Speed of Sound at High Pressures

When looking for information about the speed of sound at high pressures, I ran across the following website.... http://www.peacesoftware.de/einigewe...gewerte_e.html
It has calculators for Oxygen, Nitrogen, and Carbon Dioxide, which allow you to find the speed of sound at various combinations of temperature and pressure.... This is the only place I have ever found information on the speed of sound at high pressures.... I used the calculator to determine a bunch of data points, and then plotted them using Excel.... First for HPA at 20*C....

http://i378.photobucket.com/albums/o...psbe789913.jpg

I extrapolated the data for air using the mix of Nitrogen and Oxygen in the atmosphere (78:21), but it ignores the other components in air.... However, it comes out to 1130 at 20*C which is just about right on, so I have no reason to believe it isn't pretty darn close at higher pressures.... Next for CO2....

http://i378.photobucket.com/albums/o...ps72ce2a56.jpg

There is very little "normal" for the chart on CO2.... Instead of the speed of sound increasing with pressure as happens with Nitrogen and Oxygen, it drops.... In all cases I plotted the speed of sound of the gaseous component, not the liquid.... The boiling curve spans pretty much the whole range where CO2 can exist as both liquid and gas, from -55*C to about 30*C.... As the temperature increases (increasing the pressure), the speed of sound drops.... In practical terms, we are really only interested in what happens between 0*C (freezing) and 40*C (103*F), and of particular importance is 20*C (room temperature, 68*F).... so I plotted those three temperatures at all pressures up to the maximum that would normally occur (without over filling the container)....

I then looked at what would be the typical pressure at the exit of the valve for the three temperatures over the bulk of the fill conditions for a tank containing CO2.... For the 0*C case, the pressure is about 500 psi, and the speed of sound is about 695 fps.... For the 20*C case, the pressure is about 800 psi, and the speed of sound is about 659 fps.... At 40*C, the pressure varies as the tank empties, starting at about 1500 psi but quickly dropping to 1300 at 90% full, then gradually dropping to about 1100 psi before dropping quickly again as the tank drops below 30% full.... It spends most of the time between 1100-1300 psi, and the corresponding speed of sound averages about 680 fps.... The average value I came up with for the speed of sound at the exit of the valve, while the valve is open, over the typical range of temperatures (0-40*C) is 680 fps.... I think that would be a good velocity to use for any calculation of sonic choking in the ports.... As the pressure drops, the speed of sound increases and the choking becomes less of an issue, so I think using 680 fps makes sense....

Bob

The measurements are at the valve end/exit, correct? If so, the sound 'barrier' can't destabilize the projectile while it's in the barrel, so the pressure behind the pellet at the muzzle end would be the larger issue I'm thinking. That being said, is there some sort of correction factor that can be plugged in for different barrel lengths?

Or, was the point to determine the optimum pressure point to keep the noise level down?

No, nothing to do with noise level or pellet stability, but related to the concept of "sonic choking" of the ports because they are (usually) smaller than the boresize.... If the port is 1/2 the diameter of the bore, then it's area is 1/4.... so the velocity through the port will be 4 times as great.... It isn't the muzzle velocity that is critical, however, but the velocity of the pellet (and hence the air column behind it) at the instant the valve closes.... That is the highest velocity the ports will ever see....

For a real world example, let's take a port that is 75% of boresize, it's area would be 56% (0.75 x 0.75).... If the pellet velocity at the point the valve closes is, say, 700 fps (which might produce a 1000 fps MV) the velocity through the port would be (700 / 0.56) = 1250 fps.... If the speed of sound is 1130 fps (as we have assumed), then the flow through the port would be supersonic, causing shockwaves to form in the port, increasing the friction, and lowering the flow, partially limiting the efficiency (and power) of the gun.... However, if the speed of sound is 1360 fps (as it would be at 3000 psi), then the flow would not be supersonic.... That is the importance of the speed of sound under pressure, or at least why I was investigating it....

Bob