Updated May. 05/02
Case Neck Angles and Twists.
A Discussion about Science by a Non-Scientist.
During a recent E-mail exchange I was ask what the difference is between a 280 Ackley improved and 280 RCBS improved. Both have the same case dimensions except the shoulder angles The Ackley has a 40-degree shoulder and the RCBS has a 30-degree shoulder. Both hold the same amount of powder, at least the two that I have and had. With good loads and barrels, there is no apparent difference as far as I could tell. The 30- degree shoulder seemed not as finicky getting a load developed. Perhaps side by side chronograph testing with every thing the same may put one ahead of the other by 10 or 15 feet I never chronographed the RCBS. Besides the two guns had different barrel length.
I am using the 40-degree shoulder right now, because the Redding competition dies that I use, are a standard stock items, while the 30- degree is a custom order. I think it should be the other way around. Why the 40-degree shoulder is more popular is a matter of believes than anything else, I think? I do know that the 30-degree shoulder is less prone to jam in a bolt action with a magazine. ?I am talking about hunting rifles. And I never use a clip type magazine for hunting, because they get lost.
May 1998 Ron Jeter wrote an article in P.S. Magazine, "Turbulence Point Wild Cat Cartridges". The basis for his article is the accuracy of the 6-mm PPC cartridge. Which has a 30-degree shoulder and a .285 neck length. The turbulence point of this cartridge is 73.7% of neck length. This cartridge is one of the most accurate rifle cartridges ever developed. To mimic the shape and or protract it is understandable. To convert other cases to perform similar as the 6 mm PPC is the idea behind the T.P.Wildcats. Here is the formula.
(.243/2)=. 1215=a, b=a (cot A) (0.1215x1.732)=0.210=(b/l)=%, (0.210/0.285)=73.7% that is the point where the shoulder angles converge. The theory of Ron is, if you take the trimmed neck length of the parent cartridge and use the 73.6 percentage for the turbulence point you then calculate the shoulder angle. If we do a similar calculation for the 280 RCBS and substitute the trimmed parent neck length of 0.325" and work this formula in reverse starting with a 73.7% T.P.of (.325x.73.7%) =0.2395 =b.
a=(.284/2)=.142, b= 0.2395, tanA=(a/b)=cosB, (.142/.2395)= .5929 tan inv=A= 30.66 degrees.
This approximates the 6-mm PPC shoulder and neck shape very close. However the ratio of shoulder diameter and case length has a great deal influence on the powder combustion. A general consensus is that a shorter wider powder column provides better primer ignition. Ron also specified that the body taper should be 0.005" per inch length like the PPC. With a .460" shoulder the 280 RCBS Improved would qualify.
My personal opinion is that the 30-degree shoulder creates less turbulence than the 40-degree. The deflection of powder gases off the neck wall is less. The collision of the gases in the center of the neck is at a lesser angle and consumes less energy, trying to get down the barrel. All this takes place still 26% below the top of the case. It is however important that the neck is of sufficient length. A shorter and wider case like the Lazzeroni is a way in the right direction.
If we are talking about a hunting rifle for deer size game the 308 case with a longer neck is a very good compromise. For instance a 7mm improved with a .460 shoulder diameter and a .320 long neck made from a 30-06 case and shortened to an improved 7mm-08 body, will equal the performance of a 270 Winchester shooting 140 gr bullets close to 3000 ft/sec. This is good performance in a short action using considerable less powder. Now if we follow the concept of the TP Wildcat we would use a 30-degree shoulder and get custom dies. But we will try available 40-deg stuff for savings.
We will prove that we can't have a Wildcat without the Ackley shoulder. Our quest for performance and accuracy will now point to the rifling twist and velocity. This hotly debated subject is on the mind of all accuracy minded shooters; furthermore twist is dealt with much compromise. The sad point is that only one bullet will achieve the optimum accuracy with one specific twist and one specific velocity. With the multitude of available bullets on the market this becomes a major obstacle to gilt-edge accuracy.
Rifling
Twists.
To get to an acceptable compromise the twist plays a major role in the equation. There have never been better-designed bullets, than we have now. The competition is fierce among the bullet makers to produce a better bullet. Depending on the game we play, because of their quality the bullet can almost be dismissed as a major factor in the accuracy department. The problem we have is to stabilize these fine bullets, from the muzzle to the target. Stabilization is a function of twist, rotational velocity and gyroscopic balance. The Greenhill Formula for twist is the general yardstick and produces useable results. However its simplicity does not address some of the ballistic happenings, and in general it over stabilizes the bullet by some margin. Here is the formula.
T=twist in inches, d=bore diameter, l= length of bullet in inches.?
Using this formula for a 139-gr Hornady flat base spire point. We get the following: 150x.284x.284/1.125=T=10.754". I have used this bullet and the 160 gr Speer with outstanding accuracy in 7x61 S&H with a 1-12" twist and in the 280 Ackley Improved with a 1-11" twist. Both bullets clock 3000ft/sec plus muzzle velocity.
The Grenhill Formula ?provides a stability factor of 1.7, which overstabilizes bullets, erring on the faster twist side. Which in it's self is no problem, but sacrifices accuracy. That is at least what I think. According to Eric Williams, using 20% to 25% less twist will still give the bullet a stability factor of about 1.275. Using this factor with the 10.75" Greenhill twist would mean a 12.9" to 13.25 twist for the 139gr Hornady bullet. Even a 10% reduction for 1.4 stability factor would make it 11.825" twist. So for bullets with a MV above 2800 ft the constant of 150 in the formula can be increased to 185 or a bit more if one wants to experiment with a custom bullet.
When a bullet is launched into the bore, it makes contact with lands. The lands are at an angle to its pass. The greater the angle the more the bullet suffers from this collision, however minimal that may be. From a straight start the bullet is forced to rotate while being pushed forward.
By selecting a bullet for a caliber that gets the job done is the way to go. You would not select a bullet for moose to shoot prairie dogs or visa versa. If you have only one rifle you cannot expect it to do both jobs equally well. If you hunt only deer size game and you have a 7mm Mag. why use a twist of 1-8.5" for the heaviest 180 gr or bigger bullets when you only hunt deer with 140 gr. bullets. Besides if you going after real big game get a bigger caliber. But this one gun scenario is based on economy, and it should not surprise anyone that the rifle is not grouping with this or that bullet. Rifle manufacturer supply rifles on the fast twist side for utility not accuracy. And here I am after accuracy for the best possible hunting ammo, suited to the game hunted.
A few years ago I tried a 7-mm barrel with a progressive twist. The starting twist was 1-19" and the ending twist 1-11.25. The barrel had cut rifling, but was not lapped. The barrel maker told me that his barrels are smooth enough and did not need lapping and recommended regular break in. The barrel fouled up badly whether from the twist or the lack of lapping, I don't know?
Some mathematics revealed that the engraved land would widen on the bullet forward side of the bullet shank by something like 0.005". When you multiply that by six grooves, that metal has to go somewhere. I exchanged the barrel for a standard 1-11". Progressive twist barrels are advertised and claim superior accuracy? At the time I did not know about the Micro Hone process, this would have helped to find out whether the progressive twist barrels are really more accurate.
PS Magazine published an article "Bullet Stability" by Eric Williams, June 1997 issue. He included a formula that will provide the right twist for a given bullet. The formula is very involved and precludes knowledge of ballistic science and mathematics. Without the text it would not help very much to provide it here. I may write to PS Magazine for permission to print it on my page.
Below is a chart for rifling twist angles to show comparative angles values. Here is the formula.
Note: A 1-6" Twist in 17 cal has an
angel of 5.24 deg.
A= twist angle, pi=3.14 constant, d= bore diameter, T=twist length in
inches.
For the experimenter I have a formula embedded in MS Excel, which works
in reverse of the below. Input the twist angle and caliber to get length of
twist
|
Cal. |
Circ. |
1- 7" |
1-8" |
1-8.5 |
1-9 |
1-10 |
1-11 |
1-12 |
|
.172 |
.540 |
4.414 |
3.864 |
3.637 |
3.436 |
3.093 |
2.812 |
2.578 |
|
.224 |
.703 |
5.741 |
5.027 |
4.733 |
4.471 |
4.025 |
3.660 |
3.356 |
|
.243 |
.763 |
6.224 |
5.451 |
5.132 |
4.848 |
4.366 |
3.970 |
3.640 |
|
.257 |
.807 |
6.579 |
5.763 |
5.426 |
5.126 |
4.616 |
4.198 |
3.849 |
|
.264 |
.829 |
6.757 |
5.919 |
5.573 |
5.265 |
4.741 |
4.312 |
3.954 |
|
.277 |
.870 |
7.086 |
6.208 |
5.846 |
5.523 |
4.973 |
4.523 |
4.148 |
|
.284 |
.892 |
7.264 |
6.364 |
5.992 |
5.662 |
5.098 |
4.637 |
4.252 |
|
.308 |
.968 |
7.870 |
6.897 |
6.494 |
6.136 |
5.527 |
5.027 |
4.610 |
|
.323 |
1.014 |
8.248 |
7.229 |
6.808 |
6.433 |
5.794 |
5.271 |
4.834 |
|
.338. |
1.062 |
8.626 |
7.561 |
7.121 |
6.729 |
6.061 |
5.514 |
5.057 |
|
.358. |
1.125 |
9.128 |
8.003 |
7.537 |
7.123 |
6.417 |
5.338 |
5.354 |
|
.375 |
1.178 |
9.553 |
8.377 |
7.891 |
7.458 |
6.719 |
6.113 |
5.607 |
|
.458 |
1.439 |
11.615 |
10.196 |
9.608 |
9.083 |
8.188 |
7.452 |
6.837 |
|
|
|
|
|
|
|
|
|
|
|
Cal. |
Circu |
1-13 |
1-14 |
1-15 |
1-16 |
1-17 |
1-18 |
|
|
.172 |
.540 |
2.380 |
2.210 |
2.063 |
1.934 |
1.821 |
1.719 |
|
|
.224 |
.703 |
3.099 |
2.878 |
2.686 |
2.518 |
2.370 |
2.239 |
|
|
.243 |
.763 |
3.361 |
3.121 |
2.913 |
2.732 |
2.571 |
2.429 |
|
|
.257 |
.807 |
3.554 |
3.301 |
3.081 |
2.889 |
2.719 |
2.568 |
|
|
.264 |
.829 |
3.650 |
3.390 |
3.165 |
2.967 |
2.793 |
2.638 |
|
|
.277 |
.870 |
3.830 |
3.557 |
3.320 |
3.113 |
2.930 |
2.768 |
|
|
.284 |
.892 |
3.926 |
3.646 |
3.404 |
3.192 |
3.004 |
2.838 |
|
|
.308 |
.968 |
4.257 |
3.954 |
3.691 |
3.461 |
3.258 |
3.077 |
|
|
.323 |
1.014 |
4.463 |
4.146 |
3.870 |
3.629 |
3.416 |
3.227 |
|
|
.338. |
1.062 |
4.670 |
4.337 |
4.049 |
3.797 |
3.574 |
3.376 |
|
|
.358. |
1.125 |
4.945 |
4.593 |
4.288 |
4.021 |
3.785 |
3.575 |
|
|
.375 |
1.178 |
5.178 |
4.810 |
4.491 |
4.211 |
3.964 |
3.745 |
|
|
.458 |
1.439 |
6.316 |
5.868 |
5.479 |
5.139 |
4.838 |
4.570 |
|
It can be seen from the chart that a light bullet driven at a faster speed would suffer from a faster twist angle and would loose some accuracy. When we look at a 95-gr Barnes-x bullet, which is 1.095" long in cal. 0.243. Applying the Greenhill formula would mean a 1-8" twist. Since the Barnes-x Bullet is made from solid copper that is only 2/3 the density of a comparable lead core bullet, is another factor to consider. The lesser density dictates a longer bullet for a given caliber weight.
This of course changes the distance between the center of gravity and the center of pressure, the greater this distance the more twist or stability is needed. If you like to shoot the Barnes-x bullets you have to go for more twist. The 130gr and the 140gr shoot well in a 1-9" twist in a 7mm over 3000ft/sec. perhaps a 1-8" twist would prove better? With the bigger calibers the disparity is not as large, in the .338 Magnums the Barnes-x bullets shoot very well indeed in a 1-10" twist. Also they foul less in the bigger bores. Why?
Note added Oct. 6, 99. In resent reading expert scientists have stated that an overstabilized bullet is less accurate then one that is adequately stabilized. An overstabilized bullet flies with its point elevated or the way it left the bore. While an adequately stabilized one will fly with it's point following the trajectory curve. Visualize a diver entering the water head first, no ripples, while the other makes a belly splash. The point up bullet flight will add friction and area for the wind to act on. This scientific statement was unknown to me at the time I wrote this article. But I always maintained that overstabilized bullets were not desirable, and the lesser and appropriate rotation produced better accuracy.
Here are questions from reader
"Charles" with my reply in red.
Fred,
I just read your page on rifling twist. Very interesting. I do not have
an in depth knowledge of optimal twist rates or bullet flight stability but
thought of something that was not addressed. If a bullet leaves the barrel at a
twist rate that provides optimal stability; how far in flight will the bullet
maintain that level of stability (((I am not a
ballistic expert either but have done extensive reading on the subject, and
have a working knowledge on the subject? Optimal is not the right word it is
either adequate or insufficient. An adequate stabilized bullet "SELECTED
for the job on hand" will retain its stability to the end of task.
Well now, isn't that a mouth full? But that is the way it is.)))
To apply this thought to a hunting rifle - Would it not be necessary
to over stabilize a bullet at the muzzle in order to have good
stability at the longest anticipated shooting range. (((One
bullet, no. A spectrum of bullets yes. You have to make a realistic assessment
of your abilities and how far your longest range is, and what the main use for
this rifle will be. A 7mm Rem Mag for deer will only need a max twist of 1-12.
A 1-11 will stretch the utility a little. Both with outstanding accuracy and
killing power to 550 yards with 140 gr bullets.))) Or, if a particular
bullet/cartridge combo is used for 100yd. Benchrest and 500yd PD shooting, wouldn't
the PD gun require a faster twist? Charlie (((A 6mm PPC is loaded to about 3150 with a bullet of 65 and
70 gr and 28-31 gr of powder. Using 1-14 and some 1-15 twists. Rifles are only
used at 100 and 200 competition. This combination will sock PDs without trouble
at 500 yards as long as you don't use heavier bullets and go for lighter ones
with some more velocity. So the multi use scenario is in question, one simply
would not use the same rifle and loads for the two purposes for more than just
one obvious reason. But a revamped 6 mm PPC bench rest rifle makes one hell of
a good PD gun using 55 gr bullets. But if you want to shoot PD's at1000 yards
across canyons with a 6mm, you need a 6mm-284 with a 1-8 twist using 108 gr VLD
bullets and 60 gr of powder, or a 1-6 with 136 gr VLD bullets. In other words
you can't have your cake and eat it too. Take notice of the one million 30-30
deer rifles. A 170 gr bullet 1-12 twist @ 2200 ft/sec with 34 gr powder. Every
time a dead deer in the bush or at max 200 yards, not for utility or multi
purposes just for the bush. ))) Best regards
Fred
Important Note: February 1/01. Here
is the scientific revelation (How a bullet flies?) that puts a "TWIST"
on many misconceptions. I am pleased that my assumptions and statements in
general are pretty close. http://www.nennstiel-ruprecht.de/bullfly/~4n6/
Thank you for visiting my "Angelfire"
web page. Please direct your comments to "Fred".
