This chapter introduces key concepts in hull geometry needed for naval architecture. It discusses how a ship's complicated 3D hull shape is represented graphically through lines drawings, including body, half-breadth, and sheer plans. The chapter also covers how lines plans are converted into numerical tables of offsets and defines important hull geometry terms like length between perpendiculars, block and prismatic coefficients, and rise of floor. Mastering the representation and terminology of hull geometry forms a crucial foundation for further naval architecture studies.

1. LNB 20303
Naval Architecture 1
CHAPTER 2: HULL GEOMETRY
Prepared by: Muhammad Nasuha Mansor
Hull Form
The way to represent hull form?
The Lines Plan
What is lines plan???
1

2. •A
ship's hull is a very complicated 3 dimensional
shape.
•The ship's hull form is represented graphically by a
lines drawing.
•The lines drawing consist of projections of the
intersection of the hull with a series of planes.
•Planes in one dimension will be perpendicular to
planes in the other two dimensions.
•these series of planes are p j
p
projected to represent views
p
from the front, top, or side of the ship.
•This three separate projections, or views, called the
Body Plan, the Half-Breadth Plan, and the Sheer plan,
The Projection of Lines onto 3 Orthogonal Planes
2

3. The Half-Breadth Plan
The Profile Plan
3

4. The Body Plan
Example 1: Lines Plan of the USNA Yard Patrol
Craft
4

5. Example 2: Lines plan
5

6. Example 3: Lines plan
6

7. Table of Offsets
To calculate geometric characteristics of the hull using
numerical techniques, the information on the lines plan
drawing is converted to a numerical representation in a
table called the table of offsets.
It is a digital description of the entire hull (hull form
representation in coordination form)
The table of offsets lists the distance from the center plane
to the outline of the hull at each station and waterline. This
distance is called the “offset” or “h lf b dth di t
di t
i
ll d th “ ff t” “half-breadth distance”. B
” By
convention this is the “y” direction.
It is needed during the calculation of geometric properties of
the hull such as sectional area, waterplane area,
submerged volume and the longitudinal center of flotation.
Example 1: Table of Offsets of the USNA Yard Patrol Craft
7

8. Example 2: Table of Offsets
TABLE OF OFFSETS (HALF BREADTH) in metres
Waterline Name and Distance from Baseline in metres
Station Name and Distance from Station 0 in metres
D
BASELINE
TRSM
AP
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
5.0
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
FP
WL 0.5m
WL 1.0m
WL 2.0m
0.25
0.25
0.25
0.25
0.25
0.25
0.27
0.27
0.27
0.27
0.27
0.93
2.09
2.90
2.43
2.04
1.59
1.14
0.74
0.37
0.27
0.27
0.27
0.27
3.20
3.83
4.06
4.04
3.51
3.09
2.57
1.99
1.42
0.86
0.38
0.29
0.29
2.54
4.24
4.43
4.49
4.50
4.50
4.50
4.16
3.85
3.44
2.92
2.31
1.65
0.96
0.31
-3.50
0.00
.14
2.28
3.41
4.55
5.69
6.83
7.96
9.10
11.38
13.65
14.79
15.93
17.06
18.20
19.34
20.48
21.61
22.75
WL 3.0m
3.09
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.37
4.20
3.92
3.52
2.98
2.33
1.58
0.77
0.00
WL 4.0m
3.09
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.50
4.47
4.42
4.29
4.03
3.64
3.09
2.37
1.51
0.33
WL 5.0m
3.09
4.50
4.50
4.48
4.46
4.45
4.43
4.42
4.41
4.41
4.40
4.46
4.50
4.48
4.45
4.37
4.11
3.57
2.70
1.39
Example 3: Table of Offsets
T A B L E O F O F F S E T S (H A L F B R E A D T H) i n m e t r e s
Waterline Name and Distance from Baseline in metres
Station Name and Distance from Station 0 in metres
D
BASELINE WL 0.25m
TRSM
AP
2.0
4.0
6.0
8.0
10.0
12.0
BP
14.0
15.0
16.0
17.0
18.0
19.0
20.0
20 0
21.0
22.0
23.0
24.0
24.5
25.0
FP
26.0
26.5
27.0
-1.20
0.00
2.40
4.80
7.20
9.60
12.00
14.40
15.40
16.80
18.00
19.20
20.40
21.60
22.80
24.00
24 00
25.20
26.40
27.60
28.80
29.40
30.00
30.80
31.20
31.80
32.40
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0 00
0.00
0.00
0.00
0.00
0.20
0.53
0.79
0.88
0.86
0.83
0.79
0.76
0.71
0.67
0.62
0.55
0 55
0.48
0.39
0.31
0.21
0.07
WL 0.50m
0.08
0.31
0.78
1.12
1.38
1.59
1.75
1.76
1.72
1.66
1.59
1.51
1.43
1.33
1.24
1.10
1 10
0.95
0.79
0.62
0.43
0.27
0.03
WL 0.75m
2.08
2.17
2.34
2.47
2.57
2.65
2.70
2.65
2.59
2.49
2.38
2.27
2.14
2.00
1.86
1.66
1 66
1.43
1.18
0.94
0.66
0.47
0.20
WL 1.00m
3.42
3.42
3.42
3.42
3.42
3.42
3.42
3.41
3.41
3.40
3.18
3.02
2.85
2.67
2.48
2.21
2 21
1.90
1.57
1.25
0.89
0.67
0.37
WL 1.25m
3.47
3.47
3.47
3.47
3.46
3.46
3.46
3.46
3.45
3.44
3.44
3.43
3.41
3.37
3.10
2.76
2 76
2.38
1.97
1.56
1.13
0.87
0.55
0.00
WL 1.50m
3.52
3.52
3.52
3.51
3.51
3.51
3.50
3.50
3.49
3.49
3.48
3.47
3.45
3.42
3.36
3.25
3 25
2.85
2.36
1.88
1.36
1.08
0.73
0.15
WL 2.00m
3.62
3.62
3.61
3.61
3.60
3.60
3.59
3.58
3.58
3.57
3.57
3.56
3.54
3.51
3.47
3.38
3 38
3.21
2.93
2.52
1.97
1.49
1.09
0.48
0.13
WL 2.50m
3.72
3.72
3.71
3.70
3.69
3.68
3.68
3.67
3.66
3.66
3.65
3.64
3.63
3.61
3.58
3.52
3 52
3.40
3.20
2.88
2.40
2.07
1.67
1.02
0.63
WL 3.00m
3.79
3.78
3.77
3.76
3.75
3.75
3.74
3.74
3.73
3.72
3.71
3.69
3.66
3 66
3.59
3.47
3.24
2.83
2.55
2.20
1.64
1.29
0.69
WL 3.50m
WL 4.00m
3.80
3.80
3.80
3.80
3 80
3.78
3.74
3.59
3.26
3.03
2.74
2.26
1.96
1.42
0.38
3.80
3.80
3.80
3.80
3 80
3.80
3.78
3.69
3.43
3.25
3.02
2.66
2.41
2.00
1.36
8

9. Hull Geometry
Forward Perpendicular (FP): A perpendicular the point where
the foreside of the stem meets the summer load line.
After Perpendicular (AP): A perpendicular drawn at the point
where the aft side of the rudder post meets the summer load
line. Where no rudder post is fitted it is taken as the centre line
of the rudder stock.
Length Between Perpendiculars (LBP): The length between the
forward and aft perpendiculars measured along the summer
g
load line.
Amidships: A point midway between the after and forward
perpendiculars.
Length Overall (LOA): Length of vessel taken over all
extremities.
9

10. Moulded dimensions are often referred to; these are
taken to the inside of plating on a steel ship.
10

11. Base Line: A horizontal line drawn at the top of the keel
plate.
plate All vertical moulded dimensions are measured
relative to this line.
Moulded Beam: Measured at the midship section is the
maximum moulded breadth of the ship.
Moulded Draft: Measured from the base line to the
summer load line at the midship section.
Moulded Depth: Measured from the base line to the heel
of the upper deck beam at the ship’s side amidships.
Extreme Beam: The maximum beam taken over all
extremities.
extremities
Extreme Draft: Taken from the lowest point of keel to the
summer load line. Draft marks represent extreme drafts.
Extreme Depth: Depth of vessel at ship’s side from
upper deck to lowest point of keel.
Half Breadth: Since a ship’s hull is symmetrical about the
longitudinal centre line, often only the half beam or half
breadth at any section is given.
11

12. Freeboard: The difference between the depth at side
and the draught It is vertical distance from the waterline
draught.
to the upperside of the deck plating at side
Sheer: Tendency of a deck to rise above the horizontal
in profile.
Camber (or Round of Beam): Curvature of decks in the
transverse direction. Measured as the height of deck at
centre above th h i ht of d k at side.
t
b
the height f deck t id
Rise of Floor (or Deadrise): The rise of the bottom shell
plating line above the base line. This rise is measured at
the line of moulded beam.
Tumblehome: The inward curvature towards the middle
line (centerline) of the side shell above the waterline
Flare: Th outward curvature t
Fl
The t
d
t
towards th midle li
d the idl line
(centerline)of the side shell above the waterline. It
promotes dryness and is therefore associated with the
fore end of ship.
Stem Rake: Inclination of the stem line from the vertical.
12

13. Last but not least, in the hull geometry definition, there
a e certain coefficients, called
are ce a coe c e s, ca ed as form coe c e s
o coefficients
Non- dimensional
They will later used as the values as guide to describe
the fatness of slimness of the hull, especially below the
waterline.
4 basic form coefficients are:
1.Bl
Block coefficient, Cb
k
ffi i t Cb.
2.Midship coefficient, Cm.
3.Waterplane area coefficient, Cwp
4.Prismatic coefficient, Cp
1.
Block coefficient, Cb
Gives the ratio of the volume of the underwater body (∇)
and the rectangular block bounded by length (Lpp)
(Lpp),
breadth (B), and draught (T).
A vessel with a small Cb is referred to as ‘fine’ (fast
ships).
Customary values for the Cb of several types of vessel:
Type
Cb
Form
Very fast ship
0.50 - 0.65
Fine
Ordinary cargo ship
0.65 – 0.75
Moderate
Slow bulk carrier
0.75 – 0.90
Full
13

14. 1.
Midship coefficient, Cm
Ratio of the immersed midship section area (Am) to the
area of the rectangular having th same b dth and
f th
t
l h i the
breadth d
draught of the ship.
0.85 fast ship, 0.99 slow ship
14

15. 1.
Waterplane coefficient, Cwp
The ratio of the area of the waterplane area to the area
of the rectangular having a length (L) and a breadth (B)
equal to the ship moulded breadth.
1.
Prismatic coefficient, Cp
The ratio of the volume of displacement to the volume of
prism (
i
(equal t th l
l to the length b t
th between perpendiculars , L
di l
Lpp
multiply with a cross- sectional area of the midship, Am
Approximate range of values: 0.55 fine ship, 0.85 full
ship.
15

16. SUMMARY
As groundwork, knowledge of Naval Architecture can be started with
the familiarization of types of floating objects and ships and how they are
categorized. Insightful of this part could bring better perspective in going deeper
about Naval Architecture study. At the same time terminologies and geometries
of the typical ship, progressively can b di
f th t i l hi
i l
be digested.
t d
Types of floating objects and ships basically are categorized in several
ways. It can be possibly classed base on the functions, and some references
clustered the types of ship according to their means of physical support while
in operation. Three broad classifications that are frequently used by naval
architects are aerostatic support, hydrodynamic support and hydrostatic
support.
Definitely with the well briefed of basic terminologies and geometries
of the ship will be helpful for learner to further explore about the naval
architecture. The earliest drawing in this study that should be discussed is called
a lines plan drawing. A ship's hull basically is a very complicated 3 dimensional
shape. The lines plan graphically represents this hull form in scaled 2D view.
The drawing usually displays information in three reference planes. These
series of planes are projected to represent views from the front, top, or side of
the ship.
In marine terminology, it is called the Body Plan, the Half-Breadth
Plan, and the Sheer plan (sometimes known as Profile plan). The basic
lines plan consists of three (3) reference lines drawn in each of those views.
They are station lines, buttock lines and waterlines. Besides, lines plan
drawing should also include principle dimensions of that particular ship. This
basically describes a size of the ship in term of length, breadth, height and many
more.
This lines plan drawing can also be interpreted into numerical
presentation. It is called a table of offsets. Table of offsets is a digital
description of the entire hull form, represents in coordinates form. It is needed
in order to calculate geometrics of the hull using numerical techniques,
which mainly a part of the naval architecture works.
The completed lines plan drawing and table of offsets basically will be
the main input to proceed with the next stage. Hydrostatics calculation is one of
the earliest parts in naval architecture study, and can be determined right after
the lines plan and table of offsets are generated.
16