Amos Lowrey Ayre.

The theory and design of British shipbuilding online

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against the hull, result in the frictional resistance, the amount of
which is dependent upon the speed, the roughness of the immersed
surface of the vessel, its area, and the length. The late Dr. Froude
performed interesting and valuable experiments in connection with
skin frictional resistance upon plane surfaces of varying lengths
and nature of surface, by towing them in the experimental tank at
Torquay, obtaining results at various speeds. In estimating this
Frictional Resistance, the length, area and nature of surface, speed
at which it is travelling, and the density of the water are taken into
account, the calculation being made by using data obtained from
such experiments, in connection with the following formula :

R x - / S V",
Rs being the skin fractional resistance of the vessel in pounds.

/, a co-efficient varying according to the length of the vessel and
also the nature of the surface.

S is the area of the wetted surface in square feet, being found
as described in Chapter III., or by the formula 15-5 A/W X L>.
which is given by Mr. Taylor. W being the displacement in tons
and L the length of the vessel. Fairly good results are quickly
obtained by this formula, especially when the co-efficient is obtained
from a similar ship.

V is the speed in knots per hour.

n, an index accounting for the variation of the resistance with
the speed.

For steel plated vessels in salt water, with the immersed surface
painted and in clean condition, the following figures for / and n
may be used.

The Theory and Design of British Shipbuilding. 113

Length of ship 100 ft. 200 ft. 300 ft. 400 ft. 500 ft,

/ -0097 -00944 -00923 -0091 -00904

n 1-83 in all cases.

These figures will also take into account the eddy- making re-
sistance for vessels of ordinary and good form. For a vessel 350
ft. long, with a wetted surface area of 24,500 sq. ft., the skin frictional
and eddy resistance when moving in salt water at the speed of 11
knots per hour will be -00916 x 24500 x Hi- 83 = 18,064 Ibs. At
first sight it may appear that the square of the speed may be used
instead of the 1-83 power, the latter seeming to be near to the square ;
this, however, is far from being admissable, and 1-83 must be strictly
adhered to. At low speeds the frictional resistance forms a large
proportion, being about 80 to 90 per cent, of the total at speeds of
6 to 8 knots in vessels with clean bottoms. At about 20 knots,
when wave-making is playing an important part, the frictional
resistance is about 45 per cent, to 60 per cent. The frictional re-
sistance being of such a large proprotion at the slower speeds, it is
obvious that economy is obtained in full-lined vessels of slow speed,
in which a larger proportion of displacement to wetted surface is
obtained, than in the case of fine-lined vessels.

Eddy-making Resistance. Blunt endings of the immersed body
of a vessel, such as full sterns and broad stern-posts, cause eddies
which draw upon the power of the vessel in the shape of setting up
extra resistance to be overcome. Such endings should, therefore,
be avoided as far as possible. In modern, well-formed vessels
eddy making is of small amount, and is usually taken as being 5
per cent, of the skin frictional resistance. However, in the figures
above for / and n allowance is made for the extra 5 per cent, and
when these figures are used, no separate calculation is required for
the eddy -making.

Wave-making Resistance. In addition to the statical crests
formed at the bow and stern, as already mentioned, other waves
of reduced height will also be generally noticed ; a series of waves
will be found abaft the bow wave and another series abaft the stern
wave. The two series being of distinctly separate creation, an
interesting relation is, therefore, obtained when the bow series joins
the stern series. Should it happen that a crest of the bow series
coincides with the stern statical crest, the wave of the former is
piled up on top of the latter, as shown in Fig. 53, causing a large


The Theory and Design of British Shipbuilding.

stern crest with a following train of large waves, the wave -making
resistance being greatly augmented thereby. If a hollow of the
bow wave series had coincided with the stern statical crest there
would have been a counteracting effect, and consequently fairly
flat water astern resulting in a reduction of wave-making resistance,
The distance in feet, from crest to crest of the bow wave series in
deep water, is found to be about -56 V 2 (V being the speed in knots
per hour). By use of this formula a vessel can, therefore, be designed

Fig. 53.

so that, at her working speed, the hollow of a bow wave will coincide
with the stern statical crest. The distance between the statical
crests in fine ships is about equal to the water-line length ; in full
ships the distance being about 1-1 times the water-line length. In
a fine-line vessel of 20 knots, the first echo of the bowwave will be
56 x 20 2 = 224 ft., which would, of course, be a very bad length
for a vessel of this speed, while 336 ft. would be very good, since
we would, in this case, obtain a " bow series hollow " coinciding
with the stern statical crest. Propellers, or abnormal form of lines,
may modify these natural waves, or even create additions. If a
vessel is run at varying speeds, and a curve of corresponding horse-
powers constructed, it is generally
found to be of an uneven character,
as shown in Fig. 54, this being caused
by the above-mentioned maximum
and minnimum wave effects, the
humps shown by h being at speeds
where the stern statical crest is
augmented by a wave of the bow
series. The following formula, given
Fig. 54. by MJ. Taylor, may be used :

Wave-making Resistance in Ibs.


(RJ = 12-5 x C X - - X V 4
L 2

V = speed in knots per hour, D displacement in tons,
L = length in feet, and C = block co-efficient.

The Theory and Design of British Shipbuilding.


Air Resistance. Air resistance is only of importance at high
speeds, or when a vessel is steaming against a head wind. At low
speeds it is generally neglected because of its small amount, but at
high speeds it becomes worthy of notice, and is usually allowed for
to the following extent :

Air Resistance in Ibs. (R a ) = -005 A V 2

A being the area of the hull and erections exposed ahead, and V
the speed, in knots per hour, of the air past the vessel.

Model Experiments. To calculate resistance in this way a model
of the proposed vessel is towed in a tank, the speeds and correspond-
ing resistances being recorded and then proportionately increased
to suit the vessel's dimensions. In converting the results of a model
experiment " Froude's Law of Comparison " is used. According
to this law, the corresponding speeds of two ships, or a ship and a
model, vary as the square root of the length ratio

/ ship length

= \/l = variation

V model length

of speeds, therefore the speed of the model multiplied by V'l will
give the corresponding speed of the ship ; also, at corresponding speeds,
the residuary resistance (i.e., resistances other than the Skin friction)

ship length

will vary as the length ratio cubed : I - - j 3 = Z 3 .

model length

It should be remembered that skin frictional resistance does not
follow the " Law of Comparison." In Fig. 55, A represents a curve

of total resistance in Ibs., as
constructed from the recorded
3 results of experiments made
J upon a model towed at
various speeds. By means
& of the formula / S V w , the
frictional resistance of the
ft model at various speeds is
calculated, and deducting the
amounts from the curve A,
the curve B, which is residuary
Law of Comparison " applies to



<? > ~


Fig. 55.

resistance, is obtained. The

this curve, and by this means it is converted to suit the ship.

116 The Theory and Design of British Shipbuilding.

simply altering the scales of speed and resistance the curve B can
be used for the ship, therefore by multiplying the model speeds by
Vl a new scale of corresponding speeds for the ship is obtained, and
by multiplying the model resistance scale by / 3 we obtain a scale
of ship resistance, a further multiplication of 1-026 being necessary
if the experiment was made in fresh water and the ship's resistance
is required in salt water. These two new scales being annexed to
the diagram, we can readily obtain the residuary resistance of the
ship from the curve B, but the total resistance being required, the
skin frictional resistance is next calculated for the ship, and the
amounts added to the curve B gives C, which is the curve of total
resistance of the ship. Co-efficient / and index n for paraffin wax
models in fresh water :

Length. /. n.

10 ft. ... -00937 ... 1-94

11 ft. ... -00920

12 ft. ... -00908

Horse Power. The unit of force taken as being 1 lb., and the
unit of speed as 1 ft. per minute, gives the unit of power as follpws :

Force X Speed = = Power.

1 lb. X 1 ft. per minute = 1 ft. lb. per minute

(the unit of power).

33,000 of such units are regarded as 1 horse power. In the case of
a ship the resistance is the force ; therefore, if R is the resistance
in Ibs. and v the speed in feet per minute, then the horse power
required to overcome this resistance will be :

R X v


or, if we deal with speed in knots per hour, as this is the usual way
of expressing it, and which is represented by V, we have :

RxVx- = R x V x 101-33


Horse power = 33000


= R X V x -0030707

The latter is a much handier expression, and is obtained by con-
verting the speed of knots per hour into feet per minute by multi-

The Theory and Design of British Shipbuilding. 117

plying by the number of feet in 1 minute for the rate of 1 knot per
hour, which is 101-33. This being divided by 33000 gives -0030707,
which now gives a much simpler and reduced formula.

Effective Horse Power. This is the amount of power that is
consumed in the actual propulsion of the vessel, being the amount
necessary to overcome the total of the various resistances which
have been previously dealt with i.e., the tow rope resistance. It
may be termed the tow rope horse power, because it is equal in
amount to that which would be transmitted through a tow rope
when towing the vessel at the given speed, the effect of the presence
of the tug being, of course, eliminated. On account of power being
consumed by means of friction of the machinery, working of auxil-
iaries off the main engines, inefficiency of propeller, etc., an amount
of power much larger than the E H P must be generated in the
vessel's engines, since the E H P is simply the amount which is
usefully employed in overcoming the external resistances to the
vessel's motion.

Indicated Horse Power. This is the amount of power that is
actually generated in the vessel's engines, being measured from the
engines by the instrument known as the indicator, from which the
name is derived. By use of the Indicator, diagrams are obtained
which graphically show the variation of the steam pressure in the
cylinders, the mean pressure being calculated from such diagrams.
If P = the so found mean pressure in Ibs. per square inch and A
= the area of piston in square inches, we have P A = the total mean
pressure (i.e., the force) upon the piston in Ibs. This pressure
multiplied by the speed will equal the work done, which when divided
by 33,000 gives the I H P. The speed is equal to the distance run
by the piston in 1 minute, which is as follows : If L == the length
of the stroke of the piston in feet, then during one revolution the
distance will be 2 L, and if N is the number of revolutions per minute,
the distance run in 1 minute will be 2 L N. We therefore now
have a force of P A pressure in Ibs., and a speed in feet per minute
of 2 L N.

PA x 2 L N = ft. Ibs. per minute (units of power),

PA x 2LN

or, = indicated horse power.


118 The Theory and Design of British Shipbuilding.

A simple way of remembering this is by constructing the word
" Plan " from the above letters, viz. :

2 P L AN


= I H P.

Indicated horse power will be seen to vary as the steam pressure
P, the cylinder capacity L A, and the number of revolutions N.

Propulsive Co-efficients. The ratio of the E H P to the I H P
is known as the " Propulsive Co-efficient " : for instance, in the
case of a vessel where 1,000 I H P is necessarily provided to drive
her at a speed at which the E H P is 600, the propulsive co-efficient is

E H P 600

= = -6.



It is sometimes expressed as a percentage, which, in this case,
would be 60. This co-efficient varies at the different speeds of a
vessel, owing to the fact of some of the losses being nearly constant

in amount, therefore absorbing a
larger proportion of the I H P at the
slower speeds, and also owing to the
propellers being designed to give the
maximum efficiency at the designed
top speed of the ship. The higher
the propulsive co-efficient the greater
is the efficiency, therefore the co-
efficient should reach its maximum
at the designed top speed, a curve
of such co-efficient giving a shape
as shown in Fig. 56. The following
are typical values :

45 to -5


II 12

Fig. 56

Modern single-screw cargo vessels of full form

(The former being a good figure for estimates)
Modern twin-screw vessels of fine lines with independently

worked auxiliaries (liner type) ... ... ... -5 to *55

Cross Channel steamers ... ... ... ... ... '5

From the above it will be seen that the average propulsive co-efficient
is -5, showing the necessity of generating twice as much power as
would be required to overcome the tow rope resistance.

The Theory and Design of British Shipbuilding. 119

Losses. Commencing at the engines, at which the I H P is obtained,
the first loss encountered is initial friction, and is due to the dead-
weight of working parts, working of auxiliaries off main engines,
friction of packing and bearings, etc. This initial friction causes
a loss to the I H P, a good average for which is about 1\ per cent,
of the I H P. It is practically constant at the top speeds of different
vessels, but in the same vessel it varies directly as the speeds.

To show how it varies in the same vessel, take the following
example of a vessel of 800 I H P and 10 knots speed. Suppose the
speed is reduced to 5 knots, then assuming the I H P to vary as the
cube of the speeds, we have :

800 x (TO) S = 100 I H P at 5 knots.

The initial friction at the top speed would consume
800 X 7J per cent. = 60 H P.

and this varying as the speed ,we would have
60 x fV == 30 H P

consumed by the initial friction at 5 knots speed. Now, while at
the top speed we have 7^ per cent, of the I H P consumed by means
of initial friction, at the reduced speed of 5 knots we have 30 per
cent, consumed in this way. The next loss is the load friction, it
being equal to the thrust or load friction on the thrust block. The
amount of this loss is about 7| per cent, of the I H P, this being a
good average figure. Load friction varies with the speed and thrust
of propeller, or practically as the I H P. We therefore see that
before reaching the propeller we have lost a total of 15 per cent, of
the I H P, there being now only 85 per cent, left, which is termed
the " propeller horse power." The ratio of this " propeller horse
power " to the I H P (85 per cent.) is known as engine efficiency


and = - . Now, at the propeller we have a further loss

first of all the propeller loss itself, which is due to slip and friction
of the water on the blades, and then the augmentation of resistance
allowing for the wake again. Slip is the loss caused by the yielding
of the water at the propeller and the screw not progressing to the
full extent of its pitch ; for instance, a vessel at 10 knots
travels 10 x 6,080 = 60,800 ft. per hour with a propeller
of 13 ft. pitch and 100 revolutions per minute ; 60 X 100 = 6,000

120 The Theory and Design of British Shipbuilding.

revolutions per hour, and 6,000 revolutions x 13 ft. pitch = 78,000
ft. per hour, which is the resultant forward propeller speed, while
the vessel only travels 60,800 ft. in the same time, a difference of
78,000 60,800 = 17,200 ft., which is 22 per cent, apparent slip ;

PR v

or it may be written - x 100 = per cent, of apparent


slip, P being the mean pitch of the screw in feet, R the revolutions
per minute, and v the speed of the ship in feet per minute. In this
case we would have

10 x 6,080
13 X 100 -


- = 22 per cent.

13 x 100

This is not the real slip, as for this it is necessary to take into account
the wake at the after end of the vessel, which tends to reduce the
speed of the water past the propeller from that of the ship. However,
from the above apparent slip the meaning of this propeller loss will
be seen. The propeller frictional resistance is also to be accounted
for in making up the propeller loss. It may be said that in efficiently
designed propellers not more than 70 per cent, of the propeller horse
power can be actually used in the propulsion of the vessel, and
although some experiments have given better results, the 70 per
cent, is a safe figure to use. Up to now, we have 85 per cent, of
the I H P, equal to the propeller H P, and from this P H P we have
to deduct 30 per cent, for propeller losses, since, as above mentioned,
it is only possible to usefully employ 70 per cent, by means of the
propeller. (85 per cent, of I H P = P H P) x 70 per cent. = 59-5

per cent, of I H P remaining.

Another loss, which is caused by the propeller, though not accounted
for in propeller losses, is the augmentation of resistance. From the
stream line theory we know that by the rounding in of the stream
lines aft the vessel receives a pressure helping her forward motion.
The propeller, disturbing this stream line action of the water at the
after end, therefore causes an increase of resistance over what would
be found were the propeller absent, as in the case of the tow rope
resistance. It is obvious that in a single-screw ship the augment
will be larger than in the case of a twin-screw vessel, as in the latter

The Theory and Design of British Shipbuilding. 121

the screws are placed further away from the ship, and, therefore,
having less effect upon the stream lines ; but here we must make
allowance for " wake gain " obtained by the propeller from the
forward motion of the water at this part of the vessel. A single -
screw ship obtains a larger advantage from the " wake " than one
with twin-screws, because of the forward motion of the " wake "
being greatest at the centre line. We therefore see that on account
of the above mentioned augment and " wake gain," we have a
deduction and also a gain to consider. The gain due to the " wake "
is of less amount than the augment of resistance, and the ratio that
the former is to the latter is termed " hull efficiency."

Wake gain

- = hull efficiency.

Propeller augmentation of resistance

Typical values for hull efficiency are as follows :

Single- screw vessels 90 ' of the horse power remaining

to 95 per cent.
Twin-screw vessels 95
to 100 per cent.

after having made the de-
duction for the efficiency of
the propeller.

Summing up the foregoing we have :

Per cent.
Indicated Horse Power ... ... ... = 100

Deduct H P consumed in initial friction . . . = 7|

Deduct H P consumed in load friction ... = 7J

Propeller Horse Power ... ... ... = 85

To allow for propeller losses take only 70

per cent. ... ... ... ... = X '70

= 59-5
For hull efficiency take 95 per cent. ... = X -95

Effective Horse Power remaining ... ... = 56-5

Therefore the propulsive co-efficient in this case is :

E H P 56-5

= -565.
I H P 100

122 The Theory and Design of British Shipbuilding.

Composition of I.H.P. The following summary shows how the
total generated power is consumed :

Eddy-making Resistance.
-|- Wave-making Resistance

= Residuary Resistance

-j- Skin Frictional Resistance

+ Air Resistance

= Total Resistance overcome by the E H P

-j- Loss due to Hull Efficiency

-f- Loss due to Propeller Slip, Friction, etc.

= Propeller Horse Power

-+- Loss due to Load Friction

-f- Loss due to Initial Friction

= Indicated Horse Power.

Nominal Horse Power. (N H P), as given in the ship's register, is,
like the registered tonnage, a fallacious figure, and one of little use
in representing a close valuation of the vessel's actual power, which
is the I H P. The proportion of N H P to I H P is found to have
great variation when comparing different ships, an average figure
being :NHP = JIHP, though it varies greatly between J I H P
and I I H P.

The Theory and Design of British Shipbuilding. 123




Admiralty Co-efficient. The most commonly used approximate
method for estimating I H P is that known as the " Admiralty
Co-efficient," the formula for which is as follows :

V 3 xD
IHP = -


where V = the speed in knots per hour,
D = the displacement in tons,
C = the " co-efficient of performance " obtained from

previous similar ships, where V, D and IHP

are known, by :

V 3 x D
C = -


The following assumptions are made :

1. That the total resistance will vary as the skin frictional re-
sistance, which will therefore vary as the wetted surface area. Since
the wetted surface area of two similar ships varies as the displacement
to the two- third power (D ), we can therefore use D as representing
the proportion of this resistance.

2. That the resistance will vary as the square of the speed. Of
course, the 1-83 power (V 1 ' 83 ) would be more accurate for skin
frictional resistance, but the difference will help to account for wave
resistance. The E H P necessary to propel the vessel will vary as
the cube of the speed (V 3 ). This will be obvious since we have
assumed the resistance to vary as V 2 , and we know that E H P

R x V

, so therefore we use V to the third power up to the time


124 The Theory and Design of British Shipbuilding.

of obtaining E H P. The speed integer is, therefore, in all cases
one high when dealing with power than in the case of resistance.

3. That the I H P of the engines will vary as the E H P.

It should be strictly remembered that in this method we deal
with similar ships at corresponding speeds i.e., speeds which vary
as the square root of the lengths of the vessels, and in such cases
only can it be relied on to give satisfactory results. In estimating,
the vessel chosen as the basis should be of similar form, also fairly
alike in size and type as the proposed vessel. The co-efficient should
be taken at the top designed speed so as to have the same engine
efficiency in both cases. It is, therefore, a difficult task to obtain
a vessel where the engine efficiency is the same as that of the pro-
posed vessel at the corresponding speed, since the corresponding
speed of the basis vessel may be so much different to her designed
speed that the engine efficiency will have greatly altered. The
importance of making comparisons only with vessels in all ways
similar to each other is therefore seen. We first assumed the total
resistance to be skin frictional resistance (R s ) varying as W S X V 2 ,
and consequently that E H P will vary as W S X V 3 (W S being
the area of the wetted surface), and according to the assumption
that I H P varies as E H P, then I H P will also vary as W S X V 3 .
W S X V 3 may be considered as a measure of the I H P since we
thus assume it to vary. We may term W S X V 3 as a figure having
a relation to the I H P, the proportion being :

W S x V 3

- = c


In similar ships this proportion C would be very nearly the same,
and may, therefore, be used in proportioning the power of one ship
from another by

W S x V 3

= I H P

In the designing and estimating stages it is improbable that the
wetted surface area W S would be known, therefore W S is sub-
stituted by Df , which has the same variation, and the formula is
reduced to one which can be quickly applied, since T> is one of the
first figures determined at these stages.

The Theory and Design of British Shipbuilding.

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Online LibraryAmos Lowrey AyreThe theory and design of British shipbuilding → online text (page 9 of 14)