### #1

Posted 18 October 2005 - 09:26 PM

### #2

Posted 18 October 2005 - 09:37 PM

I did some experimentation to determine what would be the optimal barrel length for a given plunger size. The goal was to find the barrel length for which the dart would exit the barrel as the plunger reaches the end of the plunger tube. I started off by matching the volume of the plunger to the volume of the barrel. I knew that this was going to produce too long a barrel but it was a good place to start. This would assume that the air inside the plunger and barrel is incompressible and that there are no leaks. In the real world this is not the case. I reduced the barrel length until I had found the length at which the dart was leaving the barrel as the plunger was reaching its stop, coinciding with the maximum attainable range. Experimentally the plunger volume seems to be about 4 times that of the barrel. The relation for barrel to plunger size can be summed up in the following equation,

where rb is the barrel radius, rp is the plunger radius, lb is the barrel length, and lp is the plunger length. For Nerf applications the barrel is almost always 1/2" PVC or CPVC. rb can then be set as a constant at 0.25" and removed from the equation. Since we are trying to solve for the barrel length with a given plunger size, the equation can be rearranged and simplified to:

This simple equation makes it easy to roughly but quickly size a barrel to a given plunger. The equation could also be used to size a plunger for a given length barrel. This equation is based on experimental data and is not perfect. Four is not the golden number. This produces the optimal barrel length for the situation I was testing. The type of dart, dart-barrel friction, and total system volume will likely effect the optimal ratio. Nevertheless, the above equation can be used as a starting point.

That's the most technical approach to it that I can remember seeing. When determining barrel sizes for myself, I just figure the more powerful the gun, the longer the barrel. I start at 12" and just work down from there until I get a size that works. Most 'rifle' guns that I have use 1/2" PVC couplers, so I already have some barrels lying around that I can try.

gets to your house before the police.

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### #3

Posted 18 October 2005 - 09:40 PM

~Rings

EDIT: BloodMoon's approach beat me to it. That's a good one.

**Edited by LordoftheRing434, 18 October 2005 - 09:42 PM.**

"I bluff it. I don't throw my weight around and say I know what I'm doing." ~ Mick Jagger

### #4

Posted 18 October 2005 - 09:50 PM

I agree.

Thanksfor the help.

### #5

Posted 18 October 2005 - 10:05 PM

and what type of spray paint will do the best job?

I know it's off topic but I didn't want tostart another thread.

### #6

Posted 18 October 2005 - 11:14 PM

Can someone make sense of this for the mathematically inept. I want to know how to do this. like fool proof step by step instruction on how to punch this in on the calculator.I did some experimentation to determine what would be the optimal barrel length for a given plunger size. The goal was to find the barrel length for which the dart would exit the barrel as the plunger reaches the end of the plunger tube. I started off by matching the volume of the plunger to the volume of the barrel. I knew that this was going to produce too long a barrel but it was a good place to start. This would assume that the air inside the plunger and barrel is incompressible and that there are no leaks. In the real world this is not the case. I reduced the barrel length until I had found the length at which the dart was leaving the barrel as the plunger was reaching its stop, coinciding with the maximum attainable range. Experimentally the plunger volume seems to be about 4 times that of the barrel. The relation for barrel to plunger size can be summed up in the following equation,

where rb is the barrel radius, rp is the plunger radius, lb is the barrel length, and lp is the plunger length. For Nerf applications the barrel is almost always 1/2" PVC or CPVC. rb can then be set as a constant at 0.25" and removed from the equation. Since we are trying to solve for the barrel length with a given plunger size, the equation can be rearranged and simplified to:

This simple equation makes it easy to roughly but quickly size a barrel to a given plunger. The equation could also be used to size a plunger for a given length barrel. This equation is based on experimental data and is not perfect. Four is not the golden number. This produces the optimal barrel length for the situation I was testing. The type of dart, dart-barrel friction, and total system volume will likely effect the optimal ratio. Nevertheless, the above equation can be used as a starting point.

I don't feel the way I used to do.

I know its bad,

After what we had,

But I’m just not the angel you knew.

### #7

Posted 19 October 2005 - 05:33 AM

A "fool proof step by step" guide would start with defining the variables:

r1 = half of the diameter of the pressure chamber

l1 = pressure chamber length

r2 = half of the diameter of the barrel

l2 = barrel length (what you would solve for)

Then,

4((r1)^2)(l1)/(r2^2) should equal the ideal barrel length (l2) for those sizes. (I think that I reordered the equation correctly, but I have to leave in a minute so I rushed, correct me if I am wrong.)

### #8

Posted 19 October 2005 - 12:43 PM

Start by looking at what has been successful for similar mods, then adjust and experiment.

### #9

Posted 19 October 2005 - 02:01 PM

You are absolutely right about that. I derived that empirically and more importantly it was derived for the specific situation I intended on using it for: a plunger weapon. It iwll not work for a compressed air system. One of the big factors I used to come up with that was the lack of compressibility. I later factored that in with a constant that was derived empirically. My tests were with a setup exactly like I was going to use on a the finished product. If you scale the system down that magic constant may not hold true.Optimal barrel length varies a great deal with factors such as dart weight, length, pressure, air delivery speed, etc. Nothing against BoltSniper who I have the greatest respect for, but the quoted passage is only directly applicable to the FAR or another gun with very similar characteristics. The only reliable way of sizing barrels is empirical.

Start by looking at what has been successful for similar mods, then adjust and experiment.

There are too many variables to analytically design the optimal barrel length. If you are going to build or mod a spring gun the equation I provided may be a good starting point. That equation gives a barrel length that is slightly too long, so to obtain the optimal length you are going to have to go shorter.

The only real way to do it is experimentally.

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