Submarine Roll

Hi,

Quick question that bugging me - does a neutrally buoyant submarine roll around its centre of buoyancy, its centre of gravity or half way between the two?

Thanks.

 

Neither, it rolls about its center of hydrodynamic mass (i.e. the "normal" CG with any free floods contained within the "shell" added). And you get cross-coupling just like a surface ship so the actual instant center is shape and rate dependent. One of the snap roll issues.

 

Hi, thanks for that. So assuming the that there are no free flood spaces (just a solid shell) and it was stationary, it would rotate about the VCG?

 

Yes, for a solid body, considering rotation only, it would be about the VCG. If the body cross section was round (i.e. a body of revolution) and the VCG was at the center and you forced rolling it would only roll. In the normal case for a stable body of revolution, where the VCG is slightly below the VCB, the vehicle also sways as it rolls. In fact it is this distance between the VCB and the VCG that causes rolling of a submerged body when it sways with the wave orbitals.

 

John,

In your first post you mention "snap roll".

I have looked for a definition of it for some time to no avail.

What causes it, what are the variables, why does it happen?

 

Snap roll is a hydrodynamic issue relating to the body going thru the water at an angle of attack, it really has nothing to do with a static roll situation.

 

Snap roll is the sudden heeling of the sub in a turn. It is caused by hydrodynamic forces that arise due to the asymmetric appendages (fairwater). I think that it first became an issue when submarines started going fast underwater and the out of plane hydrodynamic forces become much larger than the static righting moments.

 

As Johneck says it is a roll caused by dynamic and hydrodynamic forces during a turn. It is a function of alpha flow, appendage lift, and the static BG; so unlike what was stated, it is intimately linked to static roll and cross-coupling.

All verically stable floating bodies have a roll in any turn, wether they have appendages or not, but going fast makes the problem more pronounced. The term "snap roll" was first applied to then new high speed submarines with overlarge fairwaters, however it was soon recognized that the issue always had existed and could explain some control features exhibited by other high speed shapes. On most displacement surface ships during a turn the roll is "out", on submerged bodies of revolution, the roll is "in", and on appendaged submerged bodies it depends on the size and arrangement of the appendages.

 

To clarify, the BG obviously has an effect on the magnitude of the resulting roll, but the hydrodynamic forces that cause the roll are not related to the static couple that would result in an outward roll due to the CG aboce the CB. I believe that if the body were simply an unappended body of revolution shape, there would be no snap roll.

 

No, it will roll in and sway in because of the VCG below the VCB (i.e. the CG swings out in the turn due to centrifugal force but there is more area above the CG than below so the body rolls in) and does happen on effectively smooth bodies of revolution. FWIW, snap roll really isn't a problem unless BG is too large for the speed or it is accompanied other appendage issues. The Albacore/Skipjack "snap roll" was a problem because it was unpredictable in onset (hull shadowing) and was accompanied by a sharp pitch down due to the roll making the fairwater turn lift point down and the rudder force drive the stern up.

 

Can you explain why roll is about VCG rather than some point between VCG and VCB please?

Suppose the fully submerged body was actually positively buoyant but tethered to the sea bed. Does it still rotate around the VCG? Suppose then that the tether was attached slightly to one side. I can imagine that in one direction the tension in the tether acts as a pin joint, but in the other it doesn't (as a tether has no compressive strength).

 

Do not confuse the instant center with the center of roll. In free-free body, all forces and monents are resolved about the center of mass. About that point there can only be the motion in the 3 direction vectors and rotation about the 3 direction vectors. All motion is related to the center of mass. The instant center is a fictious point, frozen in time, that the cross-coupled rotation and translation of the center of mass (or any other reference point) appears to rotate around at that instant in time (i.e. all motion resolved into a single vector cross-product). It is not a constant, but changes with the interaction of the BG pendulum and the cross-coupling of roll-heave-sway.

FWIW, a tethered bouyant behaves differently than a free-free body because it now becomes a link system and subject to normal rigid body kenimatics (think upside down pendulum). From a hydrostatic perspective everything changes depending on the connection.

From where you are going in this line of questions, I think you book you want to get your hands on and read is Buoy Engineering by Berteaux of WHOI (ISBN 0-471-07156-0, J Wiley & Sons, 1976).