Rifling Twist

[rsterne]

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:

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

[rsterne]

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

[rsterne]

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

[rsterne]

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

[rsterne]

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 thinner the nose, the faster the bullet needs to spin to be stable.... (WRONG, SEE POST ABOVE).... This is quite logical, as longer, more pointed bullets have the Center of Drag further ahead of the Center of Gravity.... 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

[rsterne]

Well, this is embarrassing.... I just looked back at my comments about the different bullet shapes, and the comments are bass-ackwards.... If we look at the optimum twist (for a stability factor of 1.5) at just below the speed of sound, we find that for the cylinder it is 16", for the round nose with meplat it is ~17.3", for the round nose, it is 18", and for the pointed it is 18.5".... That means that the blunter the bullet (and the more forward the CG) the FASTER it has to spin to be stable.... I guess the center of drag is more forward with the blunter shape (makes sense, now that I think of it) and moves aft on the more streamlined shapes so they are more stable....

Bob