Basic but perplexing stability question

Discussion in 'Stability' started by Paddlelite, Mar 8, 2013.

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So as I currently understand, initial instantaneous stability is dependent on the waterplane inertia, which is mostly a function of width (or its cube) and length (if not at the expense of width.) And beyond initial stability, what governs is how the submerged volume changes its shape as the hull tilts -- specifically how much the new center of buoyancy (CB) moves to the side in comparison with the center of gravity.

So I’m trying to apply that to this paddleboard hull from Hobie, as pictured. The design claim is that the mild protrusions running under the edges of the hull are roughly equivalent to the added stability of a half-inch wider hull. If you do some rough math, it's true that the width-adjusted volume distribution is roughly equivalent to that of a half-inch wider hull. And intuitively, it seems like placing more volume under the edges would increase stability.

But . . . that shouldn't help stability because 1) the initial stability based on width and length is not affected as it would be with a wider hull, and 2) as long as the protrusions stay completely submerged, the changing underwater shape as the hull tilts doesn't have a further and more favorable shift in its CB than it would without the protrusions. Only if one side of the hull were to completely lift from the water, would the protrusion on the submerged side create more stability by further shifting the CB.

Am I analyzing this correctly?

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daiquiriEngineering and Design

Yes you are.

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johneckSenior Member

Yes, I agree. The instantaneous stabilty is based on the waterplane inertia (LXB^3). However if the waterplane changes drastically as the vessel heels then the stability will also change. I would expect that the effect of the ridge along the side would vary greatly depending on the weight of the paddler.

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You need to look at the whole picture, not just one aspect. What does the change in CoB do to the KM? Hint, see attached:

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Right, but I'm picturing it more like this at small angles. I don't see the CoB movement being influenced at all by the increased volume under the edges.

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johneckSenior Member

Exactly, if the bump stays completely immersed, it has no effect. It may help keep the edge on the high side from coming out of the water and the edge on the low side from going under, which would result in a decrease in stability. But once again, I think that it will be very sensitive to weight, so I am not sure you can make a blanket statement.

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TANSLSenior Member

Can help these figures in the discussion?

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Thanks; I wish I could have done that.

Would it be too general a statement to say the following?

As long as as the angle of heel does not expose the first "chine" where the true "bottom shape" begins, then there is no difference in stability between different bottom shapes (round, V, flat, concave) in otherwise identical hulls.

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Easier to just say if the waterplane does not change significantly, stability will remain the same.

If the bumps on the bottom are added to an existing box hull, the hull will float higher and require a higher heel angle before imersion of the deck edge.

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Looks like TANSL drew those "dots" to be joined nicely for you

The point being adding those "bits", what does it do?...well, it will move the CoB. I showed one on the right side, just one, and it has an influence. But with two, any athwartship movement of the CoB is cancelled out, i.e. it remains as-is because its symmetrical. (Assuming the blips are not below the existing baseline).

So the BM is governed by the...IT and the Volume.

As you rightly pointed out, (and reiterated by Tad) the IT remains the same. So the only change is the volume part. The addition of the blips add a small amount of volume, and if we assume the extra structure is negligible, the hull will then float a little higher. So there is a small change in the KB. Thus a lowering of the CoB.

But will this improve the stability?...well, the lowering of the KB does this effect the BM? Well the volume has now changed, so that alters the BM. The KB is related to the draft and the increase in volume is proportional to the draft, so it is fair to say the 2 relationships would probably cancel each other out. So highly likely the BM remains unchanged, but with no change in the IT all that is left is the location of the KM. This would lower by the same amount of the change in KB, i.e. very little. (assuming everything else remaining the same).

So, as Tad says, the hull will float higher (not much if the blips are very small) and thus the angle of deck edge immersion shall be a little higher, and highly likely the positive range of stability and the righting arm remains unchanged too. All in all, not much, if any, difference. Not one that you will notice anyway. But this is also assuming the blips are small in relation to the addition of volume to that of the main hull. Since you could take this to the extreme and have a hull shaped like an inverted "T" with the 'flange' parts having more volume than the vertical 'hull' part..but that's another story.!!

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philSweetSenior Member

In order to answer the question properly, we need a sketch of what that midsection looks like and a waterline. As others have said, it really only matters when the section is heeled to the point that the flat hull would have lifted its chine. That probably isn't very much in the case of a paddle board. It may offer some advantages in terms of wobble resistance via an added mass effect. That's nice because the added mass is only there when you need it. It's real reason for being there probably has something to do with manufacturing or packaging. I'd guess it is desirable to the builder and is being sold as a feature. Don't get mad about this. It has to get made before it can get used. Usability and manufacturability are always at odds. Could be just a handling convenience for the assemblers (a finger grab). It would also stop the bottom from getting scuffed at the store and at home or trundling down a roller table at the plant.

One other bit of confusion. When considering the stability of very small boats like canoes and kayaks and paddle boards, the KM thing isn't the final word as far as how stable the boat is in real terms. Occupants apply a sway force along with torque. It depends on posture and it bodgers up the math. And there is little point to consider non time-dependant stability in tiny craft because the occupant is going to react. Altering the response time (adding damping or increasing the proper moment of inertia) can be very helpful here, but has no impact on the flat water response of a boat with a dead load.

So an additional effect is to increase the proper moment of inertia of the section, regardless of whether or not the change in the second moment of area is useful. This improves the human response.

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daiquiriEngineering and Design

I think that the explanation of this shape is much simpler than that. No math or stability diagrams are necessary.

The guy who designed it has probably reasoned in simple terms of volumes, buoyancy and marketing. My guess is that he thought something like: "if I put more volume below the chines, then I will get more hydrostatic force in that area. More force for the same lever arm means more stability. It is so intuitive that the average Joe will easily endorse the idea and will want to buy this cool-looking board!"

We know that physically it doesn't work that way. The equal volume added under the port chine of the hull will cancel the stabilizing effect of the added volume under the starboard chine. But it is not important, imo.

What really counts is the product-marketing impact of this board shape, not the scientific accuracy of claims which support it. They now have a board which is different from what the others produce. And they have a marketing claim which is in line with the intuititive thinking of an average buyer, when it comes to stability. It teases and seduces the buyer to show him that his intuition was right.

That, together with a reknown brand-name, is often all that it takes to sell a product as new and innovative. Ship stability theory is pretty irrelevant in this picture, imo. After all, it's only a paddleboard - not a multi-million dollars worth ship. Who's ever going to bother making an experimental verification of their claims?

Just my opinion.

Cheers

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Uhh... that would be me.

Welcome to my laboratory. No diff with flotation under hull, big diff on edge.

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daiquiriEngineering and Design

Great! Can't wait to hear the news!

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