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pendent upon the weight of the vessel. When a vessel is floating in equili-
brium in still water she must displace an amount of water the weight of
which is equal to the weight of the vessel. We now, therefore, see that by
displacement is meant the amount of water displaced (or put to one
side) by a vessel, its amount being, in weight, exactly the same as
the total weight of the vessel, consequently the word " displace-
ment " is used to represent the total weight of a vessel. If we
say that a certain ship is 5,000 tons displacement, we mean that
her weight, including everything on board, is equal to that amount
It is usually expressed in tons, being, first of all, measured in cubic
feet, by calculations made from the drawing of the lines of the
vessel's underwater form. Salt water being taken at 64 Ibs. per
cubic foot, we have 2,240 -f- 64 = 35 cubic feet of salt water per

The Theory and Design of British Shipbuilding.

15

ton, therefore, by dividing the amount of cubic feet (as found by
the calculations) by 35, we have the vessel's displacement in tons.
Fresh water weighing 62J Ibs. per cubic foot, we have 2,240 -f- 62J
= 36 cubic feet per ton.

Methods of Calculating Displacement are mentioned in a follow-
ing chapter.

Centre of Buoyancy. Centre of Buoyancy is the centre of gravity
of the displacement of water i.e., the centre of gravity of the volume
occupied by the vessel's underwater portion, or we may say : " It is
the centre of gravity of the displaced water while in its original
position i.e., before the introduction of the vessel." To determine
the position of the Centre of Buoyancy of a ship, calculations are
made, like the displacement, from the drawings of the lines ; of
course, only dealing with the portion up to the water-line that the
vessel is floating at. Its position is given in two directions fore
and aft and vertically. The fore and aft position, which is spoken
of as the Longitudinal Centre of Buoyancy, is measured either from
the after perpendicular or from 'midships ; if the latter, the direction
must be stated, viz., forward or aft of 'midships. The vertical
position, spoken of as the Vertical Centre of Buoyancy, is measured

Fig. 11.

above the top of keel. In a following chapter the methods of obtain-
ing the positions in these two directions are mentioned. The position
of the C B must not be confused with the position of the vessel's
C G. They are totally different, the Centre of Buo} r ancy being
solely dependent upon the shape of the vessel's underwater portion,
while the Centre of Gravity is determined according to the dis-
tribution of the vessel's structure and the various weights thereon.
There is, however, a most important relation between the C B and
C G. The C B being the centre of the supporting buoyancy, and
the C G being the point through which the downward force of the

16

The Theory and Design of British Shipbuilding.

vessel's weight is acting, it will be obvious that for the vessel to be
at rest in still water the two forces should act in the same vertical
line i.e., the Centre of Buoyancy and the Centre of Gravity -should
lie on the same vertical line, thereby balancing each other. In
Fig. 11 we have shown the longitudinal position of the Centres of
Buoyancy and Gravity by B and G respectively, the direction of
the two forces being also shown. It will be seen that this is an
impossible condition for the vessel to be in, since the two forces
are not acting through the same point. The vessel must, there-
fore, adjust herself until G and B are vertically in line, as is shown
in Fig. 12. In Fig. 11 it is obvious that the tendency is for the
vessel to trim by the stern. In Fig. 12 this condition is shown.

Fig. 12.

This alteration in trim has caused the Centre of Buoyancy B to
shift aft, until it has become immediately below G, as is shown
by B i . The shift of B is obtained by the wedge of buoyancy W F
W\ being added by means of its immersion and the wedge L F L t
being deducted by means of its emersion. The displacement being
equal in both cases, the volumes of the wedges must therefore be
equal.

We now. therefore, see that for a vessel to be floating in equilibrium
in still water she must displace an amount of water, the weight of which
is equal to the weight of the vessel, and also that the Centre of Gravity
must lie in the same vertical line as the Centre of Buoyancy.

Deadweight. This is the amount of weight that can be put on
board a vessel in the shape of cargo, bunkers, stores, etc., after the
completion of the structure and fittings and with the propelling
machinery in steaming order. When completed in this condition,
which is known as the Light Draught, the displacement is deter-
mined and spoken of as the Lightweight. All weight put 011 board

The Theory and Design of British Shipbuilding. 17

of a vessel in excess of the lightweight is Deadweight. If the light-
weight of a vessel is 2,000 tons and then 4,500 tons of cargo, bunkers,
etc., are put on board, the displacement will then become 6,500
We therefore see that the amount of deadweight a vessel is able
to carry is the difference between the light and load displacements,
or at any intermediate draught, it is the difference between the
light displacement and the displacement at the particular draught.
Fig. 13 represents a Deadweight Scale such as is generally supplied
to a vessel by the builders. Upon it is shown a scale of draughts
ranging between the light and load condition, opposite which is
shown the corresponding amount of deadweight. In this case the
light draught is shown to be 7 ft. 3 in., and since this corresponds
to the lightweight, the deadweight will therefore be nil. The scale
of deadweight is shown by intervals of 100 tons, until 4,500 tons
is reached, at 19 ft. 6 in. draught, which is the maximum, and
corresponding to Lloyd's Summer Freeboard. From this dead-
any particular draught within the range of the light and load. For
instance, suppose it is required to know the amount of deadweight
on board the vessel when floating at draughts of 15 ft. 10 J in.
forward and 17 ft. 1-|- in. aft :

15 ft. lOf in. j . , .

* > = mean draught of 16 ft. 6 in.

Upon the deadweight scale, at the draught of 16 ft. 6 in. the amount
is read off as 3,350 tons.

Composition of Deadweight. The following are generally included
stores, fresh water, reserve feed water ; sometimes engine spare
gear and water in donkey boiler are also included.

Tons per Inch. The number of tons necessary to be placed on
board of a vessel so as to increase the mean draught to the extent
of 1 in., or to be taken out to thereby decrease the mean draught
by that amount, is known as the " tons per inch." If the draught
is increased or decreased 1 in., the added or deducted layer of dis-
placement is obviously equal in amount to the weight that is being
added or deducted from the vessel, seeing that the displacement
of the water must be equal to the total weight of the vessel. There-
fore, if at any draught we obtain the amount of displacement con-

18

The Theory and Design of British Shipbuilding.

tained in a layer 1 in. thick, we will have the amount of weight
corresponding to that layer. The tons per inch is found as follows :
Assume that a waterline, at half-depth of a layer 1 in. thick, has
an area which is a mean between the areas of the water- lines at the
top and bottom of the layer. For instance, if we have a layer
whose top water-line has an area of 6,000 sq. ft. and the bottom
water-line 5,980 sq. ft. then the water-line at half-depth of layer
is 6,000)

5,980 f

5,990 sq. ft., the mean between the top and bottom areas.
Fig. 13.

IS-9

IWr

Win

U4.

1L

6

^

W

saa.

iAaa.

3>o-.

3o

V)-5

T7

The Theory and Design of British Shipbuilding. 19

Now, by multiplying this mean water-line area by the depth of the
layer, we obviously obtain the volume, which, if divided by 35
(salt water), will give the amount of displacement of the layer in
tons, which, as stated above, is the " tons per inch." In the above-
mentioned case we would have.

5,990 sq. ft. x iV ft. = volume in cubic ft.

35

= A - X iV X A- = WIT = 14-26 tons per inch.

It will be seen that the " tons per inch" is equal to the area of the
water-line divided by (12 x 35) or 420. In the case of a ship we
have the areas of water-lines generally increasing as the draught
deepens, therefore causing the tons per inch to alter. The number
of tons necessary to increase or decrease the draught of a vessel
to the extent of 1 in. from any particular draught being often re-
quired, it is, therefore, extremely useful to have the variation of
tons per inch shown on the deadweight scale, as is shown in Fig. 13.

It may sometimes be necessary to approximate the tons per
inch of a vessel when the calculated figures are not available. When
such is required, the following formula may be used :

At the load draught : CD

In modern full formed cargo steamer 470 70

In vessels of medium form 530 77

In fine lined vessels 600 88

Difference in Draught Sea and River Water.
Salt water is taken at 64 Ibs. per cubic ft. =

2240

= 35 cubic ft. per ton.
64

Fresh water is taken at 62J Ibs. per cubic ft. =

2240

- 36 cubic ft. per ton.
62J

20 The Theory and Design of British Shipbuilding.

River water is usually taken at 63 Ibs. per cubic ft. = '

2240

- = 35-555 cubic ft. per ton.
63

When a vessel passes from salt to river water it is obvious that
she must sink lower in the water, seeing that one ton of her weight
will displace 35 cubic ft. of salt water, while, in river water, that
amount of weight will displace 35-555 cubic ft. Therefore, for
every ton of the vessel's weight we require -555 cubic ft. extra
volume of displacement when the vessel enters river water.

If W = the weight of the vessel in tons.

then W X -555 = the addition, in cubic feet, to the volume of
displacement when the vessel enters river water.

It is very often required to know what will be the sinkage of a
vessel on her leaving salt water and entering river water. In Fig.
14 we have represented the section of a vessel both in salt and river

it**

f-

Fig. 14.

water. It will be seen that when in river the draught has been
increased to the extent of S, the sinkage. S may also be termed
the thickness of the layer, W Wi L L\. The layer containing the
the required addition of volume in river water, it will be seen from
the above, has a volume in cubic feet of :

W x -555.

Having found the volume of the layer, we can now proceed to find
its depth, which is the amount of sinkage :

The Theory and Design of British Shipbuilding. 21

Volume of layer = W X -555 cubic ft.,

W x -555

therefore its displacement in salt water = - - tons.

35

The displacement- in tons of the layer, divided by the tons per inch,
will obviously give the thickness of the layer in inches. Let t = the
tons per inch in salt water at the water-line W L .

(The displacement of the layer having been taken in salt water,
the tons per inch must therefore be taken in salt water. Of course,
the displacement of the layer is really river water ; it could have
been taken as such, but, in that case, it would have been necessary
to use a river water tons per inch. It not being usual to calculate
the tons per inch for river water, we have taken the displacement
in salt water, and by using a salt water tons per inch we obtain the
same result as if we had dealt in river water.)

Displacement of layer -f- t == sinkage in inches.

i
W.X-S&S

^^~ : , * = sinkage in inches.
n

< W _ sinkage in inches when passing
63t from sea to river water.

While this simple formula is very useful, yet a shipmaster or officer
may be debarred from its use owing to their not being in possession
of the value of W, the displacement. The following is therefore
given so that approximations may be made when only the form of
the ship is known :

Draught -f- d = sinkage or rise in feet.
Values of d are given in above table.

The same formula is used when passing from river to sea water.
Knowing the vessel's displacement and the tons per inch, it will
therefore be a very simple thing for a ship's officer or any person
to estimate the amount of sinkage or rise, as the case may be. For
instance, suppose a certain vessel has to be loaded so that her
draught on entering sea water will be 19 ft. The vessel loading
in river, it will therefore be necessary to load her a little further
than the 19 ft. on account of her rising on entering the sea water.

22 The Theory and Design of British Shipbuilding.

The amount of extra immersion while in the river would be as
follows :

From the scale ascertain the amount of displacement in tons
(i.e., the deadweight plus the lightweight), also the tons per inch.

Referring to the scale in Fig. 13, we have at 19 ft. draught (salt
water

plus 2,000 lightweight,

= 6,310 ,, displacement,
tons per inch = 32.

Then, by using the formula, we have :

W 6,310

- = 3-13 in. of rise on the vessel entering salt
63t 63 X 32

water, therefore she may be loaded in the river down to a draught
of 19 ft. 3 in., say.

Co-efficients. The Co-efficient most commonly used is the Block
Co-efficient of displacement. This is the ratio that the actual dis-
placement of a vessel bears to the displacement of a block which has
the same length, breadth and draught as the vessel.

For instance, take a vessel 300 ft. long x 40 ft. breadth x 17 ft.
6 in draught. The displacement of a block having the same dimen-
sions would be :

300 ft. x 40 ft. x 17-5 ft. = 210,000 cubic ft.
or 210,000 -=- 35 (salt water) = 6,000 tons.

But suppose that, owing to the fineness of the ends, bilge, etc.,
the vessel has a displacement of only 4,500 tons.

The ratio that the vessel's actual displacement bears to the dis-

4,500

placement of the block is -75, which is the Co-efficent,

6,000

or, written in the usual way :

4,500 X 35

= .75.

300 ft. x 40 ft, x 17-5 ft.

The Theory and Design of British Shipbuilding.

23

Should the Co-efficient be known and the displacement be required :

300 ft. x 40 ft. x 17-5 ft.

X -75 = 4,500 tons.
35

It will be seen from the above that, by knowing a vessel's Block
Co-efficient, we are in a position to form an idea of the shape of her
underwater lines, to the extent of being able to say whether she
is oifull, fine, or medium form. For instance, a vessel whose Block
Co-efficient is -8 would be termed full, while -5 would be fine, and
65 medium.

'Midship Section Area Co-efficient. This is the ratio that the
immersed area of a vessel's 'midship section at any draught bears to
area of a rectangle whose breadth is equal to the breadth of the vessel
and its depth equal to the given draught. Fig. 15 represents the
'midship section of a vessel floating at the water-line W L.

^ i The draught

of the vessel is
17 ft. 6 in. T K,
f taken over the

j . . widest part of the

flj^ frame is 40 ft.

The area of the

c i r c u m scribing

rectangle is there -
- "- 1 fore, 40 X 17-5

Fig. 15. = 70 *1- ft '

i

f

Let the actual immersed area of the vessel's 'midship section be

665

665 sq. ft., then - = -95, which is the 'Midship Section Area
700

Co-efficient. Should the Co-efficient be known and the area be
required, 40 X 17-6 X -95 = 665 sq. ft.

Prismatic Co-efficient of Displacement. This is the ratio that
the actual displacement of a vessel bears to the displacement of a prism
whose length is equal to that of the vessel and the section of the same
shape as the 'midship section of the vessel. Fig. 16 shows such a

24 The Theory and Design of British Shipbuilding.

prism. This Co-efficient is found in a similar manner as the Block
Co-efficient.

Fig. 16.

area of mid. sect, x length
Displacement of prism in tons = -

35 (salt water).

665 x 300
Using the above figures we have - - = 5,700 tons, and

35

taking the actual displacement of the vessel at 4,500 tons, we have
4,500

- = -789 Prismatic Co-efficient, or, written in the usual way,
5,700

4,500 X 35

- = -789.
300 X 665

Co-efficient of Waterplane Area. This is the ratio that the actual
area of a vessel's waterplane bears to the area of a rectangle whose
length and breadth are equal to the length and breadth measured at the
widest portion of the waterplane.

Let Fig. 17 represent a waterplane of the vessel referred to
above, the actual area being 10 5 800 sq. ft. The area of the
circumscribing rectangle being 300 x 40 = 12,000 sq. ft., the

10,800
Co-efficient will therefore be - - = -9.

12,000

Soo'-o

VJir ^^JO^ I A?

Fig. 17.

The Theory and Design of British Shipbuilding.

25

The dimensions used in all cases are moulded i.e., length between
perpendiculars* breadth moulded, and the draught taken from the
top of keel. The displacement used is also moulded i.e., the dis-
placements of the shell plating, bar-keel, or any other appendages
are not included.

TABLE OF CO-EFFICIENTS GIVING THE AVERAGE FOR VARIOUS TYPES.

Type.

Fast Atlantic Liner
Cargo and Passenger,

Fast Cross -Channel

knots ...

10 knots
Small Carg
Coaster, ah
Screw Tug
Trawler
Herring
Sailing Vessel

knots ...
Steam Yacht, above 11

knots ...
Battleship
Cruiser
Torpedo Boat Destroyer

1

3

64

72
50

77

fi
67

75
54

79

2

a

95

96
92

98

82
71

84

Approximate
Dimensions

s f

10 sM

J*EH

S Q

70 ... 30

650 ...

520 ...
290 ...

480 ..

61 ... 27
36 ... 15

58

30

ts
,bout 8-J- knots
5

80 ...
77 ...
73 ...
52 ...

48 ...

81 ...
79 ...
77 ...
59 ...
68 ...

985...
98 ...
95 ...
88 ...
71 ...

87
85
83
73

70

... 350 ...
250
... 150 ...
... 130 ...
... 115 ...

48
37
25

27

99

... 24
17*
... 12
... 10
... 11

)rifter
jssel

43 ...
70 ..

61 ...
74 ...

70 ...
95 ...

64

80

... 80 ...
,. 265 ...

18

42

... 7
... 20

44

46
63
50
45

62

63
67
55
64

71

73

94
90
70

70
74
63

66

200

125
410
500
210

24 ... 11

20 9
77 ... 26i
71 ... 26'

21 . 8

Relation of Co-efficients to Each Order. The Block, Prismatic
and 'Midship Section Area Co-efficients are closely related to each
other, as is shown in the following, where it will be seen that, if any
two Co-efficients be known, the remaining one can be found :

Block Co-efL = Prismatic Co-eff. x Mid. Sec. Area Co-eff.

Pris. = Block

Mid. Sec.

Area Co-eff. = -f- Prismatic Co-efficient.

* In single-screw ships, where we have a propeller aperture, the length
for displacement is sometimes measured to the foreside of the aperture, as
shown by x y in Fig. 1. When the displacement length is taken to the per-
pendicular, in such ships it is very fairly assumed that the displacement of
the propeller and rudder counterbalances the effect of the aperture. Also,
by this method, the displacement of the hull above the aperture is taken
into account. In twin-screw ships the length taken is always the length
between perpendiculars. For Co -efficient purposes, however, the length
between perpendiculars is used in any case.

26 The Theory and Design of British Shipbuilding.

CHAPTER III.

ESTIMATE or REQUIRED AMOUNT OF DISPLACEMENT. DETER-
MINATION OF DIMENSIONS. REQUIRED LONGITUDINAL CENTRE
OF BUOYANCY AND TRIM. THE SHEER DRAUGHT. CONSTRUCTION
OF " LINES " TO FULFIL THE REQUIRED CONDITIONS. FINAL
" DISPLACEMENT SHEET " CALCULATIONS, INCLUDING LONGITUDINAL
AND VERTICAL CENTRES OF BUOYANCY, ETC. THE DISPLACEMENT
SCALE AND THE VARIOUS CURVES.

In the designing of a vessel the first step taken is to estimate the
required Amount of Displacement in the Load Condition. The
the light displacement or lightweight of the vessel, we therefore
see that, having given the deadweight, it remains for us to estimate
the vessel's lightweight, the sum of which two will then give the
load displacement required. First of all, an approximate estimate
is made for the proposed dimensions, and with these and a corres-
ponding approximate estimate of displacement the block co-
efficient is determined. This preliminary determination is merely
to ascertain if the resultant block co-efficient is one which is suitable
for the vessel's required speed. It is fairly obvious that a fast
vessel requires a finer co -efficient than a slow vessel. In high speed
ships, where the wave-making resistance forms a large proportion
of the total, it is imperative that the ends should be finely shaped
so as to minimise the wave-making. The following formula is
most useful in obtaining a suitable block co-efficient for ordinary
vessels with a given speed :

speed in knots
1-06

2 x A/length.

Should the preliminary co-efficient appear to be too full, the
dimensions must necessarily be increased, or, if it is on the fine
side, we can afford to decrease them.

The Theory and Design of British Shipbuilding. 27

We now have a basis to work upon, from which the actual design
can be determined. These proposed dimensions must now be con-
sidered from an economical point of view. In the various laws
and rules which apply to ships, grades occur where changes in the
stipulations take place. These grades being dependent upon the
vessel's dimensions, it is therefore necessary to ascertain in what
position the proposed dimensions will place the vessel. Should it
happen that she is just over a grade, it will generally be an advantage
from an economical point of view, to make slight reductions in
the proposed dimensions. (There are rare cases, however, where
even a lighter and cheaper vessel can be built through the means
of making the vessel on the high side of a grade.) By means of
careful work, in this way it is possible to obtain a design in which
the cost per ton of deadweight comes out at a low figure compared
to one where the dimensions are fixed at random. Such a carefully
designed vessel is also one in which the cost of maintainence and
working expenses are low. Therefore, an owner, or some person
on his behalf, thoroughly versed in all the intricate branches of
ship design work, should carefully make all the necessary delicate
investigations before making the final decision a decision upon
which depends not only the first cost, but the all-important paying
capabilities of the vessel. Not only should the proposed vessel
be considered from the cutting down point of view, but also from
that of ascertaining what will be the resulting effect if additions
are made. For instance, the author has known cases where, if a
few feet had been added to the length of the vessel's bridgehouse,
poop or forecastle, the draught would have been increased to the
weight at the expense of about 25, or the exceedingly low rate
This great advantage would have been due to a change taking
place in the freeboard rules, the addition in length of the erections
enabling the vessel to obtain the benefit of another rule. There
are many things to take note of at this stage. For example, the
length. In the calculation for tonnage the number of intervals
taken, is governed by the vessel's length at various grades. It
may be possible, by means of a slight deduction, to reduce the
number of intervals by two, which would, in most cases, tend to
reduce the vessel's tonnage. This reduction may not appear to
be much, but still it has effect throughout the vessel's existence,
and in the shape of working expenses amounts in the end, or per

28 The Theory and Design of British Shipbuilding.

annum, to a fairly large sum in favour of the owner. Again, perhaps
it would be easily possible to avoid some heavy additional scantling
required by the rules of registry to which the vessel is built. In
the case of the breadth, we have it governing the number of rows
of hold pillars and the size of the beams, therefore it should again
be ascertained that we are not just over a grade. Depth also has

Online LibraryAmos Lowrey AyreThe theory and design of British shipbuilding → online text (page 2 of 14)