scantling calculations

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HALSS Feasibility Study Design Report- Appendix A 18 December 2006

Watertight & Deep Tank transverse bulkheads (Vertical stiffeners) Center Hull Side Hull

Top of the overflow of tank taken as 0.910 abv the Bulkhead Deck Bhd dk height: 17.100 22.500 m ABL

WT Bulkhead plating3-2-9/5.1 t = sk (qh) /c + 1.5 mm but not less than 6 mm or s/200 + 2.5 mm, whichever is g

1 DeepTank

reater

3-2-10/3. Bulkhead plating t = sk (qh) /254) + 2.5 mm but not < 6.5 mm or s/150 + 2.5 mm, whichever is greater.

Therefore deep tank rules govern for the collision (Fore Peak) bulkhead.

k = 1

For WT bulkheads, h is from the bottom of the plate to the bulkhead deck at center, c = 254 for collision bulkhead, 290 others

Deep Tank h = bottom of plate to a point 1.3m above the top of the tank (or 2/3 overflow ht). = 1.025

PL Botm PL Top plate Top of Tk Watertight Bhd Deep Tank Bhd

m ABL m ABL height S (m) s(mm) q m ABL h, m t, mm h, m t, mm

4.000 7.000 3.000 3.000 800 1.00 0.662 22.500 18.500 9.7 19.800 11.4

7.000 10.000 3.000 3.600 900 1.00 0.662 22.500 15.500 9.9 16.800 11.8

10.000 14.500 4.500 4.500 900 1.00 0.662 22.500 12.500 8.9 13.800 10.7

14.500 17.100 2.600 3.420 900 1.00 0.662 22.500 8.000 7.1 9.300 8.8

17.100 22.500 5.400 3.820 900 1.00 0.662 22.500 5.400 7.0 6.700 8.5

0.000 3.600 3.600 7.200 900 1.00 0.662 17.100 17.100 10.4 18.400 12.4

3.600 6.750 3.150 6.300 957.76 1.00 0.662 17.100 13.500 9.9 14.800 11.8

6.750 9.900 3.150 6.300 957.76 1.00 0.662 17.100 10.350 8.6 11.650 10.5

9.900 13.500 3.600 7.200 900 1.00 0.662 17.100 7.200 7.0 8.500 8.5

13.500 17.100 3.600 7.200 900 1.00 0.662 17.100 3.600 7.0 4.900 8.5

Bulkhead stiffeners

, k = (3.075 2.077)/(+ 0.272) where 1 2 q = 235/Y = 1.00 (.662=AH36, 1=mild stl)

k

SM = 7.8 c h s l Q cm3

3-2-9/5.3 WT Bulkheads: Q=1, c = 0.30 for stiffeners having effective bracket attachments at both ends, or 0.43 for

stiffeners w/ brackets at one end and horizontal girders at the other end, or 0.60 for stiffeners between horizontal girders

h from middle of stiffener to same as PL, but if h < 6.10 m, h is to be 0.8 times the distance plus 1.22 m

3-2-10/3.3 DeepTank Bulkheads: (3-2-1/5.5) Q = .72=AH36, .78=AH-32, 1=mild stl)

For the end connections listed above, c = 0.594 or 0.747 or 1.00, respectively. H is to same point as plate.

H - L c From To h, m s, m l, m Q SM, cm3 Att PL t SM, cm3 A, cm2 t,%

S-IB 0.59 7.800 7.800 16.000 0.900 3.600 0.72 622.6 11.8 670.3 46.70 44%

S - Dk 0.59 10.900 10.900 12.900 0.900 4.500 0.72 784.3 10.7 793.3 50.13 52%

S - dk 0.59 15.400 15.400 8.400 0.900 3.420 0.72 295.0 8.8 312.9 32.30 41%

S - dk 0.59 18.000 18.000 5.800 0.900 3.820 0.72 254.1 10.7 256.8 29.60 31%

C -IB 0.59 7 64%

C -Mid 0.5 .30 37%

C -Mid 0.59 7.200 7.200 11.200 0.958 3.000 1 8.5 356.0 32.40 40%

C -Strgr 0.59 9.900 17.100 4.900 0.900 8.5 777.1 50.13 66%

C -top 0.59 10.800 10.800 7.600 0.900 8.5 215.8 23.60 31%

C -top 0.59 13.950 13.950 4.450 0.900 3.000 0.72 120.2 8.5 125.6 17.80 23%

3-2-10/3.7.1 Stringers supporting the bulkhead stiffeners

.10

.923.600 9.900 11.650 0.900 6.300 0.72 1388.2 11.8 1442.4 6

9 4.500 4.500 13.900 0.958 3.000 0.72 399.7 10.5 399.7 37

0.72 322.

7.200 0.72 762.6

3.000 0.72 205.4

SM = 4.74 c h s l2

cm3 c = 1.50

h & s are similar to stiffeners. Where effective brackets are fitted, l may be modified as indicated in 3-2-6/7.1.

3.7.2 Proportions: Girders and webs minimum depths = 0.145l(0.0833lif struts are fitted), plus 1/4 the depth of the stiffener

slots, not < 3x the depth of the slots. 7.11

The thickness is not to be less than 1% of the depth plus 3 mm but need not exceed 11.5 mm.

From To h, m s, m l, m SM,cm3

Min D,m min t,mm SM, cm3 A, cm2 t,mm

5.660 11.650 15.145 3.600 5.990 22,888 0.969 9.7 23,117 298.10 70%

4.600 15.100 8.550 3.000 10.500 33,087 1.623 11.5 33,720 394.20 111%9.900 9.900 8.500 6.750 7.925 42,161 1.249 11.5 42,145 434.75 55%

9.900 9.900 8.500 6.750 15.000 151,040 2.275 11.5 155,808 147.00 15%

9.900 9.900 8.500 6.750 15.000 151,040 2.275 11.5 151,542 733.50 77%

4.600 15.100 8.550 22.500 13.500 410,206 2.058 11.5 410,521 1480.80 72%

4.600 9.900 11.150 3.000 5.300 10,993 0.869 8.7 16,534 222.50 63%

9.900 15.100 5.900 3.000 5.200 5,600 0.854 8.5 9,026 187.87 53%

On CL Longitudinal bulkhead, typical web fr full height adds 111% to 11.8mm PL weight.

A horizontal mid-height stringer with mid-span vertical adds (77%+72%)/2 + average(63%,53%) = 132% i.e. no benefit.

Stringer scantlings are indicative only, giving approximate depth and cross-sectional area. 14PL webs would actually be

12mm PL with stiffeners adding about 20%. Vertical at Fr 40, 61, would actually be a swash bulkhead.

BP200*9

BP160*9

Side > 4th dk

Side < 3d dk

Centr IB

Centr - Mid

Centr - Strgr

Centr - top

Vert, Typ MT875x305x13/25.4

Hull - Below

Side < IB

Side, >IB

Side,


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Deck structure Plating, Longitudinal Stiffeners, Transverse Beams, Longitudinal Girders & Pillars

Wheel-Load CALCULATIONS FROM 2006 ABS RULE 3-2-3/5.17.

Flight Deck Net t incl stfnrs + webs+grdrs+cols (for wgt est) is 23.09 mm = 85% Use 12.5 mm AH-36

t = 12.27 mm for sea-going conditions.

t = kKn CW mm where k = 25.2 for tf units, K is obtained from 3-2-3/Figure 1. W = stat ic wheel load, in tf

n = 1.0 where l/s2.0 and 0.85 where l/s = 1.0, interpolate for intermediate values. C=1.5 for oceangoing or 1.1 in port.For higher-strength steel, use thts = tms( 24 / Y ) = tms* 0.816 for AH- 36

For wheel loading, the strength deck plating thickness is not to be less than 110% of that required above. See Notes.

C-130J Tire pressure = 93 psi max= 6.200 Kg/cm2 135,000 Lb max = 61.224 t on 4 wheels

Wheel dimensns 1 wheel

Ka b a/s b/s C W, t Rule t thts

900 762 483 0.84 15.306 15.03 12.27 4.159 Kg/cm2

900 762 483 0.847 0.537 0.145 1.1 22.500 18.23 14.88 6.113 Kg/cm2

0 483 0.567 0.537 0.155 1.1 15.306 16.04 13.10 6.214 Kg/cm2

900 434 483 0.482 0.537 0.158 1.1 13.000 15.07 12.31 6.200 Kg/cm2

Case - cm.

484.0

m

Rule

7 0.537 0.145 1.1

900 51

1 M = W a b/l= 15.31 73.2 847.0 Case 2 M = W a (b/l)2= 15.31 76.85 0.5533 650.8 t

Use With attached PL, SM = 498.3 cm3 H-36 q = 0.72 SMr = q M / f =

Stiffener Area As = 41.3 cm2 Equivalent t = As / s = 4.6 m

3-2-7/ 3.1 SM = 7.8chsl2= 127.2 cm3 for c 0.879 = 1/(1.7090.651k), k = SMr Y / IA= 88%

h = 2.290 m, s = 0.900 m,andl= 3.000 m.

Deck transverse Webs & Longitudinal Girders (2006 ABS Rule 3-2-8 / 5.3 but also 3-2-7/ 5.3)

SMr = 3513 cm3 Use MT600x203x12/19.1 Available SM = 3,500 cm3 w/ 3,000 12.5 m

0% Margin Weight = 28.9% of PL Weight equivalent t= 3.6 m

2-7/ 5.3: Case 1 M = W a b/l= 30.61 322.8 6928 t - cm. H-36 Q = 0.72 SMr = Q M / f = 3

.

m PL

m

3- ,513

72=AH-36, 1=M.S.

3 8 / 5.3 SMr = 4.74cbhl2

, cm3, where c = 1.0

Beam b, m h, m l, m Q SMr m depth, web thk Use SM, cm3 Equiv t d=700

Tr.

-2-

in

Webs 3.00 2.290 10.800 0.72 2,735 630 11.9 MT600x203x12/19. 3,500 3.61 3.46

L.Girders C=1.33 10.70 2.290 9.000 0.72 9 9.2 MT600x450x12/31.,029 525 9,026 1.95 1.85

Tire Pressurestiffener s

MaxTO,lowPres

MxGrsWt,HiPres

MxTOW

MxLdgW ,HiPres

t,HiPres

t

BP260*12

For Stiff

longitudi

eners, use ABS Rule 3-2-7/ 5.3, Beams with Containers. Allowable stresses (static loads, q=1) are 1.26 t / cm2 for

nal stiffeners and 1.42 t / cm2 for transverse web frames, assuming fixed ends. Max shear = 1.055 tf / cm2 for both.

x b/l= =xx xx

x

x

mm mm mm

Girders and transverses are to have a depth of not less tha b thickness at least 1 mm per 100 mm of depth plus 4

mm, or 8.5 mm where the face area is = 190 cm

2.

mm mm mm

n 0.0583l, and we

88

b/l=b/l=


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Columns (2006 ABS Rule 3-2-8/3.1 & 3.3):

3.3 Calculated Load W = nbhs, where n = .715 t/m3,

Transverse Column Spacing b = 10.800 m Longitudinal Column Spacing s = 9.000 m, and

, i.e. 63.2 t per dk.

For r 61.2 t, total = 231 t.

3.1 Allow le e, in meters, r is the gyradius in cm,

= 12m

0.41

Lower R

60% o ck Loads: t = 12.68 mm for sea-going conditions.

2 wheels

Drive Ax

60% 1 /cm2

/cm2

Columns tatic Load per column = 3 decks = 296.1 t, or h = 4.260 m, i.e. 296.1 t - use 300 t.

Use l = 4.200 m, A = 206.5 cm2, r = 9.5 cm, Wa= 298 t.

i.e. a W14 x 109# d = 363.7 tw = 13.3 bf = 371.0 tf = 21.8 mm.

This has an equivalent plate thickness of 0.89 mm. for weight estimating.

The allowable load provides enough margin for one C-130J directly on one stanchion.

Stiffeners:

Case 1 M = W a b/l= 19.05 45.72 738.1 Case 2 M = W a (b/L)2= 19.05 121.92 0.35236 818.3 t - cm.

Use With attached PL, SM = 480.0 cm3 H-36 q = 0.72 SMr = q M / f = 467.6

Stiffener Area As = 38.7 cm2 Equivalent t = As / s = 4.3 mm

Rule 3-2-7/ 3.1 SM = 7.8chsl2= 150.8

bridge-deck beams, i.e. column f of 3-2-7/Table 1 h = 0.910 m

pilla s below the Main deck, use h = 2.440 m, i.e. 169.6

ab Load Wa = (1.8480.918 l / r) A where lis the length from deck to girder faceplat

and A is the column area in cm2. Use l = 2.800 m, A = 149.7 cm2, r = 7.7 cm, Wa= 227 t.

i.e. a W12 x 79# d = 314.5 tw = 11.9 bf = 306.8 tf = 18.7 mm. s

This has an equivalent plate thickness of 0.43 mm. for weight estimating.

oRo Decks: Net t incl stfnrs + webs (for wgt est) is 23.72 mm = 90% Use 12.5 mm AH-36

f MidTerm Sealift Cargo Handling Tru

le Ld stiffener s a b a/s b/s K C W, t Rule t thts

40 900 914 559 1.016 0.621 0.135 1.1 19.048 15.53 12.68 3.728 Kg

900 554 224 0.615 0.248 0.173 1.5 5.497 12.50 10.21 4.441 Kg

: Max S

cm3 for c= 0.796 = 1/(1.709 0.651k), k = SMr Y / IA= 69%

h = 3.000 m, s = 0.900 m,and l= 3.000 m.

Deck transverses (2006 ABS Rule 3-2-8 / 5.3 but also 3-2-7/ 5.3)

SMr = 3596 cm3 Use MT600x210x11/20. Available SM = 3,555 cm3 w/ 3,000 12.5 mm PL

-1% Margin Weight = 28.2% of PL Weight equivalent t= 3.53 mm

3-2-7/ 5.3: Case 1 M = W a = 19.05 372.4 7,092 t - cm. H-36 Q = 0.72 SMr = Q M / f = 3,596

.72=AH-36, 1=M.S.

Beam b, m h, m l, m Q SMr min depth, web thk Use SM, cm3 Equiv t

Tr. Webs 3.00 3.000 10.800 0.72 3,583 630 10.3 MT600x210x11/20. 3,555 3.53

L.Girders C=1.33 10.70 3.000 9.000 0.72 11,829 525 9.2 MT600x500x12/40. 11,936 2.50

Transverse Strength Estimate

Side Hull displacement at Crossover Deck draft (22.5m) = 9,499 t Double skin depth = 1.800 m

Side Hull displacement at full load draft (12m) = 5,122 t109 t each.

Weight of Side Hull + 85 t each.

Design for a static lo over 91 web frames, or 85 t each.

ABS Rule 3-2-7/ 5.3 Max Shear Stress = 1 tf / cm2 requires 80.77 cm2 or 4.49 mm PL.

Loa 852 t - m

ABS Rule 3 7 cm3

SM = Depth x Flg area. hickness t = 8.00 mm PL.

Shell plating should be thicker because it's in compression. Deck plating will never see a compressive load more than about

22% of the above tensile load.

CH-53

BP260*11

=

Wheel dimensns

sure

t h for

or the beams at the top of the pillar plus the sum of the heights given

s ... above, which allows for reduced loads as above. The height for

devoted to passenger or crew accommodation may be taken as the height given in 3-2-7/3 for

the height h for any pillar under the first superstructure above the freeboard deck is not to be less than 2.44m. The heigh

any pillar is not to be less than the height given in 3-2-7/3 f

the same paragraph for the beams of all complete deckin

any tween decks

t plus one C-130J

E stowed

Tire Pres

x

x =

x = =xx=

Max Wave Load = 5,122 t, Frames 18 -64 or

outboard decks+sponsons PL+framing = 7,755 t, Frames 0 -90 or

ad of 7,755 t

.055

d is applied 10.000 m outboard of the side shell giving a maximum moment M =

-2-7/ 5.3 Max Bending Stress = 1.42 / q = 1.972 tf / cm2 requires SM = 43,20

Flg width = Fr spcg = 3.000 m, giving required t

mm

mm

mm mm mm

mm mm mm

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HALSS Feasibility Study Design Report- Appendix B 18 December 2006

Appendix B Weight Estimates

The following is a brief summary of the Light Ship Weight Estimate.

Center Extents Extents

Length Effect Thickns No of Stiffng Weight VCG LCG Aft Fwd Aft Fwd

or hgt, m W, m mm Pieces Allownc tonnes m ABL m-AP m-AP m-AP Fr # Fr #24.0 14.0 7.0 7.8 100% 288 39.5 24.0 12.0 36.0 4 12.0

327.5 41.5 12.9 1.0 85% 2,546 30.3 163.8 0.0 327.5 0 109.2

276.0 13.4 14.0 1.0 85% 750 30.3 138.0 0.0 276.0 0 92

27.0 48.8 10.0 1.0 80% 186 27.0 271.8 261.0 288.0 87 96

66.5 44.5 14.0 1.0 80% 586 24.2 293.0 261.0 327.5 87 109.2

126.0 54.9 6.0 2.0 80% 1,172 25.6 198.0 135.0 261.0 45 87

135.0 54.9 10.9 2.0 90% 2,413 24.7 67.5 0.0 135.0 0 45

126.0 58.9 10.0 1.0 90% 1,106 22.0 198.0 135.0 261.0 45 87.0

147.0 11.7 12.0 2.0 90% 616 20.8 73.5 0.0 147.0 0 49.0

261.0 23.55 9.5 1.0 80% 825 16.9 117.5 0.0 261.0 0 87

126.0 13.9 9.9 2.9 78% 703 10.3 198.0 135.0 261.0 45 87

249.0 18.5 14.0 1.0 90% 961 3.3 135.6 36.0 285.0 12 95

36.0 5.7 14.0 2.0 90% 86 5.6 84.0 66.0 102.0 22 34

285.0 30.4 19.0 2.0 90% 4,918 10.0 151.5 9.0 294.0 3 98

156.0 20.7 18.0 4.0 100% 3,642 13.3 120.0 42.0 198.0 14 66

300.0 8.0 12.0 2.0 85% 836 28.0 150.0 0.0 300.0 0 100

75.0 5.4 8.0 1.0 80% 46 19.8 103.5 66.0 141.0 22 4733.0 6.3 8.0 2.0 80% 47 14.0 118.5 102.0 135.0 34 45

36.0 21.0 8.0 1.0 80% 85 8.9 56.4 33.0 69.0 11 23

17.1 23.0 10.5 8.0 90% 492 8.6 148.5 12.0 285.0 4 95

5.4 24.5 8.0 9.5 90% 150 19.8 148.5 12.0 285.0 4 95

18.5 4.4 10.5 11.0 90% 140 13.3 111.0 54.0 168.0 18 56

8.0 54.9 8.0 6.0 90% 314 26.5 141.0 12.0 27

43.7 12.0 25.0 2.0 90% 391 5.0 33.9 12.0

.0 6.0 27.0 4.0 95% 139 9

keg (Shaft Alley)

heads Abv 3d Dk 0.0 4 90

55.7 4 18.6

14 .0 6.0 3.0 9.0 1 3

333.0 10.0 7.0 1.0 95% 357 30.3 166.5 0.0 333.0 0 111.0

25.0 12.0 9.0 7. 95% 289 30.3 135.3 36.0 267.0 12 89

81.0 12 27

42.4 21.2 80.8

5.0 16 45

85.5 36.0 135.0 12 45

33.0 30.0 36.0 10 12

90 26.0 -1.5 -3.0 0.0 -1 025,349 18.21 137.37

No

2,300 2 4,600 10.0 85.5 72.0 99.0 24 33

315 3 945 5.3 46.5 15.0 78.0 5 26

240 4.0 960 7.0 124.5 117.0 132.0 39 44

146 4.5 658 7.2 108.8 84.0 117.0 28 39

106 3 317 5.3 18.8 12.0 39.0 4 13

7,480 8.58 84.80

101 1 101 12.5 118.5 111.0 126.0 37 42

50 5.0 250 16.0 85.5 72.0 99.0 24 33

20 7.0 140 16.0 69.0 66.0 72.0 22 24

200 3.5 700 26.1 139.5 54.0 225.0 18 75

1,191 21.65 118.10

80 3 240 26.0 276.0 270.0 282.0 90 94

80 0 0 0.0 0.0 0.0

40 0 0 0.0 0.0 0.0

15 1 15 24.0 45.0 36.0 54.0 12 181,200 125% 1,500 12.0 81.7 12.0 174.0 4 58

1,755 14.02 107.92

20 3 60 33.0 14.4 0.0 36.0 0 12

0.4 1600 690 26.7 198.0 135.0 261.0 45 87

1,800 1 1,800 17.1 140.0 0.0 333.0 0 111

2,550 20.06 152.74

11059.03649 12,976

8.58 38,324 497.065

Purifier Room Long'l Bulkheads

2nd Dk Fr 87-96

Passenger Dks 2 & 3

3rd Dk (Shell PL) Fr 87-109

Fuel Tank Lgl Bhds - ctr

Stbd Main Deck outb'd of flight deck

Outboard Sides above 3rd Deck

CL Longl Bhd > 4th Dk

4th Dk - ctr

Crossover Dk outbd aft AH-36

Subtotal Electrical

Outfit & Machy Subtotal

Lighting+House Elect & Distribution (1=crew, 3=Troops)

Mooring & Anchor

Joiner Work & furniture &c for troops

Transverse Bulkheads - Ctr 17.1-22.5

Tonnes each

Transformers (3=Troops)

Sta

Switchbds & VFC

Mn Engines - ctr - Sulzer 14 RTA 96 @ 80MW ea

5MW D-G sets - Wartsila 12V32

Foundations

Masts & Spars

Hinged Stern Ramp

Note - Fixed ramps included in deck weights

Subtotal Propulsion

Propulsion Generators + (Gear+Motors)

Side Eng + SSDG = Wartsila 18V46 @ 18MW ea

From Esti-MateSubtotal Steel Weight

Ctr Hull S

Sponsons (P)+ Bow Sponson

Sponsons (S) AH-36

Rudder & Horn

Propellers

Deckhouse Decks & L. Bhds

Flight Deck - AH-36 PL & Frs

2nd Dk+3d=Cargo Dk AH-36

Crossover Dk outbd + Pass Deck 3A

Mn Propulsion Shafting (sides = 1/2 ctr)

Bilge Keels (

Moveable Ramps

Sideport Doors

Subtotal Outfit & Furnishings

Rescue & Lifeboats

Cargo Elevator

Paint

Pipe & Aux (25% = Troops)

Subtotal Auxiliary Systems

Total Lightship Weight =

Transverse Bulk

Double Bottom - ctr

Double Bottom - wings

Ctr Hull Shell PL

Side Hull Shell PL

Transverse Bulkheads - Ctr


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HALSS Design Report Appendix C - Maneuvering Assessment

Appendix C Maneuverability Assessment for the HALSS

References: This Report is developed in accordance with the following vesseldocumentation and reference material:

1. Jun-Wu Zhang and David Andrews, Manoeuvrability Performance of aTrimaran Ship, RINA Conference on High Speed Craft Motions andManeuverability, Feb 1998

2. Martin Renilson, Bob Scrace, Mike Johnson and Chris Richardsen, Trials toMeasure the Hydrodynamic Prtformance of RV Triton, RINA Conference onDesign and Operation of Trimaran Ships, London, UK

3. Scrace, , R. J., QuinetiQ Report FST/CR02 4287/1.0, RV TRITON, Phase1a: Calm water manoeuvring trials. Final report (UC), Unclassified Limited Distribution

4. Winnifred R. Jacobs, Estimation of Stability Derivatives and Indices of

Various Ship Forms and Comparison with Experimental Results, DavidsonLaboratory Report 1035, September 1964

5. l. Folger Whicker and Leo, F. Fehlner, Free-Stream Characteristics of aFamily of Low-Aspect Ratio, All-Movable Control Surfaces for Application

958

6. Wartsila Lips D SS Project, FigureV

200613 GA.dwg, 8/9/2006

8. IMO Resolution MSC.137(76) adopted 4 December 2002, MSC 76/23/Add.1

10. USCG NVIC 7-89, 8 Jan 1990

to Ship Design, David Taylor Model Basin Report 933, December 1

efence, Power Absorption Diagram, HAL

7. HALSS

9. IMO Circular MSC/Circ.1053, 16 December 2002, Ref. T4/3.01

PRINCIPAL PARTICULARS

Length, over all ..............................................................................327.45 mLength, between perpendiculars ....................................................300.00 mBreadth (extreme) ............................................................................54.90 mDepth @ side (center hull, molded) .................................................22.50 m

esign Draft (molded) .....................................................................12.00 mD

INTRODUCTION

In the development of the design of the Heavy Air Lift Seabasing Ship (HALSS)trimaran, questions have arisen on the maneuvering characteristics that should beexpected of such a large and innovative hull configuration. In particular, ship steering at

a under rudder control, and slow speed maneuvering in harbor with only the side hullpropellers operating instead of bow thrusters, require an initial assessment to confirm thatse

91


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the rudders main dimensions and the side propeller thrust range would be sufficient toensure adequate maneuverability in all conditions.

The method by Zhang and Andrews [Ref. 1] of the University College London (UCL) isused to estimate the maneuvering performance of the HALSS in this study. This paper

focuses primarily on high speed trimaran steady turning circles but the methodology usedis also suitable for predicting relatively low speed turning radii under the action of sidepropellers. In brief, the method by Zhang and Andrews is a force and moment balancethat aims to estimate the value of the steady turn radius, given values for ship speed (notthe result of a resistance/thrust balance) and rudder angle (both quantities are consideredconstant and uncoupled from the resulting turning characteristics). Multi-hullydrodynamic derivatives are computed assuming no interaction between main hull and

ssion series, those of the sideulls are assumed equal to a very low aspect ratio lifting surface.

lthough turning circles do not provide a complete picture of a ship maneuveringults with current IMO and USCG

quirements for commercial ships is deemed sufficient for the purpose of qualifying thisaspect of the initial design. In this respect, please note that although the current IMO andUSCG requirements for commercial ships are based on the value of the tactical diameter

houtriggers, and rudder and propeller forces (only used to estimate differential thrustmoments) are estimated linearly and independently from each other. Whilst thederivatives of the main hull are derived from standard regreh

Acharacteristics a comparison of these numerical resre

ther than the value of the steady turn diameter ra , the difference between half tacticalically less than the margin the HALSS has on IMOteady turn diameter derived for the HALSS using

ethod is compared directly with the current IMO and USCGuirements. In support to this way of proceeding, a comparison of the tactical diameter

diameter and steady turn radius is typequirements. For this reason, the sr

Zhang and Andrews mreqand the steady turn diameter measured during sea trials of the trimaran RV TRITON[Ref. 2 and 3] is given next. Comparison of Figure 50 with Figure 45 confirms the abovethesis.

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94

IMPLEMENTATIONThe paper by Zhang and Andrews [Ref. 1] provides most details about the numericalmethod therein proposed. Nevertheless, some small variations and additionalassumptions were made in order to either bridge the occasional gap or in order tofacilitate the code implementation. These variations and assumptions were as follows:

1. The side hulls resistance differential is ignored. The reason for this assumption isthat individual resistance regression lines for the side hulls are not available forthe HALSS, RV TRITON or UCL model. This assumption is justified by theconclusion in [Ref. 1] that the influence of this element on the overall turningmoment is negligible.

2. B-Series were used in order to estimate thrust coefficients for the side propellers.This is probably a coarse assumption for all three vessels since the actualpropeller geometries are quite different from those of the Wageningen series. Thereason to adopt these coefficients is that they are well established, readilyavailable and would serve relatively well the purpose of an initial estimation of

the propulsion characteristics.3. The thrust of a side propeller backing was estimated in two ways. As suggestedby Zhang and Andrews [Ref. 1], one way would be to assume it equal to thepropeller bollard pull. This can be estimated using the B-Series simply by settingthe speed of advance equal to zero. It is believed that this method mightunderestimate the steady turn radius. For this reason it was not employed toestimate the HALSS slow speed maneuvering but only to compare HEC resultswith UCL data.A second way is to consider the thrust of the backing propeller equal toapproximately 20% of the equivalent forward thrust for the same RPM and speedconditions. This is in accordance to what is stated in [Ref. 3 for RV TRITON]and most probably a more realistic assumption than the first one. Results for theHALSS were calculated with this method.Note that the four quadrants propeller characteristics of the B series could also beused to estimate the propeller thrust in any speed-RPM combination, using Ct-Beta characteristics. However, the Triton experience is deemed to be moreaccurate than the analytical model of four quadrants propeller characteristics forsuch an original ship configuration.

CALIBRATION

In addition to the very detailed description of their numerical method, Zhang andAndrews also provide som tests that can be used tocalibrate the spreadsheet im ee Table 27).

In the following comparison, one needs to bear in mind that not all input parameters wereavailable for the UCL trimaran in Zhang and Andrews paper. In Appendix A, the valuesof the input parameters that were directly available from the paper are highlighted in boldblue characters. All other parameter values (normal blue characters) were eitherestimated from other similar ships or deduced from other data available in the paper.

e experimental results from modelplementation put together by HEC (s


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Because of the above assumptions, the com ison of the numerical results obtained byHEC for the turning circles corresponding to the operation of the rudder only (nodifferential trust from the side pro ental data provided by UCL isnot an exact match (see Figure rtheless that the difference in

results is not excessive and that the error gets progressively smaller as the rudder angle isincreased. This indicates that the implementation of the methodology is basically sound.

Table 27: Steady turn radius experimental data for UCL trimaran - Rudder Only

par

pellers) and the experim46). One should note neve

Zhang and Andrews paper - Fig. 4

Rudder Angle Turning Radius

(deg) (m)

5.0 1600.0

10.0 800.0

20.0 400.0

35.0 220.0

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

1600.0

1800.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Rudder angle (deg)

Turningra

dius(m)

UCL experiments

HEC numerical

Figure 46 Steady turn radius experimental data versus HEC numerical predictions for

UCL trimaran - Rudder only

The same comparison presented above for the case of sole rudder operation, was alsocarried out for two modes of differential side propulsion: with one propeller pushing andone idling (case a) and with one propeller pushing and one reversing (case c). The

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geometry and thrust of the TRITONs side propeller. For these reasons, the thrustdifferential portion of HEC spreadsheet remains not fully validated.

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

Rudder angle (deg)

Turningradius(m)

QuinetiQ Trials

HEC

Figure 49 - TRITON steady turn radius sea trials data versus HEC numerical predictions

Rudder only

RESULTS

Steady turn radius estimates were run for the HALSS trimaran for the same operationmodes as the ones run for the UCL model:

- Rudder only- No rudder, one propeller pushing and the other one idle- No rudder, one propeller pushing and the other one reversing

Figure 50 to Figure 54 show the results of these calculations. It should be noted thatwhen steering under differential propulsion only, the steady turn radius is both a functionof the ships speed and ed thatthe ship speedtotally available for steering.

Figure 50 also shows the current IMO/USCG requirement for merchant vessels. Thisstipulates that the tactical diameter should be less then five times the vessel length. Forthe HALSS, this is approximately equivalent to a steady turn radius of less than about750 m.

the side propellers RPM. In this exercise, it was assumwould be provided by the center hull propulsion so that side propellers are

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0.00

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

Rudder angle (deg)

200.00

400.00

600.00

800.00

Turningradi

1,000.00

1,400.00

1,600.00

us(m)

1,200.00

HEC

IMO Res. MSC.137(76)

Figure 50 - HEC numerical predictions of HALSS steady turn radius

Rudder only

0.00

200.00

400.00

600.00

800.00

1,000.00

1,200.00

1,400.00

1,600.00

m)

1,800.00

100 110 120 130 140 150 160 170 180 190 200

RPM

Turningradius(

HEC


One propeller idling Speed = 10 knots

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0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

0.00 5.00 10.00 15.00 20.00 25.00

Speed (knots)

Turningradius(m)

HEC


One propeller idling - RPM = 190

0.00

500.00

100 110 120 130 140 150 160 170 180 190 200

RPM

1,000.00

1,500.00

2,000.00

2,500.00

3,000.00

Turningradius(m)

HEC


One propeller reversing Speed = 10 knots

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0.00

500.00

1,000.00

1,500.00

2,000.00

2,500.00

3,000.00

3,500.00

4,000.00

4,500.00

0.00 5.00 10.00 15.00 20.00 25.00

Speed (knots)

Turningradius(m)

HEC


One propeller reversing RPM = 190

CONCLUSIONS

In terms of comparison to existing IMO criteria, the HALSS in her current configurationdisplays satisfactory turning ability.

The above results show that for high speed turning, rudder control is always requiredsince side propulsion differential quickly becomes inadequate as the ship speed increases.The reason for this is that the propeller thrust decreases as the speed of advance increases,whilst the hydrodynamic resistance of the hulls to turning increases as the ship speedincreases. Since the power (RPM) of the side propellers is limited, the vessel willquickly get to a point (ship speed) where the turning moment from the side propellerswill simply not be enough to turn the ship.

Unlike the differential thrust turning moment provided by the propellers, the ruddersturning moment increases with ship speed in the same way as the hydrodynamicresistance of the hulls to turning (they are both functions of the ship speed squared). Thisis what makes rudders such effective steering devices at higher speeds. In fact, accordingto Zhang and Andrews methodology, the steady turn radius under rudder action only isindependent of the ships speed. This is also confirmed by the data in [Ref. 3].

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For low speed tur ery effective butside propulsion would allow extremely tight turns. This is hardly surprising when theside propellers are compared to standard bow thrusters, where side propellers typicallyhave larger diameters (thrust is a function of ropeller diameter to the power of four) anddelivered power than bow thrusters, as well as the possibility to be operated in opposition

(one propeller pushing and the other one reversing). Including the fact that the resistancefrom the bow thrusters ducts cannot be reduced by operational means, while sidepropellers can be made to idle in order not to produce extra resistance, makes this astrong argument for avoiding bow thrusters in the design of the HALSS. One shouldnevertheless remember that the crabbing capability provided by bow thrusters could bedifficult to match using rudders, side and center propellers only.

One final word is finally due in regard to the course keeping characteristics of theHALSS. Using the hydrodynamic derivatives estimated by Zhang and Andrews method(see Appendix B and C), one can estimate if the inequality:

ning, the picture is instead reversed. Rudders are not v

p

0YN

YN

'v

'

v''

r

'

r

is satisfied or not. For the RT TRITON one obtains:

0055.1Y

N

Y

N'v

'v

''r

'r

For the HALSS one obtains instead:

0279.0Y

N

Y

N'

'

v''

'

r vr

The above inequality, when satisfied, expresses the control fixed straight line stability ofa craft. This means that under the simplifying assumptions of Zhang and Andrewsmethod, both HAL line path after adisturbance, even if their rudders are held fixed to zero. Note that the above analysis is

served that low speed course stabilityility when the assumptions of linearity

SS and the RV TRITON will resume a new straight

speed-independent. In practice, though, it is obmight not necessarily entail high speed course stabof the hydrodynamic derivatives used by Zhang and Andrews method break down.

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HALSS Design Report Appendix C - Maneuvering AssessmentConstants

Sea water density - rho (MT/m^3) = 1.025

Variables

Ship speed - speed (kn) = 1 20.00 30.00

lta (deg) = 1 0.00 0.00

00

.00

1 14.50

Side hull sway-yaw derivative - Nvs (N*sec) = 0.000 0.000

Side hull yaw-yaw derivative - Nrs (N*m/rad*sec) = 0.000 0.000

Ship sway-sway derivative - Yv (N/m*sec) = -1,076,343.179 -1,614,514.769

Ship yaw-sway derivative - Yr (N/rad*sec) = 37,580,394.984 56,370,592.476

Shp sway-yaw derivative - Nv (N*sec) = -47,848,845.000 -71,773,267.500

Ship yaw-yaw derivative - Nr (N*m/rad*sec) = -3,349,419,150.000 -5,024,128,725.000

Wing propeller thrust (starboard) - Tws (N) = 253,603 192,668

Wing propeller thrust (port) - Twp (N) = 0 0

Ship's turning rate - rr (rad/sec) = 0.001 0.001

Ship's steady turning radius - TurningRadius (m) =

Rudder angle - de

Trim - deltaT (m) = 0.00 0.00

Parameters

Center hull length at WL - L (m) = 1 150.00

Center hull beam at WL - B (m) = 1 10.80

Center hull draft at MS - T (m) = 1 5.50

Center hull block coefficient based on WL data- Cb () = 0.700

Ship displacement - disp (MT) = 1 5,400

Rudder sweep angle - lamda (deg) = 1 5.00

Rudder area - Ar (m^2) = 1 29.00

Rudder length - l (m) = 1 5.00

LCG from MS - xg (m) = 0.

Distance of rudder 1/4 line from MS - xr (m) = 75

Distance from wing propeller to CL - ys (m) =

Profile area of side hull under WL - Af (m 2) = 162.00

Side hull length at WL - Ls (m) = 1 60.00

Side hull draft at WL - Ts (m) = 1 3.00

Distance of middle side hull from MS - xs (m) = 0.00

Pitch/diameter ratio - () = 1 1.68

3.50Propeller diameter - (m) = 1

Number of blades - () = 4

RPM - (1/min) = 1 127 166

Blade area ratio - () = 1 0.80

Wake fraction - () = 1 0.00 0.00

KT = 0.184 0.082

KQ = 0.050 0.025

Va (m/sec) = 10.288 15.432

J = 1 1.389 1.594Thrust (N) = 126,801 96,334

Bollart Pull (N) = 534,649 913,435

Eta0 = 0.810 0.828

PS (MW) = 1.644 1.833

Derived quantities

Ship mass - m (kg) = 5,400,000 5,400,000

Longitudinal velocity - u (m/sec) = 10.288 15.432

Rudder area as a % or lateral center hull area - () = 3.52% 3.52%

Rudder aspect ratio - a () = 0.862 0.862

Rudder lift curve slope - dClddelta (1/deg) = 0.021 0.021

Rudder force control derivative - Ydelta - (N/deg) = 33,694.893 75,813.508

Rudder force - Ydeltadelta - (N) = 0.000 0.000

Rudder moment control derivative - Ndelta (N*m/deg) = -2,527,116.950 -5,686,013.136

Rudder moment - Ndeltadelta (N*m) = 0.000 0.000

Center hull sway-sway derivative - Yvc (N/m*sec) = -808,000.524 -1,212,000.786

Center hull yaw-sway derivative - Yrc (N/rad*sec) = 37,580,394.984 56,370,592.476

Center hull sway-yaw derivative - Nvc ( N*sec) = -47,848,845.000 -71,773,267.500

Center hul l yaw-yaw derivat ive- Nrc (N*m/rad*sec) = -3,349,419,150.000 -5,024,128,725.000

Side hull aspect ratio - as () = 0.100 0.100

Side hull lift curve slope - dCldbeta (1/rad) = 0.157 0.157

Side hull sway-sway derivative - Yvs (N/m*sec) = -134,171.328 -201,256.991

Side hull yaw-sway derivative - Yrs (N/rad*sec) = 0.000 0.000

7,135.23 21,131.70

UCL One propeller idling

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HALSS Design Report Appendix C - Maneuvering AssessmentConstants


Variables

Ship speed - speed (kn) = 1 20.00 30.00

lta (deg) = 1 0.00 0.00

00

.00

1 14.50

Side hull sway-yaw derivative - Nvs (N*sec) = 0.000 0.000

Side hull yaw-yaw derivative - Nrs (N*m/rad*sec) = 0.000 0.000

Ship sway-sway derivative - Yv (N/m*sec) = -1,076,343.179 -1,614,514.769

Ship yaw-sway derivative - Yr (N/rad*sec) = 37,580,394.984 56,370,592.476

Shp sway-yaw derivative - Nv (N*sec) = -47,848,845.000 -71,773,267.500

Ship yaw-yaw derivative - Nr (N*m/rad*sec) = -3,349,419,150.000 -5,024,128,725.000

Wing propeller thrust (starboard) - Tws (N) = 253,603 192,668

Wing propeller thrust (port) - Twp (N) = -534,649 -913,435

Ship's turning rate - rr (rad/sec) = 0.004 0.004


Rudder angle - de

Trim - deltaT (m) = 0.00 0.00

Parameters

Center hull length at WL - L (m) = 1 150.00

Center hull beam at WL - B (m) = 1 10.80

Center hull draft at MS - T (m) = 1 5.50

Center hull block coefficient based on WL data- Cb () = 0.700

Ship displacement - disp (MT) = 1 5,400

Rudder sweep angle - lamda (deg) = 1 5.00

Rudder area - Ar (m^2) = 1 29.00

Rudder length - l (m) = 1 5.00

LCG from MS - xg (m) = 0.

Distance of rudder 1/4 line from MS - xr (m) = 75



Side hull length at WL - Ls (m) = 1 60.00

Side hull draft at WL - Ts (m) = 1 3.00

Distance of middle side hull from MS - xs (m) = 0.00

Pitch/diameter ratio - () = 1 1.68

3.50Propeller diameter - (m) = 1


RPM - (1/min) = 1 127 166

Blade area ratio - () = 1 0.80

Wake fraction - () = 1 0.00 0.00

KT = 0.184 0.082

KQ = 0.050 0.025

Va (m/sec) = 10.288 15.432

J = 1 1.389 1.594Thrust (N) = 126,801 96,334

Bollart Pull (N) = 534,649 913,435

Eta0 = 0.810 0.828

PS (MW) = 1.644 1.833

Derived quantities

Ship mass - m (kg) = 5,400,000 5,400,000

Longitudinal velocity - u (m/sec) = 10.288 15.432

Rudder area as a % or lateral center hull area - () = 3.52% 3.52%

Rudder aspect ratio - a () = 0.862 0.862

Rudder lift curve slope - dClddelta (1/deg) = 0.021 0.021

Rudder force control derivative - Ydelta - (N/deg) = 33,694.893 75,813.508

Rudder force - Ydeltadelta - (N) = 0.000 0.000

Rudder moment control derivative - Ndelta (N*m/deg) = -2,527,116.950 -5,686,013.136

Rudder moment - Ndeltadelta (N*m) = 0.000 0.000

Center hull sway-sway derivative - Yvc (N/m*sec) = -808,000.524 -1,212,000.786

Center hull yaw-sway derivative - Yrc (N/rad*sec) = 37,580,394.984 56,370,592.476

Center hull sway-yaw derivative - Nvc ( N*sec) = -47,848,845.000 -71,773,267.500

Center hul l yaw-yaw derivat ive- Nrc (N*m/rad*sec) = -3,349,419,150.000 -5,024,128,725.000

Side hull aspect ratio - as () = 0.100 0.100

Side hull lift curve slope - dCldbeta (1/rad) = 0.157 0.157

Side hull sway-sway derivative - Yvs (N/m*sec) = -134,171.328 -201,256.991

Side hull yaw-sway derivative - Yrs (N/rad*sec) = 0.000 0.000

2,295.61 3,680.86

UCL One propeller reversing

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Appendix C-2: Validation Spreadsheets

Constants


Variables

Ship speed - speed (kn) = 10.00 10.00 10.00 10.00

Rudder angle - delta (deg) = 10.00 20.00 30.00 40.00

0.00

Center hull beam at WL - B (m) = 7.20

Rudder area - Ar (m^2) = 7.69

Centerh ull y aw-yaw derivative -N rc (N*m/rad*sec) = -261,097,741.580 -261,097,741.580 -261,097,741.580 -261,097,741.580

Side hull aspect ratio - as () = 0.124 0.124 0.124 0.124

Side hull lift curve slope - dCldbeta (1/rad) = 0.194 0.194 0.194 0.194

Side hull sway-sway derivative - Yvs (N/m*sec) = -20,219.392 -20,219.392 -20,219.392 -20,219.392

Side hull yaw-sway derivative - Yrs (N/rad*sec) = -45,493.633 -45,493.633 -45,493.633 -45,493.633

Side hull sway-yaw derivative - Nvs (N*sec) = -45,493.633 -45,493.633 -45,493.633 -45,493.633

Side hull yaw-yaw derivative - Nrs (N*m/rad*sec) = -102,360.674 -102,360.674 -102,360.674 -102,360.674

Ship sway-sway derivative - Yv (N/m*sec) = -204,790.138 -204,790.138 -204,790.138 -204,790.138

Ship yaw-sway derivative - Yr (N/rad*sec) = 4,874,283.598 4,874,283.598 4,874,283.598 4,874,283.598

Shp sway-yaw derivative - Nv (N*sec) = -6,412,966.481 -6,412,966.481 -6,412,966.481 -6,412,966.481

Ship yaw-yaw derivative - N r (N*m/rad*sec) = -261,302,462.928 -261,302,462.928 -261,302,462.928 -261,302,462.928

Wing propeller thrust (starboard) - Tws (N) = 0 0 0 0

Wing propeller thrust (port) - Twp (N) = 0 0 0 0

Ship's turning rate - rr (rad/sec) = 0.011 0.023 0.034 0.046


Trim - deltaT (m) = 0.00 0.00 0.00

Parameters

Center hull length at WL - L (m) = 90.00

Center hull draft at MS - T (m) = 3.65

0.557Center hull block coefficient based on WL data - Cb () =

Ship displacement - disp (MT) = 1,350

Rudder sweep angle - lamda (deg) = 2.20

Rudder length - l(m) = 3.20

LCG from MS - xg (m) = 2.20 aft

Distance of rudder 1/4 line from MS - xr (m) = 43.03

Distance from wing propeller to CL - ys (m) = 10.00


Side hull length at WL - Ls (m) = 34.80

Side hull draft at WL - Ts (m) = 2.15

Distance of middle side hull from MS - xs (m) = 2.25 aft

Pitch/diameter ratio - () = 1.68

Propeller diameter - (m) = 1.05


RPM - (1/min) = 70 70 70 70

Blade area ratio - () = 0.80Wake fraction - () = 0.00 0.00 0.00 0.00

KT = 1.229 1.229 1.229 1.229

KQ = 0.010 0.010 0.010 0.010

Va (m/sec) = 5.144 5.144 5.144 5.144

J = 4.199 4.199 4.199 4.199

Thrust (N) = 2,084 2,084 2,084 2,084

Bollart Pull (N) = 1,313 1,313 1,313 1,313

Eta0 = 80.307 80.307 80.307 80.307

PS (MW) = 0.000 0.000 0.000 0.000

Derived quantities

Ship mass - m (kg) = 1,350,000 1,350,000 1,350,000 1,350,000

Longitudinal velocity - u (m/sec) = 5.144 5.144 5.144 5.144

Rudder area as a % or lateral center hull area - () = 2.34% 2.34% 2.34% 2.34%

Rudder aspect ratio - a () = 1.332 1.332 1.332 1.332Rudder lift curve slope - dClddelta (1/deg) = 0.031 0.031 0.031 0.031

Rudder force control derivative - Ydelta - (N/deg) = 3,261.621 3,261.621 3,261.621 3,261.621

Rudder force - Ydeltadelta - (N) = 32,616.212 65,232.423 97,848.635 130,464.847

Rudder moment control derivative - Ndelta (N*m/deg) = -140,334.512 -140,334.512 -140,334.512 -140,334.512Rudder moment - Ndeltadelta (N*m) = -1,403,345.122 -2,806,690.244 -4,210,035.365 -5,613,380.487

Center hull sway-sway derivative - Yvc (N/m*sec) = -164,351.353 -164,351.353 -164,351.353 -164,351.353

Center hull yaw-sway derivative - Yrc (N/rad*sec) = 4,965,270.864 4,965,270.864 4,965,270.864 4,965,270.864

Center hull sway-yaw derivative - Nvc (N*sec) = -6,321,979.215 -6,321,979.215 -6,321,979.215 -6,321,979.215

449.23 224.62 149.74 112.31

TRITON Rudder only

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Appendix C-3: HALSS Spreadsheets

Constants


Variables

Ship speed - speed (kn) = 10.00 10.00 10.00

Rudder angle - delta (deg) = 10.00 20.00 30.00 35.00 40.00

Trim - deltaT (m) = 0.00 0.00 0.00 0.00 0.00

(m) = 300.00

0

0

0.583

64,152

Rudder sweep angle - lamda (deg) = 6.90 2.20

Rudder area - Ar (m^2) = 84.60 7.69

Rudder length - l (m) = 9.30 3.20



Distance from wing propeller to CL 10.00

Profile area of side hull under WL - 39.52

157.15

8.00

tio - () =

5

in) 106 10 106

rearat 0.75t ion - 0 0.00 0. 0.00

3 0.293 0.2 0.293

6 0.046 0.0 0.046

c) = 4 5.144 5.1 5.144

5 0.485 0.4 0.485

) = 22 6,622 1,216,6 1,216,622

ull (N 61 ,061 1,945,0 1,945,061

.489 0.4 0.489

= .060 13.0 13.060

quan

ss - m 00 ,000 ,152,0 64 64,152,000

inal v /sec) = 44 .144 5.1 5.144

a eral cen = % 35% 2.3 2.35%

ec = 22 .022 1.0 1.022

ft cur Cl 25 .025 0.0 0.025

orce at eg) = 97 .197 ,677.1 28 28,677.197

orce a - 72 .943 0,315.9 ,003 1,147,087.886

er *m/d 31 .331 2,109.3 ,112 -4,112,109.331

el 12 .624 3,279.9 ,923 -164,484,373.249

ull sw riv c) 56 .156 7,683.1 ,837 -1,837,683.156

ull ya iva sec) 93 3.393 5,103.3 ,895 178,895,103.393

ull sw iva = 00 0.000 6,320.0 ,776 -227,776,320.000

ull ya t *sec - 00 0.000 2,160.0 ,13 -31,433,132,160.000

0.102 0.1 0.102

0.160 0.160 0.160 0.160

Side hull sway-sway derivative - Yvs (N/m*sec) = -504,144.426 -504,144.426 -504,144.426 -504,144.426 -504,144.426

Side hull yaw-sway derivative - Yrs (N/rad*sec) = -17,152,858.692 -17,152,858.692 -17,152,858.692 -17,152,858.692 -17,152,858.692

Side hull sway-yaw derivative - Nvs (N*sec) = -17,152,858.692 -17,152,858.692 -17,152,858.692 -17,152,858.692 -17,152,858.692

Side hull yaw-yaw derivative - Nrs (N*m/rad *sec) = -583,603,718.263 -583,603,718.263 - 583,603 ,718 .263 -583 ,603 ,718 .263 -583,603,718.2 63

Ship sway-sway derivative - Yv (N/m*sec) = -2,845,972.007 -2,845,972.007 -2,845,972.007 -2,845,972.007 -2,845,972.007

Ship yaw-sway derivative - Yr (N/rad*sec) = 144,589,386.010 144,589,386.010 144,589,386.010 144,589,386.010 144,589,386.010

Shp sway-yaw derivative - Nv (N*sec) = -262,082,037.383 -262,082,037.383 -262,082,037.383 -262,082,037.383 -262,082,037.383

Ship yaw-yaw derivat ive - Nr (N*m/rad*sec) = -32,600,339,596.526 -32,600,339,596.526 -32,600,339,596.526 -32,600,339,596.526 -32,600,339,596.526

Wing propeller thrust (starboard) - Tws (N) = 0 0 0 0 0

Wing propeller thrust (port) - Twp (N) = 0 0 0 0 0

Ship's turning rate - rr (rad/sec) = 0.004 0.007 0.011 0.012 0.014


10.00 10.00

Parameters HALSS

Center hull length at WL - L

Triton

90.00



Center hull block coefficient based on WL data - Cb () =

Ship displacement - disp (MT) =

7.20

3.65

0.557

1,350

10.69 aft

143.39

- ys(m) = 23.58

Af (m^2) = 1,195.70

Side hull length at WL - Ls (m) =

Side hull draft at WL - Ts (m) =

Dis tanc d le side hu ll from MS - xs (m)

34.80

2.15

2.2e of mid = 34.02 aft 5 aft

Pitch/diameter ra

Propeller diamet

1

6.00er - (m) =

es - () =Numberof blad

1/mRPM - (

Blade a

=

io - () =

6 106 106

Wake frac () = 0.0 00 0.00

KT = 0.29 93 0.293

KQ = 0.04 46 0.046

Va (m/se

J =

5.14

0.48

44

85

5.144

0.485

Thrust (N 1,216,6 1,21 22 1,216,622

Bollart P

Eta0 =

) = 1,945,0

0.489

1,945

0

61

89

1,945,061

0.489

PS (MW) 13.060 13 60 13.060

Derived tities

Ship ma (kg) = 64,152,0 64,152 64 00 ,152,000

Longitud elocity - u (m 5.1 5 44 5.144

Rudder are as a % or lat ter hull area - () 2.35 2. 5% 2.35%

Rudder asp

Rudder li

t ratio - a ()

veslope - d

1.0

0.0

1

0

22

25

1.022

0.025ddelta (1/deg) =

Rudder f control deriv ive - Ydelta - (N/d 28,677.1 28,677 28 97 ,677.197

Rudder f

Rudder mome

- Ydeltadelt

nt control d

(N) =

ivative - Ndelta (N

286,771.9

-4,112,109.3

573,543

-4,112,109

86

-4,11

15 1

31 -4

,701.900

,109.331eg) =

Rudder moment - Ndeltad ta (N*m) = -41,121,093.3 -82,242,186 -123,36 37 -143 ,826.593

Center h ay-sway de ative - Yvc (N/m*se = -1,837,683.1 -1,837,683 -1,83 56 -1 ,683.156

Center h w-sway der tive - Yrc (N/rad* = 178,895,103.3 178,895,10 178,89 93 178 ,103.393

Centerh

Centerh

ay-yaw der

w-yaw deriva

tive - Nvc (N*sec)

ive - Nrc (N*m/rad

-227,776,320.0

31,433,132,160.0

-227,776,32

-31,433,132,16

-227,77

-31,433,13

00 -227

00 -31,433

,320.000

2,160.000) =

Side hull aspect ratio - as () = 0.102

Side hull lift curve slope - dCldbeta (1/rad) = 0.160

02 0.102

1,451.49 725.75 483.83 414.71 362.87

IMO Standard = 750.00

HALSS Rudder only

107


26/70


Cons

S

tants

ea water density - rho (MT/m 3) = 1.025

Variables

Ship speed- speed (kn) = 10.00 10.00 10.00 10.00 10.00

0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

WL - L (m)

ter hull beam at WL - B (m) =

ter hull draft at MS - T (m) = 12.00

ter hull block coefficient bas on b () = 0.583

143.39

23.58

Profile area of side hull under WL - Af (m^2) = 1,195.70

ide hull length at WL - Ls(m) = 157.15

ide hull draft at WL - Ts (m) = 8.00

stance of middle side hull from MS - xs 34.02 aft

tch/diameter ratio - () =

peller diameter - (m) =

5

106 170 190

Wake fra = 0.00 0. 0.00

0.383

0.046 0.0 054 0.056 0.058

5.144 5.1 5.144

5 0.3 0.271

T 148 2,944 5,101,663

B (N) = 555 3,894 6,249,262

E 9 0.407 0. 0.285

P 0 737 43 93.902

D uantit

S - m (k 00 000 152, 64,152,000

L vel sec) = 44 5.144 5. 5.144

R al cente % 5% 2.3 2.35%

R pect r 22 1.022 1. 1.022

R curv lddelta ( 25 0.025 0. 0.025

R ce co tive - Yd 97 197 677. 28,677.197

R ce - Y (N) = 00 0.000 0. 0.000

R ment ivative - 31 331 109 4,1 -4,112,109.331

R ment lta 00 0.000 0. 0.000

C sway va ec) = 56 156 683 1,8 -1,837,683.156

C yaw ati ec) = 93 393 103 8 178,895,103.393

C sway ati = 00 000 320 7 -227,776,320.000

C yaw tiv *sec) -3 00 - 000 160 1 -31,433,132,160.000

S spect = 02 0.102 0. 0.102

S t curv Cl 60 0.160 0. 0.160

S way- tiv ) = 26 426 144 -5 -504,144.426

S aw-s ve ) = 92 692 858. 1 -17,152,858.692

S way- ve 92 692 858. 1 -17,152,858.692

i aw-ya ve - Nr ec) = 63 18.263 03,718.2 83,603 -583,603,718.263

hip sway-sway derivative - Yv (N/m*sec) = -2,845,972.007 -2,845,972.007 -2,845,972.007 -2,845,972.007 -2,845,972.007

hip yaw-sway derivative - Yr (N/rad*sec) = 144,589,386.010 144,589,386.010 144,589,386.010 144,589,386.010 144,589,386.010

hp sway-yaw derivative - Nv (N*sec) = -262,082,037.383 -262,082,037.383 -262,082,037.383 -262,082,037.383 -262,082,037.383


Wing propeller thrust (starboard) - Tws (N) = 2,433,244 4,150,296 5,889,263 7,907,144 10,203,326

Wing propeller thrust (port) - Twp (N) = 0 0 0 0 0



Rudder angle - delta (deg) =

Trim - deltaT (m) =

Parameters

ter hull length atCen

Cen

Cen

= 300.00

25.00

Cen ed WL data - C

Ship displacement - disp (MT) = 64,152Rudder sweepangle - lamda (deg) = 6.90


Rudder length - l (m) =

LCG from MS - xg (m) =

Distance of rudder 1/4 line from MS - xr (m) =


9.30

10.69 aft

S

S

Di (m) =

Pi

Pro

1

6.00

Number of blades - () =

RPM - (1/min) =

Blade are () =

130 150

a ratio -

ction - ()

0.75

0.00 00 0.00

KT = 0.293 0.333

51

0

0.

.355 0.371

KQ =

) =Va (m/sec

J =

44

96

5.144

0.343

5.144

0.3030.48

1,216,622hrust (N) = 2,075, ,632 3,953,572

ollart Pull

ta0 =

1,945,061

0.48

2,925, ,969

357

5,002,872

0.317

S (MW) = 13.06 26. .319 65.446

erivedq

hipmass

ies

g) = 64,152,0 64,152, 64, 000 64,152,000

ongitudinal ocity - u (m/ 5.1 144 5.144

udder area as a % or later r hull area - () = 2.35 2.3 5% 2.35%

udder as atio - a () = 1.0 022 1.022

udder lift

udder for

e slope - dC

ntrol deriva

1/deg) =

elta - (N/deg) =

0.0

28,677.1

025

197

0.025

28,677.19728,677. 28,

udder for deltadelta - 0.0 000 0.000

udder mo

udder mo

control der

- Ndeltade

Ndelta (N*m/deg

) =

) = -4,112,109.3

0.0

-4,112,109. -4,112, .331 -

000

12,109.331

0.000(N*m

enter hull

enter hull

-sway deri

-sway deriv

tive - Yvc (N/m*s

ve - Yrc (N/rad*s

-1,837,683.1

178,895,103.3

-1,837,683.

178,895,103.

-1,837,

178,895,

.156 -

.393 178,

37,683.156

95,103.393

enter hull -yaw deriv ve - Nvc (N*sec) -227,776,320.0 -227,776,320. -227,776, .000 -227, 76,320.000

enter hull -yaw deriva e - Nrc (N*m/rad = 1,433,132,160.0 31,433,132,160. -31,433,132, .000 -31,433, 32,160.000

ide hull a ratio - as () 0.1 102 0.102

ide hull lif e slope - d dbeta (1/rad) = 0.1 160 0.160

ide hull s

ide hull y

sway deriva

way derivati

e - Yvs (N/m*sec

- Yrs (N/rad*sec

-504,144.4

-17,152,858.6

-504,144.

-17,152,858.

-504,

-17,152,

.426

692 -17,

04,144.426

52,858.692

ide hull s

de hull y

yaw derivati

w derivati

- Nvs (N*sec) =

s (N*m/rad*s

-17,152,858.6

-583,603,718.2

-17,152,858.

-583,603,7

-17,152,

-583,6

692 -17,

63 -5

52,858.692

,718.263S

S

S

S

1,708.30 1,001.55 705.81 525.69 407.39

HALSS One propeller idling

108


27/70


Constants


Variables


0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00

length at WL - L (m) =

Center h ull beam a t W m) =

Centerhull draft a tM T (m)= 12.00

Center hull block coef ent () = 0.583

64,152

r (m 2) = 84

10

14

23

Profile area of side hull under WL - Af (m 2) = 1,195.70

Side hull length at WL - 15

Side hull draft at WL - T

Distance of middle side hull from MS - xs (m) = 34 2 aft

Pitch/diameter ratio - () =

Propeller diameter - (m) =

190 190

ea ratio - () =

action - () = 0.0 0.00

= 0.383 0.32 0.268

= 0.05 0.043

Va (m 6 10.288J = 0.541

Thrust 5, 60 3,563,836

Bollar 6, 262 6,249,262

Eta0 = 0.537

PS (M 54 69.712

Deriv ties

Ship g) = 64 00 64,152,000

Long city - u 6 10.288

Rudd l ll 35% 2.35%

Rudd atio - a ( 1.022

Rudd slope - 5 0.025

Rudd ntrol deri - ( 7 2 694 114,708.789

Rudd deltadel 0.000

Rudd control elt 8 -4,11 995 ,448,437.325

Rudd - ) = 0 0.000

Cent -s Yvc ( -918 -1,83 735 675,366.313

Cent sw c (N ,447 178,89 2 0 ,790,206.787

Cent -y vc (N ,888 27,77 -3 000 ,552,640.000Cent ya c (N ,566 433,13 -47,1 0 ,264,320.000

Side ra 0.102

Side e (1/ra 0.160

Side w s (N/ -25 -50 638 008,288.851

Side a (N/ra -17,15 - 037 ,717.383

-17,15 - 037 ,717.383

-583,603,718.263 -875,405,577.394 -1,167,207,436.526

Ship sway-sway derivative - Yv (N/m*sec) = -1,422,986.004 -2,845,972.007 -4,268,958.011 -5,691,944.015



Ship yaw-yaw derivati ve - Nr (N*m/rad*sec) = -16,300,169,798.263 -32,600,339,596.526 -48,900,509,394.789 -65,200,679,193.052

Wing propeller thrust (starboard) - Tws (N) = 11,464,328 10,203,326 8,747,210 7,127,672

Wing propeller thrust (port) - Twp (N) = 0 0 0 0


HALSS One propeller idling


im - deltaT (m) =Tr

Parameters

Centerhull 300.00

25.00L - B (

S -

f ic i based on WLdata - Cb

Ship displacement - disp (MT) =Rudder sweep angle - lamda (deg) =

Rudder area - A

6.90

.60

Rudder length - l (m) =


Distance of rudder 1/4 line from MS -xr (m) =


9.30

.69 aft

3.39

.58

Ls (m) =

s (m) =

7.15

8.00

.0

1

6.00


RPM - (1/min) =

5

190 190

Blade ar 0.75

0.00Wake fr 0.00 0

KT

KQ

0.430

0.064

8

10.058

5.144/sec) = 2.572 7.710.135

732,164

0.271

5,101,663

0.40

4,373,

6

5(N) =

t Pull (N) = 249,262 6,249,262 6,249,

0.145 0.285 0.417

W) = 103.661 93.902 82. 6

ed quanti

mass - m (k

itudinal velo

,152,000

2.572

64,152,000

5.144

64,152,

7.71

0

(m/sec) =

er area as a % or

er aspect r

ateral center hu

) =

area - () = 2.35%

1.022

2.35%

1.022

2.

1.022

er lift curve dClddelta (1/deg) = 0.025 0.025 0.02

er force co vative - Ydelta N/deg) = ,169.299 8,677.197 64,523.

er force - Y

er moment

ta - (N) =

derivative - Nd

0.000

,027.333

0.000

2,109.331

0.00

-9,252,245.

0

-16a (N*m/deg) = -1,02

er moment Ndeltadelta (N*m 0.000 0.000 0.00

er hull sway way derivative - N/m*sec) = ,841.578 7,683.156 -2,756,524. -3,

er hull yaw- ay derivative - Yr /rad*sec) = 89 ,551.697 5,103.393 68,342,655.09 357

er hull swayer hull yaw-

aw derivative - Nw derivative - Nr

*sec) =*m/rad*sec) =

-113-15,716

,160.000 -2,080.000 -31,

6,320.0002,160.000

41,664,480.49,698,240.00

-455-62,866

hull aspect tio - as () = 0.102 0.102 0.102

hull lift curv

hull sway-s

slope - dCldbeta

ay derivative - Yv

d) =

m*sec)=

0.160

2,072.213

0.160

4,144.426

0.16

-756,216.

0

-1,

hull yaw-sw y derivative - Yrs d*sec) = -8,576,429.346 2,858.692

2,858.692

25,729,288.

25,729,288.

-34,305

-34,305Side hull sway-yaw derivative - Nvs (N*sec) = -8,576,429.346

Side hull yaw-yaw d erivative - Nrs (N*m/rad*sec) = -291,801,859.131

109


28/70


Cons

S

tants

ea water density - rho (MT/m 3) = 1.025

Variables

Ship speed- speed (kn) = 10.00

0.00

10.00 10.00 10.00 10.00

0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

WL - L (m)

L - B (m) =

S - T (m) =

ter hull blockcoefficient bas on WL data - Cb () =

ip displacement - disp (MT) = 64,152der sweep angle - lamda (de = 6.90

10.69 aft

8

1,195.70

157.15


Distance of middle sidehull from 34.02 aft

Pitch/diameter ratio - () =

Propeller diameter - (m) =


RPM - (1/min) = 150 170 190

0.75

0.00 0.00 0.00

.33 0.383

0.05 0.058

5.144 5.14 144 5.144 5.144

0.485 0.39 0.271

) = ,622 75,14 2,9 5,101,663

(N) = 55 3,8 6,249,262

E 9 0.407 0. 0.285

P 0 737 43 93.902

D uantiti

S - m (k 000 152, 64,152,000

L velo /sec) = 44 5.144 5. 5.144

R al cente % 5% 2.3 2.35%

R pect r 22 1.022 1. 1.022

R curv lddelta ( 25 0.025 0. 0.025

R ce co tive - Yd 97 197 677. 28,677.197

R ce - Y (N) = 00 0.000 0. 0.000

R ment ivative - 31 331 109 4,1 -4,112,109.331

R ment lta 00 0.000 0. 0.000

C sway va ec) = 56 156 683 1,8 -1,837,683.156

C yaw ati ec) = 93 393 103 8 178,895,103.393

C sway ati = 00 000 320 7 -227,776,320.000

C yaw tiv *sec) -31, 00 -3 000 160 1 -31,433,132,160.000

S spect = 02 0.102 0. 0.102

S t curv Cl 60 0.160 0. 0.160

S way- tiv ) = 26 426 144 -5 -504,144.426

S aw-s ve ) = 92 692 858. 1 -17,152,858.692

S way- ve 92 692 858. 1 -17,152,858.692

S aw-y e - ) = 63 263 718 6 -583,603,718.263

5,972.007 -2,845,972.007 -2,845,972.007 -2,845,972.007

S ,386.010 144,589,386.010 144,589,386.010 144,589,386.010

Shp sway-yaw derivative - Nv (N*sec) = -262,082,037.383 -262,082,037.383 -262,082,037.383 -262,082,037.383 -262,082,037.383


Wing propeller thrust (starboard) - Tws (N) = 1,216,622 2,075,148 2,944,632 3,953,572 5,101,663

Wing propeller thrust (port) - Twp (N) = -243,324 -415,030 -588,926 -790,714 -1,020,333




Trim - deltaT (m) =

Parameters

Center hull length at

Center hull beam at W

ter hull draft at M

= 300.00

25.00

Cen

Cen

12.00

0.583ed

ShRud g)


Rudder length - l (m) = 9.30




Profile area of side hull under WL - Af (m^2) =

Side hull length at WL - Ls(m) =

MS - xs (m) =

1

6.00

5

106 130

Bladearea ratio - () =

Wake fraction - () = 0.00 0.00

KT =

KQ =

0.293

0.046

0 3

1

0.355

0.054

0.371

0.056

Va (m/sec) =

J =

4

6

5.

0.343

44,632

94,9

0.303

3,953,572

2

Thrust (N

B

1,216 2,0 8

5ollart Pull

ta0 =

1,945,061

0.48

2,925, 69

357

5,002,87

0.317

S (MW) = 13.06 26. .319 65.446

erived q es

hip mass g) = 64,152,000 64,152, 64, 000 64,152,000

ongitudinal city - u (m 5.1 144 5.144

udder area as a % or later r hull area - () = 2.35 2.3 5% 2.35%

udder as atio - a () = 1.0 022 1.022

udder lift

udder for

e slope - dC

ntrol deriva

1/deg) =

elta - (N/deg) =

0.0

28,677.1

025

197

0.025

28,677.19728,677. 28,

udder for deltadelta - 0.0 000 0.000

udder mo

udder mo

control der

- Ndeltade

Ndelta (N*m/deg

) =

) = -4,112,109.3

0.0

-4,112,109. -4,112, .331 -

000

12,109.331

0.000(N*m

enter hull

enter hull

-sway deri

-sway deriv

tive - Yvc (N/m*s

ve - Yrc (N/rad*s

-1,837,683.1

178,895,103.3

-1,837,683.

178,895,103.

-1,837,

178,895,

.156 -

.393 178,

37,683.156

95,103.393

enter hull -yaw deriv ve - Nvc (N*sec) -227,776,320.0 -227,776,320. -227,776, .000 -227, 76,320.000

enter hull -yaw deriva e - Nrc (N*m/rad = 433,132,160.0 1,433,132,160. -31,433,132, .000 -31,433, 32,160.000

ide hull a ratio - as () 0.1 102 0.102

ide hull lif e slope - d dbeta (1/rad) = 0.1 160 0.160

ide hull s

ide hull y

sway deriva

way derivati

e - Yvs (N/m*sec

- Yrs (N/rad*sec

-504,144.4

-17,152,858.6

-504,1

-17,152,858.

44. -504,

-17,152,

.426

692 -17,

04,144.426

52,858.692

ide hull s yaw derivati - Nvs (N*sec) = -17,152,858.6 -17,152,858. -17,152, 692 -17, 52,858.692

ide hull y aw derivativ Nrs (N*m/rad*sec -583,603,718.2 -583,603,718. -583,603, .263 -583, 03,718.263

Ship sway-sway derivative - Yv (N/m*sec) = -2,845,972.007 -2,84

hip yaw-sway derivative - Yr (N/rad*sec) = 144,589,386.010 144,589

2,847.17 1,669.25 1,176.36 876.15 678.98

HALSS One propeller reversing 20% fwd thrust

110


29/70


Constants


Variables


Rudder angle- delta (deg) = 0.00 0.00 0.00 0.00

Trim - deltaT (m) = 0.00 0.00 0.00 0.00

Parameters

Center hull length at WL - L (m) = 300.00



Center hull block coefficient based on WL data - Cb () = 0.583

Ship displacement - disp (MT) = 64,152Rudder sweep angle - lamda (deg) = 6.90


Rudder length - l (m) = 9.30




Profile area of side hull under WL - Af (m^2) = 1,195.70

Side hull length at WL - Ls (m) = 157.15


Distance of middle side hull from MS - xs (m) = 34.02 aft

Pitch/diameter ratio - () = 1

Propeller diameter - (m) = 6.00


RPM - (1/min) = 190 190 190 190

Blade area ratio - () = 0.75

Wake fraction - () = 0.00 0.00 0.00 0.00

KT = 0.430 0.383 0.328 0.268

KQ = 0.064 0.058 0.051 0.043

Va (m/sec) = 2.572 5.144 7.716 10.288

J = 0.135 0.271 0.406 0.541

Thrust (N) = 5,732,164 5,101,663 4,373,605 3,563,836

Bollart Pull (N) = 6,249,262 6,249,262 6,249,262 6,249,262

Eta0 = 0.145 0.285 0.417 0.537

PS (MW) = 103.661 93.902 82.546 69.712

Derived quantities

Ship mass - m (kg) = 64,152,000 64,152,000 64,152,000 64,152,000

Longitudinal velocity - u (m/sec) = 2.572 5.144 7.716 10.288

Rudder area as a % or lateral center hull area - () = 2.35% 2.35% 2.35% 2.35%

Rudder aspect ratio - a () = 1.022 1.022 1.022 1.022

Rudder lift curve slope - dClddelta (1/deg) = 0.025 0.025 0.025 0.025

Rudder force control derivative - Ydelta - (N/deg) = 7,169.299 28,677.197 64,523.694 114,708.789

Rudder force - Ydeltadelta - (N) = 0.000 0.000 0.000 0.000

Rudder moment control derivative - N delta ( N*m/deg) = -1,028,027.333 -4,112,109.331 -9,252,245.995 -16,448,437.325

Rudder moment - Ndeltadelta (N*m) = 0.000 0.000 0.000 0.000

Center hull sway-sway derivative - Yvc (N/m*sec) = -918,841.578 -1,837,683.156 -2,756,524.735 -3,675,366.313

Center hull yaw-sway d erivative - Yrc (N/rad*sec) = 89,447,551.697 178,895,103.393 268,342,655.090 357,790,206.787

Center hull sway-yaw d erivative - Nvc (N*sec) = -113,888,160.000 -227,776,320.000 -341,664,480.000 -455,552,640.000

Center hull yaw-yaw derivative - Nrc (N*m/rad*sec) = -15,716,566,080.000 -31,433,132,160.000 -47,149,698,240.000 -62,866,264,320.000

Side hull aspect ratio - as () = 0.102 0.102 0.102 0.102

Side hull lift curve slope - dCldbeta (1/rad) = 0.160 0.160 0.160 0.160

Side hull sway-sway derivative - Yvs (N/m*sec) = -252,072.213 -504,144.426 -756,216.638 -1,008,288.851

Side hull yaw-sway derivative - Yrs (N/rad*sec) = -8,576,429.346 -17,152,858.692 -25,729,288.037 -34,305,717.383

Side hull sway-yaw derivative - Nvs ( N*sec) = -8,576,429.346 -17,152,858.692 -25,729,288.037 -34,305,717.383

Side h ull yaw-yaw deri vative - Nrs (N*m/rad*sec) = -291,801,859.131 -583,603,718.263 -875,405,577.394 -1,167,207,436.526

Ship sway-sway derivative - Yv (N/m*sec) = -1,422,986.004 -2,845,972.007 -4,268,958.011 -5,691,944.015



Ship yaw-yaw der ivative - Nr(N*m/ rad*sec) = -16,300,169 ,798 .263 -32 ,600,339,596.526 -48,900,509,394 .789 -65 ,200,679,193 .052

Wing propeller thrust (starboard) - Tws (N) = 5,732,164 5,101,663 4,373,605 3,563,836

Wing propeller thrust (port) - Twp (N) = -1,146,433 -1,020,333 -874,721 -712,767


Ship's steady turning radius - TurningRadius (m) = 151.07 678.98 1,782.02 3,887.87

HALSS One propeller reversing 20% fwd thrust

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foundation girders forward of frame 45 to provide a good transition, in addition to providingbrackets to taper the inner skin bulkheads aft of frame 45.

Longitudinal Strength Curves Strategic Mobility Departure

Longitudinal Strength Curves - Strategic Mobility Arrival

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Longitudinal Strength Curves - Early Entry Departure

Longitudinal Strength Curves - Early Entry Arrival

The maximum shear force requires the side shell plating to be 16.5mm vs 16.0 provided, if alllongitudinal bulkheads are ineffective. In the area of maximum shear, the main enginefoundation girders and centerline longitudinal bulkheads provide additional shear area whichshould be sufficient to achieve adequate shear strength with no increase in shell plate thickness.

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APPENDIX E: Model test results (Tables)

The test results are presented in the following Tables

--------------------------------------------------------------------------------------

EHP RESULTS FROM EXPERIMENT NUMBER = 1

DTRC MODEL NUMBER = 5651

MODEL CONDITION = HALSS: Center Hull Only @ 11.5 m Draft, Bare Hull, Bow Bulb

SHIP MODEL

LENGTH 950.83 FT (289.8 M) 17.61 FT (5.367 M)

WETTED SURFACE 101780.0 FT2 (9456.0 M2) 34.90 FT2 (3.24 M2)

DISPLACEMENT 47297.TONS (48054. T) 0.29 TONS (0.29 T)

RHO 1.9905 (31.885 N S2/M4) 1.9367 (31.023 N S2/M4)

NU (E+5) 1.2816 (0.11906 M2/SEC) 1.9905 (0.18493 M2/SEC)

LINEAR RATIO 54.000

ITTC FRICTION LINE

CORRELATION ALLOWANCE (CA) 0.00000

--------------------------------------------------------------------------------------

VS PE FRICTIONAL POWER FN V-L 1000CR

--------------------------------------------------------------------------------------KNOTS M/S HP KW HP KW

--------------------------------------------------------------------------------------

10.0 5.14 1460.0 1088.7 1318.3 983.1 0.096 0.324 0.160

12.0 6.17 2472.9 1844.0 2228.1 1661.5 0.116 0.389 0.160

14.0 7.20 3886.1 2897.9 3473.0 2589.8 0.135 0.454 0.170

15.0 7.72 4900.0 3653.9 4236.5 3159.2 0.145 0.486 0.222

16.0 8.23 6139.5 4578.2 5102.2 3804.7 0.154 0.519 0.286

18.0 9.26 8981.8 6697.7 7163.9 5342.1 0.174 0.584 0.352

20.0 10.29 12397.8 9245.1 9705.9 7237.7 0.193 0.649 0.380

22.0 11.32 16546.8 12338.9 12775.2 9526.5 0.212 0.713 0.400

24.0 12.35 21547.6 16068.0 16418.5 12243.2 0.232 0.778 0.419

25.0 12.86 24447.0 18230.1 18469.8 13772.9 0.241 0.811 0.432

26.0 13.38 28168.1 21004.9 20681.9 15422.5 0.251 0.843 0.481

28.0 14.40 39821.0 29694.5 25611.3 19098.3 0.270 0.908 0.731

30.0 15.43 58747.2 43807.8 31252.0 23304.6 0.289 0.973 1.15032.0 16.46 76241.2 56853.0 37649.2 28075.0 0.309 1.038 1.330

34.0 17.49 90197.5 67260.3 44847.7 33442.9 0.328 1.103 1.303

35.0 18.01 98117.6 73166.3 48761.3 36361.3 0.338 1.135 1.300

36.0 18.52 107798.8 80385.6 52891.9 39441.5 0.347 1.167 1.329

38.0 19.55 134710.9 100453.9 61826.1 46103.7 0.367 1.232 1.500

40.0 20.58 177729.2 132532.6 71694.3 53462.4 0.386 1.297 1.871

42.0 21.61 235008.2 175245.6 82540.2 61550.2 0.405 1.362 2.324

44.0 22.64 301014.3 224466.3 94407.4 70399.6 0.425 1.427 2.739

45.0 23.15 337488.7 251665.3 100737.4 75119.9 0.434 1.459 2.934

--------------------------------------------------------------------------------------

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-------------------------------------------------------------------------------------EHP RESULTS FROM EXPERIMENT NUMBER = 2DTRC MODEL NUMBER = 5651MODEL CONDITION = HALSS: Center Hull Only @ 11.5 m Draft, Bare Hull, Stem Bow

SHIP MODELLENGTH 926.18 FT (282.3 M) 17.15 FT (5.228 M)WETTED SURFACE 98633.0 FT

2(9163.0 M

2) 33.82 FT

2(3.14 M

2)

DISPLACEMENT 46938.TONS (47689. T) 0.29 TONS (0.29 T)

RHO 1.9905 (31.885 N S2

/M4

) 1.9367 (31.023 N S2

/M4

)NU (E+5) 1.2816 (0.11906 M

2/SEC) 1.9905 (0.18493 M

2/SEC)

LINEAR RATIO 54.000ITTC FRICTION LINECORRELATION ALLOWANCE (CA) 0.00000

------------------------------------------------------------------------------------- VS PE FRICTIONAL POWER FN V-L 1000CR-------------------------------------------------------------------------------------KNOTS M/S HP KW HP KW-------------------------------------------------------------------------------------10.0 5.14 1590.6 1186.1 1281.7 955.7 0.098 0.329 0.360

12.0 6.17 2699.9 2013.3 2166.1 1615.2 0.117 0.394 0.360

14.0 7.20 4249.8 3169.1 3376.3 2517.7 0.137 0.460 0.371

15.0 7.72 5294.3 3948.0 4118.4 3071.1 0.147 0.493 0.406

16.0 8.23 6562.7 4893.8 4959.9 3698.6 0.156 0.526 0.45618.0 9.26 9596.4 7156.0 6964.0 5193.0 0.176 0.591 0.526

20.0 10.29 13402.8 9994.5 9434.8 7035.5 0.196 0.657 0.578

22.0 11.32 17882.4 13334.9 12418.2 9260.2 0.215 0.723 0.598

24.0 12.35 23302.5 17376.7 15959.4 11900.9 0.235 0.789 0.619

25.0 12.86 26655.2 19876.8 17953.3 13387.7 0.244 0.821 0.649

26.0 13.38 30661.1 22864.0 20103.4 14991.1 0.254 0.854 0.700

28.0 14.40 43543.9 32470.6 24894.5 18563.9 0.274 0.920 0.990

30.0 15.43 65872.8 49121.3 30377.1 22652.2 0.293 0.986 1.532

32.0 16.46 84397.5 62935.2 36594.8 27288.7 0.313 1.051 1.700

34.0 17.49 100591.5 75011.0 43591.2 32505.9 0.332 1.117 1.690

35.0 18.01 108985.3 81270.3 47394.9 35342.4 0.342 1.150 1.674

36.0 18.52 119031.9 88762.1 51409.5 38336.1 0.352 1.183 1.689

38.0 19.55 148240.3 110542.8 60092.8 44811.2 0.372 1.249 1.872

40.0 20.58 194627.6 145133.8 69683.7 51963.1 0.391 1.314 2.275

42.0 21.61 254744.2 189962.7 80224.8 59823.6 0.411 1.380 2.74544.0 22.64 324798.0 242201.9 91758.4 68424.2 0.430 1.446 3.188

45.0 23.15 360731.1 268997.1 97910.4 73011.8 0.440 1.479 3.361-------------------------------------------------------------------------------------

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--------------------------------------------------------------------------------------


DTRC MODEL NUMBER = 5651MODELCONDITION

= HALSS: Center Hull @ 11.5 m Draft. Side Hulls @ 7.5 m Draft, Middle

Longitudinal Location, and Inboard Transverse Location.

SHIP MODEL

LENGTH 950.83 FT (289.8 M) WETTED SURFACE 172,524.0FT2(16,028.0 M2)

17.61 FT (5.367 M) 59.16 FT2(5.50 M2)

DISPLACEMENT 59,393.0 TONS (60,343.0 T) RHO 1.9905(31.885 N S2/M4) NU (E+5) 1.2816 (0.11906 M2/SEC)

0.37 TONS (0.37 T) 1.9367 (31.023 N S2/M4)1.9905 (0.18493 M2/SEC)

LINEAR RATIO 54.000

ITTC FRICTION LINE


------------------------------------------------- -------------------------------------


--------------- -------------------- --------------------- ---------- ---------- ----------

KNOTS M/S HP KW HP KW

------- -------- ---------- ---------- ---------- ----------- ---------- ---------- ----------10.0 5.14 3105.3 2315.6 2234.7 1666.4 0.096 0.324 0.580

12.0 6.17 5281.2 3938.2 3776.8 2816.3 0.116 0.389 0.58014.0 7.20 8275.9 6171.4 5887.0 4390.0 0.135 0.454 0.58016.0 8.23 12460.5 9291.8 8648.6 6449.3 0.154 0.519 0.62018.0 9.26 18533.8 13820.6 12143.4 9055.3 0.174 0.584 0.73020.0 10.29 26358.9 19655.8 16452.2 12268.4 0.193 0.649 0.82522.0 11.32 36518.9 27232.2 21654.9 16148.1 0.212 0.713 0.93024.0 12.35 48995.6 36536.0 27830.6 20753.2 0.232 0.778 1.02026.0 13.38 61966.9 46208.7 35057.4 26142.3 0.251 0.843 1.02028.0 14.40 74715.8 55715.6 43413.1 32373.1 0.270 0.908 0.95030.0 15.43 92691.4 69120.0 52974.6 39503.2 0.289 0.973 0.98032.0 16.46 113003.6 84266.8 63818.4 47589.4 0.309 1.038 1.00034.0 17.49 135016.1 100681.5 76020.4 56688.4 0.328 1.103 1.00036.0 18.52 168090.9 125345.4 89655.9 66856.4 0.347 1.167 1.120

38.0 19.55 226698.2 169048.9 104800.1 78149.4 0.367 1.232 1.48040.0 20.58 311735.9 232461.4 121527.5 90623.0 0.386 1.297 1.98042.0 21.61 423490.1 315796.5 139912.1 104332.4 0.405 1.362 2.55044.0 22.64 563433.4 420152.2 160027.9 119332.8 0.425 1.427 3.155

45.0 23.15 635809.1 474122.8 170757.8 127334.1 0.434 1.459 3.400

--------------------------------------------------------------------------------------

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EHP RESULTS FROM EXPERIMENT NUMBER = 6DTRC MODEL NUMBER = 5651MODELCONDITION


Longitudinal Location, Middle Transverse Location.

SHIP MODEL


17.61 FT (5.367 M) 59.16 FT2(5.50 M2)

DISPLACEMENT 59,393.0TONRHO 1.9905 (NU (E+5) 1.2816 (

S (60,343.0 T) 31.885 NS2/M4) 0.11906M2/SEC)

0.37TON1.9367(311.9905 (0.

S (0.37 T).023 N S2/M4)18493 M2/SEC)

LINEAR RATIO 54.000

ITTC FRICTION LINE


------------------------------------------------- -------------------------------------


--------------- -------------------- --------------- ------ ---------- ---------- ----------


------- -------- ---------- ---------- ---------- ----------- ---------- ---------- ----------10.0 5.14 3105.3 2315.6 2234.7 1666.4 0.096 0.324 0.580

12.0 6.17 5281.2 3938.2 3776.8 2816.3 0.116 0.389 0.58014.0 7.20 8275.9 6171.4 5887.0 4390.0 0.135 0.454 0.58016.0 8.23 12460.5 9291.8 8648.6 6449.3 0.154 0.519 0.62018.0 9.26 18271.1 13624.8 12143.4 9055.3 0.174 0.584 0.70020.0 10.29 25698.5 19163.3 16452.2 12268.4 0.193 0.649 0.77022.0 11.32 34441.2 25682.8 21654.9 16148.1 0.212 0.713 0.80024.0 12.35 44430.6 33131.9 27830.6 20753.2 0.232 0.778 0.80026.0 13.38 56162.8 41880.6 35057.4 26142.3 0.251 0.843 0.80028.0 14.40 73727.3 54978.4 43413.1 32373.1 0.270 0.908 0.92030.0 15.43 92691.4 69120.0 52974.6 39503.2 0.289 0.973 0.98032.0 16.46 113003.6 84266.8 63818.4 47589.4 0.309 1.038 1.00034.0 17.49 151535.0 112999.6 76020.4 56688.4 0.328 1.103 1.28036.0 18.52 203806.9 151978.8 89655.9 66856.4 0.347 1.167 1.63038.0 19.55 273645.5 204057.4 104800.1 78149.4 0.367 1.232 2.05040.0 20.58 350161.8 261115.6 121527.5 90623.0 0.386 1.297 2.38042.0 21.61 440171.2 328235.6 139912.1 104332.4 0.405 1.362 2.70044.0 22.64 560876.1 418245.2 160027.9 119332.8 0.425 1.427 3.13545.0 23.15 626234.5 466983.0 170757.8 127334.1 0.434 1.459 3.330

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EHP RESULTS FROM EXPERIMENT NUMBER = 7DTRC MODEL NUMBER = 5651MODELCONDITION


Longitudinal Location, Outboard Transverse Location.

SHIP MODEL


17.61 FT (5.367 M) 59.16 FT2(5.50 M2)


0.37 TONS (0.37 T) 1.9367 (31.023 N S2/M4)1.9905 (0.18493 M2/SEC)

LINEAR RATIO 54.000

ITTC FRICTION LINE


------------------------------------------------- -------------------------------------


--------------- -------------------- --------------------- ---------- ---------- ----------


------- -------- ---------- ---------- ---------- ----------- ---------- ---------- ----------10.0 5.14 3225.3 2405.1 2234.7 1666.4 0.096 0.324 0.660

12.0 6.17 5488.7 4092.9 3776.8 2816.3 0.116 0.389 0.66014.0 7.20 8605.4 6417.1 5887.0 4390.0 0.135 0.454 0.66016.0 8.23 12706.4 9475.2 8648.6 6449.3 0.154 0.519 0.66018.0 9.26 18096.1 13494.2 12143.4 9055.3 0.174 0.584 0.68020.0 10.29 24857.9 18536.5 16452.2 12268.4 0.193 0.649 0.70022.0 11.32 34601.0 25802.0 21654.9 16148.1 0.212 0.713 0.81024.0 12.35 45260.6 33750.8 27830.6 20753.2 0.232 0.778 0.84026.0 13.38 57350.0 42765.9 35057.4 26142.3 0.251 0.843 0.84528.0 14.40 74056.8 55224.2 43413.1 32373.1 0.270 0.908 0.93030.0 15.43 92691.4 69120.0 52974.6 39503.2 0.289 0.973 0.98032.0 16.46 113003.6 84266.8 63818.4 47589.4 0.309 1.038 1.00034.0 17.49 135016.1 100681.5 76020.4 56688.4 0.328 1.103 1.00036.0 18.52 175794.4 131089.8 89655.9 66856.4 0.347 1.167 1.23038.0 19.55 246465.5 183789.3 104800.1 78149.4 0.367 1.232 1.72040.0 20.58 344397.9 256817.5 121527.5 90623.0 0.386 1.297 2.32042.0 21.61 462412.6 344821.0 139912.1 104332.4 0.405 1.362 2.90044.0 22.64 584530.7 435884.5 160027.9 119332.8 0.425 1.427 3.320

45.0 23.15 648119.3 483302.5 170757.8 127334.1 0.434 1.459 3.490

--------------------------------------------------------------------------------------

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--------------------------------------------------------------------------------------


DTRC MODEL NUMBER = 5651MODELCONDITION

= HALSS: Center Hull @ 11.5 m Draft. Side Hulls @ 7.5 m Draft, Aft

Longitudinal Location, Inboard Transverse Location.

SHIP MODEL


17.61 FT (5.367 M) 59.16 FT2(5.50 M2)


0.37 TONS (0.37 T) 1.9367 (31.023 N S2/M4)1.9905 (0.18493 M2/SEC)

LINEAR RATIO 54.000

ITTC FRICTION LINE


------------------------------------------------- -------------------------------------


--------------- -------------------- --------------------- ---------- ---------- ----------


------- -------- ---------- ---------- ---------- ----------- ---------- ---------- ----------10.0 5.14 3480.5 2595.4 2234.7 1666.4 0.096 0.324 0.830

12.0 6.17 5929.6 4421.7 3776.8 2816.3 0.116 0.389 0.83014.0 7.20 9305.6 6939.2 5887.0 4390.0 0.135 0.454 0.83016.0 8.23 13751.6 10254.6 8648.6 6449.3 0.154 0.519 0.83018.0 9.26 19496.7 14538.7 12143.4 9055.3 0.174 0.584 0.84020.0 10.29 27019.4 20148.3 16452.2 12268.4 0.193 0.649 0.88022.0 11.32 39236.0 29258.3 21654.9 16148.1 0.212 0.713 1.10024.0 12.35 56258.1 41951.6 27830.6 20753.2 0.232 0.778 1.37026.0 13.38 70409.

scantling calculations

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