sample of calculation

8/3/2019 Sample of Calculation

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Sample of calculation

Calculation for table HYD-1: Water plane area

WL NO : 2 d: 0.88(m) LWL: 23.21(m) BWL: 4.48 (m) h: 1.7 (m)

Water plane area,

Aw= 2 x SR x h x fAw *SR = 1/3 for 1st rule, 3/8 for 2nd rule (Simpson Rule)

= 2 x1/3 x 1.7 x 64.814

= 73.456 m2

ST1/2B

(Cm)

1/2B

(m) full

scale

SM fAW Lever fML Lever fIL (1/2B)3 SM fIT

0 0 0 0.5 0 16 0 16 0 0 0.5 00.5 0 0 2 0 15.5 0 15.5 0 0 2 0

1 0.36 0.1512 1.5 0.2268 15 3.402 15 51.03 0.003457 1.5 0.005185

2 1.3 0.546 4 2.184 14 30.576 14 428.064 0.162771 4 0.6510853

3 2.22 0.9324 2 1.8648 13 24.2424 13 315.1512 0.8106 2 1.6212007

4 3.01 1.2642 4 5.0568 12 60.6816 12 728.1792 2.020447 4 8.0817861

5 3.76 1.5792 2 3.1584 11 34.7424 11 382.1664 3.938324 2 7.8766473

6 4.38 1.8396 4 7.3584 10 73.584 10 735.84 6.225442 4 24.901769

7 4.86 2.0412 2 4.0824 9 36.7416 9 330.6744 8.504655 2 17.009309

8 5.18 2.1756 4 8.7024 8 69.6192 8 556.9536 10.29763 4 41.190507

9 5.33 2.2386 2 4.4772 7 31.3404 7 219.3828 11.21836 2 22.436726

10 5.33 2.2386 4 8.9544 6 53.7264 6 322.3584 11.21836 4 44.873453

11 5.13 2.1546 2 4.3092 5 21.546 5 107.73 10.0023 2 20.004604

12 4.7 1.974 4 7.896 4 31.584 4 126.336 7.692038 4 30.768154

13 3.85 1.617 2 3.234 3 9.702 3 29.106 4.227952 2 8.4559042

14 1.97 0.8274 4 3.3096 2 6.6192 2 13.2384 0.56643 4 2.2657216

15 0 0 1.5 0 1 0 1 0 0 1.5 0

15 1/2 0 0 2 0 0.5 0 0.5 0 0 2 0

AP 0 0 0.5 0 0 0 0 0 0 0.5 0

64.814

fML 488.11

fIL 4346.2 230.142fA

w

fIT


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Longitudinal 2nd

moment of inertia

IL = 2 x SR x h3 x fIL

= 2 x 1/3 x 1.73

x 4346.2

= 14235 m

4

(about AP)

Longitudinal Center of Floatation

LCF = ( fML/ fAw ) x h

= (488.11/64.814) x 1.7

= 12.802 m aft from AP

Transverse moment of inertia

IT= 1/9 x h x fIT

=1/9 x 1.7 x 230.42

= 43.471 m4

(about centerline)

Calculation for HYD 2: Water plane Area Particulars

Longitudinal moment of inertia of water plane about F

ILCF = IL - Aw x (LCF)2 Density, = 1.025 Tonne/m

3for sea water

= 9375.12 45.56 x (13.52)2

= 1047.189 m4

Water plane coefficient

CW = Aw / ( Lwl x Bwl )

= 45.56/ (20.67 x 3.28)

WL d(m)LWL

(m)

BWL

(m)AW (m

2)

LCF (m+ From

AP

IL (m4) ILCF (m

4) IT (m

4) CW TPC MCTcm

1 0.44 20.67 3.28 45.56 13.52 9375.12 1047.189 13.991 0.672 0.467 0.5193

2 0.88 23.21 4.48 73.45 12.802 14235 2197.191 43.47 0.70638 0.7529 0.9703


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Tonnes per centimetre

TPc = x Aw / 100

= 1.025 x 45.56/100= 0.467

Moment to change trim 1cm

MCTcm = x ILCF / (100 x Lwl)

= 1.025 x 1047.189/ (100 x 20.67)

= 0.5193 Tonnes-m

Calculation for HYD 3: Sectional Area

Station no: 1

(a) (b) (d) (e) (f) (g) (h) (i) (j) (k) (l)

WL 1/2B (m) SM fAs SM fAs fAs Lever fMZ Lever fMZ fMZ

0 0 0 1 0 0 0

1 0.15 0.0588 4 0.2352 1 0.2352

2 0.36 0.144 1 0.144 1 0.144 2 0.288 2 0.288

3

0.63 0.252

fA s 0.3792 4 1.008 0.3792 fMZ 0.5232 3 3.024 0.5232

4 0.96 0.384 1 0.384 1 0.384 4 1.536 4 1.536

5

1.37 0.548

4 2.192 fA s 1.536 1.9152 5 10.96 fMZ 4.848 5.3712

6 1.86 0.744 1 0.744 6 4.464 6

fA s 3.32 5.2352 fMZ 16.96 7 22.3312


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Calculation for HYD 4 : Sectional Area Particulars

Station no: 1

As = 2 x SR x w x fAs

= 2 x 1/3 x 0.44 x 0.3792

= 0.1112 m2

Mz = 2 x SR x w2x fMz

= 2 x 1/3 x (0.44)2

x 0.5232

= 0.0675 m4

Z = w x fMz/ fAs or Z = Mz/ As

= 0.44 x 0.5232/0.3792

= 0.6071 m from WL 0

WL d fAs As fMZ Mz Z

2 0.88 0.3792 0.1112 0.5232 0.0675 0.6071

4 1.76 1.9152 0.5618 5.3712 0.6932 1.2340

6 2.64 5.2352 1.5357 22.3312 2.8822 1.8769

ST No. 1


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Calculation for HYD 5: Volume from WP Area

Calculation for HYD 6: Volume and VCB

WL d (m) f fMV VCB(m) fromwl 0

2 0.88 255.69 75.0024 329.14 1.930892878

4 1.76 826.5 242.44 2079.28 3.773647913

6 2.64 1537.88 451.111 5646.04 5.506970635

Example calculation for WL 2

= SR x w x f

= 1/3 x0.44 x 255.69= 75.0024 m

3

WL AW (m2) SM f SM f f Lever fM Lever fM

fM

0 0 1 0 0 0

1 45.56 4 182.24 1 182.24

2 73.45 1 73.45 1 73.45 2 146.9 2 146.9

3 96.55 f 255.69 4 386.2 255.69 fMV 329.14 3 1158.6 329.14

4 111.16 1 111.16 1 111.16 4 444.64 4 444.64

5 119.32 4 477.28 f 570.81 826.5 5 2386.4 fMV 1750.14 2079.28

6 122.94 1 122.94 1 6 737.64 6

7 f 711.38 4 1537.88 fMV 3568.68 7 5647.96


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VCB= w X fMv / f

= 0.44 x 329.14/ 255.69

= 1.930892878m (m from WL 0)

Calculation for HYD 7: Volume from Sectional Area

Example calculation for waterline 2

WL : 2 d : 0.88 (m) h : 0.44 (m)

ST As SM f Lever fML0 0 1 16

1 0.1112 4 0.4448 15 6.672

2 0.5262 2 1.0524 14 14.73363 0.9335 4 3.734 13 48.542

4 1.3 2 2.6 12 31.2

5 1.654 4 6.616 11 72.776

6 1.989 2 3.978 10 39.78

7 2.47 4 9.88 9 88.92

8 2.477 2 4.954 8 39.632

9 2.581 4 10.324 7 72.268

10 2.652 2 5.304 6 31.824

11 2.387 4 9.548 5 47.74

12 1.969 2 3.938 4 15.752

13 0.882 4 3.528 3 10.584

14 0.242 2 0.484 2 0.968

15 0 4 0 1 0

AP 0 1 0 0 0

f 66.3852 fML 521.3916


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Calculation for HYD 8: Volume and LCB

WL d f fML LCB (m)from AP

2 0.88 66.385 38.94586667 521.39 15.70806658

4 1.76 213.758 125.4046933 1567.35 14.6647143

6 2.64 397.354 233.1143467 2849.72 14.34348213

= SR x h x f

=1/3 x0.88 x 66.385

= 38.94586667m3

LCB = h x fML / f

= 0.88 (521.39/66.385)

=15.70806658

m from AP

Calculation for HYD 9a: Hydrostatics Particulars

Example calculation for water line 2

mld = x

= 38.946 x 1.025

= 39.920 tonnes

WL d (m) AW (m2) AM (m2) LCF (m)From AP

(m3) mld

(Tonnes)

ext

(Tonnes)

VCB

(m)

From BaSe

LCB (m)From

2 0.880 73.450 2.477 12.802 38.946 39.920 40.119 1.965 13.639

4 1.760 111.160 6.773 11.720 125.405 128.540 129.183 3.896 12.679

6 2.640 122.940 11.498 12.020 233.114 238.942 240.137 5.652 12.181


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ext = mld x 1.005

=39.920

x 1.005

= 40.119 tonnes

Calculation for HYD 9b: Hydrostatics Particulars

Example calculation for water line 2

WL d (m) CB

CM

CW

CPL

CPV

ILCF (m4) IT (m4)

2 0.880 0.426 0.314 0.706 0.761 0.603 1489.100 53.188

4 1.760 0.527 0.376 0.822 0.701 0.641 1878.400 125.780

6 2.640 0.618 0.406 0.857 0.760 0.720 1326.110 153.420

CB = / (Lwl x Bwl x d) Cm = Am / (Bwl x d)

= 38.946 / (23.21x3.28x 0.88) = 2.4768 / (23.21 x 0.88)

= 0.426 = 0.314

CPL= / (Am x Lwl) Cpv = / (Aw x d)

= 38.946 / (2.4768 x 23.21) = 38.946 / (73.450 x 0.88)

= 0.761 = 0.603


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Calculation for HYD 9c: Hydrostatics Particulars

Calculation for water line 2

WL d (m) TPC

(Tonnes)

MCTcm

(Tonnes-m)

BMT

(m)

BML

(m)

KMT

(m)

KML

(m)

2 0.880 0.753 0.970 1.116 56.417 3.047 58.348

4 1.760 1.139 1.857 0.963 38.142 4.737 41.916

6 2.640 1.257 2.293 0.538 25.613 6.048 31.123

KMT = VCB + BMT BMT= IT /

= 1.965+ 1.116 = 53.188/ 38.946= 3.047 m = 1.116m

BML = ILCF / KML= VCB + BML

= 1489.1/ 38.946 = 1.965+ 117.482

= 56.417m = 56.417m

Calculation for HYD 10: Bonjean Data

Example calculation for station no: 1

ST No :1

WL d AS Z

0 0 0 0

2 0.88 0.112 0.6071

4 1.76 0.562 1.234

6 2.64 1.535 1.877

As and Z get from HYD 4

sample of calculation

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