I ran some more numbers today and got some interesting results:
31 Jan 09 Ballistic Testing

Patuxent River
33.9 °F 42% 30.09 in (Rising) Clear NW at 9.0 mph 3:03 PM EST

Elevation 105 feet, all shots taken with Prairie III regulated at 3600 PSI

.32 Bishops, 94gr
3 yards; 911.6 FPS, 173.5 FPE
42 yards; 776.3 FPS, 125.8 FPE
JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 911.6 ft/s Far Velocity: 776.3 ft/s
Distance: 117.0 ft Drag Function: G1
Temperature: 33.9 °F Pressure: 30.09 in Hg
Humidity: 42.0 % Altitude: 105 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No
Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1089.1 ft/s

Ballistic Coefficient: 0.039 Time of Flight: 0.139682 s
31 Jan 2009 12:08:16, JBM [http://www.eskimo.com/~jbm]

Chairgun value: .030 STP value: .039 (STP is the ballistics program on Brad Troyers’ site)


.32 Falcons, 77.2gr
3 yards; 955.0 FPS, 156.4 FPE
42 yards 793.3 FPS, 107.9 FPE
JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 955.0 ft/s Far Velocity: 793.3 ft/s
Distance: 117.0 ft Drag Function: G1
Temperature: 33.9 °F Pressure: 30.09 in Hg
Humidity: 42.0 % Altitude: 105 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No
Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1089.1 ft/s

Ballistic Coefficient: 0.036 Time of Flight: 0.135309 s
31 Jan 2009 12:11:53, JBM [http://www.eskimo.com/~jbm]

Chairgun value: .026 STP value: .036


.32 Cans, 114gr
3 yards; 867.7 FPS, 190.6 FPE
42 yards; 775.6 FPS, 152.3 FPE
JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 867.7 ft/s Far Velocity: 775.6 ft/s
Distance: 117.0 ft Drag Function: G1
Temperature: 33.9 °F Pressure: 30.09 in Hg
Humidity: 42.0 % Altitude: 105 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No
Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1089.1 ft/s

Ballistic Coefficient: 0.054 Time of Flight: 0.142891 s
31 Jan 2009 12:15:49, JBM [http://www.eskimo.com/~jbm]

Chairgun value: .043 STP value: .054


.32 Boat tails, 112.2gr
3 yards; 877.8 FPS, 192.0 FPE
42 yards; 804.9 FPS, 161.4 FPE
JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 877.8 ft/s Far Velocity: 804.9 ft/s
Distance: 117.0 ft Drag Function: G1
Temperature: 33.9 °F Pressure: 30.09 in Hg
Humidity: 42.0 % Altitude: 105 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No
Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1089.1 ft/s

Ballistic Coefficient: 0.072 Time of Flight: 0.139369 s
31 Jan 2009 12:18:28, JBM [http://www.eskimo.com/~jbm]

Chairgun value: .056 STP value: .072


.32 Pepper Grinders, 114.7gr
3 yards; 871.2 FPS, 193.4 FPE
42 yards; 777.8 FPS, 154.1 FPE
JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 871.2 ft/s Far Velocity: 777.8 ft/s
Distance: 117.0 ft Drag Function: G1
Temperature: 33.9 °F Pressure: 30.09 in Hg
Humidity: 42.0 % Altitude: 105 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No
Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1089.1 ft/s

Ballistic Coefficient: 0.053 Time of Flight: 0.142399 s
31 Jan 2009 12:22:45, JBM [http://www.eskimo.com/~jbm]

Chairgun value: .043 STP value: .054


.32 Totem Poles, 177.7gr
3 yards; 784.5 FPS, 242.9 FPE
42 yards; 731.65 FPS, 211.3 FPE
JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 784.5 ft/s Far Velocity: 731.6 ft/s
Distance: 117.0 ft Drag Function: G1
Temperature: 33.9 °F Pressure: 30.09 in Hg
Humidity: 42.0 % Altitude: 105 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No
Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1089.1 ft/s

Ballistic Coefficient: 0.080 Time of Flight: 0.154502 s
31 Jan 2009 12:25:39, JBM [http://www.eskimo.com/~jbm]

Chairgun value: .070 STP value: .079

For todays' test I ran the gun a lot hotter than I did for the first test. Today I had the spring set to high verses low for the first test. For the light Falcons this change took the velocity from 787 @ 3 yards to 955 @ 3 yards.

I found that at the higher velocity all the BC values came out lower than they did in the first run. Decreasing BC with increasing velocity is expected but the magnitude is more than I anticipated, especially for the boat tail slugs that had a huge drop compared to the first test but still out performed all but the very long Totem Poles.

The really interesting thing I learned today is how little the BC and ballistics programs match up. For instance the value that Chairgun computes for the BC of the Totem Pole is .070 while the JBM program says .080 and the STP program says .079. Even worse; if you use the STP BC value in the STP trajectory calculator, it does not calculate the observed values at 3 and 42 yards. If I enter the Chairgun BC value into the STP program it calculates numbers for velocity at 3 and 42 yards close to actual. Likewise, if I use the Chairgun calculated BC in Chairgun, it does not compute a trajectory that matches the 3 and 42 yard measurements! Chairgun is closer to observed using its own BC but still a little optimistic.

Reading the notes in the help file and observing the graphs, it is clear that Chairgun assumes and calculates retained velocity as a linear function. My data suggest that a curve accounting for lower BC at higher velocity would be more accurate. I think that is consistent with what many of the experts have written but the nature of the curve is the part that is not so easy to calculate. None of the pellets I tested looks like the form factor they are compared to in the G1 calculation (I don't think Chairgun uses the G1 drag table but JBM does and STP must as it is nearly consistent with JBM).

Sierra bullets are rated with different BC values for different velocity ranges. This is important as they may be loaded to different performance levels and of course the trans-sonic region is noted for greatly reduced drag as velocity decreases. What surprised me was that you can't just take "below trans-sonic" as one region with one BC as Sierra does. Clearly the BC changes enough between 900 and 600 FPS to impact trajectory calculations. At least for the tested pellets.

Why does Chairgun provide such an accurate ballistic chart and scope tape for pellets but not for the bullets I tested? Neil for instance, has shown that the tape he made for his Falcon is dead on from near to 139 yards! That can't be an accident. Could it be that the higher base drag of the typical diablo style pellet results in a more linear velocity curve?

I'd be interested in a trajectory computation program that allows for the entry of more than one BC value. All the research on the topic agrees that BC varies with velocity yet the programs I've seen all use one BC. Given the available computing power these days, I'm sure that a variable BC program could be executed. Given the fact that we're using guided weapons more and more these days, you can bet that the government won't be spending money on ballistics though and nobody else has the resources to do this work without a clear profit path.

With the numbers I have, it looks like I might get a reasonable scope tape for a limited set of ranges for the Falcon or Bishop slugs. For the rest of the slugs I'll just have to go old school!

That's some serious data Jerry. I see how the fixed density of the air (during the flight of the bullet) would remain solid ... yet the shock waves created by the geometry of the bullet in flight would be relative to the velocity (and thus continually changing). I suspect that some geometric features would even create a situation where two or three waves ... (off of various rings and/or grooves) would intersect ... sometimes cancelling out the drag (or magnifying it). If that logic had merit ... the multiple waves would be converging or diverging as velocity changed.

I'd think that to really take all variables into account, there'd need to be a NASA quality effort to plot all of those issues. Sounds a bit beyond my 40 year old calulator. However; that would be my guess why one slug (appearing relative similar to another) would have a dramatically different BC. Some factor of the waves generated by the geometry.

Gary

Yes Gary, the shock wave theory is not just valid but has been proven for high velocity projectiles. For very fast slugs the dominant drag component is often shock wave formation. If you follow the development of very long range sniper rounds these days, you'll find that the new cartridges coming out and competing for government dollars all stress the smoothness of their bullet shape. It turns out that at very high velocity even the transition from a secant nose to a barrel mid-section can cause the formation of a drag inducing shock wave. (As an aside, it is unfortunate that we didn't have the ability to see these drag inducing shock waves years ago. During the early days of mach 2 fighters we lost more than a couple aircraft to jets chasing down their own bullets. A smoother, faster bullet might have prevented some losses.)

Fortunately for us, the lower velocity of our slugs generally prevents the formation of multiple shock waves beyond the nose and base. We do remain at the mercy of simple form drag though and every protuberance contributes to that regardless of whether or not the velocity supports shock wave formation. Unless, laminar flow creates an different effective shape... There are enough variables that onlt testing can determine the actual drag figures at any given velocity, at least for now.

Aberdeen Proving Grounds actually did a lot of "NASA quality" ballistics work until the "peace dividend" kicked in some years ago. They developed some very accurate equations that supported ballistic predictions very accurately. You might remember M1 tanks blowing up T72s at several thousand yards during the first Gulf War. Unfortunately for us, the results of that research and modeling remain classified or pertain to velocities that start well above the trans-sonic region. Fortunately for us, our tankers could destroy the enemy before he could even see our guys in many cases! Ballistics wasn't the only factor, but but it was one.

Anyhow, I would still like to see a program that accounted for different BC as a function of mach number or simple velocity...

Jerry, nice work with those BC figures. I will see if I can dig out the Raptor velocities for you to run. It might be that with your figures and Chairgun I can come up with accurate scope tapes for the big bores.
As to Chairgun and small bores, I think it is fair to say that Chairgun does a good job out to 150 yards with the Falcon. The picture below shows that the first shot tried at this distance with a brand new scope tape hit the bull! The remaining shots drifted in the wind, but I was pretty chuffed with the accuracy of the program.....


Cheers
Neil

Hi Neil,
That picture and the post you wrote about the scope tape is exactly what I was referring to. I don't know if its a happy accident or if the pellets' drag function really is close to linear but you've have some great results with the Chairgun derived scope tapes.

Jerry, I dug out these figures, for the 220.5 grain .454 match grade Raptors, through the 909 twin tube:
Muzzle velocity 608 fps
50 yards 543 fps

The settings in Chairgun were:

Temp 20 degrees Celcius
Gravity 32.2 Ft/s2
Pressure 29.9 in Hg
Altitude 400 feet

Interested to see what you come up with....

Hi Neil,
Here's what JBM calculated:

JBM Ballistic Coefficient (Velocity) Output
Input Data
Near Velocity: 608.0 ft/s Far Velocity: 543.0 ft/s
Distance: 150.0 ft Drag Function: G1
Temperature: 20.0 °C Pressure: 29.90 in Hg
Humidity: 55.0 % Altitude: 400 ft
Std. Atmosphere at Altitude: No Corrected Pressure: No

Calculated Parameters
Atmospheric Density: 0.1 lbs/ft³ Speed of Sound: 1126.1 ft/s

Ballistic Coefficient: 0.055 Time of Flight: 0.261186 s

04 Feb 2009 08:20:30, JBM [http://www.eskimo.com/~jbm]

I just took a guess for humidity. I don't think humidity makes that big a difference anyhow. I think these results are similar to what you got with chairgun right?

Thanks for that Jerry, and yes, that was exactly the figure that I got through Chairgun.
I hope to shoot the 909 this weekend so will check the accuracy of the scope tape if I get a chance.
Regards
Neil

Excellent! I know at least three of us will be shooting this weekend!

and to think most of us just bung in a slug and never give them a secont thought till the hole apears in the paper , or whatever , thats some in depth stuff . very interesting too.