# Is this correct reasoning? Questions on the physics of pneumatic spud gun.

1. Jun 5, 2015

### Comfort_Cube

I'm building a pneumatic spud gun, and am thinking about the volume of the muzzle/barrel. It will be cylindrical (a pvc pipe). The projectile will either be a spherical or cylindrical object (same mass). The muzzle will be connected to the air chamber via a sprinkler valve. So, the aim in this case is to get optimal muzzle velocity.
In relation to volume (and this is where my question relates), the diameter should be exactly fitting the diameter of the projectile, so that as much as possible, the pressure coming from the rapidly expanding gas is directed towards the surface area of the side facing the incoming air. As for the length, the muzzle should be long enough to make use of all the pressure difference, because as the projectile is moving towards the end of the muzzle, the total volume being occupied by the air (volume of chamber + volume so far of muzzle) is increasing and the pressure would be decreasing - Boyle's law. The pressure will continue to decrease until it reaches the pressure within the chamber before the loading of the air into it (until all the pressure difference is accounted for).
As for the projectile, the cylindrical projectile will have the higher muzzle velocity because the side facing the incoming air is completely perpendicular to the velocity of the incoming air, whereas, for the sphere, the side facing the air has only one point that is perpendicular to the velocity of the incoming air, and the rest will be angled, and so the force in the direction of the muzzle will be less than what it would be if the surface were completely perpendicular. However, because the cylindrical projectile will face more air resistance - for the same reason it has a faster muzzle velocity - the total distance covered at some point will be equal to the spherical projectile, and beyond that, less, and before that, more, assuming that both projectiles stay long enough in the air to experience that.
That's what I've got so far from the physics of it. This is just through thinking, so "is this correct reasoning?" I'm not really familiar with the actual mechanics of it, so if you could also give some of the equations describing all this, that would be good.

Last edited: Jun 5, 2015
2. Jun 5, 2015

### Comfort_Cube

Ow God. I forgot to take into account friction... The sphere will have less friction that the cylinder (unless the cylinder was just one point thick), so really, the net force in the direction of the muzzle would be something like (varying force of air pressure) - (friction + air resistance). So again, at some point, the cylinder will be equal in muzzle velocity to the sphere, and beyond that, it will be less, and before, more.

3. Jun 5, 2015

### Comfort_Cube

Ow, and also, there are a lot of ideal set ups assumed here in this situation, so if you can also highlight what those are, that'd be great too.

4. Jun 5, 2015

### Comfort_Cube

Ow wow! I think I got it! The optimal design for the projectile will be something like a bullet! Maximum use of force from the air expansion by the flat surface on one side, minimum friction by making an incredibly thin edge, and minimum air resistance by the other surface by making it pointed and round-ish. It would also be a compromise of all that stuff along with manufacturing processes and materials. Cool.