METRIC Instructional MANUAL CONTENTS Chapter Page 1 Introduction 1 2 Ship Draft, Trim and Stability Notes 14 3 Draft Survey 30 4 Cargo Deadweight 50 5 Trim and Stability 58 6 Grain Loading 73 7 Rolling Period Test for GM 88 Appendix 94 Draft and Stability Problems and Answers 94 - 1 - CHAPTER 1 INTRODUCTION PURPOSE 1.1 This Handbook is intended to assist Deck Officers with their loading calculations. Practical solutions are emphasised, and the most common questions about ship loading are answered. 1.2 More detailed knowledge may be obtained from published tomes on the subject which will provide fuller coverage of stability. DESCRIPTION 1.3 Chapter One, Introduction - describes the purpose of the Handbook. There is a summary of the contents of each chapter. An alphabetical listing of abbreviations used, a listing by chapter of formulas, and some recommended materials and equipment for performing ship-loading computations are also included. 1.4 Chapter Two, Ship Draft, Trim and Stability Notes -defines and discusses points and practices which have a practical effect on safe and economic ship loading. 1.5 Chapter Three, Draft Survey - describes in detail, complete with worked examples, the procedure for performing an International Standard Draft Survey. 1.6 Chapter Four, Cargo Deadweight - summarises the main considerations when performing cargo deadweight calculations. Each step in the procedure is then described in detail, complete with worked examples. 1.7 Chapter Five, Trim and stability - summarises the main considerations when performing trim and stability calculations. Each step in the procedures is then described in detail, complete with worked examples. - 2 - 1.8 Chapter Six, Grain Loading - summarises the IMCO and SOLAS requirements for loading grain. Each step in the procedure is then described in detail, complete with worked examples. 1.9 Chapter Seven, Rolling Period Test for Timber Carriers -describes the procedure for measuring the rolling period of a ship. This is most frequently required when there is timber deck cargo, but is applicable for any vessel or cargo. The calculations to convert rolling period into GM are then described in detail, complete with worked examples. 1.10 Appendix I, Problems - consists of twenty-seven (27) questions relating to the material covered in this Handbook. All questions are worked out in detail. 1.11 The following abbreviations are commonly used through- out the text: AP After Perpendiculars DISP Displacement DWT Deadweight FP Forward Perpendiculars GM Metacentric height KB Transverse Centre of Buoyancy KG Transverse Centre of Gravity LBP Length Between Perpendiculars LCB Longitudinal Centre of Buoyancy (Pg.26) LCF Longitudinal Centre of Flotation LCG Longitudinal Centre of Gravity (Pg 22) LKM Longitudinal Metacentric Distance MG Centre of Gravity from Midship or LCG MTC Moment to Change Trim by One Centimetre P Port - 3 - QM Quarter Mean S Starboard SF Stowage Factor [M3/T ] Sg Specific gravity [ T/M3 ] TKM Transverse Metacentric Height TPC Tonnes per Centimetre (Immersion) VHM Volumetric Heeling Moment VVM Volumetric Vertical Moment FORMULAS 1.12 The following formulas are used in ship loading computations: DRAFT SURVEY (Chapter 3) Forward Draft = Fwd(P) + Fwd(S) 2 Aft Draft = Aft(P) + Aft(S) 2 Mid Mean = Mid(P) + Mid(S) 2 Trim = Aft - Fwd Fwd/Aft Mean = Fwd + Aft 2 Mean of Mean = Fwd & Aft Mean + Mid Mean 2 QM = Mean of Mean + Mid Mean 2 DISPLACEMENT correction = TPC x Draft remainder in cm. Displacement = DISP + DISP correction - 4 - First correction = TRIM xTPC x LCF x 100 = Corr for trim LBP Vessel trimmed by the STERN: LCF is Fwd - you SUBTRACT LCF is Aft - you ADD Vessel trimmed by the HEAD: LCF is Fwd - you ADD LCF is Aft - you SUBTRACT Second Correction = T² x 50 x MTC diff = Final Trim Correction LBP Displacement = TPI x Draft remaining in inertia First Correction = Trim x TPI x LCF x 12” LBP Second Trim Correction = T² x 6” x MTI diff LBP MTC difference ( Metric ) : (a) QM + 50cm = MTC (Found from Ship’s Data) (b) QM - 50 cm = MTC (Found from Ship’s Data) MTC diff = a – b (a) MTC - (b) MTC = MTC difference MTI difference (Imperial): (a) QM + 6” = MTI ( Found from Tables ) (b) Qm – 6” = MTI ( Found from Tables ) WEIGHT DEDUCTIONS ( Metric ) : FUEL OIL_________________ MT DIESEL OIL ____________ MT LUBE OIL ____________MT FRESH WATER ____________MT DRINK WATER ____________MT BOILER WATER ___________MT BALLAST WATER _________MT - 5 - SLUDGE __________________MT STORES,etc _______________MT CONSTANT _______________MT TOTAL weight deductions WEIGHT DEDUCTIONS ( Imperial ) : Calculations are done in LT - Long Tons. CARGO DEADWEIGHT (Chapter 4) ; Pg 70 Cargo DWT = DISP. corrected for density (2nd condition) - TOTAL weight deductions (2nd condition) = NETT displacement (2nd condition) - NETT displacement (lightship = 1st condition) = CARGO LOADED PERCENTAGE (%) = Hold Capacity x 100 Total Capacity DEFLECTION = MID MEAN Hogging = MID MEAN - FWD & AFT MEAN [ Peregib ] , See Pg.23 Sagging = MID MEAN - FWD & AFT MEAN [ Progib ] , See Pg.23 Even Keel = MID MEAN - FWD & AFT MEAN TRIM FORMULAS (Chapter 5) ; Page 58 LCG(FP) = LBP + MG 2 MG is Aft - you ADD MG is Fwd - you SUBTRACT Longitudinal Moment = Weight x LCG(FP) New LCG(FP) = Total Longitudinal Moments Displacement - 6 - Trim Lever = LCG(FP) - LCB(FP) TRIM = Trim Lever x Displacement x 100(m) MTC Final Longitudinal Moments = DISP x LCG(FP) Longitudinal Moments of Constant = Final - all other Longitudinal Moments LCFG(FP) of the Constant = Longitudinal Moment Weight (CD) Change of Draft = Trim 2 Mean Sinkage = + Weight TPC Distance = 2 x MTC TPC Weight = TPC x Trim(cm) 2 Vertical Moment = Weight x KG KG = Total Moments (P) _ Total Moments (S) Total Weights (P) Total Weights (S) New KG = Old KG = Total Change in Moments Total Change in Weights GM = TKM - New KG *GG = Total Inertia / Total Weights G1M = GM - GG1 Rolling Period : ( Imperial ) ( Metric ) 0.44B Ft___ 0.7978B Metres sq.rt of G M sq. rt of GM Rise of G due to Free Surface = _L x B³ x Sg___ 12 x DISP x n² - 7 - Where: L = Length of tank B = Breadth of tank Sg = Specific Gravity of liquid in tank n = # of Longitudinal compartments into which the tank ROLLING PERIOD TEST (Chapter 7) ( IMPERIAL ) ( METRIC ) GM = 0,1936 x B² GM = 0,6532 x B² T² T² Where : T = Rolling Period in Seconds of time B = Breadth of Ship GG1 = w x dKG DISP Where: GG1 = Shift in Centre of Gravity DISP = W +/ - w W = Original Displacement w = Weight to be loaded or discharged dKG = Distance from KG to G of weight GM = W x D x cot.0° DISP Where: W = Weight D = Distance from water line cot.0° = Angle of List - 8 - GRAIN LOADING (Chapter 6) HHM = ___VHM___ SF( cargo) G0 G1 = VHM DISP x SF CUBIC METRES ( M ³) = Cubic Feet ( Ft³ ) 35.315 NECESSARY MATERIALS 1.13 Work Forms are recommended to ease the work of calculations. Several forms are included as part of the examples in this Handbook. These may be used as is, or altered to suit personal or operational requirements. 1.14 Stability Booklet and Loading Manual, complete with: - hydrostatic and deadweight tables; - grain loading plan; - general arrangement plan; - capacity plan, and - tank capacity plan or manual. These items are all supplied by the shipbuilder to the ship and should be studied with care. 1.15 Certified hydrometer and water sampler (water thief). These are used to measure the specific gravity (Sg) of the water in which the ship is floating. A special hydrometer for measuring the Sg of fuel and lubricating oils should also be available. - 9 - 1.16 A sounding tape for measuring tank contents, and a standard tape for measuring holds, lockers, and other spaces. 1.17 A good calculator will speed up calculations. Any of the better scientific calculators will have a program for integration by Simpson’s Rule. - 10 - - 11 - - 12 - Figure 2 - 14 - CHAPTER TWO SHIP DRAFT, TRIM AND STABILITY NOTES CONSTANT 2.1 The constant, in draft survey calculations, includes all weights aboard ship, which are not included in the manuals. These would include crew, crew's effects, provisions and stores, lifesaving equipment, water in pipelines, mud in the chain locker, and fouling of the hull. 2.2 A vessel’s constant will alter appreciably over a period of time. It must be checked, and probably recalculated, for every loading survey. Stores, paint especially, together with lubricating oils, spare cylinder liners, and additional equipment will often change the constant by more than 100 tonnes in 6 months. 2.3 The constant also increases with age. Corrosion and the accumulation of “it might be useful” stores are the main causes for this increase. The old rule of thumb was: "For a vessel of 10,000 tons, add one inch of draft for each five years of vessel life". Most vessels are now much larger, so the estimate will have to depend on the surveyor’s experience. Check for unlisted stores especially used lumbers and rope. 2.4 The weight of bottom growth is the most difficult to allow for. It is frequently significant, and value of 50 - 15 - Kg/M² has been suggested. A check of the fouling exposed when the vessel is light can be helpful. A bottom survey by a qualified diver provides the most accurate data. 2.5 One apparent change in constant must be guarded against. A draft survey at anchor, or alongside with one anchor down, will be minus the weight of the anchor and chain. If, at the discharge port, both anchors are put on the bottom whilst alongside, the difference between the initial and final surveys will produce an apparent increase in the weight of the cargo out-turn. 2.6 Ensure the weights of anchors and chains are properly added or subtracted from the loading and unloading constant calculations.