Stability and Trim Shanghai Maritime University 2017

Course description • Basic knowledge • Transverse stability • Longitudinal stability —— Trim • Hull strength • Applications

n What is stability n Initial stability ØCalculation of ship’s Vertical Center of Gravity (KG) ØDetermining Height of KM ØCalculating GM ØThe inclining experiment n Stability at large angles of inclination n Free surface

Basic knowledge n n n Geometry of the ship Draft readings and water density Some calculations with drafts

Chapter 1 Geometry of the ship • Principle dimensions a. Length 1) length between perpendiculars (LBP) 2) length over all (LOA) 3) length on the waterline

load water line Crossing points Bow and waterline Base line Rudder stock

b) Breadth 1) moulded breadth 2) extreme breadth c) Depth 1) moulded depth 2) extreme depth

Under side of deck plating Base line (top of keel) Extreme draught=moulded draught + thickness of shell plate

d) draft and trim Mean draft is the mean of drafts for the whole ship Moulded draft is distance between the water surface and the base line(top of the bottom plate). Trim is the difference between the drafts forward and aft. When the draft is changed, the change of trim is the algebraic difference of the changes of draft forward and after.

WL WL 1 When the ship is designed to have a greater draft than forward, she is said to be designed with a drag. The difference between drafts aft and forward when floating at the designer's waterline is the drag The maximum drafts to which merchant ship may be loaded without voiding their insurance, are indicated by a mark on the side of the ship at the midship section. This is known as the loadline mark.

Plimsoll marks

e) Freeboard The vertical distance from the water line to the weather deck edge at any section in the length of the ship.

Form coefficients The coefficient of fineness of the water-plane area (Cw) Coefficient of fineness= Aw Area of water-plan = Area of rectangle Lx. B L=L on the water line

The midships coefficient (Cm) Midships area (AM) Midships coefficient (Cm)= Area of rectangle = Midships area (AM) Bxd AM= Cm x B x d B=Breadth Moulded

The prismatic coefficient (Cp) Volume of ship The prismatic coefficient (Cp)= Volume of prism ▽ Am=B x d x Cm = L x Am ▽=L x Am x Cp

Block coefficient of fineness of displacement (Cb) Volume of displacement Block coefficient (Cb)= Volume of the block = ▽ Lx. Bxd Cb=Cp x Cm ▽ = x Midship area x L Midship area Bxd

Cb values at fully loaded drafts the following table gives good typical value Ship type Typical Cb Fully loaded ULCC 0. 850 General cargo 0. 700 ship Supertanker 0. 825 Passenger liner 0. 625 Oil tanker 0. 800 Container ship 0. 575 Bulk carrier 0. 750 Coastal tug 0. 500 Volume of displacement= L x B x d x Cb Medium form ships= Cb approx. 0. 700, full-form ships= Cb>0. 700 Fine form ships=Cb<0. 700

Thinking d B L Cw Cm Cb Cp = = 1. 0 0. 5 1. 0

Exercise Light displacement= L x B x draft x Cb cu. m =64 x 10 x 1. 5 x 0. 6 = 576 cu. m Load displacement= L x B x draft x Cb cu. m =64 x 10 x 4 x 0. 75 = 1920 cu. m Deadweight =Load displacement – light displacement =1920 -576 cu. m =1344 x 1. 025 tonnes = 1377. 6 tones

Chapter 2 Draft reading and water density n Reading the vessel’s draft marks Location

Draft mark systems English Metric 5 M 16 XVI 14 feet 9” 50 8 48 15 XV 6 46 4 44 2 42 4 M 40 8 38 6 36 14 XIV 13 XIII 11 feet 6’’ 6” 11 feet 1 m=3. 2808 feet 1”=2. 54 cm 12 XII 6” 11 XI 10 X 12 feet 3. 3 m 10 cm 3. 2 m 4 2 34 10 cm 3 M 32 4. 5 m 3. 4 m

Exercise 10. 0 m 22'00" 20'06" 9. 7 m 9. 15 m 14'09"

Draft =4. 75 m

Effect of density on draft n The effect on box-shaped vessels New mass of water displaced =old mass of water displaced New volume x New density = Old volume x Old density New volume Old volume = L x B x New draft L x B x Old draft = New draft Old density New density Volume=L x B x draft Old density New density = Old density New density

n Example 1 A box-shaped vessel floats at a mean draft of 2. 1 metres, in dock water of density 1020 kg per cu. m. Find the mean draft for the same mass displacement in salt water of density of 1025 kg per cubic metre. New draft Old density New density = New draft = Old density New density = 1020 1025 = 2. 09 m x Old draft x 2. 1 m

Correction to displacement for density n Formula: Correction to displacement for density (1. 025 -observed density)(displacement) = 1. 025 Mass density of FW= 1000 kg per cubic meter or 1. 000 tonne/m 3 Mass density of SW= 1025 kg per cubic meter or 1. 025 tonne/m 3 Density of FW Density of SW ▽FW = ▽SW

n Your drafts are: FWD 23'-03", AFT 24'-01". Use the blue pages of the Stability Data Reference Book to determine the vessels displacement if you are in fresh water. (d. F+d. F) Mean draft = 2 =23’ 03”+24’ 01” =23’ 08” 2 ▽SW=12300 tons Density of FW ▽FW = Density of SW ▽SW Density of FW ▽FW= Density of SW 1. 000 = 1. 025 = 12000 tons X ▽SW X 12300 tons

n You are scheduled to load 3900 tons of cargo, 45 tons of crew effects and stores and 359 tons of fuel. Use the blue pages of the Stability Data Reference Book to determine the vessel's mean draft in fresh water. Dead weight = 3900+45+359 t=4304 t Old density New draft = New density Draft F. W. = 1. 025 1. 000 x Old draft X 17’ 08” =18’ 1” 17’ 08 ”

Some calculations with the forward and after draft readings Calculating the hull deflection 1. sagging Mean forward and aft draft<Mean midship draft compression 2. hogging tension Mean forward and aft draft>Mean midship draft tension compression

Example bow 4. 990 m Port side 5. 010 m Starboard side Mean forward = d. FP+d. FS draught 2 = 4. 99+5. 01 m 2 = 5. 00 m 5. 900 m 6. 140 m Mean midship = draught d. MP+d. MS 2 = 5. 90+6. 14 m 2 = 6. 02 m 6. 980 m 7. 020 m stern Mean forward and aft draft = (5. 00+7. 00)/2 m=6. 00 m Mean aft d. AP+d. AS = draught 2 = 6. 98+7. 02 m 2 = 7. 00 m This demonstrates that the vessel’s hull is sagging by 0. 02 m

Questions 1. Your vessel has a midships engine room and the cargo is concentrated in the end holds. The vessel is _____ A. sagging with compressive stress on main deck. B. hogging with tensile stress on main deck. C. hogging with compressive stress on main deck. D. sagging with tensile stress on main deck. 2. If a vessel is sagging, what kind of stress is placed on the sheer strake? A. B. C. D. Compression Tension Thrust Racking