Ballistics 101: What is Form Factor?

BCs

In the second installment of Ballistics 101, we took a look at the concept of a “ballistic coefficient”, or a drag model based on an empirically tested projectile, against which other projectiles can be measured and compared. Mentioned in that post – but not explained – was the concept of form factor, which is the subject of today’s installment.

If ballistic coefficient indicates how well a given projectile resists drag when compared to the model projectile, form factor indicates how much more or less aerodynamic that projectile’s shape is than the model projectile’s. The important difference between the two is that form factor exists irrespective of sectional density (SD). Form factor does not tell you how well a projectile resists air drag, but it does indicate how efficient a projectile with that shape and of a given sectional density will be. It’s important to note that form factors are specific to their respective ballistic coefficients; we’ll see why in a minute.

Let’s take an example. The 147gr bullet of 7.62mm M80 Ball has a ballistic coefficient of approximately 0.200 G7. We can calculate its sectional density using the common formula of bullet weight / (projectile diameter)^2 / 7000:

147 gr / (0.308 in)^2 / 7000 gr/lb = 0.221 lb/in^2

Now the G7 ballistic coefficient and the i7 form factor* are related, but the i7 form factor exists without respect to the sectional density, whereas SD is a factor in calculating ballistic coefficient. This means to get the form factor of this bullet, we need to divide the projectile’s sectional density by its G7 BC:

0.221 lb/in^2 SD / 0.200 G7 BC = 1.105 i7 FF

So what is form factor useful for? Well, if you have two bullets of the same shape but difference sizes and/or weights, and you know the ballistic coefficient of one, you can calculate the ballistic coefficient of the other. For example, let’s say we took that 147 gr M80 bullet above, and made one just like it on our lathe, but out of aluminum instead. What would its G7 ballistic coefficient be?

First, we weigh the new bullet and the scale reads 40 grains. Now, we calculate sectional density:

40 gr / (0.308 in)^2 / 7000 gr/lb = 0.060 lb/in^2

We can divide that sectional density by the i7 FF for M80 shown above to derive the G7 BC of the new aluminum bullet:

0.060 lb/in^2 SD / 1.105 i7 FF = 0.055 G7 BC

Wow, that BC is really low! Maybe the new bullet would make a good short-range training round?

*Standard form factor nomenclature is the same as for ballistic coefficients, except with a lower case “i” instead of the upper case “G”; e.g. “a 0.228 G8 BC and 0.95 i8 FF.”



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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  • politicsbyothermeans

    I’m really enjoying this series, Nathaniel. I never learned much beyond the most cursory explanation of some of the terms primarily because the material was, ahem, dry. This is imminently more readable and retainable.

  • Aono

    If the form factor is a measure of ballistic efficiency, is it appropriate to use form factor as an apples-to-apples comparison of the ballistic efficiency between bullets, even of different caliber? I think that it is.

    For example, the Berger 105 6mm Hybrid has a form factor of ~0.924, ever so slightly inferior to the Berger 140 6.5mm Hybrid at ~0.923 but slightly superior to the Berger 130 6.5mm Hybrid at ~0.928.

    Assuming that you could seat all of these bullets within mag length, at the same case depth relative to shank and neck-shoulder junction, and could chamber all of the respective barrels with the same relative distance between projectile ogive and lands, you might predict that the superior form factor efficiency of the Berger 140 compared to the 130, given the same maximum pressure, would result in better external ballistics.

    Where it gets interesting is when comparing different caliber bullets. If you were deciding whether to chamber 6mm Creedmoor vs 6.5 Creedmoor, the form factors would indicate that, all things being equal as described above, the 105 Berger in a 6CM would do the same job as the 140 Berger in 6.5CM with significantly less recoil.

    On the other hand, the more “overbore” (another topic) nature of the 6mm vs the 6.5mm might lead to reduced throat life for the 6CM vs the 6.5CM. And an apples to apples comparison is not truly possible because the powder will not produce the same pressure curve in the same barrel length due to the different bore volumes. Still, as a general principle I think that form factor is still a good metric to employ when making such decisions.

    Side note: I believe that the working definition of a VLD bullet is one that has a form factor lower (lower is better) than 0.950. Supposedly the 5.45 7N6M has a form factor of 0.929, an astonishingly good value that probably also results in a greater tendency to yaw and tumble in tissue. If that is true it is an extraordinarily efficient (and deadly) bullet.

    • PK

      7N6M is indeed an exceptional projectile in terminal performance, especially for a FMJ. Even the original 7N6 is no slouch!

      • Cmex

        It’s a good round, but a tad controversial. I wouldn’t feel undergunned with it.

    • Aono,

      Yes, form factor can approximate the ballistic efficiency of different bullets and calibers. However, remember that what we’re talking about here with both BCs and FFs are very rough empirically derived approximations of extremely complex aerodynamic effects. That means that strange things can happen that completely flout our expectations from BC and FF. For example, boundary layer effects can change the dynamics of smaller caliber bullets, and lead to decreases in form factor when meplats are made too fine, something that runs directly counter to conventional wisdom about VLDs.

      The 7N6 contour bullet has a measured i7 FF of 0.929, according to data from the Aberdeen Proving Grounds. This should be an extremely reliable figure to use, therefore. The 7N6 is one of the best-designed small caliber projectiles ever developed, from an aerodynamic perspective. It’s certainly a model for future small-caliber projectile efforts.

      • ostiariusalpha

        Coefficient of form is a good shortcut to create an approximate ballistic coefficient from, but a coefficient of drag obtained from empirical measurement of actual performance is always going to be more accurate. It’s just that most of us don’t have a finely tuned doppler radar handy, so we make do with an abstract drag model.

      • Aono

        Hornady’s doppler is showing the way, isn’t it? It’s bizarre to me that Sierra, for example, still uses a triple-G1 BC and seems content that their competitor’s chief ballistician is a more authoritative source for ballistic info for Sierra’s products than they themselves are. I don’t know how much Hornady’s doppler cost them, but I do know that the other players need to get on it. Then maybe they could all market actual drag curves and not BCs or FFs and the consumer would have true apple to apples comparisons.

        Hornady’s claims about their new tips are interesting as well, and it seems like the new Flat Line projectiles are setting an entirely new standard for what projectile shapes should be.

    • Baggy270

      I have no idea what you are talking about….seems way too complicated for casual reloader and shooter……I’ll just go by the BC’s the manufacuters give…..

  • MPWS

    This series is really gaining popularity… and serves as good refresher of fading knowledge, at least for me.
    Form factor being part of Ballistic coefficient is “mass-less” representation of bullet and that’s understood by most I guess. What was not discussed so far was mass dislocation within bullet’s shape (due to its construction) which is also part of flight characteristic due to centre of pressure vs. centre of mass relation. Will this be tackled in on of future lectures? I am patient and know it has its order of precedence.

    • PK

      Agreed, this is an excellent refresher every time. A lot of this information just isn’t used commonly or referenced very much at all, and it sort of slips out of the grey matter!

  • michel Baikrich

    good post