Some Confirmation from ChairGun on Avoiding Transonic Velocities

[rsterne]

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....



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

[Bullit]

Bob, Another great illustration and explanation against going into the transonic zone.  Lotta effort for low returns...and you didn't even need to address pellet instability.  This should open some eyes.
I hope this gets read alot.   Thanks.

[nervoustrigger]

Another excellent analysis as always, Bob.  I'll have to check out the graphs tonight on my home PC.  Guess it's dumb luck that I tuned both my B51 and QB78 to shoot the JSB 18.1 at velocities of right around 900fps but they sure do seem to like it!

[Bwalton]

Bob just when I have read all your papers, and decided to do some great mods on my AT 4410 Tac that you came up with, now stay under 900fps   Ok give me a new rout to  take lol

[oneied]

Thanks Bob. Thats some food for thought while I start to tune in my new Talon SS in .22.  I havent even put it across the chrony but when I do I will be looking for around 800-850 fps max. Maybe even lower if I can tune it down to 700 fps

[Oldnoob]

so it looses velocity, and acceleration, but does it also loose distance?

[Laz]

So Bob, you are telling us that your guns aren't tuned for max possible efficiency?? With your 960 fps, laser accurate, 1", 100 yarders?? 

[rsterne]

It's very much a matter of balancing efficiency vs. velocity and power, right?.... If you notice I didn't say NOT to push a bit beyond 900 fps, only that there is a price to pay when you do.... There is so little difference between the 900 fps graph and the 700 I wouldn't worry too much about going to 900 instead of 800-850.... UNLESS you are using light pellets, or ones with a poor BC (such as wadcutters).... In that case, I wouldn't even push to the 900 point, in fact wadcutters are literally a drag past about 700....

I typically aim for a velocity of around 950 fps with whatever weight of JSB Exact shoots well in that particular gun.... That isn't enough past 900 to pay a great price in efficiency, either inside the barrel in trying to achieve that, or after the pellet is in the air.... I have a couple of rifles tuned for around 1000 fps, but they are shooting heavy pellets (.25 cal and above) that are still accurate at that velocity.... Once you push into the 900-1000 fps range, it becomes very much a matter of compromise, that's all I'm saying....

Bob

[rkr]

Bob, does this apply to bullets as well or is this for pellets with numerically low BC only?

[rsterne]

The trend is very similar for bullets, but the numbers (the actual Cd) are different.... Here is a graph from Chairgun comparing all the various ballistics models....



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).... Secondly, 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.... The same basic trend for the drag exists for bullets and pellets, however, with a sharp increase in the transonic region.... The actual point where the drag increases rapidly actually has a name, the "Drag Divergence Mach Number".... and it varies a bit depending on the shape.... Interestingly, a bullet with a moderate Meplat (flat nose profile) tends to have a slightly later transition point compared to a pure round nose design.... That is the reason I chose a 60% Meplat for my Bob's Boattails.... You can push them to about Mach 0.85 (960 fps) before the drag turns upwards instead of at Mach 0.8 (900 fps).... In addition, the rebated boattail design lowers the Cd in the subsonic region by about a third or more compared to a flat-base bullet....

Bob

[nervoustrigger]

Fantastic analysis!  Bob, your ability to mine out the interesting facts and present them in an easy-to-understand manner is always much appreciated.

[wwonka]

Interesting post as always.

For bullets the story is a little different, as some of your data and graphs hint at. The whole point in the design of a diabolo (ie a "pellet") is A) to drag-stabilise, and B) to slow down very very quickly for safety - so you will expect that diabolos will do just that.

For bullets, the BC vs. velocity vs. efficiency story is not that cut and dried, and mileage may vary (pun intended).

[rsterne]

Most of the difference in ballistics between pellets and bullets is caused by the Sectional Density.... ie bullets tend to be heavier for the same diameter.... Since the BC is proportional to the SD, and bullets usually have a higher SD, they also have a better BC and tend to carry further for the same initial velocity.... Add in that they usually start out supersonic, and in fact many stay supersonic for hundreds of yards.... and yes, they are a lot more dangerous at long distances.... Add to that the diabolo (waisted) shape, with its inherently higher drag for a given SD.... and they do act quite differently.... However, bullets still have a very sharp rise in drag in the transonic region, starting at roughly Mach 0.8.... This is of particular significance when using bullets in higher powered airguns, where the internal efficiency of the much lower pressures means that it is wasteful of air to try and go supersonic.... While bullets can stand a slightly higher velocity than pellets when used in an airgun, trying to push them supersonic is still likely to disappoint....

Bob