center of flotation calculation and implications?

[Fanie]

Look, even if the output is not the most accurate software there is, at least one have something that you can see improves performance or not.

There's a very good chance we're going to build the 9m hull, and I'll get a chance to play with it in real life, check speeds etc and compare to the software. Be a good exersize.

[sorenfdk]

Originally Posted by Fanie

Just for interest sake -

I fiddled with a hull design here, I actually scaled a 10m hull to a 9m size and was quite amazed at the result. The smaller hull was faster than the bigger hull with the same power input. When comparing the differences it seems the smaller hull's CP was 6.9 where the bigger hull was 6.2. Both are 2000kg displacement and the same beam.

This just means one thing - the 10m hull is not optimised !

It also means that your CPs are way off! CP is always smaller than 1!

[Fanie]

Hi Søren,

I'm typing with my thumbs here

They should be ZERO POINT 69 and ZERO POINT 62

Dunno why I do it, probably comes from doing more than one thing at a time...

I fiddled with a hull design here, I actually scaled a 10m hull to a 9m size and was quite amazed at the result. The smaller hull was faster than the bigger hull with the same power input. When comparing the differences it seems the smaller hull's CP was 0.69 where the bigger hull was 0.62
Both are 2000kg displacement and the same beam.

This just means one thing - the 10m hull is not optimised !

[Fanie]

And before you ask, no, it didn't get any better when I scale it even more

[TeddyDiver]

Fanie wrote:
"The smaller hull was faster than the bigger hull with the same power input. When comparing the differences it seems the smaller hull's CP was 0.69 where the bigger hull was 0.62. Both are 2000kg displacement and the same beam."

So..
There's something you have omitted now.. wetted surface which is lesser with the smaller version. You have also modified the hull form a bit to keep the same displacement. Otherwise the Cp's would have been the same but displacement less with the smaller one..

[Eric Sponberg]

I was going to restrict this topic to just Sail Area/Displacement ratio, but it is closely related to Sail Area/Wetted Surface ratio, and so a single discussion on both is in order.

The next topic in our quest for better understanding of naval architecture with regard to sailing yachts rests on two ratios related to sail area. The first and more important one is Sail Area/Displacement ratio (SA/D in short-hand notation), and its little sister is Sail Area/Wetted Surface ratio (SA/WS). The reason I regard one higher than the other is because SA/D is easily calculated from published data, and it gives a better indication of power versus weight—a true power-to-weight ratio—at normal sailing speeds when drag due to displacement—the full total of friction, form, and wave making drag—is significant.

SA/WS ratio is a power-to-drag ratio that gives an indication of the power available to a sailboat for light air sailing when friction drag is the primary drag component and wave making drag is minimal. Few sources publish the wetted surface of boats, so generally, we cannot compare our numbers to other designs, and that limits its usefulness. But we do have some guidelines to follow.

Both ratios are truly dimensionless, and we’ll start with SA/D ratio. Here is the formula:

SA/D = Sail Area/(volume of displacement)^0.667

In words, SA/D = the sail area divided by the 2/3rds root of the volume of displacement. We have units of square feet divided by units of square feet. It also works directly in metric units being units of square meters divided by units of square meters—so it is universal in any consistent system of units. Typically, you use the upwind sail area and the design displacement for calculating SA/D ratio.

We calculate volume of displacement, of course, by dividing the weight of displacement by the density of seawater. In imperial units, divide weight in pounds by 64 lbs/cu.ft. of seawater (the norm) or by 62.4 lbs/cu.ft. of fresh water. In metric units using Kgf and cubic meters, we know that 1,000 Kgf = 1 metric ton = 1 cubic meter of fresh water. We want to use sea water to easily compare to other designs. So to convert displacement to cubic meters of sea water, divide the weight in metric tons by 1.025 which is the specific gravity of seawater = volume of displacement in cubic meters of sea water.

We raise the volume of displacement to the 2/3rds power to convert it from cubic units to square units. We leave sail area alone.

There are various published ranges of normal SA/D ratio. Interestingly, Skene’s “Elements of Yacht Design” ignores this ratio. Ted Brewer’s book on Sailboat Design gives the following ranges which are as good a description as any. Generally, the higher the ratio, the more power the sailboat has, and so the faster it will be.

BOAT TYPE………………………………...……..SA/D
Motorsailers………………………………............13 – 14
Slow auxiliary sailboats………………….............14 – 15
Average offshore cruisers……………….............15 – 16
Coastal cruisers………………….........................16 – 17
Racing yachts…………………….........................17 – 19
Ultra light racers, class racers, daysailers.…..…20+

Larsson and Eliasson, in “Principles of Yacht Design,” cite a paper by Miller and Kirkman, “Sailing Yacht Design—A New Appreciation of a Fine Art” (SNAME Transactions, Vol. 98, 1990, which is an update of a 1963 similarly titled paper published in SNAME Transactions by Henry and Miller) which offers a graph, Fig. VII-5, showing a typical range of SA/D ratios between 15 to 22 over lengths on the waterline between 20’ and 50’.

In another very good design paper by Jay Paris, “Performance Criteria and the Design of Sailing Yachts” (New England Sailing Yacht Symposium, January 24, 1976, SNAME), Figure 7 shows a lower limit of SA/D of 15 – 17.5, and an upper limit of 17 – 20.5 over the same waterline lengths. All these papers, by the way, are available from SNAME.

In my own experience, the Open Class boats of the 1990s era had very high SA/D ratios, upwards of 40-50. Project Amazon, my Open Class 60 for the 1998 Around Alone Race, had a design SA/D of 42.1. Others of my designs are:

Bagatelle, 1998-9, ultra-light ocean racing: SA/D = 38.71, later with heavier keel, 27.47
Saint Barbara, 2002, light Great Lakes racing/cruising: SA/D = 22.90
Globetrotter 45/Eagle, 2004-5, light auxiliary cruising: SA/D = 21.38
Globetrotter 66 (currently in design), light ocean cruising: SA/D = 20.84

I have not been keeping track of design trends in the latest Open Classes, the Volvo Round the World Race, or the America’s Cup, but my inclination is that all their SA/D ratios are quite high. The ranges given by Ted Brewer above generally still hold for typical sailing yacht designs.

You use the SA/D ratio to make sure you are not over-powering or under-powering your design. Generally, you want to be within these ranges, or if you are outside these ranges, then justify yourself to your customers as to why. Be prepared to explain.

Moving onto SA/WS ratio, the formula is very simple:

SA/WS = Sail Area/Wetted Surface

Again, this is a true dimensionless ratio and is consistent in all measurement systems. The sail area is again the upwind sail area, and the wetted surface is the entire wetted surface including the keel and rudder (all of the boat is dragging through the water, so the entire wetted surface is included). Obviously, the higher the ratio, the more power the boat has in light air.

Ted Brewer doesn’t talk about SA/WS, I guess because most of his designs generally have large wetted surface areas. Larsson and Eliasson refer to the Miller-Kirkman Paper. Skene’s Elements of Yacht Designs gives some guidelines which I will repeat here. Paris’ paper summarizes the latter two. Basically, Skene’s offers Figure 44 (Kinney, 8th edition, page 287) which shows that for keel boats up to 80’ Lwl, the lower limit on SA/WS is about 1.9 at 25’ Lwl to 2.88 at 80’ Lwl. The upper limit for the same waterline lengths ranges from 2.35 to 3.28. Centerboard boats straddle this upper limit.

SA/WS is usually more important in round-the-buoys racing where light air conditions can prevail over a whole course for a whole race. In the current era, we see lots of racing yachts with minimal keel and rudder planforms, and their Cp’s are reduced to the minimum, so wetted areas are very small. Such boats like to sail in flat water (i.e. light wind and tiny waves) and so minimizing friction drag is of paramount importance. Such boats, however, are overpowered easily unless there are lots of crew on board to sit on the rail to keep the boat upright. Therefore, crew commitment and organization plays a huge roll in winning races. We could get into a philosophical discussion about the impact of crew on racing boats, and when do crew elements and issues overpower design elements—but that is for another time in a pub somewhere over a beer.

SA/WS is of little concern in an offshore cruising yacht. Such yachts have so much displacement just to carry the owner’s stuff, and have keels that are large enough to support the weight of the boat on shore in out-of-the-way places, that wetted surface is necessarily high. We do not try to optimize wetted surface on such designs. As a result, we are more concerned with SA/D ratio.

So, we know that SA/D is a power-to-weight ratio—the higher this ratio, the faster the boat will be. And from our last lesson, we know that Displacement-Length Ratio, DLR, is an indicator of drag—the higher this ratio, the slower the boat would be. We can learn some interesting things if we plot the SA/D ratios versus the DLR ratios for any given population of yachts, such as in the attached picture.

The data for this plot is something that I have collected over the years, and you can see that the data points form a crescent, if you will, that peaks at the upper left (fast speeds) and again at the lower right (slow speeds). The potential to surf increases going up and to the left. You can match your own designs with a similar plot. This graph is very similar to Figure 8 in the Paris paper, and again, it represents the norm for a lot of production boats—these are typical. If your boat design is outside this range, then it is either because you are trying to design something new and different, or it’s because you have made a bad mistake somewhere and need to check your work.

This discussion now leads us to the next question: Is there a way to rate sailboat performance on a scale of 1 to 10? Indeed there is—it is called the S Number, which I refer to in short-hand as S#. S# is not new; I first learned about it in 1988. But next week will be the first time, as far as I am aware, that it will have a worldwide release. And you’ll read about it first, right here. Stay tuned!

Questions?

Eric

[TeddyDiver]

Great stuff Eric... Thanks!

[ancient kayaker]

Yet another fascinating lesson! It reminded me of a simple study of scaling that I performed a few years ago when I was trying to understand various aspects of boat design.

If one were to scale a boat design up by a factor of 2 in every direction, keeping everything in proportion, then the displacement would increase by 8 times and the sail area by 4. The overturning moment of the sails, assuming identical fluid pressures (not true) would increase by 8 times, but at a given angle of heel the righting moment would increase by 16 times.

My interest had been sparked by observing that large yachts such as the America's cup contestants carried vastly more sail for their size than smaller sailboats, and in particular, model racing yachts. The study explained this for me, and also explained why a true-to-scale scale model of a powerful racing boat or ship cannot compete with a similar sized purpose design racing model.

Of course, I am ignoring multihulls, boats with shifting ballast or movable keels and so forth, but the same scaling rules still apply.

In the smallest of manned sailboats, the ballast is self-powered and can be shifted quickly and the hull is often designed for planing, so the sail areas carried by such can be greater. Sure enough, the two alternative rigs I am building for my own very light sailboat, which I outweight 3:1 (!) will give it the SA/D of a motorsailer (small rig) or an ultra-light racer. Indeed, the later category shares similar SA/D ratios with daysailers.

I well remember hours of lecture room torment as professors droned on about pure theory, never once grounding the lesson in a practical example. Therefore, Eric, here are my particular thanks for the way you provide a link to the real world with your lessons. Either you are a great teacher, or the academic world is missing out on some real talent.

i checked out the specs for Ranger, one of the great J-class America's cup boats. At 168 tons and 7546 sq ft it had a SA/D ratio of almost 93.

[frank smith]

Very helpful info Eric.
Thanks again,
Frank

[Eric Sponberg]

Originally Posted by ancient kayaker

Therefore, Eric, here are my particular thanks for the way you provide a link to the real world with your lessons. Either you are a great teacher, or the academic world is missing out on some real talent.

Thank you very much. I am glad people are pleased with the articles. I guess I have inherited some teaching genes. My father was a vice president of a university, and later president of two other universities in succession. My mother taught music in her earlier years, and later was a master degree professional organist. My older brother and sister are both PhDs and teachers. And my younger sister and brother work at universities in administration. It kind of runs in the family.

Coming up after the S#, I thought I would talk about Ted Brewer's Motion Comfort ratio because that can be tied in with S#. I thought I would then touch on Bruce Number for multihulls, and then finish off with Dave Gerr's Displacement Speed formula and George Crouch's Planing speed formula.

For the record, when this series is done, I will collect the articles into a single pdf document and post it on my website for anyone to download in the future.

Eric

[LyndonJ]

Hello Eric

On another thread another designer talked about the traps in sail area ratios when not considered along with GZ. In otherwords the 'Power of the hull'. a powerful hull being one which could stand up to the sail area set (and with minimal leeway).

It seems some designs have vast sail areas but have poor GZ curves?
Also a boat may have a SAD of 18 or 20 on the sales brochure but it spends its time on passages with much smaller sails for a variety of reasons.

I am interested as to whether the required SAD scale with vessel size?

Thanks

[Paul Kotzebue]

Originally Posted by ancient kayaker

.
At 168 tons and 7546 sq ft it had a SA/D ratio of almost 93.

168 long tons = 5880 cubic feet. SA/D = 23.16, not 93.

[ancient kayaker]

Originally Posted by Paul Kotzebue

168 long tons = 5880 cubic feet. SA/D = 23.16, not 93.

Agreed: I did not save my calculation so I don't know where I went wrong! So it is right on Eric's datum for a class racer.

[sailor54]

Culled from sailing mag 'Bateaux', mainly 70's and 80's (N = 76, mostly from R. Tristan then at CRAIN http:// www.craintechnologies.com)
LWL is metric
Note the slight upward trend with increasing LWL

Thanks Eric for that wonderful tutorial

[ancient kayaker]

SA/D of some other famous ships FYI:
America (yacht 170 T) 16.1
Cutty Sark (clipper 2100 T) 18.2
HMS Victory (3500 T) 23.7
Preussen (windjammer 11150 T) 11