Home Forums Hunting & Shooting Ask The Gunwriters Mr Howell... of twist rates, RPMS, etc.

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"Barrel twist rate in correlation to RPMs"

I find it very hard to believe a bullet will somehow gain a faster spin after it leaves the barrel. I was led to believe a bullet's spin rate will be what the rifling gave the bullet, regardless of velocity.
If a bullet is unstable at 1000 FPS, how can an increase to 3000 FPS make it stable? It can't, right? I was led to believe it's the twist rate the stabilizes bullets, not it's velocity/RPM's.
Discussing this with a few other folks is becoming a confusing issue. Your help is greatly appreciated. Thanks. ~~~Suluuq

No, the bullet does not spin faster after it leaves the muzzle. There's no additional force "out there" to spin it faster -- and there's very little retardation force to make it spin slower. So it spins at very nearly the same time-related rate (revolutions per second or per minute) for the full distance of even its extreme trajectory -- especially during the supersonic segment of its travel, during which time a near-vacuum surrounds it.

As the bullet sheds velocity along its way, the spin per unit of time stays very nearly the same -- which means more revolutions per unit of distance traveled, which may seem to some people a "faster spin."

Thanks for bringing this up. I'd just never gotten around to deriving the equations for calculating spin rate from the twist rate and the muzzle velocity. Now -- thanks to your raising the matter -- I have. Even went so far as to construct a Mathcad "work sheet" so that all I have to do now is to plug-in the muzzle velocity and the twist and get -- automatically -- the spin in revolutions per second and per minute.

In these two equations, the constants 12 and 720 incorporate the figures for 12 inches per foot and 60 seconds per minute. In both equations, s = spin rate (per second or per minute), v = muzzle velocity (ft/sec), and t = twist (one turn in t inches).

The spin imparted by twist and velocity is

12 � v � t = s revolutions per second
720 � v � t = s revolutions per minute

If you prefer to use the intuitive approach, start with the fully modular (and most convenient) twelve-inch twist. At any muzzle velocity, from one foot of twist, the spin rate is obviously the same as the velocity. IOW, one turn in one foot of travel is a rate of 3,000 revolutions per second if the velocity at the muzzle is 3,000 feet per second. From a six-inch twist, the same velocity would give the bullet exactly twice as much spin -- 6,000 revolutions per second. A nine-inch twist would spin it 2/3 as fast as the six-inch twist, half-again as fast as the twelve-inch twist. And so on.

Stability is a function of both twist rate and muzzle velocity, therefore there's a certain range or spectrum of twists and velocities that stabilize bullets of any given length. Below that range or spectrum of either element (twist or velocity), the bullet is unstable. Beyond that range or spectrum of twist or velocity, the bullet is over-stabilized and may be spinning too fast for its construction to hold it together. There may also be a narrower range or spectrum, below or beyond which the bullet is less accurate even though it holds itself together and point-on clear out to a distant target.

All this brings to mind several questions that I plan to explore with carefully designed experiments -- such as the maximum spin rates for the accuracy and the integrity of certain bullets. How fast is too fast? IOW, for maximum accuracy and to keep the bullets from becoming brief little gray clouds in the air.

I've just spoken briefly with a friend who, with his mentor, had conducted some experiments along the lines I referred-to above: "... the maximum spin rates for the accuracy and the integrity of certain bullets. How fast is too fast ... for maximum accuracy and to keep the bullets from becoming brief little gray clouds in the air."

With a wildcat cartridge very much like my .220 Howell, these fellows tested the 75-grain Hornady .224 A-Max in several twists at several muzzle velocities. With that bullet, fired from those test barrels, the best accuracy occurred at about 292,000 revolutions per minute, and the bullets flew apart in the air at about 330,000 r/m. The Sierra 80-grain fared better (stronger jacket).

These fellows identified two contributing factors that keep the above figures from being absolute values (valid for other barrels, other bullets, etc):
� quality of the barrel (mainly smoothness of the bore)
� number of lands and grooves (scoring & deformation of jacket)

Smoother rifling and fewer lands and grooves score, distort, or deform the bullet the least, leaving the structural strength of its jacket nearer its best.

In their tests, the 75-grain A-Max fired through an eight-inch twist was most accurate at a muzzle velocity of 3,250 ft/sec (292,500 rev/min). From a similar barrel with a nine-inch twist, the most accurate velocity for this bullet is very likely to be about 3,650 ft/sec (292,000 rev/min).

Just something else to wonder about ...

Ken, several years ago, I saw a article about deformities in cast bullets. The detail showed the effect of pretty substantial notches cut in the bases and noses of both rifle and pistol bullets. The cast bullet article conclusion was that small deformities in the nose of cast bullets probably won't seriously effect cast bullet accuracy. Was that because the notch is so close to the center longitudinal line of the bullet revolution? It would seem that on jacketed bullets driven at 3000fps or so that even small deformations made to the nose would cause them to wobble until they tore themselves apart. Yet, who among us haven't taken a fingernail or knife and wacked off a bent lead tip on a bullet? Why, when these bullets rotate at 300,000 rpm aren't they more suseptable to bullet deformities?

You nailed it, Rolly, with " ... because the notch is so close to the center longitudinal line of the bullet revolution." You can spin a needle a lot faster than you can spin a propeller shaft, for example, without pieces flying off. I once (once too often!) made the mistake of spinning a long-shank small grinding wheel too fast in my high-speed hand grinder. All went well until the sideward pressure on the wheel so upset the balance of its spin that it instantaneously bent the long shaft 90� and slung the wheel off the end of the shank. The grinder was vibrating so wildly that I could hardly hold it. The little grit wheel flew out of its socket at the end of the shank, glanced off my face beside one eye, and went on to hit the wall. The spin was in five figures of RPM but wasn't a problem as long as the mass of that small wheel was centered on (or very close to) the axis of rotation. But once even that small mass got pushed off the axis of rotation, it went wild. I was just lucky that it only scuffed a hole in my face and didn't get the eye. Even after my face and a couple of yards of travel slowed it down, it smacked the wall with a pretty good thump.

IIRC, the physics term that's crucial here is the moment of inertia. If I've got the term wrong, one of the better technical brains around the fire will correct me. AAR, what matters is the radius of the mass in revolution around the axis of revolution. At the tip of the bullet, very little mass is revolving right on or very close to the axis of rotation. A little farther out, a few grains of imbalance make a lot more difference. (This is one of the technological marvels of the turbine blades in a huge jet engine -- even made of titanium, they have to be amazingly well balanced to keep their very fast revolutions from slinging them off their shafts.)

The laws of physics are remarkably simple....break one of these laws and the consequences can sometimes be fatal.

Spinning an unlimited hydroplane propeller at 20,000 rpm, loading one blade at a time as two others ar out of the water subjects this device to incredable stresses, break one blade and twist a 1inch hardened steel shaft into a pretzel faster than you can think it destroying a 30 ft 200mph boat in the process. Imigine the stress an object has at near 300,000 rpm The farther away from the centerline an inbalance is the greater the potential for destruction.


Bullwnkl

Thank you very much, Mr Howell. I did understand a portion of your responce, as I've previously learned it. What I did learn today was that a bullet can be stabilized by a higher velocity. I had thought that could only happen with twist rate, regardless of bullet speed. Thank you for clearing this up. ~~~Suluuq

Using the computer whiz-bang of Mathcad to do all the calculations, I've just put together a table of bullet spin rates (in thousands of revolutions per minute) for twists ranging from six to sixteen inches and muzzle velocities from 2,000 to 4,000 ft/sec. Anybody who'd like to have a copy can send a stamped, addressed 4.2 � 9.5 envelope to me at 407 Spring Street; Stevensville, MT 59870, and I'll run one off for you. (Tried to post it here by copy-and-paste but lost the table format and got a royal mess.)

Mr. Howell, are you aware of how to calculate required spins at different air densities?

Using your 75 gr. Amax example, what would the change in minimum RPM be for a reduction in air density by 15%? Not coincidentally, 15% is the difference between sea-level and 5,000 feet elevation, where I happen do do my shooting. TIA, Dutch.

Dutch, I doubt that the density of the ambient air has any effect on how fast the bullet spins. Remember, at velocities that drape a Mach cone back over the bullet (faster than 1,500--2,000 ft/sec, say), a virtual vacuum surrounds the spinning bullet inside that Mach cone or conical "bow wave." It's not as though the bullet were spinning in a stationary chuck of some kind. My guess is, then, that the equation for revolutions per minute applies equally at mean sea level and atop Everest -- and from the muzzles on fighter aircraft at humongous altitudes. Any difference, I'd think, would be on an order of magnitude not far from that of the gravitational influence exerted by the moon's mass or the drift caused by the rotation of the earth. I'm talkin' wee here! (But what do I know?)

Sir, I agree with your analysis -- I can't imagine the drag on the bullet spin varying substantially due to air density --- the air compressed by the bullet would surely overwhelm that factor.

But, I obviously did not phrase my question understandably; please let me try again. The question comes forth from the fact that the higher the density of a medium, the faster a bullet must spin (revolutions/time) in order to stabilize in that medium. As an illustration, we know that in the field, bullets that are gyroscopically stabilized in the air on the way to the target may lose their stability and yaw (or "tumble") once penetrating tissue. The Vietnam era FMJ 5.5 NATO bullet is a particularly a propos and well-documented example.

Another example comes from 223 match shooters. Some are unable to stabilize the 77 gr. SMK at temperatures below 40 degrees from their space guns. Here, the (denser) colder air requires more spin to stabilize a bullet. The difference in density is very slight (about 2% between 40 and 80 degrees, IIRC), but obviously significant, if you fall off the knife's edge.

With that in mind, if:
*some "air" is lighter than other; and
*heavier mediums require a higher rate of spin for stability;
how does one calculate or approximate the revolutions/time required for stability in "100% density air" vs. "85% density air"? Dutch.

I've been trying to figure out stabalization requirements myself.

I cant figure out if the true requirement is:

Rev/sec/bullet length, regardless of velocity & barrel twist.
Or rev/sec/bullet length/distance travelled
(velocity)

I don't understand what effects VELOCITY has on stab REQUIREMENTS. If any.

It may be too simple. But to me, it would seem that there is a minimum required spin rate for a given bullet to fly with its nose following trajectory.
And velocity plays only a minimum roll.

I would think that a bullet spinning 3500RPS at 4500FPS is just as stable as the same bullet spinning 3500RPS at 3000FPS.
I think Bullet stabalization requirements should be listed in RPS, rather than barrel twist.

If thats true, then we could back off on twist for most wildcats, to keep the bullets intact. We're simply spinning everything way faster than necessary!

What do ya think Ken?

You are right in that a bullet spinning at say 3500 rpm is as stable at all speeds, and if that 3500 keeps bullet stable without wobble it does the job.
So rpms are the factor, but they are given to the bullet by the twist in rifling in the barrel, and combination of twist and muzzle velocity determines rpms.
Velocity slowing down range doesn't slow spin.Very little spin is lost.So in above example you could get 3500 rps by a twist rate of 1 to 12 inches at
3500fps(1 rev of twist per ft).Or you could get same rpms by a twist rate of
1 to 6 inches at 1750fps(2 rev of twist per ft in barrel).Velocity has no great bearing on stabilization requirments, bullet length does. But velocity does
impart the spin in conjunction with twist to stabilize bullet.If bullet isn't
stable you increase twist in barrel and/or velocity.Example, a 458 500 gr bullet in some rifles is a little unstable at 2000 fps with a slow 1 to 22 twist,
but you get it up to 3000fps and rpms increased 50% and it is very stable.
Like my wild cat 458 can do.Ed.

Thanks Ed. Thought I was loosing my mind. The last time I thought about it was 20+yrs ago & thats the way I remembered it.

What I don't really understand, is why I had to revisit it. I'm cruzin along, ordering barrels. And all the sudden I notice that every spin rate calc I have, and all those on the net, and every chating thread, and bullet Mfg, steer around it. Kinda feels like waking up at the drive thru in the morning!

A lot of this discussion can be demonstrated by selecting a group of components which should work reasonably well together. To obtain accuracy we begin with a starting load and work up. Groups will shrink to a smallest group and then begin to open back up as velocity increases. Or take your most accurate load that is not max pressure and work up and back and see what it does to the group size. On a particularly good bench gun you will also have to contend with harmonics and other variables, but the twist and velocity issue can be very neatly demonstrated. Speed is a good thing as long as it is not degrading accuracy. sundog