Understanding Displacement / Stability Relationship (Not GM)

Discussion in 'Stability' started by Jeff in Boston, May 16, 2021.

  1. Jeff in Boston
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    Jeff in Boston Junior Member

    As described in other threads I'm taking a 5200 lb displacement deep keel sailboat (Pearson 26) and removing the 2200 lb cast iron keel to create a displacement speed electric cruiser. No sails. The hull of the boat is *relatively* flat bottomed.

    20210115_135159.jpg

    I'll be making a fiberglass keel to replace the iron keel, ending up probably 300 lbs or so.

    I have a good handle on how the metacentric height affects stability, and how to adjust the metacentric height with more ballast and where I put that ballast. I also understand that keeping the weight away from the COG will increase the roll inertia. I will be using a roll period test to ensure I have a safe boat.

    My confusion is on stability change when increasing displacement without changing metacentric height. I've read and been told that increasing displacement will improve stability, but I'm unclear on exactly how that happens.

    I figure:

    1) Raising the waterline means a wider beam.

    2) Increased displacement will reduce the reaction to load shifts. If I am a smaller percentage of the total mass of the boat it doesn't tilt as much if I move from one side of the boat to the other.

    3) The righting force will be higher (same righting arm, more force).

    Is there something I'm missing?

    If the boat does well on the roll period test, but still feels "tippy" I should add more weight without changing the metacentric height?

    Thanks!
     
  2. Mr Efficiency
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    Mr Efficiency Senior Member

    The relatively flat bottom is a blessing for your purposes, I'd be inclined to either do a full stability study on it minus the keel, or just plonk it in the water and suck it and see, you should get a feel for whether it is tippy or not just pottering around in sheltered waters with a temporary power source like an outboard.
     
  3. Mr Efficiency
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    Mr Efficiency Senior Member

    Not forgetting to remove the mast !
     
  4. Jeff in Boston
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    Jeff in Boston Junior Member

    I need to do something to fill the slot in the bottom of the boat, and the trailer was designed around having a 4" x 4" keel to rest on and be centered on.

    The mast, boom, and all sailing gear will be sold this summer so I can buy other supplies.
     
  5. bajansailor
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    bajansailor Marine Surveyor

    Here is some info on the Pearson 26 for reference.
    https://sailboatdata.com/sailboat/pearson-26

    Can you tell us a bit more about the fibreglass keel that you propose to build please?
    Will it be a long shallow skeg, or the same length as the existing ballast keel?

    Re the electric cruiser, will you have an outboard motor, or an inboard with a shaft drive?
    If the latter, will you keep the original spade rudder?

    One basic formula for stability is BM = I/V where BM is the distance from the centre of buoyancy to the metacentre, I is the second moment of area of the waterplane, and V is the volume of displacement.
    If you increase the displacement, the odds are that the I of the waterplane area is not going to increase an awful lot, so you will probably find that the BM decreases a bit.
     
  6. Jeff in Boston
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    Jeff in Boston Junior Member

    It will be a long shallow keel into a skeg. About 4" deep under the deepest part of the hull and going from the start of the keel slot back 10 or 12 feet.

    I will start with a 5HP gas long shaft outboard as it's cheap, and then plan to move to heavy duty trolling motors. I'm sure I can get 4mph out of them, and hopefully 5 to 6 mph.

    I will not be keeping the rudder. It will be sold as it is a modern replacement. I may make a shorter rudder depending upon if the cockpit ergonomics work better.
     
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  7. Heimfried
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    Heimfried Senior Member

    Hi Jeff,
    may be I misunderstood what you wrote regarding the GM. The actual GM is changing not only with changing of CoG but also with the angle of heel or trim.
    The (transversal) stability will not normally increase if you increase the displacement and not changing CoG. On the contrary the initial GM and also the maximum of the righting arm will decrease a bit.
     
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  8. Jeff in Boston
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    Jeff in Boston Junior Member

    I guess I'm confused. I though GM wasn't considered to change much with minor angles of heel?

    It sounds like if I increase displacement without moving the COG, I will increase the KB, right? That moves the center of buoyancy up relative to the keel.

    BM = I / V mentioned above... V will change but I won't change as much? Meaning BM gets smaller.

    So M doesn't move much, and GM doesn't move much because G didn't move? So the rolling period stays the same? Increased mass + increased stiffness = same period?

    But the boat gets more resistant to change in passenger load as passenger movement change COG less?

    (Thanks for helping with this! I know the way I learn something new can be a bit odd.)
     
  9. Heimfried
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    Heimfried Senior Member

    If you calculate a wallsided hull (e.g. big freight ship) the I won't change much if displacement is (moderately) increased.
    But on a boat as yours the behaviour of I depends on the hull shape and the draft.
    Two calc sheets with diagrams below, the third diagram shows the waterline plane of the boat in certain circumstances (at designed waterline).
    I the second sheet I lowered the displacement very much to show the effect of a waterline intersecting a hull part with little slope.
    You see a much tinier waterline plane.

    The I of an ellipse, which may be the rough approach of the waterline plane of a boat, increases with breadth power 3. So if the breadth is 10% up, I is 33% up.

    In short: rule of thumb is sometimes not helpful in hydrostatics.

    initial.jpg disp_minus.jpg
     
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  10. jehardiman
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    jehardiman Senior Member

    Do not confuse the metacenter with the point the vessel rolls around or assume the metacenter controls the amount the vessel rolls.

    The location of the metacenter (KM) is only a function of the vessels weight and form. The location of the CG (KG) only effects the GM (i.e. GM = KM-KG) not the metacenter. The GM, not the metacenter, is what effects the moment to heel some small angle (i.e. moment = W*GM*sin theta for small theta....low GM means the boat feels "tippy") and only if the wall sided assumption is correct. Many hulls never conform to the wall sided assumption (like most sailboats where KG is below KB), and therefore cannot be analyzed by evaluation of GM. Removing the keel will greatly reduce the GM (by increasing KG) without significant change to KM.

    Note the GM does not have to be positive to have a stable vessel. A vessel capsizes because it loses righting moment, which has nothing to do with the original metacenter, only the KG to KB couple and the instant metacenter. If GM is negative the vessel will loll (i.e. list to some calculatable angle) until the instant GM is identically equal to zero. The vessel is stable at this point; however, if forced back upright, it will continue to roll until it reaches the loll angle on the other side. Freely moving weights (i.e. passengers, suspended loads, fluids in tanks) can significantly reduce GM and should not be underestimated in a situation where KG is above KB. This is why stability is defined by the area under the righting curve, not GM in any form.

    See this discussion on GM...Calculation of GM http://www.boatdesign.net/forums/boat-building/calculation-gm-8852.html#post60405 (and please ignore the scarcasm in it).
    And this thread on the interaction between CG and KM..... Metacentric Height https://www.boatdesign.net/threads/metacentric-height.27171/
     
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  11. TANSL
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    TANSL Senior Member

    No, that's not correct, wessels weight has nothing to do with KM.
     
  12. jehardiman
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    jehardiman Senior Member

    Would you prefer the term displacement or volume? As long as you account for the water density it makes no difference <shrug> Yes we could argue semantics but KM = BM+KB where KB is a function of the vessels form, weight, and fluid density; and BM is a function of the vessels form, weight, and fluid density.
     
  13. TANSL
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    TANSL Senior Member

    Okay, let's just leave it there if you want. Excuse the interruption in your explanations.
     
  14. Mr Efficiency
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    Mr Efficiency Senior Member

    If a lines plan was available, this would get a lot easier to analyse. Without it, it becomes partial guesswork. It isn't the COG that will throw a spanner in the works as much as the shape of what is left in the water after the 2000 lbs comes off the boat. Just looking at the front on view though, it does appear to be more favourable than a lot of monohull sailboats are to convert to powerboats. It is no good having a boat that has satisfactory ultimate stability, but is murderously tippy in terms of initial stability and flopping around uncomfortably.
     

  15. Jeff in Boston
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    Jeff in Boston Junior Member

    Here's an image of the lines drawing I was given by Dan Pfeiffer. If I get the okay, I will share the DXF / DWG if that would help.

    I do feel kind of dumb that I bought the boat not understanding the impact of the hull form on initial stability. I am thinking I got lucky in that department.

    lines-modified-dwg.png
     
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