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  #1  
Old 05-29-2009, 05:51 AM
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Ballistics Math


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Does anyone have a base formula for determining bullet drop given certain muzzle velocities, and I would also be interested in a formula for determining windage with a given windspeed?

As stated in my profile, I'm a big math fan and would like to play around with the math behind ballistics.

Thanks
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  #2  
Old 05-29-2009, 06:19 AM
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Check out:
Hornady.com (Best and easiest to use)-
norma.com ( Will show graphible trajectory, and is user adjustable)-
Eskimo.com ( Very popular)
Biggameinfo.com (OK)
Handloads.com (OK)
Realguns.com (OK)
Just a few that are popular.

Last edited by Uncle Mike; 05-29-2009 at 07:44 AM.
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  #3  
Old 05-29-2009, 07:33 AM
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Mike,

Welcome to the forum. Rules are to join in and have fun and play nicely with the rest of us kids.


Winni,

I'll move this thread to the ballistics forum.

The places Mike directed you to have lots of information and useful calculators. If you are advanced in math and enjoy, as I do, visualizing the shapes described by triple integration or using differential equations to find the equilibrium points that establish projectile stability, position, and drag through its trajectory, you will want to buy and study the late Robert McCoy's, Modern Ballistics. It gets down to the nitty-gritty.

If this is all new to you, the beginning point is that you will discover bullets have a G1 ballistic coefficient (B.C.) or a set of them published by their makers. This number scales your bullet's drag to that of the Gavré Commission's standard projectile, which is an old artillery shell standard shape from the 1800's, and whose B.C. is assigned to be 1.000. As a practical matter, it lets you calculate how many feet it takes for your projectile to lose a certain amount of velocity as compared to the distance that standard projectile would cover while losing the same velocity under the same atmospheric conditions.

For example, it takes the G1 standard projectile 100 yards to drop from 3000 fps to 2904 fps at Army standard meteorological conditions (std. metro.). If your bullet has a B.C. of 0.5 in that velocity range, it will drop from 3000 fps to 2904 fps in 50 yards (100 yards x 0.5). So, the bigger your bullet's B.C. is, the less drag its particular shape and weight have, and the more slowly it will lose velocity, and the less it will be deflected by wind. If the shape of the projectile is different from that of the standard (and they always are, since nothing is made in that antique shell shape these days) then a given G1 B.C. only works over a limited range of velocities. That is why you will see target bullets specified with different B.C.'s over different velocity ranges. Their drag curve shapes just don't match the old shell well at those different velocity ranges and have to be adjusted. It is why most trajectory calculators accommodate those multiple B.C. arguments for calculating trajectories, which they do by piecewise iteration.

The Ballistic Research Laboratory went on to establish standard projectiles with different shapes that more closely match those of modern projectiles. There is a G5 ballistic coefficient that compares your bullet's drag to that of a boattailed radial ogive bullet shape. There is a G7 B.C. that does it for a secant ogive VLD shape. There are B.C.s for straight cylinders and for round balls, too. In each case, the purpose is to have a projectile to scale drag to whose shape matches the drag function of your particular bullet closely enough that just one B.C. works for all velocities in doing the comparison.

Unfortunately, while an increasing number of programs will handle the different types of B.C.'s, bullet manufacturers are not publishing them because their not cross-compatible and don't rank bullet performance across the different standards. That is, a match bullet might have a G1 B.C. of 0.50, but a G7 B.C. of 0.32, because the G7 standard projectile is more aerodynamic than the old G1 standard projectile and doesn't loose velocity as quickly. But a shooter who sees a hunting bullet that has a G1 B.C. published of 0.35 will look at the G7 B.C. for the match bullet of 0.32 and think it doesn't fly as well as the hunting bullet, when it would actually fly about half again better in terms of drag. The manufacturers publish just one old G1 standard so bullet aerodynamics will be ranked by their published B.C.'s. Bigger is better.

Also, be aware that manufacturer's often don't measure real B.C.'s for their bullets, but publish a computer estimate of them. You can use velocity loss measurements to work out actual B.C.s for yourself, including the different G numbers, and may prefer to, as that will give you better predictions for your gun. That is because a measurement will takes into account actual additional drag introduced by tip coning and nutation, bullet jump, jacket slip, and any other factors your particular loading practices and gun may introduce?

The concept of B.C.'s was to curve fit real performance to a standard to help artillery tables and calculators work back before the more complex math of aerodynamics was worked out. It's an ancient system now, but it still in use.

Incidentally, Art Pesja has a method of calculating bullet drop that is more accurate than B.C.'s and software iterative approximation. It comes within about half an inch at 1000 yards. However, it requires you know the real drop of your load at some range significant enough for adequate resolution. At, say, 500 yards. If you don't have a long range for making such tests, the computers and B.C.'s are still your best bet. Art's method is in his book, New Exact Small Arms Ballistics.

Welcome to the wonderful world of ballistics.
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Last edited by unclenick; 07-13-2009 at 08:34 AM. Reason: typo
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Old 05-29-2009, 05:58 PM
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Great info

Thanks so much Nick and thanks to Mike for the links.

Wow, what a wealth of info. I am new at this but I do have a passion for math and I also have a real interest in ballistics. I will do a little more research to try and ID and work out some of the methods you suggested. Even though it may not be as accurate at this time, I will try to learn useing te B1 tables and trying my own calculations in oeder to get a base. Once I understand the math then I will try reading the books you listed.

One question, in order to use Art Pesjas' method, how do you figure drop?..Would you 1) have a long enough range as you alreadt stated, and 2) put the gun in a benchrest while firing to ensure consistency? I assume this would be the only way to measure bullet drop?

Thanks again, I'm sure I'll come up with some more questions as I dig deeper into it, so you have been forewarned.

Thanks
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  #6  
Old 05-29-2009, 08:57 PM
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This site has the external ballistics articles from the last two Sierra manuals.
http://www.exteriorballistics.com/ebexplained/index.cfm

Bye
Jack
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  #7  
Old 05-30-2009, 05:02 PM
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I'll have to review Pesja's method, as I read of it awhile ago in Precision shooting, but haven't had occassion to use it. I just remember that if you knew the drop at one range you could plug in a relatively simple formula based on the fact the drop to that point had already told you enough about the bullet's drag to get very close at other ranges. But I don't see why it wouldn't be adequate simply to know the moa of sight elevation above parallel with the bore needed to hit the middle range?
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  #8  
Old 06-01-2009, 07:06 AM
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Ballistic calculations are extremely complex and vary considerably with bullet shape so that the use of a G1 B.C., although near universal, isn't always the most accurate fit. For a very good description of how the various drag coefficients are used please check out the site found here:

http://www.shootingsoftware.com/coefficients.htm

The bottom line is that trajectory and wind drift are dependant on initial velocity and drag (which changes as velocity changes). Modern military ballistic data is usually based on doppler radar which gives extremely accurate readings regarding the velocity and rate of deceleration.

The most accurate most of us will get is to run a fair number of rounds through 2 chronographs at least 100 yards apart. 200 yards would be better but it would require a fair bit of faith in the accuracy of the rifle at 200 yards. Then by plugging the average velocities of the rounds at 20 feet and 100 or 200 yards into most ballistic programs (I use eskimo.com)you get a pretty accurate estimate of the ballistic coefficient. By using the drag coefficient that best suits the bullet shape you can extrapolate the trajectory and wind drift quite closely but there is NO replacement for actually shooting and learning how your rifle shoots.

Last edited by Kanuck; 06-01-2009 at 07:11 AM.
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  #9  
Old 06-01-2009, 07:05 PM
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IIRC, RSI's Ballistic Lab software (the shootingsoftware.com link you put up) will also let you work out your bullet's own drag function and BC if can gather enough data? It and QuickTARGET Unlimited, which now comes with QuickLOAD, will both match you to any of the BRL drag functions as well as the old G1 drag function. So do the free online JBM ballistics calculators. They let you work them out either from velocity loss or bullet transit time over a known distance.
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Last edited by unclenick; 07-13-2009 at 08:37 AM. Reason: typo
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  #10  
Old 06-02-2009, 10:46 AM
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Thanks everyone for the links and info. I still have not had time to practice playing with the numbers(even if right now they would be hypothetical) due to school. I am currently taking precalc and trig over the summer which are accelerated courses so it is quite a lot of work atm. However, do not think that I am not interested in everything you fine folks post, because I am going to try this stuff out. My main goal with the rifle is to be as accurate as possible even at great distance. Guns/weapons have been a hobby of mine for several years now , but I am just now gettng into being a rifleman. The only ballasicts I have dabbled in was when I was in the Navy. We turned our rear directors into a send/recieve antennae that could track TBM's( Theater Ballistic Missles), but all the math calcs were done by the computers. I want to know how to do it on paper, call me crazy (most people do).

Keeps the info coming..thanks a lot.

Winni
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  #11  
Old 06-03-2009, 05:04 PM
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Well...great stuff....try this for a "back of the envelope" solution using the factory ballistic tables....

Let's say we have a are shooting a round that the ballistic tables say drops 10.2" at 200 yards.....how do we use that information? Well...if the sights were on the centerline of the barrel then all we would have to do is to raise the rear sight enough to bring the point of impact up 10.2". On the other hand, most sights are mounted above the centerline of the barrel. Typically 1.5". So we would have to adjust the sights to cause the point of impact to be 11.7".


Now...for that to apply to any other range, just multiply the number by 11.7 and divide by 200. For this to apply to hold over, consider a range of 400 yards. This would be 11.7 x 400 or 4,680 divided by 200 or 23.4. If the ballistic table lists bullet drop at 400 yards to be 47.8" then hold over by 24.4" for the 200 yard zeroed rifle.

btw...24-25 inches is the boiler room for a good sized deer.
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  #12  
Old 06-03-2009, 06:59 PM
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You forgot to mention the 23.4" is subtracted from the table's 47.8" drop to give the 24.4" holdover.

23.4" is just the same elevation correction in moa at 400 yards as 11.2" is at 200 yards. Since that elevation already partly corrects for the range table drop, it has to be subtracted from the range table drop to find what is left over to be corrected by hold over.
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