Pressure factor question - The math eludes me

[kowalski]

This is regarding implosion depth.
I'm a little confused by the math in this.
Submarine hull]http://www.lmnoeng.com/Statics[/url] /pressure.htm
pressure of seawater 1600ft deep = 715psi
Watched Crimson Tide yesterday and they said the hull would blow at 1850 on the U.S.S. Alabama. 1850ft deep = 826psi.

Someone please help me out here...

[petn7]

First of all, the Thresher

First of all, the Thresher did not have HY-100 steel for it's hull. I think it was HY-80. This fact still wouldn't answer your question, though.

Second, there are openings, seals, etc. that can not withstand the pressure like the steel hull can. This might contribute to the reduced hull crush depth.

[thordesign]

First of all, the tensile

First of all, the tensile strength is 100 ksi, that is a much different quantity than the allowable stress, or the ultimate yield strength. These are completely different animals and mean much different things. You cannot directly translate the pressure depth to the allowable stress. Directly comparing the pressure at depth to the ulitmate tensile strength of steel is like comparing the surface tension of hot cocoa to the brinell hardness of the coffee bean. There is very little relationship.

You must calculate the hull stress by using the thin walled vessel theory. This is a series of engineering equations based upon the external compressive or internal pressure stresses (or a combination of the 2) comparing the O.D. to the thickness of the material. Refer to Shigley 5th edition if intested, or the latest ASME Section VIII, Div. 1 pressure vessel code. In addition there are a series of internal structures that support the subs hull. These must also be taken into account.




Edited By ThorDesign on 1122692939

[kowalski]

I did some searching and

I did some searching and found an authour named Shigley in the mechanical engineering category. Which text by him were you mentioning? I did a look around for that ASME thing, it seems to be a $510 book, a bit steep just to check out a formula.

[anonymous]

Shigley Mechanical Design, or you

Shigley Mechanical Design, or you can use Rourke's or Mark's standard handbook. The ABS standards can be used as well.

If you live near an engineering university, you may be able to access their library, or pick up a used version from one of the starving students...

As mentioned in one of the previous posts, there are seals and other hull penetrations that "knockdown" the theoretical strength. In addition, deviation from a perfect cylinder, or sphere, will have a significant effect, as will the change in microstructure of the alloy from welding ( or stress concentrations in machined parts, blah, blah, blah....).

Another fun aspect of design for these vehicles is including factors of safety and shock loading conditions (and of course coefficients of thermal expansion, or contraction due to the cold temps at those dark depths...)

[tom dougherty]

I'm not going to add

I'm not going to add anything to the fine engineering explanations that Matt posted; they do an excellent job of describing the differences in how metal strengths are determined. I would note that hokey Hollywood crap like the Crimson Tide "they said the hull would blow at 1850 on the U.S.S. Alabama." Engineers calculate a safe "test depth" (maximum operational depth) that has a considerable safety factor built in. If a submarine were rated with a test depth of 1300 ft, it may very well be that somewhere around 1800-2000 ft it would implode. Or not. The exact depth (1850 ft) is never known and can only be determined experimentally only once (and you don't want to do that...). An individual hull will have manufacturing differences and hence otherwise "identical" submarines of the same class might vary considerable as to the depth where they would collapse.

What drives me crazy is the Hollywood scenes in which the collapse depth is announced with great precision ("The hull will collapse at 1852 ft, 9 inches depth"!), and then they stop just 5 feet short of collapse. Wow, that was close!! Gene Hackman as fishfood....

The more accurate picture is that of Das Boot, in which the submarine significantly exceeded it's test rated depth and held. A real life example would be the infamous uncontrolled dive of USS Chopper in the late 60's. This Balao class fleet boat was rated for a test depth of 400 ft. Skippers during the war took Balaos to 600 ft, but were sternly warned that the engineers thought that around 700 ft was pushing it. The Chopper, built in 1944, and converted to a Guppy, accidentally went out of control in an almost vertical dive in 1969, and the forward part of the boat exceeded 1000 ft in depth. and the stern was at 700 ft. She held together, well past her expected "crush depth", and the crew lived. Hence, there isn't a unique figure one can quote for the actual point at which a hull will fail. See the link for the story.

A word of caution about your submarine]USS Chopper "deep dive"[/url]

[kowalski]

Found the book for download.

Found the book for download. Haven't looked yet, but someone provided this explanation]Imagine for a moment that the Sub has 1/12 inch thick hull and is a cube, 1 foot on a side. If we examine on face of the cube, it's got 144 square inches of surface area. At 3,000 psi, this means that we're seeing 432,000 pounds of force on that face. Now supporting that face are the four walls of the cube, each is 1/12" x 12 inch, or one square inch,
making a total of four square inches supporting the weight of water pressure on any given side of the cube. 432,000 pounds on a side divided over 4 Square inches of high strengths steel supporting that side gives us a rought stress in the steel of 108,000 psi. Unfortuantely, the steel can only take 100,000 psi, so 3000 psi sea pressure is going to crush our
steel box.

Get it? Pressure _on_ the hull and stress _in_ the hull are realated but
not at a one to one ratio. [/quote]

Ok, I think I get it...the first 1/12" didn't enter into the area
calculation since the box was 12 by 12 by 12. But then the side of the box, holding up the face, is 1/12" each wall. He calculated that was too thin to hold up the side. But what about the height? It would still be held up by a foot of steel. Doesn't make a difference?

[thordesign]

No, you are still misunderstanding

No, you are still misunderstanding the relationship between depth and ultimate strength. The steel is NOT capable of withstanding 100,000 psi, that is its theoretical ultimate yield point, not its design yield strength. Its actual design yield is lower and design allowable is much lower than that. But, the higher the ultimate it can be safely assumed that the design allowable and design yield are elevated as well.

As Chris appropriately pointed out, there are many factors that effect the use of these values, one being a design margin or factor of safety, shape constants and factors, and a myriad of other design factors.


Below are some design factors that go into submarine design. As you can see, it is quite complicated and is affected by many different variables.


If you really want a headache and want to understand try the following link and download it. Go through the math and it will become apparent to you how diameter of the submarine, its many discontinuities, and the overall hull(shell) thickness are related to each other. You will also see how the yield strength varies from alloy to alloy and how it affects the design crush depth. Pay special attention to section 4.

http://swhite.me.washington.edu/~tuttle/ME354/pressure.pdf

a few of the factors considered in submarine hulll design as it relates to pressure.

C = attachment coefficient
d = internal diameter of vessel, in inches or meters.
E = joint efficiency factor, usually 1, except for welded vessels. (See Ref. 1, Table UW-12 in Appendix F, for welded joint efficiencies.)
hG = radial difference between the bolt circle and the pressure-seal circle on a bolted-end enclosure(hatch) inches or meters.
k = ratio of specific heats, cp/cv.
P = maximum allowable working pressure, psig or Pa.
ri = inner radius, inches or meters.
ro = outer radius, inches or meters.
R = ro/ri.
Sa = allowable stress of material, psi or Pa.
SFu = safety factor based on ultimate strength of the material.
u = ultimate strength of material, psi or Pa.
y = yield strength of material, psi or Pa.
t = wall thickness, inches or meters.
U = energy, ft-lb or joules.
v = volume, in.3 or m3.
W = total bolt load for circular hatch, lb or N. (Pressure force plus required gasket sealing force
For thin-wall vessels, where R is less than 1.1, use Eq. (1) or (2) to calculate p (the MAWP) (Ref. 6, chapter 12).



And to add to what Chris said, Blah, Blah, Blah....

Does this bring back memories of your sophmore year Chris? Yuck! Now we live this crap...







Edited By ThorDesign on 1122694975

[kowalski]

I'll look into that pdf,

I'll look into that pdf, thanks! But for now, as annoying as this question may be....can't we just blindly increase hull thickness?
Say I was building an Alvin submersible using HY100 for the pressure hull.
(Like the Turtle (DSV-3) has a HY100 1.33" thick sphere rated for 10,000')
Now, the real Alvin has a 1.92" thick titanium and is rated for theoretically 14000ft.
What if I made my 8ft diameter pressure sphere 8 inches thick? It might sound like overkill, but (and this is the whole point) would the added thickness automatically allow me to go deeper than the Alvin?

[tom dougherty]

To some degree, you might

To some degree, you might be able to thicken the hull in a spherical system such as Alvin, but the weight would increase drastically and you would not be buoyant. Likewise in a submarine; no, you can't just increase hull thickness. One of the heaviest items in the submarine is the pressure hull, so increasing thickness adds tremendous weight. The other "big ticket" heavy item is the reactor plant. Right now, US submarines have relatively little reserve buoyancy, and adding additional weight in the form of a thickened hull would mean they would submerge exactly once and permanently!! You would have to increase the buoyancy if you thickened the hull. And no, you can't just add bigger ballast tanks.....

As with any complex engineering project, you can't modify one parameter (like the hull) without having profound effects on others. That is why the focus is using stronger steels (eventually, maybe HY-130), HY-100 (Seawolf, Virginia) vs. the earlier HY-80. More strength per unit thickness. These steels don't buy you major increases in diving depth, however- a few hundred feet at best.

Remember the hull isn't some monolithic entity as far as diving. There are plenty of hull penetrations (condenser cooling seawater, waste pipes, etc.) that would need to be strengthened to withstand increased pressurea. Pumps would have be redesigned to work against the greater pressure head. The biggest problem would be to beef up the ballast tank blow systems to operate at higher pressures. There's a reason the deep diving submersibles dump lead shot rather than blow ballast to surface.



Edited By Tom Dougherty on 1122725953

[thordesign]

Tom is 100% correct.

Another problem

Tom is 100% correct.

Another problem with increasing the hull thickness is manufacturing. It is very difficult to manufacture a hull over about 3" thick. Remember this must all be welded, and anything over 1 1/4" thick must be PWHT(post weld heat treated). Roll forming, welding, and then PWHT an 8" thick section of HY100 or HY 80 is next to impossible to do efficiently, and really is just plain silly. There are other methods other than just adding steel. Tom is very adept at pointing out the reason by extreme depth vehicles carry droppable ballast instead of tanks.

[kowalski]

Thor, how about actually casting

Thor, how about actually casting the hemispheres instead of trying to weld the plates into a sphere?
Tom, doesn't the syntactic foam surrounding the pressure sphere make up for the lost buoyancy involved in increasing hull thickness?

[anonymous]

Good questions, but the knockdown

Good questions, but the knockdown factors are higher for cast materials as opposed to wrought (i.e hot rolled). It's tough to get a large casting not only homogenous, but porosity free. Then you'd have to weld the sections, unless you're thinking of casting a sphere with minimal penetrations in place to remove the core that forms the ID. That is a thermal nightmare.

To Matt's point, it's hard making really large thick sections. It's even harder to perform NDT (non-destructive testing) on these components. X-ray, Dye-pen, magnaflux, whatever, all become very difficult to perform and interpret with large thicknesses. And if you can't verify it, you can't use it.

Hate to sound like a negative-nelly here, unfortunately it's the nature of the beast. People don't realize the amount of shear brain power, and experience earned the hard way, that goes into these things.

Someday, who knows, the manufacturing/materials technology may develop to the point where we sit back and think how silly/scary it was to design subs from rolled&welded steel plate.

ps... Matt, it was *so* much easier back in sophomore year with all of those massless, frictionless systems....

[tom dougherty]

Tom, doesn't the syntactic foam

Tom, doesn't the syntactic foam surrounding the pressure sphere make up for the lost buoyancy involved in increasing hull thickness?

The amount of foam on the existing Alvin is indeed calculated to make it buoyant. But, if you now make the hull thicker so you can dive deeper, then you will need a lot more foam to counterbalance the increased weight and keep it buoyant. That means a larger fiberglass body (foam filled) surrounding the sphere. Oh, wait, larger wetted hull surface, more frictional drag; the slow speed will now become even slower and requires bigger thrusters and more power just to move. That means bigger (heavy) batteries. Ooopps, that adds more weight, will need even more foam....gets bigger, needs more battery power.....

Are you starting to get the picture? Any system, submarine or submersible is an integrated whole system, and you can't play with one factor without affecting others. As in all engineering, it's a series of tradeoffs that are made at the design stage to give overall balance to the design. You can't just sketch in a thicker sphere to the design and think it will all work. That's why we have engineers like Matt Thor.....

[kowalski]

Still, the pressure sphere in

Still, the pressure sphere in itself is very buyoant in the existing Alvin. I would imagine that the steel version would be heavier but necessary be a one way trip downward. It might not float back up as fast as they say the Alvin would but anyway....you are right that many calculations would need to be made.
The Trieste II however has a 5.94" thick pressure sphere, made of HY120 steel. Supposedly it is rated for 36,000' depth. So 8" would be overkill. Even the Turtle DSV is only 1.33" of HY100, and it's rated safe for 10,000'.

By the way, the Trieste II is a huge thing, nowhere near as compact as Alvin. There's that buoancy/energy compensation thing again...