Ballistics 101: What Is Ballistic Coefficient?

BCs

When a bullet flies through the air, forces called “drag” are exerted upon it. These forces slow down the bullet as it flies, but they don’t act the same way on every bullet. While the subject of aerodynamics is extremely complex, one way to account for differences in bullet drag that is commonly used in the world of small arms is the “ballistic coefficient”.

A ballistic coefficient is a comparative value for a given bullet, showing its relative resistance to drag versus a model projectile that has an empirically established set of drag characteristics. There can be as many model projectiles as there are different bullets, but which ballistic coefficient type is used depends on the model and how good of a match it is for the bullet being measured.

There are nine primary drag models, two of which are commonly used. These are:

G1:
g1

This drag model is one of the oldest, and is the one in most common use by far. However, as its shape suggests, it’s a poor model for most modern bullets.

G2:
g2

This projectile has a conical ogive, which is uncommon among small arms projectiles, but more common in autocannon projectiles.

G5:
g5

The G5 model has a tangent ogive and boattail, making it useful for bullets that share that basic shape. However, it is so close to G7 that it is almost never used.

G6:
g6

The G6 ballistic coefficient is very useful for accurately predicting the behavior of of flat-based tangent ogive bullets, such as the common S-Patrone type military spitzer projectile. However, most outlets erroneously use G1 or G7 BCs for projectiles of this shape.

G7:
g7

The G7 model is the second most common, and is a much more accurate model for modern rifle projectiles than the G1 model. However, even it is overused, being often applied to flat-based bullets that do not really share its shape.

G8:
g8

The G8 model is similar to the G6 model, but for secant-ogive flat-based bullets. It is rarely used due to both secant-ogive flat-based bullets being relatively uncommon, and because of its similarity to the G6 model.

GL:
gl

The GL model is for now-obsolete military round nosed FMJ projectiles. It is almost never used, but could be useful for reconstructing the performance of older military ammunition.

GS:
gs

The GS model is for perfect spheres, and could be used for musketballs and BBs, however very few ballistic calculators support it.

Finally, there’s RA4:
ra4
This model is designed for heeled bullets commonly used in rimfire rounds like the .22 Long Rifle. It is rarely used.

For a given bullet, its ballistic coefficient as matched with an appropriate model can be calculated via the formula below:

Sectional Density / Form Factor = Ballistic Coefficient

We will discuss form factor in a later post, but the important thing to know now is that form factors are not universal. An i7 Form Factor value only works with the G7 ballistic coefficient; you need to use a different form factor for a different ballistic model. Sectional density is, as I’ve covered before, calculated by the formula below:

(Mass of the bullet in grains / (Diameter of the bullet in inches)^2) / 7000

Most ballistic calculators only allow you to use one, or maybe two different ballistic coefficients (G1 and sometimes also G7), but the ballistic calculator at JBM Ballistics allows you to use all of the ones I have discussed here (except GS), plus a GI model that I don’t think I’ve ever seen before. I have gotten really good results from JBM’s calculator, and have used it for all of the ballistic models I’ve produced for TFB. Unlike many other calculators, it properly accounts for the reduction in wave drag that comes as a projectile loses speed, especially in the transonic and subsonic flight regimes. Plus, it has by far the most options of any free calculator I have used.

If you are interested in doing your own calculations, I have over the past several years collected and created ballistic coefficient figures for various projectiles, the list of which you can find in a spreadsheet over at my blog. It is based on a list originally collated by Fr. Frog over at his website, although I started modifying the spreadsheet so long ago now that it’s difficult for me to tell what parts of the work were whose. I do know that for my spreadsheet, much of the original work was done by Brian Litz, so many thanks to him.



Nathaniel F

Nathaniel is a history enthusiast and firearms hobbyist whose primary interest lies in military small arms technological developments beginning with the smokeless powder era. In addition to contributing to The Firearm Blog, he runs 196,800 Revolutions Per Minute, a blog devoted to modern small arms design and theory. He can be reached via email at nathaniel.f@staff.thefirearmblog.com.


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  • Fascinating!

  • Anonymoose

    GL could still be used for classic lever-gun rounds and superheavy hunting bullets like Woodleighs. I found out recently about Hornady’s 220gr .308 that they don’t sell in full cartridge form in the US (you can still buy the bullets for handloading, though).

  • Anthony

    Thanks for the info, but I don’t feel I know what ballistic coefficient is after reading the article. You state, “A ballistic coefficient is a comparative value for a given bullet,
    showing its relative resistance to drag versus a model projectile that
    has an empirically established set of drag characteristics.” Could you give an example? Is a lower number better? What happens when one used the incorrect drag model? What does any given coefficient tell us about a bullet?

    • ostiariusalpha

      “Resistance to drag” gets used a lot in definitions of Ballistic Coefficient, but it would probably be more precise to say that that coefficient measures susceptibility to drag instead; because the lower number does indeed mean that drag has less influence on the projectile. The drag models are a convenient shorthand that allows you to quickly know the coefficient of form for your bullet, but they do so by making some simple presumptions about the geometry of the projectile (boattailed, flat-based, round nose, secant ogive, tangent ogive, etc.). If those assumptions don’t match the actual geometry of the bullet, then you won’t be able to plug in the relevant dimensions to get an accurate coefficient of form. In the end, the ballistic coefficient will only tell you about the abstract trajectory the projectile at a given velocity. It won’t tell you about any empirical factors that the bullet might be affected by, such as air pressure, humidity, wind speed and direction, inclination of the target to the shooter, coriolis, or any potential deflective material like brush or grass. It certainly won’t tell you how your barrel harmonics will effect the flight path, or your spin rate, or especially how the bullet is actually going to perform at termination.

    • ostiariusalpha

      The higher the ballistic coefficient number, the greater the projectile’s resistance to drag; that is the only sense in which it is “better,” since high drag bullets can have beneficial effects on terminal performance at certain ranges. The drag models are a convenient shorthand that allows you to quickly know the coefficient of form for your bullet, but they do so by making some simple presumptions about the geometry of the projectile (boattailed, flat-based, round nose, secant ogive, tangent ogive, etc.). If those assumptions don’t match the actual geometry of the bullet, then you won’t be able to plug in the relevant dimensions to get an accurate coefficient of form. In the end, the ballistic coefficient will only tell you about the abstract trajectory of the projectile at a given velocity and what the retained energy will be at any point in that trajectory. In the real world, you’d have to add in empirical factors that the bullet might be affected by, such as air pressure, humidity, wind speed and direction, inclination of the target to the shooter, or coriolis. It certainly won’t tell you how your barrel harmonics will effect the flight path, or your spin rate, or especially how the bullet is actually going to perform at termination.

    • Hi Anthony, thank you for the feedback. I’ll try to make up for what the article lacked here in this comment.

      Ballistic coefficients are essentially an estimate of how aerodynamically efficient a projectile is. They are derived by comparing a projectile with a known model projectile that has been empirically tested. True ballistic coefficients have to be derived empirically as well, but the resulting value is a very convenient figure for use in ballistic models. Essentially, the value is a modifier, so for example a 0.250 G7 BC means that the projectile flies the same way as the G7 model, but is 1/4th as efficient (i.e., it suffers 4 times as much from drag). Therefore higher BCs are better, while lower Form Factors are better.

      When you use the incorrect drag model, you get an incorrect result. For example, here I have created ballistic outputs for a given bullet, one with G1 and one with G7 BC (note that while G1 can sometimes be approximated as 2 times G7, that is not a true equivalency, although it happens to work here; you can verify it with JBM’s BC converter):

      http://i.imgur.com/rsIaYLa.png

      Now, G7:

      http://i.imgur.com/ZX4iORe.png

      You can see that the G1 gives substantially better results at long range, but this is because the model is a poorer fit. Incidentally, this is one reason manufacturers like using G1, it makes their products look better!

      G6 and G8 are not often used because they aren’t that different than G7, although they can give different results over long enough distances. For example, we know that .30-06 M2 Ball has a .210 G8 BC, which converts to a .202 G7 BC, but the results are still quite different:

      http://i.imgur.com/0Z2Q0lb.png

      http://i.imgur.com/Bw5IkJo.png

      So it is important to use the right drag model!

      Ballistic coefficients can also be accurately approximated by comparing two projectiles of the same shape and adjusting the value based on their relative sectional densities. Since ballistic coefficient is a dimensionless value, all it tells you is just the ballistic coefficient itself. If you also know the sectional density, you can then derive the form factor, and make a guess as to the projectile’s shape characteristics based on that value, but that’s about it.

      And, of course, you can plug the BC into a calculator to learn a lot more about how it flies, too.

      • Freek de Man

        Thanks a lot. I know shooting is as much science as it is a gut feeling of when to “gently squeeze”, but understanding the science really helps.

  • John Yossarian

    I’ve used Fr. Frog’s BC table quite a bit myself. The other information I’ve often needed on bullets, to calculate stability, is bullet length. The best table I’ve found for that is at JBM Ballistics.

  • Wanderlust

    I always thought it would be kind of neat to make an apparatus to measure the actual drag experimentally. Would need some very fast moving compressed air a vertical tube (because if horizontal gravity has some odd effects and a really sensitive strain guage). Still would be really hard to do without some graduate level aero/fluid dynamics technical knowhow. Maybe some graduate student in engineering or physics could make there thesis on this.

  • MPWS

    In courses given in Sprinfield Armory (author J.Rocha) in mid 60’s is following interpretation of the subject: CD = W / i d^2
    where W is weight of projectile [lb]
    i is coefficient of form [1]
    d is diameter of projectile [in]
    On subject of coefficient of form, text states following;
    “The coefficient of form depends upon ratio of the bullet ogive to the bullet diameter and the effect of air resistance on the tip.” There is more in discussion on following pages.

    Other sources such as Rheinmetal book of weaponry is not concerned with BC but instead considers ballistic coefficient based on resistance coefficient which is subject to change pending velocity.

    Certainly it is convenient to use customary BC term since it is important part of ballistic calculation for small arms. However, it appears that wherever is an “empirical estimate” instead of precisely obtained measurements, we are bound to be in some degree of error. Just for interest sake.

  • StraightshooterJeff

    I don’t understand RA4. Heels slug up to bore diameter so the picture above is not a fair representation. Heel bullets become flat base on firing.

  • iksnilol

    Yeah, but what profile provides the most dakka for given velocities?

    I remember reading something about a pointy shape (like the G7) being a waste on pistol cartridges such as 9×19 due to too low velocity. Whilst in other cases a tear drop shaped bullet (reverse G7) was better for subsonic .308 than the standard pointy tip to the front shape.