Ship-Calculations Ver 0.98

Kalyan Chatterjea, Sep 14, 2015

[color=#1551b5]These tutorials could be used in a beginner's course on Ship Stability, developed at <a href="http://wavelinklms.edu.sg">Wavelink Maritime Institute, Singapore</a> . The material is based on the well-known text book - Reeds Vol 13: Ship Stability, Powering and Resistance (Reed's Marine Engineering and Technology), 2014 [Christopher Patterson, Jonathan Ridley]. It is hoped that these calculation-examples using GeoGebra will reduce the calculation load for the students and help them explore various what-if situations easily. If you have any comments on these calculations, please email to Kalyan.Chatterjea@gmail.comhere[/color] [b]Vessel's Specifications:[/b] LBP - 100 m Lightship Information: Δ - 2615 tonnes KG - 7 m TCG - 0 m LCG - 44 m FOAP (Ford of After Perpendicular) Tropical Δ - 7530.9 tonnes Summer Δ - 7329.0 tonnes Winter Δ - 7129.4 tonnes Tropical FWA - 135 mm Summer FWA - 133 mm Winter FWA - 131 mm Tropical draught - 7.146 m Summer draught - 7.000 m Winter draught - 6.854 m

Table of Contents

  1. Numerical Methods
    1. Area Calculation by Simpson's 1st Rule
    2. X-Y plotting, curve-fitting and area under the curve example
    3. Area Calculation using a 4th Degree Function
    4. Waterplane area & its centroid calculation - Simpson's Rule
    5. Volume & Centroid of Volume Calculation - Simpson's Rule
    6. Volume & Centroid of Volume Calculation II - Simpson's Rule
    7. Volume & Centroid Calculations with Appendage
    8. Second Moment of Area for a Ship's Waterplane
  2. CG Change - Mass Addition Removal & Shift
    1. Effect in KG when New Cargo Loaded on CL
    2. Effect in KG when Cargo Removed from CL
    3. Example of Mass Change in Practice
  3. Hydrostatic Data from MV Reed
    1. Hydrostatic_Property-01-Draught_Displacement
    2. Hydrostatics-01a-Displacement_Draught
    3. Hydrostatic_Property-02-Draught_LCB
    4. Hydrostatic_Property-03-Draught_LCF
    5. Hydrostatic_Property-04-Draught_KB
    6. Hydrostatic-Property_05-Draught_KM
    7. Hydrostatics_Properties-06_Draught-TPC
    8. Hydrostatic_Property-07-Draught_MCTC
  4. Initial Stability
    1. Calculation on Initial GM
    2. Effect of TCG Changes on List of Vessel
    3. Initial Stability - Effect of Changing Draught KG n Breadth
    4. Adding Cargo/Ballast to Correct List
  5. Large Angle Stability
    1. Exercise on Large-Angle Stability
    2. KN-GZ Curve

1.

Numerical Methods

Ship's curves are not regular and numerical methods are used to facilitation calculations of areas, volumes and their first & second moments. GeoGebra makes these calculations a breeze!

  • 1. Area Calculation by Simpson's 1st Rule
  • 2. X-Y plotting, curve-fitting and area under the curve example
  • 3. Area Calculation using a 4th Degree Function
  • 4. Waterplane area & its centroid calculation - Simpson's Rule
  • 5. Volume & Centroid of Volume Calculation - Simpson's Rule
  • 6. Volume & Centroid of Volume Calculation II - Simpson's Rule
  • 7. Volume & Centroid Calculations with Appendage
  • 8. Second Moment of Area for a Ship's Waterplane

1.1.

Area Calculation by Simpson's 1st Rule

This is a ship's waterplane area calculation example! Your task for this tutorial is given at the bottom!
Calculate the area if the length is changed to 160m[br]You should get an area 2578.94 sq.m
– Kalyan Chatterjea

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

CG Change - Mass Addition Removal & Shift

This happens often during ship operation as we load or discharge cargo/ballast or shift these to alter list/trim or sometimes to lower the CG of the vessel to improve stability.

  • 1. Effect in KG when New Cargo Loaded on CL
  • 2. Effect in KG when Cargo Removed from CL
  • 3. Example of Mass Change in Practice

2.1.

Effect in KG when New Cargo Loaded on CL

The example shows the effect on ship's KG when a new cargo is added at a certain height on the centre line of the ship.

The task is to find the new cargo mass when the KG is changed to 6.05. You need to iterate a bit!
– Kalyan Chatterjea

2.2.

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2.3.

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3.

Hydrostatic Data from MV Reed

  • 1. Hydrostatic_Property-01-Draught_Displacement
  • 2. Hydrostatics-01a-Displacement_Draught
  • 3. Hydrostatic_Property-02-Draught_LCB
  • 4. Hydrostatic_Property-03-Draught_LCF
  • 5. Hydrostatic_Property-04-Draught_KB
  • 6. Hydrostatic-Property_05-Draught_KM
  • 7. Hydrostatics_Properties-06_Draught-TPC
  • 8. Hydrostatic_Property-07-Draught_MCTC

3.1.

Hydrostatic_Property-01-Draught_Displacement

Ref: Hydrostatic Properties of MV Reed for problem-solving
Use these values to solve problems
– Kalyan Chatterjea

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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4.

Initial Stability

  • 1. Calculation on Initial GM
  • 2. Effect of TCG Changes on List of Vessel
  • 3. Initial Stability - Effect of Changing Draught KG n Breadth
  • 4. Adding Cargo/Ballast to Correct List

4.1.

Calculation on Initial GM

Based on MV Reed Data go through the tutorial. You need to refer to Hydrostatics-01 & Hydrostatics-05 (Ref. p 62, Reeds Vol.13)
Now solve the problem given the new data for bunkering on MV Reed! Good LucK!
– Kalyan Chatterjea

4.2.

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4.3.

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4.4.

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5.

Large Angle Stability

  • 1. Exercise on Large-Angle Stability
  • 2. KN-GZ Curve

5.1.

Exercise on Large-Angle Stability

Go to Spreadsheet A41 to start

Draw the GZ curve by opening Hydrostatics-11a in a New Window!
– Kalyan Chatterjea

5.2.

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Information