Cannon Bore Measured in Pounds

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Figure 1: 17 Pdr Anti-Tank Gun on Sherman Firefly .

Figure 1: 17-Pounder Anti-Tank
Gun on Sherman Firefly . (Source)

I have been pulling together some WW2 data for an article that I want to publish in the next year or two. During my research, I have noticed that the British specified the caliber of their artillery by the nominal mass of the projectile (lbm or pound mass) and not by the bore diameter. I was curious as to how the British came to this particular system and decided to investigate further. As with many military standards, it traces its history back hundreds of years.

Back in the mid-17th century, cannons fired solid iron, spherical shot. This means that the application of a bit of geometry allows one to relate the diameter of the shot to the mass of the shot. The use of mass to determine the size of something was very common in the old days when weight measurements were far easier than dimensional measurements. We still see thread diameter measured using pounds – as long as the thread is made consistently (standard length, consistent thickness and material), weight can be used to specify thread diameter.

Equation 1 shows the formula that I will use to relate the diameter of spherical shot to the its mass. I will use Equation 1 to calculate a table that I found in a document from 1768 (Muller, pg. 6) that lists both the diameter of the shot and the gun to the mass of the projectile. Note that breach-loading artillery must have a bore diameter (referred to as the caliber) that is slightly larger than the diameter of the shot so that the shot can be forced down the barrel when covered in wadding. In 1768, the standard was that the caliber was 5% larger than the shot diameter.

Eq. 1 \displaystyle M=\rho \cdot \frac{4}{3}\cdot \pi \cdot {{\left( {\frac{D}{2}} \right)}^{3}}\Rightarrow D=\sqrt[3]{{\frac{{6\cdot M}}{{\rho \cdot \pi }}}}

where

  • M is the mass the round shot.
  • ρ is the density of the material making up the solid shot.
  • D is the diameter of the round shot.

The calculation of the cannon caliber (i.e. bore diameter) is simply 1.05·D, where D is the output of  Equation 1. I used the Excel spreadsheet here to generate my version of the original table (Figure 2).

Figure M: My Version of the Muller Table.

Figure 2: My Version of the Muller Table.

The values I compute are close to those shown in the original table (Figure 4).  I assume the errors are due to routine calculation errors on the part of the human calculators,  which can easily occur when using logarithm tables. I shudder just thinking about performing these calculations by hand using logarithms. I spent weeks in Osseo Junior High School  mastering interpolating log tables for just such hand calculations. Very little had changed between 1768 and 1971.

I should mention that Muller computes the density of the shot material based on a 9 pound projectile with 4 inch diameter – this projectile constituted both a diameter and weight calibration reference similar in spirit to the international prototype kilogram and meter.  I compute the density of the shot reference as  7.43 gm/cm3, which is very close to the density of pure iron (7.874 gm/cm3).

Using the term pounder to express the diameter of an artillery projectile today is not particularly useful because the mass of a projectile today does not uniquely determine its diameter. In fact, the vast majority of modern projectiles are composed of multiple types of materials (e.g., steel, copper, tungsten, explosive, tantalum, etc) in multiple types of geometries (e.g., shells, arrows, winged, rocket-boosted, etc)  based on their function. Thus, diameter and mass are not as strongly correlated today as 300 hundred years ago. Figure 3 shows how the pounder unit relates to the projectile diameter for some modern UK artillery. Notice how projectile mass does not uniquely determine the diameter of a modern projectile. This approach has become unworkable and the UK now specifies projectile diameter.

Figure 3: List of Modern Artillery With Their Bore Diameters and Pounder Designation.

Figure 3: List of Modern Artillery With Their Bore Diameters and Pounder Designation. (Source)

Appendix A: Original Table from Muller Document

Figure 4 shows the original table from the Muller document. Note that I actually corrected one obvious error in this table – duplicate values of 3.668 in the top caliber row (marked in red). Errors like this are very common. I have spent hours trying to find errors in old WW2 records. I do have sympathy for the poor yeoman who had to type in all this data.

 Figure 3: Table of Shot Masses, Diameters, and Calibers.


Figure 4: Table of Shot Masses, Diameters, and Calibers.

 
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