"What is the math for working up BC?"

Sectional Density

Lots of talk about the best pellet for long range shooting here lately. Perhaps we're seeing all this since EBR was just last month, and RMAC not much before that. 

Kind of fun to watch everybody cite their anecdotal experiences and try to make a case for the specific weight and caliber that represents the basket they've put all their eggs into. 

Earlier today, in a somewhat parallel thread, the titular question was asked, "what is the math for BC collection?" As was stated, a true BC from a particular gun/barrel/pellet really has to be collected for that particular setup and can even vary with conditions. As I contemplated all this, it was kind of fun to calculate sectional densities (SD), which doesn't get us too far from an idea of what kind of BC a pellet might be capable of.

I thought I remembered seeing it in a big discussion somewhat lead by R Sterne a while back. An airgun buddy just told me yesterday that he went on the deep dive into that multiple year's long conversation again and I was skimming through it this afternoon in some downtime. Really a lot of good info in that particular discussion. Here it is, if interested: https://www.gatewaytoairguns.org/GTA/index.php?topic=84534.0 

Bob makes the case that the BC is the sectional density/form factor. "and the Form Factor doesn't vary as much as you might think, being 1.0 for the G1 Model , and 1.55 for a roundball, with most good pellets lying in between...."

Yes, yes, diabolo pellets are supposed to use the GA drag model, but out to 100 yards, with the ballistics calculator fiddling that I've done, GA and G1 produce surprisingly similar impact points. 

So, I calculated the SDs of some pellets of interest to myself. Bob teaches that the SD is the weight of a pellet (in pounds) divided by the caliber squared. 

I applied that to some of the stuff I shoot a bunch of.

  • The 15.89grain .20 = SD = 0.00227 (this is the weight of the pellet in pounds)/0.04 (this is the caliber squared) = 0.05675 = I've measured a BC with the speed at two distances method as high a 0.049 with these, so not far off, assuming a form factor as low as 1. 
  • The 10.34grain .177 = SD = 0.00148/0.031329 = 0.04724. The highest I've measured here was 0.035.
  • The 18.13grain .22 = SD = 0.00256/0.0484 = 0.05289. The highest I've measured here was a 0.035. 

Now, lets get into the long range/high power EBR/RMAC type shooters.... It seems that the argument revolves around which is better between the:

  • .22/25.4grain,
  • .25/34grain .
  • 30/44.75grain
  • .30/50.1grain (to a lesser extent than the 44.75s)

Same math as above, applied to those:

  • .22/25.4grain = SD = 0.00363/0.0484 = 0.075
  • .25/25.4grain = SD = 0.00363/0.00625 = 0.05808 (included this one just for fun, doesn't seem like the greatest choice, not being much better than .20/15.89s or .22/18.13s
  • .25/34grain = SD = 0.00486/0.0625 = 0.07776
  • 30/44.75grain = SD = 0.0.00639/0.09 = 0.071
  • .30/50.1grain = SD = 0.00716/0.09 = 0.07956

Sort of interesting to see just how similar those 4 main "best" long range pellets SDs are. 

The specific form factor is where thing's get a bit nebulous and prevents an entirely trustworthy calculation of a BC. 
 
From here:

https://en.wikipedia.org/wiki/Ballistic_coefficient#General

This:

bc1.1636339743.jpg


bc2.1636339755.jpg


bc3.1636339770.jpg


What part of that should we start with? This is the math you need to understand to "work up a BC". Assuming you are going to actually "work one up" in the first place and you are not merely going to explain what a BC "is" actually. That by the way is explained fairly well on the Wikipedia page I linked. It is a quite good read actually. I've scanned it.

Edit: Oh! Lookie, we get a do over. If I can help with these equations, please ask me. It might take me an hour or two to wrap my head around it but I am absolutely certain I can write that code and would be happy to do it.


 
OldCrow, You were asked by admin less than an hour ago not to comment on my posts, and here you are again, commenting (22 minutes ago). 

That lasted a long time.

Your involvement is death to a constructive discussion. I won't comment on any of your posts, please grant me the same respect. 


We were told to stop fighting. We were not asked to not communicate we were told to stop making work.

Here is an olive branch, take it, please. I do understand BC and how the math works. I'd be more than happy to try to respectfully work with you.
 
:"please just stay out of each others topics"

Seems pretty straightforward, yet here you


The thing about the truth is it is not subjective, you don't get to see it the way you want to see it. Here is the whole quote and YES it is pretty straight forward.

Guys

If you two can't maintain a civil conversation… then please just stay out of each others topics. https://www.airgunnation.com/topic/what-is-the-math-for-working-up-bc/?view=all#post-1124368

Period.

Thank you

Ok, you don't want to be friends. Your thread by all means. God bless you.