OV. 21, 1903.] 
X 
1 
HE second cruising competition given by this paper 
.sed on Nov. 15. Our first attempt in this direction 
s a great success, and we were therefore prompted 
give another, but the reception accorded the second 
ceded our most sanguine expectations. There were 
jr three times the number of . stories submitted in 
second than in the first, and the standard of the 
lises was much higher. In neai'ly every instance 
conditions governing the completion were ad- 
ed to, and the stories dealt with cruises made on 
irly all the navigable waters in the United States' 
sessions; one of the stories treated of a trip around 
remote island of Honolulu. 
/Vhen we organized these cruising and designing 
npetitions we hoped they would prove of practical 
i lasting value, and that the publication of the 
ties and designs would be of universal interest, 
^r. Theodore Zerega has again agreed to act as 
ge, and inake the awards. Mr. Zerega judged the 
ries in last year's competition with great care and 
client judgment. 
Me are confident we have accomplished all we 
nned, and from now on we propose making these 
npetitions a feature of this department. 
/Ve will soon make public the conditions for another 
igning competition. The prizes will be larger than 
ore given, and the design will be for a centerboard 
ter or yawl of about 40ft. waterline. This is a con- 
rably larger craft than has been attempted in any 
bur competitions, but it is a very popular size, and 
Doat of that length enables one to secure sufficient 
ommodation so that two or three men can make 
ir home on board for a period of several months 
i have many of the comforts and conveniences that 
uld be impossible on a smaller craft, 
"he old 40ft. class was in many ways one of the best 
t this country ever saw. Much good racing was had 
ween these boats, and many of them are still being 
d as cruisers. The nearest approach to this class 
the modern boat are the 43-footers on Long Island 
und. They have been accepted as being most .'::uc- 
sful for racing and cruising. Take for instance Mira, 
ort, Challenge, Mimosa II. and Aspirant, all these 
_ts have been raced hard and have afforded their 
ners fine sport. Nevertheless, every one of them 
ample room below for quarters that are roomy and 
nfortable. Another splendid craft of about this size 
Irondequoit, the winner of the Canada's cup last 
nmer. She is very fast and able, and has a vast 
ount of room below. Such a vessel with a snug 
would make an admirable cruiser, and could be 
handily with two or not more than three paid 
ds. A boat of that size and type has a wide cruis- 
range, and her field of usefulness is great. This 
the kind of boat we had in mind, and there aie 
.ny men of moderate means who are looking for 
t such a boat. We believe that this competition will 
'et with the success and approval that it deserves, 
he possibility of a universal measurement rule ap- 
irs so remote that many of the enthusiasts have fin- 
/■ abandoned the plan, believing it to be hopeless, 
e rules that have been tried thus far, both on this 
e of the water as well as abroad, have met with very 
ifferent success, and to-day the situation is worse 
ftn it has ever been before. Four rules of measure- 
jnt are now in force among the clubs, and the asso- 
tion on Long Island Sound, and yachtsmen, after 
ding what the situation was, neither built new boats 
r raced their old ones. 
iestricted and one-design classes seemed to be the 
y solution of the problem, and new restricted classes 
being formulated by the Massachusetts Y. R. A. 
i the Y. R. A. of Long Island Sound. We are 
ongly opposed to one-design classes in particular 
i restricted classes in general, but still such racing is 
ter than none at all, and we console ourselves with 
s thought. 
n this issue of Forest and Stream there appears 
able article on the measurement question by Charles 
ne Poor, owner of the 43-footer Mira. We wish to 
1 special attention .to Mr. Poor's article, as it ad- 
nces several new theories, all of which seem good, 
i his comments on time allowance appear very 
md and practical. We trust that this paper may re- 
e interest in this question that is of such vital im- 
rtance and be the means of bringing about some 
leficial results. When the racing dies down the life 
yachting is killed, and the present situation is a 
ive one, and it is undermining the very foundation 
the sport. 
Notes on the Measurement of 
Racing Yachts. 
BY CHARLES LANE POOR, PH.D. 
)URiNG the last quarter of a century great advances 
re been made in the designing and buildmg of yachts, 
dle-of-thumb" methods have been discarded, and the 
dern racing yacht is the result of deep study and 
Dorate calculations as to weight and strength of ma- 
al. Yet with all this advance in designmg and build- 
, no commensurate advance has been made m the 
nciples of classifying and rating such yachts for racmg 
■poses. The rule's of measurement under which yachts 
-e to-day are constructed upon "rule-of-thumb" 
thods. According to racing yachtsmen and designers 
rules thus constructed are all unsatlsfactor3^ and 
t produced, and are producing, bad types of yachts, 
no consistent attempt has been made by any club to 
dy the scientific principles involved in the problem, 
laving in mind the importance of the subject, both 
m a scientific and a sporting point of view, ttie wriier, 
the following notes, has attempted to bring clearly 
ore all yachtsmen the fact that the present rules of 
isurement are founded upon certain assumptions as 
ards the speed of yachts; to show that such assump- 
is are not clearly warranted by the data at their com- 
nd; and to indicate the principles on which the 
measurement and classification of yachts should be based. 
Time Allowance and Classification, 
The table of time allowance is the most important ele- 
ment in the problem. Except in one-design classes, all 
systems of classification and handcapping rest on the time 
allowance table. In many of the larger events each year 
boats of widely different sizes race together, and the 
prize is won or lost by the aid of time allowance. The 
table of allowances Avhich is in common use in all clubs 
was first adopted in 1883. At that time length was recog- 
nized as the prime factor in producing speed, and the 
tables were based on the rule generally accepted by^ naval 
architects, that "within economic limits, opportunities for 
speed vary in different vessels as the square roots of their 
respective lengths." This simply means that under nor- 
mal conditions a boat 100 feet long should sail at the 
rate of ten miles per hour, ten being the square root of 
one hundred, and that a boat 36 feet long should, under 
the same conditions, sail at the rate of six miles per 
hour, six being the square root of thirty-six. The 
larger boat should thus sail one mile in one-tenth of an 
hour, or six minutes; the smaller boat in one-sixth of an 
hour, or ten minutes, and hence the larger boat allows 
the smaller the difference between these times, or four 
minutes per 'mile. Computing thus the times for boat-s 
of all different sizes, a complete table of allowances Is 
formed, which is thus nothing more than a table of 
inverse square roots. As in practice it was found that 
this allowance was too large for ordinary summer racing, 
eight-tenths only of the allowance is actually given, and 
the table, as found in the New York Y. C. book, gives eight- 
tenths of the full allowance. That is, the thirty-six foot 
boat receives only 3.2 minutes per mile instead of the 
full 4 minutes. These figures can be verified by compari- 
son with the tables in the New York Y. C. book, from 
which we find the allowance in this case would be 192 
seconds, which is the same as 3.2 minutes. 
It was at once seen, however, that length is not the 
only factor in producing speed. Motive power is cer- 
tainly a factor, and in a sailing yacht motive power is 
furnished by the sails, and the amount of such motive 
power varies with the sail area. In order to take account 
of this, speed producing factor, in computing the time al- 
lowance from the above rule, the fiction of a "racing 
length" was introduced— the length in the rule being 
replaced by the "racing length." Such "racing length" 
was, and is, determined from measurements of hull, 
spars, and rigging, and does not bear any direct relation 
to the simple length of hull. Sail area was thus intro- 
di'ced and appears in all rating formulae; and in the 
latest rule — the New York Y. C. rule adopted this year — 
a third factor— displacement — is brought in. The' two 
principal rating formulae are the old New York and the 
new New York as given below : 
R L. = 1-5- 
1. Vs. A. 
3 
(2). 
The Larchmont rule and the rule adopted by the Yaclit 
Racing Association of Long Island Sound are but modi- 
fications of (i), the principal factors being the sam.e 
arid introduced in the same way. 
We have already seen that all methods, so far adopted, 
for computing time allowance assume that speed is pro- 
portional to the square root of racing length. Now, an 
examination of the above old and new New York rules 
shows that for either rule, so far as sail area affects 
rr.cing length at all, that effect is proportional to square 
root of sail area. If, then, as we have seen, the time 
allowance table always makes speed proportional to 
square root of racing length, then, so far as sail area 
can affect speed, according to either New York rule, that 
effect must be proportional to the square root of the 
square root of sail area, which is the fourth root of sail 
area. In other words, if the time allowance tables and either 
of the New York rules are correct, then the speed of a 
yacht must vary according to the fourth root of sail area. 
We shall see further on that such is not the case in actual 
sailing. 
In view of the above considerations, we see the adop- 
tion of the measurement rule (i) involves the assump- 
tions that speed is proportional to 
a. the square root of length of hull, 
b. the fourth root of sail area, 
and that the new New York rule (2) involves these two 
assumptions, and the additional one that speed is propor- 
tional to 
c. the inverse sixth root of displacement. 
On what basis do these assumptions rest ; why use the 
sixth root of displacement, instead of the fourth root, or 
the tenth root? The printed report of the committee 
throws no light on this subject. The only imaginable 
reason for the introduction of these factors in this way 
seems to lie in the supposed necessity for reducing every 
factor in the rating formula to the dimension of 
"length." There may be other and good reasons, but if 
so they are not made apparent in the reports of various 
committees. In fact, the report of the committee m iSSj 
regarding the original rule seems to indicate plainly that 
this was the sole reason for thus introducing sail area. 
The square root of an area is a length, and m 18S3 such 
square root was somewhere near the length of the yacht 
itself, and as a length could be readily added to a length, 
the square root of sail area was adopted in the rating 
f.-.rmula The cube root of displacement is a length, so 
cube root of displacement is used in the fonnula. There 
is no valid reason why the rating formula should con- 
tain nothing but length factors, and a brief review will 
show upon what weak foundations the various measure- 
ment rules and table of allowances rest. 
a. Assumption as to length. 
The assumption, in all rules, that speed is proportional to 
the square root of length of hull seems to be fairly well 
i ustified The fact that the longer hull can be driven faster 
bv the same power has been demonstrated time and 
again but the exact relation between length and speed 
is not so easy to deduce. Naval architects hold, as result 
of experience, that for moderate speeds, and within cer- 
tain' limits, opportunities for speed in boats of similar 
design vai'y as the square foots of their respective 
lengths. This- relationship holds fairly well for speeds 
up to twelve miles per hour, a speed far in excess of the- 
average speed of even the largest yacht during races. 
Thus tests and the experience of naval architects seeni 
to show that this assumption is not radically wrong, and 
that it represents the truth fairly well; sufficiently close^ 
at least, for the purposes of yacht measurement. Simple 
waterline length is, however, no longer a proper measure 
of length in the modern yacht with its excessively long 
and full overhangs. The waterline length does not repre- 
sent the actual length of the boat, when heeled over, and 
a modification of waterline should be used in the formula. 
Such modifications have been introduced, as in the 
Larchmont rule and the New York rules. 
c. Assumption as to displacement. 
The relationship between speed and displacement is 
extremely complicated, and there appear to be no data 
at hand by which this assumption can be tested. As a 
result of one season's racing, it seems to be estabhshed 
that the present rule gives too much advantage to dis- 
placement; in other words, the present rule uses displace- 
ment wrongly. Tests and experiments alone can show 
how this factor should be introduced into the rule, and 
what the real relationship between speed and displace- 
ment is. 
b. Assumption as to sail area. 
The assumption in all measurement rules that speed is 
proportional to the fourth root of sail area does not seem 
to be founded on any substantial basis. In fact, all inves- 
tigations and tests seem to show that this assumption is 
radically wrong; speed seems to be more nearly propor- 
tional to the square root of sail area. To test this point 
we have elaborate experiments upon the power neces- 
sary to drive boats at different speeds. Probably the best 
and most satisfactory tests are those of Froude, whose 
investigations are of the highest order of merit. The re- 
sult of such tests is that for moderate speeds (up to 
twelve knots) the power necessary to drive a hull 
through water is very nearly proportional to the square 
of the speed. That is,- if engines of a certain size can 
drive a hull four miles per hour, it will take engines_ of 
four times the power to drive the same hull eight miles 
per hour. In a steamer the power is developed by' the 
engines, in a sailing vessel by the sails, and the power de- 
veloped by the sails is proportional to the area of the 
sails themselves. As few yachts ever sail a race, or por- 
tion of a race, faster than twelve miles per hour, these 
tests show that in actual practice power, which is pro- 
portional to sail area, varies as the square of the speed. 
In other words, they show that speed varies as the square 
root of sail area, and not as the fourth root, as assumed 
by all rules now in force. Therefore, as long as the 
present tables of time allowance are used, the RL should 
contain the factor SA, and not the factor VSA, as at 
present. 
W^e thus see that, under all rules in force since 1883, 
sail area, or power, has not been taxed sufficiently : boats 
with greater sail area have not given their due 
amount of allowance: This fact developed early, and the 
rule adopted in 1883 was modified by changing the co- 
efficient of VSA. While this increased_ the tax on sail, 
it did not increase it enough, nor did it increase it in the 
right proportions. Naturally designers have developed 
that factor which is not duly taxed, and hence we have 
had boats with constantly increasing sail area. The sail 
area carried by a cup defender has doubled during this 
period. 
I have made the following attempt to test the correct- 
ness of the assumption contained in all rules 
that speed is proportional to the fourth root of sail 
area, by comparing the races of two yachts dur- 
ing the years 1902 and 1903. These yachts sailed 
many races over the same course during each year, and 
I here specify them as M and E respectively. During 
both of these years yacht E was in the same condition 
and sailed by the same crew. In the spring of 1903 yacht 
M had her sail greatly reduced, but was otherwise in the 
same condition as in 1902, and was sailed by the same 
crew, amateurs and professionals, during the two seasons. 
Therefore the only difference in the condition of races 
was the decreased sail area of M, and the results of these 
races should throw some light, therefore, on the value 
of sail area as a factor to speed. Unfortunately for an 
exact comparison, the strength of the breeze was much 
weaker in 1903, it taking the yachts on an average much 
longer time to cover this same course than it did in 
1902. The following tables give the results of three races 
held in 1902 and four races in 1903, all seven races hav- 
ing taken place over the same course, and as near as pos- 
sible under the same conditions. In each season one or 
more races are omitted from the series, as they were 
mere drifting matches, having taken over five hours to 
cover the course. 
RACES — 1902. 
E wins by 
Minutes. Seconds. 
12 46 
2 40 
4 -20 
Time of Race. 
Hours. Minutes. 
2 48 
3 25 
Av. 3 8 
Average Speed — 
M 7.18 miles per hour 
E 7.44 miles per hour 
35 
.26 miles per hour difference 
RACES 1903. 
Hours. Minutes. 
4 I 
3 43 
4 S 
4 14 
Minutes. Seconds. 
Av. 4 ^ 
Average Speed- 
M 
39 
I 
17 
II 
12 
2 
18 
21 
38 
5.62 miles per hour 
E 6.17 miles per hour 
.55 miles per hour difference 
