Stability In Low Free board Vessel When Submerged

I'm curious about evaluating pitch stability during submergence due to wave action particularly in low freeboard and/or low reserve bouyancy vessels such as the Civil War era USS Monitor, the Amas of older trimarans or some fully enclosed kayaks. This analysis, considering the dynamic nature of a passing wave, seems fairly complex. Much more complex than a submarine or static calcs I've studied for surface ships. I have (for fun) shown the USS Monitor with a scaled 10ft swell over it and it can be seen that 3/4 of the deck is completely below the water. 10ft is not particularly large for an ocean going vessel and I doubt it is stable during full submergence (maybe why it sunk). And of course having the LCB directly above C.G. is not necessarily stable, since you may have a driving force low and resistance forces high on the hull there's a potential for pitching moment and then deceleration may cause a moment too. Any tips/tricks or rules of thumb for evaluating this condition?
Thanks!

 

This may sound harsh, but have you had a vessel dynamics course? I ask this because your question and especially your USS MONITOR example shows a profound lack of understanding about hull form and dynamic response.

I know I can teach all the necessary hydrostatics to satisfy NSTM 096 to an eighth grade algebra student in about a month, but 6 DoF hydrodynamics needs a fair bit of differential equations to do the heavy lifting. If you need a good basic text I would suggest Dynamics of Marine Vehicles by Rameswar Bhattacharyy (he was a professor at USNA and made this basic text on the subject). It leads you through the entire process without digging too deep into the math.

FWIW, USS MONITOR was lost of Hatteras in seas of ~20ft with a very short wavelength (typical of Hatteras/Lookout/Frying Pan Shoals) due to downflooding (primarily through the forced draft vents), not stability. Even with over two feet of water throughout the vessel, there was enough dynamic stability to make motions extremely harsh (the real issue with raft type hull forms). Later monitor type vessels corrected the downflooding issues and made several trans-oceanic voyages; most notably the USS MIANTONOMOH 's tour of Europe and the USS MONADNOCK rounding South America via Cape Horn to take up duties in the Pacific.

 

No. I'm a mechanical engineer without formal naval architecture education. Looking to learn... Book suggestion noted.

You say the issue with raft type hull forms is the extremely harsh motions. I presume this is due to the large waterplane area causing high accelerations. However, what I'm interested in is vessels with very low reserve buoyancy. In the case where the vessel is almost neutrally buoyant, heave force is limited and thus heave acceleration (F=ma) to that of the difference between the submerged vessel's total displaced volume and mass of the vessel itself. With a very low reserve buoyancy, I believe even a large waterplane raft would have low vertical accelerations, 'piercing' through waves vice riding over them. Obviously this disregards viscous forces of the water 'pushing' on the hull. I falsely assumed the Monitor had a low reserve buoyancy based on the minimal freeboard but understand that with the large waterplane the low freeboard still provides adequate reserve bouyancy... sorry, it was a bad example

I'm interested in something like a trimaran with an ama that is ballasted to be just barely positively bouyant when comparing it's submerged displacement to the total vessel weight. Would this ama not pierce waves and attenuate the motions transferred to the main hull (assume the main hull is flying)? My goal is to provide a smooth ride, motion decoupled from sea-state. Let's not get bogged down with over-turning moment from the sails and associated issues.

 

I think that would be a bad idea for a number of reasons. In vessel dynamics it is the hydrodynamic mass and buoyant volume (and they are two different things) that determine the response, the actual mass and buoyancy being just a portion of those. In your proposed situation there is little added mass making the hydrodynamic mass nearly the same as the buoyant volume giving no significant damping. The only thing this would do is add mass moment of inertia to the hull, which could as well been done with just making the vessel a catamaran, which would have less deleterious drag effects. Additionally, a large mass and low buoyant waterplane make for a very high response magnification factor (i.e. low damping as stated above). This would cause large forces that reverse phase at the natural period of heave of the ama leading to deep submergence of the aka. This is not good for structural design. Furthermore, what exactly are you trying to accomplish? If the main hull is flying and the ama moves into a trough, the lack of buoyancy of the ama is just going to pull the main hull into a forced roll, possibly causing a spin-out.

This is beginning to look like that useless mastrabatory development fiasco of the 2010 America's Cup. A vessel that only works in very specific conditions that there are better options for if speed and ride are your design goals (foiling anyone?)

 

Thanks again jehardiman. Your reply will take me a while to unpack. I am aware of hydrodynamic added mass, but I don't have a working understanding of it and dynamic response, etc. I've ask for "Dynamics of Marine Vehicles" for Christmas, so that should help as I currently don't follow you.

In regards to the distinction you made between Tri and Cat. I've tried to simplify my concept in order to make it easier for someone else to envision, but in doing so, I have misconstrued what I am looking at doing. From a basic free body diagram point of view, a trimaran flying it's hulls is no different than a catamaran flying a hull given the same beam, length, disp, etc. Whether you call that center volume a "hull" or a "cabin", is immaterial to the hydrodynamics if it's up in the air. But I should have described this as a HYSWAS, where the demi-hull is not fully submerged but just barely breaking the surface. So instead of a typical 80% displacement / 20% foil lift, the demi hull is 101% displacement (almost neutral buoyant) and foils are used for stability control only, not to lift the vessel. The intent is very slow speed operation of a HYSWAS where foil lift becomes impractical due to the large surface area needed to generate lift.

You mention natural period of heave. Compare a cork to a wine bottle mostly full of water, the cork will certainly have higher accelerations (high frequency) following the surface than the bottle when you introduce waves. Thus the wine bottle attenuates heave, right? The natural frequency of a neutrally buoyant vessel is zero... it does not oscillate. In the design concept, the "ama/demi-hull" would essentially always ride at the trough-level of the waves because upward acceleration is almost zero, while downward acceleration can approach 'g' as the ama breaks out of the back of a wave. Hence the title of the thread concerning submergence stability.

This vessel will operate in displacement mode, Fn<4.5, and foiling is not practical at these speeds. Small foils may be used for stability control, and of course yaw as always.

 

I am not sure if I am understanding the question. A completely submerged hull will be highly dampened, compared to a hull that goes over the waves. I think that hull shape has more influence that reserve buoyancy if they are considered as a single factor. Large reserve buoyancy, as in hulls with large overhangs, will likely pound and pitch more than a vessel with little overhangs and less reserve buoyancy

 

No, you do not understand because you don't understand buoyancy with respect to waves. Buoyancy is the integral of pressure over the wetted surface of a body. In perfectly quiescent water the natural period of a perfectly neutral floating body is not "zero"; that would mean that it moves back to its original position instantly, i.e. fixed in space like being rigidly attached to the bottom. In perfectly quiescent water the natural period of a perfectly neutral floating body is actually infinite; i.e. you disturb it into a new position and it never comes back. Unfortunately, neither of those conditions exist in real life. That is because waves vary the pressure over the body with their spectral periodicity. Floating bodies move in waves not due to the surface of the wave, but due to the variation in pressure over the body; the surface of a wave is just a manifestation of the periodic energy in the mass of the wave. (For how pressure varies with depth and with waves check out the video I attached to this post. Wave Tank Question https://www.boatdesign.net/threads/wave-tank-question.66324/page-2#post-939404 ). If there is very little reserve volume and little vertical damping (like your wine bottle or a bobbing deadhead and I don't mean a old NorCal hippie) even the most begien seaway can set up an oscillation between too little and too much buoyant pressure. Until you have actually seen a 2 foot in diameter tree trunk pop vertically 6-8 feet out of the water then slide just a quick back under, I understand your disbelief but it is the physics of the matter nonetheless.

Of course you are correct if you think about it the way ztine did; i.e. perfectly quiescent water and perfectly neutral floating body. Perhaps it is my fault that today after years of working with it, I immediately think about submerged bodies motion at depth due to spectra. While it is true that damping is infinite for an outside force on a perfectly neutral floating body in perfectly quiescent water; for the damping on a perfectly neutral floating body under waves is small to the point of non-existence. Think of it this way, you have a large plastic bag full of water in the water column; it moves with the wave orbitals. Now I make that plastic bag rigid, remove the water and stuff it full of toys the exact weight of the water I removed; it still moves with the wave orbitals. Now I attach an infinitely stiff, infinitely thin rod that comes up to the surface; it does not track the surface of the wave, but the wave orbital at the CoB of the body. Now I place a mass on the top of that rod (ballastium, all weight, no volume); NOW there is apparent damping

I concur, motions is all about shape.

 

I agree about the the effect of waves. I was thinking about semi-submerged being highly damped.

 

Inaddition to the comments above by JEH et al,

Not sure how you achieve this, since the HYSWAS works on the premise of speed....and when stationary/slow speed, it 'sit's on its main hull. That provides the initial stability.
Without which, the hull will just roll to an angle where the upper part of the hull eventually hits the water to provide a buoyancy.
Thus if your intention is to 'sit' (float) when stationary on the strut, it'll behave in this manner.

Well, no. If a cork is floating, its period of encounter matches the wave period.
If you take a 1.0m wave of say 5 seconds period, this equates to 0.16g, not much.
If the wave is a 2.0m wave of say 7 seconds period then you have 0.16g again.... etc etc.

How will you do that at zero/slow speeds?

 

JEH your reply is very helpful. I believe I'm mostly on the same page. Regarding the water-logged tree 'jumping' out of the water, my understanding now of such a low reserve buoyancy vessel is that the forces & damping are small in mostly calm water, but the small forces can build to large vertical displacement similar to pushing on a swing. Note, the concept vessel would have some active stability control (eg foils, etc) as mentioned above. So the small forces can easily be cancelled out by small opposing forces of a foil or other active stabilizing device. would you agree?

Ok, back to the wine bottle/bag full of water example and specifically the mass being above the water, or not. I am having a hard time understanding why the location of the mass (in air on the infinitely thin/rigid rod verse inside the bottle/bag) impacts the damping given that both would have to have the same total mass to remain neutrally buoyant, since the submerged volume/shape has not changed. See figure attached. I understand that the mass on the rod will move the C.G. away from the CoB and result in rotational moment when wave orbits apply a non-vertical force to the bottle, I do not see why this results in "damping". Assuming the rod is infinitely long, then the angle of rotation is infinity small, and i believe the two bottles would follow identical paths, right? In the bag analogy, it easy to see the bag follows the orbital. But is it true that 'all' neutrally buoyant objects in a wave orbital will follow the wave orbital regardless of it's shape? Will the neutrally buoyant wine bottle really follow the identical path as the plastic bag assuming both are submerged at the same depth?

Hi Ad Hoc, Yes, I understand that when riding a bicycle, you need to put your foot down when you come to a stop (or use other stabilizing methods). When I said slow speed operation, I was trying to distinguish this from HYSWAS which operates well above the hump (SLR > 2). I did not mean it would operate nearly stopped at 1 or 2 knts. It will operate at displacement speeds ~1.3>SLR>1, so 9-10 knts for a 60ft length. Anchoring (stopped) is off-topic for this academic discussion as the vessel would require some method to provide static stability at rest.
.............
Stabilization Force: To stabilize the bottle in the wave, the force applied by the water requires an equal & opposite force. We know the diameter and speed of the surface orbital is equal to the wave height and the wave rotational velocity. Given a 2m wave height and 7 sec period, the centrifugal force to maintain constant orbit is m*w^2*r. For a 1L or 1kg bottle, the force required to negate motion of the bottle is 1kg * ( 2 * pi * 1/7 = 0.897 )^2 * 1m = 0.805N or 0.18lbf. A 10,000kg boat would then need 8,050N or 1,800lbs of force to negate orbital wave motion near the surface... Is that correct? If traveling perpendicular to waves, this force causes sway and heave. If running with the waves, or into them, the orbital forces act in surge and heave directions. But since the boat is not a singular point, pitch will also be impacted when traveling with the wave, and roll/yaw when perpendicular.

Interesting, If we assume just vertical oscillation, acceleration is double the centripetal acceleration since you multiply angular Freq. by Amplitude (2m) vice radius (1m), hmm... w^2*Amplitude = (2*3.14*(1/7))^2 * 2m = 1.6m/s^2 .. I believe this to be an erroneous approximation of acc. of a particle on a wave, because this oscillation assumes the particle velocity is zero at the crest and trough and accelerates from zero to a maximum at the inflection. However, the particle really follows a ~circular path at constant speed (ignoring propagation). I conclude centripetal acceleration is a better approximation.

w = angular frequency = 2*pi*Freq(Hz)
Amplitude = wave height = 2m = diameter of orbit
r = radius = 1m

 

A floating cork, as in your example, is not a wave particle tracing and orbital path. Otherwise, how can anyone swim in waves?!
Orbitial radii diminish quickly with depth too.
The cork is 'floating' and thus its acceleration is related to the eqn you cite above. Since the wave period is the encounter period.

It is the relative difference between the effective mass at the wave crest and wave trough. At the crest the gravity less the centrifugal force the floating body has less 'mass', which has implications.
For example, when a boat is on the crest of a wave, as the boat floats "less" in the water, it can greatly diminishing its stability, depending upon the form and initial stability.

 

Absolutely not, especially with small forces. People who have not designed and installed an active control seem to think it is simple when actually it is very difficult, not only from system implementation perspective, but from the speed and magnitude of force reversal needed. There are many failed attempts to do what to you appears straightforward. Like balancing a pencil on its point, smaller forces does not make it easier control, only easier to upset.

First off, your left hand model is off because it shows the "bottle" neck out of the water. In that case the bottle is "free floating" (same as the right hand model), not neutrally buoyant. All free floating items have some damping. Perhaps you misunderstand what damping is?

Secondly, it is not the separation of CG and CB per se, but the cross coupling of the the 6 DoF mass matrix with the hydrodynamic forces (i.e. the body surface shape and fluid energy). As I said back in my first post, get a good text and be prepared for the math.