# World War 2 Submarine Hull Thickness Math

Quote of the Day

How are the children?

— Masai warrior greeting, intended to ensure that the warriors always keep their number one priority in mind.

I was reading a blog post on Gizmodo that did a bit of math to determine why a pipe breaks the way it does when the water inside freezes. As I looked at the post, I realized the math was the same as would be used to determine the hull thickness for a submarine rated to operate within a specified depth range. To verify my realization, I decided to do a bit of historical math and apply the formula to figuring out the hull thickness for a famous type of World War 2 submarines, the Balao Class Fleet Submarine (Figure 1).

Figure 1: Photograph of USS Balao.

The calculations are shown in Figure 2. The calculations agree with the pressure hull thickness actually used on this submarine. I have found a number of discussions on the Balao's operating depth (example). Richard O'Kane operated USS Tang down to 600 feet during sea trials. Apparently, the crews had great confidence in the construction of the Balao class.

Normally, I go through derivations of these equations. In this case, there are numerous discussions available on the web (e.g. here and here).

Figure 2: My Rough Analysis of the Required Steel Plate Thickness for a Balao-Class Submarine.

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### 2 Responses to World War 2 Submarine Hull Thickness Math

1. Robert Perugini says:

I am not an accomplished mathimation but I love to see how these guys (experts in their field approach these situations.

2. mike sawrun says:

aside from just building one and lowering it into the ocean, if I were in charge I would establish parameters . these would start with material specs. then I would design and perform a series of tests to determine the ability of these materials to resist the pressure of the sea . any suitable material would have to be able to absorb repeated deformation due to pressures going up and down. it would also have to be available in quantity and workable by the current construction methods. then after I knew how thick to make the hull I would double that as a safety factor. don't forget the enemy is going to try to blow it up. that said our side did well because of our subs survived.