Ballistic Coefficients based on G1 model?`

Ballistic Coefficients based on G1 model?`

Joined: March 6th, 2009, 8:57 pm

October 4th, 2009, 3:11 pm #1

QUESTION 1-- Are the ballistic coefficients which are tossed about for pellets based on the G1 model?

Looking at webpage "A Short Course in External Ballistics" at:
http://www.frfrogspad.com/extbal.htm
I noticed that the absolute drag curve for balls (GC curve on top of graph)) about 3/5 way down the page, is very non-linear above about 500fps.

QUESTION 2 - Are diabolo pellets really more like balls (very large drag) then G1 bullets?

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There was also a study by Miller on Round Balls which I have not been able to locate on the internet as of yet.
Ballistics tables for spheres 7.5 to 25 mm (0.3 to 1 in.) in diameter
by Miller, Donald Gabriel, 1927-
Livermore, Calif. : Dept. of Energy, Lawrence Livermore Laboratory ; [Springfield, Va. :b for sale by the National Technical Information Service], 1979. 1979.
Work performed by the UCLLL under contract no. W-7405-ENG-48 Jan. 31, 1979

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Joined: May 12th, 2001, 1:29 pm

October 4th, 2009, 3:27 pm #2

...uses a constant Cd model, in which drag force is proportional to velocity squared.

Despite its simplicity, the accuracy of this approximation for airgun pellets at subsonic speeds has been pretty well verified.

Steve
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Joined: March 6th, 2009, 8:57 pm

October 4th, 2009, 4:09 pm #3

QUESTION 1-- Are the ballistic coefficients which are tossed about for pellets based on the G1 model?

Looking at webpage "A Short Course in External Ballistics" at:
http://www.frfrogspad.com/extbal.htm
I noticed that the absolute drag curve for balls (GC curve on top of graph)) about 3/5 way down the page, is very non-linear above about 500fps.

QUESTION 2 - Are diabolo pellets really more like balls (very large drag) then G1 bullets?

---------------
There was also a study by Miller on Round Balls which I have not been able to locate on the internet as of yet.
Ballistics tables for spheres 7.5 to 25 mm (0.3 to 1 in.) in diameter
by Miller, Donald Gabriel, 1927-
Livermore, Calif. : Dept. of Energy, Lawrence Livermore Laboratory ; [Springfield, Va. :b for sale by the National Technical Information Service], 1979. 1979.
Work performed by the UCLLL under contract no. W-7405-ENG-48 Jan. 31, 1979
The raw data on 9/16 (edit..) inch spheres can also be seen on page 136 of the following pdf file:

Aerodynamic Data for Spinning Projectiles
http://www.dtic.mil/cgi-bin/GetTRDoc?AD ... tTRDoc.pdf

Image:


Looks like "y-axis" is 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.44(?)

The data evidently came from BRL Report 514, by Charters, A.C., and Thomas. R.N., "The Aerodynamic Performance of Small Spheres from Subsonic to High Supersonic Velocities"
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Joined: July 9th, 2001, 12:24 am

October 4th, 2009, 4:24 pm #4

QUESTION 1-- Are the ballistic coefficients which are tossed about for pellets based on the G1 model?

Looking at webpage "A Short Course in External Ballistics" at:
http://www.frfrogspad.com/extbal.htm
I noticed that the absolute drag curve for balls (GC curve on top of graph)) about 3/5 way down the page, is very non-linear above about 500fps.

QUESTION 2 - Are diabolo pellets really more like balls (very large drag) then G1 bullets?

---------------
There was also a study by Miller on Round Balls which I have not been able to locate on the internet as of yet.
Ballistics tables for spheres 7.5 to 25 mm (0.3 to 1 in.) in diameter
by Miller, Donald Gabriel, 1927-
Livermore, Calif. : Dept. of Energy, Lawrence Livermore Laboratory ; [Springfield, Va. :b for sale by the National Technical Information Service], 1979. 1979.
Work performed by the UCLLL under contract no. W-7405-ENG-48 Jan. 31, 1979
I've got a couple of friends who've just written and are now beta testing a new Ballistic Calculator program:
http://ammoguide.com/cgi-bin/bcalcdev.cgi

Use the 'Demo' log in to check it out.

G1 is the general model used (even when not stated). However, as I understand it, Berger Bullets (and maybe some others?) use G7, so that is an option.

So yes, the BCs we toss around are based on the G1 model. And the point you raise seems also right to me, pellets are not well modeled that way. This is no doubt why at least one bullet maker lists 3 different BCs for their bullets based on speed (and I'm told 'in house' programs use even more). Small arms bullets are not really a good fit with the 120 plus YO Krupp model of a one inch diameter, flat base, blunt nose one pound projectile, airgun pellets even further off the mark (which is no doubt why we have BCs of .020 and the like).

http://www.frfrogspad.com/bcdata.htm
http://en.wikipedia.org/wiki/External_ballistics

Yes, G1 poor as it is, is the standard.

Doug Owen
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Joined: March 6th, 2009, 8:57 pm

October 4th, 2009, 4:35 pm #5

...uses a constant Cd model, in which drag force is proportional to velocity squared.

Despite its simplicity, the accuracy of this approximation for airgun pellets at subsonic speeds has been pretty well verified.

Steve
Steve, thanks for the clarification that the BC's are no relative to G1.

But is it really reasonable to assume that the BC is a constant between 400-1000 fps?

Harry showed some data recently in which there was a large change in BC for a small drop in muzzle velocity.

http://www.network54.com/Forum/79537/message/1253695252

Using two chronys maybe 15 yards apart, a PCP could be shot down to 400 fps or so would give enough data to play with. Of course if you determine a BC for your gun in using the muzzle velocity at which you'd shoot, and to the range interest, then the "average BC" would change.

You of course need two chronys so that you can "pair" the readings. The BC would be based on the difference between the two. Thus as the muzzle velocity of the PCP drops, you still get good data.

In part I'm have also looked at the data by pellet and gun at the Straight Shooters website. I've been trying to figure out if at least part of the discrepancy between the BCs for different guns for the same pellet is due to starting muzzle velocity.
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Joined: May 12th, 2001, 1:29 pm

October 4th, 2009, 4:47 pm #6

I've got a couple of friends who've just written and are now beta testing a new Ballistic Calculator program:
http://ammoguide.com/cgi-bin/bcalcdev.cgi

Use the 'Demo' log in to check it out.

G1 is the general model used (even when not stated). However, as I understand it, Berger Bullets (and maybe some others?) use G7, so that is an option.

So yes, the BCs we toss around are based on the G1 model. And the point you raise seems also right to me, pellets are not well modeled that way. This is no doubt why at least one bullet maker lists 3 different BCs for their bullets based on speed (and I'm told 'in house' programs use even more). Small arms bullets are not really a good fit with the 120 plus YO Krupp model of a one inch diameter, flat base, blunt nose one pound projectile, airgun pellets even further off the mark (which is no doubt why we have BCs of .020 and the like).

http://www.frfrogspad.com/bcdata.htm
http://en.wikipedia.org/wiki/External_ballistics

Yes, G1 poor as it is, is the standard.

Doug Owen
...Airgun Expo, Perry Babin, CTAC, etc. exterior ballistic calculators.

So I sort of know whereof I speak.

Steve
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Joined: May 12th, 2001, 1:29 pm

October 4th, 2009, 4:51 pm #7

Steve, thanks for the clarification that the BC's are no relative to G1.

But is it really reasonable to assume that the BC is a constant between 400-1000 fps?

Harry showed some data recently in which there was a large change in BC for a small drop in muzzle velocity.

http://www.network54.com/Forum/79537/message/1253695252

Using two chronys maybe 15 yards apart, a PCP could be shot down to 400 fps or so would give enough data to play with. Of course if you determine a BC for your gun in using the muzzle velocity at which you'd shoot, and to the range interest, then the "average BC" would change.

You of course need two chronys so that you can "pair" the readings. The BC would be based on the difference between the two. Thus as the muzzle velocity of the PCP drops, you still get good data.

In part I'm have also looked at the data by pellet and gun at the Straight Shooters website. I've been trying to figure out if at least part of the discrepancy between the BCs for different guns for the same pellet is due to starting muzzle velocity.
...to beyond 700yds. So yes. I'd say its practical accuracy has been prettywell verified over a wide range of velocities.

Steve
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Joined: March 6th, 2009, 8:57 pm

October 4th, 2009, 4:56 pm #8

I've got a couple of friends who've just written and are now beta testing a new Ballistic Calculator program:
http://ammoguide.com/cgi-bin/bcalcdev.cgi

Use the 'Demo' log in to check it out.

G1 is the general model used (even when not stated). However, as I understand it, Berger Bullets (and maybe some others?) use G7, so that is an option.

So yes, the BCs we toss around are based on the G1 model. And the point you raise seems also right to me, pellets are not well modeled that way. This is no doubt why at least one bullet maker lists 3 different BCs for their bullets based on speed (and I'm told 'in house' programs use even more). Small arms bullets are not really a good fit with the 120 plus YO Krupp model of a one inch diameter, flat base, blunt nose one pound projectile, airgun pellets even further off the mark (which is no doubt why we have BCs of .020 and the like).

http://www.frfrogspad.com/bcdata.htm
http://en.wikipedia.org/wiki/External_ballistics

Yes, G1 poor as it is, is the standard.

Doug Owen
Since the calculators are a black box, it is sort of hard to figure out what is being done.

--------------
I'm certainly not try to trap anyone, but I was reading the Cardew's book "The Airgun from Trigger to Target" last night when the question popped into my head. Around pages 209 and 210 they go into the details of how they calculated the BC. They refer to some ballistic table even they don't really elaborate what it is. It was obviously for some projectile, but the projectile wasn't identified. G1 popped into my mind...

In a couple of places the Cardews noted discrepancies between calculations and experimental data for pellet flight. They offered some explanations but over all they admitted that they didn't really understand the discrepancy. If the BC was changing over velocity, that easily would seem to explain the differences.

-----------------

In physics there is a way to calculate an absolute drag based on velocity drop over a distance, and then convert that to a "BC." In other words, the "form factor" is built into BC.

-----------------

In some of the BC tables, there is data for round balls. Right or wrong, the calculations should at least be some what consistent. The BCs for pellets and the round balls are in the range 0.01-0.03 which is fairly similar. Bullets on the other hand like a 0.22 firearm are in the range 0.1 to 0.3.

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Joined: March 6th, 2009, 8:57 pm

October 4th, 2009, 5:15 pm #9

...Airgun Expo, Perry Babin, CTAC, etc. exterior ballistic calculators.

So I sort of know whereof I speak.

Steve
The Cardew's data for the BC was based on a 10 grain, 0.177 pellet, 700 fps muzzle velocity and a downrange velocity of 600fps at a range of 90 feet.

* Cardew's BC = 0.0225 (using G1? - some sort of table look-up for "standard projectile"...)

* CharirGun2 BC = 0.024

* AirGun Expo calculated (also done by Steve in NC?) = 0.0243 = 0.024
http://www.airgunexpo.com/calc/calc_bcc.cfm?

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Joined: July 9th, 2001, 12:24 am

October 4th, 2009, 5:16 pm #10

Since the calculators are a black box, it is sort of hard to figure out what is being done.

--------------
I'm certainly not try to trap anyone, but I was reading the Cardew's book "The Airgun from Trigger to Target" last night when the question popped into my head. Around pages 209 and 210 they go into the details of how they calculated the BC. They refer to some ballistic table even they don't really elaborate what it is. It was obviously for some projectile, but the projectile wasn't identified. G1 popped into my mind...

In a couple of places the Cardews noted discrepancies between calculations and experimental data for pellet flight. They offered some explanations but over all they admitted that they didn't really understand the discrepancy. If the BC was changing over velocity, that easily would seem to explain the differences.

-----------------

In physics there is a way to calculate an absolute drag based on velocity drop over a distance, and then convert that to a "BC." In other words, the "form factor" is built into BC.

-----------------

In some of the BC tables, there is data for round balls. Right or wrong, the calculations should at least be some what consistent. The BCs for pellets and the round balls are in the range 0.01-0.03 which is fairly similar. Bullets on the other hand like a 0.22 firearm are in the range 0.1 to 0.3.
Funny you should mention the Cardews, John and I were discussing just that last week over lunch (small world and all) trying to figure out how to relate his new Ballistics program to pellets. Based on what we both recalled of the shadowgraphs in the book shock waves seem to shift around with velocity. Perhaps this is changing the drag and therefore BC?

Which is how we got to the multiple BCs relative to speed discussion.

We discussed doing a series of MV drop tests using the Condor at various speeds and then matching MV with other .22s using the same pellet and see what happens to BCs. How much change is gun related and how much speed related?

Fun stuff.

Doug Owen
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