About dinghy intrinsic stability : proposition for a standard assessment

I am pleased to share with you my thoughts and a proposition of standard to assess the intrinsic stability of a dinghy. I mean by intrinsic stability two complementary aspects :
> the initial stability at rest, that which one feels as soon as one goes on board, this propensity to take more or less heel angle as soon as one moves on board,
> the « dynamic » stability during large roll motions, which can happens during a tack, a gybe, ... due the sudden change of the sail force, the effect of a transversal wave, .., and including the clumsiness of the sailor reaction.

Dinghies are a very special category of sailboat when it comes to stability, since the proper weight of the sailor/the crew is a significant fraction of the total weight, usually from ~ 50% to 75 %. Consequently, the way in which the sailor positions himself, how he moves during maneuvers or to face variable wind conditions, has a decisive influence in maintaining balance. During manoeuvers or transition phases, the avoidance of capsizing depends on the ability of the sailor (of the crew) to move inside the dinghy and maintain or restore balance by using his own body weight, and there the more or less intrinsic stability of the dinghy can offer more or less tolerance to the sailor.

So it can be useful, especially for the designer who wants to offer an efficient but remaining controllable dinghy by the greatest number, to have a criteria and a scale for the intrinsic stability offered.

To support this investigation, I generated a serie of six 14' hulls sharing the same lenght overall Loa (4,27 m) , beam B (1,52 m) and light weight (60 kg), sharing also the same sheer line and free-boards. The main differences of the serie are the sections shape and waterline beams varying, when the load is 100 kg, from Bwl 1,11 m to 0,85 m (i.e. from 73% B to 56% B).

The initial stability is adressed through the metacentric height GM. But to set a standard is to adopt a standard position for the sailor/the crew weight (= the “load”) in the dinghy for its computation. Investigation of the longitudinal X position were done and the standard proposed is Xload at 40% Lhull / aft transom. Idem for the Zload, and the standard proposed is + 0,65 m / waterline. With this standard and from the numerical tests with the serie of 6 hulls, a scale is proposed :
Poor to nul : GM1° < 0,3 m
Moderate : 0,3 m < GM1° < 0,6 m
Good : 0,6 m < GM1° < 0,9 m
Very good : GM1° > 0,9 m

The dynamic stability is adressed through the area under the righting moment RM curve for the heel range 0° – 25° , i.e. the righting energy available for large angles roll but before the sheer line immersion or a capsize start. But instead of using RM directly which strongly depends of the load, I propose to use dy such as :

Righting moment = RM – load x dy = 0 >>> dy = RM / load (= GZ (weight + load) / load)

, meaning, from this static equivalent situation, that at each heel angle the RM can be vanished if the mobile load (i.e. the sailor) moves transversaly on the wrong side of a value dy. So the lower the dy, the less margin of error for the sailor movement, it is a kind of measure of the skill required from the sailor.

RM is computed with the total displacement (dinghy weight + load) and for the load, with using the same X and Z standards as above for the initial stability. Then, from the dy curve, a dY average value is computed, equal to the area under the dy curve on 0° – 25° span divided by 25. And it is for this average value dY that a scale can be proposed, still based on the numerical investigation done with the serie of 6 hulls :
Poor to nul : dY < 5 cm
Moderate : 5 cm < dY < 10 cm
Good : 10 cm < dY < 15 cm
Very good : dY > 15 cm

So we have reached our goal : the dinghy intrinsic stability can be assessed with two parameters (GM for the initial stability, dY for the dynamic stability), a common standard for their computation (Xload at X 40% Lhull / aft transom, Zload at + 0,65 m / waterline) and a scale for each parameter to graduate the stability, from nul to very good.

And I finished the investigation in the document attached by an illustration, by comparing two hulls sharing the same waterlines under a hard chine line, but of very different shape above (concav versus convex). The two hulls so share the same initial stability by differ for their dynamic stability.

PS : You may be wonder why I do not include in this intrinsic stability notion the uniform sailing situation when the heeling moment due to the sails forces is balanced by the righting moment due to the hiking of the crew. It is because in this condition the righting moment is almost exclusively due to the crew bodies weight and extension windward. There, the dinghy hull shape has quite no role, it is just that more sails area needs more crew weight or extension to maintain the balance. It is clear that too much sail area for a too light sailor leads to major problem of stability, but it is not due to the hull shape, that does not involve the intrinsic stability.

 

Dolfiman; Thank you for the dinghy analysis. I appreciate articles of that kind.

Not to veer from the stability study, but one of your images shows the CE of the Sail to be forward of the CLR of the boat. Does that not imply a lee helm ? When the sail is eased that would make the lee helm more severe because the CE would be even farther forward of the CLR. In broad reaching or running that could be a problem it seems to me.

Please help me understand the line of reasoning for which I am not fully aware. I am an ancient old guy who is still intent on discovering things that I did not know.

 

The "CE" of a sail is the area centroid in side view. While labeled as "Center of Effort" the actual line of action of the aerodynamic force on the sail will usually not pass through the CE. Similarly "CLR" is the area centroid of the submerged portion of the boat, projected in side view. The actual line of action of hydrodynamic force on the boat may be ahead of the CLR.

Empirically placing the CE a fraction of the waterline length ahead of the CLR has been found to result in a well balanced boat. The key is what fraction of the waterline length to use.

 

Dear @messabout, thanks for your kind message.
About your question, David already gave you the core of the answer. I just add here attached a figure to illustrate the issue.
From a given equilibrium meaning the sail vector is aligned with the hull+appendages resistance vector in the top view, any extra heel tends to move aft the sail vector / hull-appendages one because the arm of the CE is higher / rotation axis than the one of the CLR. Then a bit of weather helm brings a complement LR2 force so that LR1 + LR2 becomes again aligned with F.
For the naval architect, it is delicate issue because the real CE position as well as the real CLR position can't be computed exactly, while that determines the relative position of the sailplan versus the one of the keel . So he uses methods based on statistics (see for example the chapter "Balance" in the "Principles of yacht Design" by Larsson-Eliasson). For a dinghy, you may object that it is less important because the heel can be zero or quasi. But upwind, you can have a sailing with heel 5° -10° in average and it is sufficient to also foresee some Lead (= CE-CLR in % of Lw) with a lower figure than for a keel boat.

 

I'm really pleased to see such a thorough study of the topic.Messabout might find the material prepared by Andy Claughton for presentation at HISWA a few years ago to be of interest.

http://www.rsyc.org.uk/Uploads/Documents/Claughton HISWA 2013.pdf

I would be curious about the numbers that apply to the latest generation of National 12's or Merlin Rockets as they both exhibit fairly wide overall beam and very fine entries on hulls that are quite narrow at the waterline.The bottom line being that if a new design has qualities that make it faster-its up to the sailors to keep it upright if they want to win races.

 

Thank you all for the input. I have been guilty of using a too basic set of observations. A lot of stuff is going on with a dinghy underway, and powered by a sail or sails. The force vector of a sail probably cannot be reliably predicted as the location of its centroid, nor can the CLE be reliably assigned to that which we establish in a drawing. Wrestling with the many variables are part of the fun.

Back to the original premise, intrinsic instability............ I had no intention of derailing the thread.