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125

The formula, therefore, now becomes as given at the commence-
ment.

The following are average values for C :

Atlantic liner, about 23 knots 270

Large cargo and passenger, of medium form and speed 290

Cross -Channel, about 20 knots ... ... ... ... 220

Large cargo, about 12 knots ... ... ... ... 300

Small cargo, about 9 to 10 knots 230

Trawler, about 9-| to 10 knots 130

Herring drifter, about 9 knots 115

At different speeds of the same ship we have a variation in the value
of C. In Fig. 57 the variation is shown for a vessel of ordinary
proportions about 390 ft. ling and 7,800 tons displacement. The-

Fig. 57.

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value of C varies greatly in different vessels, but when discriminately
obtained from a basis vessel the formula is very useful in the early
stages of a design.

Extended Law of Comparison Method. In making a comparison
between two vessels by this method it is assumed that the total
resistance follows the " law of comparison " When applied to
vessels of similar size and form, the results are fairly good, but, of
course, it cannot be used in comparing a ship with a model, since
in such a case the skin frictional resistance must be specially separately
computed for the reasons mentioned and .as described in the article
on Resistance. With two similar vessels the difference due to assum-
ing the skin resistance as following the " law of comparison " is.

126 The Theory and Design of British Shipbuilding.

extremely small. It is also assumed that the engine efficiency at the
speeds used in comparison, which should be " corresponding speeds,"
is equal. From the law of comparison we know that the residuary
resistance varies as the length cubed or as the displacement, and
also that corresponding speeds vary, as

~ -

V L

L, ' D,

therefore, assuming the I H P to vary as the E H P, we have
IHP RxV DxDJ

I HPT B, XV, DT xD^

IHP D i

The extended law is therefore = I 1

IHP, V IV

In estimating the I H P by this means, the speed of the basis ship,
-corresponding to that of the proposed ship, is first found as follows :

Corresponding speed of basis ship = '

/Length of basis ship
Speed of proposed ship x

V Length of proposed ship.

The I H P of the basis ship at this corresponding speed is
next obtained from the curve of power, and multiplying this by

displacement of proposed ship ,

displacement of basis ship
the IHP according to the extended law is obtained.

I H P of basis ship at"! / _\ ""_ I H P of proposed

corresponding speed , \ / similar ship.

**l

This is a quick method of estimating IHP, and, with moderate
comparisons, good results are obtained. When a smaller ship is
used as the basis, the result is on the high side, since the skin frictional
resistance has been taken to vary to the same extent as the residuary
resistance i.e., as L 3 or D while we know that the skin frictional
resistance only varies as L 2 or Df.

The Theory and Design of British Shipbuilding. 127

Model Experiment Method. In a previous chapter the methods
of performing this experiment and obtaining the total resistance
was dealt with. We know that this total resistance is to be over-
come by the E H P ; therefore, having obtained this amount of

R X v

resistance, the E H P is found by - - = E H P.

33000

Where R = the total resistance in Ibs. and
v = the speed in feet per minute.
or R x V x -0030707 = E H P,
where V = the speed in knots per hour.

Suppose that, from a model experiment, the total resistance of
a ship at 15 knots is found to be 12,000 Ibs., then

E H P = 12000 X 15 X -0030707 = 552-73.

The E H P having been obtained, the I H P is next determined by
using a propulsive co-efficient applicable to the type of the vessel.
Say, in this case, the probable propulsive co-efficient (as obtained
from the data of previous similar ships) is -55, or 55 per cent, as it is

552-73 x 100

sometimes given, then theIHP=- - I H P = 1050.

55

Independent Estimate Method. By this method we estimate the
various resistances skin frictional, eddy making and wave making,
and their corresponding E H P, separately, adding them together
to obtain the total E H P.

Skin frictional ... HP

Eddy making ... HP

Wave making ... HP

Air resistance ... H P (if necessary)

Total = E H P

Skin frictional HP- -0030707 (/.S.

It will be seen that we have the formula /. S. V 1 - employed to give
the resistance in Ibs., which is next multiplied by -0030707 and also
by the speed so as to obtain H P, the latter being introduced by
increasing the index n as shown. In the case of an ordinary ship
where the index n is 1-83 we have 1-83 + 1 = 2-83 to use when

128 The Theory and Design of British Shipbuilding.

estimating H P. Eddy making H P may be taken as 5 per cent, of
the skin frictional H P if Froude's co-efficients have been used in
the above frictional resistance formula. If Tideman's figures are
used no separate estimate for eddy making H P is required, since
they are high enough to allow for this. Wave making H P : This
is calculated by using the formula given by Mr. Taylor, as was
mentioned in the article on Resistance, but in this case the speed
integer is one higher V 5 instead of V 4 and the whole is multiplied
by -0030707, giving

D
Wave making H P = 12-5 x C x - X V 5 x -0030707

L 2

(The speed integer being increased when dealing with H P, for the
reasons previously stated). Summing up these independently
estimated H P's we obtain the total E H P, and then by using a
suitable propulsive co- efficient, the I H P is found.

Another Method. The following formula gives very good results,
especially when the co-efficient a, is obtained from a similar ship :

D x V 3
= I H P

L x v'M S A x a

D = displacement in tons. V speed in knots. L = length.
M S A = 'midship section area in square feet, a = a co-efficient
for which the following are average values.

Atlantic Liner, about 23 knots 2-0

Large Cargo and Passenger of medium form and speed 2-4

Cross Channel, about 20 knots ... ... ... ... 2-0

Large Cargo, about 12 knots ... ... ... ... 2-7

Small Cargo, about 9-10 knots 2-5

Herring Drifter, about 9 knots ... ... ... ... 2-1

High Speeds and Low Speeds. Corresponding speeds vary as the
square root of the lengths of vessels, therefore we may say that speeds
are relative to the length of ship. To obtain a real comparison of
the speeds of various ships we should therefore compare the speeds
with the square root of the respective lengths by finding the ratio :

V

The Theory and Design of British Shipbuilding. 129

Say a vessel 400 ft. long has a speed of 11 J knots,

11-25

then - = -56 == speed-length ratio

\/400

This ratio is representative of a cargo vessel of moderate economical
speed, and is applicable to such vessels of all sizes ; for instance,
take a vessel 256 ft. long :

A/256 X '56 =9 knots, which is a moderate speed for a vessel
of this length.

V
The following are average values for :

VL

Cargo steamers of slow speed ... ... ... ... *45

Cargo steamers of moderate speed ... ... ... -55

Cargo steamers of good speed ... ... ... ... -65

Cargo and passenger steamers ... ... ... ... -75

Atlantic liners ... ... ... ... ... ... -90

Battleships .................. -95

Cross- Channel steamers and cruisers ......... 1 10

Destroyers ............ . ..... 2-00

We may say that when the ratio is below *5 the vessel is of low
speed, at -9 ratio the speed is high, and at 1-2 we have speeds that
are excessive and only obtained with a large expenditure of power.
The following example shows the application of the speed-length
ratio to two vessels of the same speed but different lengths. Say,
one vessel is 400 ft. long, the other 100 ft., and the speed in both
cases 10 knots. In the larger vessel,
10

= -5 speed-length ratio ;
A/400

and the smaller vessel,
10

- = 1-0 speed-length ratio.

It will be seen that while 10 knots is quite a low speed for the 400
ft. vessel, yet it is a very high speed for the vessel 100 ft. long.

Speed Trial Trips. The trial trip is one of the most eventful
occasions during the vessel's career. It is the occasion during which

10

130 The Theory and Design of British Shipbuilding.

the owner has the opportunity of practically ascertaining the cap-
abilities and efficiency of the engine and boilers when under full
power. He also obtains the speed, maximum I H P developed by
the engines, and the consumption of fuel necessary to obtain the
speed and pOAver. On the other hand, the shipbuilder takes the
opportunity to obtain data for future designing purposes in the
shape of the amount of I H P necessary to propel the vessel at
various speeds ranging up to the maximum, number of revolutions,
slip and efficiency of propellers. The following are the methods
usually adopted for obtaining the speed of the vessel :

1. Successive runs in opposite directions on a measured mile.

2. A continuous run at sea, the number of revolutions being
counted during the time occupied and the mean speed for the run
found as afterwards described.

3. A continuous run at sea past a series of stations of known
distances apart, the times being recorded when the ship passes.

4. Patent logs.

The last method is of little use for trial trips, the results not being
sufficiently accurate for this purpose, although it is extremely useful

Progressive Trials on the "Measured Mile." So as to obtain a

true course for these trials, posts are erected on the coast is positions

as shown in Fig. 58, which represents the measured mile near the

mouth of the Tyne. The course is marked by buoys or by a compass

bearing, as in the case of the Tyne mile, where the course is north

and south. A number of runs are usually made over the course at

various speeds, making at least one run each way for each speed.

If the trial is not to be a progressive one, and the vessel is to be run

at full power only, then two or three runs are made in each direction

making four or six in all. In progressive trials it is best to make

these numbers of runs for each speed taken and to find the " mean "

as is afterwards described, although the mean of two runs, one with

and one against the tide, would give a fairly accurate result. Some

progressive trials are commenced at the top speed, while in others

the first run is made at a very low speed. For instance, if the latter

is adopted in the case of a vessel of 5,000 maximum I H P, the first

series of runs would be made with an I H P of about 1,000, and after

having carefully noted all the results, as mentioned later, the power

would be increased to about 2,000, when the second series of runs

would be made. The next runs would be made at progressive I H P's,

The Theory ami Design of British Shipbuilding.

131

until the maximum is reached. The results of one series of runs
would be ascertained as follows : The times of passing the posts
carefully taken with chronometer stop watches by observers on deck,
the number of revolutions and the I H P being noted by the engine-
room officials. Under precisely similar conditions, these particulars
are again taken with the vessel steaming in the opposite direction.
The power being increased for another series of runs, records are
again made. The results of progressive trials are arranged in dia-
grammatic form, as shown in Fig. 59. The amounts of I H P are
obtained by the engine-room staff, by means of taking indicator
diagrams and then setting off the results at their respective speeds ;

Fi?. 58.

the curve is drawn as shown. The numbers of revolutions being
noted for these speeds they are also set off, as shown. The Admiralty
co-efficients, corresponding to the trial results, are generally calculated
and a curve also drawn for them. These curves are extremely
useful in the designing of future ships ; for instance suppose it was
required to know the amount of I H P necessary to drive a proposed
similar ship at a given speed, the Admiralty co- efficient method being
employed. In the above, it was said that, when using this method
it is necessary to obtain a co -efficient for a previous similar ship at
the corresponding speed. From the curve shown in Fig. 59, the
co-efficient can be quickly read off after determining the corresponding
speed, and by use of this co-efficient the I H P may be estimated for
the proposed vessel. Other curves may be added to this diagram,
such as slip, indicated thrust, etc.

132 The Theory and Design of British Shipbuilding.

Precautions necessary. Seeing that trial trips are always looked
upon as being obtained under the most favourable conditions, it is
of the utmost importance that such shall be the case. The vessel's
bottom should be in clean condition and the wind and sea favourable,
the machinery in perfect order and under good control. The course
chosen should be of sufficient depth to suit the speed of the vessel,
and not to interfere with the resistance, as is sometimes the case of
high speed ships in shallow water, when the resistance is increased,
although, in extreme cases of high speed vessels, very shallow water
has been found to aid the speed. The resistance is influenced by
means of the shallow water affecting the wave formation. It is
found that normal wave formation is obtained where the depth of
water, in feet, under the vessel's bottom exceeds -28 V 2 , V being
the speed of the vessel in knots. Say a vessel of 14 knots : -28 x
14 2 =55 ft. A good steersman should be at the wheel so as to get
the vessel upon the right course and keep her steady. It is very
important that the vessel be kept on a straight course, this being
very obvious when we remember the definition of a straight line as
being the shortest distance between two points. Although the
course may be straight, care must also be taken that it is in the
right direction i.e., parallel to the two outer posts, or north and
south on the above-mentioned course, because any other direction
but this will lengthen the distance run. At each end of the course
there should be a space in which to take a steady turn to get the
vessel into position again and be running at full speed before passing
the first post on the return run. There should be three or four
chronometer stop watches used in the taking of the times, these,
of course, being in perfect order. The observers should accurately
start and stop the watches, and the mean of the times should be taken,
because one person may anticipate, while another may delay until
he sees the posts actually open. The timing is one of, if not the,
most important observation of the trial trip : a difference of one
second on the mile would mean -1 of a knot at a speed of about 20
knots per hour.

To Obtain the True Mean Speed. This is done by finding the
mean of means, by which method the tidal and wind effects are
eliminated. Since the tide varies in speed and direction of flow, it
is necessary to obtain the mean speed, as seen in the following example
which I- shows the ordinary method of finding the mean of
means :

The Theory and Design of British Shipbuilding. 133

Knots.

Run 1. With tide ... 15-000 ) u . 344
Run 2. Against ... 13'688 [ \ 14-375 .

- 14.407 I \ 14-431 *

Run 3. With ... 15-126 { 14-487 14-467 } ,. ,

14-567 I 14-503 \14-472knts

Run 4. Against ... 14-008 14-520 ' 14-477 J means P eed

14-473 14-450 j

Run 5. With ... 14-938 ! J 14-380 '

Run 6. Against ... 13-636 | 14 ' 287

86-396 ^ 6 = 14-399 knots.

It will be seen that if the ordinary average of the six speeds is taken
we have 14-399 knots against 14-472 as the true mean, a difference
of nearly -1 of a knot. To be strictly correct, the mean speed should
be found by first of all finding the mean time instead of the mean
knots per hour, as is usual, and as is done in the above example.
For instance, if the above were correct, we would say that, in the
case of a vessel which runs one way on the mile at the rate of 20
knots per hour and returns at the rate of 10 knots per hour, the
mean speed was

= 15 knots per hour.

such is not the case, as the following will show :

at the rate of 20 knots, the time occupied was 3 minutes.

10 6

therefore 2 knots were run in 9 ,,

being a mean of 1 knot in 4J

60 minutes -f- 4-| = 13 J knots per hour,

which was the mean speed of the vessel, and not 15 knots. This
example is, of course, exaggerated in the amount of difference
between the speeds (20 and 10 knots), yet it proves that the correct
method is to find the mean of the times and then for the mean speed
to take that corresponding to the mean time. In ordinary trials,
however, the effect due to this is very slight. If in the above example
we had found the mean of means for the time occupied in running
the mile, the corresponding speed would have been 14-46 knots, a
difference of only -012 knot. During the running of these trials,
the displacement and trim should be as near as possible to those
designed for. The second method of conducting trials is performed
as follows : The revolutions are counted during a continuous run
at sea of 8 hours, say. and the total divided by the time occupied
in minutes will give the mean number of revolutions per minute.

134 The Theory and Design of British Shipbuilding.

7*0

Having first of all
constructed a dia-
gram as shown by
Fig. 59, from the re-
sults obtained on the
measured} mile trial,
the speed corres-
pending to this mean
number of revolu-
tions is easily found.
From the point on
the curve of revolu-
tions corresponding to
,,. the number found as

above (in Fig. 59 the

point is shown by x), drop a perpendicular down into the scale of
speed, where the mean speed during the continuous run will be
obtained. In Fig. 59 it is shown to be 13-2 knots.

The third method The series of stations is obtained by placing
vessels at distances apart of about three knots. Persons aboard
the station ships note the times that the trial ship passes in addition
to those on board the trial ship also noting the times, a good check
being thereby obtained. The observers on board the station ships
also make measurements of the speeds of the tide and wind, and
then, by making these corrections, a most accurate result of the
trial is obtained.

Coal Consumption. When the coal consumption is measured,
the method employed is usually as follows : First, by using two
bunkers, a spare one and a sealed one. Coal from the spare bunker
is used until the vessel actually enters upon the trial, and then,
with ordinary fires, the spare bunker is sealed up and the sealed bunker
broken. At the end of the trial, the fires being left in ordinary
condition, the latter bunker is again fastened up and the coal from
the spare bunker used. By knowing the original weight in the
sealed bunker, and then measuring or weighing the remaining amount,
the exact quantity used during the trial can be obtained. The
second method is to have a weighing party on board, and by means
of weighing machines to weigh the exact amount of coal used in
the fires. The amount of coal used per I H P developed during the
time can then be found.

The Theory and Design of British Shipbuilding. 135

CHAPTER XIII.

THE STEERING or SHIPS. TYPES OF RUDDER. CAUSES OF PRESSURE

ON RUDDER. CALCULATION FOR PRESSURE. TWISTING MOMENT

ON RUDDER HEAD. CALCULATING THE REQUIRED DIAMETER OF

The Steering of Ships. In Fig. 60 we have represented the
two types of rudders usually fitted, A being the " ordinary " type
hung at its forward edge, and B shows the " balanced " type, which
has an amount of area forward of, as well as abaft of, its axis. In
the latter it will be seen that the after stern-post is omitted, the

Fig. 60.

rudder being supported in only two places ; sometimes, however,
the bottom bearing is dispensed with and only one large bearing is
fitted at the top. It is obvious that to obtain steerage effect from
the rudder we must have motion of the ship through the water, or
a flow of water past the rudder, so that an excess of pressure may be
obtained on one side of the rudder, which will then cause the vessel
to alter her course. In the case of a screw ship the propeller race is, in
this way, the means of giving the vessel steerage way, even before
the vessel herself has obtained motion. To keep a single -screw
vessel on a straight course it is usually found necessary to hold the

136 The Theory and Design of British Shipbuilding.

rudder over to a small angle, but for our present purpose we will
assume that the vessel's rudder, while on the centre line, will give
this result. Suppose a vessel, while steaming in a forward direction,
is put under a port helm i.e., the rudder is put over to the starboard
side, as shown in Fig. 61 . This obviously causes an excess of pressure
(P) on the starboard side, forcing the vessel's stern in an outward
direction (to port), as shown by the arrow D, resulting in the
vessel changing her course and her head coming round in a
starboard direction. The steering power of a vessel being firstly
dependent upon this pressure P, it will, therefore, be interesting
to investigate the items influencing its amount.

J?

L

Fig. 61.

The pressure on the rudder depends on :

The area of the immersed surface of rudder.
The angle at which the rudder is held over.
The speed of water past the rudder.

While the rudder is lying in a fore and aft direction, according to
the above assumption, we have no pressure ; but if it is held at right
angles to the line of motion of the water a direct resistance is obtained,
the pressure of which is, in Ibs., equal to :

1-12 A v 2 , where A = area of immersed surface in square feet
and v = the speed in feet per second.

If the line of motion is assumed to be parallel to the keel line, then
at any angle to this line the above pressure varies as the sine of the
angle :

1-12 A v* sin pressure in Ibs. for any angle 9.

The line of motion is not, however, parallel to the keel line, and it may
be fairly assumed to be parallel to a water-line representing a mean of
those contained in the immersed portion of the after part of the
vessel. The angle used in the formula should, therefore, be increased
to suit this. This point is illustrated in Fig. 61, where the mean
water-line is shown, and it will be seen that while the rudder is only

The Theory and Design of British Shipbuilding. 137

held over to 45 deg. (usually the most efficient), yet the impingement
of the water, giving the resultant pressure P, is acting nearly at
right angles to the rudder surface. The speed used should be that
of the water past the rudder, and here the effect of the propeller
must be accounted for by increasing the vessel's speed by 10 per
cent., which will allow for the difference between the vessel's speed
and propeller speed, also accounting for the forward motion of the
wake.

Twisting Moment on Rudder Head. When a rudder is held over
by means of steering gear or tiller and subjected to such a pressure
as the above, a twisting stress is brought to bear upon the rudder
stock. If the centre of pressure is found relative to the axis of the
rudder we then have the lever through which the above pressure is
acting, and the pressure in Ibs., when multiplied by the lever in feet,
will give the twisting moment in foot-lbs.

Twisting moment in ft.-lbs. = (1-12 A v 2 sin 9) X I
I representing the lever.

At first sight it may appear that the centre of pressure will coincide
with the centre of gravity of the immersed rudder area ; this is not
the case, and for rectangular plates we may take the distance from
the leading edge as follows :

10 deg. = -24 of breadth. 50 deg. = -42 of breadth.

20 = -315 60 = -44

30 = -365 70 = -46

40 =-400 80 =-48

45 = -405 90 - -50

Owing to varying speed and direction of steam lines at the stern
of a ship and the interruption caused by the propeller, the above
values may not be exactly correct when dealing with a ship's rudder,
but they may be considered as being fairly near to the correct figure.
When a vessel is moving in a sternward direction the after edge of
the rudder becomes the leading edge, and the centre of pressure

Online LibraryAmos Lowrey AyreThe theory and design of British shipbuilding → online text (page 10 of 14)