Amos Lowrey Ayre.

The theory and design of British shipbuilding online

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IRLF




HE

& DESIGN
RITISH
'UPBUILDING




.



The

Theory and Design

of

British Shipbuilding.



By A. L. AYRE,

Honours Medallist and King's Prizeman.



Illustrated by 85 Diagrams.




Printed and Published by

THOMAS REED AND CO., LTD.,

184 HIGH STREET WEST, SUNDERLAND.
D. VAN NOSTRAND COMPANY

& WAKRKN ST., NEW YORK



A 7.

gin eer
Library




CONTENTS.



CHAPTER I.

Dimensions : Explanations of Length, Breadth and Depth. Rules for
Areas, Volumes, Moments and Centre of Gravity. Simpson's First
and Second Rules : Five, plus Eight, minus One Rule, and Rule
for Six Ordinate Figure. Sub-divided Intervals.- Application of
Various Rules and Practical Examples ... ... ... page 1

CHAPTER II.

Displacement Defined. Centre of Buoyancy Denned. Deadweight and
Deadweight Scale. Composition of Deadweight. Tons per Inch.
Difference in Draught : Sea and River Water. The Block Co-efficient
of Displacement. Co-efficient of 'Midship Area. Prismatic Co-
efficient. Co-efficient of Waterplane Area Average Values of
Co-efficients in Various Types. Relation of Co-efficients to each
other page 14

CHAPTER III.

Estimate or Required Amount of Displacement. Determination of
Dimensions. Required Longitudinal Centre of Buoyancy and
Trim. The Sheer Draught. Construction of " Lines " to Fulfil
the Required Conditions. Final " Displacement sheet " Calcula-
tions, including Longitudinal and Vertical Centres of Buoyancy,
etc., The Displacement Scale and the Various Curves... page 26

CHAPTER IV.

Initial Statical Stability : Conditions. The Transverse Metacentre
Explained. Formula for Calculating the Position of the Transverse
Metacentre. Average Values of Metacentric Heights. The Meta-
centric Diagram : Its Construction and Use ... ... page 44

CHAPTER V.

Metacentric Stability. Effect of Inclination and Successive Metacentres.
To Determine Practically, by Inclining Experiment, the Height
of a Vessel's Centre of Gravity ; the Procedure and Necessary Pre
cautions. Example of Inclining Experiment ... ... page 57

CHAPTER VI.

Co-efficients for Heights of Centre of Gravity in Typical Vessels. Effect
of Free Water in the Tanks, or Liquid Cargo in the Holds of Vessels.
Effect on Initial Stability due to Adding Water Balla&t in Double-
Bottom, Deep Tanks and on Deck, etc. ... ... ... page 69

CHAPTER VII.

Effect on Stability when passing from Salt to Fresh Water, or vice-
versa. Loss of Initial Stability due to Grounding ; the Case of a
Vessel in Dry Dock. Effect on Stability due to Vessel being partly
in Mud page 8 1

CHAPTER VIII.

Statical Stability at Large Angles of Inclination : Definition. Atwoods'
Formula. Ordinary Curve of Stability. Cross Curves : Remarks.
Influencing the Shape of Stability Curves ... ... page 92



CONTENTS Continued.



CHAPTER IX.

Dynamical Stability : Definition. Moseley's Formula. Construction
of Curve. Stability of Sailing Ships : Heeling Produced by Wind
Pressure oil Sails, and Effect of Area of Statical Stability Curve.
Effect of Dropping a Weight Overboard... ... ... page 98

CHAPTER X.

Longitudinal Stability : Metacentre and Calculation. Trim and Moment
to Change Trim 1 in. Estimating the Trim ... ... page 104

CHAPTER XI.

Resistance. Water Resistance and Stream Line Theory. Fractional
Resistance, Eddy-making Resistance, Wave -making Resistance
and Air Resistance. Model Experiments. Horse Power.
Effective Horse Power. Indicated Horse Power. Propulsive
Co-efficients. Losses. Composition of Indicated Horse Power.
Nominal Horse Power page 111

CHAPTER XII.

Estimating Horse Power. The Admiralty Co-efficient Method, and
the assumptions made. Average Values of Admiralty Co -efficient.
Extended Law of Comparison. Model Experiment Method.
Independent Estimate and another Method. High Speeds and Low
Speeds. Speed Trials. Precautions Necessary. Obtaining, the
True Mean Speed. Coal Consumption ... ... ... page 123

CHAPTER XIII.

The Steering of Ships. Types of Rudder. Causes of Pressure on
Rudder. Calculation for Pressure. Twisting Moment on Rudder
Head. Calculating the required Diameter of Rudder Head.
Turning Trials page 135

CHAPTER XIV.

The Strength of Ships. The Positive and Negative Loading of Ships,
and Strains caused thereby. Construction of the Curves of Weight-
Buoyancy, Loads, Shearing Forces and Bending Moments. Formula
for the Determination of the Amount of Stress. Effect of Super-
structures page 141

CHAPTER XV.

Freeboard and Reasons of its Provisions. Reserve of Buoyancy.
Effect on Stability and Strength. Board of Trade Rules. Amend-
ments in 1906 page 147

CHAPTER XVI.

Tonnage : Under Deck, Gross and Net Register. Method of Measure-
ment and Computation. Allowance for Spaces Occupied by Pro-
pelling Power, and Effect of Recent Act ... page 153

CHAPTER XVII.

Types of Ships : A Comparison of Vessels of Full Strength, Spar Deck.
Awning Deck. Shelter Deck, and Minor Types ... page 159



The Theory and Design of British
Shipbuilding.



CHAPTER I.

DIMENSIONS : EXPLANATIONS OF LENGTH, BREADTH AND DEPTH.
RULES FOR AREAS, VOLUMES, MOMENTS, AND CENTRE OF GRAVITY.
SIMPSON'S FIRST AND SECOND RULES ; FIVE, PLUS EIGHT, MINUS
ONE RULE ; AND RULE FOR Six ORDINATE FIGURE. SUBDIVIDED
INTERVALS. APPLICATION OF VARIOUS RULES AND PRACTICAL

EXAMPLES.



Dimensions. The measurements of ships are given in terms of
Length, Breadth and Depth. While they are so often used by
shipping people in stating the dimensions of a vessel, yet, owing to
each of these terms being themselves measured in various ways,
confusion is often caused and they are not always understood. It
will, therefore, be advisable in this first chapter to explain the
various points to which they are taken.

Length. The length most commonly used is length between per-
pendiculars (sometimes called builders' length). It is generally
denoted by B.P., and is measured from the fore side of the stem to
the after side of the stern post at the intersection of the line of the
upper deck beams. (See Fig. 1).

The measurement of LENGTH for the purpose of determining
scantlings is also measured in this manner according to the Rules
of Lloyd's Register, except in the case of a cruiser stern where length
of vessel is to be taken as 96 per cent, of the extreme length from
fore part of stem in range of upper deck beams to the aftermost
part of the cruiser stern, but it is not to be less than the length from
forepart of the stem to after side of stern post, where fitted, or
to the fore side of rudder stock, where a stern post is not fitted.
British Corporation measure the length from the fore side of the
stem to the aft side of the stern post, taken on the estimated summer
load-line, where there is no rudder post, the length is to be measured
to the centre of the rudder stock. Registered length is that measured



The Theory and 'Design of British Shipbuilding.



from the fore side of the stem to the after side of the stern post,
asjshown'in Fig. 1.

Length overall is taken from the foremost part of the bowsprit
or stem to the aftermost part of the counter.




Breadth is usually given as Moulded or Extreme, and is measured
at the widest part of the vessel. Breadth Moulded is measured
over the frames, i.e., from outside of frame on one side to the outside
of frame on the opposite. Both Lloyd's and British Corporation



The Theory and Design of British Shipbuilding.



use the Moulded Breadth in finding the numerals for scantlings.
Breadth Extreme is taken over the side plating at its widest part.
(See Fig. 2). In the case of a vessel with fenders or sponsons another
breadth would sometimes be given, as Breadth over Fenders or Breadth
over Sponsons. Registered Breadth is exactly the same as Breadth
Extreme.



Fig. 2.



I

1 I - "

. . *> c




J!^-i

11- i
1 1

?i Sji
SI ^


1

1


^^^^^^


JLT-K.


ft AT Km KM.- /\^ - '/2_lfAetKJ?Cti5 ; _^
s_fe ftAPtH_iXTJ^iL


f

i

!



Depth is measured at the middle of the vessel's length i.e.,
amidships, or Centre between Perpendiculars (C.B.P.). Depth
Moulded is taken from the top of keel (T.K.) to the top of upper
deck beam at the side of the vessel, at mid length between perpen-
diculars.

Lloyd's Register use the Depth Moulded in their numerals for
scantling purposes.

British Corporation use the depth moulded, taken at the middle
of the length of the load-line. Depth of Hold is measured from the
top of ceiling (or tank top if ceiling is not fitted) to the top of beam
at the centre line of the vessel and taken at 'midships. Registered
Depth, measured at 'midships on the centre line of the vessel and
to the top of beam, the lowermost extremity being the top of double-
bottom, and if no double-bottom is fitted amidships, the top of
floors. Should ceiling be fitted amidships, it is measured to the top,
assuming its thickness to be 2J in. in all cases. In Fig. 2, A shows
the registered depth measured to the top of double-bottom.

Camber of Beam is represented by C in Fig. 2.



4 The Theory and Design of British Shipbuilding.

Rules for finding Areas, Volumes, Moments and Centre of Gravity
of Curvilineal Figures. A knowledge of these rules is a first
necessity before engaging in ship calculations. This is very apparent,
remembering the curved form of a vessel's hull.

Areas. The rules applicable to this work are : Simpson's,
Tchebycheff's and the Trapezoidal. The second is, nowadays,
coming more into vogue on account of its accuracy and quickness
as compared with the others, particularly in the case of calculations
referring to stability. The first is most commonly used in British
yards, and will therefore be dealt with in the present chapter.

Simpson's First Rule. This rule assumes that the curve is a
parabola of the second order. Suppose it is required to find the
area of the portion of Fig. 3 from A to C, shown shaded. The portion

Fig. 3.




of the base A C is divided into two equal parts by the ordinate B, the
common interval being h. Measure the lengths of the three ordinates
A, B and C. To the sum of the end ordinates (of the shaded portion).
A and C, add four times the middle ordinate B. The total so ob-
tained and multiplied by one-third of the common interval h gives
the area :

^h (A + 4 B -f C) = area of figure from A to C.

NOAV, suppose the total area of Fig. 3 is required i.e., from A to
E the interval h being equal throughout, the same rule could be
applied to the three ordinates C, D and E, and the two areas so



The Theory and Design of British Shipbuilding.



found added together would give the total area from A to E. In
Fig. 3 is shown the multipliers that would be used, 1, 4 and 1 from
A to C, and 1, 4 and 1 from C to E. It will be seen that the ordinate
C is twice taken into account ; therefore, reading from A, the mul-
tipliers become 1, 4, 2, 4, 1. If the figure were further lengthened
to the extent of two additional ordinates the multipliers would then

be 1, 4, 2, 4, 2, 4, 1. It

C lo-O Feer is obvious that this rule

only applies to figures with
an odd number of ordin-
ates. If Ave number the
ordinates from A, as is
shown at the top of the
sketch, we may put the
rule into the following
words : Divide the base into
an even number of parts
and erect ordinates extend-
ing from the base up to the
curve. To the sum of the
lengths of the end ordinates
add four times the length of the even numbered ordinates and twice the
length of the intermediate odd numbered ordinates. The total so
obtained multiplied by one-third of the commom interval gives the area.

As an example, let Fig. 4 represent the section of a side coal
bunker, the ordinates being as shown and the common interval 3-30 ft.




No. of
Ordinate

1
2
3
4
5



Length of
Ordinates

10-0 feet.

9-4

8-5

7'4
6-0



Simpson's
Multipliers

1
4

2

4
1



Functions
10-0
37-6
17-0
29-6
6-0



Sum of functions = 100-2
Multiplied by J interval = 3-3^-3= 1-1



Area == 110-22 sq.ft.

Simpson's First Rule is the one most frequently used in ship
calculations. However, in certain cases, where the positions of
ordinates are given, this rule is not applicable ; for instance, in
the case of four, six, eight, ten, etc., ordinates. If four ordinates



6



The Theory and Design of British Shipbuilding.



are given, Simpson's Second Rule is employed,
multipliers are :



In this rule the



Four Ordinates =

Seven

Ten =



1, 3, 3, 1

1, 3, 3, 2, 3, 3, 1

1, 3, 3, 2, 3, 3, 2. 3 ; 3, 1, etc.

The sum of functions obtained by using these multipliers is next
multiplied by three-eights of the common interval, the result being
equal to the total area. Example : Interval == 4 ft.

Simpson's
Multipliers

1



No. of
Ordinate



Length of
Ordinates



10-0 feet.

94

8-5

74

6-0

3-9
1-0



Multiplied by



Functions

10-0
28-2
25-5
14-8
18-0
11-7
1-0



Sum of functions = 109*2
interval = f X 4 = 1-5

Area = 163-8 sq. ft.



Should an area be required between two consecutive ordinates,
the Five, plus Eight, minus One Rule is used. Three ordinates are
required. Rule. To eight times the length of the middle ordinate
add five times the length of the other ordinate which bounds the required
area and from this sum deduct the length of the acquired ordinate which
lies outside the figure. The remainder multiplied by one-twelfth of
the common interval will give the area. Example : Suppose that in
Fig. 4 the area between numbers 4 and 5 ordinates is required :

No. of Length of

Ordinate Ordinates Multipliers Functions

5 ... 6-0 feet. ... 5 ... 30-0

4 74 8 59-2



8-5



89-2
8-5



80-7



Multiply by T V interval = 3-3 X iV =



275



Area = 22-19 sq.ft.



The Theory and Design of British Shipbuilding.



Six Ordinate Rule. If six ordinates are given, it will be seen
that neither Simpson's First nor Second Rules can be used. By
using the following multipliers : 1, 4, 2, 3f, 3, 1J, and the sum of
functions multiplied by one-third of the commom interval, the
area can be found. It is seldom, however, that six ordinates are
used in any calculation, but when such does occur, the above rule
is reliable.

Subdivision of Intervals is generally necessary in the case of
the curve being of a very sharp nature at any particular point.
For instance, in Fig. 5 the spacing of the ordinates between C and
E would give a quite satisfactory result ; but between C and A, where
there is a large amount of curvature, the result would not be so
accurate, and it is advisable in such a case to subdivide the intervals
as shown by x and y ordinates. The interval having been reduced

by one-half, it is there-
fore, necessary to re-
duce the multipliers by
the same amount.
From A to C the multi-
pliers will now become
i, 2, 1, 2, J, and then
commencing from C we
have 1, 4, 1. Adding
together the two multi-
pliers for C, we have
the new multipliers as
shown in Fig. 5.




B



SIMPSON'S MULTIPLIERS

Fig. 5.



In applying these rules to the form of a ship, with the ordinates
spaced longitudinally, it is usual to subdivide the end intervals
because of the rounding in of the vessel's form at these parts. In
Fig. 19 this will be seen in the sheer draught, where the first and
last two intervals are subdivided.

Volumes. By means of the same rules we can find the volumes
of curved bodies. Example : Let Fig. 6 represent a side coal bunker
of a vessel. Divide its longitudinal length up into a suitable number
of parts, say for Simpson's First Rule, as shown by the sections
1, 2, 3, 4, and 5. Find the area of each section by means of the
rules, as was previously done in the case of Fig. 4, and then put
these areas through the rule as follows :



The Theory and Design of British Shipbuilding.



No. of Section Area in Sq. Ft.


S.M.


Functions


1 ... 89-54


1


89-54


2 ... 95-25


4


381-00


3 ... 90-03


2


180-06


4 ... 81-25


4


325-00


5 ... 60-44


1


60-44


Sum


of functions


1,036-04


Multiply by*J of longitudinal interval = 9 X


i = 3



Volume = 3,108-12 cb. ft.



Fig. 6.




Having found the cubic capacity, the quantity in tons is easily
found by dividing the total number of cubic feet by the number
of cubic feet necessary to stow one ton of the coal that is to be put
into the bunker. Taking the coal at 45 cubic ft. per ton as stowed
in bunker, then 3,108-12 -i- 45 = 69 tons that can be stowed in
the above bunker.

Moments and Centres of Gravity. A Moment is a weight multiplied
by a distance for instance using the ton as the unit of weight
and the foot as the unit of distance, we have the moment given in
foot-tons. In Fig. 7 we have represented a bar 30 ft. long and a
weight of 50 tons suspended from the point D, therefore 50 tons
X 30 ft. = 1,500 foot-tons moment acting about the point A, from
which the distance is measured ; or if the 50 tons were suspended
at C we would have 50 tons X 20 ft. = 1,000 foot-tons moment.



The Theory and Design of British Shipbuilding.



(These simple examples of moments are introduced here so
that, in addition to the subject of Centre of Gravity, they may be
of use in aiding the description necessary when considering the
question of trim in later chapters, since the alteration of trim in
any vessel is directly dependent upon the amount of Moment obtained
by the weight multiplied by the distance it is moved in a fore and
aft direction.)




Fig. 7.

The distance which is generally termed lever, being reduced,
has a very obvious effect in the reduction of moment. We also see
that a small weight acting with a large leverage can have the came
effect as a larger weight and small leverage. For instance, in this
case, 50 tons at 30 ft. out, gives a moment of 1,500 foot-tons ; while
75 tons, at the point C, has a moment of exactly the same amount
75 tons x 20 ft. == 1,500 foot-tons moment,

To find the amount of weight necessary to be placed at the point
B so as to give the same amount as the 50 tons at D :

50 X 30 ""== 1,500 foot- tons moment with 50 tons at D ; 1.500
foot-tons -f- 10 ft. (the distance out to B) = 150 tons. Another
way to look at the question is as follows : In Fig. 8 we have a bar
supported at the point S, the overhang of one end being 10 ft. and
20 ft. the other, a weight of 60 tons being suspended from the short
end. What weight would require to be hung on the opposite end
to allow of the bar remaining horizontal ? Neglecting the weight
of the bar, we have : Moment for short end = 60 tons x 10 ft.
- 600 foot-tons, then 600 foot-tons 4- 20 ft, lever == 30 tons re-
quired.



10



The Theory and Design of British Shipbuilding.



Centre of Gravity of Weights. The Centre of gravity is the point
about which we Jmve the moments on either side balancing each other.

It will therefore be obvious that, in the case of Fig. 8 the centre
of gravity of the two weights lies upon the vertical line which passes
through the point S since the moments on each side of that line
are equal. In the case of a system of weights, the points at which
we imagine the total to be concentrated so as to produce the same
effect as the original distribution would be the centre of gravity.



Fig. 8.




IQ'-Q



20-0



In Fig'. 9 we have a system of weights, their quantities and dis-
position being shown. Find the centre of gravity relative to the
vertical XY :



Fig. 9.



Weight

5 Tons
20
10
15
10



Distance from XY

15 Feet
30
50
70
100



Moment

75 Foot-tons

600

500
1,050
1,000



60 Tons Total Weight. Total 3,225 Foot-tons.

X

^0 >S>*^ IQTU.J,-



10 lH -3 \3*

Fft M



']-"'



* 5 '_* 33 'J 5o J 7^>'>L JOO '_J

- ~ ^ - ^ ^t if - - jn



The Theory and Design of British Shipbuilding.



11




L



12 The Theory and Design of British Shipbuilding.

3,225 foot-tons total moment -f- 60 tons total weight == 53-75 ft.
from X Y, which is the position of the centre of gravity (C G),
Therefore, we see that if 60 tons were placed at 53-75 ft. from X Y,
we should have the same effect as is obtained by the distribution
shown in the figure. To take a more practical example : Let Fig.
10 represent the profile of a vessel, her holds being filled with cargo
of the amounts and positions of C G ; s as shown, also bunkers.
Find the position of the C G of cargo and bunkers, relative to 'mid-
ships. ('Midships is denoted in the sketch by C B P) :

Moments
Position Weight Lever from C B P Forward Aft

No. 1 hold 1,200 tons ;; 115 Ft. (forward) 138,000

No. 2 hold 1,800 tons ; 55 (forward 99,000

Bunkers 800 tons : 25 (forward) 20,000

No. 3 hold 1,300 tons x 75 (aft) 97,500

No. 4 hold 900 tons x 130 (aft) 117,000



Total Cargo 6,000 Forward 257,000 214,500

and Bunkers Aft 214,500



Difference = 42,500 = net

" Forward " Moment.

The forward moment being in excess, the C G will obviously lie
in that direction.

Net " forward " moment, 42,500 foot-tons -^ total cargo and
bunkers, 6,000 tons = 7-08 ft., which is the position of the C G
forward of 'midships.

Centres of Gravity of Areas of Curved Surfaces. The Centre
of Gravity of an Area having a curved boundary can be found
at the same time as the area is determined by the use of Simpson's
rules. If we go back to Fig. 4 and suppose that it is required to
find the position of its C G relative to the end ordinate No. 1, proceed
as follows :



The Theory and Design of British Shipbuilding. 13



No. of


Products for


Ordinate


Length


S.M.


Functions


Levers*


Moments


1 ...


10-0


... 1


10-0


... ...





2 ...


94


... 4


37-6


... 1 ...


37-6


3 ...


8-5


... 2


17-0


... 2 ...


34-0


4


7-4


... 4


29-6


... 3 ...


88-8


5 ...


6-0


... 1


6-0


... 4 ...


24-0



Function of j Function of) 184-4

. > 1UU*< ,...

Area \ Moment)

184-4 X common interval 3-3 ft. -f- 100-2 = 6-07 ft. = distance
of C G from No. 1 ordinate.

If the position of C G is required relative to the line A B, the
method is as shown in the following, where the rule is : Half of
of the sum of functions of " squares of ordinates " divided by the
sum of functions for area equals the position of C G from the base
line, from which the ordinates are measured.

In the case of the bunker (Fig. 4) we have :

No. of Square of Function of

Ordinate Length S.M. Functions Ordinates S.M. Squares

1 ... 10-0 ... 1 ... 10-0 ... 100-00 ... 1 ... 100-00

2 ... 9-4 ... 4 ... 37-6 ... 88-36 ... 4 ... 353-44

3 ... 8-5 ... 2 ... 17-0 ... 72-25 ... 2 ... 144-50

4 ... 7-4 ... 4 ... 29-6 ... 54-76 ... 4 ... 219-04

5 6-0 1 6-0 36-00 1 36-00



Function of Area = 100-2 Function for Moment = 852-98
852-98 x -f- 100-2 = 4-25 ft. = C G from A B.



* " Levers " represent the number of intervals from the given ordinate.
The actual distance from the given ordinate could be used by multiplying
the above number of intervals by their distance apart. The calculation is
simplified by not making this multiplication until the sum of products for
moments has been obtained, where the one multiplication serves the same
purpose.



14 The Theory and Design of British Shipbuilding.



CHAPTER II.

DISPLACEMENT DEFINED. CENTRE OF BUOYANCY DEFINED.
DEADWEIGHT AND DEADWEIGHT SCALE. COMPOSITION OF DEAD-
WEIGHT. TONS PEE, INCH. DIFFERENCE IN DRAUGHT.: SEA
AND RIVER WATER, THE BLOCK CO-EFFICIENT OF DISPLACEMENT.
CO-EFFICIENT OF MID-SHIP AREA. PRISMATIC CO-EFFICIENT.
CO-EFFICIENT OF WATER PLANE AREA. AVERAGE VALUES OF
O-EFFICIENTS IN VARIOUS TYPES. RELATION OF CO-EFFICIENTS

TO EACH OTHER.



Displacement. When a ship or any object is floating in water
a certain amount of water is displaced from its position and put to
one side. This amount of displaced water is obviously exactly
^qual in volume to the volume of the underwater portion of the
vessel. If the amount of displaced water is measured and expressed
either in volume or weight, we have what is known as displacement.
However, if, instead of measuring the amount of water displaced,
we measure the under water volume of the vessel to the outside
of the skin plating, we have a practicable means of finding the amount
of displacement. Suppose we have a graving dock filled with water
up to the quay level and then a vessel to be lowered in from above.
The result will, of course, be an overflowing of the water, the amount
of which will be the displacement of the vessel i.e., the amount of
water she has displaced. If the overflowing water were run off
into a reservoir we could measure its quantity and express the amount
either in volume or weight. The quantity of displaced water is de-


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