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Still Don't Understand C:B Ratio on Pnuematics...

Post questions and info about pneumatic (compressed gas) powered cannons here. This includes discussion about valves, pipe types, compressors, alternate gas setups, and anything else relevant.
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Unread postAuthor: Technician1002 » Tue Jun 22, 2010 11:48 am

btrettel wrote:When you say "the math" what precisely are you referring to here? GGDT? I'm interested in this phenomena so I'd like to know what doesn't model it well.


I was referring to the math where the assumption of a 1:1 ratio is best. A chamber and barrel volume of 700 cubic inches was the math. This test showed a longer barrel was better.

If trying the other math for no chamber pressure, the 60 PSI would expand out way beyond the length of the barrel used. Acceleration fell off way before the chamber volume expanded out to the volume required to be no pressure left.

GGDT models the flow losses quite well once you find your valve efficiency. It took some time working backwards from muzzle velocity, projectile positions, and such to find my valves to get a match with GGDT's graphs. I have a thread on that.
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Unread postAuthor: btrettel » Tue Jun 22, 2010 12:17 pm

jackssmirkingrevenge wrote:Airgunners in the UK are painfully aware of this effect, they are limited to a strict 12 ft/lbs muzzle energy level above which an air rifle is considered to be a firearm which needs a license, failure to own the latter means a potential 5 year stretch at her majesty's pleasure.


I can see that my reply wasn't phrased right. The point wasn't that projectile mass increases efficiency (others have noticed that); the point was that it could be used to compensate for slow valves. The two are obviously related.

If you look at my first post in this thread, all I say is that "[if] the projectile is heavy enough then performance can be nearly independent of valve flow." I say nothing about efficiency. This was the "performance regime" that I referred to; the one where the projectile is so heavy that the chamber and barrel pressures are essentially identical. This basically means that performance is independent of the valve performance, use of a detent, friction, etc. I am not aware of any similar statements.

With respect to my statement about high speed guns, I meant more specifically that even a perfect valve isn't fast enough, so you can compensate with something else like a detent or heavy projectile. Efficiency also comes into play here, but that wasn't my larger point.

Again, to reiterate, my point was that heavy projectiles allow you to compensate for slow valves, and that there is a certain regime where basically how fast your valve is doesn't matter much.

jackssmirkingrevenge wrote:True, however from the same launcher a heavier projectile will have a lower muzzle velocity and correspondingly larger rate of projectile drop over a given distance, for which reason if long range shooting or target penetration is the goal this is not the ideal solution.


Right. Don't lose track of your larger goals, whatever they may be. I'm just saying that heavy projectile can allow for worse valves to be used without affecting the performance and that people should consider this in design.

Technician1002 wrote:I was referring to the math where the assumption of a 1:1 ratio is best. A chamber and barrel volume of 700 cubic inches was the math. This test showed a longer barrel was better.


A C:B ratio of 1:1 is plainly wrong in most cases, so I'm not surprised you found differences with real world testing.

Technician1002 wrote:If trying the other math for no chamber pressure, the 60 PSI would expand out way beyond the length of the barrel used. Acceleration fell off way before the chamber volume expanded out to the volume required to be no pressure left.

GGDT models the flow losses quite well once you find your valve efficiency. It took some time working backwards from muzzle velocity, projectile positions, and such to find my valves to get a match with GGDT's graphs. I have a thread on that.


Could you be a little more precise? What is "the other math"? Boyle's law? Boyle's law is better than assuming a 1:1 ratio, but it's still plainly wrong in most cases.

Using any sort of process relationship assumes that the chamber and barrel pressures are approximately the same. We know this isn't true in general. As I've alluded to before, this assumption is valid when the dimensionless projectile mass is above a certain amount (i.e. when the projectile is heavy enough). The critical dimensionless projectile mass is a function of the valve performance, friction, and other factors.

My non-dimensional simulation is very similar to GGDT at the moment, and a theoretical equation based on adiabatic process relationships fits the data in the critical regime very well.

CB = (1 + Vd*) / ((Pc* / (1 + Pf*)) ^ (1 / k) - 1)

Pf* = Pf / Patm (Pf is the "pressure of friction" much like how GGDT does friction)
Vd* = Vd / Vb (Vd is the "dead" volume)
k 0s the ratio of specific heats (1.4 for air)

Remember, as I've noted, this only applies when the pressure in the barrel and chamber are approximately equal. That was not the case in your tests Technician.
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Last edited by btrettel on Tue Jun 22, 2010 4:17 pm, edited 2 times in total.
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Unread postAuthor: Technician1002 » Tue Jun 22, 2010 12:59 pm

Started the project without any of the advanced math stuff, cooling by expansion, valve efficiency or any of that. Started with an often given value of near 1:1, and gas expansion not accounting for temperature change. Assumed a lot of high speed air flow friction loss (turned out correct) and then trimmed to best performance with real world measurements to fine tune it down to size.

I was expecting to go much shorter on the 4 inch barrel with the foam ball because I expected more choking of the flow by the 2 inch valve than I got, so I was pleasantly surprised when the foam ball was able to exceed 500 FPS when the 4 inch barrel was fed from a 2 inch valve. This was not expected since the 4 inch barrel has 4X the cross sectional area of the 2 inch valve.
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Unread postAuthor: Ragnarok » Tue Jun 22, 2010 7:14 pm

btrettel wrote:I think I'm the only person to have identified this performance regime.

Not really. I've been fully aware of such (i.e that higher projectile inertia means that valve flow becomes less important) for quite a while, although it doesn't really interest me. Slow, heavy projectiles aren't really an area of interest.

The inverse, that valve flow becomes more important as projectile mass goes down is more valuable knowledge in my opinion.

jackssmirkingrevenge wrote:
Ranger wrote:I dont understand it either, I just know that 1.5 C/B ratio is a good start.
It depends, for a high pressure launcher that ratio would most probably be excessive.

Or possibly awesome.
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Unread postAuthor: Technician1002 » Tue Jun 22, 2010 7:19 pm

Denting a car door with a marshmallow is a sign of success in valve flow. :shock:

Speed and flow become important with low mass projectiles and short barrels.
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Unread postAuthor: btrettel » Tue Jun 22, 2010 8:39 pm

Ragnarok wrote:The inverse, that valve flow becomes more important as projectile mass goes down is more valuable knowledge in my opinion.


You have good insight. I hadn't thought of it that way. That is certainly more important for most spud gunners.

Another thought... what is "heavy" or "light" is relative. My dimensionless projectile mass is the projectile mass divided by atmospheric air density multiplied by the gas chamber volume. This is the parameter that is large when valve performance is not important. Does this mean that larger chambers make valve performance more important? The math tells me yes, but my intuition tells me no. I'm not certain a more physical non-dimensionalization exists, but I'll take another look at the math...
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Unread postAuthor: jimmy101 » Tue Jun 22, 2010 9:04 pm

The problem is really pretty straight forward and as much as I love a technical approach common sense is really enough.

Imagine a pneumatic with an absurdly large chamber, CB of 100:1. When fired and the projectile moves through the barrel the pressure in the chamber really doesn't change. If it started at 100 PSI then it is still 99 PSI even when the ammo exits the barrel. This setup get the greatest projectile energy out of a particular barrel + ammo + starting pressure arrangement. So it produces the most power (as kinetic energy) in the ammo. If you happen to have a shop compressor then the "cost" to pump up the absurdly large chamber is basically zero and the "efficiency" is irrelevant, it doesn't matter if it cost $0.000001 or $0.001 per shot.

Now imagine you are pumping up the gun with a hand pump. Suddenly that absurdly large chamber doesn't look like such a great idea. If it takes you ten minutes of hard work to pump up the chamber then the concept of "efficiency" suddenly starts to be as important as muzzle energy. You want as much of the energy you put into the pumping to end up in kinetic energy of the ammo. You don't want the ammo exiting the barrel when there is still 99 PSI pushing it since that 99 PSI is wasted and you worked hard to put that into the chamber.

Now start playing the simple mind-math games and see what the balance is you find acceptable. If the chamber and barrel are the same volume then at ammo exit the pressure in the system has dropped by 50%. You still have pretty good pressure on the ammo and you are not wasting quite so much energy. If your CB is 1.5 then at exit the pressure is 60% of the starting pressure. Is that 50% increase in chamber volume worth the basically 5% increase in pressure over the course of the barrel?

The idea of an "optimal" CB in a pneumatic is really kind of silly (usually). Yes, there is an efficiency optimum but at that optimum the performance will really suck. The majority of pneumatics are going for decent performance and reasonable size and that comes at a significant cost in efficiency. In a pneumatic you are willing to waste the XXX PSI pressure that is still in the gun at ammo exit because that extra pressure helped performance (muzzle energy) by a lot.
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Unread postAuthor: btrettel » Tue Jun 22, 2010 9:20 pm

jimmy101 wrote:The idea of an "optimal" CB in a pneumatic is really kind of silly (usually). Yes, there is an efficiency optimum but at that optimum the performance will really suck.


The point of the C:B ratio is that it's independent of size. So if the performance is too low, you increase the size as scaled by the C:B ratio. High performance and high energy efficiency aren't mutually exclusive goals. Ideally you get both.

Edit: I just realized that air cylinders (or something similar) could potentially increase efficiency dramatically if they contract during the shot. I'll investigate this.
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Unread postAuthor: Technician1002 » Wed Jun 23, 2010 1:58 am

btrettel wrote:Edit: I just realized that air cylinders (or something similar) could potentially increase efficiency dramatically if they contract during the shot. I'll investigate this.


Welcome to the effeciency of springers. That is why they don't require massive pumping. They are highly effecient.
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Unread postAuthor: btrettel » Wed Jun 23, 2010 7:51 am

The goal is to reduce the amount of air left in the gas chamber when the shot is finished, and the only real way to do this is to have a collapsing chamber.

I haven't examined the efficiency of springers in much detail, but I have thought they could be more efficient, and this is a reason to think that.

However, I doubt the average springer is more than 30% efficient... we're now possibly looking at the possibility of a 70% efficient pneumatic, which would be nice.
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Unread postAuthor: Ragnarok » Wed Jun 23, 2010 9:10 am

btrettel wrote:Does this mean that larger chambers make valve performance more important?

Depends on exactly what you mean by that, but in certain interpretations, yes.

Here's a simple modelling of HEAL:
Image

The X axis is the C:B ratio (or at least, the C part of it). The independent variable in this is chamber volume.
The Y axis is the fraction of the theoretical maximum performance from the barrel (i.e. chamber pressure x barrel area x barrel length) achieved.

The blue line is just a simple integration of decompression using the ratio of specific heats. In other words, performance without valve or flow losses.
The red line is simulated figures with a 20 gram projectile.
The green line is simulated figures with a 20 gram projectile and halved valve diameter.

As you can see, the higher valve performance is, the more benefit is gained from a larger chamber. Or, vice versa, you only benefit from a larger chamber if you've got a good valve.
It's only really piston valve cannons with high valve bores that can make meaningful use of C:B ratios past about 1:1

Another thought... what is "heavy" or "light" is relative.

Well, I'm in the habit of designing cannons where the projectile mass is within an order of magnitude (either way) of the mass of the propellant gasses. I think we can reasonably safely say those are pretty light projectiles.

Not exactly efficient - but having seen what power to weight ratios of eight million horsepower per tonne can do for a projectile, I'm happy enough.

The goal is to reduce the amount of air left in the gas chamber when the shot is finished, and the only real way to do this is to have a collapsing chamber.

It has been discussed before, but the problem that usually comes up is that most methods mean that after the shot, you've then got quite a fast piston hurtling towards the end of the chamber, and you have to work out how to stop it without damaging the launcher.
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Unread postAuthor: Technician1002 » Wed Jun 23, 2010 10:15 am

Ragnarok wrote:It has been discussed before, but the problem that usually comes up is that most methods mean that after the shot, you've then got quite a fast piston hurtling towards the end of the chamber, and you have to work out how to stop it without damaging the launcher.


In a proper springer this is not the case. If you have a fast piston at the end of the shot, that is wasted energy and LOW effeciency.

Idealy, the chamber is voided as the piston comes to a stop at the end of the chamber on the pressure spike of air that is now in the barrel pusing the projectile. As the piston stops, the pressure drops leaving no left over pressure or kinetic energy in the launcher. The KE should be in the projectile for high effeciency.

Getting this balance is a fine art.

Spring to KE of heavy piston (relatively) compresses air and imparts KE and pressure to the air depleting energy from the spring driven piston. Think of it like a Newtons Cradle, but with a lever so the first ball stops as before on impact, and ejects a smaller ball at higher speed.
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Unread postAuthor: Hailfire753 » Wed Jun 23, 2010 10:54 am

Technician1002 wrote:
btrettel wrote:Edit: I just realized that air cylinders (or something similar) could potentially increase efficiency dramatically if they contract during the shot. I'll investigate this.


Welcome to the effeciency of springers. That is why they don't require massive pumping. They are highly effecient.


Anyone have links to more information on springers, or cannons that use this? I have seen cannons that use air cylinders as both the chamber and the way to cycle the breach...
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Unread postAuthor: mobile chernobyl » Wed Jun 23, 2010 11:34 am

btrettel wrote:I think I'm the only person to have identified this performance regime.

........

That's the same effect, yes, but I'm talking about projectile mass. As far as I can tell, projectile mass was never considered to have this effect previously.


I thought this was somewhat common knowledge to anyone with access to Hall's GGDT software??

Maybe not - but I know it's been discussed previously amongst any of the "large bore" cannon owners on here, esp when regarding some of the projectile's shot out of them can weigh over 2 lbs.

It's always cool to see it backed quantitatively tho! :D
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Unread postAuthor: jimmy101 » Wed Jun 23, 2010 3:25 pm

btrettel wrote:
jimmy101 wrote:The idea of an "optimal" CB in a pneumatic is really kind of silly (usually). Yes, there is an efficiency optimum but at that optimum the performance will really suck.


The point of the C:B ratio is that it's independent of size. So if the performance is too low, you increase the size as scaled by the C:B ratio. High performance and high energy efficiency aren't mutually exclusive goals. Ideally you get both.

Edit: I just realized that air cylinders (or something similar) could potentially increase efficiency dramatically if they contract during the shot. I'll investigate this.

No, high performance and high efficiency are indeed mutually exclusive. If you make what you think is "high performance and high efficiency" then just increase the volume of the chamber, you'll boost performance (so it wasn't "high" to begin with) at the expense of inefficiency.

It would be more accurate to say you can get OK performance with high efficiency. In most cases though the cost of increasing performance (at the expense of efficiency) is darn near zero so it comes back to, for most pneumatics, efficiency really isn't much of a design goal.
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