Measuring Effectiveness of Cartridges: Optimum Game Weight Formula

We've studied several empirical formulae in the last few pages: The Taylor KO Factor, the Thorniley Stopping Power Formula and the Hatcher Formula. In todays article, we will study another formula called the Optimum Game Weight formula.

This formula was devised by Edward A. Matunas and was first published in the April 1992 issue of Guns magazine. The author claimed that this formula was devised based on studying the effects of kinetic energy, momentum, bullet sectional density, diameter, bullet nose shape and other criteria. However, the author did not elaborate on how he managed to derive his formula.

The Optimum Game Weight formula is defined as:

OGW = V³ * W² * 1.5 * 10^-12

where:
OGW = Optimum Game Weight in lbs.
V = velocity of bullet in feet per second
W = weight of bullet in grains

For hunting bullets, the constant used in the equation is 1.5 * 10^-12. For varmint bullets, it is recommended to use 5.0 * 10^-13 instead. What the OGW value tells us is the approximate maximum weight in lbs. of an animal that can be reliably killed by a particular cartridge. It is assumed that the hunter has selected an appropriate bullet type for the job.

For an example, let us consider the same rifle and cartridge that we studied with the Thorniley Stopping Power formula, two posts earlier. This is a .30-06 rifle that fires a bullet of .308 inch diameter, weighing 180 grains at approximately 2900 feet/sec. Plugging the numbers into the formula above, we get:
OGW = 2900³ * 180² * 1.5 * 10^-12 = 1185.31 lbs.

This means that this formula indicates that the rifle and cartridge combination can be used to kill animals weighing up to 1185 lbs or so. Remember though that this formula is empirical and the values obtained are approximate. Also, bear in mind that we computed the velocity of 2900 feet/sec at the muzzle of the weapon and if we measured the velocity of the bullet at some distance from the rifle, it may have decreased to something like 2500 or 2600 feet/sec. Therefore the OGW value will decrease over distance.

The author included a table listing the OGW values for various common cartridges. While these numbers seem to agree with many hunters experiences, there are also some issues with this formula. Even though the author claims to have considered bullet section density, bullet diameter, bullet nose shape and bullet construction in his study, none of these appear in the formula. Therefore, according to this formula, a 150 grain bullet moving at 2800 feet/sec will behave the same, whether it is a .270 Winchester or a .30-06 bullet, whereas the performance of these two bullets are very different in real life. Also note that this formula does not care if the bullet type is a jacketed bullet, lead bullet, hollow-point, round nose etc.

Measuring Effectiveness of Cartridges: Hatcher Formula

In our last two posts, we studied a couple of empirical formulae that were proposed by big-game hunters, the Taylor KO Factor by John "Pondoro" Taylor and the Thorniley Stopping Power Formula by Peter Thorniley. Today, we will study another empirical formula, this one invented by a military man, the Hatcher Formula.

The Hatcher formula was proposed by Major General Julian Hatcher of the US Army. He was originally a Navy man, before transferring to the Army. He worked his way up in the Army Ordnance department over several years. During the World War II time period, he served as Commanding General of the Ordnance Training Center at Aberdeen Proving Ground, Chief of the Military Training Division, Office of the Chief of Ordnance and later, Chief of Field Service, Ordnance Department. Due to the nature of his job, he became a well known firearms expert and after he retired from the military, he served as technical editor for American Rifleman magazine and wrote several books on firearms as well. One of his contributions to the literature was the Hatcher Formula, designed to measure the effectiveness of pistol cartridges. He also came up with a corresponding Hatcher Scale to put some meaning behind these empirical values.

Public domain image of Major General Julian Hatcher

The Hatcher formula was originally developed in the 1930s when Major General Hatcher was working in the US Army's Ordnance department. It uses the bullet mass, velocity, frontal area of the bullet and also a 'form factor' which depends on the type of bullet. Unlike the Taylor KO factor and Thorniley Stopping Power formula which only consider the diameter of the bullet in their calculations, the Hatcher formula uses the bullet cross-sectional area in its calculation. It also uses the bullet momentum formula (we studied this three posts back) as part of its equation. Additionally, unlike all the other formulae we have studied until now, this one includes the bullet type (jacketed, non-jacketed, flat point, round nose etc.) as part of its calculation. The Hatcher Formula is:

RSP = M/(2*g) * A * F

where:
RSP = Relative Stopping Power
M = Momentum of the bullet in foot-pounds/sec (momentum = mass * velocity where mass is in lbs and velocity is in feet/sec)
g = Acceleration due to gravity in feet/sec².
A = Frontal area of the bullet in square-inches
F = A bullet form factor that depends on the type of the bullet (see notes below)

In General Hatcher's original paper, he quotes the formula as RSP=M*A*F and prints a table of the calculated RSP values for a variety of common handgun bullet types. However, he calculates the momentum incorrectly as (kinetic energy/velocity), which ends up calculating a value of 1/2 of the actual momentum (since kinetic energy = 1/2 * mass * velocity²). He also incorrectly divides by g (acceleration due to gravity) when converting grains to lbs (no need to, because grains are a units of mass, not weight). Therefore I've updated the original formula to match the numbers on his original table and translated the equation to M/(2*g)*A*F.

The values for bullet form factor for some bullet types are defined as:
    F                      Bullet Type
  700     Fully Jacketed Pointed
  900     Fully Jacketed Round Nose
  1050   Fully Jacketed Flat Point
  1100   Fully Jacketed Flat Point (Large flat)
  1000   Lead Round Nose
  1050   Lead Flat Point
  1100   Lead Flat Point (Large Flat)
  1000   Jacketed Softpoint (unexpanded)
  1350   Jacketed Softpoint (expanded)
  1250   Lead Semi-wadcutter
  1100   Hollow Point (unexpanded)
  1350   Hollow Point (expanded)

In an earlier version of this article, your editor had accidentally quoted the numbers as 0.7, 0.9, 1.05 etc. instead of 700, 900, 1050 etc. Apologies for that and thanks to reader Nathaniel Fitch for pointing it out in the comments below (boy, do I have egg on my face now :-))

Because the type of bullet is part of the calculation, cartridges of a particular caliber meant for a single firearm can have different RSP values because they have different bullet types. For example, for a .45 ACP bullet which has a mass of 185 grains and moving at 1000 feet/sec, we compute a RSP value of 65.661 if the bullet is a Lead Round Nose bullet, but 88.642 for a Hollow Point (expanded) bullet. How do we get these numbers, you ask?
Weight of bullet = 185 grains.
We know that 1 lb = 7000 grains.
Therefore, mass of bullet in lbs = (185/7000) = 0.0264285 lbs approximately
Velocity of the bullet = 1000 feet/sec
Therefore, Momemtum of the bullet (M) = 0.0264285 * 1000 = 26.4285 foot-lbs/sec

Diameter of the bullet = 0.451 inches. Therefore, radius of the bullet = 0.451/2 = 0.2255 inches
Frontal area of bullet (A) = pi * r² = 3.1415927 * 0.2255² = 0.160 inches² approximately

Now, let's assume acceleration due to gravity (g) = 32.2 feet/sec² approximately.

For a lead round nose bullet, the form factor bullet F = 1000 from the table above.
Therefore RSP for this bullet is calculated as:
RSP = M / (2*g) * A * F = 26.4285 / (2 * 32.2) * 0.160 * 1000 = 65.661

For a hollow point (expanded) bullet, the bullet form factor F = 1350 from the table above.
Therefore RSP for this bullet is calculated as:
RSP = M / (2*g) * A * F = 26.4285 / (2 * 32.2) * 0.160 * 1350 = 88.642

Special thanks go out to reader Nathaniel Fitch for pointing out the errors in an earlier version of the article. His comments are posted below. Give him a big round of applause folks!

For self-defense purposes, the Hatcher scale recommends that the RSP be between 50-55 for effective stopping power. Values of RSP beyond 55 lead to diminishing returns, as the increase in stopping power is offset by the extra recoil strength that must be managed by the user. Per the Hatcher scale, values below 30 give a user a 30% chance of stopping the target in one shot. For values between 30 and 49, the chance of a one-shot stop rises to 50%. For values above 50, the chance of a one-shot stop rise to 90% per the Hatcher scale. Most .45 ACP cartridge types have a RSP value over 50, while 9 mm. Luger cartridges are mostly between 30 and 40. This means Hatcher's formula tends to favor .44 Magnum and .45 ACP over 9 mm. Luger for stopping power.

While the Hatcher formula does not consider factors such as bullet penetration, it is considered a fairly decent formula to determine the effectiveness of pistol ammunition.

Measuring Effectiveness of Cartridges: Thorniley Stopping Power

In our last post, we looked at a formula called the Taylor Knock Out Factor, which was developed by a big-game hunter with extensive experience with African wildlife. In this post, we will look at another empirical formula which was developed by another hunter, this one had extensive experience with wildlife in both Africa and North America. His name is Peter Thorniley and he developed the Thorniley Stopping Power Formula.

The Thorniley Stopping Power Formula is similar to the Taylor KO Factor we studied in the previous page. It is calculated as:

TSP = 2.866 * v * (m/7000) * sqrt(d)

where:
TSP = Thorniley Stopping Power
v = velocity of the bullet in feet per second
m = mass of the bullet in grains
sqrt = square-root function
d = diameter of the bullet in inches.

Since this formula uses the square-root of the bullet's diameter (unlike the Taylor KO factor formula, which uses the bullet's diameter without taking the square root), the values are on a different scale than the Taylor KO factor numbers. Like the Taylor KO factor, the values obtained by the TSP formula are empirical.

The Thorniley scale is as follows:

Thorniley Stopping Power	Suitable For
45	Antelope
50	White-tail Deer, Mule Deer etc.
100	Black Bear
120	Elk, Moose, Kudu, Zebra etc.
150	Lion, Leopard, Grizzly Bear, Brown Bear
250	Hippopotamus, Rhinoceros, Cape Buffalo, Elephant

The values in the table above are based upon Peter Thorniley's long experience as a hunter.

Let's say that we have a .30-06 rifle (such as the M1903 Springfield rifle or the M1 Garand rifle). Let us assume that this rifle fires a bullet weighing about 180 grains and .308 inch diameter moving at around 2900 feet/sec. Plugging the numbers into the formula above, we have:
TSP = 2.866 * 2900 * (180/7000) * sqrt(0.308) = 118.61 approximately.

Looking up the TSP value on the table above, we see that a .30-06 rifle can be used to hunt antelopes, deer, black bears, elk, moose, kudus, zebras etc. (since 118.61 is pretty close to 120), but probably not such a good idea against lions, grizzly bears, hippopotamuses, rhinoceroses, elephants etc.

Measuring Effectiveness of Cartridges: Taylor KO Factor

In the previous two posts, we saw how some people obtain a figure of merit for a cartridge by measuring the kinetic energy and the momentum. While these two methods have a basis in physics, the next method which we will study in this post is more of an empirical formula. This is called the Taylor KO Factor (where the KO stands for Knock Out). This term is also sometimes called the Taylor Knock Out Formula or simply abbreviated as TKOF.

The inventor of this formula was a famous 20th century big-game hunter and ivory poacher named John Howard "Pondoro" Taylor. Born in Dublin, Ireland, he developed a passion for hunting and decided to become a professional hunter in Africa. As a result of this, he became an expert in hunting with various rifles and cartridge combinations. In a career spanning over thirty years, he is credited with hunting over 1,000 elephants (though many of these were illegally hunted) as well as thousands of other African big game like hippo, rhinos, lions, cape buffalo etc. He received the nickname "Pondoro" (meaning "lion" in some African languages) from some of the locals, because of his lion hunting skills. Allegedly he was so busy hunting in remote African jungles that he didn't realize that World War II had broken out (he signed up for the King's African Rifles regiment after he finally got the news!)

John "Pondoro" Taylor (1904-1969)

John Taylor wrote quite a few books on the subjects of big game hunting and African hunting. In one of his books, African Rifles and Cartridges, published in 1948, he makes mention of a formula he came up with to test for cartridge effectiveness when hunting big game.

The story behind his formula is that during his long hunting career, Taylor had observed that some cartridges were more suitable for stopping elephants than others. While he admitted that many cartridge types would work at killing an elephant when aimed accurately at an elephant's brain, he was more concerned with situations where he missed the brain and the elephant would become enraged and charge at him. He wanted to evaluate cartridges that could stun an elephant, even if the bullet didn't hit a lethal spot, reasoning that a "knock-out" blow on the elephant would give the hunter enough time to reload and follow up with a more accurately aimed shot. It was really meant to calculate the effectiveness of solid big-bore bullets. John Taylor himself used this formula to make the point that big-bore bullets were more effective at stopping larger game than the lighter and faster bullets available at that time.

His formula is an empirical one and is defined as:

where:
m_bullet = Mass of the bullet in grains
v_bullet = velocity of the bullet in feet per second
d_bullet = diameter of the bullet in inches.
The dividing by 7000 is because his formula converts grains to pounds (1 pound = 7000 grains).

The TKOF obtained by this equation is a dimensionless number, as there isn't really a science behind it and it is merely a figure of merit for comparing different cartridge types. A higher TKOF value indicates better stopping power for the cartridge. For people who like to work with metric units, the calculation is defined as:

TKOF = m * v * d / 3500

where m is in grams, v is in meters per second and d is in millimeters.

Consider a NATO standard 5.56x45 mm. cartridge. The bullet from this cartridge normally weighs 4 grams (62 grains), has a velocity of 940 meters/sec (3100 feet/sec) and a diameter of 5.70 mm. (.223 inches). Using these values in the above formula, we get TKOF = 6.12 approximately.

The following table lists TKOF values for some common cartridges:

(Figures taken from wikipedia)

TKO Factor	Name	Mass (gr)	Velocity (fps)	Bullet Diameter (in)
19.6	.308 Winchester	168	2650	0.308
147	.50 BMG	660	3050	0.510
4.72	.380 ACP	95	980	0.355
6.20	.38 Special	158	770	0.357
8.56	.357 Sig	125	1350	0.355
24.9	.300 Winchester Magnum	180	3146	0.308
4.64	5.45x39mm	49	3000	0.221
35.5	.338 Lapua Magnum	250	2940	0.338
20.8	7.62×54mmR	181	2580	0.312
70.3	.458 Winchester Magnum	500	2150	0.458
29.8	.480 Ruger	325	1350	0.475
19.9	.44 Magnum	240	1350	0.429
12.3	.45 ACP	230	830	0.452
20.8	.30-06 Springfield	170	2850	0.308
10.4	.40 S&W	165	1080	0.400
11.3	.357 Magnum	158	1400	0.357
14.9	.30-30 Winchester	150	2250	0.308
7.31	9mm Parabellum	115	1250	0.355
6.12	5.56 x 45 NATO	62	3100	0.224
1.33	.25 ACP	50	750	0.251
1.33	.22LR	30	1400	0.222

Per the above table, we can see that a .44 Magnum has better stopping power than a .45 ACP as it has a larger TKOF value, but a .308 Winchester is considered nearly equivalent to a .44 Magnum in stopping power since their TKOF values are close to each other. Similarly, it suggests that a 7.62x54mmR is equivalent to a .30-06 Springfield and .25 ACP is equivalent to .22LR in stopping power, while a .50 BMG outdistances everything else by a very wide margin.

Unlike the kinetic energy and momentum formulae, the Taylor KO Factor takes the bullet diameter into account as part of the calculation. It tends to favor big-bore heavy solid bullets and is really meant for big-game hunting. If we were to calculate the kinetic energy and momentum of 7.62x54mmR and .30-06 Springfield, they would both suggest different stopping powers for the cartridges, but per the Taylor KO Factor calculation, these two are pretty close to each other in stopping power.

Measuring Effectiveness of Cartridges: Momentum

In our last post, we looked at one way to study the performance of cartridges by calculating the average kinetic energy of the bullet. In this post, we will look at another method that some people use to calculate the effectiveness: momentum.

Back in physics class in school, some might have studied that momentum = mass * velocity. So all we need to do is use a scale to measure the mass of the bullet and use a chronograph to measure bullet velocity and we can calculate the momentum of a bullet.

The idea is that when a bullet hits the target, the collision will cause the momentum will be transferred to the target. Unlike the calculation for kinetic energy, which we studied in the previous post, momentum is proportional to the velocity, whereas kinetic energy is proportional to the square of the velocity.

Calculating the momentum of bullets for comparative purposes works when the bullet speeds and bullet weights are both moderate. This method completely ignores factors like bullet diameter, bullet shape, bullet material etc. Therefore some of the results could be a bit stilted. For instance, a 500 grain .458 Winchester magnum fired at 2000 feet/sec has slightly less momentum than a 3 pound bag of cotton moving at 50 feet/sec. However, no sane person will ever argue that the 3 pound bag of cotton will effectively stop a charging elephant or rhino!

On the other hand, if the bullets are made of similar material and of similar shape, then comparing their momentum values is not a bad idea to measure which one will be more effective than the other. Most of the authors that use momentum to compare bullet effectiveness tend to be fans of big-bore heavier bullets.

Measuring Effectiveness of Cartridges: Kinetic Energy

In our last post, we discussed the basics of cartridge effectiveness. In this post, we will discuss one of the methods used to measure cartridge effectiveness, by measuring the kinetic energy of the bullet.

Some of you may recall that in physics class, we were taught that kinetic energy is the energy possessed by a body in motion. Therefore, a bullet in motion has a certain amount of energy in it, given to it by the burning propellant. When the bullet hits a target, it slows down and transfers the kinetic energy onto the target.

The formula for kinetic energy that we learned in physics class is:

where
E_k = Kinetic energy of the bullet
m = mass of bullet
v = velocity of the bullet.

In SI units, if the mass of the bullet is in kilograms and the velocity of the bullet is in meters/sec, then we have the energy of the bullet in joules. Similarly, in imperial units, if we have the mass in pounds (lb. or slugs), and velocity in feet/sec, then we have the kinetic energy in foot-pound force (ft-lbf).

In some American firearms related articles, the kinetic energy is also defined as:
E_k = m * v² / 450240
where
m = weight of bullet in grains
E_k = kinetic energy of the bullet in foot-pounds force

So why is this formula different and where did this 450240 come from. Actually it is simply a reworking of the previous formula.

Recall that 1 grain = 1/7000 pound force (lbf)
Also, acceleration due to gravity is roughly 32.16 feet/sec². Therefore, 1 pound force (lbf) = 1/32.16 pounds mass (lb.)
Therefore, if we measure our weight in grains, we need to convert it into lb. first, which works out to:
Mass in pounds = weight in grains / (7000 * 32.16) = weight in grains / 225120
Now applying this to the formula E_k = 1/2 * m * v², we can write this as:
E_k = 1/2 * weight in grains/225120 * v²

which can be further simplified into:
E_k = weight in grains/450240 * v²

The listing below shows the kinetic energies for some common pistol cartridges in both imperial and SI units.

Average kinetic energies for common cartridges

Cartridge	Kinetic energy
	ft-lbf	joules
.380 ACP	199	270
.38 Special	310	420
9 mm Luger	350	470
.45 ACP	400	540
.40 S&W	425	576
.357 Mag	550	750
10mm Auto	650	880
.44 Mag	1,000	1,400
.50 AE	1,500	2,000

Calculations of the above were taken from wikipedia.

Measuring the kinetic energy of bullets tends to favor bullets of higher velocity and lower mass, because the kinetic energy increases as a factor of the square of the velocity. Measuring the cartridge effectiveness by calculating the kinetic energy does not take into consideration factors such as diameter of the bullet, shape of the bullet, physical characteristics of the bullet (solid vs. hollow point, round nosed vs. flat nosed etc.). Some manufacturers tend to favor this method as it has a basis in science, as well as the fact that it is easy to measure the velocity of the bullet and its mass.

Measuring Effectiveness of Cartridges: An Overview

There are several formulae to determine the effectiveness of various types of ammunition. Some of these methods are based on some scientific principles, others are just empirical formulae that produce a number (i.e. a figure of merit) which can be used for comparative purposes against other ammunition types. We will study some of these formulae in the following posts.

One of the terms that is often mentioned in discussions of this sort is "stopping power". It is defined as the ability of the cartridge to cause enough ballistic injury to incapacitate a target where it stands. The physical characteristics of the bullet, the type of target and the shot placement has a large effect on stopping power. For example, a bullet capable of stopping a human will not stop a charging cape buffalo, a grazing shot will not have as much effect as a hit to center of mass etc.

Some of the methods used to measure cartridge performance include:

1. Kinetic energy - This is a scientific method and is often used by cartridge manufacturers to tout the superiority of their products.
2. Momentum - Another scientific method that is sometimes used by cartridge manufacturers
3. Taylor KO Factor - This is an empirical formula devised by John (Pondoro) Taylor, a 20th century big game hunter and poacher in Africa.
4. Thorniley Stopping Power Formula - Another empirical formula, devised by Peter Thorniley, who is another big game hunter in North America and Africa.
5. Hatcher Formula - Developed by Major General Julian Hatcher of the US Army in the 1930s, to determine the effectiveness of various types of pistol ammunition.
6. Optimum Game Weight Formula - Developed by Edward A. Matunas and first appeared in the April 1992 issue of Guns magazine.

Some of these methods (such as kinetic energy and momentum) ignore the diameter of the bullet and some of the others formulae take the size of the bullet into consideration. Only one of these methods (Hatcher formula) considers the construction of the bullet (e.g. an expanding bullet may be more effective than a non-expanding one) and the shape of the bullet (e.g. a solid wide nose bullet vs. a round nosed one) to be factors in performance, the others don't consider these factors as important at all. However, they all do help in simplifying some of the details of bullet effectiveness.

We will study these methods in detail in the following days.

What's Wrong With This Picture?

A couple of months ago, we discussed a hilarious video about how not to shoot a firearm. Now here's a screen capture from the popular TV series The Walking Dead.

Scene from The Walking Dead. What's wrong with the above picture? Read on to find out.

So what's wrong with the above picture? First, notice the character's off hand. He's holding a pretty sharp knife in it, while attempting to support his rifle at the same time. Not a very good idea.

Next, notice how he's intently peering through the sights. Wait, did I say sights? I should have said "sight". If you look closely at the picture, notice that the rifle is missing the rear sight! This person must be one heck of an expert shot to not need a rear sight!

Always Make Sure of Your Ammunition Type

In the world of firearms, ammunition comes in several calibers (e.g. .22, .357, 7.62 mm, 9 mm, .45 etc.). However, when purchasing ammunition, one must be careful to specify the exact type of ammunition. We will see the reason why in this post.

Back when we studied rimfire cartridges, we noted that there are several cartridges in .22 caliber, such as .22 Short, .22 Long and .22 Long Rifle (i.e. .22LR). Besides these three, there are other cartridges too, such as .22 Remington Jet, .22 Reed Express, .22 CB etc. Most of these, except the last one have .223 inch diameter bullets, but the length of the cartridges and the bullets differ. Therefore, if a firearm takes (say) .22 Long cartridges, the user will never be able to fit a .22 LR cartridge into the chamber.

The same thing is true with other calibers as well. For example, we have .380 vs. .38 S&W vs. .38 Special vs. .38 Short Colt vs. .38 Long Colt. In mathematics, we are taught that 0.380 = 0.38, but when it comes to cartridge sizes, they are two completely different things, as the image below shows:

.38 Special (left) vs. .380 (right)

Not only are the lengths and cartridge profiles dramatically different, the two bullets are also slightly different diameters as well: .38 special has a .357 inch diameter bullet, whereas .380 has a .355 inch diameter bullet.

Similarly, when referring to .45 caliber ammunition, it should be specified if the user wants .45 ACP, .45 GAP, .45 Webley etc. As before, all of these have dramatically different cartridge shapes and bullet weights.

.45 GAP (left) vs. .45 ACP (right)

As before, the reader may observe the difference in the sizes and shapes of the cartridges. Incidentally, ACP stands for Automatic Colt Pistol and GAP stands for Glock Automatic Pistol, the names of the manufacturers whose products these cartridges were originally designed for.

Finally, we have many cartridges in 7.62 mm: 7.62x25 mm. Tokarev, 7.62x51 mm. NATO, 7.62x39 mm. Soviet, 7.62x54 mmR etc. The two most famous ones are the 7.62 NATO (i.e. 7.62x51 mm. used by FN-FAL, M14, Heckler & Koch G3 etc.) and the 7.62 Soviet (i.e. 7.62x39 mm. used by the AK-47, AKM and Type 56 rifles).

NATO 7.62x51 mm. (top) vs. Soviet 7.62x39 mm. (bottom)

As the reader may note, it is pretty easy to tell that the two cartridges are drastically different.

The same thing applies to many other calibers as well. So, the buyer must note the exact cartridge type when purchasing new ammunition. As amazing as it may seem, quite a few people are not aware of the differences between the cartridges or that the other cartridges exist. There have been several instances where a buyer has walked into a local firearm store and asked for .38 cartridges and ended up walking out with either .38 S&W or .38 Special, when they really wanted .380 cartridges, or asked for .22 Long when they really wanted .22 Long Rifle etc. It is a source of frustration to both the buyer as well as the owner of the firearms shop.

Therefore, it is very important to note down the exact type of cartridge that a firearm accepts.

Measuring a Barrel's Twist Uniformity

In our last post, we discovered how to measure the twist rate of a barrel. Measuring the twist rate of the barrel is one thing, but how do we ensure that the rifling inside the barrel is uniform? We will study that process in this post.

Back when we studied different methods of rifling barrels, one of these methods was called Button Rifling, where a tool is pulled or pushed through a barrel to create the rifling grooves. One of the problems we noted at the bottom of that post was that if the button slips inside the barrel while it is being pulled or pushed through it, the grooves may be non-uniform. So even if the twist rate is (say) 1 turn in 10 inches, the rate of twist may not be uniform throughout the 10 inches of length. So how do we verify the uniformity of the twist throughout the barrel.

The solution was an invention called the Twist Deviation Machine invented by Mr. Manley Oakley of Seattle, WA.

Mr. Manley Oakley, inventor of the Twist Deviation Machine

Mr. Oakley was a world-class benchrest shooter and had won the National Bench Rest Shooters Association (NBRSA) trophy several times. He was a well known figure in the Northwest chapter of NBRSA and they now award an annual trophy in his name.

Mr. Oakley's theory was that if a barrel had a uniform twist rate, or the twist rate slightly increased as it approached the muzzle, all other features being normal, the barrel would be an accurate one. On the other hand, if the barrel's twist rate changed non-uniformly (e.g. speeded up and then slowed down, or vice-versa) or if the twist rate decreased towards the muzzle, the barrel would be less accurate. He verified this theory by testing barrels that were known to be accurate against other less accurate barrels of similar physical characteristics. In order to determine the uniformity of a barrel's twist, he invented the Twist Deviation Machine to measure it.

It consists of a hollow steel tube with a thinner steel rod passing inside it. The steel rod is free to rotate inside the steel tube. To the steel rod is attached a plastic washer and about three inches away from this washer is a second plastic washer attached to the steel tube. This apparatus is then pushed through the barrel. As the washers are being pushed through the barrel, they engage the rifling and start to rotate as they are pushed through, which results in the steel rod and the steel tube rotating as well. Now if the rifling is uniform throughout the barrel, the rod and tube will both rotate at the same rate. However, if the rifling is not uniform, then one of them will rotate faster or slower than the other and this can be easily observed by looking at the parts of the rod and tube that are sticking out of the barrel. This allows the user to measure if the twist rate is increasing or decreasing through the whole length of the barrel.