_Extract from Letter to the FIELD in 1892._--'With shame I
confess that the problems and calculations, the combinations
of straight and crooked lines, with large and small numerals
and Latin and Greek letters, the mathematical contortions
and algebraic hieroglyphics ... are meaningless to my
uncultured eyes. They are fascinating; I admire their
beauty, and can well understand that inventing rules for
rating must be a most charming pursuit for intellectual
yachtsmen....
'DUNRAVEN.'
An attempt will be made to treat the subject as simply as possible, so
that anyone who knows a little arithmetic may follow it.
The following 'hieroglyphics' will be used:--
B. Beam
D. Draught
F. Freeboard
G. Girth
L. Length
L.O.A. Length over all
L.O.M. Length between official marks
L.W.L. Length on W.L.
M. Area of immersed mid-section
M.S. Mid section
R. Rating, whether Y.R.A., or corrected length, or other
S. Sail area
T. Tonnage
U.Y.F. Union des Yachts Français
W. Weight of yacht complete in English tons dead weight same as her displacement
W.L. Water level
Y.R.A. Yacht Racing Association
If the subject of rating were treated historically, it would be
necessary to begin with the old tonnage rules; but we live in the
present, and the more important of the existing rules will therefore
be examined first. The old tonnage rules will more conveniently be
described at the end of the chapter, with existing tonnage rules.
England and America have used rating rules for some years, and France
determined to do the same in October 1892.
The efficiency of a sailing yacht can be calculated very similarly to
that of a steam yacht, the sails being the motor in one, the engines
in the other. But we know that the efficiency of a steamer should vary
directly as her indicated horse-power, and inversely as her
displacement. The same idea should apply to sailing yachts. It is, in
fact, almost impossible to rate a sailing yacht satisfactorily without
taking into account both her sail-area and her displacement--or
something very closely allied with the latter.
A length and sail-area rule proposed by Mr. Dixon Kemp in 1880 was
adopted in 1883 for second-class racing, and in 1886 this alternative
rule was adopted as the sole rule. It is--
English R = L × S ÷ 6,000 (I.)
This important step was taken after a careful and exhaustive inquiry
conducted by a special committee appointed by the Council, Y.R.A., and
presided over by Sir William Forwood. The committee took the evidence
of our most noted yacht architects, and finally reported in favour of
Rule (I), and of the present classification (except 2-1/2 rating,
which was afterwards added by the Council). The report met with
general approval; the Y.R.A. put its seal upon it, and gave it a
tenure of seven years; subject, however, to General Rule 12, by which
any change at any time can be made by the requisite majorities.
The tonnage time scale in use before 1886 was altered to agree with
the new rating, which cannot be said to represent anything but what it
really is--viz. the product of a yacht's taxable length and her
sail-area.
The classification and the divisor do not alter the rule one iota.
They are purely arbitrary, as was very clearly stated in an excellent
letter by Mr. G. B. Thompson, published in the 'Field' of December 17,
1892. He said very truly that the 5-rating class is in reality the
30,000 class, and the 10-rating class is the 60,000 class. If the
divisor 6,000 be altered alone, the result is precisely the same as
altering the rating itself in like ratio, and in the same direction.
Thus (R. × divisor) and (L. × S.) must each equal 120,000 in the 20-R.
class, and must each equal 240,000 in the 40-R. class, and so on. In
short, the Y.R.A. rule may be regarded thuswise:--In each class L. ×
S. = a constant, for boats at the top of the class.
By a recent decision in general meeting, Y.R.A., December 6, 1892, L.
will in future be measured between the outer edges of the official
marks, which must be affixed by the owner and always show clear above
W.L. when a yacht lies in smooth water in racing trim.
L., therefore, is no longer L.W.L., but L.O.M. (length by owner's
marks), rather longer than L.W.L.
By Rule 3, Y.R.A., in calculating a yacht's R., a fraction of or
exceeding 0.01 counts as 1.0 in classes exceeding 10 R.; but in
classes exceeding 1.0 R. and not exceeding 10 R., a fraction less than
0.1 counts as 0.1; and in classes not exceeding 1.0 R. fractions from
0.01 to 0.99 inclusive count for their value.
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, assuming 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 assumptions
(1) and (2) mentioned in the book, but on the further assumption (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 classes, 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
classes. The evolution in the small classes 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 classes 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
classification 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 Classes.
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 quantities.
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 class,
so these rules can take the forms
L + [V¯]S = constant, in any class III.
2L + [V¯]S = constant, in any class 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 classification, which latter has been simply
the length of hull on water-line. Hence, yachts built for the same
class 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 class, 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.
[Illustration: 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
class.]
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 Classes 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 class for winning prizes in a
given climate. It depends far more upon the average wind-pressure
during the racing season than on any assumed 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 classes, 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.
Still another factor governs the _best length_ in any class, viz.
lightness of construction; and this depends on four other factors:
cost, design, workmanship, and strength of materials.
We are therefore met by quite a crowd of considerations when
endeavouring to determine _best length_; but in comparing the rating
rules we can eliminate many of them by making a few assumptions and
reasoning therefrom.
_First_, assume that a new boat is built with the lightest possible
hull consistent with strength, and of the best possible design for the
40-R. class 1894, and that her L.=62 ft., therefore S=3,871. (See
preceding table.)
_Second_, assume that a longer boat and a shorter boat equally well
built and designed are tried and are beaten, and that 62 ft. is then
acknowledged to be _best length_ for 40-ratings in our climate.
_Third_, assume that the class is converted in 1895 into one rated at
61.5 American R., 'Queen Mab' being thereby placed at the top of the
class by the Seawanhaka rule without alteration. The 62-ft. yacht,
however, must clip to 3,721, or 150 off her S. as a 40-rater.
But the shorter boat, say a 'Queen Mab' 59 ft. L.W.L., which we
assumed to fail when racing under our rule, could now _add_ 30 ft. and
sail against the crack 62-footer with an advantage of no less than 180
sq. ft. of canvas.
Evidently, the best length under our rule being 62, the best length
under the American rule is something less; how much less being only
determined by trial, and depending on the numerous factors before
mentioned. Moreover, an arbitrary limit of L.W.L. is thus shown to be
less necessary under the American rule than under ours; and with L. so
greatly developed in our racers at the present time, it may be that we
have already gone beyond the best length for the American rule,
especially in the small classes. This was carefully pointed out by the
present writer in two letters to 'Land and Water,' October 5 and 9,
1892. Mr. R. E. Froude also stated the case very clearly in the
'Field,' December 31, 1892; but it is very difficult to convince the
defenders of the Y.R.A. rule that any other rule is superior.
Mr. Dixon Kemp, in his excellent work on 'Yacht Architecture,' says
(p. 15, 2nd edition) in comparing rules I., III., IV.: 'Of these
rules, that of the Y.R.A. admits of the employment of the greatest
length for any given rating'; and the length referred to was evidently
_best length_ in a given climate.
The Seawanhaka rule is therefore superior to ours if excessive length
be feared; and being a plus formula, it lends itself readily to the
adoption of any desired tax on other linear dimensions.
For instance, Mr. Watson's proposal (II.) might be put into the plus
form, thus:--
American R = (2L + 2B + D + [V¯]S) ÷ 3.8 (VI.)
This shows the value of a plus rule over a multiplying rule and the
value is not lost when a plus rule is converted into an English rating
rule by cubing the former and dividing by a constant. Thus, the recent
Rule Committee proposed to convert the Seawanhaka rule into an English
rating rule by cubing it and dividing by 6,000, the result being:
English R = (L + [V¯]S){3} ÷ constant, say 48,000 (VII.)
The variable within brackets in VI. can be cubed and divided by a
constant in a similar manner. But the cubic forms of the 'plus' rules
are clumsy, and seem difficult to those who cannot compute by
logarithms. No real advantage is gained by adhering to the English
rating and time scale and classification. In fact, the American time
scale is simpler. If, therefore, a 'plus form' of rating be ever
adopted, it would be much better to adopt 'corrected length' as the
rating, together with the American time scale. The classification
could, of course, be chosen in such a manner that our own racing
yachts would be at the top of the classes without any important
alterations.
Another rule was proposed in a leading article of the 'Field' on
October 15, 1892. It is:--
English R = L{2}[V¯]S ÷ constant, say 6,000 (VIII.)
It gives a sail-curve nearly parallel to the one produced by the New
York rule, and may almost be regarded as that rule dressed in Y.R.A.
uniform; but the advantages of a plus rule are lost, whereas in the
conversion of the Seawanhaka rule proposed by the Y.R.A. Committee
1892 they are retained.
Similarly, the Y.R.A. rule--varying as [3V¯]L.S. (see V.), or
as [3V¯]L. × [V¯]S. × [V¯]S.--may be considered as equivalent
to the plus formula L. + 2 [V¯]S. ÷ constant, and the English and
American rules may therefore be regarded to vary as follows:
In linear measure
New York as 2 L + [V¯]S
Seawanhaka as L + [V¯]S
Y.R.A. as L + 2[V¯]S
Mr. Herreshoff has recently proposed a rule of rating based on L. [V¯]
S., which is an area, but the cube root of tonnage is placed in the
divisor; and this being linear, it converts the rating into linear
measure, an area divided by a line being a line. The result being
linear, it is translatable into American rating and time allowance.
Mr. Herreshoff's proposed rule is:--
American R = ( L [V¯]S / [3V¯]T ) ÷ constant, say 15 (IX.)
A critique on this rule by the editor of the 'Field,' December 17,
1892, suggests that the cube root of 100 T. should be taken, as there
are 100 cubic feet in a registered ton. This is unnecessary. So long
as S. is superficial, and T. cubic, the [V¯]S. and the [3V¯]T. will be
linear; and a constant can be selected which will convert the quotient
resulting from the rule into corrected feet or inches, or metres, as
required for the linear rating adopted.
Mr. Herreshoff's rule when tested is not encouraging; 'Doreen's'
length so corrected being 2-1/2 per cent. smaller than 'Decima's.' The
rule evidently does not encourage that compactness of hull-dimension
which Mr. Watson considers desirable. It also appears to put a
premium on abnormal freeboard, so as to increase T. by means of a
large body over the water-level.
This was pointed out by the editor of the 'Field,' December 24, 1892,
and an improved rule suggested in which displacement was used as a
divisor in place of tonnage. W. the total weight of yacht in English
tons dead weight is of course her displacement, and the rule proposed
may be written:--
English R = ( L{2}S / [3V¯]W ) ÷ 10,000 (X.)
So far as L. and S. are concerned this rule would produce a similar
sail-curve to the Y.R.A. rule (see diagram); but the divisor would
encourage a large powerful hull, and the rule would therefore produce
a shorter type with more sail than now exists in English racers. The
practical difficulty of discovering W., either by measurement or by
some system of weighing the yacht complete, has to be considered in
connection with this rule.
The most important point to be noted about these rules (IX. and X.) is
the fact that Mr. Herreshoff and Mr. Dixon Kemp proposed them--showing
that two of the leading experts consider it necessary to encourage
greater displacement by means of the rating rules. The question,
therefore, arises whether the desired result cannot be effected in a
less objectionable manner; and it appears to the writer that dividing
the present Y.R.A. rule by some area proportional to that of the
immersed mid-section would have the desired effect, and would avoid
the difficulties already mentioned. The actual area of M.S. cannot be
found without encroaching on the secrets of a yacht's design; but M.
the area of immersed mid-section can be easily found if measured
internally, and the Y.R.A. rule may take the form:--
American R = LS ÷ constant (say 72) (XI.)
--
M
L.S. being cubic, and the variable divisor M. being superficial, the
quotient is linear, and a constant divisor can be chosen which will
convert the result into American rating, which is expressed in
'corrected' feet.
The general tendencies of the Y.R.A. rule would be modified by the
introduction of M. as proposed in XI., a large immersed M.S. being
encouraged, without the necessity of employing a deep narrow body, as
may be seen on the following table, where 'Bedouin' figures out very
well owing to her large but not deep immersed M.S. The author claims
with some confidence that this modified rule presents the best
solution of the problem yet suggested. But there is really no problem
requiring solution at present. So long as yachts like 'Britannia' and
'Satanita' are built for racing under the Y.R.A. existing rule of
rating, grumblers will not command an audience. In the event, however,
of yachts like 'Pilgrim' or 'Jubilee' winning in our waters a change
of some sort will be required.
The measurement of M. can be easily done in a few minutes, with yacht
afloat, as described on p. 87 of the 'Field,' January 21, 1893.
The Seawanhaka rule (III.) can be treated similarly, the divisor 2
being thereby avoided. It becomes
American R = L + [V¯]S - [V¯]72M (XII.)
The action of these rules may be seen from the table on p. 180; column
headed XI. giving the rating under the modified Y.R.A. rule, and
column headed XII. giving the rating under the modified Seawanhaka
rule. Each result is in 'corrected length.'
The dimensions in above were obtained from the drawings in Dixon
Kemp's 'Yacht Architecture,' 2nd ed., except 'Decima's' and
'Doreen's,' which were kindly given by their designers.
It will be found on trial that 72 M. is approximately equal to the
mean value of S and L{2} in successful yachts.
_The New French Rule_
On November 5, 1892, it was announced in the 'Field' that the Union
des Yachts Français had decided to adopt a hull-and sail-area rating,
it being considered by the 'active element in French yacht racing'
that 'the type ... produced by the French length and girth rule is
inferior to the type produced by the British and American rules ...
British yachts having defeated those of France, although handicapped
by the French rule of rating.' The conclusion was scarcely a logical
sequence from the premisses. It should have been that French racing
yachts were not the correct evolution of the French rule of rating.
But we are now concerned with the new French rule (proposed by M.
Godinet) in which sail is an important factor.
+---------------+-------+-------+--------+--------+--------+-------+
| Name of yacht | L | S | [V¯]S | M | XI. | XII. |
+---------------+-------+-------+--------+--------+--------+-------+
| Genesta | 81.0 | 7,643| 101.40 | 91.27 | 94.21 | 87.39 |
| Volunteer | 85.9 | 10,270| 87.43 | 105.42 | 100.24 | 93.30 |
+---------------+-------+-------+--------+--------+--------+-------+
| Chiquita | 45.5 | 2,636| 51.36 | 31.32 | 53.20 | 49.35 |
| Ghost | 46.5 | 2,577| 50.77 | 34.60 | 48.10 | 47.38 |
| Minerva | 40.0 | 2,700| 52.00 | 29.73 | 50.39 | 46.00 |
+---------------+-------+-------+--------+--------+--------+-------+
| Dis | 36.0 | 1,658| 40.71 | 22.37 | 36.23 | 36.00 |
| Decima | 35.67| 1,679| 40.94 | 22.17 | 37.23 | 36.71 |
| Doreen | 38.05| 1,572| 39.62 | 21.67 | 38.34 | 38.23 |
+---------------+-------+-------+--------+--------+--------+-------+
| Oread | 28.2 | 1,063| 32.60 | 13.33 | 31.25 | 29.82 |
| Quinque | 33.0 | 900| 30.00 | 13.33 | 30.93 | 32.02 |
| Valentine | 29.8 | 996| 31.56 | 14.47 | 28.50 | 29.08 |
| Bedouin | 30.0 | 1,000| 31.62 | 14.96 | 28.00 | 28.92 |
+---------------+-------+-------+--------+--------+--------+-------+
| Madcap | 21.0 | 714| 26.72 | 9.97 | 20.89 | 20.97 |
| Lady Nan | 23.0 | 653| 25.55 | 8.63 | 24.16 | 23.63 |
| Dolphin | 25.7 | 581| 24.10 | 8.27 | 25.07 | 25.41 |
+---------------+-------+-------+--------+--------+--------+-------+
In its simplest form, it is:--
English R = (4L - G) G[V¯]S ÷ 520 (XIII.)
G. being the greatest girth from top of deck planking port, round keel
to ditto starboard, plus extreme beam. Each of the three factors L. G.
[V¯]S. being linear (metric measure) the result is given in cubic
form, and is converted into English rating by the divisor selected,
and the Y.R.A. time scale has been adopted by the Union des Yachts
Français.
The editor of the 'Field' considers that 'the rule is calculated to
produce a poor kind of vessel for match sailing or anything else'; but
it is hazardous to prophesy the evolution of any rule, more especially
one which taxes L., B., D., bilge, and S. No doubt the tax on D. is
doubtful policy, and it seems very unnecessary when we consider the
small depth of water in many French harbours, which is the most
efficient check on D. it is possible to conceive for large yachts, and
in the small classes D. gives grip and power to windward, and
seaworthiness.
A careful analysis of the rule by the writer leads him to believe that
the conclusion arrived at by the editor of the 'Field' is correct. It
certainly appears that the rule has a sail-curve nearly as steep as
the New York rule, which has been abandoned because it encouraged such
large sail-plans. For this reason, therefore, if for no other, the new
French rule seems to be inferior to the Y.R.A. and the Seawanhaka
rules. A good letter on the subject of girth, by one of our leading
designers, was published in the 'Yachtsman,' September 8, 1892.
On the whole, English yachtsmen would probably feel very disinclined
to adopt the new French rule for British yacht-racing.
* * * * *
This concludes the examination of the more important national rules in
which sail-area and some hull dimension or dimensions are combined in
the formula for the rating, whether the result be cubic, linear, or
otherwise.
We therefore now pass to the simple sail-area rule proposed by Mr.
Richardson in 1886, viz.
R = S ÷ 100 (XIV.)A
The rating so obtained being neither cubic nor linear, but
superficial, difficulties as regards time scale arose, and neither Mr.
Richardson nor the Council appeared to notice that the rule could
easily be made linear by putting it in the form
American R = [V¯]S (XIV.)B
when American rating and time scale could have been adopted. Also that
it might have been rendered
English R = S [V¯]S ÷ constant (XIV.)C
which is the cubic form, suitable for the Y.R.A. rating and time
allowance.
The graphic result in the sail-diagram is the same in each case, viz.
a horizontal line for any given class, the limit for each class being
one of sail-area alone.
It was not adopted because the Council considered that the type
evolved from it would be one of excessive length and small
displacement; and our experience with the Y.R.A. rule, which
approaches it more nearly than any other hull- and sail-area rule, has
shown that this estimate was correct.
* * * * *
We will now examine a few of the rules which rate yachts entirely by
hull-measurement. The simplest of the kind is the pure length rule,
used for some years on the Solent for racing small yachts up to 30 ft.
of L. _See_ chapter on Solent Racing.
American R = L (XV.) A
Some trouble was taken in 1884 to produce a special time scale for
this formula. It was quite unnecessary, because the time scale for
tonnage (see XVIII.) then in use could have been employed, (XV.) A
being modified to
R = L{3} ÷ constant (XV.) B
and by adjusting the constant this form of the length rule can be
adapted to the time scale of _any_ cubic rule. Thus, the divisor 5,000
adapts it to the Y.R.A. time scale for _rating_.
The type resulting from the length rule was, of course, a very fast and
powerful boat for its L., carrying an enormous sail-spread--somewhat
costly to build and race.
Our grandfathers raced their yachts under the old tonnage rule,
Tonnage R = L × B × H ÷ 96 (XVI.)
H. being depth of hull to deck beam, and L. being measured in various
ways at different times. After 1854 it was taken on deck from
stem-head to sternpost, and certain deductions made for rake.
Eventually the Thames Rule,
(L - B) × B × 1/2B ÷ 94
or B{2}(L - B) ÷ 188 (XVII.)
_The Rating Rules and Proposals_
+-----+-------+------------------------------+---------------------+-------------+
| | No. | Name of rule or proposal | Rule or proposal | Examples |
| Date| in +------------------------------+---------------------+------+------+
| | text | Cubic rules | Variable÷constant |Decima|Doreen|
+-----+-------+------------------------------+---------------------+------+------+
|1886?| I. |Y.R.A. rule (Dixon Kemp) | LS ÷ 6,000 | 9.98| 9.96|
+-----+-------+------------------------------+---------------------+------+------+
|1892 | II. |Ditto modified (Watson) |(2L+2B÷D)S ÷ 17,000 | 10.06| 9.89|
+-----+-------+------------------------------+---------------------+------+------+
|1892 | VIII. |New York modified (Dixon Kemp)|L{2} [V¯]S ÷ 6,000 | 8.69| 9.56|
+-----+-------+------------------------------+---------------------+------+------+
|1892 | X. |Y.R.A. modified (Dixon Kemp) |(L{2}S)/[3V¯]W÷10,000| 8.80| ? |
+-----+-------+------------------------------+---------------------+------+------+
|1892 | VII. {Seawanhaka modified }(L+ [V¯]S){3}÷48,000 | 9.39| 9.75|
| | {Y.R.A. Committee's rule } | | |
+-----+-------+------------------------------+---------------------+------+------+
|1892 | XIII. |U.Y.F. rule (Godinet) |G(4L-G) [V¯]S ÷ 520 | 8.57| 9.02|
+-----+-------+------------------------------+---------------------+------+------+
|1892?| XIX. |Old French rule |G{2}(2L-B) ÷ 176 | 12.58| 13.53|
+-----+-------+------------------------------+---------------------+------+------+
|1876?| XVI. |Old English tonnage rule |L B H ÷ 96 | ? | 10.60|
+-----+-------+------------------------------+---------------------+------+------+
|1876-| XVII. |Thames tonnage rule |B{2}(L-B) ÷ 188 | 15.9 | ? |
| 80 | | | | | |
+-----+-------+------------------------------+---------------------+------+------+
|1880-| XVIII.|Y.R.A. tonnage rule |B(L+B){2} ÷ 1,730 | 13.8 | 17.9 |
| 86 +-------+------------------------------+---------------------+------+------+
| | XIV. C|Richardson's rule, cubic form |S [V¯]S ÷ 6,000 | 9.97| 15.7 |
| +-------+------------------------------+---------------------+------+------+
| | XV. B |Length rule, cubic form |L{3} ÷ 5,000 | 9.08| 11.01|
+-----+-------+------------------------------+---------------------+------+------+
+-----+-------+------------------------------+---------------------+-------------+
| | No. | Name of rule or proposal | Rule or proposal | Examples |
| Date| in +------------------------------+---------------------+------+------+
| | text | Linear rules | Variable ÷ constant |Decima|Doreen|
+-----+-------+------------------------------+---------------------+------+------+
|1882?| III. |Seawanhaka rule | L+ [V¯]S ÷ 2 | 38.33| 38.82|
+-----+-------+------------------------------+---------------------+------+------+
| ?| IV. |New York rule | 2L+ [V¯]S ÷ 3 | 37.45| 38.57|
+-----+-------+------------------------------+---------------------+------+------+
| ?| V. |Y.R.A. Rule (Dixon Kemp) | [3V¯]LS ÷ 1 | 39.12| 39.11|
+-----+-------+------------------------------+---------------------+------+------+
| 1893| XI. |Y.R.A. modified (Thalassa) | LS/M ÷ 72 | 37.23| 38.34|
+-----+-------+------------------------------+---------------------+------+------+
| 1893| XII. |Seawanhaka ditto (Thalassa) | L+ [V¯]S-[V¯]72M÷ 1 | 36.71| 38.23|
+-----+-------+------------------------------+---------------------+------+------+
| 1893| IX. |Herreshoff's new rule | L [V¯]S / [3V¯]T÷15 | 38.69| 37.01|
+-----+-------+------------------------------+---------------------+------+------+
| 1892| VI. |Watson's rule, linear form | 2L+2B+D+[V¯]S ÷ 3.8 | 37.60| 38.58|
+-----+-------+------------------------------+---------------------+------+------+
| ?-86| XV. A |Length rule | L ÷ 1 | 35.65| 38.05|
+-----+-------+------------------------------+---------------------+------+------+
| 1886| XIV. B|Richardson's rule, linear form| [V¯]S ÷ 1 | 41.00| 39.60|
+-----+-------+------------------------------+---------------------+------+------+
_The following Dimensions were used in the Examples_
+--------+-------+------+------+------+------+-----+----+------+------+
| ---- | L | L{2} | S |[V¯]S | B | D | G | M |W tons|
+--------+-------+------+------+------+------+-----+----+------+------+
| Decima | 35.67 | 1272 | 1679 | 41.0 | 11.0 | 8.5 | 36 | 22.2 | 14.3 |
| Doreen | 38.05 | 1448 | 1572 | 39.6 | 11.2 | 8.5 | 36 | 21.7 | ? |
+--------+-------+------+------+------+------+-----+----+------+------+
N.B.--G is only approximately correct. It is measured in the French
way was evolved and adopted by the Y.R.A. in 1876. And in 1878 it was
decided to measure L. on the water-line. In 1880 the Y.R.A. altered
the rule to
English T = B(L + B){2} ÷ 1730 (XVIII.)
The type evolved, as might have been anticipated, had a long, narrow,
heavily ballasted, deep-bodied, wall-sided hull, possessing little
beauty, small _initial_ stability, and no great speed, considering the
sail-area employed to drive it. There was little scope for
improvement, and the energies of our best designers were directed to
producing yachts which carried large sail-plans on narrow hulls, their
L.W.L. often approaching and sometimes exceeding six beams.
Nevertheless, this '1730 Rule,' as it is often called, governed
first-class racing in British waters from 1880 to 1886.
Another hull-measurement rule is the one used for some time in France,
and often called the 'Girth Rule.' In its simplest form, it was:--
French T = G{2}(2L - B) ÷ 176 (XIX.)
G., the girth, is taken as in Rule XIII. The rule taxes draught
heavily, and does not appear to have given satisfaction, or it would
not have been changed last October to No. XIII.
Many other hull-measurement rules might be mentioned; in fact, a short
time ago the yachting press was full of such proposals; but those who
make them must be aware of the general feeling among sportsmen in
England, France, and America, viz. that sail-area should be taxed in
the formula for rating. Any lengthy discussion on rules which do not
conform with this opinion is, therefore, a waste of time and energy,
and the hull rules just described have been noticed principally on
account of their historical interest.
* * * * *
The rules are numbered consecutively in the order in which they have
been examined; the tonnage rules last, although some of them are the
most ancient. But it may be convenient for the student to have them
grouped somewhat differently and this has been done in the tables on
pp. 183, 184, which also afford an opportunity to compare two yachts
of similar hull-dimensions, but differing in regard to their length
and sail-area, except that the product is equal. 'Doreen' and 'Decima'
make an excellent pair for such a comparison, being each 10-rating by
the Y.R.A. rule, and of nearly the same beam, draught, girth, and
depth of hull, but differing in length and sail-area.
The tendencies of those rules which aim at encouraging larger body,
like Mr. Herreshoff's, or larger immersed body, like X., XI., and
XII., are shown in the tables on pp. 183 and 184, and the student is
invited to work out some examples for himself to test their action, as
the New York committee has reported in favour of some such
modification of existing rules.