Kendall,
I find this exchange very interesting and I hope that the other forum friends agree.

I think that we should first understand each other, because we probably speak different languages... :-) not just Italian vs English!
What you call "Figure of Merit Tables" for me are just "Tables of basic measurements" real, quasi real or just theoretically computed, at this stage, it is not very important. I agree with you that they are few and probably insufficient to characterize what you want to characterize - but this is another story. Then come what you call "performance and stability metrics" and I call simply "indicators"; they are just ad-hoc functions of the basic measurements, mainly suggested by experience or whatever. As I hinted before they are a-priori infinite and somehow arbitrary; their meaningfulness can be checked only a-posteriori, I am afraid.
My previous post regarded the indicators and, in particular, the ones I saw defined on the cited web sites; I was just suggesting to check them and be sure that they are defined in a non-dimensional way. It is always possible to define non-dimensional indicators if you properly combine the basic measurements and this is important because such indicators are already scale invariant and there will be no need to normalize as you suggest.
I think that this is advisable especially because you are searching the rationale (or philosophy) of boat design throughout a wide range of sizes.
The further analyses you propose are extremely interesting and I hope to see the results soon.

Daniel, 411/004

All,

Most recently, hull draft has been measured from the graphical documents found on the site here. It was determined after making the assumption that the accommodation plan diagrams depict the keels and hull shapes in a spatial and quantitative accurate manner. A graphical technique was developed and applied similarly to each model's accommodation plan side view.

The technique's primary goal was to establish a line which delimited the bottom of the hull where the keel is attached. With that line established, the distance between the waterline and bottom of the keel could easily be proportioned between the hull and the keel.

Some stability indices require the hull draft. This technique will likely be questioned by a purist.. but it does provide some needed information for this analysis.

If you know your model's hull draft, and are interested, please forward it so that I might get a measure of the validity of this method.

Please find the current Metric and Imperial figures of merit tables below. I opt to call this set Version 1.0.

Thank you,

Kendall

All,

Find attached below some performance and stability indices for all the S&S Swan models listed in the Figure of Merits tables.

I have relied primarily on the following two sites to obtain the formula and to learn about the meaning of the indices.

http://www.tedbrewer.com/yachtdesign.html

http://www.johnsboatstuff.com/Articles/estimati.htm

There is an additional stability index I will implement soon located at the US Sailing site:

http://www.sailingusa.info/formula.htm



Once updated with the additional stability index (Angle of Vanishing Stability), the indices matrix will serve as the input for the various analyses I have mentioned earlier in this thread.

The second attachment below gives some information about the type of information each index conveys and also the specific formula used for each of the metrics included so far.

Discussions with several members and often ones with Lars Ström has led me to conclude that this group of indices is not the optimal group to have at our disposal. Unfortunately, the more meaningful indices require specific input parameters that are not now available.

Thank you,

Kendall

The stability screening value (SSV) from the US sailing website mentioned in the previous note was added to the table of indices. Now there are a total of eleven (11) indices calculated (5 performance, 6 stability)

Two plot graphics are attached to give an indication of the nature of the data. A matrix of XY plots shows the full index dataset. The 11 dimension data space is not easy to review and draw conclusions from. Each individual plot here has 37 X,Y pairs indicating each S&S Swan model's associated performance or stability metric.

To simplify and look for major characteristics, a second plot showing correlation coefficients (graphically) is presented. It represents the same data as before but now the correlation between each index pair is displayed. Ellipses are modulated to convey the information of the correlation values. A line represents perfect correlation, a circle indicates no correlation (no linear association) between the pairs of variables. Positive and negative correlations are indicated by orientation. Notice along the diagonal, lines sloping 45 degrees up indicate perfect correlation (a variable with itself in this situation).

The mix of high/low, positive/negative correlated data suggests the data set as a whole may be instructive for further analysis.

Kendall

Key
*************************************************
SAtoDispR--------Sail Area to Displacement Ratio
DisptoLR---------Displacement to Length Ratio
VelR-------------Velocity Ratio
LtoBeamR---------Length to Beam Ratio
SAtoAFAR---------SailArea to Anti Fouled Area Ratio
CSF--------------Capsize Screening Factor
CF---------------Comfort Factor
BtoDispR---------Beam to Displacement Ratio
RollPer----------Roll Period
StabIndx---------Stability Index
SSV--------------Stability Screening Value

In the last message, there was a mistake. There are 39 models/configurations listed on the Figure of Merit tables, not 37 as was mentioned.

The attached plot displays correlation ellipses again, but this time the data matrix has been transposed and individual models are arrayed along the X and Y axes. These data have been normalized by subtracting the mean and dividing by the standard deviation for each of the indices which were calculated. This normalization has the effect of giving equal importance to each of the eleven indices. After the normalization, each has a mean of 0 and unit standard deviation.

These ellipses again show the possibility of an interesting/informative dataset as demonstrated by the range of low/high and positive/negative correlations.

For those interested, the descriptive statistics for each calculate index is displayed in the second image attached here.

Attached, is the result of applying a hierarchical clustering algorithm to the correlation matrix derived from the normalized data. This method partitions the S&S Swan models into various groups. Its the intent of the method to produce groups having members that are similar to each other (and dissimilar from members in other groups).

What does this tell us? I ask for your help .

We look at the large clusters first. By using a y-xis height cutoff of 1, two large groups result in this analysis. I offer this result and ask the group to interpret these two groups. If you just saw two lists having the members listed there, What is your guess of why they are grouped as they are? Except for the model 48, the model derivatives group closely with the base model.

first group has Swan Models:
48Shorrt1,48Short2,65,55,44,41,36,40

second group has Swan Models:
76,57,37,431,38,47,48CBup,48CBDOWN,43,411

OK, SO WHAT NOW? WHAT DOES THIS MEAN? DO WE ALL SELL OUR BOATS AND BUY OTHERS IF SO WHICH ONES? A PRESTO PIPPO 411/22

Pippo,

I am confident this analysis will not suggest what you have mentioned. The cluster analysis here is simply showing groupings of similar S&S designed Swans based on performance and stability indices (which are based on the basic measurements only).

Please know I will certainly not be selling mine.

Kendall 431/25

Histograms of each of the eleven (performance/stability) indices are presented below. Each histogram shows the distribution of the 39 S&S Swan models for the various indices. By looking up your model's eleven indices (listed a few messages prior), you can determine how your model compares to all other S&S Swans. I'll show the Model 431 comparison next.

Model 431 summary:

Performance Indices

1 SAIL AREA TO DISPLACEMENT RATIO 16.122
2 DISPLACEMENT TO LENGTH RATIO 319.515
3 VELOCITY RATIO 1.060
4 LENGTH TO BEAM RATIO 3.225
5 SAIL AREA TO ANTIFOULED AREA 1.981

Stability Indices

6 CAPSIZE SCREENING FACTOR 1.737
7 COMFORT FACTOR 35.247
8 BALLAST TO DISPLACEMENT RATIO 0.449
9 ROLL PERIOD 3.970
10 STABILITY INDEX 0.971
11 Stability Screening Value 19.826


My model 431 falls in the middle of the distributions for the first three parameters.. so she behaves like an average S&S Swan with respect to performance in medium winds (SAIL AREA TO DISPLACEMENT RATIO), performance in strong winds (Displacement to length ratio) and potential max speed (Velocity ratio). She is at the extreme end of the distribution of the length to beam ratio (suggesting she handles more loosely/softly than all the other S&S models).

The distribution for Sail Area to Antifouled area shows her near the middle (suggesting average Swan performance for light winds).

Again the 431 shows up at the edge of the distribution for Capsize screening factor. All S&S Swan models have a value below 2 (making them ocean racing appropriate/strong). Of all the S&S models the 431 is the most susceptible to harsh weather at sea (but still ocean strong). The CF (comfort factor) parameter shows up also near tail of the distribution for the 431.

The model 431 shows up in the middle of the Ballast to Displacement Ratio distribution.. She is gravity stabilized (close to the average of all the S&S Swan models).



Roll Period and Stability Index locations in the distributions suggest she is on the tails of the distributions w.r.t. stability indices (compared to the other S&S Swan models. Stability Screening Value of 19... middle of the distribution.. not sure what this means yet..

Summary 431..

Performance is S&S Swan middle of the pack. Stability is S&S Swan edge of the distributions. Weaker relative stability.

Model 431 locations on the distributions of the performance and stability indices.

The two clusters discussed in message #27 of this thread are indicated below using ovals and rectangles to show the cluster memberships. Since the ordering of the models in the listing are chronological, the clusters represent groupings based on early models (ellipses) and later models (rectangles). The cluster algorithm determined this grouping solely on the basis of the information in the performance and stability indices matrix.

Three models (43SHORT, 43TALL and 37) belonging to the earlier period are more closely associated with the larger cluster which predominately was made up of later model S&S Swans.

A statistical summary of the indices partitioned by these cluster memberships may reveal which index (indices) are important in contributing to the cluster result.

Such a summary and analysis will soon follow.. Kendall

Histograms using color to display the locations of the Velocity Ratio and the Stability index are presented below. The cluster analysis partitioned the S&S Swan models into two major groups that I opted to associate with the names of "early" Swans and "late" Swans.

These histogram results show the two clusters of models seem to have systematically different measures of central tendency for the Velocity Ratio and for the Stability Index.

Clearly the design concept changes that played out in the offices at Sparkman & Stephens during Nautor's Swan period systamatically effected these figures of merit.

Contrastingly, other indices seem to offer little discriminating power to separate the "early" and "late" Swan clusters from each other. The histograms below show the distributions of the Beam to Displacement Ratio and Sail Area to Anti-Fouled Area Ratio. The central tendency of both of the clusters seem to overlap each other in these cases (red and blue shares approximately the same locations along the x-axis).