ChairGun Ballistics Profiles

I just downloaded the latest version of ChairGun Pro Version 4.1.6, and it has an App that is pretty cool.... You can look at, and modify, the Ballistics Profile of projectiles, including the ability to create your own custom profile.... There are 7 profiles in the program, and the plots show the Drag Coefficient vs. the velocity, as follows:

http://i378.photobucket.com/albums/o...ps58453282.jpg

A couple of comments.... These are a plot of the Cd, which shows how the drag varies with velocity.... To calculate the ACTUAL drag of the bullet, you need other information, such as the Sectional Density and Velocity.... The Ballistics Coefficient is a combination of the Cd and the SD....

G1 (black) is the old standard artillery shell shape used for years....
GA (red) is a profile for airgun pellets, and is the default profile for the program.... note they have slightly lower drag than the G1 profile in the subsonic range....
RA4 (purple) is a .22LR bullet, which should be a good starting point for round nosed cast bullets in big-bore airguns....
GL (yellow) is for "blunt nose - exposed lead" bullets, which, with no other information, may be useful for cast bullets with a flat (meplat) nose....
GS (blue) is for spheres (roundball)....
GC (grey) is for cylinders....
Gx (green) is the custom profile, which you can modify yourself....

There are a few very important things I get from the above chart, however.... Firstly, the red line shows what happens with typical pellets, in terms of the sharp increase in drag above Mach 0.8 (900 fps).... Secondy, their "typical pellet" is at minimum drag between about 500-800 fps, which leads me to believe the graph was drawn using a round-nose design, as I have measured sharp increases in drag for wadcutters at anything over about Mach 0.6 (650 fps).... Thirdly, you can see the marked similarity in the drag curves for all the different types of projectiles. with the sharp rise in drag in the transonic region between Mach 0.8 - 1.2.... Interestingly, both spheres and cylinders start their upwards drag curve earlier than pellets and bullets, at about Mach 0.6 - 0.7.... and their data on a .22LR shape shows a later transition, starting at about Mach 0.9 (1000 fps)....

Since the BC is proportional to the SD, heavier pellets in a given caliber will have a better BC.... Also, similarly proportioned pellets in a larger caliber will have a better BC because their SD is higher.... However, once again I find compelling evidence to stay below the transonic region, as trying to push velocities into the steep part of the drag curve will just end up in you losing all that hard fought for velocity in the first few yards of flight....

Bob

I have found that if you push the velocity of a pellet much beyond Mach 0.8 (~900 fps) you start losing a large piece of the additional velocity in the first few yards.... The new version of ChairGun, based on the GA (airgun) drag model, produces the following graphs for residual velocity for a typical round-nosed pellet....

http://i378.photobucket.com/albums/o...ps1c5bba0d.jpg

To compact the charts I cut the bottom off them, but the X axis is 100 yards, with the light vertical lines being 5 yard increments and the heavier ones being 10 yards.... The upper left graph starts at 700 fps, so the entire chart is right near the plateau of Cd at it's lowest value (ie basically a constant Cd model), and the decrease in velocity is nearly linear, with 60% of the muzzle velocity remaining at 100 yards.... Only 5% is lost in the first 10 yards and 10% in 20 yards.... The upper right starts at 900 fps, and you can see a slight curvature at the beginning, losing 6% in 10 yards, 12% in 20 yards, but then the line tracks the same slope as the 700 fps version, and is down to 58% at 100 yards.... The lower left chart is at 1100 fps, and the curvature at the beginning in quite marked, the pellet losing nearly 10% of its velocity in 10 yards, and about 17% in 20 yards, with 55% remaining at 100 yards.... Push the muzzle to 1300 in the chart on the lower right, and the pellet loses 15% of it's velocity in just 10 yards, and about 23% (300 fps) in 20 yards.... At 100 yards, it only has 48% remaining....

I've measured the loss in velocity over the first 5 and 25 yards of flight with several weights of JSB Exact pellets, and I've found that as you push the pellet over about 900 fps, you start losing a large percentage of the muzzle velocity in the first few yards.... To me, that is just one more reason to stay below the transonic region.... One experiment I conducted with a MV of 1101 fps using a .22 cal JSB Exact RS, showed that the pellet lost 64 fps in just 5 yards (5.8%) losing 11.3% of it's FPE in that short distance.... Interestingly, that is just what is predicted by the 1100 fps chart above.... Another test I did, using a 14.3 gr. JSB Exact Express at a MV of 1067, showed the velocity was down to 857 fps at 25 yards (80%).... which is just a bit worse than predicted above.... The very same pellet, starting at 901 fps was cruising along at 789 fps at 25 yards, only losing 12% of it's MV instead of 20%.... My calculations show a BC of 0.024 at 901 fps, dropping to just 0.014 at 1067 fps.... I simply can find no evidence for a constant Cd drag model.... If you push the velocity into the transonic region, it costs you extra air to do that, and you give most of it back in the first few yards.... You have to ask yourself if it's worth it, or if you should switch to a heavier pellet....

Bob