Projectile acceleration in barrel

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    Acceleration Projectile
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Discussion Overview

The discussion revolves around the calculations and considerations involved in designing a pneumatic airgun, specifically focusing on the relationship between pressure, barrel length, and muzzle velocity for a 0.2 gram 6mm BB. Participants explore the physics of projectile acceleration, energy requirements, and practical implications of their calculations.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant calculates the force exerted on the BB using pressure and area, leading to an acceleration calculation that results in an impractical barrel length of 5.64 meters for achieving a velocity of 300 m/s.
  • Another participant points out that the pressure behind the BB does not instantaneously reach the maximum pressure and that the increasing volume behind the BB complicates the pressure dynamics.
  • Another perspective suggests using energy calculations instead of acceleration, proposing that 9 Joules of kinetic energy would imply a shorter barrel length of about 4.7 meters, but questions arise regarding the accuracy of this calculation.
  • A participant notes that using CO2 as a propellant, which has a higher vapor pressure, could reduce the required barrel length to approximately 1.2 meters.
  • Concerns are raised about the feasibility of achieving nearly Mach 1 speeds with the proposed setup, alongside legal energy limits for air guns in different regions.
  • A participant clarifies that they are building an air rifle, not an airsoft gun, and discusses the visibility of the BB in flight compared to traditional firearms.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and assumptions regarding pressure dynamics, energy requirements, and practical barrel lengths. There is no consensus on the correct approach or the validity of the calculations presented.

Contextual Notes

Participants highlight limitations in the assumptions made regarding pressure behavior, fluid dynamics, and the implications of using different propellants. The discussion remains open to further refinement and exploration of these factors.

cheekibreeki
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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?
 
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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.
 
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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.
 

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