center of flotation calculation and implications?

Except that the published displacement is never accurate.

Comparisons are endlessly fascinating and I thank Eric for bringing this S# method forward. I'm no mathematician but it seems to me that if you use displacement twice you compound the error if that displacement is mistaken. The only displacement numbers I believe are the ones I've established myself, and even then they are all accompanied with little fudge factor notes.

Looking at Eric's spreadsheet I find one boat with which I am intimate....the Hinckley 70. The inputs for this design are incorrect....sorry I can't help being a nitpicker.... But I mean well.

Hinckley Sou'wester 70
LOA = 70'3"
LWL = 52'4"
Beam = 17'6"
Draft = 6'6" and 16'2" board down
Sail area = 2250 sq ft.

Published displacement is 90,000 pounds.
Light ship displacement was calculated at 78,000 pounds
1/2 load sailing displacement was calculated at 85,000 pounds
Design (DWL) displacement is 87,000 pounds
Full Load displacement was calculated at 90,100 pounds
Actual sailing displacement is probably upwards of 95,000 pounds.

I think the S# will be far more accurate for a boat like Paul's meter boat or any day racer type, than for the typical cruiser. Unless a boat is only being used as a weekender it will be overloaded....the degree of overloading depends on the owner.

 

I was wondering how long it would take for someone to ask me for the original article. I scanned it into a pdf file and it is attached. It does not include the derivation of S#; I don't know how it was derived, I only know that it was. The article is not clear on that. You'll see in the nomograph on page 35 that the S# scale goes below 0, but in fact I have never seen S# go into negative numbers in the time that I have been calculating S# myself.

My point was about terms was that, prior to knowing about S#, your definition of what a "racer-cruiser" was is probably different from mine or anyone elses--what is a "racer-cruiser" as opposed to a "cruiser"--who knows--that's the problem, as stated at the beginning. S# just defines what these terms could mean by the application of a number in specific ranges, if necessary. The numbers always fall between 1 and 10. And in fact, if, over time, people think that the spread of these definitions for the labels is incorrect--and I am only repeating Brooks' original definitions--then the definitions can be changed. Make the spread different. Make the labels different. The names for the labels can be anything--fruits or vegetables--it does not really make any difference. What matters is the number itself. If you see that you have a low number, the boat is going to be slower than a similar sister with a higher number. This is not about absolutes; it is about comparisons between boats. If the labels are a problem, then delete the labels entirely--you don't need labels to use S#. I think the labels are there just to add a little correspondence of S# to what was used before.

As for accurate data, certainly, you need accurate data. If you don't have that, garbage in--garbage out, as the old saying goes.

There is a mistake on the Hinckley 70. I went back to the original published article, and you'll note in the list that the Hinckley 70 and the Hinckley Sou'Wester 61 on the next line down have identical numbers. That's because in the original magazine, on widely separated pages, the articles are for the different boats, but the data is exactly the same! So the design particulars were published wrong, and stupid me, I did not catch it at the time (I don't pay real close attention to Hinckleys). Never mind, if you put in your correct data, Tad, and then vary the displacement according to your displacement range (78,000 to 95,000 lbs), the S# varies from 2.50 (Cruiser) down to 1.80 (Lead Sled). And of course, the S# is going to change, and if a customer or the builder are concerned about that, it really is not so much what you call the boat, it is the fact that you have a number between 1 and 10 on which to rate it. Anyone will understand that different data going in makes for different results coming out.

Eric

 

OK ... if the S# predicts a boat will have the performance of a 4.5 but it actually performs like a 3 the S# is not valid. False predictions will invalidate the formula.

 

Is not important if the formula coefficients are not accurate.

The idea is very interesting.

I think that, if we need do certain adjustments, in function of the data used for the regression, go to do. I think that this is simple.

But I do not think that we will have greats differences in the formula.

 

This is a matter, then, of collecting actual experience. What do we actually perceive a 4.5 to be? What do we perceive a 3 to be? How do we judge unless we actually sail on the boats? That may come with experience. It could very well be that the S# is not a good enough indicator of boat performance. If S# is NOT a good indicator, then other things are happening with the boat, not related to DLR and SA/D, that cause its performance to be different. That, then, would have to be determined.

Eric

 

Again: These ratios and numbers are only crude indicators of performance. Don't put too much in them!

BTW: A boat doesn't perform - a boat + crew performs!

 

Motion Comfort Ratio

At the end of last week’s discussion of S#, I mentioned Motion Comfort Ratio which was included in the S# spreadsheet. Motion Comfort Ratio (MCR) is the invention of yacht designer Ted Brewer, which he describes as follows in his book Ted Brewer Explains Sailboat Design:

“This ratio is one that your author dreamed up for an article in Cruising World magazine. The article was tongue-in-cheek but the comfort ratio has been accepted by many as a measure of motion comfort, and indeed, it does provide a reasonable comparison.”

“Tongue-in-cheek”??? Well, if he thought it a bit whimsical, Ted nevertheless had some sense of science in creating MCR. He does not show us too much about MCR in his book other than to state the equation and how it works. However, the Cruising World article appeared in the September 1990 issue, and MCR was mentioned in a sidebar article called “Looking At The Numbers,” written by Danny Greene, one of Cruising World’s editors. I attach a pdf file of the sidebar article, and MCR is described on the last page.

Here is the equation:

MCR = Displacement/(0.65*(0.7LWL + 0.3LOA)*BEAM^1.333)

Displacement is in pounds and the lengths for LWL, LOA, and BEAM are in feet. This is not a dimensionless number—we have units of pounds per feet^2.333 (add exponents of like units when they are multiplied together.)

In the Cruising World article, Brewer divides comfort zones into three parts [Commoditas est omnis divisa in partes tres.—“All comfort is divided into three parts.", to coin a phrase, with apologies to Julius Caesar. I can't help it; my sister is a Latin teacher.] These are called Lesser, Average, and Greater comfort. Not clever or original, but they get the point across. It is actually easiest to simply quote Ted Brewer’s own description from his book, which is pretty clear:

The comfort ratio is based on the fact that motion comfort depends on the rapidity of the motion; the faster the motion, the more upsetting it is to our human gyroscopes. Given a certain force, such as a wave, the speed of motion depends upon the weight of the object (the boat) and the amount of surface that is acted upon (the LWL area). Greater weight, or lesser area, means a lower motion, thus more comfort.

Beam enters into it also as wider beam will generate a faster reaction, particularly in beam seas. In effect, the comfort ratio measures the displacement of the vessel against its waterline area, adds a factor for beam, and thus is a means to compare motion comfort for boats of various sizes and types.

One finds that smaller yachts, having a higher beam/length ratio, are lower on the comfort scale. Also, older designs get higher marks for comfort as they are from the era of heavy displacement and narrower beam. Comfort ratios will range from 5.4 for a Lightning class daysailing sloop to the high 60s for a heavy vessel such as a Colin Archer pilot boat. The moderate and successful ocean cruiser, such as the Whitby 42 [a Ted Brewer design—EWS] and Bob Perry’s Valiant 40, will be in the low to middle 30s.

And that is the sum total of what Ted says about MCR.

The chart in Cruising World magazine is a little more revealing, displaying a chart of MCR versus Length. I am guessing that Ted came up with these divisions with some sense of actual experience, because there is no other way in analyzing MCR that one could sense where the divisions should be based on the equation alone. Ted himself does not even have this chart in his book, nor does he state the definitions of the three parts, and he does not even list MCR in the index, so I wonder how seriously he takes this. Maybe not very much. But there it is, he gave it to us, so let’s take a closer look.

In the spreadsheet, look at MCR Chart 01, which I have separated out in a pdf file. This is exactly the same chart as in the Cruising World article, except that I have carried both length and MCR down to the origin: Length = 0 and MCR = 0. We see that the division lines between Greater, Average, and Lesser are all straight lines. That means that the MCR limits are always a set ratio in relation to length. Ah, but which length—LOA or LWL? Both Ted and Danny Greene speak in generic terms of LOA: “Whitby 42,” “Valiant 40”, “light displacement 50-footer”, “heavy displacement 30-footer”. So I take “length” in the Cruising World chart to be LOA. That is how we think of boats in regular terms, by their LOA. If this is so, then in my chart I found that the division line between Greater and Average is always MCR => 0.835 of LOA, and the division line between Average and Lesser is always MCR <= 0.626 of LOA. So this gives us a useful tool—with any population of boat designs, we can easily calculate both the MCR and what division it is in.

Before I go further, let’s have a closer look at the equation. The numerator is easy, it is simply displacement in pounds. But look at the denominator, we basically have an equation for waterplane area = 0.65 x L x B. The 0.65 is a generic waterplane coefficient, but L is actually two parts, 70% of the length on the waterline plus 30% of the length overall. This gives a length that is just longer than the design flotation waterline, and the reason for doing this is to simulate an “actual” wetted waterline length as the boat moves through the water. The beam is overall beam raised to the 1.333 power to give it a bit more influence in the equation.

But why the power of 1.333? It is probably because we know that a boat’s rolling motion will have higher accelerations if the metacentric height is really large, and lower accelerations if metacentric height is really small. It’s the accelerations that kill you and make you feel uncomfortable. Metacentric height, GM, is proportional to the moment of inertia of the waterplane, which in turn is proportional to length and to beam cubed. Therefore, comfort is inversely proportional to L x B^3. Large beam is going to give higher metacentric height, and therefore lesser comfort. But in his MCR equation, I think Brewer is looking for “influence”, not equality. He wants a resulting MCR number that has the same order of magnitude as length, caused by the influence of beam. He could have used beam cubed, but that would make MCR a pretty small number. And if naval architects like anything, it is reasonable numbers, so Brewer lets beam have some greater influence, but not too much.

Now look at MCR Chart 02. This is a plot of S# versus MCR. The regions for S# are defined by colored horizontal lines, and the regions for MCR are the two diagonal lines across the chart. All regions for both factors are labeled. How did I come up with this chart? I did a sort of the data and plotted only those boats with high S#s and MCR labels of “Lesser” comfort, and drew the Lesser comfort boundary appropriately to the right side of all the data. Then I did the same with the Average boats and set that boundary. Finally, all the Greater comfort boats ended up in the lower right part of the chart. It was simply a brute-force method of charting. I show labels where some of my own designs, as I have mentioned before, appear to fall.

If you think about it and study the chart, it seems to make sense. Certainly, boats with higher S#s are going to be faster, more lively, and therefore have less comfortable motion. Boats with lower S#s will be slower, less lively, and have more comfortable motion. It is all consistent and makes sense. So here we have in this chart a very interesting and revealing picture of boat performance. I show this to my clients as we discuss their new boat designs, and it reveals how a potential new design will fit in the overall scheme of things and in relation to other boats of known performance. With just the basic design parameters of length, beam, displacement and sail area, you can calculate both S# and MCR, vary the parameters, and see how the proposed boat moves around this chart. This helps the client and designer decide what the overall proportions should be for the performance that is desired. It is quite a useful analytical tool.

Next week, I would like to discuss Dellenbaugh Angle.

Questions?

Eric

 

Interesting concept, as ALF noted when he was examining a flush toilet for the first time! If displacement is expressed as cu.ft then the expression has the dimensions L^0.667 -while that would only hold true for scaling a given design linearly, it helped me to get a handle on what is going on, and I can see how it makes sense.

There is a difference between experiencing acceleration vertically for a fraction of a second, perceived as a "bump", and the same acceleration maintained for several seconds, perceived as a major deviation from the straight and narrow. This may have been factored into the exponent of 1.333 applied to Beam.

However, establishing an expression for comfort is closer to the realm of black art than science IMHO at least until we have a numeric definition of comfort itself. One can imagine the controversy over that and the battles between the vested interests in the automotive sector for one example, which would be worse than gas consumption! Nonetheless, it's a way of comparing boats of different design and size, and thought provoking too.

Edit note: I deleted my comments on the exponent of Beam which were based on a misunderstanding.

 

Metacentric height (GM) is not proportional to the moment of inertia of the waterplane (I), but metacentric radius is. GM is dependent on the metacentric radius and the position of the center of gravity. While an increase in beam will result in an increase in GM (all else being equal), there is no direct relationship between GM and I. Brewer's MCR does not consider the center of gravity which is enough to disqualify it from being a meaningful analytical tool IMHO.

I'm not sure what is meant by "comfort is inversely proportional to L x B^3". It is more or less accepted that comfort is related to acceleration which is related to roll period (an over simplification). The roll period is proportional to the radius of gyration and inversely proportional to the square root of GM. The radius of gyration (k) increases with beam, but I think it is an over simplification to assume k is proportional to B. However, the increase in k with wider beam will offset the effects of the increase in GM to some extent.

Of course any serious study of comfort at sea is going to look at acceleration which is not necessarily proportional to roll period. It is possible to have a relatively long roll period with relatively high amplitude, which will result in higher roll acceleration and less comfort. The reason roll stabilizers work so well is they reduce the roll amplitude and acceleration, but have little effect on the roll period.

We need to be careful how we use formulas that seem to produce reasonable results for a given set of data. There is a difference between curve fitting and analysis.

 

So, you guys went on and proceeded without me... *snif*



Sorry I got distracted, go ahead I'll catch up one day...

 

Eric

Acknowledging that you are trying to popularize a complex subject; but this performance prediction considers only a small subset of the performance parameters. Also its only for light to moderate wind.

It would be nice to see Wetted surface, lateral plane area, and a stability factor at the very least included in any general basic performance prediction. This would move the general performance out of 'light to moderate' weather and into a more realistic prediction.

For example an over-canvassed, lightweight, low stability index, high windage sailboat with low lateral plane area might look very good on the S-meter and to the marketers.

I don't think I've been involved in a vessel design yet where smooth water VPP actually matched the tank test data. Particularly for sailboats. (For the learners here VPP takes a reasonably thorough set of vessel data ).

I'm looking forward to your essay on the compromises that have to made and traded in vessel design

Cheers

 

Mike,

I disagree that the S# is relegated only to light to moderate weather. As stated before, wetted surface plays a part in light wind sailing because it is directly connected with friction drag which is the lion's share of the drag in light air and slow speeds, yet the S# does not include a wetted surface factor. SA/D and DLR both play a part in moderate to heavy air sailing because they relate to volume of displacement which is related to wave making resistance at higher speeds. So S# does not work, really, solely for light air performance. All that you can say about that is that boats in the "Racing Machine" category tend to be light weight, and lightweight boats tend to have small wetted surface. So if you want a good light air performer, you need a boat with an S# greater than 5. That is as sophisticated as this gets, which is not very much.

Also, the point of the S# was to take easily obtainable published data and manipulate it to provide a useful guideline so that any person, particularly boat owners and buyers, could calculate S# on a calculator and maybe learn something. Wetted surface, lateral plane area, and stability factors are rarely published. If you can't find the data, you're stuck.

Compromises--that will be a never-ending discussion! Last year, designers Chuck Neville, Steve Seaton and I were guests on the podium for a forum at one of Passagemaker Magazine's TrawlerFests, and the subject of our panel discussion was "Compromises in Yacht Design." We had a hoot! The audience was large and animated, and the discussion was very interesting and fun. We easily could have gone on for another hour or so talking about all manner of things.

I am limiting this thread to the subjects of design ratios and those simpler equations that we use as tools in yacht design. As I mentioned, next week will be Dellenbaugh Angle, which was more popular at one time for looking at sailing yacht stability, less so now. But it is mentioned in "Skene's Elements of Yacht Design" and in "Principles of Yacht Design" by Larsson/Eliasson. I used it not too long ago in my analysis for the Scandinavian Cruiser 40 in order to show and explain the stability of the boat to my client.

Eric

 

Mike: if there was a single expression of an aspect of sailboat performance that one wished to optimize, a computer could design the perfect boat and that would be that. But it's not going to happen.

 

Eric

There’s no indication if the vessel is over-canvassed in that formulae but a high scoring lofty rig - large sail area counts regardless.

For example an Open 60 with a 15 foot keel or a 5 foot keel will score the same performance with the S prediction but the 5 foot keel version will shorten sail by 50% at 10 knots. The ‘rated’ sail area is then misleading . So you are back to some knowledge required to interpret the result. I think some form of stability index should be incorporated.

Without this in the formula it will incorrectly indicate light air only sail areas as good overall performers.
A conservatively rigged blue water cruiser may perform on a passage closer to the S rated ‘racing sled’ than might otherwise be indicated. Which is why we use RAO’s in commercial design. Just putting a big engine in a hull relative to D doesn’t make it fast, you are still limited by the hull itself and other parameters hard to extrapolate from D alone. Then as Tad said earlier D is a very variable and often misrepresented figure.

In reality the differences in similar form displacement sailing vessels in a seaway tends to be in the light to moderate wind arena say up to 10 knots of breeze. Where the heavy displacement vessel needs proportionately more sail. Once the wind rises above 14 knots the heavier vessels performs very closely to the lighter vessels with the same relive sail area (Delft series). If you were looking at a vessel for charter in the trades for example many of these ratios are not indicative of the real relative performance.

I’d like to see the Dellenbaugh angle re-defined as taken from the GZ curve rather than fudged from indicators. Manufacturers could easily supply this data and they often publish (although tongue in cheek ) GZ curves.

 

Terry
I think that will happen, just not for a while.