Example: 'Dacia's' certificate, June 1892, recorded S. = 887.6 and L.

= 33.83 and R. = 5.00. But her S. L. 6,000 = 5.005 and 0.005 is 'a fraction smaller than 0.1'; consequently, by the wording of Rule 3, her R. = 5.01, and she was over-rating; but the secretary, Y.R.A., when questioned, stated that the 'Y.R.A. only recognises two places of decimals,' and words to this effect were added to Rule 3 at the general meeting February 22, 1893.

_The Time Allowance_

The time scale for differences of R. under Rule 1. was based on the conception that a racing yacht's 'capability for speed varies as the fifth root of the rating,' the argument leading to this being that--

speed varies as [V]L (1)

and that sail varies as L[V]B (2)

and by the rating rule, R varies as S L

it therefore follows from (2) that R varies as L{2}[V]B

and, a.s.suming that B varies as L (3)

it follows that R varies as L{2}[V]L or L{5/2}

therefore ... L varies as R{2/5}

Hence, by (1), speed varies as [V]R{2/5} or [5V]R.--Q.E.D.

The Y.R.A. time scale therefore rests not only on the two a.s.sumptions (1) and (2) mentioned in the book, but on the further a.s.sumption (3), which we know to be incorrect.

However, the 5th root of R. gives a time scale which is found to act fairly well in practice, and this being so, the theory of the time curve is a matter of minor importance.

At first (1886 and 1887) the adoption of the unrestricted rule met with some opposition, especially in the small cla.s.ses, where a few of the most experienced yachtsmen advocated restrictions in L.W.L. or L.O.A., and in mainsail area. But the majority determined, and rightly, to give the rule free scope; and the results on the whole have been highly satisfactory, fine seaworthy vessels, driven by a small sail-area at great speed, having been produced in the large cla.s.ses. The evolution in the small cla.s.ses has been more rapid, and in 1892 some rather undesirable types were prize-winners, and yachtsmen who wished to protect themselves against similar vessels in the large cla.s.ses induced the Y.R.A. to appoint a special committee to consider whether the unrestricted and unaltered rule should be continued beyond the seven-years period, terminating in 1893. This committee, under the presidency of Sir George Lampson, obtained the opinions of our leading designers, as was done in 1886, and the designers themselves met in conference twice, and jointly addressed two letters to the Rule Committee in which they finally recommended the adoption of the Seawanhaka rule for rating racing yachts and a cla.s.sification of corrected lengths suitable for our existing racing fleet; also other details, the most important being a proposal to tax overhang above the W.L. and cut away keels below it.

The Rule Committee adopted the recommendation as to change of rating rule, but proposed a modification whereby the British rating and time scale could be retained.

When this report was brought before the Council it was upset, some of the committee themselves voting against their own report. But the action of the Council has since been justified by the production of several splendid specimens of yacht architecture to race under the Y.R.A. rule of rating.

The elements of the fastest types which have developed in small yachts under the rule can be studied in the tables given in the chapter on Racing in the Solent Cla.s.ses.

One of our ablest designers has consistently advocated the introduction of a tax on beam into the formula. He did so in 1886, and again in 1892, when he proposed to tax draught also.

Unfortunately the mathematics of the rule make it difficult, if not impossible, to do so, because the blow on L. is lessened when it is shared by other quant.i.ties.

Thus by Mr. Watson's modification of the rating rule, proposed in October 1892, viz.

English R = (2L + 2B + D) S {constant, say 17,000} (II.)

'Doreen' is of smaller rating, although both longer and more beamy than 'Decima.' They are of the same rating for racing by the Y.R.A.

rule. Mr. Watson's formula would therefore encourage even greater length of hull than the Y.R.A. rule. No such difficulty is encountered by the introduction of such taxes into the Seawanhaka rule, where the plus sign replaces the multiplying sign used by us. This rule was adopted by the American Yacht Club of its name in 1882, the form being

American R = (L + [V]S) 2 (III.)

The New York Yacht Club has raced for a number of years under a similar rule for time allowance,[6] viz.

American R = (2L + [V]S) 3 (IV.)

and just as the Y.R.A. rule can take the form

L S = constant in any cla.s.s,

so these rules can take the forms

L + [V]S = constant, in any cla.s.s III.

2L + [V]S = constant, in any cla.s.s IV.

It then becomes evident that any sacrifice of S. to obtain greater L.

under Rule IV. is only half as effective as the same process under Rule III. Conversely, any sacrifice of L. to obtain more S. is twice as effective under Rule IV. as under Rule III.

[Footnote 6: But not for cla.s.sification, which latter has been simply the length of hull on water-line. Hence, yachts built for the same cla.s.s have varied much in their sail-area; 'Vigilant' and 'Valkyrie'

for instance.]

Again, as comparisons between L. and S. must be brought to some common measure, the Y.R.A. form ... L. S. = constant in any cla.s.s, may be read L. [V]S. [V]S. = constant, and it then becomes clear that any sacrifice of S. to get L. is twice as effective as in Rule III., and four times as effective as in Rule IV.; and conversely, that any sacrifice of L. to get more S. is half as effective as in Rule III., and one-fourth as effective as in Rule IV.

The author of the Y.R.A. rule has pointed out that it can be converted into the American form of 'corrected length,' thus:--

American R = [3V]L S (V.)

See his second edition of 'Yacht Architecture.' The sail curve is precisely the same as that from the Y.R.A. rule.

An examination of this form of the Y.R.A. rule is interesting. By cubing V. and comparing it with I., it will be seen that six thousand times the English rating equals the cube of the American rating derived from formula V.

[Ill.u.s.tration: Diagram of sail curves, showing the relation of sail to L.W.L. in the Y.R.A., New York, and Seawanhaka Rules. 40-rating cla.s.s.]

When English and American rules are examined diagraphically, the sail-curves take three positions that differ considerably in their steepness--the Y.R.A. rule giving a curve nearest to the horizontal which indicates R. = S. constant, proposed by Mr. Richardson in 1886 (or R. = [V]S constant if expressed in American measure; or R. = S.

[V]S divided by a constant if expressed in English measure); and the New York rule taking a position nearest to the vertical denoting R. = L., under which the Solent Length Cla.s.ses used to sail.

The Seawanhaka rule gives an intermediate curve--perhaps the 'happy medium.'

The curves have been plotted for yachts of 40-rating by our rule, and the following table gives the actual numbers:--

+---------------------------------------------------------------------+ | | Sail-area allowed to | | +------------------------+------------------+-----------------+ |L.W.L. | 40-raters, Y.R.A. Rule | 61.5 Corrected L.| 61 Corrected L. | | | | Seawanhaka Rule | New York Rule | +-------+------------------------+------------------+-----------------+ | ft. | ft. | ft. | ft. | | | | | | | 54 | 4,444 | 4,761 | -- | | 56 | 4,286 | 4,489 | 5,041 | | 58 | 4,139 | 4,225 | -- | | 59 | 4,068 | 4,096 | 4,096 | | 60 | 4,000 | 3,969 | -- | | 62 | 3,871 | 3,721 | 3,481 | | 64 | 3,750 | 3,481 | -- | +-------+------------------------+------------------+-----------------+

_The Turning-point of Maximum Efficiency, or best Length_

Each L. and S. rule for rating racing yachts must have a turning-point, or best length, in each cla.s.s for winning prizes in a given climate. It depends far more upon the average wind-pressure during the racing season than on any a.s.sumed connection between L. and [V]S. It will vary on different days, and for different seasons, and for different localities. The average wind-force is stronger on the Solent than on the Clyde, and stronger at Rothesay than at Sandy Hook.

But type is another matter. Type is governed by the racing rule, and differences of climate have very little effect upon it. The best proportional length also varies in different cla.s.ses, the water being rougher and the wind harder, comparatively speaking, on small than on large yachts, thus causing the former to develope L. and sacrifice S.

to the utmost. Under the tonnage rules it is true that the small yachts carried the larger comparative sail-plan, but this was due to other causes, such as their greater comparative draught and ballast.

The _best length_ under L. and S. rules also varies with the rating rule, those rules having sail-curves nearest to the line R. = S.

developing the greatest length, and those having sail-curves nearest to the line R. = L. developing the greatest sail.