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Theory of barrel twist rate and bullet mass and diameter?

Discussion in 'Rifle Country' started by Bill_Rights, Nov 15, 2012.

  1. Bill_Rights

    Bill_Rights Well-Known Member

    We have at least three threads going on now/recently that raise the question of rifling twist rate versus bullet weight. Here they are:

    Thoughts on fast twist 6.8 SPC barrel

    180gr in a .270 Winchester?

    Rossi 92

    What determines the minimum twist rate of a barrel? [For "low" twist rate, I would cite 1 turn in 30 inches, as some old big-bore black powder rifles have. For "high" twist rate, I would cite 1 turn in 7 inches, as some 5.56mm/.223" short-barrel rifles have.]

    How does twist rate play in? I have picked up that, if twist rate is not high enough, the bullet will not "stabilize". [By the way, what do we mean "not stabilize"?] Is that true? (I assume this is true, in extreme cases.)

    But I am seeing people post here on THR that for heavy bullets, you need a higher twist rate than with a light bullet of the same caliber. How's that?

    What is the total picture? What is the theory? I also picked up that smaller calibers have higher twist rate while larger calibers have lower twist rate. Why?

    So it looks like desirable or ideal twist rate depends upon both bullet mass and bullet diameter. Does it also depend upon bullet speed? (expected muzzle velocity?) That is the same as saying that it depends on powder loading of the cartridge. right?

    I know that the absolute spin rate of the flying bullet (rpm, revolutions per minute) is faster the faster the bullet travels. For example, for a 1-in-12" twist rate, a bullet exiting the muzzle at 2000 fps would be spinning at 2000 rotations per second = 2000 rps * 60 sec/min = 120,000 rpm. For the same 1-in-12" twist rate, a bullet exiting the muzzle at 3000 fps would be spinning at 3000 rotations per second = 3000 rps * 60 sec/min = 180,000 rpm.

    I would guess that what matters for in-flight ballistics is the spin rate of the flying bullet, not the twist rate of the barrel, right?

    So what is the formula where bullet mass, bullet diameter and bullet speed factor into the desirable spin speed or twist rate?

    Are there any other factors? I have also picked up here on THR that length of the bullet matters. True? Or is it sectional density or other measurement?

    HELP! I am in the dark here. :confused:
  2. creeper1956

    creeper1956 Well-Known Member

    Yep... yep it does. The Greenhill formula. ;)
  3. Bill_Rights

    Bill_Rights Well-Known Member


    Thanks for the link to EBR's web site. I was unaware of that company. They aer specialists in subsonic performance. This other EBR page on that is interesting. That's handy to know.

    OK, so the Greenhill formula is good - that's what I asked for. Thanks.

    Twist Rate = 150 * SQRT(density) / Bullet-Length

    I notice EBR leaves out the density factor (square root of density is set equal to "1") for rough estimates. They do not give the units of density, like pounds/cu.ft. or grams/cc or whatever. So we couldn't use it if we wanted to.

    This is an empirical formula. I would like a little more detail. I may look up the origin of and more detail on the Greenhill formula, when I get a chance.
  4. creeper1956

    creeper1956 Well-Known Member

    Back when I shot benchrest competition and was based in Phoenix, but would travel all over the country and a few times to Europe, I used the Greenhill (and suggestions from Walt Berger and Gary Ocock) to decide what twist I wanted for the 6mm 68gr Berger HPFB match (6PPC).
    When I had a high paying job :p, I had Shilen make up 3 otherwise identical barrels... one in 1:14, 1:13 and a 1:11.5 so I could experiment as conditions dictated. Here's why.

    Effects of Altitude and Temperature on Rifling Twist, by Dan Lilja.

    Of course, it's far more complicated and ultimately far less precise than your typical perfectionist would like... but it makes for interesting reading. :D

    Cheers Bill. Have fun with it. :evil:
  5. helotaxi

    helotaxi Well-Known Member

    The Greenhill formula works well for relatively short, fat bullets. The Miller stability formula is better applied to typical long range bullets.

    The general rules are the same though. The higher the ratio of the bullet length to the bullet caliber, the faster that it needs to spin in order to achieve gyroscopic stability. The Miller formula accounts for the increase in upset force caused by the fact that the center of aerodynamic force is typically acting forward of the center of mass of a long slender bullet and that the forces trying to cause the bullet to tumble increase with muzzle velocity. The good news is that the increased velocity also increases spin rate for a given rate of twist and the increase in stability imparted by the marginal increase in RPM is higher than the marginal increase in upset force. The overall effect is that once the bullet is going fast enough to be stable from a given rate of twist, increasing velocity increases stability margin.
  6. sansone

    sansone Well-Known Member

    Bill, I realize this explanation is over simplified, forgive me..
    Years ago an old reloader told me bullets that are long for their weight need more spin to stabilize.
  7. helotaxi

    helotaxi Well-Known Member

    Bullets that are long for their caliber need more spin. Weight doesn't matter. A bullet of a given length in a given caliber needs essentially the same amount of spin to be stable whether it is light for its length or heavy for its caliber.
  8. MTMilitiaman

    MTMilitiaman Well-Known Member

    Twist rate depends not so much on bullet mass but on bullet length. It just so happens, however, that when comparing bullets of the same diameter and basic construction, the heavier one tends to be longer.

    The longer a bullet is, the faster the twist rate is needed to stabilize it. Now think of a top spinning on a table. Notice how when it loses enough rotational velocity, it tends to wobble and eventually fall over? Most bullets are heavier towards the base and thus have a tendency to want to fly base forward. The point of rifling is to induce enough spin to make them stable in flight. If the twist rate isn't fast enough for the length of bullet being used, it tends to wobble in flight, and in extreme cases tumbles or keyholes through the air.

    It is much harder to overstabilize a bullet than it is to understabilize it, so you are generally safer erroring on the side of caution and going with a faster twist rate than is necessary than vise versa. You can still shoot 40 and 50 gr varmint bullets from a .223 Rem with a 1:7 twist, but you can't shoot the heavier 69 to 77 gr HPBT Match rounds through a .223 Rem with a 1:12 twist, to give one example.

    Also keep in mind that bullet construction and atmospheric conditions also come into play. For example, the crop of newer homogenous bullets on the market are typically longer for their weight than a traditional lead core bullet of the same mass and caliber because copper is less dense than lead. So lighter homogenous bullet like the Barnes might require a faster twist rate than a heavier lead core bullet in the same caliber. Also, air density matters because the more dense the atmosphere is, the faster a bullet has to be spun to get it stable. Cold air is more dense than warm air, so back when the military was experimenting with Eugene's black rifle, they found a 1:14 twist would stabilize the 55 gr M193 in most conditions, but not in artic conditions. So they went with a slightly faster 1:12.
  9. helotaxi

    helotaxi Well-Known Member

    And when they went to the 62gn FMJ and its corresponding tracer they found that while a 1:9 would work most of the time, a 1:7 was needed when it was silly cold.

    Also, there is no such thing as "overstabilization". You can spin a bullet so fast that you tear it apart, but that is an integrity problem, not a stability problem.
  10. MCMXI

    MCMXI Well-Known Member

    A bullet's stability is definitely affected by it's muzzle velocity. The faster the bullet's velocity, the greater the moment exerted by the air on the bullet in flight which is trying to flip the bullet over (rotate it about its center of mass). The faster the bullet's angular velocity the more resistant it is to being overturned. Bullets in flight generally become more stable as they lose linear velocity because their angular velocity decreases at a slower rate. So a bullet's gyroscopic stability will increase as it slows down ... for some distance anyway.
  11. powell&hyde

    powell&hyde Well-Known Member

    Yup the numbers seem astronomical but in reality, the time to target is only a little more than one-tenth of a second.

    -100 yards times 36 inches is 3600 inches
    -one turn in 10" twist barrel---3600 divided by 10= 360 bullet revolutions per 100 yards
    -1/9 twist--400 complete rotations of the bullet out to 100 yards
    -1/7 twist--514 revolutions of the bullet out to 100 yards
    The revolutions remains almost constant until the bullet stops. So at 400 yards the bullet in a 1/10 twist will have turned completely 1440 turns. The bullets do not rev up after firing and exiting the barrel but they have a constant 1 turn in whatever twist the barrel is and velocity will change bullet rpms. Now if the bullet was traveling through the air for a total time of one minute the total number of rpms would be the high numbers such as 200,000 or more.
  12. Zoogster

    Zoogster Well-Known Member

    Actually higher twist rates are going to generate more friction in the barrel and lead to higher wear and shorter life.
    So higher than needed does have its down side.

    Also when dependent on the bullet destablizing after impacting a target to deliver most of it's energy on target or fragment, such as the military when using FMJ, you could have overstabilization. The bullet will penetrate further before it begins to yaw with higher rates of stabilization. Reducing wounding. Not an issue with expanding ammunition.
  13. MCMXI

    MCMXI Well-Known Member

    I think the math is a little more complicated than that. The linear velocity of the bullet is decreasing at a faster rate than the angular velocity. If you assumed that the angular velocity was constant over the 400 yards, the bullet would rotate more times in the last 100 yards than the first 100 yards.
  14. CraigC

    CraigC Well-Known Member

    Velocity does indeed play a role, as does pressure. The faster you drive a bullet, the slower your twist can be. Which is why the .454 has a typical 1-24" twist, compared to the usual 1-16" twist of the .45Colt. Drive the bullet faster, use a slower twist rate and pressures will also drop.
  15. MCMXI

    MCMXI Well-Known Member

    Another issue is that a bullet needs dynamic stability in addition to gyroscopic stability. Gyroscopic stability is easy to achieve but dynamic stability is a tougher nut to crack. Consider that a 220gr SMK loaded in a .300 AAC Blackout shell and shot out of a 1:7 twist barrel at 1,000 fps has a velocity corrected SG of 2.6 which is well above the 1.4 requirement. So theoretically that bullet should be stable at 100 yards but it is far from stable. The problem is that the center of pressure is well forward of the center of gravity so despite having gyroscopic stability, it's not dynamically stable.
  16. DanTheFarmer

    DanTheFarmer Well-Known Member

    A bullet that is not properly stabalized will not be accurate. In flight it will look like a Tim Tebow pass vs. an Aaron Rodgers pass. When it goes through a paper target it won't be a nice circle. Instead it will make an oval shape because the paper intersected the bullet "mid-wobble". That is keyholing.

    I did some calculations like you did and I was skeptical that 120000 rpm vs. 180000 rpm would make a difference, so I did an experiment. I have a 7mm-08 with a 1 in 12 or so twist. This is good for the shorter (lighter!) bullets appropriate for the caliber. I worked up a load with 120 grain bullets and I could cover the group with a quarter at 100 yards. I also had some 175 grain bullets (MUCH longer) for a different 7mm-08 with a faster twist. It isn't a great load but it shoots 3 - 4" at 100 yards in the fast twist rifle. When shot through the slow twist rifle the 175 grain bullets were a foot apart and made oval shaped holes in the paper. The 175 grain bullets are too long to be properly stabalized in the 1 in 12 twist barrel. It amazes me that 120000 rpm or so is not enough to work properly but my test showed that to be true.

    Good Luck.

  17. Col

    Col Well-Known Member

    ???? beats me
  18. MCMXI

    MCMXI Well-Known Member

    Marlin's 1894 chambered for .45 Colt has a 1:38 twist. They listed the twist on their web site as 1:16 for ages but finally got around to changing it. Ruger's revolvers for .45 Colt have a 1:16 twist though. If you run the numbers through the Miller Stability Formula, a 1:38 twist is more than adequate to spin stabilize common .45 Colt bullets from 200gr to 300gr.
  19. CraigC

    CraigC Well-Known Member

    Up to 300gr yes, but only at maximum velocity. Certainly not at standard pressures for the .45Colt. Anything over 300gr and you need a substantially faster twist but the Marlin won't feed them anyway.
  20. pseudonymity

    pseudonymity Well-Known Member

    I am pretty sure that it is not true that weight does not matter, but I would agree that for common useful bullet shapes with lead cores, the weight could be ignored.

    The Greenhill formula does take specific gravity into account, but sets up the terms so that for lead core bullets the specific gravity is = 1, so it effectively cancels out of the equation. If you had bullets constructed out of steel or tungsten for instance, you would need more or less twist relative to a bullet of the same dimensions constructed with a lead core.

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