C/B ratios and diminishing returns

[dewey-1]

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[Gippeto]

I noticed the same thing. My chamber started out being 1.51"idx18" long. Running numbers, this has shrunk to 1.51"id by 10" long (with a 1" barrel running through!) That's down to about 10 cu.in. Performance loss was noticeable but acceptable (at least according to ggdt). I didn't run numbers at lower pressures, but would expect to see the similar results.

[DYI]

As much as I appreciate your intents, was this really worth a topic?

It is common knowledge that, for a fixed chamber size and pressure, increasing barrel length up to a certain point (~0.2:1 @100 psi) will increase performance, and that for a fixed barrel size and pressure, increasing chamber size is always beneficial, although gains become less noticeable the larger the chamber gets.

The trick is finding a happy medium where you don't have a massively long barrel and/ or overly high gas consumption (which is only really a problem when using bottled gases, which cost big $s in some cases). I'm not really the one that should be talking about happy mediums though. I often find my thinking straying more along the lines of "hmm... if I put another 12' section on the barrel, I bet I could get over 10k ft/lbs..."

Gas consumption becomes a real problem when larger chamber sizes and higher pressures are involved. Since money is an ever present problem for spudders, finding better sources of high pressure gas becomes very important as more power is desired. I think that hybrids may become increasingly popular in the near future, especially since DDT has been shown to be less of a concern than was first expected.
[/semi-irrelevant tangent]

[Hotwired]

*shrug*

The C:B ratio for my signature cannon is about 3:2 (1.6 to 1.8 is a ratio eh?)

It wasn't for any purpose of efficiency or even for power. It's like that because it looks nice. Seriously.

However an oversized chamber does allow for rather more flexibility in pressure useage and lets you dream of one day attaching a ridiculously long barrel and putting a hole through a wall

Gas consumption isn't really an issue unless you've carelessly designed above your supply and are left with a foot pump to get a 20L chamber to 150psi. However if anyone does do that, please post for for the laughs

[DYI]

Gas consumption is a REAL issue for the SCTBDC, and has prevented me from making it more powerful.

My nitrogen tank holds 91 cubic feet of gas, and costs a total of $56 to fill.
The SCTBDC at full power uses 3.36 cubic feet of gas, resulting in a cost of ~$2.07/shot, just for gas. Add in the fact that the last ~21 cubic feet of gas can't be used, and the per shot cost rises to ~$2.69. This also means that, with absolutely no leaks (which is rather far from the truth), I can only get an absolute maximum of 21 shots from a full tank. Add in the fact that the tanks sometimes come about 200 - 300 psi below what they're supposed to be at, and you will realise that gas consumption is a real problem for some designs. I can't viably increase the chamber size, without renting a cylinder so big that I need a cart to move it.

[Hotwired]

Operating at the extreme end of pressure and volume has to have some drawback or we'd all be in there

[DYI]

Well, the volume is only 170 ci or so, not large by spudgun standards, but the pressure makes a big difference. As a rough comparison to the SCTBDC's gas consumption, the SWAT would use a bit more than 10 cubic feet of gas for a 5 bar shot. The difference is, schmanman doesn't have to pay at all for his 10 cubic feet of air at ~75 psi, but I have to pay almost $3 for my 3.36 cubic feet at 500 psi. If it weren't for the fact that I'd have to have about 5 cascade stages rather than 2, I'd increase the porting on my launcher to 3" and use a 3" chamber of equivalent volume. If I'd had pressure rated PVC available here, I never would have taken the high pressure route in the first place.

[Ragnarok]

Well, the volume is only 170 ci or so, not large by spudgun standards, but the pressure makes a big difference.

Erm... that's (pokes calculator into life) 2800cc. I would have said that was quite large for a pneumatic using more than what a small compressor can put out. HEAL's chamber is only 40 ci, and I'm using only 2/3rds of the pressure (for now... I'll get a lot closer when I have the time to make that 30 bar compressor) - you're getting 20 times the muzzle energy though.
Makes the HE in my acronym sound a bit generous, but it also shows the losses involved in my trying to accelerate low mass projectiles to near the sound barrier.

And you're not going to be able to hit 10,000 ft-lbs, even if you bolt another 12 ft to the barrel. At your 500 psi limit, your chamber only contains 7100 ft-lbs of energy stored in the gas, and you can't get energy from nowhere. Frankly, it's amazing you're getting the efficiencies from it that you are, it's mainly a matter of your heavy projectiles being able to absorb as much energy as they do.

And yes, if they had had rated PVC here, I doubt I would have chased the high pressure route either. See what you can get when people adapt to the resources.

[DYI]

GGDT seems to disagree with you; it says that the total available energy in the chamber is over 100 000 ft/lbs, and that I'm getting 5% efficiency (still fairly good for a pneumatic). I was comparing it to PVC pneumatics, which often have 3 or 4" diameter chambers with over 200ci volume with ridiculously small barrels bolted on.

The muzzle energy won't get very much over 7k with my current chamber size however, even with a 24' barrel. If I doubled the chamber volume and doubled the barrel length, I could get about 10k. By increasing porting to 3" with my current chamber volume, I could get over 7k with my current projectiles with a 12' barrel. And to show just how useful more pressure is, if I doubled the pressure from 500 psi to 1015 psi, leaving the chamber at 170ci, the porting at 1.61", and the barrel at 3" x 12', the muzzle energy would climb over 10k with my current projectile.

And I think you meant "muzzle energy", not muzzle velocity

[Ragnarok]

GGDT seems to disagree with you; it says that the total available energy in the chamber is over 100 000 ft/lbs, and that I'm getting 5% efficiency (still fairly good for a pneumatic). I was comparing it to PVC pneumatics, which often have 3 or 4" diameter chambers with over 200ci volume with ridiculously small barrels bolted on.

It's known that GGDT's efficiency box is more broken than my psyche, the Titanic and the NHS put together, you should ignore it.

Energy in the chamber in Joules can be found as volume in cubic metres * pressure in pascals.
Or, in more practical units, cubic centimetres * pressure in bar / 10.
The /10 corrects the units.

Using approximate values:
2800cc * 35 bar /10 = 9800 joules energy.
Dividing 9800 by 1.356 (number of Joules to 1 ft-lb) - gives 7200 ft-lbs. Getting 7000 ft-lbs KE from that is a phenomenal feat, so much so I think GGDT may be a little generous. If you want more energy, more barrel won't help much, if at all - you need more chamber.

If you're interested, HEAL's chamber stores about 1000 ft-lbs at 300 psi. That will go up to about 1500 at 30 bar. The C:B ratio is about 1.5:1, which wastes quite a bit. I may shorten the chamber a little in the future to get it to 1:1, and I should retain most of the ME.

And you're quite right about the velocity/energy thing, I was swapping between tabs talking about velocity and rifling in one thread and this one, and I obviously ended up mixing them up - I'll change it.

[clide]

It's known that GGDT's efficiency box is more broken than my psyche, the Titanic and the NHS put together, you should ignore it.

Energy in the chamber in Joules can be found as volume in cubic metres * pressure in pascals.
Or, in more practical units, cubic centimetres * pressure in bar / 10.
The /10 corrects the units.

I know GGDT's efficiency box is broken because I remember that discussion with D_Hall. But I still don't think that equation you give is the right equation for the energy in the chamber. I brought this up during the previous discussion (with Joanna I believe) and never really got an answer for how that can be the energy stored in a chamber.

Take a simple piston cylinder arrangement and calculate the energy with that equation and you get the same energy no matter where the piston is because there is a constant PV (assuming ideal gas). Yet by making the volume smaller you are storing more energy in the gas.

I believe you would need to do the approach D_Hall used to calculate the energy stored in a pressure vessel. Although he did it wrong he approached it by calculating the work done compressing the gas from atmospheric to the chamber pressure. Now how much work is done depends on the path you take. Equations for different paths can be seen http://www.cbu.edu/~rprice/lectures/compress.html

[Hotwired]

Interesting catch there clide.

The energy/volume increases in compression but it's not reflected in a simple PV equation.

This page looks particularly tasty, in particular the last post by Shootingstar who gives the eventual formula at the bottom.

[Ragnarok]

But I still don't think that equation you give is the right equation for the energy in the chamber.

Take the ideal gas law:
pV = nRT

If we take the units for p and V - N/m² (which is pascals in it's raw units) and m³ respectively - and multiply them together, we get Nm - which is Joules (or torque, but here it's energy).

You can put that in terms of compressing the gas if you want. Imagine a cylinder with a piston in it that can be moved to compress the gas in it. Work is force times distance.

The distance the piston needs to move will be the initial gas volume / piston area, and the force the piston needs to exert will be the integral of the pressure * piston area.

Because those are multiplied together, the area terms cancel.
As pressure * volume is a constant value here (assuming no leaks, and no heating), the integration can also be omitted.

And that simplifies down to pressure * volume again.

Both ways of calculating it come back to the same solution. I use it in the "cubic centimetres * pressure in bar / 10" form because those are the units I most often use, and it saves converting to cubic metres and pascals.

It took me a while to get my head around the whole "If P*V is constant, how does compressing it add energy?". Thing is, it doesn't add energy to the air. The air still has the same amount of energy in it, but the thing is, you've created a "pressure gradient" for it to flow across, and when you talk about the "energy in the chamber", you talk about the amount of energy that can flow across that gradient.

Weird this science stuff.

[Hotwired]

Theres an interesting part in the page I linked where instead of E=PV...

In an ideal gas whose volume is V, the internal energy is (3/2)PV

Theres a useful page going under the title of Kinetic Molecular Theory that goes through it.

So instead of 9800J it's 14,700J of stored energy in DYI's cannon chamber of 2800cc @ 35 bar.

[dewey-1]

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