How thick is the hull on James Cameron's submarine?

Okay, so we figured out that James Cameron's submarine probably can withstand external pressure of about 17 - 18 kpsi.  How thick would the hull have to be to survive?  The NYT article mentioned that the capsule is only 43 inches wide.  I assume that that is on the inside not the outside.

The thing is shaped like a torpedo, so I'll use the model of a hollow cylinder with a half sphere at either end.  Spheres are the strongest solids, so the cylinder will be the limiting factor.  Granted it's going to have ribs that will increase the strength of the cylinder, but this will work for a good ballpark figure.

I got this equation for hoop stresses (the inward or outward stresses on a circular piece of metal) from efunda.com:

      P * r

σθ = -------

        t

Where:

σθ = Hoop stress (in psi)

P = pressure

r = internal radius of the vessel

t = wall thickness

James Cameron's submarine has an internal diameter of 43 inches, the radius is 21.5 inches.

The hoop stress will be the main stress of concern, which we calculated to be about 17kpsi.  So we rearrange and get:

     P * r

t = -------

      σθ

Now for a material.  I have no idea what that thing is made of, but let's assume a titanium alloy (it's pretty strong, right?) with a yield strength of about 120ksi (120,000psi), so...

     P * r     (17 ksi) * (21.5 inches)

t = ------- = -------------------------- ≈ 3 inches

      σθ              (120 ksi)

Bear in mind that this would cause the submarine to start to deform at the bottom of the trench, so give it a safety factor of about 1.5 and you get a thickness of about 4.5 inches.  Add support ribs on the inside and the thickness can be reduced.

So all in all, the thickness of the hull is probably about 3 to 4 inches.