# Ballistic coefficient relationship to velocity ... a set of data .. trend.

Joined: April 25th, 2003, 11:44 pm
which may be of some interest to those who didn't see it before.

Shot with one rifle and one pellet type JSB Exact 15.9 gr.

The 40 shots are rank ordered according to near range velocity. Each shot shows near range velocity at 6 ft and far range velocity at 36 ft and the BC for that individual shot.

The right side column shows mean near range velocity, average Mach number and average BC for each ten shots according to their ranked number
(not the order of shooting) and so are random in terms of possible environmental changes.

Errata: the # 4 shot from the top should read BC .0254

[/IMG]

It can be seen that there is a trend for BC to go up as near range velocity goes down. It should be noted that muzzle velocity would be some 6+ fps faster than at near range. The velocity range brackets the velocity of 875 fps to 880 fps favored by many shooters as being a desirable velocity for precision shooting. ......... Kind regards, Yrrah.

Joined: February 4th, 2005, 11:51 pm
Thanks a lot, Harry, for running this test. Finally, some data to chew on instead of rumor and conjecture.

BC changes much more than I would have guessed. So, the diabolo pellet is slipperier at low velocities.

This also debunks the theory that the BC of a pellet changes drastically with the gun. It doesn't. It changes with the velocity, even if in the same gun. Granted, there are other factors at play including obturation, but these would seem to be minor in comparison to what Harry has found.

Joined: March 6th, 2009, 8:57 pm
which may be of some interest to those who didn't see it before.

Shot with one rifle and one pellet type JSB Exact 15.9 gr.

The 40 shots are rank ordered according to near range velocity. Each shot shows near range velocity at 6 ft and far range velocity at 36 ft and the BC for that individual shot.

The right side column shows mean near range velocity, average Mach number and average BC for each ten shots according to their ranked number
(not the order of shooting) and so are random in terms of possible environmental changes.

Errata: the # 4 shot from the top should read BC .0254

[/IMG]

It can be seen that there is a trend for BC to go up as near range velocity goes down. It should be noted that muzzle velocity would be some 6+ fps faster than at near range. The velocity range brackets the velocity of 875 fps to 880 fps favored by many shooters as being a desirable velocity for precision shooting. ......... Kind regards, Yrrah.
Fantastic data Harry...

For a quick and dirty analysis, I took first and last 10 values and averaged them.

0.0267 1
0.0243 2
0.0288 3
0.0254 4
0.0254 5
0.0248 6
0.0288 7
0.0273 8
0.0304 9
0.0259 10
0.0268 Mean
0.0020 Std. Dev.
0.00063 Std Dev Mean
Mean: 0.0268 +/- 0.0-13 with 95% confidence

0.0346 1
0.0306 2
0.0383 3
0.0334 4
0.0334 5
0.0394 6
0.038 7
0.0294 8
0.0353 9
0.0352 10
0.0348 Mean
0.0032 Std. Dev.
0.00103 Std Dev Mean
MEAN: 0.0348 +/- 0.0020 with 95% confidence

No look at difference:
(0.0348-0.0268)/0.0348 * 100 = 23%

There is a 23% increase when dropping from about 895fps to about 865fps

That is quite a change for about 30fps difference!

Joined: March 6th, 2009, 8:57 pm
Thanks a lot, Harry, for running this test. Finally, some data to chew on instead of rumor and conjecture.

BC changes much more than I would have guessed. So, the diabolo pellet is slipperier at low velocities.

This also debunks the theory that the BC of a pellet changes drastically with the gun. It doesn't. It changes with the velocity, even if in the same gun. Granted, there are other factors at play including obturation, but these would seem to be minor in comparison to what Harry has found.
Without a doubt Harry's data shows a great difference in BC by just a slight change in velocity.

However, the dynamics of ballistics are complex. The data does not prove that there is no dependency on different guns. In fact that seems likely too.

It is also likely that a pellet with the same weight, but a different brand would start out at roughly the same muzzle velocity. The BC would be different and the change in the BC over the velocity drop would be different.

So no ONE cause ... there are many interactions

Joined: March 6th, 2009, 8:57 pm
Fantastic data Harry...

For a quick and dirty analysis, I took first and last 10 values and averaged them.

0.0267 1
0.0243 2
0.0288 3
0.0254 4
0.0254 5
0.0248 6
0.0288 7
0.0273 8
0.0304 9
0.0259 10
0.0268 Mean
0.0020 Std. Dev.
0.00063 Std Dev Mean
Mean: 0.0268 +/- 0.0-13 with 95% confidence

0.0346 1
0.0306 2
0.0383 3
0.0334 4
0.0334 5
0.0394 6
0.038 7
0.0294 8
0.0353 9
0.0352 10
0.0348 Mean
0.0032 Std. Dev.
0.00103 Std Dev Mean
MEAN: 0.0348 +/- 0.0020 with 95% confidence

No look at difference:
(0.0348-0.0268)/0.0348 * 100 = 23%

There is a 23% increase when dropping from about 895fps to about 865fps

That is quite a change for about 30fps difference!

Quick paired T test on first and last 10 velocities...

897 856 41 1
896 851 45 2
895 857 38 3
895 852 43 4
895 852 43 5
895 851 44 6
894 856 38 7
894 854 40 8
893 857 36 9
893 851 42 10
--------- 41 Mean
--------- 2.9 Std. Dev.
--------- 0.93 Std Dev Mean

874 843 31 1
874 839 35 2
872 844 28 3
871 839 32 4
870 838 32 5
865 838 27 6
865 837 28 7
864 828 36 8
862 832 30 9
861 831 30 10
--------- 30.9 Mean
--------- 3.0 Std. Dev.
--------- 0.94 Std Dev Mean

(1)So the difference in BC's is due to only a difference of about 10fps between two chronys.

(2) The Standard Deviations of these two different strings of 10 are not statistically significantly different.

Joined: February 4th, 2005, 11:51 pm
Without a doubt Harry's data shows a great difference in BC by just a slight change in velocity.

However, the dynamics of ballistics are complex. The data does not prove that there is no dependency on different guns. In fact that seems likely too.

It is also likely that a pellet with the same weight, but a different brand would start out at roughly the same muzzle velocity. The BC would be different and the change in the BC over the velocity drop would be different.

So no ONE cause ... there are many interactions
The differences between guns are going to be obturation from the bore. From Harry's data, that effect pales in comparison. No way changing the pellet diameter 0.001 is going to get these kind of BC changes.

You introduce a third factor that Harry and I both held constant, a different shaped pellet. Everyone knows a wadcutter has poorer BC than a spitzer of the same weight. No news there.

Joined: February 4th, 2005, 11:51 pm
Quick paired T test on first and last 10 velocities...

897 856 41 1
896 851 45 2
895 857 38 3
895 852 43 4
895 852 43 5
895 851 44 6
894 856 38 7
894 854 40 8
893 857 36 9
893 851 42 10
--------- 41 Mean
--------- 2.9 Std. Dev.
--------- 0.93 Std Dev Mean

874 843 31 1
874 839 35 2
872 844 28 3
871 839 32 4
870 838 32 5
865 838 27 6
865 837 28 7
864 828 36 8
862 832 30 9
861 831 30 10
--------- 30.9 Mean
--------- 3.0 Std. Dev.
--------- 0.94 Std Dev Mean

(1)So the difference in BC's is due to only a difference of about 10fps between two chronys.

(2) The Standard Deviations of these two different strings of 10 are not statistically significantly different.

Harry used one chrony, not two, he said. Dunno why you said 'two chronys' please explain.

The uniformity of the first and last strings of ten tell me that Harry's results are statistically significant. That is, we can trust that the BC is changing due to velocity and not some other factor.

Joined: May 1st, 2008, 3:43 pm
which may be of some interest to those who didn't see it before.

Shot with one rifle and one pellet type JSB Exact 15.9 gr.

The 40 shots are rank ordered according to near range velocity. Each shot shows near range velocity at 6 ft and far range velocity at 36 ft and the BC for that individual shot.

The right side column shows mean near range velocity, average Mach number and average BC for each ten shots according to their ranked number
(not the order of shooting) and so are random in terms of possible environmental changes.

Errata: the # 4 shot from the top should read BC .0254

[/IMG]

It can be seen that there is a trend for BC to go up as near range velocity goes down. It should be noted that muzzle velocity would be some 6+ fps faster than at near range. The velocity range brackets the velocity of 875 fps to 880 fps favored by many shooters as being a desirable velocity for precision shooting. ......... Kind regards, Yrrah.
So you're absolutely certain that both chronys are absolutely accurate.

Joined: March 6th, 2009, 8:57 pm
Harry used one chrony, not two, he said. Dunno why you said 'two chronys' please explain.

The uniformity of the first and last strings of ten tell me that Harry's results are statistically significant. That is, we can trust that the BC is changing due to velocity and not some other factor.
Harry didn't explicitly say if he used one chrony or two. He also didn't mention the gun, although I assume a PCP running on one fill of air.

Harry did say "Each shot shows near range velocity at 6 ft and far range velocity at 36 ft and the BC for that individual shot."

I ASSUMED that the velocity of "each shot" was measured at two different ranges, and the BC calculated. Hence two chronys.

My assumption may be wrong. I hope Harry will clarify this point.

Joined: March 6th, 2009, 8:57 pm
The differences between guns are going to be obturation from the bore. From Harry's data, that effect pales in comparison. No way changing the pellet diameter 0.001 is going to get these kind of BC changes.

You introduce a third factor that Harry and I both held constant, a different shaped pellet. Everyone knows a wadcutter has poorer BC than a spitzer of the same weight. No news there.
Sorry to be obtuse.

The point that I was trying to make was simply that there seems to be some quirky marriage between a particular brand of pellets and a particular type of gun.

It wouldn't surprise me to find out that the group size for GUN B shooting the JSB pellet was different. If gun B shoots a much better group size, then it seems possible that the pellet's flight is more stable. More stable flight might have different BC.

I certainly can not prove at this point that the guns makes as much difference, or any significant difference. Obviously the test between guns would have to be done with the same pellet in same velocity range.

All I'm saying is that we'd have to shoot a number of different types of guns and determine the results. You can't say that there is no difference between guns just because there is a dependency on velocity.

-------
For example, the data from Straight Shooters for the Benjamin Sheridan Marauder

JSP Exact, 15.9 grains, 862 fps muzzle, 0.016 for BC

The gun used in Harry's data had a muzzle velocity at low end of about 865 fps with BC of 0.0348

We of course don't know what other experimental conditions changed. But it should give one pause and keep one from saying that there is no difference between guns.