Computing Ballistics with a Slide Rule
November 27, 2018
As shooters, we are living in a golden age of information and access to information. In a matter of seconds, we can find information or data about nearly anything we want. This unprecedented access has opened up windows to highly technical information that 40 or 50 years ago was unavailable to the public.
For instance, exterior ballistics solvers were only wishful thinking not that long ago. Now, nearly every bullet company has an online solver.
Applied Ballistics, Gun-werks and JBM Ballistics all offer advanced ballistic coefficient (BC)-based solvers. Hornady took it a step further with its Four Degrees of Freedom (4DOF), which is a drag-coefficient, projectile-dynamics-based program that previously was only available to defense contractors and the government.
Today’s reloading guides are outstanding, all based on standardized equipment and instrumentation, and available from every bullet and propellant manufacturer. There are also interior ballistics calculators such as Quick Load, which models propellant thermodynamics and combustion.Powley Power
Those of us older than 45 can remember when about the only information or data available on ballistics was what was printed in a catalog, magazine or reloading guide. At times, some of this information was questionable. There was no Internet or computer or ready access to anything that allowed the average shooter to play around with determining their own ballistics, except for the Powley Ballistics Slide Rule Calculators. Even then, many of us had never heard of Homer Powley or his brilliant contributions to the science of ballistics.
Homer Powley was born in 1909 and was a chemist, mathematician and a gun writer. In his later years, he served as the ballistician for Frankford Arsenal. Powley made tremendous contributions to the science of ballistics in the shooting industry. He worked with industry legends such as Joyce Hornady and Vernon Speer on both reloading data and branded calculators. Powley was a brilliant mathematician and was one of the few people who understood the physics of both interior and exterior ballistics and could put math to it. This was no small feat considering everything was done on a slide rule and paper.
Powley had access to the ballistics data of the DuPont Company and the IMR line of propellants, which at the time was the standard for small arms propellants. His understanding of the science of interior ballistics and math allowed him to take a huge amount of data, separate it by the variables that controlled the interior ballistics, such as case capacity, expansion ratio, barrel length, etc., and determined equations to fit this data and variables.
By use of these equations, he could predict both the muzzle velocity and pressure in Copper Units of Pressure (CUP) for virtually any practical combination of case, bullet and barrel length using IMR propellants. By extension, these calculations worked for propellants with similar speeds and performance to IMR propellant types.
It is important to note that the Powley PSI calculator is a bit of a misnomer. It is actually calculating chamber pressure in CUP. The pressure measurements at the time were done mechanically with copper cylinders that were crushed by the pressure in the cartridge case. This method did not actually measure the real pressure inside the cartridge, but was an adequate way of controlling the loading, safety and reliability of ammunition.
CUP was largely replaced in the 1980s by the Piezoelectric transducer, which does measure the real (Piezo) pressure in the case. The copper-crusher method of pressure measurement in small arms ammunition generally gives lower values as compared to Piezo. As an example, the SAAMI specification for maximum pressure in the .30-’06 Springfield is 50,000 CUP. The corresponding Piezo maximum pressure as measured by a Piezo transducer is 60,000 pounds per square inch (psi).
Powley also understood small-caliber exterior ballistics and used the same type of approach as he used with the interior ballistics calculators and developed equations to predict the exterior ballistics of small-caliber, flat-firing projectiles. Today, the availability of computers would make what Powley did seem easy using virtually any spreadsheet program. However, Powley did all this by hand, which is a testament to his brilliance.Team Power
Powley had figured all this out by the late 1950s and needed a way to put it all into a slide-rule-type calculator, the standard of the time. Enter Bob Hutton, technical editor of Guns & Ammo magazine from 1959 to 1974.
In addition to being an editor for G&A, Hutton owned and operated the Hutton Rifle Ranch in Topanga, California, a shooting and firearms testing and training center.
Powley approached Hutton for help with the calculator. The two worked together to verify Powley’s equations and put it all into a calculator. It was quickly decided they needed help to design and produce a slide rule calculator. Enter Bob Forker, retired handloading editor and writer for G&A whose experience spanned some 40 years.
At the time, Forker worked for a company that made slide rules and was a budding shooting enthusiast. Forker’s work on this project and his association with Hutton and Powley launched his long career as a writer and ammunition and ballistics expert. The team of Powley, Hutton and Forker designed the Powley Computer for Handloaders, the Powley PSI Calculator and the Powley Ballistics Calculator. The earliest records I can find of any of these calculators being available is 1961.
Powley’s slide rule calculators can be found occasionally on Internet auction sites. They are also available through the Wayne Blackwell’s “Load From a Disk” software. The loads and pressures calculated by this program are from the Powley Computer for Handloaders and PSI calculator.Calculating History
A fascinating tie-in of the Powley Calculators to the history of ammunition development is the 5.56 NATO, which was the predecessor of the .223 Remington.
The military’s requirements for the 5.56 NATO were quite ambitious at the time. The military wanted a cartridge that would fire a 55-grain projectile from a 20-inch barrel, exceed supersonic velocity at 500 yards — approximately 1,100 feet per second (fps) — penetrate .135-inch of steel and be roughly the size of the .222 Remington. The requirements led to a muzzle velocity of approximately 3,300 fps.
Eugene Stoner approached Hutton for help with developing loads for this new cartridge from 1962 to 1964. His initial work with IMR 3031 and 4895 failed to achieve the required performance. Although I can find no direct evidence that the Powley calculators were used in this endeavor, it is hard to imagine that Powley and his calculators did not play a role in Hutton’s work and the development of the 5.56 NATO and WC 844 propellant that was used in the M193 55-grain load of the Vietnam War.Test Time
Now that we have discussed the history of the Powley ballistics calculators, let us use them to do an analysis of the 5.56 NATO. Keep in mind that the calculator was designed around the IMR line of propellants. With a certain amount of caution, the calculations could be extended to other propellant types that match up to IMR propellants for speed and charge weight.
The Vietnam-vintage SP1 M16 load consisted of a 55-grain full-metal-jacket (FMJ), boattail (BT) projectile with approximately 26.5 grains of WC 844 propellant. This was essentially a 100-percent charge density load that completely filled the case to the bottom of the projectile. Muzzle velocity from a 20-inch barrel was 3,260 fps.
We have to throw out a few caveats for our chamber pressure discussion. The 5.56 NATO ammunition was not tested with copper crushers, the standard when Powley developed his Handloaders and PSI calculator. The maximum chamber pressure of the 5.56 NATO is approximately 62,500 psi Piezo pressure, which equates to approximately 53,000 CUP. This is what the Powley PSI calculator is actually deciphering. The 55-grain FMJ-BT projectile has a G1 BC of approximately .245. Using the JBM online trajectory solver, it predicts a remaining velocity at 500 yards for the 55-grain M193 projectile fired with a muzzle velocity of 3,260 fps to be 1,538 fps.
Using the vintage Powley Ballistics calculator, I fed it the BC and muzzle velocity from above to get a remaining velocity at 500 yards of approximately 1,540 fps. (The resolution of the slide rule is about 10 fps.) As you can see, the Powley Ballistics calculator was certainly up to the task of predicting the exterior ballistics performance required of the 5.56 NATO.
Now let’s look at the interior ballistics of the 5.56 NATO using the Powley Computer for Handloaders and the Powley PSI (CUP) Calculator.
As I stated above, the Powley Computer for Handloaders was based on IMR propellants. IMR propellants do not have as high a loading density as Ball Powder propellants and therefore cannot achieve the charge weight in a given case capacity as a Ball Powder propellant.
At the time Hutton was doing his charge development work on the 5.56 NATO, the best IMR propellant for the M193 load would have been IMR 4895. Based on my experience as a ballistician, about 24.5 grains of IMR 4895 is about as much as you can reliably get in the case with automatic loading equipment. Consulting my Hornady reloading guide, which has 5.56 NATO data, it shows that 24.5 grains of IMR/H4895 would give about 3,150 fps from a 20-inch-barreled 5.56 NATO firearm. This is significantly below the 3,260 fps muzzle velocity the U.S. Army decided was necessary to achieve their requirements. If Hutton had been using a Powley Computer for Handloaders and used the values listed in Table 1 for the 5.56, he would have calculated a muzzle velocity of approximately 3,170 fps. It matches extremely well with modern data.
Now, using the Powley Computer for Handloaders to determine the performance for a hypothetical Ball Powder propellant that could take advantage of the entire 26.5 grains of case capacity, we would arrive at the inputs listed in Table 2. Using these inputs in the Powley Computer for Handloaders, we arrive at a muzzle velocity of approximately 3,250 fps. Virtually the same as the ammunition specification!
For the last part of our evaluation, we will use the values from Tables 1 and 2 to calculate chamber pressure. Remember, the values the Powley PSI calculator will give will be in CUP. For the 24.5 grains of IMR 4895 the Powley PSI calculator gives a pressure of approximately 48,000 CUP, which would be about 53,000 psi Piezo pressure.
From my experience in the lab, this would be very close to the actual measurements. For the 26.5-grain load of Ball Powder, the pressure would be approximately 51,500 CUP, which corresponds to about 60,000 psi Piezo pressure. Again, this is right where it should be and within the specifications for the 5.56 NATO of 62,500 psi.
The Powley ballistic computers of the early 1960s were powerful tools for anyone conducting small arms ballistics research at the time. They still provide answers today that would be of value to anyone wanting to experiment with small-arms ballistics. I encourage any reader who wants to gain a better understanding of propellants and ballistics to take a look at the Powley calculators on a computer or to have some fun shopping for original Powley slide-rule computers. When you’re doing this, take a moment to reflect on what a tremendous contribution Homer Powley made to the science of ballistics.