What's the longest possible spin-stablized projectile, and why?

[neutrino_cannon]

I've been looking into extreme-distance shooting and calibers lately, .408 Chey Tac, .338 Lapua, .50 BMG and the like, and it occurs to me that the ballistic coefficient of the projectiles is quite important.

At the distance of a mere kilometer, a .600 BC .50 BMG bullet will have lost half of its velocity and therefore three quarters of its energy. There are, of course, more streamlined bullets available, IIRC Hornady makes a bullet with a BC in excess of 1.00, but this is only an incremental improvement, not an order of magnitude.

Incidentally, does anyone know how to convert ballistic coefficients to drag coefficients?

Anyhow, seeing as longer bullets seem to have higher BCs, what's the longest possible spin stabilized bullet that could be made for benchrest shooting?

The answer I've heard is six calibers long, but this seems to be one of those gun design "laws" that are based on empirical limits rather than rigorously researched and defined ones.

What happens beyond six calibers? The rifling would have to be tighter, does that make precession more likely? Does tighter rifling run the risk of tearing apart the bullets? Is this anything that more precision, tungsten an gain-twist rifling cannot solve? Remember, these people are shooting 15,000 dollar rifles to begin with, money isn't really an object.
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[MRC_Hans]

I have very limited knowledge of firearms, but basically, the longer the bullet and the faster the spin, cohesion of the projectile and its balance will be come critical. Too low cohesion, and it will disintegrate, too poor balance, and you will get precession. And of course, for a long projectile, precession will have greater impact on drag and precision. I suspect there are a number of trade-offs to work out.

I think the best way to overcome drag is mass. The larger and more massive the bullet, the less drag compared to its inertia. .. because the mass increases with size in the third power, surface only the square.

This confirmed by the fact that even a small cannon can have longer range than the best riffle.

Hans

 

[casebro]

Perhaps long, cylindrical bullets have less efficient aerodynamics? They lose more speed, take longer to get to target, more time for inaccuracies to accrue?

I've got the first 50 Gun Digests. Lots of info. I sure wish there was a digital index.

Lyman's Reloading Handbook might have soemthing.

 

[Darth Rotor]

Perhaps long, cylindrical bullets have less efficient aerodynamics? They lose more speed, take longer to get to target, more time for inaccuracies to accrue?

I've got the first 50 Gun Digests. Lots of info. I sure wish there was a digital index.

Lyman's Reloading Handbook might have soemthing.

Rusty on the details, but the magnum bullets in my 7mm mag deer rifle are shaped like a long, thin football. (American). This shape promotes laminar flow over the projectile (less turbulent flow over the surface) which makes for more efficient flight (reduced drag) and thus less drop over a similar distance than a non "lozenge" shaped projectile with the same initial muzzle velocity.

If your projectiles are already that shape, basically bevelled/pointed/conical and both ends, then switching to that projectile shape will not help your objective.

Your query on rifling, and the number/tightness of turns, excedes my competence.

DR

 

[SirPhilip]

A necked down 50 BMG case to a 6mm rifle projectile at around 300 grains would be feasible, and would likely give an ideal ballistic coefficient while remaining supersonic past 1000yards. If the length of the bullet was an issue, simply use heavier metals. Incidentally, on the subject of ballistic coefficients, heard of the 6.5 Grendel?

 

[mhaze]

Hypersonic and supersonic aerodynamics.

Short answer is L/D ratio matters a lot. But you may find it of interest that a blunt tip, up to 15% of D, actually helps.

 

[Bikewer]

I don't have the math, but you might look into the specs for the new .408 round that they profiled on Futureweapons. Thing retains plus-supersonic speeds to 1.5 miles....

It seems to me as a seat-of-the-pants ballistic guy and occasional flight geek that the profile of highly aerodynamic bullets is very similar, and related to the ideal cross-section of aircraft wings. (at least, in terms of length/width)

I recall that when attempts were being made to break the sound barrier in aircraft, the fuselage design of early designs (like the V-2 rocket) were based on known supersonic projectiles like rifle bullets.
Could be that the drag/turbulence effects increase as length increases.

 

[mhaze]

I don't have the math, but you might look into the specs for the new .408 round that they profiled on Futureweapons. Thing retains plus-supersonic speeds to 1.5 miles....

It seems to me as a seat-of-the-pants ballistic guy and occasional flight geek that the profile of highly aerodynamic bullets is very similar, and related to the ideal cross-section of aircraft wings. (at least, in terms of length/width)

I recall that when attempts were being made to break the sound barrier in aircraft, the fuselage design of early designs (like the V-2 rocket) were based on known supersonic projectiles like rifle bullets.
Could be that the drag/turbulence effects increase as length increases.

I had not heard that of the V2 and think there was a separate development there; but it was certainly the design criteria with the speed of sound breaker of Yeager, the X1. More recently folks have realized that there is an advantage to the overall cross sectional of the aircraft being similar from datum points going back from the nose; thus the Lancair sport aircraft has the canopy in front of the wing - both protruberances from the ideal circular cross section. You ain't got these issues with bullets, only that the front section must be behind the mach wave yet perform at sub and supersonic regimes, and secondly, the various issues relating to L/D, wetted area drag and the ballistic coefficient.

Make'em from depleted uranium....

 

[neutrino_cannon]

It is interesting to note that projectiles made from depleted uranium, which must have as high a sectional density as possible to ensure armor-piercing effectiveness, are not spin-stabilized but fin-stabilized. I don't know if they're more aerodynamic, but given that they're really long and pointy, and that depleted uranium is a little denser than lead, I suspect that the are.

I don't have the math, but you might look into the specs for the new .408 round that they profiled on Futureweapons. Thing retains plus-supersonic speeds to 1.5 miles....

That would be the .408 Chey Tac I mentioned in the OP. Very impressive, although some makers of custom .338 Lapua bullets claim that they can beat it.

I think the best way to overcome drag is mass. The larger and more massive the bullet, the less drag compared to its inertia. .. because the mass increases with size in the third power, surface only the square.

Extreme distance target shooters already use .50 caliber rifles, which is the largest caliber you can use without it being considered a destructive device by the BATFE (unless you have a special exemption as in the case of most shotgun gauges).

Even if the bullets could be made larger without running into legal obstacles, there are human engineering limits to keep in mind here. A rifle chambered in .50 BMG can be shot prone by an average person without undue discomfort, so long as it's on a bipod, weight about 25 pounds and has an enormous honking muzzle brake on the end.

20mm rifles, like the Finnish Lahti anti tank rifle from WWII could probably hold nice tight patterns at range if optimized for it, but they're hardly even man portable.

There's also the issue of the muzzle brake. Muzzle brakes do a fantastic job of taming recoil, but they increase the noise level in the vicinity of the shooter (that's right, they're loudeners) to the point that multiple levels of hearing protection are only doing a so-so job of preventing deafness.

For those reasons, the most practical line of development is more aerodynamic bullets.

Perhaps long, cylindrical bullets have less efficient aerodynamics? They lose more speed, take longer to get to target, more time for inaccuracies to accrue?

I don't think a cylindrical shape is ideal, but since drag coefficients are a function of frontal area, I think bullets with a lot of length compared to their diameter that are pointy on both ends will be less draggy.

A necked down 50 BMG case to a 6mm rifle projectile at around 300 grains would be feasible, and would likely give an ideal ballistic coefficient while remaining supersonic past 1000yards. If the length of the bullet was an issue, simply use heavier metals. Incidentally, on the subject of ballistic coefficients, heard of the 6.5 Grendel?

That would be a fearsome wildcat indeed. Aside from the fact that it would be fantastically noisy, expensive, and produce barrel wear that would make a 220 swift look like a blowgun, you might be looking at diminishing returns on the velocity there. Something like 2 kilometers per second is a fundamental limit for nitrocellulose propelled bullets.

And yes, I am familiar with the 6.5 Grendel. I don't think that their claim that it's the best assault rifle cartridge in the world is hyperbole at all; it clearly beats the pants off the 7.6x39mm, 5.56 NATO and 5.45x39. 6.8 SPC is a little bit closer, but past 500 meters it leaves it in the dust.

Interestingly, if you read about the development of the 6.8 SPC, it is claimed that the earliest designs revolved around a 6mm PPC case necked up to 6.5mm, which is exactly what 6.5 Grendel is!

I don't think that the AR-15 is the ideal platform or the Grendel, though. The bolt face has to be opened up (same bolt face as 7.62x39 AR conversions), and that leaves it too weak to handle hot loads. Bill Alexander, who invented the thing, suggests keeping handloads to under 50,000 PSI, which is pretty low by handloading standards.

There's also the fact that the AR-15/m-16 has no primary extraction, which is not suitable for the very straight-walled Grendel. Ideally, some sort of teflon-based case coating could be used, the same as FN uses on their 5.7x28 brass, but I have no idea how expensive that process is.

Blah blah blah blah blah. The Grendel is cool, needs a new platform, and can't do anything at range that a .260 Remington can't do better.

But yes, it is a good illustration of the importance of intermediate ballistics.

 

[MRC_Hans]

Well, my knowledge of firearms is quickly expended, but I do know a bit about aerodynamics. As for that, there is very little you can do on the rear-end of a projectile. To get a laminar flow at speeds like that, you would need a VERY long rear-end tapering to a needle point, and that is obviously not practical. A flat rear-end with a sharp edge will create a well-defined drag (effectively, there is simply a hard vacuum just behind the projectile) with very limited turbulence.

Hans

 

[neutrino_cannon]

Well, my knowledge of firearms is quickly expended, but I do know a bit about aerodynamics. As for that, there is very little you can do on the rear-end of a projectile. To get a laminar flow at speeds like that, you would need a VERY long rear-end tapering to a needle point, and that is obviously not practical. A flat rear-end with a sharp edge will create a well-defined drag (effectively, there is simply a hard vacuum just behind the projectile) with very limited turbulence.

Hans

You are somewhat correct.

Here is a typical pistol bullet:

A 90 grain Hornady 9mm hollowpoint, ballistic coefficient .099

It would typically be propelled at just over the speed of sound and is optimized for rapid expansion in flesh. It would be unreliable both in terms of accuracy and terminal ballistics beyond 150 meters.

The back end is squared off and (although you can't see it) there is a deep indentation in the front of the bullet to aid expansion.

This is a typical short range rifle bullet:

A 500 grain Hornady .45, ballistic coefficient .287

The nose has been rounded, but the lead core is still exposed to aid in expansion. This is the sort of thing one would use for hunting in thick brush where a shot would never be longer than 300 meters and usually quite a bit closer than that. Depending on the cartridge, one would fire this bullet at 500 meter/sec or so.

Finally, this is a long range target/hunting bullet:

A 105 grain Hornady A-max in 6mm, balistic coefficient .500

Note that the rear of the bullet has been "boat-tailed" to reduce drag, and the entire bullet is coated in molybdenum disulfide to reduce friction with the barrel. This bullet would be fired at two to three times the speed of sound and at such velocities, given a rifle and shooter of sufficient quality, could be expected to be effective at the better part of a kilometer.

The rear end of bullets are meddled with, and there is enough case capacity to put an isentropic spike (I hope I'm using that phrase correctly, aerodynamics are black magic to me) on the trailing end of the bullet. I suspect the reason that this hasn't been done has to do with the spin stabilization.

You will note of course that masses are given in grains and ballistic coefficients, rather than drag coefficients are given. Firearms physics, I think, are dominated by a rather unscientific mindset. "Rules" of firearms design are usually empirical guidelines rather than rigorously defined engineering, and getting a particular system to work is often the result of trial and error. This makes teasing the exact physics of a given situation rather difficult, to say the least.

 

[Soapy Sam]

Pulsars.

Because god is a bowler.

 

[casebro]

I suspect the depleted uranium rounds use fins rather than spin stabilisation due to armor pentrating requirements. It's probable that spinning a projectile 400,000 rpms would cause centrifigal forces to disintegrate the slug before it's energy could melt a hole in the armor. My spin rate is extrapolated from the rate of rifle bullets, and since tank rounds velocities are 2-3 times as fast.
So perhaps DU would be good for long range rifle bullets. But you can bet the military has discarded the idea for some reason. Some trade off that is offset by the need for penetrating armor, but is not beneficial to sniping. Possibly lack of shielding built in to ammo belts? It is depleted, but not totally.

 

[neutrino_cannon]

I suspect the depleted uranium rounds use fins rather than spin stabilisation due to armor pentrating requirements. It's probable that spinning a projectile 400,000 rpms would cause centrifigal forces to disintegrate the slug before it's energy could melt a hole in the armor. My spin rate is extrapolated from the rate of rifle bullets, and since tank rounds velocities are 2-3 times as fast.
So perhaps DU would be good for long range rifle bullets. But you can bet the military has discarded the idea for some reason. Some trade off that is offset by the need for penetrating armor, but is not beneficial to sniping. Possibly lack of shielding built in to ammo belts? It is depleted, but not totally.

The Rheinmetal L55 has a muzzle velocity of 1750 m/s, and most depleted uranium chucking cannons like the older L44 are considerably slower. There are published loads for the 22-243 Middlestead wildcat cartridge that go 1650 m/s. A practical 1500 meter target chambering, like .408 Chey Tac goes a hair short of a kilometer per second, but there are SAAMI approved factory loads; the .220 swift for instance, that exceed 1,200 m/s.

I guarantee you that there are wildcat long range target shooting cartridges that leave the L55 behind. Someone out there has surely necked down a .50 BMG to 6.5mm or something similarly depraved.

I don't buy that the rounds couldn't hold together either. For starters, many ultra high velocity rifle bullets spin in excess of 300,00 RPM, and they're just jacketed lead. Uranium has a higher Young's modulus and a higher shear modulus than lead, and in any case DU rounds are made out of a tungsten/uranium alloy that ought to be rather stronger than straight up uranium.

Also, there are .50 DU rounds.

The reason I've always heard given for why DU rounds or other dart-like projectiles aren't spin stabilized is that past a certain length to caliber ratio, it just doesn't work. What I don't know is why; MRC_Hans has given the most logical answer; namely that the aerodynamic effects of precession upon a relatively long object would be more pronounced than those upon a relatively short one.

 

[DavidS]

The reason I've always heard given for why DU rounds or other dart-like projectiles aren't spin stabilized is that past a certain length to caliber ratio, it just doesn't work. What I don't know is why; MRC_Hans has given the most logical answer; namely that the aerodynamic effects of precession upon a relatively long object would be more pronounced than those upon a relatively short one.

Disclaimer: Lay speculation follows

Drag forces won't be *perfectly* aligned with the projectile's rotational axis. Imperfections in the projectile itself may shift the drag force's line of action and the projectile's center of rotation apart. The relative motion of the projectile through the air may be misaligned with the rotation axis, due to crosswind or increasing vertical velocity due to gravity, resulting in different cross-trajectory drag forces at the head and tail. Any of these would impress a torque on the projectile and cause precession if it were rotating.

Once the projectile starts precessing, its nose and tail follow different trajectories. The airflow and drag gain a larger component across the bullet. The couple formed by drag differences at the head and tail gets larger. The increased torque increases the precession speed and deflection, further increasing the torque and the precession.

That is, a spin-stabilized projectile isn't "stable" in the sense that any misalignment of the spin axis and trajectory, once induced, increases the forces causing misalignment.

Consider a short, fat bullet. Head and tail aren't far apart so torque induced by differing drags at the ends would be "smaller". The fat cross-section yields larger moment of inertia about the trajectory axis. However initiallly induced, precession increases more slowly. If the bullet is really short and fat, misalignment and precession may not increase the total drag that much; it may be almost as draggy frontways as sideways. Spin stabilization might be enough to keep the pointy end in front long enough to do the job.

Consider a long, skinny bullet. Head and tail are far apart, yielding greater torque from misaligned drag forces. The skinny cross-section has smaller moment of inertia about the trajectory axis. Whatever starts it wobbling will more rapidly produce more torque, more precession, and more drag. Because it's long and skinny, misalignment quickly presents more area in the direction of travel, increasing the total drag.

On the other hand, the realigning torque of stabilizing fins increases with increasing misalignment. A long projectile benefits from more realigning torque at small misalignment angle, keeping the total drag low.

That's my story, anyway, worth precisely 2.7 times what you've paid for it.

 

[davefoc]

Would the greater hardness of a DU bullet preclude using rifling groves to impart spin to a DU bullet?

Maybe that problem is easily overcome by making a DU bullet encased in lead?

 

[casebro]

Would the greater hardness of a DU bullet preclude using rifling groves to impart spin to a DU bullet?

Maybe that problem is easily overcome by making a DU bullet encased in lead?

High velocity bullets are cased in copper anyways. Lead will melt in the bore, fouling it with lead build up. Copper is soft enough to catch the lands, yet hard enough to maintain the lead core's shape. Solid lead bullets will soften from the heat caused by air friction, and the centrifigal forces of the spin will vaporise them. At about 4,000 fpm.

 

[neutrino_cannon]

Disclaimer: Lay speculation follows
That's my story, anyway, worth precisely 2.7 times what you've paid for it.

That's the more precise answer of what MRC Hans said, and until I see some experimentation definitively answering this question, this is going to be my provisional explanation. It fits my two criteria for a provisional explanation of anything. 1) It makes sense. 2) I understand it, and therefore am qualified to ascertain that it makes sense.

High velocity bullets are cased in copper anyways. Lead will melt in the bore, fouling it with lead build up. Copper is soft enough to catch the lands, yet hard enough to maintain the lead core's shape. Solid lead bullets will soften from the heat caused by air friction, and the centrifigal forces of the spin will vaporise them. At about 4,000 fpm.

If were pedantic, I would point out that the case is actually the vessel in which the bullet is seated and the gunpowder contained. The copper part of the bullet is properly called the jacket or gilding. Since I am not pedantic, however, I won't point that out.

Incidentally, at the very high velocities (call it 1,200 m/s and up) copper alone becomes unsuitable for jacketing material as it too begins to melt on the rifling (actually, most centerfire rifles do get a little copper in the grooves but it's negligible as long as you clean regularly). Very high velocity bullets are best served with a molybdenum disulfide or teflon lubricant layer on the outside of the jacket. In addition, some very high velocity bullets are made completely out of brass and have no lead core. Apparently, the trade off in ballistic coefficient is worth the improved manufacturing consistency and bullet integrity.

Some ignorant types will try to tell you that teflon coating makes a bullet armor piercing. This is nonsense; a conflation of correlation and causality coupled with a misunderstanding of how body armor works. Any bullet with a muzzle velocity high enough to warrant teflon will penetrate class IIIa body armor at least. Putting teflon on a slow bullet will only reduce its already insignificant barrel friction. Body armor only cares about the mass, integrity, sectional density, and velocity of the incoming round. Teflon coating makes about as much difference to armor penetration as the color of the gun.

That's a thread for another time I suppose.

 

[davefoc]

I had wondered how Teflon coating improved armor penetration. Thanks for the explanation NC.

 

[neutrino_cannon]

As if by magic, this paper floated down from the heaven of the interwebs:

http://www.lima-wiederladetechnik.de/PDF/Kneubuehl.pdf

Now, this paper is filled with terms that I don't understand. Scratch that; the paper is written in an arcane tongue that superficially resembles English, but does in fact not transmit a single bit of semantically meaningful information to a speaker of that language save that they have gone through the unholy rites necessary to be an aerodynamics engineer.

One phrase caught my attention though: gyroscopic stability factor. I typed that into google, and here's what I found:

http://www.nennstiel-ruprecht.de/bullfly/gyrocond.htm

Looks like MRC Hans and David S were right; as a bullet is lengthened, the ratio of its moment of inertia and gyroscopic stability decrease compared to the lever arm of the forces working to throw it off course. The exact length to caliber ratio at which this becomes unacceptable depends upon the shape of the bullet, which is what the first paper attempts to quantify.

This is why, I surmise, match grade target bullets are not always produced with optimum profiles for maximizing ballistic coefficients; such profiles are less stable, and at very long ranges that loss of stability is less desirable than additional velocity.

Edit: This shadowgraph of a .308 bullet shows that other concerns trump aerodynamics as well. The bullet's cannelure, used to ensure consistent crimping, is here clearly causing aerodynamic upset.