basic geometric concepts

J. Ray McDermott – Jebel Ali, Dubai

Basic Geometric Concepts

Page 2


Reference Planes


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


Lines Plan


Lines Plan

Profile or Sheer PlanShows the hull form intersected by a center planeThe 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 andcenterline plane.


Lines Plan


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.


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.


Moulded Dimensions

Moulded Excluding Plate Thickness


Moulded Dimensions

Moulded DraughtThe perpendicular distance in a transverse plane from the top of the flat keel to the waterline.

Moulded DepthThe perpendicular distance in a transverse plane from the top of the flat keel to the underside of deck plating at the ship’s side.


Moulded Dimensions


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.


Modes of Motion

Ship moving on a surface of a sea is almost always in Motion


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.


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


Modes of Motion

Heave : Oscillatory Motion Vertically Up and Down

Roll : Oscillatory Angular Motion about the longitudinal axis


Modes of Motion

Pitch : Oscillatory Angular Motion about the Transverse axis

Yaw : Angular Motion about the Vertical axis


Coefficients of Form

Coefficient of Fineness of Waterplane (CWP)Ratio of the Area of the Waterplane to the Area of its Circumscribing Rectangle.

BL

AC

WL

wWP =



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.

BT

AC M

M =



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.

PPB BTL

C∇

=


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.

∇=Δ ρρ

Displacement or Weight of Displaced fluid, denoted by

is the density of the fluid.


Weight of the Ship


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


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.

m

mxx

∑∑

=

Center of BuoyancyCentroid 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.


Center of Floatation, Metacenter

Center of FloatationThis point is the Centroid of Waterplane Area

Metacenter (M)


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 = Moment of Inertia of the Waterplane

Metacentric Height KGBMKBGM −+=∇

=I

BM


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

Our aim shall be to reduce the number of slack tanks (partially filled tanks)

gI

GMGMs

SFΔ

−= llρ


TRIM

TRIM is the difference in drafts Forward and Aft.

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

Angle of Trim,

Trim by Aft is preferred, which is Positive Trim. It shall be 0.5% - 1.0% of Length

FA TTTrim −=

L

TT FA −=θ

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