Provide room for a long ogive

Friday, April 5th, 2019

Anthony Williams explains the importance of bullet shape:

A very basic refresher: the rate at which a bullet slows down in the air is determined by the ballistic coefficient; the higher the BC, the lower the velocity loss and the further the bullet will fly. That is, “other things being equal” — always an important qualification because there are so many variables. The BC is calculated from two other numbers, the sectional density (SD) and the form factor (FF). The SD is simple to calculate as it measures the bullet weight compared with the calibre; a 100 grain 30 cal bullet will have half the SD of a 200 grain 30 cal. The higher the SD, the better for long-range performance. The FF measures the shape of the bullet; it is not simple to calculate and its effect varies with velocity, but at a basic level it’s really common sense — a bullet with a long pointed nose, or ogive, is likely to have a better FF than one with a blunt ogive, especially at supersonic velocities. It’s the FF that I want to talk about.

I looked around for examples of bullets which are as alike as possible except in their shape in order to illustrate the importance of the FF, and found the two .50 cal bullets from Barnes Bullets shown on the screen. They are both made from solid brass to the same standards and both weigh the same — 750 grains. Barnes helpfully provides the BCs for this pair, so it’s a simple matter to feed the data into a standard ballistic calculator in order to work out the effect of the different shape. The results of this are interesting.

Barnes .50-Caliber Bullets

There are various ways of assessing the effective range of ammunition, one of them being the impact energy of the bullet on the target. The long bullet shown here has the same impact energy at 2,000 metres as the shorter bullet has at just over 1,400 metres. By this measure, that amounts to a 40% increase in effective range from using the long bullet rather than the shorter one — and it’s free! No extra ammunition weight, no extra recoil. The catch is, of course that the shorter bullet has been designed to keep within the official maximum overall length of the .50 Browning cartridge, so that the ammunition can be loaded into magazines and will function in gun actions; loaded with the long bullet, the cartridge can only be used in specialised single-shot rifles.

This problem of a short cartridge overall length, which prevents the most efficient, low-drag bullets being used, applies to at least some degree to all NATO rifle and machine gun ammunition. The long-range performance of all of these rounds is inherently limited by their inability to use such bullets. Their bullets all have quite short ogives which results in poor FFs and therefore poor BCs. The only way to improve the BC of bullets for these rounds is to use heavier bullets to increase the SD, but that puts up ammunition weight and recoil and results in a lower muzzle velocity and steeper trajectory.

NATO Small Arms Ammunition

The .338 Lapua Magnum has become the international standard long-range sniping round, but it was designed for bullets of up to 250 grains and doesn’t allow enough space for well-shaped versions of the 300 grain bullets which are becoming increasingly popular. It is interesting that General Dynamics selected the relatively obscure .338 Norma Magnum for their Lightweight Medium Machine Gun. I have heard various reasons why they chose the Norma round but one is incontrovertible; the shorter Norma case permits the use of bullets with a longer ogive, giving it the potential for a superior long-range performance.

The next slide is where things get really interesting. The standard 7.62mm NATO cartridge and its M80 bullet are shown at the top. The other pair illustrate one of my favourite examples of the merits of unconventional thinking. The Voss bullet was designed by a German ballistician, Dr Gunther Voss, in the early 1950s, when he was working for the Spanish CETME organisation. He wanted to develop a cartridge which combined a long range with a recoil light enough to permit controllable automatic rifle fire. He reasoned that for the recoil to be kept low, the bullet would have to be as light as possible, but as that would give it a poor sectional density, to achieve a long range would require giving it the best possible form factor. So his bullet is made of solid aluminium with a copper jacket over most of its length. It actually weighs 106.5 grains, which is less than the stumpy little .30 Carbine bullet, but the shape is so good that the BC is only a little lower than the 7.62 M80 which weighs 147 grains. Because the bullet is so light, it doesn’t need much propellant to drive it at a velocity comparable with the 7.62, so it uses a smaller cartridge case, saving yet more weight and further reducing recoil.

Bullet Design M80 versus Voss

By the few accounts I’ve found, Voss’s CETME round did what it was designed to do. In effect, it provided 7.62 NATO performance in a package that was similar in weight and recoil to the short 7.62mm Kalashnikov round. One potential drawback was lack of penetration, but it was claimed to be able to penetrate a contemporary steel helmet at 1,100 metres. I suspect that it might not have done so well against thicknesses of material, such as timber. Unfortunately for Voss, by the time it was ready to roll it was 1953 and the 7.62 NATO round had an unstoppable momentum, flattening all rivals in its path. The irony is that the US Army had wanted a long-range, .30-calibre cartridge with a recoil light enough for controllable automatic fire in a light rifle. The Voss design came very much closer to delivering that than did the 7.62 NATO, purely because of the superb shape of the bullet.

In the early 1970s something very similar was tried by the US Army with the 5.56mm FABRL, shown alongside the contemporary 5.56mm M193. FABRL originally stood for Frankford Arsenal and the Ballistic Research Laboratory, but it was later given the sexier meaning of Future Ammunition for Burst Rifle Launch. The aim was to reduce the recoil of the contemporary 5.56mm ammunition to make the rifles more controllable in burst fire. To achieve this the bullet weight was reduced from 55 to 37 grains by making it from steel with a plastic core, yet the much improved FF meant that the BC remained the same. Little more than half the propellant was needed to match the muzzle velocity of the M193 so the cartridge case could be shortened to leave room for the long bullet, and the chamber pressure was so low (39,000 psi instead of 52,000) that the use of an aluminium case became feasible, leading to an overall reduction in cartridge weight of 50%. The trajectory remained the same, but the recoil impulse was reduced by 35% (equivalent to a reduction in free recoil energy of over 60%).

Bullet Design M193 versus FABRL

The lesson to draw from this is not that all bullets should be made of aluminium or plastic — the two I’ve shown are clearly extreme examples — but that a well-shaped bullet gives you options you don’t have with a typical NATO bullet shape. You can keep the bullet weight the same, and enjoy an improved long-range performance; or if you don’t need to extend the range, you can reduce the bullet weight while still keeping the same BC as the NATO bullet, thereby reducing cartridge weight. If you reduce the bullet weight, you have another choice: you can leave the propellant load and cartridge case the same, and enjoy a higher muzzle velocity and flatter trajectory; or you can keep the MV the same and reduce the propellant load and size of the cartridge case, as in both examples I’ve described, gaining further reductions in recoil and ammunition weight. These are all great choices to have, but you only get them if you adopt a very well-shaped bullet, which means that the cartridge specification has to provide room for using bullets with a long ogive.

In case you didn’t already know — or didn’t deduce it from context — an ogive is a roundly tapered end, like the “point” of a bullet:

In ballistics or aerodynamics, an ogive is a pointed, curved surface mainly used to form the approximately streamlined nose of a bullet or other projectile, reducing air resistance or the drag of air. In fact the French word ogive can be translated as “nose cone” or “warhead”.

The traditional or secant ogive is a surface of revolution of the same curve that forms a Gothic arch; that is, a circular arc, of greater radius than the diameter of the cylindrical section (“shank”), is drawn from the edge of the shank until it intercepts the axis.

If this arc is drawn so that it meets the shank at zero angle (that is, the distance of the centre of the arc from the axis, plus the radius of the shank, equals the radius of the arc), then it is called a tangent or spitzer ogive. This is a very common ogive for high velocity (supersonic) rifle bullets.

The sharpness of this ogive is expressed by the ratio of its radius to the diameter of the cylinder; a value of one half being a hemispherical dome, and larger values being progressively more pointed. Values of 4 to 10 are commonly used in rifles, with 6 being the most common.

Another common ogive for bullets is the elliptical ogive. This is a curve very similar to the spitzer ogive, except that the circular arc is replaced by an ellipse defined in such a way that it meets the axis at exactly 90°. This gives a somewhat rounded nose regardless of the sharpness ratio. An elliptical ogive is normally described in terms of the ratio of the length of the ogive to the diameter of the shank. A ratio of one half would be, once again, a hemisphere. Values close to 1 are common in practice. Elliptical ogives are mainly used in pistol bullets.

Missiles and aircraft generally have much more complex ogives, such as the von Kármán ogive.


  1. Kirk says:

    I think the fundamental thing that I’ve concluded about these questions we’ve been discussing over the last little while is that the process ought to start with first answering the question of “What do I want my projectile to do…? How does that support and integrate with everything else I’m doing in combat, and what trade-offs am I willing to accept?”.

    From that, you design your projectile, then the cartridge case to support the projectile’s design and the ballistics you want from it, followed by designing the weapon itself.

    This back-asswards crap we’re doing where the starting point is “Oh, we’ve got this 5.56X45mm case we’re trying to design around…”, or “Yeah, we want it to be a .30 caliber… For continuity…”? That’s just stupidity squared.

    Start with deciding how you mean to fight, then follow that with your projectile’s ballistic solution, then case design, then weapon. Anything else is essentially half-ass, especially when you try to shoe-horn everything into a legacy design that has roots in the 19th Century.

    What’s really needed, I’m afraid, is a clean-sheet design beginning with the tactics and operational intent of the military. You don’t issue a bullet-hose to troops whose ROE is going to be predicated on precision long-range fire that is going to have to be delivered onto carefully selected targets in among targets you don’t want hit. Likewise, if your tactics are based on mass movement and fire, you don’t issue those masses of troops a weapon that is designed to deliver precision fires in a deliberate manner.

    Horses for courses–And, be damn sure you know what courses you’re meaning to run your horses on.

  2. Phil B says:

    What do I want my projectile to do…? How does that support and integrate with everything else I’m doing in combat, and what trade-offs am I willing to accept?

    That will never work. The British tried that approach and produced the .280 round for both the FN and their EM1/EM2 rifles but America insisted that a cartridge (which became the 7.62 x 51) was essential which duplicated the .30-06 ballistics. America also reneged on their agreement to adopt the FN FAL rifle as a trade off for having their round adopted as a NATO standard round and went for a modernised M1 Garand in the M14.

    Seven years later, the M14 was abandoned and a round that became the 5.56 x 49 NATO, which oddly enough did NOT duplicate the .30-06 was adopted. Once again, this was unilaterally forced onto NATO as the standard round. The British 4.84 x 49 round was rejected out of hand by the Americans (no Goddam faggot Limey rounds here in the good old US of A) for no particular reason that I can find out, other than the “not invented here” attitude.

    Now the Americans are toying with the idea of a 6.5 or the 6.8 Grendel which more or less replicates the ballistics of the British .280 round.

    Welcome to where Britain was in the late 1940′s or early 1950′s …

  3. Bruce says:

    You know how howitzer rounds nowadays have just enough rocket thrust to cancel the vacuum behind the shell and prevent tumbling? With 3-D printing we could do that with long-range rifle bullets.

  4. Alrenous says:

    Wrong measure. You don’t want impact energy. We don’t all go around in chariots with 32 pound cannon on the front. If impact energy were stopping power, then perhaps we would. However, 99% of that energy will be wasted on a human target via overpenetration. Notably, sharp bullets overpenetrate more often. In short range combat you want hollow point bullets: autoflattening rounds.

    At long range, of course you want the longest range possible, but also you can easily make do with single-shot rifles, since they can’t shoot back even if they find you.

    I would prefer a graph of energy delivered to a ballistics gel target as a function of range, which will have a decidedly nonlinear character. If we add in the author’s helmet factor, then you’ll very quickly see there’s no ideal bullet. In medium range your choice will largely depend on your enemy’s favoured tactics.

    In the (unlikely) event they prefer to pepper your forces from 2 klicks away, of course you can’t be satisfied with having to close 600 meters to return fire. If instead they’re usually ambushing you from 1 or less, then having 2 klicks of effective range is merely going to lead to flagrant overpenetration.

    Unfortunately, I also suspect you’ll find that recoil and stopping power are rather closely related. Newton’s third law and all that. You can fire an aerogel filled round at high muzzle velocity if you like, but you’ll be lucky to put out an eye with those.

  5. Anomaly UK says:

    Is that the origin of the widely-used term “form factor”?

  6. Isegoria says:

    Apparently form factor is an old technical term that became popularized:

    One of the first people to properly understand the transmission of light between surfaces was Lambert, in his book Photometria. In that volume (1760) he determined the fraction of light from one surface which was received by another surface, effectively a factor corresponding to the form (shape) of the surfaces. I reckon that some time after this the term “form factor” was used to describe this result, which would have been pretty famous. This became later corrupted by use in forestry, ballistics and high energy physics.

  7. Kirk says:

    I’m going to go out on a limb and wager that the folks who popularized the term for use describing computers, cell phones, and other technological toys likely did not have clue one about any previous usage of the term. It’s a bit of marketing-speak that I suspect was invented independently, and just happens to coincidentally match up with the technical physics terms as well.

    I could be wrong, but I doubt it. There’s just not enough correlation between how the term is used in physics, and how the marketers used it. I’m also vaguely remembering someone having taken credit for coining the term back in the 1980s in one of the magazines like Byte or PC World…

    It also kinda makes sense, when discussing things like motherboard size:

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