Measuring a Barrel's Twist Rate

When we studied the basics of rifling a while back in this blog, there was mention of a term called "twist rate" for a barrel. The twist rate is defined as the length of the barrel required for a bullet to make one complete turn of the barrel. For instance, a standard M16A2 barrel makes 1 turn for every 177.8 mm. of barrel length. It is very important to match the twist rate based on the weight, diameter and length of the bullet to ensure accuracy. We studied a couple of methods on how to calculate the twist rate for a given bullet using the Greenhill formula and the Miller Twist Rate formula. All this is good in theory, but how do we actually measure the twist rate of the barrel? This post discusses a simple way to do so.

Recall that about 16 months ago, we discussed various tools used for cleaning firearms. Well, people can use some of those very same tools to measure the twist rate of a barrel. All that is needed is a standard cleaning rod with a rotating handle, a jag and a cotton cleaning patch. The user simply attaches the cleaning patch to the jag end of the cleaning rod and then pushes it into the barrel until the cleaning patch engages the rifling of the barrel. The user then takes a piece of sticky tape and attaches it around the back of the cleaning rod near the handle like a tiny flag (or uses a marker and marks a spot on the cleaning rod). The user then measures how much of the cleaning rod is sticking out of the barrel (a ruler measuring the distance from the barrel's base to the start of the flag or mark point should do it). Then the user pushes the cleaning rod into the barrel. Because the cleaning patch has engaged the rifling, the rod rotates as it is pushed into the barrel. When the flag or mark point has made one complete rotation, the user then measures how much of the cleaning rod is sticking out of the barrel again. The difference between the two gives the twist rate. For instance, if the rod initially has 22 inches sticking out the barrel when the first measurement is made and 12 inches sticking out of the barrel when the second measurement is made, this means that the twist rate is 1 in 10 inches.

For those of you who would like to see a video of the process:

Happy viewing!

How to Calculate the Twist Rate - II

In our last post, we looked at the venerable Greenhill formula, first developed in 1879 and refined over the years. In 2005, Don Miller suggested an improved formula to calculate the twist rate, in the March 2005 issue of Precision Shooting magazine. We will look at that formula in this post.

Some of the problems with the Greenhill formula was that it was more suited to bullets from another era, where the bullet shapes were more oblong shaped (like an American football) and largely made of lead alone. Modern bullets are longer (e.g. spitzer or boat-tail shape) and made of multiple materials (such as copper and brass jackets, steel core etc.). The corrected Greenhill formula does work better than expected for modern bullet velocities of 2800 feet/sec, but it doesn't work so well for black powder velocities.

What we studied in the previous post about the Greenhill formula was actually its simplified form. The original Greenhill formula was much more complicated and involved calculating such esoteric items as polar moment of inertia, transverse moment of inertia, pitching moment coefficient, angle of attack, air density etc. To work out the original Greenhill formula, one would need a degree in physics and mathematics to make sense of all these terms, as well as access to some high quality scientific instruments to make the measurements needed to calculate all these items. What Miller did was start with the original Greenhill formula and used some empirical data to simplify the calculations so that one didn't need an advanced degree to do the whole calculation and could use basic instruments to do the measurements. The Miller formula is:

where:
     T = Twist rate in inches per turn
     m = Weight of the bullet in grains
     s = Gyroscopic stabilization factor (see below for how this is evaluated)
     d = Bullet diameter in inches.
      l = Bullet length in calibers, which is calculated as L/d, where L = length of bullet in inches.

With the Miller formula, all the information needed for the calculation (length, diameter and weight of the bullet) can be easily obtained from the manufacturer, or can be easily measured by anyone with access to a vernier caliper and a small weighing scale.

Miller notes that his constant 30 in the equation above was taken assuming a standard temperature of 59 degrees fahrenheit, standard pressure of 750 mm. of mercury at 78% humidity, velocity of bullet at 2800 feet/sec and altitude at sea level. He also notes that under the standard conditions, the gyroscopic stabilization factor s in the equation above runs from 1.3 to 2.0 (for military, it runs from 1.5 to 2.0) and he says 1.75 is a good starting value for it. He also states that cold temperatures significantly affect air density and therefore s as well. Hence, he recommends assuming s = 2.0 to account for usage in low temperature environments for preliminary calculations of twist.

With all this in mind, let us perform a sample calculation for a Sierra bullet with the following specifications:
    m = 180 grains
    L = 1.180 inches
    d = 0.308 inches

First we calculate l = L/d, which gives us l = 1.18 / 0.308 = 3.83117

Then we assume s = 2.0 to account for low temperature conditions and calculate the twist rate T, which works out to about T = 12.081. This means that a twist rate of 1 turn in 12 inches ought to work well for this bullet.

In his paper, Miller says that he used experimental data from the US Army's Ballistic Research Lab (BRL) to verify the validity of his formula.