This document discusses basic geometric concepts and properties related to ship design and stability. It defines key reference planes and dimensions used in ship plans. Reference planes include the waterline, centerline, and perpendiculars. Dimensions include length, breadth, draft, depth and volume. Ship motions such as surge, sway, heave, roll, pitch and yaw are also defined. The document then discusses coefficients of form, displacement, weight, buoyancy, centers of gravity/buoyancy/floatation, metacenters, and how these factors influence a ship's stability. Free surface effect on partially-filled tanks is also mentioned.

1. Basic Geometric Concepts
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Reference Planes
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2. Ship Geometry
Lines Plan or Lines
The exterior form of a ships’ hull is a curved surface is
defined by the lines drawing
3 Dimensions 2 Dimensions
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Lines Plan
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3. Lines Plan
Profile or Sheer Plan
Shows the hull form intersected by a center plane
The convention is that the propeller is drawn at the left side of
the page
Half Breadth Plan
Shows the intersection of the hull form with planes parallel to the
horizontal base plane All such parallel planes are called
Waterline planes, or Waterplanes
Body Plan
Shows the shape of the sections determined by the intersection
of the hull form with planes perpendicular to the waterplane and
centerline plane.
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Lines Plan
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4. Lines Plan
Forward Perpendicular (FP)
A reference point at the forward end of the ship is provided by
the intersection of the load waterline and the bow contour,
and the line perpendicular to the LWL through this point is
called the forward perpendicular.
After Perpendicular (AP)
Line perpendicular to LWL through the point of intersection of
LWL and stern contour is AP. When there is a rudder post,
the AP is located where the after side of the rudder post
intersects the LWL.
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Lines Plan
Length between Perpendiculars (LBP or LPP)
The distance between Forward and After perpendiculars is
called the Length Between Perpendiculars.
The distance between perpendiculars is divided into a
convenient number of equal spaces, often twenty, to give,
including the FP and the AP, twenty-one evenly spaced
ordinates. These ordinates are referred as Stations.
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5. Moulded Dimensions
Moulded Excluding Plate Thickness
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Moulded Dimensions
Moulded Draught
The perpendicular distance in a transverse plane from the top
of the flat keel to the waterline.
Moulded Depth
The perpendicular distance in a transverse plane from the top
of the flat keel to the underside of deck plating at the ship’s
side.
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6. Moulded Dimensions
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Volume of Displacement
Denoted by (∇)
Total volume of fluid displaced by the ship.
Best conceived by imagining the fluid to be wax and the
ship removed from it; it is then the volume of the
impression left by the hull.
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7. Modes of Motion
Ship moving on a surface of a sea is almost always in
Motion
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Modes of Motion
X axis (denoted by Xb)
Passes through the centerline of the ship, positive towards
the bow.
Y axis (denoted by Yb)
Passes through the midship of the ship, positive towards the
port side.
Z axis (denoted by Zb)
Passes through the intersection of x and y axis, positive
upwards.
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8. Modes of Motion
Surge : Linear motion in the X direction, motion backwards and
forwards in the direction of ship travel
Sway : Linear motion in the Y direction
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Modes of Motion
Heave : Oscillatory Motion Vertically Up and Down
Roll : Oscillatory Angular Motion about the longitudinal axis
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9. Modes of Motion
Pitch : Oscillatory Angular Motion about the Transverse axis
Yaw : Angular Motion about the Vertical axis
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Coefficients of Form
Coefficient of Fineness of Waterplane (CWP)
Ratio of the Area of the Waterplane to the Area of
its Circumscribing Rectangle.
Aw
CWP =
LWL B
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10. Coefficients of Form
Midship Section Coefficient (CM)
Ratio of the Midship Section Area to the Area of a
Rectangle whose sides are equal to the draught and the
breadth extreme.
AM
CM =
BT
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Coefficients of Form
Block Coefficient (CB)
Ratio of the Volume of Displacement to the Volume of
a Rectangular Block whose sides are equal to the
breadth extreme, the mean draught and the length
between perpendiculars.
∇
CB =
BTL PP
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11. Displacement and Weight
Archimedes Principle (Law of Buoyancy)
The fundamental physical law controlling the static behavior of
a body wholly or partially immersed in a fluid.
By Archimedes principle the weight of displaced fluid is equal
to the weight of the ship and its contents.
Displacement or Weight of Displaced fluid, denoted by Δ = ρ∇
ρ is the density of the fluid.
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Weight of the Ship
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12. Reserve of Buoyancy
Reserve of Buoyancy:
The watertight volume of the ship above the waterline is
called the Reserve of Buoyancy. It is the measure of ship’s
ability to withstand the effects of flooding
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Center of Gravity, Buoyancy
Center of Gravity
Point through which the resultant of the system of parallel forces formed
by the weights of all the particles of body passes, for all positions of the
body. A given body has a definite Center of Gravity. ∑ mx
x=
∑m
Center of Buoyancy
Centroid of the underwater portion is called the Center of Buoyancy.
Vertical Center of Buoyancy (VCB)
This is the distance from the Keel to the Center of Buoyancy,
also denoted by KB.
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13. Center of Floatation, Metacenter
Center of Floatation
This point is the Centroid of Waterplane Area
Metacenter (M)
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Geometric Properties
Metacentric Height (GM)
Distance between the Center of Gravity and Metacenter.
Factor deciding Stability of the Ship / Barge
Metacentric Radius (BM)
Distance between Center of Buoyancy and Metacenter.
I I = Moment of Inertia of the Waterplane
BM =
∇
Metacentric Height GM = KB +BM − KG
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14. Free Surface Effect
When a barge with partially filled tanks heels over, contents
will shift.
This results in shifting of center of gravity, making vessel less
stable
Reduction is Stability can be equated to reduction in GM
ρl I l
GM F = GM S − g
Δs
Our aim shall be to reduce the number of slack tanks
(partially filled tanks)
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TRIM
TRIM is the difference in drafts Forward and Aft.
Trim = TA − TF
TA is Draft Aft and TF is Draft Fwd.
An excess draft aft is called Trim by Stern, while an excess forward is
called Trim by Bow
T A − TF
Angle of Trim, θ=
L
Trim by Aft is preferred, which is Positive Trim. It shall be 0.5% - 1.0%
of Length
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