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cdoc42

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I found a calculation for twist rate and compared all the bullets I have used in my 6.5 Creedmoor and Hart .25-06 (converted from .270 WIN)

Twist rates

A longer bullet requires a faster twist rate for stability

Calculation: D2 x C/L= twist
D= bullet diameter squared
C= constant of 150
L= bullet length

Browning 6.5 Creedmoor Twist: 1 in 9"
Length Twist
Hornady ELD-M 147gr 1.462 7.2
Berger 140 Hunting 1.400 7.5
Hornady SST 140 1.398 7.5
Hornady ELD-M 140 1.397 7.6
Barnes Match 140 1.344 7.8
Sierra 140 SPBT 1.272 8.2
Hornady 140 SP 1.255 8.3
Speer 140 Hot Core 1.216 8.6

Most accurate have been last Sierra BTSP and Hornady SP
and both have the same impact point

Hart Barreled .25-06 Twist 1:9"
Hornady 120gr HP (new version) 1.178 8.4
Hornady 120gr HP (old version) 1.160 8.5
Nosler 120 Partition 1.166 8.5
Speer 120 BTSP 1.137 8.7
Speer 120 Deep Curl 1.121 8.8
Sierra 117 BTSP 1.113 8.9

Most accurate has been Sierra 117 BTSP
Have to redo both Speer bullets

Note: Bullets were measured from base to tip; true bearing surface would be base to ogive; not sure if that makes a difference
 
Cdoc42,

What you found is the shortened version of the Greenhill formula, a rule of thumb created by A.G. Greenhill in 1879 for quick guess use by students and artillery officers. The non-shortened version of this rule of thumb is:

Where,

SG = the Specific Gravity of your bullet (10.4 is a common jacketed bullet value)

C = 150 for velocities below 2800 fps
C = 180 for velocities at 2800 fps and up

Twist = D²C/L√(SG/10.9)

(The density correction factor √(SG/10.9) = 0.977 for common jacketed bullets, 0.899 for gilding metal bullets (Hornady solids), 0.905 for solid copper bullets, 0.995 for Lyman #2 alloy, and 1.005 for typical swaged bullet alloy)

The full (non-shortcut) version of Greenhill's formula, as found in Wikipedia is:

S= s²m²/(Cmα/sin(α)tdv²)

where
• S = gyroscopic stability
• s = twist rate in radians per second
• m = polar moment of inertia
• Cmα = pitching moment coefficient
• a = angle of attack
• t = transverse moment of inertia
• d = air density
• v = velocity


The limitations of the Greenhill shortcut are that it was developed as a shortcut in 1879 and designed around a sort of football-shaped projectile fired at typical artillery velocities of the time (around 1500 fps). It did not anticipate the VLD shape, so its applicability to modern bullets is, therefore, somewhat limited. In an attempt to improve on the precision, one of Robert L. McCoy's students, Don Miller, developed a newer version that has similar simplicity but works better with modern shapes. It is:

T=√(30m/Sdl(1-l²))

Where,

m = bullet mass in grains
S = gyroscopic stability factor (dimensionless)
d = bullet diameter in inches
l = bullet length in calibers
t = twist rate in calibers per turn

Note that for the above, you need to choose a gyroscopic stability factor, S, and 1.5 is considered an optimal value for rifle bullets by many authorities, so I would just use that to get:


T=√(30m/1.5dl(1-l²))

Subsequent to that version, Miller added temperature and velocity and altitude compensation, and those additions bring it to the form used by the calculator Marco Califo linked to.
 
Holy Smoke! That certainly assures me that I chose correctly when I didn't launch a youthful path down a mathematically necessary career! But Thanks for the lesson!! I'll redo it with the modern version.

I had contacted Browning and was advised that my X-Bolt was 1:9 and that a bullet requiring 1:8 would not create a problem. Neither of the ELD's are impressive in my rifle. The Hornady and Sierra 140's suggested 8.3 and 8.2 but my 1:9 Creedmoor puts both at the same point of impact so one cannot tell which is which.

What is interesting, even though the old version formula was used, it revealed the Sierra 117gr in .25-06 predicted 8.9 twist and did, indeed, result in a 4-shot, 100 yard group of 0.243. I pulled the 5th shot on purpose to see if the hole would be where I aimed because I thought I was missing the target.

I'm gonna get my calculator out again and play with the stability factor formula that Marco offered just because, even though I can't count, I enjoy doing this. I just hope that someday Heaven doesn't require a quick answer off the top of my head for 2+2-4 divided by 4 or something like that.

I measured the twists in my 2 Model 700 Remington in .270 and both appear to be 1:10. But the Greenhill formula did not agree. I checked 12 different bullets ranging from 130gr to 150. Three 130gr results were 10.9, 11.0, and 11.0, but neither rifle will shoot these well. A Hornady SST is good in the newer rifle even though the twist calculation is 8.9, and my original Model 700 refuses to group anything well except a Hornady 150gr Spire (9.4).
 
Last edited:
cdoc42 said:
I just hope that someday Heaven doesn't require a quick answer off the top of my head for 2+2-4 divided by 4 or something like that.
Click to expand...

The answer is infinity (what you get by dividing zero by anything except zero), which seems appropriate for the location.

Note that modern match bullets and even many hunting bullets are now so well made that running a stability factor of 2 or even 2.5 also works and generally get good accuracy.

If you want a second opinion, Geoffrey Kolbe wrote an HTML twist calculator based on Robert L. McCoy's old McGyro program that is good. It takes detailed bullet dimensions from which to estimate moments of inertia to go through the modern stability calculations in detail rather than in estimating short form. The output is graphical, and you will need to stare a moment to see what it's telling you, but find the twist for a stability factor of at least 1.4 and up to 1.7 should be the cat's meow.
 
I have had great results with Lapua 120-L in my 6.5 x 47 at 1 -8 twist. Hornady and Barnes 140s not nearly as good as the 120 gr.

Unclenick: Like Cdoc42 I tend to be math challenged though given a formula I can work it.
I understand the 1.5 aspect but does say 2.0 or higher have a bad result?
 
Good posts by Unclenick.

I can tell you though, that distance matters (and some other stuff a little) as well as bullet shape.

A flat base bullet will start to lose stability before a boat tail (same weight). Nose open or sealed and shape factors also have an effect. Nutation, Yaw, transonic zone all have their impact on "precision" or repeatability of the bullet path well past where most are concerned, and (hopefully) well past where most hunters are shooting their rifles at game.

In 6.5CM for example (we have several, from 18" to 24") we found that for 1:8 twist barrels, we got excellent precision out to about 350 yards with 150g and out to about 425 yards with 147g bullets, but past that, the patterns turned to buckshot. 142 grains, all the way out to 1200 yards, precision was maintained. But drop to 120s, and the precision is only maintained out to about 800 yards.

I've also found that flat base bullets don't settle the same as boat tail bullets. Whatever group you get at 200 with a flat base can pretty much be multiplied by 1.5 for the group size you can expect at 300. But with boat tails, that number is often less than 1.5 and sometimes just a few tenths over 1 (but never less than 1).

I get very skeptical of the folks that claim they have a 4" 1000 gun when their 100 yard group is 1/2". It is just not possible, even if they claim groups shrink at range. Only a lucky anomaly could cause that.

Barrel length has an affect on these things too and I personally ascribe to the theory of a shorter stiffer barrel will hold precision longer than a longer more whippy barrel. There are some pretty complicated ballistic models that nutation and yaw rate can be used in that verify that.

So sometimes, yes, you can cheat those "standard" stability factors a little bit and get away with it if the variables stack in your favor. But twist a bullet faster than it can handle, POP and nothing happens down range.

Gain twist and solids tend to mitigate those. I'm contemplating a time in the future were we have good performing bullets that will take a faster twist and survive. But that is going beyond what most will want or need in terms of cost and benefit.
 
Interesting but there really is not much choice in flat based bullets anymore. Vast majority are boat tail (I do have some Lapua 100 gr flat base though those are RN, works fine at 100 yards)
 
I found it to be true about flat vs boattail in my son's .270 Win, Model 70, non-pre-60, "feather weight."
It shoots flat-based Speer 130gr SP MUCH more accurately than boattail out to 200 yards.
I have not tested them beyond 200.

I must say, the numbers I played with using the 1879 formula held pretty well for a 150gr RN Hornady in .270. I dropped a buck right where he stood at 60 yards in the PA woods in 1977, with my .270 that "won't shoot anything" but 150gr Hornady spire (only because I can't find any RN any more).
 
Mark is right. The 150-grain flat-base Berger .308s are about impossible to beat in 308 or 30-06 at modest ranges. As Bryan Litz pointed out, it is harder to keep a boat tail base perfectly symmetrical in manufacturing than it is to keep a flat base square. This leads to greater opportunity to introduce lateral drift components due to asymmetrical muzzle blast flow deflected off the base and to exaggerate initial yaw. The drift is too slow to be retarded significantly by drag during the TOF, so as the bullet drifts the group opens in proportion to the time of flight. That time gets longer for each successive hundred yards because the bullet is slowing down, so the number of MOA of dispersion due to the drift component increases with range.

Some bullet designs, like the 168-grain Sierra MatchKing, have stability issues in the transonic range. Litz says it's a dynamic instability. This is complicated, and I don't have an analysis for it, but have seen it occur twice with that bullet starting to tumble at about 700 yards in a cross-wind when fired from both 10 and 12-inch twist barrels. In a dynamic instability, the projectile tends to overcorrect for destabilizing influences despite spinning faster than the stability calculators say is necessary for the speed it is travelling. You can apparently mitigate the effect by spinning it more slowly. I know someone who has got those bullets to go 1000 yards using a retired and cut back Palma barrel with a 13.5 inch twist, though I don't know the wind conditions he was shooting in. That bullet's 13-degree boat tail is steeper than the 9-degree tail taper the army figured out minimizes drag by cut and try back in the 1920s (McCoy puts it closer to 8.5 degrees in the plot he published on the topic, but the difference isn't much).

The 175-grain SMK, which uses the 9 degree boat tail, has no tumbling problem in the transonic range, despite the longer bullet coming out of the same 10 or 12-inch barrel twists, and Sierra says the same is true for the new 169-grain MatchKing, which I am about to try out. I will also mention the M2 AP flat base projectile's issued for combat in WWII and Korea that weighed between 162 and 168 grains, depending on the core material and tolerance, were preferred by snipers as being more accurate at all ranges than regular issue ammunition. That included the old stockpiled M1 Ball with the 173-grain 9-degree boat tail FMJ as well as the flat base M2 Ball with 150-grain FMJ.
 
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