Geometry

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GEOMETRY OF THE SHIP
AND DEFINITIONS
Prepared By : A.CHANDA,
IMU Kolkata

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THE LINES PLAN
• A SHIP HULL IS A THREE DIMENSIONAL OBJECT
• IN MOST CASES IT IS SYMMETRICAL ABOUT THE FORE
AND AFT PLANE
• THE THREE DIMENSIONAL OBJECT HAS TO BE
DEPICATED ON A PIECE OF PAPER (IE, IN TWO
DIMENSIONS)
• THE TECHNIQUE USED IS THE LINES PLAN
• THE HULL IS REPRESENTED BY ITS INTERSECTION WITH
THREE SETS OF MUTUALLY ORTHOGONAL PLANES.

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THE LINES PLAN CONTD.
• THE HORIZONTAL PLANES ARE KNOWN AS WATERPLANES, AND
THE LINES OF INTERSECTION WITH THE HULL ARE KNOWN AS
WATERLINES . (VISIBLE IN THE HALF BREADTH PLAN)
• THE PLANES PARALLEL TO THE MID-LINE PLANE CUT THE HULL IN
BUTTOCKS AND BOWS. (VISIBLE IN THE PROFILE)
• MIDDLE LINE PLANE’S INTERSECTION WITH THE HULL IS KNOWN
AS THE PROFILE. (VISIBLE IN THE PROFILE)
• THE INTERSECTION OF THE ATHWARTSHIP PLANES WITH THE HULL
DEFINE THE TRANSVERSE SECTIONS. (VISIBLE IN THE BODY PLAN)

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THE LINES PLAN CONTD.

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LINES PLAN OF A SMALL FISHING BOAT

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THE LINES PLAN CONTD.

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THE LINES PLAN CONTD.
• THE AFT PERPENDICULAR IS THE VERTICAL
LINE THROUGH THE C.L. OF THE RUDDER
STOCK.
• THE FORWARD PERPENDICULAR IS THE
VERTICAL LINE THROUGH THE INTERSECTION
OF THE STEM WITH THE SUMMER LOAD
WATERLINE.

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BREADTH MEASUREMENTS

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CAMBER, RISE OF FLOOR AND TUMBLEHOME

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VARIOUS MEASUREMENTS OF THE HULL
• LENGTH OVER ALL
• LENGTH WATERLINE
• LENGTH BETWEEN PERPENDICULARS
• BREADTH EXTREME
• BREADTH MOULDED
• DEPTH AMIDSHIPS
• DEPTH MOULDED

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VARIOUS MEASUREMENTS EXPLAINED
• SHEER IS THE MEASURE OF HOW MUCH THE
DECK RISES TOWARDS THE STEM AND STERN.
• CAMBER IS DEFINED AS THE RISE OF THE DECK
IN GOING FROM THE SIDE TO THE CENTRE

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DISPLACEMENT AND DEADWEIGHT
• DISPLACEMENT IS THE WEIGHT OF THE WATER DISPLACED BY
THE SHIP WHICH IS EQUAL TO THE TOTAL WEIGHT OF THE SHIP
(GENERALLY EXPRESSED IN TONNES).
• DISPLACEMENT = LIGHTSHIP WEIGHT + DEADWEIGHT
• DEADWEIGHT = CARGO + FUEL OIL + FRESH WATER + LUB OIL +
STORES + WATER BALLAST + CREW AND EFFECT.
• LIGHTSHIP WEIGHT = WEIGHT OF THE SHIP INCL. HULL,
MACHINERY, OUTFIT, ELECTRICAL ETC.

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DISTRIBUTION OF DEADWEIGHT ITEMS LIKE FW, FO, LO, AV etc IN THE
TANKS

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COEFFICIENTS OF FORM
• BLOCK COEFFICIENT CB = V/ L . B. T
• V = Volumetric Displacement (M3)
• L = Length Between Perpendiculars (M)
• B= Breadth at Waterline (M)
• T= Mean Draught (M)

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BLOCK CO EFFICIENT

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TYPICAL BLOCK COEFFICIENT VALUES

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COEFFICIENTS OF FORM
• Waterplane Co efficient C WP = AWP /L.B
• AWP = Waterplane Area in M^2
• L = Length between Perpendiculars (M)
• B = Breadth at Waterplane (M)

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WATERPLANE AREA CO EFFICIENT

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COEFFICIENTS OF FORM
• Midship Area Coefficient = AM / B.T
• AM = Midship Section Area (M^2)
• B = Breadth at Waterline (M)
• T= Draught Mean (M)

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MIDSHIP AREA CO EFFICIENT

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COEFFICIENTS OF FORM
• Longitudinal Prismatic Coefficient =V/AM .L
• V = Volumetric Displacement (M^3)
• AM = Midship Section Area (M^2)
• L = Length Between Perpendiculars (M)

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COEFFICIENTS OF FORM
• Vertical Prismatic Coefficient = V/Aw. T
• V = Volumetric Displacement (M^3)
• Aw = WaterPlane Area (M^2)
• T = Draught Mean (M)

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GROSS TONNAGE AND NET TONNAGE
• THE INTERNATIONAL CONVENTION ON TONNAGE
MEASUREMENT OF SHIPS WAS ADOPTED IN 1969
• THE CONVENTION WAS HELD UNDER THE AUSPICES OF THE
INTERNATIONAL MARITIME ORGANISATION (IMO) TO
PRODUCE A UNIVERSALLY RECOGNISED SYSTEM FOR
TONNAGE MEASUREMENT.
• GROSS TONNAGE IS BASED ON TOTAL VOLUME OF ENCLOSED
SPACES IN THE SHIP.
• NET TONNAGE IS BASED ON TOTAL VOLUME OF CARGO
SPACES AND TOTAL VOLUME OF PASSENGER SPACES.
• MINIMUM NT = O.30 GT

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SPECIAL TONNAGE RULES
• SPECIAL TONNAGE RULES ARE APPLICABLE FOR SHIPS
PASSING THE SUEZ CANAL AND THE PANAMA CANAL.
• THESE RULES ARE FRAMED BY THE SUEZ CANAL AND THE
PANAMA CANAL AUTHORITIES RESPECTIVELY
• CHARGES FOR THE USE OF THE CANAL ARE BASED ON THESE
MEASUREMENTS.
• IN CASE OF ENTRY TO ANY PORT OR HARBOUR THE
INTERNATIONAL TONNAGE RULES 1969 ARE APPLICABLE AND
CHARGES ARE LEVIED BASED ON THESE MEASUREMENTS.

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NUMERICAL PROBLEMS

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MORE NUMERICAL PROBLEMS
• A Ship 64 m long, 10 m maximum beam, has a light draught of 1.5m and a
loaded draught of 4 m. The Block Co-eff is 0.6 at the light draught and 0.75
at the loaded draught. Find the deadweight.
• Solution : Light Disp = L x B x Draught X Cb M3 = 64 x10 x 1.5 x 0.6 =
576 m3
• Loaded Disp = L x B x Draught X Cb M3 = 64 x10 x 4 x 0.75 =
1920 M3
• Deadweight = Loaded Disp – Light Disp = 1920 – 576 = 1344 m3
• If the data is for Fresh Water Then Dwt = 1344 x1 = 1344 Tonnes
• If the data is for Sea Water Then Dwt = 1344 x1.025 = 1377.6 Tonnes

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