[Alternate title: Freeing my inner geek]

Over at Kevin’s place in the comments to this post Ben was wondering if he should choose a bullet with a better Ballistic Coefficient (BC) for Boomershoot. The primary reason for making that sort of decision would be because, in most cases, it would be more tolerant of cross winds. But BC isn’t the only factor to consider. Accuracy and muzzle velocity are obvious considerations as well.

What isn’t so obvious and is difficult to calculate is at what point and under what conditions do you make the choice for one cartridge or another if the low wind tolerant bullet is more accurate than the high wind tolerant bullet? For example, imagine you have two guns to choose from. One is a .223 shooting bullets that, given no wind conditions, you can shoot with 0.5 MOA accuracy. The other is a .300 Win Mag that you can shoot with 0.75 MOA accuracy.

Obviously for any reasonable load in either gun the .300 Win Mag is going to have less wind drift than the .223. But it’s not as accurate. So when do the wind errors add up to enough difference to make the .300 Win Mag the more likely gun to get a bullet on target? It depends on the range of the target, the altitude, the temperature, and how accurately you can estimate the wind. If your wind estimation skills are perfect it doesn’t matter. But if you are perfect wouldn’t be reading this blog post because you already know all the answers.

You can measure everything will good enough accuracy except the wind. But you know that you are probably within say +/- 2 MPH of the true wind speed. So now what? Which gun should you use?

It turns out I worked out the answer several years ago. The expression is not simple, but the calculation is much easier than testing at the range:

In the general case an expression for discovering wind estimation error V_w (in MPH) beyond which, at a given range (R), a less accurate but lower wind drift cartridge is the better choice.  This equation is:

V_w = 1/7563 x SQRT(( E_r2² – E_r1²)/(1/(MV₁ x (F0₁/R – 1.5))² – 1/(MV₂ x (F0₂/R – 1.5))²))

Where for each of the rifles under ideal Boomershoot conditions (3000 feet, 70F):

BC_c = 1.15 x BC
F0 = 166 x BC_c x SQRT(MV)
E_r = Error of the rifle in MOA.
MV = Muzzle velocity in fps.

So get out your calculators and start crunching those numbers!

Or you could just download the spreadsheet I made. But that would be cheating and you wouldn’t feel good about yourself for at least a week.