 Complete formula 
02232011, 12:03 PM

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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

02232011, 12:10 PM

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Re: Complete formula
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02232011, 12:12 PM

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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 1.351.5 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; 02232011 at 12:36 PM.

02232011, 12:26 PM

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Join Date: Sep 2007
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Re: Complete formula
Quote:
Originally Posted by bigngreen

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.

02232011, 01:15 PM

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Join Date: Mar 2007
Posts: 618


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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