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PROFESSOR CECIL H. PEABODY
JOHN WILEY & SONS.
Thermodynamics of the Steam-engine and other
This WOI-K -s .ntended for the use of students in
technical schools, and gives the theoretical training
required by engineers. Sixth Edition, Revised.
vii + 543 pages, 119 hgures. 8vo, cloth, $5.00.
Tables of the Properties of Steam and other
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By Prof. Cenl H. Pea body and Prof. Edward F.
Miller, viii 4- 434 pages ; 175 illustrations. 8vo, cloth,
Manual of the Steam-engine Indicator.
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Thermodynamics of the Steam Turbine.
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iii+132 pages, 29 figures. Cloth, $1.25, net.
CECIL H. PEABODY,
Professor of Naval A rchitecture and Marine Engineering,
Massachusetts Institute of Technology
FIRST EDI TION.
JOHN WILEY & SONS.
LONDON: CHAPMAN & HALL, LIMITED.
CECIL H. PEABODY.
ROBERT DRUMMOND AND COMPANY
BROOKLYN, N. Y.
THIS book gives a reliable and convenient method of design-
ing propellers, based on model experiments, and free from theo-
retical intricacies and uncertainties. For details of experiments
on which the method is based and for theoretical investigations,
reference may be had to the author's Naval Architecture.
Tables are given for two, three, and four bladed propellers,
from which the dimensions of a propeller may readily be deter-
mined, without interpolation, when the power, speed and revolu-
tions are assigned, either to give maximum efficiency or to conform
to certain restrictions such as limited draught.
Drawings and computations for propellers are much sim-
plified by using the projected contour and area of the blades,
and tables are given by aid of which exact results may quickly
be determined. The designer may, however, use the conven-
tional developed contour of blades, if he prefers; simple methods
of drawing such contours are included in the text.
A brief treatment is given of methods for determining the
power required to propel a ship at a given speed, together with
data for various types of ships and boats. It is believed that
intelligent use of this material will give satisfactory results under
ordinary conditions; the best results, expecially under extreme
conditions, can be expected only by experienced designers who
have specific information.
All methods of designing ships and propellers are based, either
explicitly or implicitly, on the theory of^ mechanical similitude.
The conclusions and methods of this theory may be stated briefly
and used easily; a presentation of the theory is given at the end
of the book for convenient reference.
IN the design of a propeller the first thing is the determina-
tion of the power required to drive the ship at the desired speed.
This is at once evident when the power is underestimated because
the engine cannot turn the propeller up to the designed number
of revolutions, and so cannot develop its power. A moderate
overestimate of power may merely result in a somewhat higher
speed provided the engine can stand a moderate increase above
its normal speed. But if the power is much overestimated
the engine will tend to run at a dangerous speed and when restrained
(as by throttling the steam) will be unable to develop its power
and therefore fail to give the designed speed. In either case a
new design for the propeller must be made suitable to the speed
at which the engine can drive the ship. For untried conditions
designers commonly estimate power liberally, and a moderate
excess over estimated speed is considered to be a triumph; but it
is at the expense of a costly engine and a reduced carrying
Methods of Estimating Power. There are four recognized
methods of estimating power for a ship-
(1) The Admiralty coefficient.
(2) The law of comparison.
(3) Independent estimate.
(4) Model experiments.
The first two methods are direct applications of the theory
of similitude and the other two employ the conclusions of that
theory with modifications. The use of the methods will be
illustrated; a discussion of the theory will be found at the end
of the book.
Admiralty Coefficient. One of the best known, and most
convenient methods of estimating power, for a ship is by aid of
I.H.P. is the indicated horse-power of the steam-engine;
D is the displacement in tons (2240 pounds);
V is the speed in knots (6080 feet) per hour;
K is a numerical coefficient known as the Admiralty coefficient.
This coefficient must be determined from some ship for which
the displacement, power, and speed are known. Values for cer-
tain ships of various types are given in the table on pages 8
and 9. The value of the coefficient may vary from 100 to 300;
it is therefore evident that the success of this method depends
on a judicious selection of the coefficient. In order that a close
concordance may be expected between the estimated speed and
the actual speed on trial of the ship, the coefficient must be
derived from a ship that is geometrically 'similar to the ship under
design, and which has the corresponding speed. These terms will
be explained on page 4. A moderate deviation from these con-
ditions will not seriously affect the value of the method.
For turbine steamers and for ships and boats which are driven
by internal-combustion engines the shaft horse-power is given
instead of the indicated horse-power, and the equation may read
The coefficient must in such case be taken from information
concerning ships or boats with turbines or internal-combustion
engines, more especially because the types of propellers are different.
If information is lacking the indicated horse-power may be com-
puted by equation (i) and the shaft horse-power may be estimated
ADMIRALTY COEFFICIENT 3
by multiplying by a factor which varies from 0.85 to 0.90; but
this method must be used cautiously.
Example. Let it be required to determine the power for a
ship to have 28,600 tons displacement and a speed of 25 knots
The express steamship Campania in the table on page 8
has 276 for the Admiralty coefficient, and using equation (i)
we find for the power,
28600* X25 3
In the solution of this equation it is convenient to take the
two-thirds power of the displacement from the table on page 123,
and the cube of the speed from the table on page 125, inter-
polating when necessary. This gives
the numerical work being most readily done by aid of a slide
If preferred, the computation can be made by aid of loga-
rithms; the parallel computations give a valuable check.
log 28600 = 4.4564 log 25 = 1.3979
_ ? _3
log 276 = 2.4409
log 52900 = 4.7237
Example. Required the power for a motor boat weighing
1600 pounds to make a speed of 15 statute miles per hour. The
speed in knots in this case becomes
= 1 knots.
The displacement is
The power consequently is by equation (2)
the Admiralty coefficient being taken for Chum, page 9. The
solution by logarithms is
log 0.714= 9.8537-10 Iogi3 =
log 165= 2.2175
log 10.6= 1.0267
Similarity. Geometrical figures are said to be similar when
they have the same form and differ only in size. A ship and its
model are made from the same lines and differ only in scale; the
-first may be several hundred feet long and the latter only a few
Mechanical Similitude. The theory of mechanical similitude
is an extension of geometrical similitude to the conceptions of
mechanics including fon e, work, and power. For the present
purpose the applications of the theory to the design of a ship and
its propeller will be stated; a simple presentation of the theory
is given at the end of the book for convenient reference.
Corresponding Speeds. The corresponding speeds for similar
ships are proportional to the square roots of their lengths.
Example. The Campania has a length of 600 feet and makes
23.18 knots per hour (page 8); a ship 700 feet long on the
same lines would have a corresponding speed of
\/6oo : Voo :: 2.18 : F /. F = 2 knots.
Example. If a ship 700 feet long makes 25 knots per hour,
then the corresponding speed for a model 20 feet long will be
A/7oo : V2o 1:25 : F, .'. F m = 4.23 knots,
which is the speed at which such a model should be towed in an
experimental towing basin in order to investigate the relative
powers of the ship and its model.
Example. Conversely if a ship 600 feet long makes 23.18 knots
per hour, then a ship to make 25 knots must have a length of
23.18 : 25 :: 600 : L, /.I, = 700 (nearly),
provided that the conditions of the theory of mechanical simili-
tude are observed.
Displacement. The displacement of a ship is given in tons
(2240 pounds); small yachts and boats may have displacements
given in pounds; this custom is commonly applied to craft that
can conveniently be weighed complete.
The volume of water displaced by a ship when afloat can be
determined from the lines and is stated in cubic feet; this may
be called the volumetric displacement.
Now 35 cubic feet of sea-water weigh one ton; for fresh water
it is customary to take 36 cubic feet to the ton. The displace-
ment of a ship in tons is obtained by dividing the volumetric dis-
placement in sea- water by 35; for fresh water divide by 36.
Similar ships have displacements proportional to the cubes of
Example. The Campania has a displacement of 18,000 tons
on a length of 600 feet; a similar ship 700 feet long will have a
600 : 700 :: 18000 : D, :.D = 28600 tons.
Example. If a ship 700 feet long has a displacement of 28,600
tons, then a model 20 feet long will weigh
700 : 20 :: 28600 : D m , /.A = 0.667 ton,
or 1494 pounds.
Dimensions. The main dimensions of a ship are length, beam,
The length is measured between perpendiculars drawn at the
load-water-line. The forward perpendicular is drawn at the
forward side of the stem, and the after perpendicular is drawn
at the after side of the stern-post.
The beam is the extreme beam. This is usually found at the
load-water-line nearly half way between perpendiculars.
The draught is measured from the water-line to the bottom of
the keel, midway between perpendiculars. If the ship has no
external keel the draught is measured to the outside of the keel-
plate. The extreme draught is frequently given also if it is dif-
ferent from the draught at mid-length, but it does not enter into
computations with the main dimensions.
Load- water-line. A ship is designed for a certain normal
displacement. The side-elevation or sheer -plan has a line drawn
on it showing the draught at this normal displacement; this line
is the load- water-line. The surface of the water when the ship
is afloat at the normal displacement will be at the height of the
normal draught; the plane of the surface of the water is the
plane of the load-water-line; it is frequently referred to briefly
as the load- water-line.
At other than the designed normal displacement the ship will
float at some other water-line. Any line or plane parallel to the
surface of the water may be called a water-line.
Problem. So far we have considered only simple examples
relating to power for a ship; in general there are various condi-
tions and restrictions on the design for a ship that will call for
consideration before the Admiralty coefficient can be chosen.
Let it be required to determine the power for a ship 700 feet
long, and having a displacement of 28,600 tons, to make 25 knots
TYPE SHIPS 7
In order to decide whether the power for such a ship can
be determined from the power of the Campania we may make the
following comparison. That ship has a length of 600 feet, a beam
of 65! feet, and a normal draught of 25 feet; at a displacement
of 18,000 tons the speed is 23.18 knots per hour.
A similar ship 700 feet long will have the dimensions,
600 : 700 :: 65! : B, /.beam = 76.1 feet.
600 : 700 :: 25 : J, /.draught = 29. 2 feet.
The displacement will be
600 : 700 :: 18000 : Z>, :.D = 28580 tons.
The corresponding speed will be
V6oo : V7oo :: 23.18 : F, .-.7 = 25.0 knots.
If the beam and draught can be accepted then the design can
be based properly on the data for the Campania; in practice the
draught for large ships is commonly restricted by the depth of
channel in harbors. Should a restriction to a draught of 28 feet
be imposed in this case then some change from similarity would
be required. We might (i) increase the beam, (2) increase the
length, or (3) use fuller lines; or any two or all three conditions
might be changed. It is but fair to say that the problem was made
up from the data of the Campania with slight modifications from
the conditions for similarity and that so close concordance cannot
generally be expected. "Since the method of the Admiralty coeffi-
cient has some flexibility a good determination of power can be
had by use of coefficients from ships that are not very dissimilar.
To complete the problem the computation on page 3 will be
T W T> 286 X 25
Type Ships. Successful use of the Admiralty coefficient (01
of the theory of similitude either directly or with modifications)
M M M
M vO vO CM
l>- ON ON NO
CM H CM CM
Cl xo CO ON
ON ON NO O
1 M M CS
CM CO 00 00 Cl O
t^ CO CO ON
O ON NO CO
' i i ; r~
Deutschland . .
La Provence . .
Minnesota 4 . . .
City of Lowell
Cargo str. L. 2
Tarantula 3 . . .
ate pas - j
f 'I '
% CO to
rt CO CM
t>. to CO CO t^ co
CM CM H CM CM CM
H M H H M M
r^ Ov o? ^T
H H H CM
CO vo to
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CM t^ 00
r)- to CO
Tf ON O
3- * ?T
vo O O
CO CM t^-
t vo 00 O
t^~ CO CM
CO P H CM
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vO vo vo vo
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O CM CM
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: I I
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City of Erie...
Quicksilver . . .
.9 H- 1
will depend on the exactness and certainty of information in the
hands of the designer, from ships which have been tested under
Some builders make a practice of testing all ships built (or at
least all types of ships) and they have means of estimating power
for new designs with certainty and precision, unless such designs
differ radically from previous ships.
There is much published information concerning power and
speed of merchant ships, but analysis of such information will
show that commonly the data (or part of the data) come from
the design and not from trials; even when trials are made
they are liable to be for ships light instead at the designed
draught, or it may [be that some of the conditions are not
definite. It is difficult to load freight ships, or freight and
passenger ships to the normal draught for trials, and trials
under service conditions are often indefinite. Published data
of designs have a value especially when given out by well-
known designers or builders.
The results of acceptance trials of warships are freely published
and conditions are frequently given completely and precisely.
And yet discrepancies between results from ships of the same
class leave much to be desired. Such ships are driven at high
speeds at which secondary influences have large effects. This
is particularly true of torpedo-boats and destroyers. Success
with such craft can be expected only by experienced builders
who keep complete trial data; even they occasionally meet with
disappointment under new conditions.
Fast yachts and motor-boats are also driven at very high
relative speeds and success demands the same conditions.
On pages 8 and 9 will be found data from various types of
ships and boats, which can be used for practice or in lack of
In addition to the dimensions of the ships, it is customary to
give the block-coefficient, the wetted surface and the horse-power
per ton of displacement. In some cases the prismatic coefficient
is given, and in our table the last column gives the speed-length-
Block-coefficient. This coefficient is the ratio of the displace-
ment of the ship to that of a rectangular block having the same
length, beam and draught. It may vary from 0.35 to 0.85.
The block-coefficient of similar ships is necessarily the same,
but ships having the same block-coefficient may be dissimilar,
On the whole this coefficient gives a fair idea of the effect of varia-
tions of form among ships of the same class.
Example. The block-coefficient for the Campania is
- 644 ' *
The numerator contains the displacement in tons multiplied
by the volume of sea- water per ton; the denominator contains
the main dimensions of the ship.
Wetted Surface. The surface of the ship in contact with the
water can be determined from the lines of the ship and is given
in square feet. The necessary operations are tedious and require
skill of the draughtsman.
For a preliminary design the wetted surface may be computed
by the equation
Wetted surface = CVDL
in which D is the displacement of the ship in tons, L is the length
in feet and C is a coefficient to be selected from the following table
where B is the beam and H is the draught.
The error of this method may amount to 2.5 per cent for ships
which are either very full or very fine. For merchant ships the
error is usually not more than 2 per cent.
Example. The wetted surface for the Campania is given on
page 8 as 49,620 sq. ft. The ratio of beam to draught is
65.25-^25 = 2.6
for which the table gives C = 15.51. The displacement is 18,000
tons and the length is 600 feet; consequently the wetted surface
may be computed to be
1 5. 5 1 Vi 8000X600 = 5 1000 sq. ft.
Law of Comparison. The theory of mechanical similitude as
applied to determining power for a ship is known as the extended
law of comparison. This law is:
The horse-powers of similar ships at corresponding speeds are
proportional to the seven- sixths powers of the displacements.
Problem. Let it be required to determine the dimensions
and power of a ship to make 25 knots per hour, using the Campania
for the type ship. The Campania makes 23.18 knots on a length