Twists of Fate, and Rifling

What separates the winners from the losers is how a person reacts to each new twist of fate.  -Donald J. Trump.

We’re not sure about twists of Fate, but a number of you have asked us about twists of rifling. The question usually comes in the context of AR-15 rifles and their clones, with rifling twists of 1:14. 1:12, 1:9, 1:8 and 1:7 all having been used.

Can you calculate optimum twist for a given caliber and projectile? Yes, you can. There are two equations that are commonly used, Greenhill’s and Miller’s.  Let’s start with the newer one, Miller’s, which was originally proposed in Precision Shooting in March, 2005:

http://www.jbmballistics.com/ballistics/bibliography/articles/miller_stability_1.pdf

Miller assumes a spitzer-pointed, boat-tailed projectile. In Imperial measurements:

T is twist
30 = a constant representing: standard atmospheric conditions, and a bullet speed of approximately Mach 2 (2800 fps at sea level in standard atmospherics). If you need real precision, Miller does provide more complete equations for that, but these approximations work for rifle velocities.
m = projectile mass, decimal grains
s = gyroscopic stability factor
d = diameter, decimal inches
l =  length in calibers (i.e. length is “l” times the caliber of the projo).

Greenhill’s rule dates originally to 1879, and is frequently used by gunsmiths as it is (or was. anyway) taught as part of gunsmithing school, repeated in Hatcher’s Notebook, and included in Patrick Sweeney’s rifle gunsmithing book among many others. Sir Alfred Greenhill of the Royal Armories at Woolwich developed a number of more complex equations. (More complex than Miller’s, too). But he also provided “Greenhill’s rule of thumb.” Sweeney describes this as follows:

“The length of the bullet in calibers, multiplied by the twist rate in calibers per turn, is 150.”

The constant 150 is good for velocities to about 2800 fps. For higher velocities, as often seen with small-caliber rifles, use 180.

Some notes on twist

As a rule of thumb, the more twist, the more stable the bullet. A bullet must meet a threshold of stability to be accurate. The less twist beyond minimal stability, the less accurate the bullet, in theory, but practical accuracy doesn’t drop off until a bullet is very overstabilized. In small calibers, varmint hunters will tell you a too-fast twist will cause bullets to self-destruct from centrifugal force before overspin hurts their accuracy.

You also need enough excess stability to account for atmospheric changes. As a rule, air density decreases with increased altitude above sea level, and air density decreases with rising temperatures. Less dense air needs less spin than more dense air. This is why the original AR-15 prototypes were found to lose accuracy during Arctic testing by the Air Force — important tests for guys who might have to defend ammo igloos in Iceland, antennas in Alaska, or missiles at Minot. These prototypes had barrels made by Winchester for Armalite in 1:14 twist, then the standard .22x varmint-rifle twist (no one pops prairie dogs in -20F weather). A change to 1:12 solved the problem, at least, for 53-55 grain bullets like those in what would become M193 ball ammunition. (Lighter weight tracer rounds have always been hard to stabilize and trajectory match in 5.56mm). The change to 63 grain ammunition drove the change to a 1:7 rifling twist.

These same calculations may not scale to all types of large-caliber, high-velocity artillery pieces such as tank guns. That’s because air is not truly dimensionless; air molecules don’t scale up as projectiles do. Aerodynamicists and exterior ballisticians can compensate for this scale effect by incorporating Reynolds Numbers in their calculations. For rifle ammo, it’s not necessary or useful.

For those who just want a cheat sheet

Simplified from Sweeney, Gunsmithing Rifles, pp. 109-110

5.56 and other .22 centerfires:

Bullet weight grains Twist ratio 1:inches Velocity
> 70 8 any practical
≤ 70 9 any practical
≤ 63 12 any practical
≤ 55 14 any practical
≤ 55 15 ≥ 4100 fps
≤ 55 16 ≥ 4300 fps

Note that this is really for civilian use in “normal” climactic conditions. For military purposes where you must meet a +140ºF/-40ºF standard, you should go one twist increment slower per bullet weight increment, and understand that you will lose some ability to use weights at the extremes removed from your selected optimum round. Not much of a factor in a military application, where the fewer different DODAAC codes (ammunition stock numbers), the better, as far as the logistics elements are concerned.

7.62 NATO and other .308 centerfires:

Bullet weight grains Twist ratio 1:inches Velocity
> 220 8 any practical
≤ 220 9 any practical
≤ 170 12 any practical
≤ 168 14 any practical
≤ 150 15 any practical

Note again that this is for civilian/sporting/normal-climactic-conditions use.  And that it applies to supersonic rounds only. You must redo the calculations for the slow, heavy bullets used in suppressed applications!

For those desirous of plug-in calculators:

For those desirous of more sheet music:

 

25 thoughts on “Twists of Fate, and Rifling

      1. Scott

        I wish. Mainly it means I haven’t been able to get the electricians back out for a few small tasks needful for my final inspection. ‘Tis the season, ho, ho, ho and all that. Hoping to get the certificate of occupancy end of next week. Famous last words.

        (Not only is the holiday season over after the 2nd, but so is deer season. Which is also widely celebrated amongst tradesmen hereabouts. I would celebrate that as well, but I have vowed to not hunt my land until we’re in the house. That is good news (this year) for the deer. It will be bad news for the coyotes, as I will vent my frustrations once we’re moved in.)

  1. Dwight Brown

    I miss “Precision Shooting”.

    Also, Scott: “Not only is the holiday season over after the 2nd…”

    Respectfully, my holiday season lasts through the night of January 6th, aka “Twelfth Night”. At least, that’s the reason I give for not taking down the Christmas decorations until January 7th: it has nothing to do with me being lazy. Nothing at all.

      1. Alan Ward

        We’d keep it up until Chinese New Year, as a nod to the better half’s ethnicity. The outdoor lights stay up +5C or the snow goes. I just unplug the extension cord.

    1. Steve M.

      Dwight, I miss that publication as well, My father worked with a guy who was married to one of the ladies who was involved in the publishing end of things there. He would give my father copies of both Precision Shooting and Accurate Rifle, who would then pass them off to me. I learned a lot from those magazines. Unfortunately, much of the content went far above my head. I wish I didn’t give the magazines away.

  2. looserounds.com

    In all my years of firing and testing sub caliber, very high velocity wildcat rounds with much faster than needed twist rates, I never observed a bullet come apart. With current better designed bullet jackets, its not common anymore. We used to drive some small short bullets VERY fast. Never saw it happen. We even tried to get a 35 grain bullet in a .220 swift driven to an unreasonable velocity to come apart one time. Couldnt get it to happen in a .17 wildcat.

    I will say anything is possible, but anyone using a rifle and ammo, bought from a commercial factory doesn’t need to even think about it happening to them under reasonable circumstances,

    1. Scott

      I’m curious, on sub-caliber, have you heard or read of Bill Eichelberger’s work in that area? It wasn’t until after he died that I found out all he was into. Wasted opportunity on my part…

        1. Scott

          What went on the in the basement of that unassuming little house in King of Prussia… (There were family rumors of a helicopter that was once built down in there.)

          As I understand it, he also signed in blood somewhere (or maybe several places) and was able to obtain the tooling to make / load his own rimfire cases / ammo.

    2. Hillbilly

      Fast twist, high velocity and thin jackets are a bad combo, but that comes down to component choices.
      I do remember reading of Berger bullets blowing up during a long string of fire either F-Class or High Power matches. I know they made the jackets thicker on their Match bullets a number of years back. I had a famous maker 6.5 140 gr. match bullet come apart on me during a 20 round string of fire once it was either round 19 or 20 (It’s been a while).

      Sierra has a 55 grain 22 caliber Blitz they warn should be kept under 3600 and used in conventional twist rate barrels.

    3. DSM

      Hardly a purpose designed and built bullet jacket but the bullet jackets I swage from 22 rimfire cases will most definitely spin themselves into oblivion. Ive had several blow apart anywhere between 25-50m down range. Not ideal of course but it is quite a sight to see the little “poof” of grey as it disentegrates.
      I sort them only by manufacturer (CCI & Rem swage the nicest for me, Federal uses a thicker, more brittle brass so you have to anneal first and then do them one at a time ensuring each is clear the draw die…pain in the rump). It could be an issue that I’ve gone a bridge too far on my annealing but as the other bullets shoot “good enough” I think it’s more of a problem with the original case having been drawn off center or bad brass or whatever.
      Speaking of, I do need to order a spool or two of lead wire this payday so I may continue my wintertime hibernation down into the basement.

    4. Bert

      Take the .22 Hornet 45gr HP (short, soft, thin jacket bullet) and load it in the .220 Swift at max velocity. You will occasionaly see a really cool smoke tracer, leaveing no hole in the 100 yard target.

  3. Aj from NJ

    Hey hognose, this is off topic but as im seeing my secret squirell ninja marsoc raider buddy today, i wanted to ask you about the status of the SCAR rifles and their adoption by DOD as a whole or SOCOM only. I know the newest tribe to the dance seems to favor the .308 heavy, although the aos they operated in were in the stans and on the dark continent. (As you know better than i and have many more sof buddies than i do, they do send the coolest pics for us average joes to drool over).

    Any thoughts on the boondoggle? I hace searched and only come up w an older post on here using thr google.

    Youre the smee!

    From the peoples republic of new germany.

  4. Simon

    I have a number of Orthodox colleagues, so i plan on celebrating a second Christmas on January 6.

  5. Brad

    Trivia questions:

    Does increase in rifling twist rate significantly increase rate of bore erosion? I presume the rotation vector and friction factor of rifling subtracts some fraction of bullet muzzle velocity? In general how much?

  6. Daniel E. Watters

    The hot .22 centerfires used by varmint shooters were not loaded with long ogive, boattail projectiles either. The USAF report that blew the whistle on the AR-15’s original 1-14″ twist noted that the rifling twist would not need to be changed if they changed the projectile shape to a flatbase. However, this change would result in reducing the effective range of the cartridge.

    You didn’t need to hit -20F either to see the difference. Charts from the various test reports published between 1963 and 1968 show that the 1-14″ barrels were less accurate than the 1-12″ barrels at all temperatures. Colt’s revisited the issue in 1967 and found that their 1-14″ barrels gave double the extreme spread. The effect of temperature on bullet stability starts to become dramatic with the 1-14″ twist once you drop below freezing. The US military’s insistance on cold weather performance was due in part to their still fresh memories of the Aleutian Islands, the Battle of the Bulge, the Chosin Reservoir, and other frozen battlefields of WW2 and Korea.

    The issue with tracers is the weight of the tracer compound, which is much lighter than lead. So you end up up with a far longer projectile than the Ball cartridge for the same starting weight. If you want a longer visible trace, then you need an even longer projectile to hold more compound.

  7. Al T.

    Long ago and faraway in another century, I attended the 1991 Small Arms Conference when it was in Atlanta as the FORSCOM representative. As I was one of the very, very few staph pukes who actually shot for fun, I had a blast. One of the DA civilians was interested in chatting as I was one of the few folks there who had fielded both the M16A2 and the M249 SAW in a conventional unit (1/6, 1st BDE, 1st Armored Division). He mentioned that the computer nominated 1 in 7/8 inches as the barrel twist best suited to the M855 projectile, the Big Army Colonel dictated that as only 1 in 7 and 1 in 8 twist barrels were tested, as those were the only two fast twist rates actually shot., that 1 in 7 was the recommendation. And 1 in 7 was more better…. Than 1 in 8 for the tracers.

  8. Bruce

    The 1:7″ twist for M856 tracer is needed because of the LENGTH of the bullet, not its “weight”.Bullet LENGTH is the key factor in all of this stabilization caper. The greater sectional density of the bullet, the shorter it will be for a given shape and mass. Start messing around with things like steel cores and aluminium bullets and things get weird very quickly.

    A classic case is to be found in .,25 Cal bullets. Rifles built to work nicely with the “traditional 87gn SP “sort-of” spitzers, and fitted with 1:14” twist barrels will be a diaster with “modern” 90gn BT HP types. It is NOT the extra THREE grains that causes dinner-plate-sized groups, but the fact that these extra 3 grains are contained in a considerably greater, streamlined length. The (Sierra) 90gn BTHPs are a waste of time in “traditional-twist” .250 Savage, .25-.303 etc. because the combination of slow-twist and “low” muzzle velocity does not impart enough RPMs to stabilize the bullet. The exact same bullet WILL perform in hotter cartridges like the .25-06 and the Weatherby job.

    Tracer bullets have to be long enough to accommodate a useful amount of tracer pellet; i.e. it needs to be still burning past 500 metres.The trick is that, in the real world, tracer, especially a projectile as noticeably different from its ball “companion”, does not have a trajectory which closely matches that of ball ammo.Where your ball rounds are going in relationship to the tracer can probably be established fairly quickly on a nice, controlled firing range.The bigger the projectile, the less difference between the size and shape of Ball vs (useful) Tracer.

    1. LSWCHP

      Yep. 6.5mm projectiles are *long* for calibre. My Zastava 6.5×55 has a 1 in 8 twist to adequately stabilise the heavier and hence very long projectiles. It’s all about the length.

  9. Silence DoGood

    I think it also was Don Miller and Bryan Litz who worked out a formula for a BC correction factor for bullets with a synthetic “ballistic” tip. Neither the Greenhill nor Miller formulas have means of correcting for the change in CG caused by the plastic tip (versus the same bullet with metal all the way to the meplat), causing them to underestimate the CG’s distance from the meplat, hence underestimating the length of the CG-CP moment arm and overestimating the Sg provided by any given twist.

    Litz also has done testing demonstrating that bullets with an Sg of <1.5 don't make the best of their BC because they don't dampen out all nutation, and that wobble — tiny though it might be — still results in enough added drag to prevent them achieving their factory-published BC.

    Hillbilly, Berger's results showed it was a combination of MV and jacket thinness. Twist (under their test conditions) was largely irrelevant. Walt and Eric Stecker (now Berger's HMFIC) were present for the testing and it was Stecker who posted details of the event at the Benchrest Central forums (in a thread titled, "Berger bullet failure test"). Basically, friction against the bore imparts enough heat to the bullet's copper jacket to melt the lead core (Stecker notes that MIT did computer modeling to confirm) and it's just a matter of time until that heat migrates across the jacket's thickness to reach the core. Which happens sooner with thin jackets than with thick, so at the range at which they were shooting, the bullets with the thinnest jackets were failing in flight, while ALL of the bullets with the thickest jackets reached the target. In his write-up, Stecker consistently refers to the core "melting" but lead will reach a plastic state prior to melting, and that plasticity should be enough for centripetal force to throw it out of balance, followed very shortly by the tell-tale puff of gray smoke.

    Brad, the answer is "No." Twist makes no difference to barrel life. Barrels don't wear out from bullet friction, they wear out from what's been called the "blowtorch effect" of the conflagrating powder charge. If bullet friction were a factor, they'd be wearing out from the muzzle, where bullet velocity is highest. But they don't, they wear out from the throat, where bullet velocity is lowest. For that matter, Litz has tested the impact of twist on muzzle velocity and found it to be almost negligible, well less than the SD of any ammunition you can buy of the shelf.

    S,
    1), Overstabilization of hand-held firearm projectiles is a myth. It only occurs with very large caliber rounds (read: tube artillery) fired at very high angles.
    2), The proper term is maximum ordinate, not apogee.

  10. Pingback: Weekend Knowledge Dump- January 6, 2017 | Active Response Training

Comments are closed.