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Author Topic: Ballistic coefficients
Tony Williams
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Member # 8202

posted 12-13-2000 01:44 PM     Profile for Tony Williams   Author's Homepage     Send New Private Message   Edit/Delete Post   Reply With Quote
Somebody asked me about ballistic coefficients so I though some of you might be interested in the answer.

There are two aspects to "ballistic coefficient". One is the sectional density ratio, the other is a form factor.

The sectional density ratio is a straightforward calculation which compares the projectile weight with the calibre. The formula basically divides the weight by the square of the calibre (there is another multiplier in there which varies depending on the units of measurement being used, to get all SDRs back to a comparable figure). Projectiles of different calibres but with the same SDR will lose velocity at the same rate (and will therefore follow the same trajectories if fired at the same muzzle velocity) provided
that they are aerodynamically comparable.

This brings in the form factor. Clearly, a streamlined bullet has less air resistance than a flat-nosed cylinder, so the SDR is modified by a "form factor" to take account of this. The end result is the ballistic coefficient (BC), which gives an accurate comparator of the rate at which different projectiles are slowed by wind resistance. It is not a simple matter to calculate an exact ballistic coefficient, because the form factor will vary with quite minor changes in projectile shape, but reasonable estimates can be made.

Incidentally, an outcome of these calculations is that for projectiles of exactly the same shape and proportions, the ballistic coefficient improves with increasing calibre in recognition of the fact that (other things being equal) big bullets travel further than little ones.

I'll give some examples from WW2 aircraft guns.

A typical 7.92mm bullet weighed 10g and had an SDR of 0.227
The .50 M2 bullet weighed 46g giving an SDR of 0.406
The 20mm M-Geschoss weighed 92g giving an SDR of 0.327
The 20mm Hispano weighed 130g giving an SDR of 0.462
The standard 30mm M-Geschoss weighed 330g with an SDR of 0.522
The 30mm Hartkern AP round weighed 355g with an SDR of 0.561

Obviously, the higher the figure the better.

Now we come to the tricky bit; the form factor. The only relevant
information I have relates to rifle and pistol bullets, but cannon
projectiles can be guesstimated from their shape. A blunt, round-nose
bullet has a form factor of 1.75, a pointed one around 1.0, a spitzer 0.8 and a match bullet (as streamlined as possible) 0.6. These factors are divided into the SDR to give the BC. The 7.92mm and .50 bullets were well streamlined, let's say 0.75. The cannon shells were blunt and cylindrical, so would be around 1.5. The Hartkern, though, was highly streamlined so would be around 0.75.

This gives the following approximate ballistic coefficients:
7.92 = .30
.50" = .54
20mm M-Geschoss = .22
20mm Hispano = .31
30mm M-Geschoss = .35
30mm Hartkern = .75

There is a direct relationship between BC and velocity loss. A bullet with a BC of .30 will lose 11% of its velocity (+/- 1%) over the first 100m, one of .15 will lose about 22%.

As you can see, their streamlined shape means that the MG bullets show up quite well against the blunt cannon shells despite their smaller calibre. The .50" in particular was a very good long-range gun.


Tony Williams

New book now available: "Rapid Fire: The Development of Automatic Cannon,
Heavy Machine Guns and their Ammunition for Armies, Navies and Air Forces"

Details on my military gun and ammunition website: http://www.users.globalnet.co.uk/~autogun/


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