[PSUBS-MAILIST] Hull Construction Questions

[Charles Perkins <chuck@memetech.com>]

Hi guys. I have some more questions about submarine pressure hulls...

First of all, regarding stiffeners: I see that the single-hull designs 
(predominant on PSUBS for reasons of simplicity and economy I'm sure) 
place the stiffeners on the inside of the pressure hull. It appears to 
me that larger dual-hulled vessels such as the fleet submarine USS 
Pampanito have their stiffeners on the outside of the pressure hull... 
perhaps to conserve interior space, I don't know.

(check out http://www.maritime.org/fleetsub/appendix/pages/figa-01.htm  
... very cool! Did the German U-Boats have their stiffeners on the 
inside or the outside?)

The question is this: does it matter whether the stiffeners are on the 
inside or the outside of the hull for pressure resistance calculations? 
Obviously stiffeners of the same thickness outside the hull vs. inside 
the hull will be heavier just because the diameter is larger. I am 
wondering if they must be made thicker as well to compensate for the 
reduced curvature... or does that not matter because the stiffeners are 
just there to stiffen the hull, not to resist pressure?

The very nifty spreadsheets on the PSUBS site don't specify whether the 
rings are on the inside or the outside of the hull. Do they assume that 
the rings are on the inside?

What I'm getting to is this: can a pressure hull have some of its 
stiffeners on the inside the hull and others on the outside? I am 
contemplating a situation with a double-hulled sub where in some places 
there is little inside clearance and in other spots there is little 
outside clearance. The diameter of the pressure hull itself would 
remain constant.

My next question has to do with the fabrication of the pressure rings 
themselves. I see them described as simple T structures with a ring 
thickness and height and a flange thickness and width. But Carsten's 
Euronaut has I-beams! Why? And how were they welded to the Euronaut's 
hull... Perhaps with a bead on either side of the I plate adjacent to 
the hull plate? Is the un-welded but adjacent portion of the I-plate 
unimportant? I presume so because I can't imagine how one could weld 
the face of one plate to the face of another plate... but then again, 
I'm no welder.

Another thing I've been wondering about is end-caps. Hemispheres and 
flattened domes are traditional... and inverted domes where the end 
bows in to the tube instead of out seem easy enough to figure out. I'm 
thinking of something different. What I'm wondering about is this:

What if I were to end the (horizontal) tube as though it were 
intersecting a vertical tube... without the vertical tube. Looking from 
the top you would see a tube ending in a round shape, looking from the 
side you'd see a tube ending in a square shape. My intuition tells me 
that it would be the same as doing a T intersection and I'd need the 
same sort of stiffening as if I were extending a tube upwards for a 
conning tower...

By the way, what kind of stiffening do I need if I'm going to extend a 
tube upwards of the same diameter as the pressure hull? (How do I 
calculate the pressure resistance of a T junction?)

And finally I need to calculate the volume of the intersection of two 
cylinders when one cylinder is smaller than the other. Imagine a 
conning tower here. It would be helpful to know how much it displaces. 
I know the formula for when the tubes are of the same diameter ... 
(16r^3)/3 ... but all of the methods for when the radii are different 
look horribly complicated. Specifically I'd like to know the 
intersection volume when r1 = 3.5 and r2 = 2.5.  Are there any math 
wizards out there that aren't frightened of the Elliptic Integral of 
the Third Kind? (shudder)

If I knew the intersection volume for 3.5 and 2.5 I'd know the 
displacement of the whole thing... that's the last bit that is missing 
as far as volume is concerned.

Once I learn the answers to some of these questions maybe I'll post a 
design for your amusement. In the mean-time any insights on the above 
matters would be greatly appreciated!

Thanks,

Chuck




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