Ship hydrostatics

Ship hydrostaticsHydrostaticsIs the study of liquids at rest

Calculation of areas, centroids, moments of inertia of areas (2nd Mmt) and volumes are the properties for hydrostatic data

This then will be plotted as a function of draught, in curves that allow further calculationHydrostatic particulars When a ship is floating at a certain draught, we can find the mass displacement of the ship if we can find its displaced volume,.

Also we can know its water plane area, calculate its TPC, KB, Cb, and etc.

These particulars which are properties of the immersed part of the ship are called hydrostatic particulars.

, , KB, LCB, LCF, KG, BMT, BML, TPC, CB, CM,CP, CW, MCTC etc.

These particulars describe the characteristics of the underwater portion of ship at a particular draught.

It is related to volumes, areas, centroid of volumes and areas and moments of volumes and areas of the immersed portion.

Once draught or trim changes, the particulars will also change.

The particulars can be presented in two forms, either as a set of curves or in tabular format.

Draught (m)Aw (m2) (m3) (tonnes)CBCWTPC 218003168.0420006547.26210010137.68212013728.010213017424.0Exercise 1A ship with length 100m, breadth 22m has the following areas and volumes at different waterlines. Calculate its , CB, CW and TPC in sea water.

Hydrostatic table can be used to obtain hydrostatic particulars once draught is known or one of the other particulars is known.

There is however a need to interpolate the table to obtain intermediate values. Hydrostatic CalculationMV MIMETPRINCIPAL DIMENSION LOA 66.00 m LBP 64.00 m BEAM 9.56 m DEPTH 7.00 mTABLE OF OFFSETS (HALF BREADTH) in metersWaterline Name and distance from Baseline in metresBLWL 1WL 2WL 3WL 4WL 5WL 6WL 70.01.02.03.04.05.006.007.00Station Name and distance from station AP in metresAP0.000.000.000.000.000.000.001.712.1713.200.000.340.410.350.122.153.123.6626.400.400.750.911.523.023.154.234.4939.600.211.312.423.624.254.504.734.77412.800.762.613.754.414.744.784.784.78619.202.654.504.764.784.784.784.784.78825.603.454.514.784.784.784.784.784.781032.003.484.544.784.784.784.784.784.781238.403.484.544.784.784.784.784.784.781444.803.124.524.754.784.784.784.784.781651.202.613.734.264.454.584.624.684.711857.600.982.472.823.023.153.913.293.37FP64.000.000.610.830.910.870.630.000.00WATERPLANE AREA, AwData :- Breadth at each station from AP to FP

Procedure :- Breadth x SM = Product Area :- repeat for each Breadth

Formula :- 1/3 x h x Product Area x 2

St1/2 BSMPAAP0.000.50.0010.0020.0020.4010.4030.2120.4240.761.51.1462.65410.6083.4526.90103.48413.92123.4826.96143.12412.48162.6125.2218 0.9843.92FP0.0010.0061.96Example :AwBL = 1/3 x h x Product Area x 2= 1/3 x 6.4 x 61.96 x 2= 264.36m2Sectional Area, AsData :- Breadth at each WL from BL to Draft(T)

Procedure :- Breadth x SM = Product Area :- repeat for each Breadth

Formula :- 1/3 x w x Product Area x 2

Example :As1 = 1/3 x w x Product Area x 2= 1/3 x 1 x 3.7 x 2= 2.47m2St 1Draught1/2 BSMPA0010.0010.3441.3620.4120.8230.3541.4040.1210.123.70LCF Data :- Breadth at each station from AP to FP

Procedure :- Breadth x SM = Product Area :- Product Area x lever = 1st Mmt Area :- repeat for each Breadth

Formula :- h x 1st Mmt Area / Product Area

ILData :- Breadth at each station from AP to FP

Procedure :- Breadth x SM = Product Area :- Product Area x lever = Mmt Area :- Mmt Area x lever = 2nd Mmt Area :- repeat for each Breadth

Formula :- 2/3 x h3 x 2nd Mmt AreaILCFData :- IL :- Aw :- LCF

Formula :- IL Ay2ITData :- Breadth at each station from AP to FP

Procedure :- ( Breadth)3 x SM = 2nd Mmt Area Area :- repeat for each Breadth

Formula :- 2/9 x h x 2nd Mmt AreaTPCData :- Aw

Formula :- (Aw x ) / 100

MCTCData :- ILCF

Formula :- (ILCF x ) / 100LVolume of DisplacementData :- As at each station from AP to FP

Procedure :- As x SM = Product Volume :- repeat for each As

Formula :- 1/3 x h x Product Volume x 2

Data :- Aw at each WL from BL to Draft(T)

Procedure :- Aw x SM = Product Volume :- repeat for each Aw

Formula :- 1/3 x w x Product Volume x 2

LCBData :- As at each station from AP to FP

Procedure :- As x SM = Product Volume :- Product Volume x lever = 1st Mmt Vol. :- repeat for each As

Formula :- h x 1st Mmt Vol. / Product Vol.

VCB @ KBData :- Aw at each WL from BL to Draft(T)

Procedure :- Aw x SM = Product Volume :- Product Volume x lever = 1st Mmt Vol. :- repeat for each Aw

Formula :- w x 1st Mmt Vol. / Product Vol.

DisplacementData :- Volume

Formula :- Vol. x

BMTData :- Volume :- IT

Formula :- IT / Vol.

BMLData :- Volume :- ILCF

Formula :- ILCF / Vol.

KMTFormula :- KB + BMT

KMLFormula :- KB + BML

CBFormula :- Vol. / LBTCPFormula :- Vol. / (Am x L)

CWFormula :- Aw / LB

CMFormula :- Am / BT

Draught (m)Displacement (tonnes)CBKB (m)BMT (m)BML (m)MCTC (tonne-m)LCB (m from )LCF (m form )8.0014820.00.724.073.66180.0190.02.502.07.5013140.00.713.673.98195.0183.02.301.507.0011480.00.703.264.46219.0180.02.000.706.509870.00.692.855.02244.0172.01.80-0.066.008280.00.672.445.66279.0165.01.50-1.005.506730.00.662.046.67327.0157.01.10-2.005.005220.00.641.638.06392.0146.00.00-3.00Table 1.0 : Hydrostatic Particulars of Bunga Melor with LBP 100mHydrostatic Curves/Data Exercise 2By using the hydrostatic particulars of Bunga Melor shown in Table 1.0 :Draw hydrostatic curves of the shipFind the values of , KB, LCB, LCF, BMT, BML, MCTC, and CB of the ship if it is floating at a draught of 6.21m.Find values of draught, KB, LCB, LCF, BMT, BML, MCTC, and CB if the ship weights 11480 tonnes.When the ship is floating at a draught of 6.5m, 2500 tonnes was added, what is its new draught

MetacenterMetacenter is a convenient reference point for hydrostatic calculations at small angles

Metacenter associated with rotating the ship in the transverse direction (MT) and another one when rotating the ship in the longitudinal direction (ML)

The location of M depends on the location of B.MOVEMENTS OF THE METACENTERTHE METACENTER WILL CHANGE POSITIONS IN THE VERTICAL PLANE WHEN THE SHIP'S DISPLACEMENT CHANGES.

TWO RULES:1. WHEN B MOVES UP M MOVES DOWN.2. WHEN B MOVES DOWN M MOVES UP.

LCF

Exercise 3Station0123456778 breadth7.38.08.79.59.28.87.55.73.51.90A ship 104 m long is floating in sea water at draught of 4m. At this draught, the ship has a displacement of10500 tonnes. The waterplane has the following offsets :

Calculate:the area of waterplaneLCF from amidships2nd moment of area about amidships, IL2nd moment of area about LCF, ILCF2nd moment of area about centreline, ITBMLBMT123= 1x245= 3x46= 4x578= 2x6St1/2 BSMPAlever1st Mmt2nd Mmt(L)(1/2B)32nd Mmt(T)07.30.53.65414.6058.40389.02194.510.508216.003.556.00196.00512.001024.0018.71.513.05339.15117.45658.50987.7529.5438.00276.00152.00857.383429.5039.2218.40118.4018.40778.691557.3848.8435.2000.000.00681.472725.8957.5215.00-1-15.0015.00421.88843.7565.7422.80-2-45.6091.20185.19740.7773.51.55.25-3-15.7547.2542.8864.317.51.923.80-3.5-13.3046.556.8613.72800.50-40000171.15114.50742.2511581.58Exercise 4Station012345678910Area(m2)10.625.636.244.048.849.248.842.635.219.84.8A ship is 65 m long, 13 m beam, floats at even keel draught of 5 m in sea water. Sectional areas are as follows:Calculate:Displacement, LCB from amidshipsBlock Coefficient, CBMidship Section Area Coefficient, CMPrismatic Coefficient, CP123= 1x245= 3x4StAsSMPVlever1st Mmt010.6110.60553.00125.64102.404409.6236.2272.403217.203444176.002352.00448.8297.60197.60549.24196.8000.00648.8297.60-1-97.60742.64170.40-2-340.80835.2270.40-3-211.20919.8479.20-4-316.8104.814.8-5-241078.20127.40Exercise 5StAP12345678991/2FP B05810.512.513.513.512.5117.5310Find BMT for a waterplane of a ship LBP = 100m with the following half breadths. At this draught the ship has a displacement of 11275 tonnes in sea water.

1234= 2x3St1/2 B SM(1/2B)32nd Mmt(T)000.50.000.000.552125.00250.00181.5512.00768.00210.541157.634630.50312.521953.133906.25413.542460.389841.50513.522460.384920.75612.541953.137812.5071121331.002662.0087.54421.881687.50931.527.0040.509.5121.002.001000.50.000.0036521.50Exercise 6St01234567899101/2 B (m)5.0 5.56.06.57.47.68.07.76.96.03.02.00A ship 105m LBP, 16m beam is floating in sea water. The waterplane has the following offsets at 5m draught :

Draught (m)00.51.02.03.04.0Waterplane Area(m2)15490750100512101270The ship has the following waterplane area at other draughts :Using all the information, calculate height of Metacentre,KMT for draught of 5.0m.123= 1x245= 2x4St1/2 B SMPA(1/2B)32nd Mmt(T)05.00.52.5125.0062.500.55.5211.0166.38332.7516.01.59.0216.00324.0026.5426.0274.631098.5037.4214.8405.22810.4547.6430.4438.981755.9058.0216.0512.001024.0067.7430.8456.531826.1376.9213.8328.51657.0286.0424.0216.00864.0093.01.54.527.0040.509.52.024.08.0016.00100.00.50.00.000.00186.88811.75123= 1x245= 3x4DraughtAwSMPVlever1st Mmt0150.57.5000.549029800.549017501.5112511125210054402028040312102242037260412704508042032051307.611307.65653814940.143773Exercise 7A ship 100 m LBP, 12 m beam is floating in sea water at 7m draught. Atthis draught her TPC is 18.2 tonnes, LCF is 1.8m aft of amidships andSecond moment of area about amidships, IL is 736000 m4. A ship has thefollowing waterplane area at draught 0 to 6.0 m in sea water.Calculate for a draught of 7.0m:

Waterplane Area, Aw Second moment of area about LCF, ILCF Volume of displacement BML KB KML Draught (m)00.51.02.03.04.05.06.0Aw (m2)61069095011901400160016501700123= 1x245= 3x4DraughtAwSMPVlever1st Mmt06100.5305000.5690213800.569019501.514251142521190447602952031400228003840041600464004256005165023300516500617004680064080071775.6111775.61712429.2728945.61115364.3Exercise 8A ship 84 m LBP, 11 m beam is floating in sea water at 5.5 m draught and has a displacement of 7635 tonnes. At this draught her TPC is 19.4 tonnes, LCF is 40.6 m from FP and Second moment of area about amidships, IL is 690700 m4.

Calculate for a draught of 5.5 m:Waterplane Area, AwLCF from amidshipsSecond moment of area about LCF, ILCFVolume of displacementBML

Exercise 9A ship 114 m LBP, 10 m beam is floating in sea water at 8 m draught. At this draught her TPC is 17.6 tonnes, LCF is 1.9 m fwd of amidships and Second moment of area about centerline, IT is 55300 m4. A ship has the following waterplane area at draught 0 to 8.0 m in sea water.

Calculate for a draught of 8.0 m:Volume of displacementMass of displacementBMTKBKMTCB

Draught (m)0123468Aw(m2)380520740960119013801514