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Rifling Twist 
PostPosted: Sun Sep 30, 2012 1:57 pm Reply with quote
rsterne
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For the most part, this is a complicated, and poorly understood subject.... It has always fascinated me, and the lack of good information on subsonic ballistics has been a constant source of frustration to me.... A while ago, I discovered a Twist Calculator in the Border Barrels (Scotland) website which works not only for supersonic flight, but also for subsonic and the transition in between.... It has numerous inputs, and I would suggest you check it out.... http://www.border-barrels.com/barrel_twist.htm

First of all, let me state that I am NOT an expert in this field.... I have, however, done a lot of reading on the subject, to try and get a grasp of what is going on.... The original "standard" method of calculating the optimum rifling twist was the Greenhill Formula which dates back to 1879.... There have been many derived since, and one of the better ones is the Miller Rule, published in 2005.... However, even with that modern formula (probably because he had no interest in it), all velocities below the speed of sound used a velocity of 1120 fps.... The Border Barrels calculator, however, presents the optimum twist in graphic form from 500 fps up, and according to their website:
Quote:
This program is basically a slick version of Robert McCoy's "McGyro" DOS program, written in the late 1980's when he worked for the U.S. Army Ballistic Research Laboratory at the Aberdeen Proving Grounds. It was later improved by William Davis Jr. of Tioga Engineering and the claim was an accuracy of 5% for super and subsonic velocities, and 10% for trans-sonic velocities.

The basic output of the calculator is a graph for a Stability Factor of 1.5, but you can also input the twist you are interested in, and it then presents a second graph giving the Stability Factor for that twist.... A Stability Factor less than 1.0 is unstable, and greater than 4.0 is considered "overstabilized" which simply means that any imperfection (ie imbalance) in the bullet can cause "precession" or wobbling, which tends to open up the groups.... The military chooses Stability Factors of 1.5 to 2.5, and benchrest shooters often opt for only 1.3, but 1.5 is generally considered a good design point....

Let's ignore velocity and bullet shape for a moment.... There are two basic concepts you have to understand about rifling twist....

First, you have to realize that all the twist equations originally worked in "calibers".... The length of the bullet, and the resulting optimum twist, were relative to the diameter of the bullet.... For a given shape of bullet (ie length to diameter ratio), the required twist was the same IN CALIBERS.... If a 15" twist was the best in a .25 cal (with a .50" long bullet), then you need a 30" twist for a .50 cal (with a 1.00" long bullet)....

Second, if you increase the length of the bullet (in a given caliber), you need to spin it faster in order for it to be stable.... Imagine how fast you would have to spin a pencil to make it fly straight (without vanes or feathers) and you get the idea....

Once you understand those two ideas, you are well on your way to understanding twist.... In the following posts, I am going to give some examples, using the Border Barrels Twist Calculator to produce the graphs....

Bob

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PostPosted: Sun Sep 30, 2012 2:20 pm Reply with quote
rsterne
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OK, so let's first look at the idea that twist is related to caliber.... Let's start by defining our "standard bullet".... I'm going to use a cylinder with a hemispherical nose, like this....



Let's start with a .25 cal that is .50" long....



Now let's look at a .50 cal that is 1.00" long....



Note that for all velocities, the optimum twist for the .50 cal bullet is twice as long as for the .25 cal bullet.... That means, however, that the twist rate is the same IN CALIBERS.... At just under 1000 fps, the optimum twist in .25 cal is 20", while in .50 cal, it is 40".... In both cases, that works out to 80 CALIBERS....

Bob

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PostPosted: Sun Sep 30, 2012 2:36 pm Reply with quote
rsterne
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Now let's look at the idea that you need a faster twist as the length of the bullet increases (within a given caliber).... Again, we will use our "standard" Round Nose bullet....

.25 cal that is .25" long (1 diameter)....



.25 cal that is .375" long (1.5 diameters)....



.25 cal that is .50" long (2 diameters)....



.25 cal that is .625" long (2.5 diameters)....



.25 cal that is .75" long (3 diameters)....



You will note that as the length of the bullet increases, you have to spin it faster to keep it stable.... The same thing would happen in a larger caliber, but the twist rates would be slower (in inches)....

Bob

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PostPosted: Sun Sep 30, 2012 3:01 pm Reply with quote
rsterne
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By now you will have noticed that there is a "discontinuity" in the graphs right at the speed of sound.... As the bullet breaks the sound barrier, shock waves form around it, and they can have a dramatic affect on the stability.... You have probably heard of pellets "tumbling" when they drop below the speed of sound, and that can definitely occur if the twist rate is too slow for the pellet to be stable right at Mach 1.... Here is a graph of such a combination of bullet and twist rate....



The graph was generated using a twist rate of 18", and I adjusted the length of the bullet until the stability dropped below 1.0 at 1100 fps.... Although the bullet would be stable in supersonic flight, and at low speeds, it would not be stable at 1100 fps, and even at 1000 fps, the Stability Factor is only 1.1, which may be unstable depending on temperature and altitude (ie air density).... Note that if the pellet was significantly shorter.... and/or if the twist rate was faster.... this tendency to tumble right at Mach 1 could be eliminated....

Bob

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PostPosted: Sun Sep 30, 2012 4:26 pm Reply with quote
rsterne
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This post will try and explain what happens when you change the shape of the bullet.... I don't fully understand it myself, and the over-riding factor in determining the twist is the length of the bullet.... but here is what I found out for a few examples.... All these bullets are .25 cal, 0.50" long (ie 2 diameters)....

.25 cal cylinder (ie shaped like a tin can)....



.25 cal Round Nose, with a Meplat (flat) of 0.125" diameter....



.25 cal Round Nose (as in the earlier post)....



.25 cal Pointed (nose radius extends all the way to the base)....



Other than just as the bullet breaks the Speed of Sound (where the optimum twist for all is about 23.5"), the larger the meplat, the faster the bullet needs to spin to be stable.... Note that our Diablo shaped pellets, with a solid head and hollow skirt, have the CG further ahead, and the CD further aft, giving them greater stablilty to start with.... Unfortunately, the Border Barrels calculator doesn't allow us to "thin out" the waist, or make a hollow base, and see what that does to the stability.... About all we can do is assume that it increases it.... That means we can PROBABLY get away with a slower twist than a solid bullet of the same length....

Bob


Last edited by rsterne on Fri Oct 18, 2013 11:19 am; edited 2 times in total

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PostPosted: Thu Oct 04, 2012 9:29 pm Reply with quote
lampy
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I'll have to read this a few more times for it to sink in Confused .... thanks for taking the time to post this info.
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PostPosted: Sun Dec 09, 2012 5:28 pm Reply with quote
gicos
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The bearing surface has the largest impact on required twist. That's why the Border Barrels calculator has nose length as an input--so it knows how long the at caliber portion of the bullet is. Very interesting topic and one I've studied at length.

To add to basic twist rate considerations, also take a look at the curve made by different shapes. The better bullet stability-wise is always a shorter for caliber stubby shape, with a relatively short nose and wide meplat. A bullet with about a 1.7 tangential ogive and meplat around 75% of caliber produces almost flat curves, both sub and supersonic. This makes it possible to select twist rates and get right on the money, versus compromising somewhere in the middle. Since either over or under stabilization hurts accuracy, this is a bigger deal than a lot of folks think. Ideally, one wants just enough and no more. This is why a number of very experienced shooters regard this type of flat nosed bullet as the most accurate thing they shoot. With a twist chart curve that's all over the place, the bullet is over stabilized at most of the time--twist must be chosen based upon what's needed to stabilize at the lowest point (highest twist) in the graph.

Of course, the ballistic coefficient of this type of bullet is lousy, so for those only concerned with ultimate speed or long range shooting, the trade off in accuracy for a more cone shaped bullet is probably worth it. They learn to compensate for the inherently less accurate shape. For those who primarily hunt, the flat nose is where the meat's at. Elmer Keith had it right. Most stuff we shoot is under 100 yards and that's where the flat nose puts all others to shame.

The following is the 46 grain Speer 218 Bee bullet. I don't think it was an accident that Mashburn ended up at 46 grains. I think it was the byproduct of other design considerations that he just nailed. This is one of the bullets regarded as extremely accurate and hard hitting:



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PostPosted: Thu Dec 13, 2012 11:14 pm Reply with quote
Myxr
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Just for personal knowledge, how does a hollow point nose factor into twist? Does it just act like a flat nose for these calcultions?

Anything about boat tails? I know these add a bit of stability in supersonic flight, so techinically you could get more 'caliber' size outta your round by adding BTs?



I'm probably way off, but I love topics like this.

'The more you know...'
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PostPosted: Thu Dec 13, 2012 11:27 pm Reply with quote
rsterne
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AFAIK, HPs are treated like a flat nose, although they do affect the density of the bullet, there may be a factor for that on the Border Barrels site.... They can do the calculations for Boat-tails....

Bob

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PostPosted: Fri Dec 14, 2012 7:48 pm Reply with quote
gicos
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HPs won't alter the twist needed. If you look at high speed photos of a bullet in flight, the air isn't actually in contact with the nose. The turbulence across the ogive creates an air pocket that diverts it. Most of the drag on a flat nose bullet is on the ogive, believe it or not. Pellets are a different animal, of course. There's little to no ogive on most.

Boattails are a mixed bag. It gets really technical really fast figuring out what they do in flight. In short, unless you're shooting extremely long ranges, say over 500 yards, they have more drawbacks than benefits. The boattail section of the bullet isn't actually caliber size--it's less. For this reason and the fact that they're designed for ultra long range shooting, they're some of the longest bullets available. Which means they require some of the fastest twist rates available. Which can quickly lead you down the road of having a barrel dedicated to just boattails, because the twist is too fast for anything else. The most in depth info I've found on this is on the Lilja Barrels site. Check out their articles section and prepare for many luscious hours of reading on all aspects of bullet performance, to include twist rates.

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PostPosted: Sat Dec 15, 2012 2:25 am Reply with quote
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lampy wrote:
I'll have to read this a few more times for it to sink in Confused .... thanks for taking the time to post this info.

after it does, then you can explain it to me. Wink I love reading Bob's threads... it's like sitting at the feet of a master. YouAreAGod

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PostPosted: Mon Feb 18, 2013 1:36 pm Reply with quote
Robw
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Very nice! And thanks for the cool link.
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PostPosted: Fri Oct 18, 2013 11:31 am Reply with quote
rsterne
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I was just reading back on this thread and found I never added the information for a boat-tail.... Here is the graph for one that is .25 cal and .50" long, the same size as the other bullets in the shape comparison....



The bullet has a base that is 1/2 the caliber (ie 1/8" diameter).... and the boat-tail is 1/2 the bullet length (ie 1 cailber)....



Interestingly, this bullet has MUCH less stability than any of the shapes with the full diameter base.... Even at Mach 1, it needs 15" of twist, instead of 23.5".... As it falls below the speed of sound, it needs an 8" twist, twice as fast as the otherwise least stable cylindrical shape....

Bob

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PostPosted: Wed Oct 23, 2013 11:52 am Reply with quote
rsterne
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One more addition to this thread.... Following on to other work I have done, here is the Stability graph for a RF design of the same proportions as the above.... .25 cal, .50" long.... but this time with a 2 Ogive nose radius, half the length of the bullet, and a .125" Meplat....





The Meplat ends up requiring the same twist rate at Mach 1 as the round nosed meplat design (17.5"), but the required twist rate as the velocity drops decreases more sharply than a round nose with meplat, but not as quickly as a round nose or pointed design.... pretty much as expected....

Bob

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PostPosted: Sat Oct 26, 2013 2:32 pm Reply with quote
rsterne
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One more set of data.... this time for the above bullet (.25 cal, 0.50" long, .25" nose length, .125" meplat), but with a 0.20" diameter Boattail base that is 0.10" long....





The faster twist rate required due to the Boattail is substantial.... At just under Mach 1, instead of needing a 17.5" twist, this bullet needs a 12.5", and at 500 fps the twist rate increases from 20" to 17".... Just above Mach 1, it increases from 23.5" to 19.5".... Although there is nearly a 50% decrease in drag below Mach 1, you need to spin this bullet MUCH faster for it to be stable....

Bob

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Rifling Twist 
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