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Conversion of pounds into inches

Conversion of old pounds artillery caliber into more modern inches and millimeters

How can you convert units of weight into units of length? You can if you're talking about old cannons.

Up until the second half of the XIX century, cannon’s caliber was expressed in pounds. For example, 24-pounds cannon. You can often meet such things in historical books. Now, how modern person can imagine such a cannon? Is it big or not? What is the 24-pounds cannon?

So, I decided to employ a little bit of logic and convert pounds to more familiar units used for gun calibers now – inches and millimeters.
(BTW, there are the tables of correspondence all over the Internet, so later I’ll use them to prove my calculations)

Here comes the deduction.

Pounds in caliber denote the weight of a cannonball, which can be fired off this gun. Now caliber is measured as the diameter of gun’s barrel and expressed in inches, or millimeters, and we can imagine how big such a gun is.

Let’s start with the conversion of pounds to kilograms. Pounds are very different by nature Pound weight, but, since I’m Russian, "Russian artillery pound", equals 494,414 grams, looks very promising to me. And, surprisingly, it was used to measure the weight of cannonballs.

After we have found the weight of the cannonball, and since it is, well, spherical, we can find the diameter of a sphere. Cannonballs were made from cast iron. The density of cast iron, according to this handbook Density of materials is 7000 kilograms per cubic meter. We have ball mass and density, so obviously, we can find the volume. On the overhand, the volume of the sphere should be \frac{4}{3} \pi R^3, and from this, we can find the radius, hence, the diameter of a cannonball.

According to common sense, the diameter of the barrel should be slightly greater than the diameter of a cannonball. But the gap should be as small as possible, so explosion impulse can be used at maximum.

Peter the Great (1672-1725) established the standard, and according to it, cannon of 24 pounds or less should have a gap between barrel and ball not greater than 1/29 of caliber, in other words, the diameter of the barrel is 29/29, and diameter of the ball is 28/29. Cannons of greater calibers have separately defined gaps.

But even this is enough information for my further deduction. 1/29 for 24-pounds caliber is 5.2 millimeters. For greater calibers, I’ll take 5 millimeters.

So, on the final step, I just add this gap (twice) to the diameter of the ball. To get inches, I simply divide millimeters to 25.4 (one inch)

The online calculator below repeats these steps and outputs the gun’s caliber in inches and millimeters given the cannonball weight in pounds.

Now, I’ve compared my results with tables.
3 pounds - 76 millimeters (mine) - 77 millimeters (tables)
4 pounds - 88 millimeters (mine) - 84 millimeters (tables)
6 pounds - 95 millimeters (mine) - 97 millimeters (tables)
12 pounds - 120 millimeters (mine) - 122 millimeters (tables)
18 pounds - 137 millimeters (mine) – 139 millimeters (tables)
24 pounds - 152 millimeters (mine) – 153 millimeters (tables)
60 pounds - 195 millimeters (mine) – 206 millimeters (tables)

Well, pretty close, I’d say. Common sense with school knowledge of physics and math can yield you and answer :)

PLANETCALC, Conversion of gun's pounds into inches

Conversion of gun's pounds into inches

Digits after the decimal point: 1
Caliber, inches
 
Caliber, millimeters
 

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