About the hull shape of sailing dinghies

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.

 

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.

 

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.

 

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 :


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


The 3 curvatures 1/R (unit : 1/m) evolution (blue n =1 ; red n=2 ; green n=4 ) :


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

 

Interesting, Dolfiman - I'd be curious what Class 40 AllaGrande Pirelli designers Gianluca Guelfi and Fabio D’Angeli or your fellow French designers Sam Manuard or Guillaume Verdier make of this. There are some points I'm struggling with a little - might be because some of our conventions and definitions of terminology are different in the U.S.

My recent practice has been to focus on the curve of areas. This may be out-of-date, but my reference is Analysis of Wave Resistance in the Design of the 12-Meter Yacht Stars & Stripes. Also Principles of Yacht Design, from which my take-away is that the LCG/LCB at displacement speeds wants to be 8/15 or 53.33% from the bow end of the waterline for a sailboat with a transom. If you're measuring from the stern that's 7/15 or 46.67%. Then I choose my Cp and use a spreadsheet to calculate exactly what the immersed area should be at each station (at least the ones I intend to use to generate my hull shape). Since I draw my planform first, my bottom shape winds up being whatever results from moving my stations vertically to achieve my calculated curve of areas. I then heel the boat, keeping my bow/forward end of waterline at the same trim, and adjust my section shapes (often near the chine) to achieve the same curve of areas when heeled.

What I wonder about what you're doing is whether you have a target speed and a target Cp. Also whether you're looking at heeled waterlines or at how the helm will balance (or not) as the boat heels.

While the designs of Paul Manuard have wide sterns, some also have BMAX farther forward than hulls from other designers. I like that, and lately I've been bringing BMAX forward to near midship. For directional stability I'm wary of allowing the CLR including rudder to be forward of the LCF (the center of the waterplane).

I don't think sharp cutwater bows do much, the friction drag of the wetted surface and the tendency to steer the bow when surfing down a wave exceeding the benefit of the very low amount of volume distributed forward. You've no doubt noticed the latest generation of IMOCAs & Class 40s have done away with sharp cutwater bows.

Anyway, let me pose another question: is there a development class you'd like to compete within? Do you think a fair test of various ideas can be arranged with models? Or perhaps someone has a CFD/VPP combination refined enough to test various ideas? Once we have a definition of the boundaries of what we are trying to achieve it might be beneficial to test several hulls, perhaps from several different designers. That's what Bill Koch did: in designing Matador^2 he had 25 designers submit 40 designs of which he built 12 sailing models. Most America's Cup development since has been done by analyzing and comparing a number of computer models as well as physical models.

I might say more about what I'd like to do in the semi-displacement powerboat discussion: Semi-displacement boats don't generate lift?, a related topic.

 

I can't think of boat types more disparate than 12 metres and dinghies!The huge ballast ratios of the 12's and the location of the measurement points dictate a much more bulbous underbody shape and there is absolutely no possibility of planing.Similalry the example chosen for Principles of Yacht Design is carrying a fair amount of ballast.This isn't a criticism of those types,simply the way it is.The recent Class 40 and IMOCA designs do seem to exhibit the characteristics of dinghy hull shape and also have the advantage of carrying a fair bit of ballast well to windward of the centreline.They also have wonderfully undistorted hull shapes as they are built to a "box rule"without bumps or dips at measurement points.It seems that Sam Manuard and VPLP have grasped the optimal way to design within the requirements and their designs are particularly fast.They seem to be feted much more in a comparatively small region of Western Europe and not that well known elsewhere-possibly due to tradition.Like dinghies,their designs have minimal rocker and this probably helps them avoid the Coanda effect that more traditional designs grapple with.

 

My way of reducing rocker while continuing to utilize the optimum theoretical curve of areas from the 12 meter paper is to hypothesize a lighter displacement than will be the full load sailing displacement of the dinghy. If I'm cutting away the sharp gripe at the bow I might continue to use the vertical bow as my reference for the 53.33%, or I might use the basic optimum curve with LCB at midship and use the actual static waterline.

It may be that there is more recent information available on what constitutes an optimum curve of areas. My point is that I believe the top designers are continuing to design with an optimum curve of areas in mind, however they go about determining what that optimum is. Paul Bieker has said (or written) about this being part of his approach to I-14 hulls. I wonder if they are applying the concept to the heeled shape as well as the upright shape, what other principles influence today's hull shapes, and whether there are trade-offs (especially in designing for semi-displacement speeds, the topic of the other thread to which I've linked).

 

My propositions here above are for a sailing dinghy and for speed focused on the Froude range 0,4 to 0,8, what is commonly called semi-planing or semi-displacement mode. It is a very interesting mode because entirely in the programme of any sailing dinghy, even the less oriented to racing. The challenge is to initiate a dynamic lift very early (and without artifice), i.e. before reaching the steepest slope of the drag due to the displacement mode, so to have what is also called an « humpless » transition to the full planing mode. And that such goal can be reached with an economy of means, i.e. sufficient ligthness (of course) and a right shape of the hull bottom, but not necessarly with an overcanvassed skiff. To note that can be also valid for a motorboat with a low installed horse power (in reference to your other thread about semi-displacement), although the thrust vector is not the same (the trim issue not the same). My propositions for the hull shape are just a tentative rationale of the consensus, not at such an original theory I think. In 3 points :

• for the bottom line, its curvature should regularly evolve from a maximum at forefoot to zero at transom, regularly can mean linear but not necessarly. As a consequence, the hull body maximum draft is always ahead of the waterline mid-length, depending of the curvature function (linear or not)
  
  
• for the sections, the preference is for a « flat and shoulders » shape, to generate a flat central zone
  
  
• for the deadrise lines, and especially the one defined by a 2° angle, delimitating the flat central area, of which shape should looks like a stretched bottle shape with an exit at transom parallell to the boat axis
  

Illustrations with the example of Velocette :

** Bottom line with a linear decrease of its curvature from a maximum at forefoot to zero at transom : as a consequence, the hull maximum draft is then at 57 % Lw (here at X 198)


** Typical « Flat and shoulders » sections :





** Waterline in red (relevant for the low speed displacement mode) + Deadrise 2° line in green (showing the shape of the flat central zone of the hull bottom, relevant to appreciate the ability to initiate and develop a dynamic lift for the planing mode)


As regard sailing by light winds, the sailor can move forward (to avoid the transom drag) and a bit leeward (for up to about 15° heel angle) in order to reduce the wetted surface. Example, still with Velocette :


About the Cp, in my opinion it is not a core driver here : because its value is very dependant of the trim of the dinghy, itself varying quite a lot with the sailor position. I prefer to pay attention to have a low draft of the hull body, because that leads to a low exit angle of the water flow at transom, < 4° at least, ~ 3° ideally, favouring speed within the planing mode.

 

While you haven't convinced me I should abandon designing to a curve of areas, this is a smart & interesting discussion - thank you.

Are you planning to compete in a development class? Will your boat have racks? Trapezes?

I've read similar hypotheses to yours that have focused on buttock shape rather than centerline rocker, comparing the desirable buttock shape to an airfoil. If you were to incorporate buttock as well as centerline shape in your theory, you'd be using longitudinal slices to more fully define a 3D hull shape, it seems to me.

 

No, I am better in tune with dinghy for average sailors, for easy fun sailing, by « fun » I mean my arguments above for early planing mode with economy of means, by « easy » I mean dinghy with a good intrinsic stability, to not fear a capsize at any tacks, gybe or puff of wind. Fortunately, « Flat and shoulders » sections are compatible with good intrinsic stability. And I already developed quantitative criteria to scale such intrinsic stability : https://www.boatdesign.net/threads/about-dinghy-intrinsic-stability-proposition-for-a-standard-assessment.66226/
I am more attracted by dinghies like Laser, the RS dinghies, Melges 14, … and enjoy to design similar versions for amateur builders if any (Velocette example).

If you look at the longitudinal view above, the buttock lines are also drawn, and you can see that for the first three of them, their aft half part vanish in the bottom line itself : it is the effect of the flat central zone of the sections. But I prefer draw and look at the 2° deadrise line, more natural and clear than to propose a guideline for the buttocks.

 

I like the type also. Might post some of my work when I get around to it; my current design is not much different from the plywood boats from your fellow French designers

• ERIC HENSEVAL: V448 V2 Full Plans https://duckworks.com/v448-v2-plans/
• JEROME DELAUNAY: Naut 395 Plans PDF https://duckworks.com/naut-395-plans/

(... except I've designed a cool gantry hung rudder.) I look forward to seeing your contribution to the genre! If you want to discuss who might be interested in building it, please let me know.

 

Note the planform of the Nivelt (NMYD) 54 Teasing Machine puts BMAX near midship, then carries it straight back to a wide stern. BMAX placement near the mast allows a wide shroud base.

 

I don't think the notion necessarily applies to sailing dinghies,other than permitting the crew weight to be as far outboard as the rules of the class permit.Also,in the case of dinghies,there is usually considerable flare so that the underwater shape can be efficient at all speeds.With the boat in post #12 a large part of the reason for the shape has to be to get all the ballast a long way to windward of the immersed section of the hull.I don't suppose the light weather performance would be great with all the wetted surface without enough wind to heel the boat.Perhaps it works best in regions that have predictable fresh breezes.These National 12's show the way in which these traits have been developed.

 

Looks like a good example of BMAX at the chainplates to me.

 

Interesting to mention the National 12 and its hull shape, because at length 12' with 2 adults on board (and no trapezes), a dinghy weight of 78 kg (fully rigged) and sails area (main + jib) of 10,4 m2 (according to the class rules), she is on the heavy side of the usual dinghies range.

** At first, let's compare the Displacement Length Ratio DLR. Here I took :

• for D : the weight of the dinghy supposed fully rigged + the crew weights (2 values)
• for L : the hull length instead of the waterline Lw usually not known and anyway quite variable with the trim.
  

National 12 with L 3,66 m and D = 78 kg (dinghy) + 110 to 140 kg (crew) >>> DLR 107 to 124

to compare with :

420 with L 4,20 m and D = 80 kg (dinghy) + 110 to 140 kg (crew) >>> DLR 71 to 83
I14 with L 4,27 m and D = 74 kg (dinghy) + 120 to 150 kg (crew) >>> DLR 69 to 80
NS-14 with L 4,27 m and D = 75 kg (dinghy) + 110 to 140 kg (crew) >>> DLR 66 to 77
445 with L 4,45 m and D = 110 kg (dinghy) + 110 to 140 kg (crew) >>> DLR 70 to 79
29er with L 4,45 m and D = 90 kg (dinghy) + 110 to 140 kg (crew) >>> DLR 63 to 73
Tasar with L 4,52 m and D = 68 kg (dinghy) + 110 to 140 kg (crew) >>> DLR 54 to 63
470 with L 4,70 m and D = 122 kg (dinghy) + 130 to 150 kg (crew) >>> DLR 68 to 76
49er with L 4,88 m and D = 94 kg (dinghy) + 140 to 170 kg (crew) >>> DLR 56 to 63
505 with L 5,05 m and D = 127 kg (dinghy) + 150 to 180 kg (crew) >>> DLR 60 to 66
Average : 64 to 73
or with singlehandle dinghy :

Moth Europe with L 3,35 m and D = 45 kg (dinghy) + 60 to 75 kg (sailor) >>> DLR 78 to 89
RS Aero with L 4,00 m and D = 48 kg (dinghy) + 65 to 85 kg (sailor) >>> DLR 49 to 58
Laser with L 4,23 m and D = 59 kg (dinghy) + 65 to 85 kg (sailor) >>> DLR 46 to 53
Melges 14 with L 4,27 m and D = 54 kg (dinghy) + 65 to 85 kg (sailor) >>> DLR 43 to 50
Finn with L 4,53 m and D = 116 kg (dinghy) + 75 to 95 kg (sailor) >>> DLR 57 to 63
Average : 55 to 62

This comparison clearly shows that the National 12 is quite outside of the usual range re. the lightness ratio, meaning less capacity to go planing, all other parameters equal.

** Secondly, if we look at the sails area SA (main + Jib) and the adimensional ratio SA/D^(2/3), with D range like above :

National 12 with SA = 10,4 m2 >>> SA/D^(2/3) 29,2 to 32,2

to compare with 0 or 1 Trapeze dinghies :

420 with SA = 10,3 m2 >>> SA/D^(2/3) 28,7 to 31,7
NS-14 with SA = 9,3 m2 >>> SA/D^(2/3) 27,3 to 30,3
445 with SA = 11,2 m2 >>> SA/D^(2/3) 28,7 to 31,2
29er with SA = 11,0 m2 >>> SA/D^(2/3) 29,8 to 32,7
Tasar with SA = 11,4 m2 >>> SA/D^(2/3) 33,1 to 36,7
470 with SA = 12,6 m2 >>> SA/D^(2/3) 29,8 to 32,1
505 with SA = 17,2 m2 >>> SA/D^(2/3) 38,4 to 42,1
Average : 30,7 to 33,5

or with singlehandle dinghy :

Moth Europe with SA = 7,2 m2 (with sailor 70 kg) >>> SA/D^(2/3) 31,0
RS Aero with SA = 9,0 m2 (with sailor 85 kg) >>> SA/D^(2/3) 35,1
Laser with SA = 7,0 m2 (with sailor 75 kg) >>> SA/D^(2/3) 27,4
Melges 14 with SA = 9,1 m2 (with sailor 85 kg) >>> SA/D^(2/3) 34,5
Finn with SA = 10,0 m2 (with sailor 95 kg) >>> SA/D^(2/3) 28,7
Average : 31,3

This comparison shows at contrary that the National 12 sails area ratio is in the standard of classic dinghies with no or one trapeze, no trapeze for the National 12 but in compensation a high beam up to 2m is allowed.

But due to his relative heavy weight, the design of a National 12 seems quite challenging and different of the other dinghies, to go through the range of speed Froude 0,4 to 0,8 with the lowest possible drag. At same hull shape and speed, the dynamic lift is a lower % of the total weight.

At this stage, you may say it can be better to rely on a narrow waterline beam to have a high Lw/Bw and go through the Fn 0,4-0,8 at low drag, like do successfully a Moth Lowrider or a catamaran when sailing on its leeward hull only. Here the goal is the reduction of the residuary drag without relying on a dynamic lift. The condition to have a significant result is Lw/Bw > ~ 7 and a DLR < ~ 100 , in order to minimise the slope step of the drag when evolving from Fn 0,3 to 0,6 (see here attached the residuary drag of a slender monohull, in adimensional form).
Lw/Bw = 7 means Bw = 0,52 m for a National 12 but again the DLR 107 to 124 cannot take a real advantage of such a narrow hull. So, for a National 12 designer, it should be a real headhache, a question of trade off really not easy to optimise. A Moth Lowrider, with a beam < 0,48 m and a DLR of 68 (the red line of the figure attached) or less, should reduce significantly its drag.