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

Unread postAuthor: BeaverRat » Tue Jun 22, 2010 2:16 am

Well,
I can say that I understand C:B ratios for combustions because really the only variable is the fuel, many of which are standard. Pneumatics on the other hand are more complicated in this matter though because the pressure is adjustable. Basically:

-What gives more power in a pnuematic, pressure, chamber size, or both? To what extent?

-How do you calculate an optimum C:B ratio?

-What is the relationship between chamber area, pressure, barrel area, efficiency, and power?

Pretty much, I don't understand anything about C:B Ratios in Pnuematics. I have done plenty of research on this site about this topic, but I still can't grasp how it all works.

Oh, and if this matters, the cannon has a 2 inch barrel sealing piston valve, a 2.5 inch barrel, and a two inch chamber. Lengths are not set yet, and I will be hand pumping it...

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

Unread postAuthor: jackssmirkingrevenge » Tue Jun 22, 2010 2:41 am

BeaverRat wrote:-What gives more power in a pnuematic, pressure, chamber size, or both? To what extent?


What I always dig up in this case, have a look at this data for a virtual launcher modelled in GGDT - in each case, we're talking about the same quantity of air, but in a reduced volume and therefore at higher pressure.

(chamber is of constant diameter but different length, projectile size, weight and valve flow/barrel length are constant)

20 inch chamber at 50 psi - 406 feet per second

10 inch chamber at 100 psi - 537 feet per second

5 inch chamber at 200 psi - 684 feet per second

2.5 inch chamber at 400 psi - 830 feet per second

1.25 inch chamber at 800 psi - 958 feet per second

0.625 inch chamber at 1600 psi - 1006 feet per second

In short, more chamber size will increase power, but and an exponentially lower rate. Increasing pressure on the other hand should provide an almost linear increase in power. The best wat to find out is to download GGDT and model your launcher there.

-How do you calculate an optimum C:B ratio?


Download GGDT

-What is the relationship between chamber area, pressure, barrel area, efficiency, and power?


It depends on your launcher to what extent these variables make a difference, download GGDT

Pretty much, I don't understand anything about C:B Ratios in Pnuematics. I have done plenty of research on this site about this topic, but I still can't grasp how it all works.


Might I suggest you download GGDT :D
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Unread postAuthor: Technician1002 » Tue Jun 22, 2010 4:05 am

Since you are hand pumping the cannon, I highly recommend a reasonably smallish chamber size. I took my 3 gallon launcher to a retreat and several of the men had ambitions for 100 PSI shots, but pooped out on the workout to get it to 60 PSI.

The small launcher on the other hand does a reasonable job (much less power) and is much less effort to get it to 100 PSI with a hand pump. Shooting marshmallows, gumballs, golfballs and to some extent tennis balls with the small launcher is much more fun than the workout required to fill the large one with a hand pump.

Just don't expect the performance of the larger launcher when launching larger heavier projectiles.

I highly recommend GGDT. Don't be too optimistic on your ability to fill a large chamber to high pressure repeatedly. Fatigue becomes real.

The small cannon on the left is a reasonable size to enjoy with a hand pump. The one in the middle is a workout with a hand pump.
Image

The one on the left is much easier to pump to destructive pressure if you are trying to punch holes in appliances. If you are lobbing eggs, a larger chamber at lower pressure can provide some very impressive long distance lobs without breaking the eggs on launch. :D

For effeciency, the highest effeciency is when the chamber pressure is gone as the projectile exits. Unfortunately just before exit, the projectile is no longer accellerating. Power suffers. Increasing either the prssure or chamber volume to have remaining pressure decreases effeciency, but increases power. Increasing chamber size for any fixed chamber pressure is a scale of diminishing returns. Larger = more power, up to a point. Going larger increases ineffeciency as air energy is wasted after the projectile has left.

Performance - effeciency is a balance you get to choose in your design.

A higher flow valve is always the best of both worlds. Better effeciency with better power. Use the biggest fastest valve you can build. Losses in a valve due to turbulance or slow speed really cuts the system effeciency.
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Re: Still Don't Understand C:B Ratio on Pnuematics...

Unread postAuthor: boyntonstu » Tue Jun 22, 2010 5:44 am

jackssmirkingrevenge wrote:
BeaverRat wrote:-What gives more power in a pnuematic, pressure, chamber size, or both? To what extent?


What I always dig up in this case, have a look at this data for a virtual launcher modelled in GGDT - in each case, we're talking about the same quantity of air, but in a reduced volume and therefore at higher pressure.

(chamber is of constant diameter but different length, projectile size, weight and valve flow/barrel length are constant)

20 inch chamber at 50 psi - 406 feet per second

10 inch chamber at 100 psi - 537 feet per second

5 inch chamber at 200 psi - 684 feet per second

2.5 inch chamber at 400 psi - 830 feet per second

1.25 inch chamber at 800 psi - 958 feet per second

0.625 inch chamber at 1600 psi - 1006 feet per second

In short, more chamber size will increase power, but and an exponentially lower rate.

That is why hammer valves worked for Lewis and Clark.

A 2,000 psi modern air rifle spits out a tiny volume of air per shot.

See: http://www.quackenbushairguns.com/

http://www.glbarnes.com/field_justice.html

What is their equivalent chamber size?
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Re: Still Don't Understand C:B Ratio on Pnuematics...

Unread postAuthor: jackssmirkingrevenge » Tue Jun 22, 2010 5:54 am

boyntonstu wrote:What is their equivalent chamber size?


My FX Monsoon has a chamber volume of 180cc, filled to 200 bar. After around 36-48 shots at 30 ft/lbs (16 grain pellets at 800-900 fps), the pressure drops to around 100 bar. Maybe Ragnarok feels like doing the math :)
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Re: Still Don't Understand C:B Ratio on Pnuematics...

Unread postAuthor: Ragnarok » Tue Jun 22, 2010 8:30 am

jackssmirkingrevenge wrote:Maybe Ragnarok feels like doing the math :)

Well, with the 100 bar drop, and the 180cc chamber, there's ~18 litres of air (at standard pressure) in that. Consequently, 400-500 cc of air per shot.

At those pressures, you're looking at "an equivalent chamber size" of 2 to 5 cc.
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Unread postAuthor: btrettel » Tue Jun 22, 2010 8:39 am

BeaverRat, did you find this thread where I posted optimal C:B ratios for pneumatics? I posted some more detailed tables and instructions on how to use these tables at NerfHaven.

These tables were calculated using a "non-dimensional" simulation. C:B ratio has no dimensions, so this simplifies things a bit. It also reduces the number of variables the problem has.

There's still some more I need to post and explain about these tables and their use, but they should be helpful to get an idea of what the optimal C:B ratio is as is.

BeaverRat wrote:What gives more power in a pnuematic, pressure, chamber size, or both? To what extent?


My tables don't really answer this as they are normalized and you just scale them up until you get what power you want. Because of this, efficiency is the only real factor to look at in terms of power. In terms of efficiency, at optimal C:B ratios, efficiency is higher at higher pressures.

BeaverRat wrote:How do you calculate an optimum C:B ratio?


Testing and/or numerical simulation. Some have suggested GGDT, which isn't a non-dimensional simulation, so it can't directly find optimal C:B ratio.

BeaverRat wrote:What is the relationship between chamber area, pressure, barrel area, efficiency, and power?


My tables do answer this one.

Technician1002 wrote:For effeciency, the highest effeciency is when the chamber pressure is gone as the projectile exits. Unfortunately just before exit, the projectile is no longer accellerating. Power suffers.


I think there's a typo here or I'm confused about what some mean by power.

Power suffers when the projectile is going as fast as it could (i.e. when it stops accelerating)? I don't understand that. :)

A higher flow valve is always the best of both worlds. Better effeciency with better power. Use the biggest fastest valve you can build. Losses in a valve due to turbulance or slow speed really cuts the system effeciency.


Good valves are important, but the non-dimensional simulations I've run indicate to me that a high flow valve is not essential for efficienct systems. If the projectile is heavy enough then performance can be nearly independent of valve flow. I'm unsure of whether most cannons meet this criteria; from the math I've done so far for my Nerf launchers, I don't think most do.

At first this surprised me because it went against conventional wisdom, but I thought about it more, and heavier projectiles logically would stay approximately in the same place for longer, allowing pressure to build up, so the gun is more "resistant" to bad valves.

I think I'm the only person to have identified this performance regime.
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Last edited by btrettel on Tue Jun 22, 2010 10:36 am, edited 1 time in total.
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Unread postAuthor: jackssmirkingrevenge » Tue Jun 22, 2010 9:01 am

btrettel wrote:At first this surprised me because it went against conventional wisdom, but I thought about it more, and heavier projectiles logically would stay approximately in the same place for longer, allowing pressure to build up, so the gun is more "resistant" to bad valves.


This is the same logic behind using a detent, if the breech is airtight and only allows the projectile to move when maximum pressure is reached, then valve opening time is irrelevant to performance.

I think there's a typo here or I'm confused about what some mean by power.

Power suffers when the projectile is going as fast as it could (i.e. when it stops accelerating)? I don't understand that.


I think what he means is that to make full use of the energy available from the pressurised chamber, at the point where the projectile reaches the muzzle the pressure in the barrel behind it should be the same as atmospheric pressure. In practice this would result in really tiny chambers, or excessively long barrels, weak launchers in the former case or massive ones in the latter ;)
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Unread postAuthor: Ranger » Tue Jun 22, 2010 10:13 am

I dont understand it either, I just know that 1.5 C/B ratio is a good start.
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Unread postAuthor: boyntonstu » Tue Jun 22, 2010 10:17 am

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


I posted findings that a tight fitting cork dart had more power than a looser fitting dart, and I gave the same explanation.

We agree.
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Unread postAuthor: Technician1002 » Tue Jun 22, 2010 10:21 am

That is what I meant. If you have the projectile exit with the chamber at no pressure (highest efficiency of the stored pressure energy) the KE of the projectile is plowing air in front of it and due to flow resistance in the barrel, there is low pressure behind the projectile. In other words, the projectile is slowing down on exit as the engine to make it go has been cut off, but all the drag is there.

In a best case, you don't quite want 100% efficiency of the chamber air. you want to make best use of your barrel, so on exit of the projectile, you want enough remaining pressure to maintain the projectile speed on exit. To do that, considerable chamber pressure will still be in the chamber on projectile exit. This is unavoidable as the losses are real.

When I designed a launcher for a competition, the barrel was trimmed much shorter than the math said was the best efficiency. This resulted in a higher launch velocity. Theory stated the longer barrel would have transferred the energy for a faster final launch. Real world testing proved otherwise.

Our launcher barrel trimming page is here. We measured the time the projectle took to travel each foot down the barrel and trimmed where the acceleration quit. With less loss due to the shorter barely, the speed increased.
https://inteltrailblazerschallenge.wikispaces.com/Barrel+length+trim+method
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Unread postAuthor: jackssmirkingrevenge » Tue Jun 22, 2010 10:24 am

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. Play with GGDT, it will give you at least a rough idea of how changing parameters will affect performance, saves a lot of hacking and modding afterwards ;)
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Unread postAuthor: Technician1002 » Tue Jun 22, 2010 10:33 am

The mass of your intended projectile makes a huge change on the ratio too. Model various projectile masses for a given chamber. For a given barrel diameter, you will find the needed length will change depending on projectile weight.

You can fine tune a barrel for a target projectile. We tuned two barrels for the contest. One for t shirts and one for 4 inch foam balls.
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Unread postAuthor: btrettel » Tue Jun 22, 2010 11:08 am

jackssmirkingrevenge wrote:This is the same logic behind using a detent, if the breech is airtight and only allows the projectile to move when maximum pressure is reached, then valve opening time is irrelevant to performance.


boyntonstu wrote:I posted findings that a tight fitting cork dart had more power than a looser fitting dart, and I gave the same explanation.

We agree.


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. Very often it's easier to make a heavier projectile than to add a detent, use a higher flow valve, make the projectile have a tighter fit, etc.

I suspect that the use of very low mass projectiles contributes to the difficulty in getting supersonic velocities.

Technician1002 wrote:In a best case, you don't quite want 100% efficiency of the chamber air. you want to make best use of your barrel, so on exit of the projectile, you want enough remaining pressure to maintain the projectile speed on exit. To do that, considerable chamber pressure will still be in the chamber on projectile exit. This is unavoidable as the losses are real.


Interesting. This is not something I had considered.

I'm doubtful that the little extra push some extra pressure in the barrel would have, especially given that it will equalize very very quickly, but I'll eventually do some tests and see.

Edit: If there was friction, there would be excess pressure at the projectile exit for "optimal" situations. I don't have time to find the post, but I derived a theoretical equation for optimal C:B ratio under the assumption that atmospheric pressure and the "pressure of friction" are where the projectile stops (this works out according to the force balance) and I found an expression that agreed very closely with my numerical results.

Technician1002 wrote:When I designed a launcher for a competition, the barrel was trimmed much shorter than the math said was the best efficiency. This resulted in a higher launch velocity. Theory stated the longer barrel would have transferred the energy for a faster final launch. Real world testing proved otherwise.


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.
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Unread postAuthor: jackssmirkingrevenge » Tue Jun 22, 2010 11:25 am

btrettel wrote: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.


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.

Most people use their rifles with medium weight pellets, using heavy pellets pushes the muzzle energy up because of the increased efficiency, for which reason most rifles are factory set to 10-11 ft/lbs.

Very often it's easier to make a heavier projectile than to add a detent, use a higher flow valve, make the projectile have a tighter fit, etc


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.
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