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# Complete formula

#1
02-23-2011, 12:03 PM
 Silver Member Join Date: Sep 2007 Location: Windsor, CO. USA Posts: 280
Complete formula

Does anyone know where I could look at a formula that incorporates ALL the variables necessary to calculate a bullet's trajectory? I'm talking wind, spin drift, Coriolis, etc. I'm not interested in lengthy derivations, just would like to see how this can be done by hand.

Also, is there a formula that relates twist rate to bullet stability?

Hicks
#2
02-23-2011, 12:10 PM
 Platinum Member Join Date: Nov 2008 Location: SW Montana Posts: 5,802
Re: Complete formula

http://www.longrangehunting.com/gearshop/applied-ballistics-for-long-range-shooting.html

Applied Ballistics for Long Range Shooting by Bryan Litz is what you need!
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#3
02-23-2011, 12:12 PM
 Platinum Member Join Date: Jan 2003 Location: The rifle range, or archery range or behind the computer in Alaska Posts: 3,830
Re: Complete formula

Quote:
 Originally Posted by Hicks Does anyone know where I could look at a formula that incorporates ALL the variables necessary to calculate a bullet's trajectory? I'm talking wind, spin drift, Coriolis, etc. I'm not interested in lengthy derivations, just would like to see how this can be done by hand. Also, is there a formula that relates twist rate to bullet stability? Hicks
If you want to do it easily and quickly by hand without 'lengthy derivations', I suggest you get a hand held computer and use ballistic software. If you really must know, there are good formulas in the Sierra reloading manual 4th addition.

Yes the are formulas that relate to twist rate and bullet stability (see the Miller system below).

([Bullet Weight]*30)/(([Twist Rate]/[Cal])^2*[Cal]^3*[Bullet Length]/[Cal]*(1+([Bullet Length]/[Cal])^2))*([Velocity]/2800)^(.333)*(([Temprature]+460)/(519)*29.92/[Barometric_Pressure])

What you are looking to do with this formula is to apply different twists to come up with a stability factor. 1.0 is concidered barely stable, 1.1 is adequete where 1.35-1.5 is optimum. At least at 1.35 you have some forgivness if you drop major elevation and are in colder temps. A 1.35 could become a 1.2 factor where a 1.1 could become unstable in cold dense enviornments.

Bullet weight in grains, caliber in inches, bullet length in inches, velocity in FPS, Temp in F and barometric pressure in inches of hg.

The greenhill method is easier but not nearly as optimum.
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Last edited by Michael Eichele; 02-23-2011 at 12:36 PM.
#4
02-23-2011, 12:26 PM
 Silver Member Join Date: Sep 2007 Location: Windsor, CO. USA Posts: 280
Re: Complete formula

Quote:
 Originally Posted by bigngreen http://www.longrangehunting.com/gearshop/applied-ballistics-for-long-range-shooting.html Applied Ballistics for Long Range Shooting by Bryan Litz is what you need!

You know, I have that book, and it is excellent, but I don't see in it where every variable he talks about is tied together in a nice pretty formula. Or maybe a set of formulas. He does some seriously indepth treatments of the different variables though. I'd like to see how all these things fit together.
#5
02-23-2011, 01:15 PM
 Official LRH Sponsor Join Date: Mar 2007 Posts: 634
Re: Complete formula

The Miller stability formula, along with corrections for velocity and atmospherics are in the appendix of my book.

If you want a similar formula for calculating trajectories, you're out of luck. The equations of projectile motion must be integrated (solved) numerically, which is an iterative/recursive process best managed by modern computers (the program takes 0.001 second time steps for the whole trajectory). The programs are 100's of lines long, and is not something intended to be done by hand.

Once you have the basic trajectory with tof, you can easily figure out spin drift, coreolis, and other effects with the formulas in my book (appendix). However that basic trajectory is a job for a computer.

-Bryan

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