# calculating bc

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by arrow, Dec 29, 2010.

1. ### arrowWell-Known Member

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i have looked all over and cant find it. is there a search somewhere on this website? maybe im just blind. anyway, how do you calculate the true ballistic coeficient of a given bullet. i know theres given data for many bullets but ive heard that the bc changes for different conditions, velocity and rifles. also if you trim the meplate on a bullet such as the sierra matchking, the bc will change. can someone tell me a way to find the true bc of a given bullet. do you messure velocity at different ranges, or drop from one range to another? please help me out here. thanks in advance.

2. ### FEENIXWell-Known Member

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The formula for calculating the ballistic coefficient for bullets only is as follows:[1][2]
where:

• BCBullets = ballistic coefficient
• SD = sectional density, SD = mass of bullet in pounds or kilograms divided by its caliber squared in inches or meters; units are lb/in2 or kg/m2.
• i = form factor, i = ; (CG ~ 0.5191)
• CB = Drag coefficient of the bullet
• CG = Drag coefficient of the G1 model bullet
• M = Mass of object, lb or kg
• d = diameter of the object, in or m
This BC formula gives the ratio of ballistic efficiency compared to the standard G1 model projectile. The standard projectile originates from the "C" standard reference projectile defined by the German steel, ammunition and armaments manufacturer Krupp in 1881.[3] The G1 model standard projectile has a BC of 1.[4] The French Gavre Commission decided to use this projectile as their first reference projectile, giving the G1 name.[5][6]
A bullet with a high BC will travel farther than one with a low BC since it will retain its velocity better as it flies downrange from the muzzle, will resist the wind better, and will “shoot flatter” (see external ballistics).[7]
When hunting with a rifle, a higher BC is desirable for several reasons. A higher BC results in a flatter trajectory which in turn reduces the effect of errors in estimating the distance to the target. This is particularly important when attempting a clean hit on the vitals of a game animal. If the target animal is closer than estimated, then the bullet will hit higher than expected. Conversely, if the animal is further than estimated the bullet will hit lower than expected. Such a difference in bullet drop can often make the difference between a clean kill and a wounded animal.
This difference in trajectories becomes more critical at longer ranges. For some cartridges, the difference in two bullet designs fired from the same rifle can result in a difference between the two of over 30 cm (1 foot) at 500 meters (550 yards). The difference in impact energy can also be great because kinetic energy depends on the square of the velocity. A bullet with a high BC arrives at the target faster and with more energy than one with a low BC.
Since the higher BC bullet gets to the target faster, it is also less affected by the crosswinds.

(http://en.wikipedia.org/wiki/Ballistic_coefficient)

I like math but I'd leave this to the pros - ballisticians. Personally, I'd go with the published BC (and use programs like what's on this site) and play around with the actual performance, drops, mV, and other factors you want to measure out of your tweaked loads at varying distances. I'm sure the pros will chime in soon.

Good luck!

Ed

Last edited: Dec 29, 2010
3. ### JeffVNWell-Known Member

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I have not been to the site lately and am working from memory, but I recall that the JBM site has a section that allows you to input velocity at distances ( and possibly other variables) and back out a BC.

JeffVN

4. ### Kevin ThomasWell-Known Member

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FEENIX,

A slight history correction to the info you posted from Wikipedia; The Krupp (1881) and Gavre Commision firings (1873-1898) were the first "modern" attempts to determine the effects of atmospheric resistance on the new high velocity jacketed projectiles which were coming into being at that same time frame. Interesting period for ballistic research. Anyway, these and several other studies around the world were all using a roughly similar projectile for most of their firings, a blunt (2-caliber ogive) bullet approximately 3 calibers long, around one inch in diameter and weighing approximately one pound. They were generally refered to by the name of the commision doing the firings, i.e., Krupp, Gavre, or later the newer tables based on these earlier works, such as Russia's Mayevski, or our own Ingalls models. These newer works were also based around the same projectiles used in the earlier firings.

The problems associated with doing the workups on the entire range of different projectiles (including small arms, artillery and even bombs) wre greatly simplified witht he development of computers which could handle the tredious calculus problems involved, and that's when the work really took off. Our own Aberdeen Proving Ground developed a series of drag models for various shapes and properties during the late forties and fifties. Winchester's E.D. Lowrey published a compendium of these tables in 1965, which utilized the series of drag models we still use today; the G1, G2, G5, G6, G7, GL, etc.. The "G" used in the designation for this series was an homage to the work done by the Gavre Commision, but I'm not entirely sure who gave them the moniker. There's a good writeup of this in Hatcher's Notebook, by MG Julian Hatcher. Hatcher was the head of Army Ordnance for many years, and had something of a front row seat to many of these developments, making his perspectives particularly interesting. In that same book, he also has a complete set of Ingalls tables for calculating Ballistic Coefficients using the Ingalls' drag model. This table, incidentally, can be used with the later G1 data and BCs virtually interchangeably, with negligable errors in the final results.

Yeah, I know, I'm a nerd, but things like the comments in Wikipedia drive me nuts!

5. ### MikecrWell-Known Member

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arrow, I don't believe there exists an 'easy way' to predict BC(no rules of thumb). Nor is there an easy way to measure it, or even express it!

The BC formula FEENIX brought in seems simple because it represents only a portion of work involved(the end calc). The "CB" in that formula(or CDtotal, or actual bullet total drag -at your velocities and conditions) does not just fall out of the sky into anyones hands...
Try a calc here for CD to get an idea-> JBM - Calculations

Here you'll find roadblocks like 'ogive radius' which is unknown and not easy to measure & determine with secant ogives. You'll find that meplat diameters matter pretty quick, and that they are difficult to measure with precision needed. Then there is more hidden work, as any BC figured has to be adjusted for air density and muzzle velocity..

And measuring BC is no simple task..
And correctly using/expressing the BC you hold is no simple task..

6. ### arrowWell-Known Member

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alright, so do you just start with the published data, typing that into the ballistic calculator and see how accurate it is? if i had a kestral 4500 and put those atmospheric conditions all into exbal and did a 100 yard zero then shot 300 and just plug in bc numbers until it matches. then try different distances? is this reliable?

if not, what im looking for are numbers people are plugging into exbal. i asume for the smk 175 .308 you would want g7 bc. is this correct? if so what numbers are you using? it will be coming out of a .308 winchester with a 20" barrel. the rifle is being built right now so i dont have velocitys yet. thanks

7. ### paphilWell-Known Member

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Last edited: Dec 29, 2010
8. ### FEENIXWell-Known Member

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Kevin,

I am glad there are nerds like you to keep us all straight. You should call wikipedia and correct them.

Arrow,

Check out this link Precision Ballistic Coefficient Estimator as another source.

Good luck!

Ed

9. ### MikecrWell-Known Member

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You can start with your bullet maker's BC, as correlated with any other sources you can find.
This is often 'rough' because they are not generally qualified.
For example, the maker might list a BC of .460 for your bullet, but without mention of velocity or atmospheric standard(much less bullet lot#), this value was based on. It was probably estimated through math rather than field validated which could introduce a small error as well.
So for you it's a generalization about as accurate as you could eyeball yourself..
But it's a start, and Berger and Lapua are advancing this process for us. Someday it won't be so difficult. Berger has lately listed BCs based on average velocities common to a bullet's use, and this is about the best information available off a bullet box.
For long range bullet's, Bryan Litz(with Berger) has measured, calc'd & tested, and provided results in a very good book: Book
Muzzle velocity is needed for sure to convert G1 BCs to G7, so plan on doing so AFTER load development across a chronograph.

To correct your BC, you could use 2 chronographs to get near & far velocities for calculating BC. This has also been done with an Oehler setup that measures 'time of flight' with a triggering chrono + downrange microphones.
Or you can shoot several distances and tweak your BC inputs to ballistic software for the closest match at all three distances. But counterintuitively, this is actually the least accurate method.
Exbal has a BC validation screen for this, and LoadBase & Pejsa's provide a process for this method as well as the others.

For a 175smk:
Sierra list's it [email protected]+
Sierra Bullets - The Bulletsmiths
I believe Sierra bases this on Standard Metro atmosphere, and converted to ICAO atmosphere this BC becomes .496
Your version of Exbal is one atmosphere standard or the other(or another) so be sure to understand this during use.
An ICAO G1 BC of .496 @ 2800fps converts to a G7 BC of .248 with same qualifiers.
You can do this here: JBM - Calculations - Drag Function Conversion
Bryan concluded a little lower G1/G7 BCs for this bullet in his book. He also provided averaged BCs throughout 1500-3000fps as .475/.243
(I hope to morally provide this info, and not burn in hell)

10. ### BuffalobobWell-Known Member

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I have used that link to calculate the BC on some of the 257 cal Wildcat bullets and then tweaked the answer to account for the rebated part. It comes very close. Of course trying to measure meplat diameter is about as goofy as figuring out exactly where to measure the boattail to get its diameter. None the less the link will get you real close to a good G1 BC and then you extrapolate a G7 from other known bullets and away you go to the range to verify it.

11. ### 270 leftyWell-Known Member

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Holy crap I should have paid more attention in my math classes!!
I'm just happy there are progremmes like exbal & bergers new program.
The interesting thing when I plug all the numbers from my Exbal print off witch is pretty darn close out to 1000yards and put into Bryans program I have to tweek the bc from .750 wildcat 169.5 to .770 to come out with the same drops time of flight ext. but the extra .20 bc adjustment puts every thing within 1/2 foot per second @1000 energy with in 1lbs time of flight nono second off I had goodgrouper do the load work up on Exbal but I used Bryans program on my last hunt adjusted every thing to 10 yard increments got on google earth to make sure elevation was correct. had to guess what temp would be but it paid off our group killed three antelope in 1 hour & 45 minuets fun but our trip was over to fast.

12. ### groperWell-Known Member

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Well i did something interesting today... i took a laptop and a microphone into the trench below the target whilst my friend shot from 1000yds away...

I recorded the soundtrack using "audacity" and then once id collected the data, i used the spectogram waveform to isolate the time difference of the sonic crack of the bullet flying overhead from the muzzle report a short time later.

Using the Time of Flight in the ballisitcs calculator, and the time it takes sound to travel 1000yds @ 26deg C, i could accurately predict his muzzle velocities to less than 1% error assuming we had an accurate BC. I recorded a string of 5 shots and even gave him the extreme spread for his load!

So, Using similar ideology in conjunction with an accurate chrony at the muzzle, we could reverse calculate a G7 BC in the same way. Beleive it or not, it is surprisingly accurate and you can clearly record time differences of .0005 seconds resolution.

Heres an article that explains the idea... - http://arxiv.org/ftp/physics/papers/0601/0601102.pdf

Last edited: Dec 29, 2010
13. ### BuffalobobWell-Known Member

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Amazing idea!!!!!

14. ### WildcatBWell-Known Member

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I read the exact same paper. That's how I plan on measuring our bullets BC's.

In fact, I nudged a kid at school into doing this for his science project. Audacity is free and most people already have a laptop.

I'd just use the time of flight and JBM's Ballistic Coefficient (Time) calculator HERE to get the BC's from the time of flight data from the sound card.

We'll see how it matches with my drop data. I'm also going to use Adobe's Sound Booth to see if the time measurements differ.