A, therefore F = PA

3 * 10^6 * 2.83 * 10^ -4 = 84,9N, so when I initially pull the trigger the air pressure is pushing my bb forward with 84,9N of force. If the pressure behind the bb at the moment I pull the trigger is 31 bar and at the moment it exits the barrel is 1 bar, this leaves me with an average force of 84.9/2 = 42,45N.

a = F/M (where a = acceleration), F is 42.45 and M = 2 * 10^ -4, 42.45/2 * 10^ -4 = 212250 m/s^2

At that rate of acceleration, my bb reaches 300 m/s after accelerating for 0.0376 seconds. The thing is, by then it has already traveled 300/2 * 0.0376 = 5.64 meters, which is a bit unpractical.

Modern air rifles use a lot less air to accelerate much heavier projectiles to similar velocities with 50/60cm barrels.

What am I doing wrong here?

Well, for one thing, even if your receiver is charged up to 31 bar, the pressure behind the bb will not instantaneously jump to 31 bar.

Secondly, as the bb moves down the barrel, the volume behind the bb is constantly increasing. You can't expect to keep a steady 31 bar in that volume at all times.

You need to give some thought to the fluid flow problem here.

I did not check your numbers; there could be other errors as well, but the one above strikes me as the big one.

it might help to think in terms of energy instead of acceleration and time.
.2 grams = .0002kg
KE=1/2mv2 so...
(3002)(.0002)(1/2)=9 Joules
Joules = force * distance so...
9=42.45x where x is the length of the barrel, so, about 4.7 meters

clearly you need more pressure. CO2 is a commonly used propellant and has a vapor pressure of 60 bar at 22 degrees C. If that pressure were maintained over the length of the barrel it would be more like 1.2 meters.

cheekibreeki
mrspeedybob said:
it might help to think in terms of energy instead of acceleration and time.
.2 grams = .0002kg
KE=1/2mv2 so...
(3002)(.0002)(1/2)=9 Joules
Joules = force * distance so...
9=42.45x where x is the length of the barrel, so, about 4.7 meters

clearly you need more pressure. CO2 is a commonly used propellant and has a vapor pressure of 60 bar at 22 degrees C. If that pressure were maintained over the length of the barrel it would be more like 1.2 meters.

How did you get those numbers? if E = F * S then 9 = 42.45 * x, then 42.45x = 9, then x = 9/42.45, x = 0.212. According to that formula the length of the barrel should be only 21.2 cm instead of 4.7 meters. ?

cheekibreeki said:
At that rate of acceleration, my bb reaches 300 m/s after accelerating for 0.0376 seconds. The thing is, by then it has already traveled 300/2 * 0.0376 = 5.64 meters, which is a bit unpractical.

Modern air rifles use a lot less air to accelerate much heavier projectiles to similar velocities with 50/60cm barrels.

That's nearly Mach 1. Can that possibly be correct? You can see the pellet as it goes away from you, unlike a .22 rifle bullet.
The limit for the energy of a legal air gun is only 12ft lbs, affair

sophiecentaur said:
That's nearly Mach 1. Can that possibly be correct? You can see the pellet as it goes away from you, unlike a .22 rifle bullet.
The limit for the energy of a legal air gun is only 12ft lbs, affair

Actually, there is no legal limit here in the Netherlands. And yes, using an airSOFT gun, which generally shoot around 70-120m/s, you can see the bb fly away, but I'm not building an airsoft gun. I'm building an air rifle, 6mm is just for the concept gun.

## 1. What is projectile acceleration in barrel?

Projectile acceleration in barrel refers to the change in velocity of a projectile as it travels through the barrel of a gun. This acceleration is caused by the force of the expanding gas from the gunpowder, pushing against the base of the projectile.

## 2. How does the length of the barrel affect projectile acceleration?

The length of the barrel can affect projectile acceleration in several ways. A longer barrel allows for a longer distance for the gas to push against the projectile, resulting in a higher velocity and therefore a greater acceleration. However, if the barrel is too long, the expanding gas may have already dissipated before the projectile exits, resulting in a decrease in acceleration.

## 3. What factors can affect projectile acceleration in barrel?

Aside from the length of the barrel, several other factors can affect projectile acceleration. These include the type and amount of gunpowder used, the weight and shape of the projectile, and any obstructions or debris inside the barrel that can hinder the gas flow.

## 4. How can projectile acceleration be measured?

Projectile acceleration can be measured using a range of instruments, such as high-speed cameras or chronographs. High-speed cameras can capture the projectile's movement through the barrel and allow for the calculation of its acceleration. Chronographs, on the other hand, use sensors to measure the projectile's speed as it exits the barrel, which can then be used to calculate acceleration.

## 5. What are some real-life applications of understanding projectile acceleration in barrel?

Understanding projectile acceleration in barrel is crucial in the design and development of firearms. It allows for the optimization of barrel length, gunpowder type and amount, and projectile weight and shape to achieve maximum velocity and accuracy. This knowledge is also important for safety purposes, as it helps prevent malfunctions and accidents caused by improper barrel design.

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