Calculating Ballistic Coefficient

[Stubbers]

I was just working out formulas to calculate BC, one using the Chairgun method, the other using the Pyramyd air method (this sites calculator uses this method as well). Are any of you familiar with either? If not here is a quick peak:

PyramydAir (and the calculator here) uses a very simplified formula from Steve_NC IIRC:
bc = -(100000*(Distance)/(8000*LN(FarVelocity/NearVelocity))/100000

While Chairgun uses:
bc = (AirDensity* Distance) / ( SQRT(FarVelocity) - SQRT(NearVelocity))

Both give similar yet quite different results.

At 50 yards distance between measured velocities, 876 near and 762 far fps, the first formula gives a bc of .0448, while the second formula gives a bc of .0407 using my air density data through Chairgun. Even with more standardized air density, Chairgun calculates .049 bc with the above given data.

Anyone with thoughts or input?

I'd suspect the second formula is more appropriate but maybe someone here knows something I do not.

---

Oh, and what my air density method formula looks like in excel if you want a headache, (or to integrate it into your own spreadsheet) For GA bc

Temp in F, altitude in Ft, Humidity as RH %, Velocity in FPS.

=round((ROUND((((((101325 * EXP(-9.80665 * 0.0289644 * (Altitude*0.3048)/(8.31432 * ((Temp- 32) * 5/9 + 273.15)))-Humidity/100*6.112*EXP((17.67*(Temp- 32) * 5/9 + 273.15-273.15)/((Temp - 32) * 5/9 + 273.15-273.15+243.5))*100)/(287.05*((Temp- 32) * 5/9 + 273.15))+(Humidity/100*6.112*EXP((17.67*(Temp- 32) * 5/9 + 273.15-273.15)/((Temp- 32) * 5/9 + 273.15-273.15+243.5))*100/(461.5*((Temp - 32) * 5/9 + 273.15))))+(Humidity/100*6.112*EXP((17.67*(Temp - 32) * 5/9 + 273.15-273.15)/((Temp- 32) * 5/9 + 273.15-273.15+243.5))*100/(461.5*((Temp - 32) * 5/9 + 273.15))))*0.062428)*0.026068* DistanceYards) / ( SQRT(Near Velocity) - SQRT(Far Velocity)),5)),4)

-Matt

Attached is the above BC calculation which includes air density: Also works with a few other drag laws.

 

[davecole]

I’ve not used Steve’s calc but I’ve used Chairgun, Chairgun Elite and AoA’s (not sure who the author is). I haven’t been able to tell which one is more accurate. I might suggest using the BC from both calcs you are using and compare the distance drop values. (I.e. .012” etc.)
I’m curious as to what the delta value is.
When I started taking TRUE BC seriously (not an internet search results) I did my muzzle at 1 yard and I did my far testing at two distances for comparison; my zero and the farthest distance I would shoot.
For AAFTA FT 30(zero) and 55 yards and XFT 35 (zero) and 100 yards. I found the delta drop pretty much negligible but I ultimately used the BC achieved at the greater distances.

 

[Stubbers]

I’ve not used Steve’s calc but I’ve used Chairgun, Chairgun Elite and AoA’s (not sure who the author is). I haven’t been able to tell which one is more accurate. I might suggest using the BC from both calcs you are using and compare the distance drop values. (I.e. .012” etc.)
I’m curious as to what the delta value is.
When I started taking TRUE BC seriously (not an internet search results) I did my muzzle at 1 yard and I did my far testing at two distances for comparison; my zero and the farthest distance I would shoot.
For AAFTA FT 30(zero) and 55 yards and XFT 35 (zero) and 100 yards. I found the delta drop pretty much negligible but I ultimately used the BC achieved at the greater distances.

AoA's is the same as PA's fwiw.

I just hope to open the discussion of which one is better. If the air density is better, it would be nice to see the calculator here updated.

-Matt

 

[Scotchmo]

The ChairGun version works well as long as you first enter the environmental conditions that were present when you collected the 876fps and 762fps readings. I would use it.

The Pyramydair and AOA calculators have no way to set the environmental conditions, so they won’t be exact. They are probably OK for rough approximations if you collected your data under conditions that were near standard. I would not use them.

 

[Scotchmo]

Another thing: the Pyramydair and AOA versions have no selection for the drag model. So I would assume that they were intended for GA pellets only. The old ChairGun app solves for a number of drag laws, including G1, G7, G8, GA, GC, GL, GS, and RA4.

 

[Stubbers]

Another thing: the Pyramydair and AOA versions have no selection for the drag model. So I would assume that they were intended for GA pellets only. The old ChairGun app solves for a number of drag laws, including G1, G7, G8, GA, GC, GL, GS, and RA4.

Testing, I see no difference between GA and G1

Same distance/muzzle values from above post, but at sea level opposed to my elevation:

GA/G1 = .0492 diabolo pellet/standard model
GL = .0496 ?
GS = .1334 (smooth sphere)
RA4 = .0504 (long rifle?)
GC = .1805 ?
GI = .0519 ?
G7 = .0265 boat-tail?
G8 = .0461 ?
GU = .0457 ?

Any clue to the others purpose? Might reverse calculate a few more for a giggle if I am bored later.

-Matt

 

[Scotchmo]

G1 and GA are very close to each other at typical airgun velocities. They deviate a little from each other at very low velocities. Neither is very accurate in the transonic range as you get above 900 or 950fps. G1 is used by some airgun slug manufacturers. GA is used by some airgun pellet manufacturers. That’s makes for a convenient way to compare airgun slug BCs with airgun pellet BCs.

RA4 works well in the transonic range for rebated and boat tail slugs that are up to two or three calibers long. G7 is probably a little better match once you get much over three calibers long. The value scales of RA4 and G7 are so much different than G1 and GA, that you can’t compare them directly. But there are conversion formulas:

JBM - Calculations - Drag Function Conversion

jbmballistics.com

 

[Ballisticboy]

The Pyramidair method uses the very old constant Cd assumption, not GA or any other drag law, and should never be used these days. It was based on sphere tests at various Reynolds numbers which gave a constant Cd in very low speed tests in various viscous fluids, and completely ignored Mach number effects. The sphere tests were used as they had similar Reynolds number values to pellets.

 

[Stubbers]

The Pyramidair method uses the very old constant Cd assumption, not GA or any other drag law, and should never be used these days. It was based on sphere tests at various Reynolds numbers which gave a constant Cd in very low speed tests in various viscous fluids, and completely ignored Mach number effects.

Ah so the bc calculator being used here, at PA and AoA are antiquated. Does the Air density method used historically by Chairgun have any value or is it missing intrinsic inputs which give lack luster outputs?

I am not a fan of the POI method in practice because, so many factors can induce inconsistent POI's, from barrel droop, bent barrel, imperfect shot angle, turbulent moderator effects on POI, ect.

-Matt

 

[Ballisticboy]

Ah so the bc calculator being used here, at PA and AoA are antiquated. Does the Air density method used historically by Chairgun have any value or is it missing intrinsic inputs which give lack luster outputs?

You would have to ask Harrys_Lad that one.

I am not a fan of the POI method in practice because, so many factors can induce inconsistent POI's, from barrel droop, bent barrel, imperfect shot angle, turbulent moderator effects on POI, ect.

-Matt

It has been well know for years that the POI method is the least accurate method. As you say, there are plenty of factors affecting POI, not just BC. One which many do not know about is a crosswind which will make a pellet land high or low depending on the wind direction, the pellet aerodynamic stability and the barrel twist rate and direction.

 

[Stubbers]

It has been well know for years that the POI method is the least accurate method. As you say, there are plenty of factors affecting POI, not just BC. One which many do not know about is a crosswind which will make a pellet land high or low depending on the wind direction, the pellet aerodynamic stability and the barrel twist rate and direction.

The Eötvös effect too yeah?

-Matt

 

[Ballisticboy]

The Eötvös effect too yeah?

-Matt

Not really for airguns unless you are going for extreme range shooting at the equator off the top of the Andes.

 

[Stubbers]

Not really for airguns unless you are going for extreme range shooting at the equator off the top of the Andes.

I just calculated the effect at 100 yards with a relatively slow moving projectile and got .007MM at my latitude. Hey, it's rather negligible but not nothing! I gotta compensate for the .0003" vertical deflection!

-Matt

 

[Scotchmo]

The Eötvös effect too yeah?

-Matt

If shooting 300yds+, I would account for it.

At my latitude (35.3 degrees) when shooting due East (90 degree azimuth) vs due West (270 degree azimuth), it makes about a 1” vertical difference at 300yds and about a 5” vertical difference at 600yds. That’s with my 7mm, according to Strelok.

 

[Stubbers]

If shooting 300yds+, I would account for it.

At my latitude (35.3 degrees) when shooting due East (90 degree azimuth) vs due West (270 degree azimuth), it makes about a 1” vertical difference at 300yds and about a 5” vertical difference at 600yds. That’s with my 7mm, according to Strelok.

For me its only .01"-.1" @ 40 degree latitude when I calculate Eotvos alone by itself at 600 yard shooting due east, but heck I could be doing it wrong and may need to re-evaluate my calcs.

The Magnus effect or Aerodynamic jump has a much greater effect than Eotvos AFAIK. @Ballisticboy definitely would know better what effects vertical stringing at long ranges more than us.

Sterloks spin drift remains static regardless of projectile velocity, not sure how much stock I put into their calculations. Geoballistics does not show any major vertical drift from 300 or 600 yards from Eotvos alone, but does show a huge difference in spin drift with velocity changes.


-Matt