Air Gun Home :: View topic - Efficiency of Airguns near the Speed of Sound

rsterne · Moderator

I have been thinking about how the efficiency of airguns drops off when the pellet approaches the speed of sound.... which it does dramatically.... I am wondering if this is partly because of a shock wave being created in the transfer port.... which is typically 75% the size of the bore diameter....

This phenomenon was used in F3 racing engines developed by Cosworth many years ago.... They built a very strong 1600 cc four-valve twin-cam engine for F2 use that developed (IIRC) about 225 HP at 9,000 rpm and was developed further from there.... In order to restrict this engine and make it last virtually "forever" for F3 use.... they fitted it with an airbox with a small inlet.... The inlet size was chosen so that when the engine reached the RPM they wanted (say, 8,000) a shock wave was created at the inlet that prevented more air from entering.... This simple but effective method allowed the engine to be made virtually "bulletproof".... It could not over-rev even in neutral.... Shocked

I have noticed in PCP guns that it takes HUGE increases in air flow to get the pellet supersonic.... In actual testing of a .22 cal PCP, I found the following:

4 turns out on hammer spring from coil bind:
11.9 gr pellet - 1098 fps - 31.9 FPE
28.7 gr. pellet - 757 fps - 36.5 FPE

2 turns out:
11.9 gr. - 1128 fps - 33.6 FPE
28.7 gr. - 850 fps - 46.1 FPE

Max:
11.9 gr. - 1128 fps - 33.6 FPE
28.7 gr. - 896 fps - 51.2 FPE

I was "just" getting a crack at 1128 fps.... in fact some shots didn't quite make it.... It was literally like the velocity hit a wall (the sound barrier).... Note, the air usage still increased, however.... Note that in going from 36.5 FPE to 46.1 FPE (a 26% increase).... the light pellet only gained 1.7 FPE (5%).... Going past ~1000 fps just takes a HUGE increase in the amount of air required to gain anything....

So the question is.... is it the air in the barrel reaching the speed of sound that is the major limiting power in efficiency.... or is the air velocity in the transfer port even higher?....

Bob

oddtodd · Silver Status Member

Very well thought out theory. But is there anyway to figure out where this figure would be on a port of an airgun? I know I don't have the engineering skills to figure it out. Does anybody else?

69Hotrod69 · Veteran Member

I might be wrong but I thought in aeronautical engineering their is the same phenomenon of increased power needed at the threshold of the sound barier then a reduction as soon as the wave has been broken. I don't know the particualars but I do remmember their being some studies done about it. That doesn't however mean that there isn't sound wave effects happening in the tranfer port. I'm very familiar with Cosworth engines though. Laughing

Just my .02

rsterne · Moderator

I couldn't copy the graph I found.... but here are the numbers for the drag coefficient (on some undefined shape):
Mach 0.7 - CD = 0.30
Mach 0.85 - CD= 0.35
Mach 0.9 - CD = 0.7
Mach 1.0 - CD = 1.3
Mach 1.5 - CD = 0.7
Mach 2.0 - CD = 0.42
Mach 2.5 - CD = 0.40

Now this is the coefficient, so you have to multiply by the square of the speed to get ratios of the actual drag....

If the drag at Mach 0.7 is 1.0 @ 790 fps
at Mach 0.85 the drag is 1.72 @ 959fps
at Mach 0.9 the drag is 3.31 @ 1015 fps
at Mach 1.0 the drag is 8.84 @ 1128 fps
at Mach 1.5 the drag is 10.7 @ 1692 fps
at Mach 2.0 the drag is 11.4 @ 2256 fps
at Mach 2.5 the drag is 17.0 @ 2820 fps

Basically, there is about three times the drag at 1000 fps than at 800.... and nearly 9 times at the speed of sound.... Shocked

It isn't much wonder that it's a lot more efficient EXTERNALLY to stay under about 950 fps.... but the question I was posing is what happens INTERNALLY that decreases the efficiency of the gun so drastically when we try and even START the pellet at near supersonic speeds?....

Bob

broommaster2000 · Moderator

There is a guy in the Netherlands who claims he got 1500 FPE from his Beaumont. This was in .32 and it would break the sound barrier.

Now I'm not sure to what extend this is true, and the numbers may be pushing it but it still sounds impressive. The idea was to push an airgun past 300 yards.

Slavia · Moderator

Interesting concept. You may have a point there - in addition to the Cosworth example you gave, take supersonic jet engines. In order for the engine to burn, it has to have subsonic air at the intake - so they use tunable cone-shaped baffles to set up a shock wave that slows the supersonic air entering the engine. http://en.wikipedia.org/wiki/Supersonic_speed

Maybe transfer ports should be shaped like rocket nozzles:
http://exploration.grc.nasa.gov/education/rocket/nozzle.html

ericb · New Member

5 grain pellet. Tube at 2000 PSI. Very accurate

rsterne · Moderator

I have seen Chrono readings as high as 1475 fps, so have no problem in believing that number.... This thread asks the question about the efficiency at those velocities, however.... If you can give information about the size of the air reservoir, starting and ending pressures, and number of shots per fill.... then that can be calculated....

Bob

yourdaddyjoe · Supporting Member

Once again Bob has fried the grey matter inside my skull.... Shocked

ericb · New Member

I have read with great interest your Canadian Airgun posts and your Technical knowledge is way beyond me, I could however give you a shot string of 1o shots with pellet weight and velocity, with the tube length, diameter and pressure, if you would like to look at the data ?

Eric

rsterne · Moderator

I would be most interested.... the calculations are quite simple.... I would need the INSIDE dimensions of the air reservoir (less any obstructions, as I have to calculate the volume) plus the starting and ending pressure (psi or Bar) and either the average velocity of each shot or better yet, the data for each shot.... If you have a accurate weight for the pellet, then the results will be more accurate than using what is printed on the tin....

Bob

ericb · New Member

I will do that next week for you ( us all actually ) I have scales and will weigh each pellet. I chronoed three shots and it dropped 100FPS on each shot, so it looks inefficient. These pellets are very accurate even at this speed from what I can tell. I bought the 10 grain .22 ones they sell and tried that in my QB 79. It is regulated to 1400 PSI.....they came out like a shotgun blast. I then bought the 13 grain ones which where bang on the money. I havent chronoed those yet.

It's my birthday so I'm away over the weekend, but am excited about getting you the data. As i say I loved the articles with the pistol in the forum, and hope my data will be of interest.

Have a good weekend

Eric

rsterne · Moderator

Make absolutely sure that your Chrony readings are not being affected by the blast of air from the muzzle.... I have seen readings vary widely if the muzzle is not about 3 feet away from the first Chrony screen....

Bob