704 
FOREST AND STREAM. 
[April 30, 1910. 
square feet of wetted surface each boat con¬ 
tained, nor could it be expected that he take off 
the iines of each boat and calculate the dis¬ 
placement, as this would involve an amount of 
labor altogether too great for the measurement 
of a racing boat. The Admiralty Formula was 
suggested, but, in view of the fact that dis¬ 
placement was one of the factors, and that an 
arbitrary constant, ranging from 90 at one end 
to 286 at the other, so that the speed calcula¬ 
tions of any one boat could be made to vary 
fully 50 per cent., depending on whether you 
used constant at either extreme, made this 
formula useless; for, if the measurer had to 
make a guess at the constant, he might as well 
guess at the other factors, or even the speed 
of the boat itself. 
The impracticability of apply the Admiralty 
Formula, as well as that of obtaining the wetted 
surface and total displacement of the boat, 
made it imperative that some simpler and more 
practical method should be devised, and not 
alone this, but that the formula should also be 
scientifically correct. In dealing with_ parallel¬ 
epipeds of similar form, immersed in water 
until the uppermost face is just flush with the 
surface, it is found, on making the necessary 
calculation, that the wetted surface is exactly 
proportionate to the two-thirds power (or the 
square of the cube foot) of the displacement; 
and it may also be noted that the wetted sur¬ 
face varies as the area of the midship section. 
These results are not quite accurate for par¬ 
allelepipeds which are not similar in form, that 
is, whose lengths, breadths and depths are not 
of a similar relative proportion, but the inac¬ 
curacy is only slight within considerable limits; 
so that, if boats of ordinary proportions are 
substituted, it is practically correct to say that 
the wetted surface varies as the area of midship 
section, and also as the two-thirds power of dis¬ 
placement. 
With the wetted surface and displacement 
both bearing a fixed relation to the midship 
section, only one more factor was required to 
make the formula complete, viz., length; and, 
as the speed in similar models varies as the 
square foot of length, it became quite apparent 
that the two resistant factors involved in the 
problem were midship section, and the square 
root of length; while the third factor was horse¬ 
power or the energy for overcoming the re¬ 
sistance of the other two. 
The horsepower being produced by the motor, 
it was necessary to be able to determine with 
reasonable accuracy the amount of power that 
a motor would develop under normal con¬ 
ditions; and, as it is well understood that the 
horsepower of any motor consists of the piston 
area, in square inches, multiplied by the num¬ 
ber of pistons in use, multiplied, by the mean 
effective pressure in pounds throughout the 
stroke, multiplied by the length of the stroke 
in feet, multiplied by the number of revolutions 
per minute, and the total divided by 33,000, it 
w r as apparent that all that was necessary was to 
get the bore and stroke of the motor, the num¬ 
ber of cylinders in operation, the number of 
revolutions per minute, and the mean effective 
pressure on the pistons throughout the effective 
stroke. 
Fortunately, at the time the writer had in his 
possession indicator cards taken from a num¬ 
ber of the then existing four-cycle motors, and 
a careful measurement of the average or typical 
cards of the different motors gave an average 
for all of them of just under 67 pounds mean 
effective pressure per square inch. When plac¬ 
ing the actual figures in the formula it was dis¬ 
covered that, by changing the mean effective 
pressure from just under 67 to 66 pounds, the 
formula would become a very simple one. As 
the four-cycle motor received one explosion 
every second revolution, the mean effective 
pressure of one cylinder would be 66 pounds 
at one revolution, and nothing on the next, or, 
if distributed equally over the two revolutions, 
it would be 33 pounds. -Then, with 33 in the 
numerator, and 33,000 in the denominator, by 
cancellation we would have 1 in the numerator 
and T.000 in the denominator, so that the 
formula would be: Multiply area of one piston 
by number of cylinders, by stroke in feet, by 
number of revolutions per minute, and divide 
the product by 1.000, equals the actual horse¬ 
power of the motor. 
With the foregoing facts established only one 
more factor remained to be considered in the 
preparation of the formula; this was the speed 
or resistance curve. In general terms it is 
understood that the speed of a vessel varies di¬ 
rectly as the cube root of the horsepower ap¬ 
plied; in other words, a curve of cubes. But 
this is not absolutely correct, for every vessel, 
whether of the moderate or high power type, 
instead of having a resistance curve which is a 
curve of cubes or a true line, has a curve with 
alternately slightly higher and slightly lower 
points in this curve, the low points coming at a 
speed in knots about equal to the square root 
of the load waterline length in feet, and multi¬ 
ples thereof, and the high points falling in be¬ 
tween. 
From this it will be seen that the load water¬ 
line length modifies the curve, so that the re¬ 
sistance curve for two boats of different length 
drawn over each other will not quite agree; but 
if a number of curves are drawn over each 
other, representing boats, say from 15 to 100 
feet in length, advancing by steps of say 5 feet, 
there will be a series of wavy curves through 
which a mean curve may be drawn that will 
fairly represent the average, and this curve will 
be practically a curve of cubes. 
Having selected the materials, it was a simple 
matter to arrange them in a formula, which, ex¬ 
pressed in ordinary terms, read as follows: 
Rating equals the cube root, of the square root 
of the load waterline, multiplied by the horse¬ 
power, and divided by the area of the midship 
section. If the factors of two boats were 
worked up according to this, and for one boat 
the rating would be 2, while it would be 3 for 
the other, the meaning would be that the boat 
having the higher rating would cover, say three 
miles, while the one with the lower rating 
would cover two miles during the same period 
of time; in other words, the rating means the 
relative speed of boats. 
Before proceeding any further with the work¬ 
ing out of the formula a number of boats were 
measured, and their rating compared with actual 
performances, the results proving thoroughly 
satisfactory. It was found, however, that the 
rating obtained from the different boats had no 
resemblance to any of the figures or dimensions 
covering the boats; but as the load waterline 
length was generally considered as a designating 
factor in describing the size of a boat, it was 
thought desirable to make the rating corre¬ 
spond with the approximate load waterline 
length of the then existing boats, and the con¬ 
stant 15 was added to the formula; so that a 
boat of approximately 45 feet load waterline 
length, rating approximately 3 would, by use 
of the constant 15 in the formula, make the rat¬ 
ing substantially the same as the load waterline 
length. It is, of course, to be understood that 
in high power boats the rating exceeded the 
load water line length, and in low powered 
boats the rating fell below it. The only pur¬ 
pose of the constant at the time was to get an 
approximate co-relation between load waterline 
length and rating in the average cruising boat 
of that time. 
It was, of course, desirable that the boats 
should be measured while in the water—their 
normal state—and that the process of taking 
the measurements should be as simple as pos¬ 
sible. It was simple enough to measure the 
load waterline length, but the midship section 
had also to be determined, the first question be¬ 
ing its position with reference to the load 
waterline length of a boat. There are many 
points where science and practice meet on com¬ 
mon grounds, and it had been demonstrated 
practically as well as scientifically that there 
were certain general proportions between beam 
and draft for power boats that gave satisfactory 
results, and, while many of the practical build¬ 
ers probably could not give a technical explan¬ 
ation, still they knew from experience that the 
results were the best when a boat was propor¬ 
tioned in a certain way. A study of the posi¬ 
tion of midship sections in steam yachts and 
motor boats covering a number of designs by 
the writer, as well as those of other naval 
architects and successful builders, showed that 
the fore and aft position of the midship section 
varied from about 52 to 58 per cent, of the 
load waterline length, measured from its for¬ 
ward end, or a mean of 55 per cent.' _ Taking 
into consideration further that a variation of 2 
per cent, in either direction would make no ap¬ 
preciable difference one way or the other, it was 
decided to take the 55 per cent, of the load 
waterline length, measured from the forward 
end, as the midship section of cruising power 
boats. 
[to be concluded.] 
Holly Beach Race. 
The joint committees of the Holly Beach Y. 
C., the Camden Motor Boat Club and the 
Yachtsmen’s Club have arranged the details of 
the long distance race from Holly Beach to the 
Camden Motor Boat Club, a distance of 100 
miles. The race will be held on July 26, the 
start being from Holly Beach, and a time limit 
of ten hours was set, although it is anticipated 
that not much more than half that time will be 
consumed by the winner. 
The Holly Beach Y. C. has offered ten cups, 
to be competed for in three groups under the 
rules of the American Power Boat Association, 
viz., those rating between 60 and 70, 70 and 80 
and 80 and over, with an additional prize for 
the boat making the fastest actual time. The 
race will be open to all owners of sea boats 
rating about 60 whose owners are members of 
any recognized yacht club. The race is held 
primarily to demonstrate the seaworthiness of 
the modern speed boats. 
The boats will start on their handicap time, 
so that the finish will determine the winner, 
and there will not be the necessity of working 
out afterward the handicaps of the different 
boats. Arrangements will be made to have re¬ 
lief boats stationed aiding the river, and con¬ 
voys will follow the contestants, so that succor 
will be handy in case of accident. The Holly 
Beach Club has secured a specialist, and will 
chart the course, and the competing boats will 
be handicapped according to this chart. The 
prizes will be awarded the winners on the night 
of the race at the Yachtsmen’s Club. 
These committees were appointed: Regatta- 
Dr. C. S. Street, Chairman; E. C. Headley, R. 
L. Young, Frederick Himmelyne and John 
C. Vanderslice. Entertainment—W. Clifford, 
Chairman; Henry Ogle, John Talley, John 
Doyle and W. W. Rogers. 
State Canals to Open May 15. 
Superintendent Stevens, of the Department 
of Public Works, has ordered the opening of 
the State canals for the season on May 15, ex¬ 
cept the Black River Canal, which will remain 
closed until June 1. The canals to open on the 
first-named date will include the Erie, Cham¬ 
plain and Cayuga-Seneca, and the Oswego 
Canal, with the exception of that portion be¬ 
tween Three-Mile Point and Fulton, which is 
to remain closed this season to permit of the 
progress of barge canal construction work. The 
State canals when in operation, give employ¬ 
ment to a small army of men as lock tenders, 
watchmen, etc., the force of these employees 
figuring up above 1,800. 
Sparks. 
Leonard H. Dyer, of Greenwich, owner of 
the raceabout Psammiad, is having a motor boat 
built as tender for the yacht. Morgan Barney 
made the drawings. The new craft is about 
finished and is 32 feet over all, 31 feet on the 
waterline, 7 feet beam, and will be equipped 
with a io-horsepower motor. 
F. R. Kellogg, who recently purchased the 
yawl Genevieve, is having an auxiliary motor 
installed under the supervision of Morgan 
Barney. 
