Revisiting the ULDB option ..., for a day-boat project.

This investigation here attached is about revisiting the ULDB option (Ultra Light Displacement Boat) for a day-boat project. The ULDB concept at such appeared at the dawn of the 70s : long waterline, quite narrow, light displacement to plane downwind, not too canvassed for their length so as to be easy to handle, and last but not least cheaper for the speed they could offer in those days.

ULDB means by raw definition a low Displacement Length ratio DLR, let'say < 100 to take a rounded value. Such ratio can be obtained of course through the use of light materials and of minimalist cabin accommodation, but above all by the deliberate choice to favour the waterline length and this without worrying about the consequence on the IOR rating of those days. That was a kind of subversive approach within the dominant era of the IOR rule, to name few iconic of these mavericks : John Spencer (NZ) / Ragtime, Bill Lee (US) / Merlin and Michel Joubert (Fr) / Subversion. To be able to win prestigious races in real time with such light and much less expensive sailboats in front of the cream of the class 1 of those days was a revelation.

I wanted to reconnect with this original approach, precisely the search for an optimum light design for a given displacement and a given sail plan, and not an optimum at constant length as undertaken now for most current modern designs. An approach actually based on an economy of means which is for me the true philosophy underlying the ULDB concept, that could be summed up by "faster for the sail area, cheaper for the length" and not just go fast downwind by breeze.

For that purpose, I have imagined to explore the variants from an initial Loa 8,15 m day-boat, keeping unchanged :

• the displacement, including unit or fixed masses involved in the mass estimate,
• the sail plan and area,
• the general shape of the hull and the proportion of its front and rear overhangs,
• the planform of the keel-bulb and of the rudder, the keel draft,
• the minimum freeboard (15 cm) at heel 30°.
  

5 hull lengths by 8 hull beams were investigated, so 40 versions of the day-boat. In order to respect the displacement, each extra length or extra beam from the initial design is made possible by reducing the keel weight, reducing so the ballast ratio : it is the main rule of the game. The minimum freeboard rule has also an impact on the hull area and so on its mass, and consequently also requiring an adjustment of the mass of the keel-ballast, in more or in less depending the cases. To mention the two extremes of the investigation :
The shortest & narrownest : Loa 8,15 m Boa 2,34 m Ballast ratio 46,2 % DLR 116
The longest & widest : Loa 11,75 m Boa 3,04 m Ballast ratio 22,9 % DLR 39
, all versions being at light weight displacement of 1517 kg and sails area upwind 33,7 m2.

We have examined both the performance issue (with light crew 2 / 140 kg) and the stability issue (with heavy crew 5 / 375 kg, aiming for Category C approval).

The performance issue / about the length at constant beam :
The longer versions give better speeds whatever the wind force and direction, and this despite the lower ballast ratio : we have shown that the reduction of the keel weight in order to have in exchange more length of hull can be done without loss of righting moment for the usual heels around 20°.

The performance issue / about the beam at constant length :
For light winds Force 2 -3, the narrowest the better although the speed loss is low when the beam increases. For winds 16 knots and over, the wider the better. For moderate winds 3-4, all beams of the range (from 2,34 m to 3,04 m) are roughly equivalent for the performance. The significant difference here introduced by more beam is for the heel angle reduction, up to 4° less with the 3,04 m versions / the 2,34 m ones.

The Froude range involved for these optimized long versions remains ≤ 0,5 for winds < 18-20 Knots. The speed benefit demonstrated by the VPP lies mostly in the reduction of the residuary drag within the displacement mode, which can overcome the increase of the friction drag. That does not show the other advantage usually granted for the ULDB, i.e. downwind for winds ≥ 20 Knots the overspeed capacity in semi-planing mode that low DLR lets you hope.

The stability ussue :
But these rewarding evolutions towards a long version with a reduced ballast ratio encountered a limit, which is not that of performance but first of all that of knock-down stability, precisely the capacity to upright from a capsized position with the masthead at water level, according to the regulatory conditions required for Cat. C. (Angle of Vanishing Stability AVS > 90°). At an early stage of the project, it is wise to aim this goal with a safety margin, i.e. a minimum of 100° to 105° AVS with the most defavorable loading (5P / 375 kg). This condition can eliminate some of the « best » solutions, e.g. the Loa 11,75 m x Boa 3,04 m x Ballast ratio 22,9 % version wich gives just 97° of AVS (but then an extra keel draft can save the affair). Generally speaking, too large beam and/or too low ballast ratio leads to a strong reduction of the AVS, it is the real stop in the search for the most efficient version for a given displacement and sail plan, before too much wetted surface.

In conclusion, this investigation gives arguments that such « vintage » ULDB concept can still be an interesting approach to design an easy, fast and fun long sailboat for its displacement and its sails area, so roughly for a given budget.

2 preliminary projects are proposed at the end, in illustration of this investigation :

Day-boat for lakes or sheltered coastal waters / average winds 2-3, max 6 :
Loa 11,75 m Boa 2,54 m Draft 1,70 m D 1517 kg Ballast 461 kg (30,4%) SA 35,7 m2 DLR 39

Day-boat for open sea coasts / average winds 3-4 , max 6 :
Loa 10,85 m Boa 2,74 m Draft 1,60 m D 1517 kg Ballast 472 kg (31,1%) SA 33,7 m2 DLR 49

Make your own choice among the 40 versions ! and anyway thanks in advance for your reading and your comments.

 

Jean-François, very interesting work. I had a similar idea and presented a paper at the HPYD in 2006 - http://www.remmlinger.com/Optimization.pdf
I also used constraints on the design parameters and the VMG to windward as the figure of merit. A genetic algorithm was the best method to find a large number of good designs. Since I had no constraint on the length or the displacement of the boat, the algorithm would run away to an infinite size. To avoid this, several constraints were tested and the most realistic one was cost! Without the constraints of a rating rule, the limit for the normal sailor is the price of the yacht. The cost were estimated from the structural weight, the sail area etc.

The results, which I got 15 years ago, are most likely not very accurate. I have today a much better method to calculate the residuary resistance and I am working on a better model for the sail-forces. The quality of the optimum that is found by the genetic algorithm is only as good as the VPP. Therefore, a realistic and detailed VPP is crucial. I am still not content with mine. From you I just learned that I might have to add a constraint for the AVS.

If I understand you right, you have drawn a linesplan for each variant. My goal is to let the computer do the searching, the "tweaking" of the lines plan and to identify the "best" design.
Uli

 

Many thanks Uli for your kind words and your comments. I read also your paper with great interest, a genetic algorithm sounds powerful and adapted to deal with a large number of parameters towards an optimization.

I hesitated to use the cost instead of the displacement as a constant, I finally prefered the displacement mostly because it is a physical parameter which makes easier as much as more relevant the interpretations that can be made on the evolution of righting moment, the ballast ratio, the wetted surface, etc … for each version. It is usual to say that the cost is in proportion of the displacement at first estimation. In my case, the rig , sails , deck fittings, cabin accomodation and equipment, rudder-helm system are exactly the same by definition, the average mass units for the hull and the deck surfaces are also the same, but for the long version (say L 11,75 m) the hull and the deck areas are larger and the keel weight is lower than for the short version (say L 8,15 m) : the longer version will need more materials and man-hours for the hull and the deck and less cast iron for the keel, so probably more budget at the end.

Yes, you need to include the stability issue in such optimization process, because at the end the approval for one category of design (A, B, C or D) is requested, which involve features and data quasi fixed at early stage of the design. In my case it happens that it is the AVS the critical criterion, STIX number being always easily above the threshold for the cat . C . But in the general case you should check both the AVS, the STIX Number and, for cat. B and cat. A, the righting energy mMO*AGz , all 3 needing the GZ curve computation with one or 2 loadings. There are some other requirements in the ISO rule, e.g. in relation with the first downflooding, but that can be definitely fixed during the detailed engineering studies, less necessary to involve them in the early stage loop, preliminary values when necessary (for STIX) can be sufficient.

The linesplan of the hull body is adjusted for each version by using only the geometrical parameters, not the adimensional ones as used in « Gene-Hull ». Manually adjusted yes, by following always the same routine, so an automation would be possible but not in the frame of my spreadsheet Gene-Hull. For example, for a version with more length :

• at first all the X of the input data are increased in proportion,
• the hull body draft Tc is decreased to obtain roughly the displacement objective,
• the keel wing and the bulb thicknesses are reduced to maintain weight # displacement.
• computation of the hull with heel 30°, to check the minimum freeboard / 15 cm objective
• adjustement of the freeboards accordingly, and re adjustment of Tc for the displacement
• slight adjustement of the keel line aft end to maintain the Cp around 0,55 and the LCB at 47% Lwl
• final adjustement of the mast position to maintain the same lead
• final back and forth adjustements between Tc and keel-bulb thicknesses to have then exactly displacement = weight = 1517 kg
• the LCB versus LCG varies very little in this process, if necessary re-adjustment of the keel position and of the mast position to have a better LCB = LCG . Exact equality is not necessary anyway for the light weight configuration, the following computations of the hull with heel for the VPP and the Stab being done with a loading (crew in the cockpit) with adjustement of the sinkage and of the trim.
  

It is long to describe but quick to do, I would say ~ 15 mn per new version for the linesplan modification, I gave some illustrations of that in the document, for the DLR chapter and the RM20° one.

 

An interesting variant of this experiment would be to try a Length VS Beam sum rule, where the Beam and Length are chained together, so the two added together always produce the same sum.

This would probably keep your costs very similar, as the amount of material needed to build each hull is more likely to be very close.

With a class of 1 ft model sailboats I invented, the Length stays the same, but the Beam and Draft are traded. Combined, they must produce the same sum.

 

You are right, budget should be very close with such added rule Loa + Boa = constant . I am not far from that rule when comparing in the performance tables :
Loa 8,15 m x Boa 3,04 m with Loa 9,05 m x Boa 2,34 m
Loa 9,05 m x Boa 3,04 m with Loa 9,95 m x Boa 2,34 m
Loa 9,95 m x Boa 3,04 m with Loa 10,85 m x Boa 2,34 m
Loa 10,85 m x Boa 3,04 m with Loa 11,75 m x Boa 2,34 m

By Force 2-3 in average or 3-4 in average, one can see that the longest version is always faster,

By winds 16 Knots and over, the trend reverses in the middle of the table :
9,05 m x 2,34 m still has an advantage of 0,15 knots in average / 8,15 m x 3,04 m
, while
11,75 m x 2,34 m shows a loss of 0,2 knots in average / 10,85 m x 3,04 m
, but the 10,85 m x 3,04 m has an AVS of 99,6° limit limit ...! , while the 11,75 m x 2,34 m has an AVS of 111,1°. Then, the draft made free can play its role to save the 10,85 m x 3,04 m version.

 

Thank you Jean-François for the detailed insight into your method. It is not as automated as mine, but in contrast, it is already working!
May be my goal is too complex and too ambitious. I will stick with the cost as the major constraint. It is difficult to assess, but once it is coded in the program, the execution is fast.
The English have a proverb: "There is more than one way to skin a cat". I enjoy the competition.

 

Thanks this is really interesting. I find it fascinating how different constraints result in different optimal layouts: fixed LOA leads to beamy, high stability boats with big rigs and plumb ends; fixed waterline length leads to overhangs; fixed sail area leads to very long, slender hulls.

It seems to me that keeping sail area constant as well as displacement unduly constrains your analysis; perhaps a shorter, wider hull could carry more sail and so compete with the longer, narrower hull?

 

Thanks Tlouth7 for your comments. As regard the set of constraints, the goal was 1) to be as close as possible to a mastered budget with fixing both the displacement and the rig/sail area, and 2) to have only 2 degrees of freedom (Loa, Boa) which kept easy both the investigation and the results presentation in the form of 2D tables. To free the rig/sail area adds a 3rd degree of freedom and then (for 3 or more degrees) a dedicated tool for optimisation, like the one proposed by Uli, is better adapted. What could be done yet, to be in line with your suggestion while keeping just 2 degrees of freedom, is to have Loa and Sail area free, to fix the displacement + to constraint the beam in function of the length, something like Loa x Boa or Loa + Boa = constant which go also towards a constant budget principle. I will try that way, by firstly checking the relative influence of Loa and Boa on the hull and deck areas, and so on materials and man.hours (?), and identify what could be a relevant function Boa = f(Loa).

 

Here is the complementary investigation when considering more sail, from a short list of the versions previously investigated, and still at constant displacement but then with variable SA/D ratio.

The 4 versions selected as starting point (Loa 11,75 m x Boa 2,44m, Loa 10,85 m x 2,64 m, Loa 9,95 m x Boa 2,84 m, Loa 9,05 m x 3,04 m) are motivated by roughly equivalent budget (through similar hull and deck areas, similar keel ballast mass) and roughly equivalent Angle of Vanishing Stability AVS.

For each version, 3 new sailplan areas SA are tested in addition to the one adopted for the previous investigation (SA 100% : 33,7 m2 for a sailing upwind) : SA 115% , SA 130%, SA 145% . Here, for each extra SA for a given hull length, it is the hull beam which is slightly reduced up to compensate the extra kg of the rig-sails sub-system and keep constant the displacement.

This complentary approach can highlight more efficient solutions both for light winds and for moderate winds conditions :

For light winds force 2-3, the longer narrower version, when associated with the maxi sailplan area, i.e. SA 145% , can show an extra average speed of 0,56 Knots (5,46 Knots / 4,90). The « cost » of this solution is a sail reduction required from 11 Knots of wind when sailing upwind.
Loa 11,75 m x Boa 2,35 m D 1517 kg Ballast 484 kg (31,9 %) SA 49,0 m2 AVS 102,8°
> DLR : 39 and SA/D^2/3 : 37,7
>>> it is a version well adapted for lakes or sheltered seas where light winds are common. To provide a light genoa for the 0-10 knots winds + a smaller jib for the 11-16 knots winds.

For moderate winds force 3-4, the trade-off length, beam, sailplan at constant displacement is less evident to detect without the help of a design and VPP process. Here, a shorter beamer version associated with SA 115% can be competitive to aim an all around performance, including by light winds when comparing with the previous best with SA 100% (average 5,01 Knots / 4,90) . And then a sail reduction is not required up to 16 knots of wind.
Loa 9,95 m x Boa 2,81 m D 1517 kg Ballast 507 kg (33,4 %) SA 38,8 m2 AVS 104,5°
> DLR : 64 and SA/D^2/3 : 29,9
>>> it is a version well adapted for coastal open waters where winds 3-4 are common.

Last but not least in the framework of an ULDB design, both versions have a low DLR (respectively 39 and 64), meaning they are able of extra speed when planing (not adressed by the VPP), when sailing downwind with sufficient wind.

 

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Since Remmlinger was kind enough to open this can of worms, I figured I'd give my two cents worth on the parameterization and morphing problem.

Kuddos for handling the weights in a realistic manner and investigating RM effects. But your morphing strategy isn't sophisticated enough to do the investigation justice. If I start with Napoleon's flagship Oriente and morph the hull your way, I don't end up with Commanche. But that is exactly what should happen if you do it right. You need to look at how the midship section shape ought to change when the immersed midsection area is adjusted for a different LWL (displacement fixed,) and when the beam/draft ratio changes.

The midsection shapes depend on the overall goal of the boat, as well as on constraints such as STIX, AVS, and area under the RM curve up to various heel angles.

If you stick with a single vessel displacement curve shape and stretch it for length changes, getting the new midsection immersed area is simple enough. The next step would be to compute the new VCG after estimating ballast adjustments, then generate a new midsection shape that produces the desired righting moment curve. My approach to doing that is to fix the midsection girth from +/- 25 degrees of heel and find the shape that maximizes some specified function of RM(heel), Area under the RM curve (heel), AVS, and wetted girth. For long skinny boats, the area under the RM curve can be approximated by the change in VCG mapped onto the midsection as it is heeled from level. The hull's RM will be something like 0.50 the RM of the midsection if the midsection was an extrusion. You can safely steal that factor from the parent hull if you keep the transom shape for all the morphs.

In summary, to get a new midsection shape -
1. Craft an objective function that incorporates design heel RM, pressed heel RM, RM30, AVS, wetted girth, and area under the RM curve. The ratio of RM30 to Area under the RM curve is a significant shaping factor and can be easily lifted from examples of the type.
2.Compute the new immersed midship section area and estimate the new vessel VCG.
3.Find shape that optimizes the objective function. I use a free plugin for Excel. Scale midsection shape to match actual immersed area.
4. Extrapolate the shape to generate sections of a new hull. You can use a fixed transom and a fixed forebody and just blend the new midsection shape into the old shape. The midsection will almost completely determine what the hull's RM curve looks like up to deck flooding angles.

Correcting/optimizing the midsection shape is hugely important for the sort of investigation you are doing. It can completely change the results given the constraints that you did (and didn't) choose. Varying VCG with both length and beam (due to shell weight,) and widely varying wetted areas, means you have to reoptimize the section shapes with an eye towards lesser shell weight and lesser wetted area rather than just accepting the values that result from scaling the parent hull's offsets.

In case you are still reading, here's how I handle the midsection shape generator. I represent the midsection as a 20 link chain from keel to sheer, or keel to the maximum heeled waterline if the heel calculations don't immerse the deck. The links are all fixed length. The deck is a profile that gets patched onto the sheer if needed. This has to be patched on each iteration since the sheer coordinates move. Each link is described by it's tangent angle. The coordinates of each vertex are calculated from keel to sheer by marching up the links.

In general, you will have goals and constraints that apply to different angles of heel, so you have several different instances of each candidate section shape healed to different angles. Each will need CB and a waterline calculated. Then the RM and area under the RM curve can be computed. Now you can test for constraint violations and hang a score on your objective function. Let the optimizer adjust the 20 link angles until your function is maximized. This requires a bunch of additional shape constraints because the problem is not well conditioned for the optimizer right out of the box.

 

Thanks Phil for your comments. My intention was not an optimisation at such but a just a walk in the landscape of possible solutions with a relatively short list of constraints (mostly at constant displacement, constant sailplan, same mass units for the hull and the deck structure, etc .....as detailed in my document), and the same routine to change from one to another version (as detailed in my quote #03, especially by reshaping at minima the hull body with changing the geometrical data, but not its adimensional parameters, within Gene-Hull). So are output : Ballast ratio, RM, wetted surface, speed, heel angle, stability (AVS, STIX), ... and of course the DLR itself.

A real optimisation is a lot more complete (and complex), all is about the set of constraints and the merit function, as Uli and you have pointed. I understand you use 2D mid section features to help go faster to a solution. Attached is the 2D formulation test for a section, which I currently use for my Gene-Hull developments, you can play with it by changing either the geometrical data (Sheer : Y1 , Z1, Keel : Zo) or the adimensional parameters. By changing just the geometrical data without changing the parameters will give you an idea (in 2D) of the routine used (in 3D). It is open source, you can recover the formulations in the ad hoc cells.

 

Optimized midsections using a fixed girth and fixed immersed area. Heel angle 25 degrees. Girth between heeled waterlines is constant. Case 1 is maximum RM at 25 degrees heel. Case 5 is maximum area under the RM curve from level to 25 degrees heel. Cases 2-4 have a minimum RM constraint and the area under the RM curve is then maximized. This shows how sensitive shape can be when using STIX-like constraints.


Girth = 40, immersed area = 50, VCG = 0

Case 1 RM= 455 Area = 36.3
Case 2 RM= 435 Area = 85.7
Case 3 RM= 410 Area = 92.3
Case 4 RM= 370 Area = 93.4
Case 5 RM= 300 Area = 94.9

Level midsections


Heeled midsections

 

Im a fan, as far as it goes that ULDB can be a cost effective way of getting some place, and sometimes quicker than some others.
Obviously you have come across the design spiral. It can only make sense to pick a hull that suits the conditions you expect most people to use the boat in, unless a very light wind location one-design type scenario.

Still a fan of single chine boats like Black Soo, but most people today will take accomodation over sailing performance. For a day boat, i expect performance to be a more important criteria.