# Resistance of submarines at different depths.

Discussion in 'Hydrodynamics and Aerodynamics' started by gonzo, Apr 26, 2013.

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### gonzoSenior Member

I was wondering what the difference in resistance is at different depths for submarines. At lower depth the higher pressure delays cavitation which should create less resistance at high speeds. Also, propellers could turn at higher RPMs.

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### Leo LazauskasSenior Member

Last edited: Apr 26, 2013
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### jehardimanSenior Member

As Leo's figures show, the main difference is how close the hull is to the boundary (surface or bottom). Once the hull is out of the influence of the boundary, 5-7 hull diameters, density is the the only thing that really effects resistance unless the design is so poor as to have a cavitation problem. This is the "deeply submerged" caveat that is always bantered about.

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Not forgetting the slenderness ratio too, dictated by the prismatic coeff. Which oddly enough shows that a value of 6 is optimal! Its the balance between skin friction (increase WSA) and viscous pressure resistance.

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### Squidly-DiddlySenior Member

I got a similar still unresolved bet about surface wave size at different atmospheric pressure if air density/viscosity is compensated for.

If in a dish of water I make a wave by moving a 1" block an inch in one second, would the wave look much different if we replaced the air with hydrogen and increased pressure so it had same density as air.

I say no (because the water's energy will be same, thus look the same), my friend says yes (because the pressure of the gas pressing down on water will change wave, smaller wave under greater pressure).

I think he is confusing pressure with gravity, and that pressure will be "in the equation" but only as it effects density.

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### ancient kayakeraka Terry Haines

The pressure of the compressed hydrogen on the surface of the water would be a constant at all places, effecting all parts of the wave equally and therefore not changing the shape at all.

Also, I think surface waves are determined by gravity and density rather than viscosity, which is negligible in this context.

The wave would be much more effected by a deep layer of oil on the water than by pressure changes. I believe the effect of the oil would be to greatly reduce the wave velocity by changing the differential force acting at the interface between the water and oil, in effect simulating a reduction of gravity.

I don't think this is the same as the effect on ocean waves of pouring oil over the surface: I think that merely delays the breaking of the waves.

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### Leo LazauskasSenior Member

Depth and viscosity both tend to reduce the amplitude of ship waves.

Viscosity preferentially damps out high frequency waves.
The amplitude of high frequency waves also decreases exponentially as
submergence depth increases.

Thus, for a submerged object, high frequency waves are hardly noticeable.

Compare the submarine wave patterns with a monohull pattern in:
where the high frequency waves are far more apparent.

Last edited: Apr 28, 2013
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### DCockeySenior Member

Based on my recollections of fluid mechanics vorticity in the waves would be needed for viscosity to have any effect.

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### Leo LazauskasSenior Member

Sure. So introduce vorticity and viscosity, and let's see your calculations.

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### jehardimanSenior Member

Getting back to the original topic, I think gonzo was asking if the depth itself makes any difference on the same hull....and the answer is once deeply submerged, realistically, no. There are a lot of secondary effects like hull squeeze, change in the cavitation number, and infintessimal changes due to density changes caused by pressure of isotemp/isosaline water, but the big picture is no changes in effective HP untill you begin to approach a boundary in isodense water.

Now off topic...

Ok, you are both sort of right, especially if you don't take a very fine knife to the term "smaller wave". Realistically, yes, your friend is correct that the density will effect shape of the pressure boundary (and waves are nothing but a disturbance in the static pressure boundary between two fluids...gas also being a fluid). And you are also correct in that the energy remains the same. The problem is how energy is carried by waves. Energy is carried in waves as a function of the length * amplitude ^2. But wave length is determined by the density difference between the two fluids (buoyancy really...assuming constant gravity). While for most gasses (low density, no matter what the pressure) there is little difference in wave shape, there would be sustantial difference if the lighter fluid was 10% or 50% or 99.9% as dense as the heavier fluid. This is how internal waves and "dead" water in fjords and even some toys work.

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### Leo LazauskasSenior Member

As a side note, internal waves in the ocean can be very high, sometimes well
over 100 metres! Fortunately, because of the small density difference, they
don't possess much energy.

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### jehardimanSenior Member

LoL, "much" being relative. Compared to a 100 m surface wave, not much. But a 100 m high (50 m amplitude) internal wave 2-3 km between crests still has a large amount of absolute energy. It's like saying tides have little energy on the open ocean because their height is so small.

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### Leo LazauskasSenior Member

Of course, a little closer to the original topic, there are also the internal waves
that submarines make. They can also make fairly high internal waves. One day
I'll get around to finishing off some work that Tuck started on that topic and
left me with.

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### gonzoSenior Member

I was considering that the higher pressure would allow higher loading and RPM on the propeller before it cavitates, which should be more efficient. Also, the foils for controls can be thinner because separation will start at a higher speed.

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### jehardimanSenior Member

No, maximum propeller efficiency is obtained when the propeller is large and slow turning. You do not want a high speed propeller.

Also "thin" (i.e. < 8% thickness) control foils only have less drag in the absolute straight ahead condition. In most cases, when the ship is not in 100% absolute perfect trim, thin foils have higher drag.

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