About the hull shape of sailing dinghies

Discussion in 'Sailboats' started by Dolfiman, Nov 22, 2022.

  1. Dolfiman
    Joined: Aug 2017
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    Dolfiman Senior Member

    I am pleased to share with you my thoughts and two propositions about the hull shape of sailing dinghies in relation with their planing mode :

    *1* One of the issues recurently evoked is the shape of the hull bottom center line (also named the keel line, although there is no longer keel at such for modern dinghies), the curvature repartition (also named « rocker »), the location of the hull body maximum draft.
    >>> I propose a simple rationale leading to a mathematical formulation, based on the idea that once the planing is initiated and progress, we want less and less curvature behind the stagnation spot of the dynamic pressure which itself tends to progress from bow to aft. And finally, a curvature vanishing to zero at aft transom level. The more the planing mode progresses, the less the needed curvature for the hull bottom still wetted : it is a bit like an airfoil, the more the speed, the less the needed camber for the foil.
    >>> If we agree with this approach, then the curvature evolution is directly deduced : a curvature less and less accentuated from bow to aft means that the curvature is maximum at the bow and zero at aft transom. This can be laid down as a basis for deducing a mathematical formulation, as detailed in the document attached, with examples. The formulation is also proposed in the .ods spreadsheet file (to use with Open or Libre Office), you can use it with various input data.
    >>> One unexpected consequence of this approach is that the location of the hull maxi draft is an output of the process, which depends of the degree n of the polynome for the curvature. Only the hull draft is to input, not its location. This point may be surprising : actually, to consider the curvature evolution as the guideline is more rational than to focus on the hull draft location because this location varies with the dinghy trim angle as the planing mode progress. It is not an intrinsic quality of the bottom center line as is the curvature repartition unchanged whatever the trim.

    *2* The second proposition is about the hull lines representation more adapted to the planing mode.
    >>> The standard representation with the waterlines at various heights is informative for the displacement mode at low speed but not much for the skimming mode on the water surface. The dynamic lift being a lot in relation with the deadrise angulation within each sections, I found useful to add the « deadrise » lines, i.e. the lines joining the points of the sections sharing the same local « deadrise » angle : 2°, 4°, 6°, etc...,20°.
    >>> This representation, especially showing the shape of the central flatness (transversal angles < 2°) from the pointy bow to the aft transom, makes easier to guess how the planing mode can occur and progress.
    >>> The attached document shows examples of such representation with « deadrise » lines.
     

    Attached Files:

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  2. messabout
    Joined: Jan 2006
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    messabout Senior Member

    The general ideas, here, comply with design concepts that have been pretty well established over a long period of time. Uffa Fox, for example, did numerous planing dinghies using the max depth forward and had the afterplane (run angle) as straight and as small as possible consistent with keeping the transom at or slightly above the waterline. This concept is described pretty well in Dave Gerrs book; The Nature of Boats.
     
  3. wet feet
    Joined: Nov 2004
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    wet feet Senior Member

    Thank you for presenting the results of a lot of work.I have not yet had time to study it,but will do so over the coming days.I think the reference to Uffa Fox is perhaps a nod to his historic significance and optimal shapes have been reconsidered since his pre-eminence in the field.and the shapes that have been arrived at since owe much to Bruce Kirby,Phil Morrison,Dave Bieker and the Bethwaites.As an aside,I can't help noticing how similar the hull shapes of IMOCA 60's have become to dinghies,which perhaps isn't too surprising since both types rely on transferring weight to the windward side to resist heeling forces.
     

  4. Dolfiman
    Joined: Aug 2017
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    Location: France

    Dolfiman Senior Member

    Many thanks for your interest.

    About the center line shape, nothing new of course, but my goal was to encapsulate in a mathematical approach the general consensus and in doing so to highlight on what is the core driver in my opinion, i.e. the idea that the curvature (in its mathematical sense) should regularly decrease from bow to aft. Reguraly is the key word, because steps of curvature are not optimal for a smooth flow of the water behind the stagnation zone. For example, a low rocker in the bow zone follow by more rocker in the midship zone then ending by a flat run through a tangent toward the transom cannot be optimal, this means steps of curvature for the water particles.

    The other aspect often debated is where to position the hull body maximum depth : I show with this approach that this is actually a consequence of how we choose to change the curvature from bow to aft, linearly, parabolically, or other … according to the degree n of the curvature polynome. Here below examples with respectively n =1 (linear) , n=2 (parabolic), and n= 4, at same hull draft :

    If I show the 3 corresponding lines at scale, you will not see the differences :
    upload_2022-11-23_14-22-55.png

    The same lines but showed a lot dilated in z, differences appear more clearly :
    blue n = 1 >>> hull draft is at 57,3 % Lw from aft ; red n= 2 >> 54,9 % Lw ; green n = 4 >> 52,5 % Lw
    upload_2022-11-23_14-23-33.png

    The 3 curvatures 1/R (unit : 1/m) evolution (blue n =1 ; red n=2 ; green n=4 ) :
    upload_2022-11-23_14-23-54.png

    So you can still choose the hull draft location, but indirectly, through the choice of n.
    If you choose a very high value for n, e.g. n = 100 , you tends to a constant curvature, i.e. a perfect arc of circle except at the aft very end when you dives to zero, and the hull draft is then at 50% L
     
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