I was trying to figure out on paper what the perfect barrel length would be under ideal conditions (zero friction, perfect seal, 100% efficiency...) to see how that compares to the 8-10" optimal effective barrel length that TK has found. What I found was quite surprising.
Let's say that cylindrical volume behind the ball is VC (Volume cylinder), and the volume between the rear face of the ball and the cylindrical volume VR (Volume rear of ball).
We can find VR by finding the volume of the disc shape bound by the barrel from the most rear point of the paintball up to hemisphere that is formed from that point to the barrel/ball interface- Then subtract the hemispherical volume from that disc volume.
Let's let the bore diameter be .692" -> r = (.692/2)
VR = [disc volume] - [hemisphere volume]
VR = [(pi)(r^2)(r)] - .5[(4/3)(pi)(r^3)]
= 0.04337674501
The cylindrical volume is found the the radius, pi, and the length. We are trying to find that length. By multiplying the cylindrical volume by a pressure, we get a potential energy of that pressurized air.
If we then set that energy to the kinetic energy of a paintball, we can find the length of barrel needed.
But this isn't all the information we need yet. The compressed air in the barrel will accelerate the paintball until the pressure in front of the paintball and behind the paintball are the same. Let's say the pressure in front of the paintball is 14.7psi.
[cylindrical volume][14.7psi] = 111.0052597in-lb
[(pi)(r^2)(L) + VR][14.7psi] = 111.0052597in-lb
(pi)(r^2)(L) + VR = 111.0052597/14.7
L = [(111.0052597/14.7) - VR]/[(pi)(r^2)]
L = 19.96"
19.96" wtf?!?
That's around twice as long as the optimal effective barrel length that TK has found.
Let's take a Viking's efficiency: 1000 shots from a 68ci 3000psi tank. That comes to 204in-lb per shot.
If we subtract the kinetic energy of a paintball from 204in-lb we get 92.995in-lb. (we are neglecting the use of energy in operating pneumatics and again the same ideal assumptions)
The Viking is one of the more efficient guns and close to half of the energy of getting that paintball to 300fps is going into overcoming friction, poor barrel/paint sealing, gas cooling, etc...
I'm wondering how much more efficient can we get?
A paintball does not deform much, so pressure plays no big role in how well it does or doesn't seal with the barrel. I'd like to get my hands on some Perfect Circle balls for some testing. It would be interesting to see how significant sealing has to do with efficiency.
I have a hard time seeing the majority of 90in-lb going to overcoming friction. I'm leaning towards the paintball/barrel seal as being the culprit in the 20" barrel length not adding up.
Or maybe friction is the painball's greatest enemy.
Let's say that cylindrical volume behind the ball is VC (Volume cylinder), and the volume between the rear face of the ball and the cylindrical volume VR (Volume rear of ball).
We can find VR by finding the volume of the disc shape bound by the barrel from the most rear point of the paintball up to hemisphere that is formed from that point to the barrel/ball interface- Then subtract the hemispherical volume from that disc volume.
Let's let the bore diameter be .692" -> r = (.692/2)
VR = [disc volume] - [hemisphere volume]
VR = [(pi)(r^2)(r)] - .5[(4/3)(pi)(r^3)]
= 0.04337674501
The cylindrical volume is found the the radius, pi, and the length. We are trying to find that length. By multiplying the cylindrical volume by a pressure, we get a potential energy of that pressurized air.
If we then set that energy to the kinetic energy of a paintball, we can find the length of barrel needed.
But this isn't all the information we need yet. The compressed air in the barrel will accelerate the paintball until the pressure in front of the paintball and behind the paintball are the same. Let's say the pressure in front of the paintball is 14.7psi.
[cylindrical volume][14.7psi] = 111.0052597in-lb
[(pi)(r^2)(L) + VR][14.7psi] = 111.0052597in-lb
(pi)(r^2)(L) + VR = 111.0052597/14.7
L = [(111.0052597/14.7) - VR]/[(pi)(r^2)]
L = 19.96"
19.96" wtf?!?
That's around twice as long as the optimal effective barrel length that TK has found.
Let's take a Viking's efficiency: 1000 shots from a 68ci 3000psi tank. That comes to 204in-lb per shot.
If we subtract the kinetic energy of a paintball from 204in-lb we get 92.995in-lb. (we are neglecting the use of energy in operating pneumatics and again the same ideal assumptions)
The Viking is one of the more efficient guns and close to half of the energy of getting that paintball to 300fps is going into overcoming friction, poor barrel/paint sealing, gas cooling, etc...
I'm wondering how much more efficient can we get?
A paintball does not deform much, so pressure plays no big role in how well it does or doesn't seal with the barrel. I'd like to get my hands on some Perfect Circle balls for some testing. It would be interesting to see how significant sealing has to do with efficiency.
I have a hard time seeing the majority of 90in-lb going to overcoming friction. I'm leaning towards the paintball/barrel seal as being the culprit in the 20" barrel length not adding up.
Or maybe friction is the painball's greatest enemy.
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