13993024 Preliminary Ship Design

PRELIMINARY SHIP DESIGNPARAMETER ESTIMATION Shi p desig n cal cul ati ons – Sele cti on of Mai n pa rame ters START Read : owner’s requirements (ship type dwt/TEU, speed) Define limits on L, B, D, T Define stability constraints First estimate of main dimensions Estimate freeboard =LBTCb (1 + s) Estimate form coefficients & form stability parameters Estimate power Estimate lightweight Estimate stability parameters Estimate required minimum section modulus Estimate hull natural vibration frequency Estimate capacity : GRT, NRT S Change parameters No D = T+ freeboard + margin No No Estimate seakeeping qualities Yes Is D >= T + freeboard Yes Yes Is= Lightweight + dwt & Is Capacity adequate? Stability constraints satisfied 1.0 The choice of parameters (main dimensions and coefficients) can be based on either of the following 3 ship design categories (Watson & Gilafillon, RINA 1977) A. Deadweight carriers where the governing equation is ( ) t lightweigh deadweight s T B L C B + · + × × × × · ∆ 1 ρ where s : shell plating and appendage displacement (approx 0.5 to 0.8 % of moulded displacement) and ρ : density of water (= 1.025 t/m 3 for sea water ) Here T is the maximum draught permitted with minimum freeboard. This is also the design and scantling draught B. Capacity carriers where the governing equation is m s u r BD h V s V V D B L C V + − − · ′ · 1 . . . where D′ = capacity depth in m m m S C D + + · m C = mean camber [ ] camber parabolic for C . 3 2 · ] ] ] · . L . C at Camber : C where 2 1 camber line straight for C m S = mean sheer ( ) ] ] ] ] ] · · + · shear aft S shear ford S shear parabolic for S S c f a f 6 1 BD C = block coefficient at moulded depth ( ) ( ) [ ] T T D C C B B 3 8 . 0 1 − − + · [1] h V = volume of ship in m 3 below upper deck and between perpendiculars r V = total cargo capacity required in m 3 u V = total cargo capacity in m 3 available above upper deck m V = volume required for c m , tanks, etc. within h V s S = % of moulded volume to be deducted as volume of structurals in cargo space [normally taken as 0.05] Here T is not the main factor though it is involved as a second order term in BD C C. Linear Dimension Ships : The dimensions for such a ship are fixed by consideration other than deadweight and capacity. e.g. Restrictions imposed by St. Lawrence seaway 6.10 m ≤ Loa ≤ 222.5 m Bext ≤ 23.16 m Restrictions imposed by Panama Canal B ≤ 32.3 m; T ≤ 13 m Restrictions imposed by Dover and Malacca Straits T ≤ 23 m Restrictions imposed by ports of call. Ship types (e.g. barge carriers, container ships, etc.) whose dimensions are determined by the unit of cargo they carry. Restrictions can also be imposed by the shipbuilding facilities. 2.0 Parameter Estimation The first estimates of parameters and coefficients is done (a) from empirical formulae available in published literature, or (b) from collection of recent data and statistical analysis, or (c) by extrapolating from a nearly similar ship The selection of parameters affects shipbuilding cost considerably. The order in which shipbuilding cost varies with main dimension generally is as follows: The effect of various parameters on the ship performance can be as shown in the following table [1] Speed Length Breadth Depth Block coefficient Table: Primary Influence of Dimension Parameter Primary Influence of Dimensions Length Beam Depth Draft resistance, capital cost, maneuverability, longitudinal strength, hull volume, seakeeping transverse stability, resistance, maneuverability, capital cost, hull volume hull volume, longitudinal strength, transverse stability, capital cost, freeboard displacement, freeboard, resistance, transverse stability 2.1 Displacement A preliminary estimate of displacement can be made from statistical data analysis, as a function of deadweight capacity. The statistical ∆ dwt ratio is given in the following table [1] Table: Typical Deadweight Coefficient Ranges Vessel Type C cargo DWT C total DWT Large tankers Product tankers Container ships Ro-Ro ships Large bulk carriers Small bulk carriers Refrigerated cargo ships Fishing trawlers 0.85 – 0.87 0.77 – 0.83 0.56 – 0.63 0.50 – 0.59 0.79 – 0.84 0.71 – 0.77 0.50 – 0.59 0.37 – 0.45 0.86 – 0.89 0.78 – 0.85 0.70 – 0.78  0.81 – 0.88  0.60 – 0.69  where nt Displaceme DWT Total or DWT o C C arg · 2.2 Length A. Posdunine’s formulae as modified by Van Lammeran : ( ) 3 1 2 2 ∆ ] ] ] + · T T BP V V C ft L C = 23.5 for single screw cargo and passenger ships where V = 11 to 16.5 knots = 24 for twin screw cargo and passenger ships where V = 15.5 to 18.5 knots = 26 for fast passenger ships with V≥ 20 knots B. Volker’s Statistics : 3 , 5 . 4 5 . 3 3 1 3 1 m in disp m L s m in V g V C L → ∇ → ∇ + · , ` . | − ∇ where C = 0 for dry cargo ships and container ships = 0.5 for refrigerated ship and = 1.5 for waters and trawler C. Schneekluth’s Formulae : This formulae is based on statistics of optimization results according to economic criteria, or length for lowest production cost. C V L PP ∗ ∗ ∆ · 3 . 0 3 . 0 Lpp in metres, ∆is displacement in tonnes and V is speed in knots C = 3.2, if the block coefficient has approximate value of C B = Fn 145 . 0 within the range 0.48 – 0.85 It the block coefficient differs from the value Fn 145 . 0 , the coefficient C can be modified as follows ( ) 5 . 0 145 . 0 5 . 0 2 . 3 + + · Fn C C B The value of C can be larger if one of the following conditions exists : (a) Draught and / or breadth subject to limitations (b) No bulbous bow (c) Large ratio of undadeck volume to displacement Depending on the conditions C is only rarely outside the range 2.5 to 2.8. Statistics from ships built in recent years show a tendency towards smaller value of C than before. The formulae is valid for 1000 ≥ ∆ tonnes, and n F between 0.16 to 0.32 2.3 Breadth Recent trends are: L/B = 4.0 for small craft with L ≤ 30 m such as trawlers etc. = 6.5 for L ≥ 130.0 m = 4.0 + 0.025 (L - 30) for 30 m ≤ L ≤ 130 m B = L/9 + 4.5 to 6.5 m for tankers = L/9 + 6.0 m for bulkers = L/9 + 6.5 to 7.0 m for general cargo ships = L/9 + 12 to 15 m for VLCC. or B = L/5 – 14m for VLCC B = m Dwt 2828 . 0 1000 78 . 10 ] ] ] 2.4 Depth For normal single hull vessels 5 . 2 / 55 . 1 ≤ ≤ D B D B/ = 1.65 for fishing vessels and capacity type vessels (Stability limited) = 1.90 for dwt carries like costers, tankers, bulk carriers etc. such vessels have adequate stability and their depth is determined from the hull deflection point of view. (3) D = 5 . 1 3 − B m for bulk carriers (5) Recent ships indicate the following values of D B/ D B/ = 1.91 for large tankers = 2.1 for Great Lakes ore carriers = 2.5 for ULCC = 1.88 for bulk carriers and = 1.70 for container ships and reefer ships 2.5 Draught For conventional monohull vessels, generally 75 . 3 / 25 . 2 ≤ ≤ T B However, T B/ can go upto 5 in heavily draught limited vessels. For ensuring proper flow onto the propeller [ ] B C T B 5 . 7 625 . 9 − ≤ Draught – depth ratio is largely a function of freeboard : D T / = 0.8 for type A freeboard (tankers) ( D T / < 0.8 for double hull tankers) = 0.7 for type B freeboard = 0.7 to 0.8 for B – 60 freeboard T = m dwt 290 . 0 1000 536 . 4 ] ] ] T = 0.66 D + 0.9 m for bulk carriers 2.6 Depth – Length Relationship Deadweight carriers have a high D B/ ratio as these ships have adequate stability and therefore, beam is independents of depth. In such case, depth is governed by D L/ ratio which is a significant term in determining the longitudinal strength. D L/ determines the hull deflection because b.m. imposed by waves and cargo distribution. D L/ =10 to 14 with tankers having a higher value because of favourable structural arrangement. 3.0 Form Coefficients M P B C C C . · and WP VP B C C C . · where C p : Longitudinal prismatic coefficient and C VP : Vertical prismatic coefficient L A C M P . ∇ · T A C WP VP . ∇ · 3.1 Block Coefficients ( ) [ ] n B F C − + · − 23 . 0 25 tan 7 . 0 1 8 1 where gL V F n · : Froude Number A. Ayre’s formulae C B = C – 1.68 F n where C = 1.08 for single screw ships = 1.09 for twin screw ships Currently, this formulae is frequently used with C = 1.06 It can be rewritten using recent data as CB = 1.18 – 0.69 L V for 0.5 ≤ ≤ L V 1.0 , V: Speed in Knots and L: Length in feet C B = ] ] ] + 26 20 14 . 0 B L n F or C B = ] ] ] + 26 20 14 . 0 3 2 B L n F The above formulae are valid for 0.48 ≤ C B ≤ 0.85, and 0.14 ≤ F n ≤ 0.32 Japanese statistical study [1] gives C B for 32 . 0 15 . 0 ≤ ≤ n F as 3 6 . 46 1 . 39 8 . 27 22 . 4 n n n B F F F C + − + − · 3.2 Midship Area Coefficient C B = 0.55 0.60 0.65 0.70 C M = 0.96 0.976 0.980 0.987 Recommended values of C can be given as C M = 0.977 + 0.085 (C B – 0.60) = 1.006 – 0.0056 56 . 3 − B C = ( ) [ ] 1 5 . 3 1 1 − − + B C [1] Estimation of Bilge Radius and Midship area Coefficient (i) Midship Section with circular bilge and no rise of floor ( ) π − − · 4 . . 1 2 2 T B C R M =2.33 (1 – C M ) B.T. (ii) Midship Section with rise of floor (r) and no flat of keel ( ) 8584 . 0 . 1 2 2 r B C BT R M − − · (iii) Schneekluth’s recommendation for Bilge Radius (R) ( ) 2 4 B B L k C BC R + · C k : Varies between 0.5 and 0.6 and in extreme cases between 0.4 and 0.7 For rise at floor (r) the above C B can be modified as ( ) 2 r B B T T C C − · ′ (iv) If there is flat of keel width K and a rise of floor F at 2 B then, ( ) ( ) [ ] { ¦ BT r r F C K B K B M / 4292 . 0 / 1 2 2 2 2 2 2 + − − − − · From producibility considerations, many times the bilge radius is taken equal to or slightly less than the double bottom height. 3.3 Water Plane Area Cofficient Table 11.V Equation Applicability/Source C WP = 0.180 + 0.860 C P Series 60 C WP = 0.444 + 0.520 C P Eames, small transom stern warships (2) C WP = C B /(0.471 + 0.551 C B ) tankers and bulk carriers (17) C WP = 0.175+ 0.875 C P single screw, cruiser stern C WP = 0.262 + 0.760 C P twin screw, cruiser stern C WP = 0.262 + 0.810 C P twin screw, transom stern C WP = C P 2/3 schneekluth 1 (17) C WP = ( 1+2 C B /C m ½ )/3 Schneekulth 2 (17) C WP = 0.95 C P + 0.17 (1- C P ) 1/3 U-forms hulls C WP = (1+2 C B )/3 Average hulls, Riddlesworth (2) C WP = C B ½ - 0.025 V-form hulls 4.0 Intial Estimate of Stability 4.1 Vertical Centre of Buoyancy, KB [1] ( ) 3 / 5 . 2 VP C T KB − · :Moorish / Normand recommend for hulls with 9 . 0 ≤ M C ( ) 1 1 − + · VP C T KB :Posdumine and Lackenby recommended for hulls with 0.9<C M Regression formulations are as follows : T KB = 0.90 – 0.36 C M T KB = (0.90 – 0.30 C M – 0.10 C B ) T KB = 0.78 – 0.285 C VP 4.2 Metacenteic Radius : BM T and BM L Moment of Inertia coefficient C I and C IL are defined as C I = 3 LB I T C TL = 3 LB I L The formula for initial estimation of C I and C IL are given below Table 11.VI Equations for Estimating Waterplane Inertia Coefficients Equations Applicability / Source C 1 = 0.1216 C WP – 0.0410 D’ Arcangelo transverse C IL = 0.350 C WP 2 – 0.405 C WP + 0.146 D’ Arcangelo longitudinal C I = 0.0727 C WP 2 + 0.0106 C WP – 0.003 Eames, small transom stern (2) C 1 = 0.04 (3C WP – 1) Murray, for trapezium reduced 4% (17) C I = (0.096 + 0.89 C WP 2 ) / 12 Normand (17) C I = (0.0372 (2 C WP + 1) 3 ) / 12 Bauer (17) C I = 1.04 C WP 2 ) / 12 McCloghrie + 4% (17) C I = (0.13 C WP + 0.87 C WP 2 ) / 12 Dudszus and Danckwardt (17) ∇ · T T M I B ∇ · L L M K B 4.3 Transverse Stability KG / D= 0.63 to 0.70 for normal cargo ships = 0.83 for passenger ships = 0.90 for trawlers and tugs KM T = KB + BM T GM T = KM T – KG Correction for free surface must be applied over this. Then , GM’ T = GM T – 0.03 KG (assumed). This GM’ T should satisfy IMO requirements. 4.3 Longitudinal Stability B L I B L I L L L C T L C C LBT B L C I BM GM . 2 3 · · ∇ · ≅ 100 . . 100 . . . 100 1 2 2 B L C L C T L C C T B L L GM cm MCT L I B L I B BP L · · ∇ · 4.5 Longitudinal Centre of Buoyancy (1) The longitudinal centre of buoyancy LCB affects the resistance and trim of the vessel. Initial estimates are needed as input to some resistance estimating algorithms. Like wise, initial checks of vessel trim require a sound LCB estimate. In general, LCB will move aft with ship design speed and Froude number. At low Froude number, the bow can be fairly blunt with cylindrical or elliptical bows utilized on slow vessels. On these vessels it is necessary to fair the stern to achieve effective flow into the propeller, so the run is more tapered (horizontally or vertically in a buttock flow stern) than the bow resulting in an LCB which is forward of amidships. As the vessel becomes faster for its length, the bow must be faired to achieve acceptable wave resistance, resulting in a movement of the LCB aft through amidships. At even higher speeds the bow must be faired even more resulting in an LCB aft of amidships. Harvald 8 . 0 0 . 45 70 . 9 t − · Fn LCB Schneekluth and Bestram Fn LCB 9 . 38 80 . 8 − · P C LCB 4 . 19 5 . 13 + − · Here LCB is estimated as percentage of length, positive forward of amidships. 5.0 Lightship Weight Estimation (a) Lightship weight = 64 . 0 1000 1128 ] ] ] dwt (4) (b) Lightship = Steel Weight + Outfil weight + Machinery Weight + Margin. 5.1 Steel Weight The estimated steel weight is normally the Net steel. To this Scrap steel weight (10 to 18 %) is added to get gross steel weight. Ship type Cargo Cargo cum Passenger Passenger Cross Channe Pass. ferry ( ) weight Steel × ∆ 100 20 28 30 35 For tankers, 18 100 · × ∆ weight Steel 5.1.1 Steel weight Estimation – Watson and Gilfillan From ref. (3), Hull Numeral E = 2 2 1 1 75 . 0 85 . 0 ) ( 85 . 0 ) ( h l h l L T D T B L ∑ ∑ + + − + + in metric units where 1 1 h and l : length and height of full width erections 2 2 h and l : length and height of houses. ( ) [ ] 70 . 0 5 . 0 1 1 7 − + · B s s C W W where s W : Steel weight of actual ship with block 1 B C at 0.8D 7 s W : Steel weight of a ship with block 0.70 ( ) , ` . | − − + · T T D C C C B B B 3 8 . 0 1 1 Where B C : Actual block at T. 36 . 1 7 . E K W s · Ship type Value of K For E Tanker 0.029 – 0.035 1,500 < E < 40, 000 Chemical Tanker 0.036 – 0.037 1,900 < E < 2, 500 Bulker 0.029 – 0.032 3,000 < E < 15, 000 Open type bulk and Container ship 0.033 – 0.040 6,000 < E < 13, 000 Cargo 0.029 – 0.037 2,000 < E < 7, 000 Refrig 0.032 – 0.035 E 5,000 Coasters 0.027 – 0.032 1,000 < E < 2, 000 Offshore Supply 0.041 – 0.051 800 < E < 1, 300 Tugs 0.044 350, E < 450 Trawler 0.041 – 0.042 250, E < 1, 300 Research Vessel 0.045 – 0.046 1, 350 < E < 1, 500 Ferries 0.024 – 0.037 2,000 < E < 5, 000 Passenger 0.037 – 0.038 5, 000 < E < 15, 000 5.1.2 From Basic Ship Steeel weight from basic ship can be estimated assuming any of the following relations : (i) × ∞ L W s weight per foot amidships (ii) . . . D B L W s ∞ (iii) ) ( . D B L W s + ∞ To this steel weight, all major alterations are added / substracted. Schneekluth Method for Steel Weight of Dry Cargo Ship u ∇ = volume below topmost container deck (m 3 ) D ∇ = hull volume upto main deck (m 3 ) s ∇ = Volume increase through sheer (m 3 ) b ∇ = Volume increase through camber (m 3 ) u v s s , = height of s hear at FP and AP s L = length over which sheer extends ( pp s L L ≤ ) n = number of decks L ∇ = Volume of hatchways L L L h and b ;  are length, breadth and height of hatchway u ∇ = ( )                       L b s D L L L u s BD h b l C b B L C s s B L C D B L ∇ ∇ ∇ ∇ ∑ + + + + 3 2 ϑ C BD = ( ) B B C T T D C C − − + 1 4 Where C 4 = 0.25 for ship forms with little flame flare = 0.4 for ship forms with marked flame flare C 2 = ( ) b C BD 3 2 ; C 3 = 0.7 C BD W st ( ) t = u ∇ C 1 ( ) [ ] ( ) [ ] 4 06 . 0 1 12 033 . 0 1 D D L n − + − + ( ) [ ] ( ) [ ] 85 . 0 2 . 0 1 85 . 1 05 . 0 1 − + − + D T D B ( ) [ ] ( ) [ ] 98 . 0 75 . 0 1 1 92 . 0 2 − + − + M BD BD C C C Restriction imposed on the formula : 9 < D L , and C 1 the volumetric weight factor and dependent on ship type and measured in 3 m t C 1 = ( ) [ ] 6 2 10 110 17 1 103 . 0 − − + L 3 m t for m L m 180 80 ≤ ≤ for normal ships C 1 = 0.113 to 0.121 3 m t for m L m 150 80 ≤ ≤ of passenger ships C 1 = 0.102 to 0.116 3 m t for m L m 150 100 ≤ ≤ of refrigerated ships 5.1.3 Schneekluth’s Method for Steel Weight of container Ships ( ) [ ] 3 2 10 120 002 . 0 1 093 . 0 − − + ∇ · L W u st ( ) 2 1 14 30 12 057 . 0 1 ] ] ] + ] ] ] , ` . | − + D D L ( ) [ ] 2 2 1 92 . 0 85 . 0 02 . 0 1 1 . 2 01 . 0 1 BD C D T D B − + ] ] ] , ` . | − + ] ] ] ] , ` . | − + Depending on the steel construction the tolerance width of the result will be somewhat greater than that of normal cargo ships. The factor 0.093 may vary between 0.09 and 0 the under deck volume contains the volume of a short forecastle for the volume of hatchways The ratio D L should not be less than 10 Farther Corrections : (a) where normal steel is used the following should be added : ( ) ( ) ] ] ] , ` . | − + − · 12 1 . 0 1 10 5 . 3 % D L L W t s δ This correction is valid for ships between 100 m and 180 m length (b) No correction for wing tank is needed (c) The formulae can be applied to container ships with trapizoidal midship sections. These are around 5% lighter (d) Further corrections can be added for ice-strengthening, different double bottom height, higher latchways, higher speeds. Container Cell Guides Container cell guides are normally included in the steel weight. Weight of container cell guides. Ship type Length (ft) Fixed Detachable Vessel 20 0.7 t / TEU 1 t / TEU Vessel 40 0.45 t / TEU 0.7 t / TEU Integrated 20 0.75 t / TEU - Integrated 40 0.48 t / TEU - Where containers are stowed in three stacks, the lashings weigh : for 20 ft containers 0.024 t / TEU 40 ft containers 0.031 t / TEU mixed stowage 0.043 t / TEU 5.1.4 Steel Weight Estimations : other formulations For containce Ships : 374 . 0 712 . 0 759 . 1 . . 007 . 0 D B L W pp st · [K. R. Chapman] → st W steel weight in tonns → D B L pp , , are in metres. st W = ( ) ] ] ] ] + , ` . | − ∗ , ` . | + 939 . 0 3 . 8 00585 . 0 2 675 . 0 000 , 100 340 8 . 1 9 . 0 D L C LBD B [D. Miller] → st W tonnes → D B L , , metres For Dry Cargo vessels 7 10 73 . 5 0832 . 0 − − · x st e x W where 3 2 12 B pp C B L x · [wehkamp / kerlen] ] ] ] ] + , ` . | · 1 002 . 0 6 2 72 . 0 3 2 D L D LB C W B st [ Ccmyette’s formula as represented by watson & Gilfillan ] → st W tonnes → D B L , , metres For tankers : ] ] ] , ` . | − ∗ ∗ , ` . | − + ∆ · D L B L W T L st 7 . 28 06 . 0 004 . 0 009 . 1 α α DNV – 1972 where 78 . 0 100 189 . 0 97 . 0 004 . 0 054 . 0 , ` . | ∗ ∗ , ` . | + · D L B L L α , ` . | ∆ ∗ + · 100000 00235 . 0 029 . 0 T α for ∆< 600000 t 3 . 0 100000 0252 . 0 , ` . | ∆ ∗ · T α for ∆ > 600000 t Range of Validity : 14 10 ≤ ≤ D L 7 5 ≤ ≤ B L m L m 480 150 ≤ ≤ For Bulk Carriers ( ) 8 . 0 4 . 0 5 . 0 2 1697 . 0 56 . 1 + ∗ , ` . | + · B st C T D B L W [J. M. Hurrey] , ` . | − + , ` . | + , ` . | − · 1800 200 1 025 . 0 73 . 0 035 . 0 215 . 1 274 . 4 62 . 0 L B L B L L Z W st , ` . | − , ` . | − ∗ D L D L 0163 . 0 146 . 1 07 . 0 42 . 2 [DNV 1972] here Z is the section modulus of midship section area The limits of validity for DNV formulae for bulkers are same as tankers except that is, valid for a length upto 380 m 5.2 Machinery Weight 5.2.1 Murirosmith W m = BHP/10 + 200 tons diesel = SHP/17 + 280 tons turbine = SHP/ 30 + 200 tons turbine (cross channel) This includes all weights of auxiliaries within definition of m/c weight as part of light weight. Corrections may be made as follows: For m/c aft deduct 5% For twin-screw ships add 10% and For ships with large electrical load add 5 to 12% 5.2.2 Watson and Gilfillan W m (diesel) . ] / [ 12 84 . 0 wt Auxiliary RPMi MCRi i + · ∑ W m (diesel-electric) = 0.72 (M CR) 0.78 W m (gas turbine) = 0.001 (MCR) Auxiliary weight = 0.69 (MCR) 0.7 for bulk and general cargo vessel = 0.72 (MCR) 0.7 for tankers = 0.83 (MCR) 0.7 for passenger ships and ferries = 0.19 for frigates and Convetters MCR is in kw and RPM of the engine 5.3 Wood and Outfit Wight (W o ) 5.3.1 Watson and Gilfilla W and G (RINA 1977): (figure taken from [1]) 5.3.2. Basic Ship W o can be estimated from basic ship using any of the proportionalities given below: 5.3.3. Schneekluth Out Fit Weight Estimation Cargo ships at every type N o = K. L. B., W o , tonnes → L, B → meters Where the value of K is as follows Type K (a) Cargo ships 0.40-0.45 t/m 2 (b) Container ships 0.34-0.38 t/m 2 (c) Bulk carriers without cranes With length around 140 m 0.22-0.25 t/m 2 With length around 250 m 0.17-0.18 t/m 2 (d) Crude oil tankers: With lengths around 150 m 0.25 t/m 2 With lengths around 300 m 0.17 t/m 2 Passenger ships – Cabin ships ∑ ∇ · K W 0 where ∑ ∇ total volume 1n m 3 3 3 039 . 0 036 . 0 m t m t K − · Passenger ships with large car transporting sections and passenger ships carrying deck passengers ∑ ∇ · K W 0 , where K = 0.04 t/m 2 – 0.05 t/m 2 B L W o × α or 1 2 1 2 0 02 2 B B L L L W W × + · Where suffix 2 is for new ship and 1 is for basic ship. From this, all major alterations are added or substracted. 5.4 Margin on Light Weight Estimation Ship type Margin on Wt Margin on VCG Cargo ships 1.5 to 2.5% 0.5 to ¾ % Passenger ships 2 to 3.5% ¾ to 1 % Naval Ships 3.5 to 7% 5.5 Displacement Allowance due to Appendages ( ) PP α ∆ (i) Extra displacement due to shell plating = molded displacement x (1.005 do 1.008) where 1.005 is for ULCCS and 1.008 for small craft. (ii) where C = 0.7 for fine and 1.4 for full bossings d: Propeller diameter. (iii) Rudder Displacement = 0.13 x (area) 9/2 tonnes (iv) Propeller Displacement = 0.01 x d 3 tonnes . app ext ext ∆ + ∆ · ∆ 5.6 Dead weight Estimation At initial stage deadweight is supplied. However, PR E C FW LO DO HFO o C W W W W W W W Dwt + + + + + + · & arg Where W Cargo : Cargo weight (required to be carried) which can be calculated from cargo hold capacity W HFO = SFC x MCR x in m speed range arg × Where SFC : specific fuel consumption which can be taken as 190gm/kw hr for DE and 215gm/kw hr for 6T (This includes 10% excess for ship board approx ) Range: distance to be covered between two bunkeriy port margin : 5 to 10% W DO : Weight of marine diesel oil for DG Sets which is calculated similar to above based on actual power at sea and port(s) W LO : weight of lubrication oil W LO = 20 t for medium speed DE =15 t for slow speed DE W FW : weight of fresh water W FW = 0.17 t/(person x day) W C&E : weight of crew of fresh water W C&E : 0.17t / person W PR : weight of provisions and stores W PR = 0.01t / (person x day) 5.7 Therefore weight equation to be satisfied is ext ∆ = Light ship weight + Dead weight where light ship weight = steel weight + wood and out fit weight + machinery weight + margin. 6.0 Estimation of Centre of Mass (1) The VCG of the basic hull can be estimated using an equation as follows: VCG hull = 0.01D [ 46.6 + 0.135 ( 0.81 – C B ) ( L/D ) 2 ] + 0.008D ( L/B – 6.5 ), L≤ 120 m = 0.01D [ 46.6 + 0.135 (0.81 – C B ) ( L/D ) 2 ], 120 m < L This may be modified for superstructure & deck housing The longitudinal position of the basic hull weight will typically be slightly aft of the LCB position. Waston gives the suggestion: LCG hull = - 0.15 + LCB Where both LCG and LCB are in percent ship length positive forward of amidships. The vertical center of the machinery weight will depend upon the inner bottom height h bd and the height of the engine room from heel, D. With these known, the VCG of the machinery weight can be estimated as: VCG M = h db + 0.35 ( D’-h db ) Which places the machinery VCG at 35% of the height within the engine room space. In order to estimate the height of the inner bottom, minimum values from classification and Cost Guard requirements can be consulted giving for example: h db ≥ 32B + 190 T (mm) (ABS) or h db ≥ 45.7 + 0.417 L (cm) Us Coast Guard The inner bottom height might be made greater than indicated by these minimum requirements in order to provide greater double bottom tank capacity, meet double hull requirements, or to allow easier structural inspection and tank maintenance. The vertical center of the outfit weight is typically above the main deck and can be estimated using an equation as follows: VCG o = D + 1.25, L ≤ 125 m = D + 1.25 + 0.01(L-125), 125 < L ≤ 250 m = D + 2.50, The longitudinal center of the outfit weight depends upon the location of the machinery and the deckhouse since significant portions of the outfit are in those locations. The remainder of the outfit weight is distributed along the entire hull. LCG o = ( 25% W o at LCG M , 37.5% at LCG dh, and 37.5% at amid ships) The specific fractions can be adapted based upon data for similar ships. This approach captures the influence of the machinery and deckhouse locations on the associated outfit weight at the earliest stages of the design. The centers of the deadweight items can be estimated based upon the preliminary inboard profile arrangement and the intent of the designer. 7.0 Estimation of Capacity Grain Capacity = Moulded Col. + extra vol. due to hatch (m 3 ) coamings,edcape hatched etc – vol. of structurals. Tank capacity = Max. no. of containers below deck (TEU) and above dk. Structurals for holds : 2 1 1 to 2% of mid vol. Structurals for F. O. tanks : of to % 4 1 2 4 1 2 mid. Vol.(without heating coils): of to % 4 9 2 2 1 2 mid vol. (with heating coils):1% for cargo oil tanks Structurals for BW/FW tanks: 2 1 2 4 1 2 to for d.b. tanks non-cemented; % 4 3 2 2 1 2 to for d.b. tanks cemented; 1 to 1.5 % for deep tanks for FO/BW/PW. Bale capacity 0.90 x Grain Capacity. Grain capacity can be estimated by using any one of 3 methods given below as per ref. MSD by Munro-Smith: 1. Grain capacity for underdeck space for cargo ships including machinery space, tunnel, bunkers etc.: Capacity = C 1 + C 2 + C 3 Where C 1 : Grain capacitay of space between keel and line parallel to L WL drawn at the lowest point of deck at side. C 1 = L BP x B ml x D mld x C C : capacity coefficient as given below C B at 0.85D 0.73 0.74 0.75 0.76 0.77 0.78 C 0.742 0.751 0.760 0.769 0.778 0.787 C B at 0.85D can be calculated for the design ship from the relationship T dT dc u . 10 1 · The C.G. of C 1 can be taken as 0.515 x D above tank top. C 2 : Volume between WL at lowest point of sheer and sheer line at side. C 2 : 0.236 X S X B X L BP /2 with centroid at 0.259S above WL at lowest point of sheer Where S = sheer forward + sheer aft. C 3 = 0.548 x camber at midship x B x L BP / 2 with centriod at 0.2365 + 0.381 x camber at above WL at lowest point of sheer. Both forward and aft calculations are done separately and added. C 2 and C 3 are calculated on the assumption that deck line, camber line and sheer line are parabolic. II. Capacity Depth D C D C = D mld + ½ camber + 1/6 (S A + S F ) – (depth of d.b. + tank top ceiling) Grain capacity below upper deck and above tank top including non cargo spaces is given as: LBD C .C B /100(ft 3 ) 2000 3000 4000 5000 6000 7000 8000 Grain Cap. (ft 3 ) 2000 3000 4000 5050 6100 7150 8200 III. From basic ship: C 1 : Under dk sapacity of basic ship = Grain cap. of cargo spaces + under dk non-cargo spaces – hatchways. C 2 : Under deck capacity of new ship. C 2= 2 2 2 2 1 1 1 1 B c BL C D B L C D B L C − × Where C B is taken at 0.85 D If D H : Depth of hold amidships and C 9 : cintoroid of this capacity above tank top then, for C B = 0.76 at 0.85 D, 1/6(S F + S A )/D H 0.06 0.08 0.10 0.12 C 9 /D H 0.556 0.565 0.573 0.583 For an increase of decrease of C B by 0.02, C 9 /D H is decreased or increased by 0.002. From the capacity thus obtained, non cargo spaces are deducted and extra spaces as hatchways etc. are added go get the total grain capacity. 8.0 Power Estimation For quick estimation of power: (a) [ ] 5 . 0 3 0 1000 / 5813 . 0 DWT V SHP · (b) Admirality coefficient is same for similar ships (in size, form, n F ). BHP V A C 9 3 / 2 ∆ · Where Coefficent Admirality A C · tons in nt Displaceme · ∆ Knots in Speed V · (c) In RINA, vol 102, Moor and Small Have proposed L N C K L V H SHP B γ − , ` . | − − + ∆ · 1500 12 ) 1 ( 400 200 40 2 3 3 / 1 Where RPM N: on constructi welded for factor correction Hull H 9 . 0 : · . , , : ' : tons in knots in V ft in L formula s Alexander from beobtained To K ∆ (d) From basic ship: If basic ship EHP is known. EHP for a new ship with similar hull form and Fr. No.- can be found out as follows: (i) Breadth and Draught correction can be applied using Mumford indices (moor and small, RINA, vol. 102) 3 / 2 3 / 2 − − Θ Θ , ` . | , ` . | · Y b n X b n T T B B basic new Where x = 0.9 and y is given as a function of L V γ / as L V γ 0.50 0.55 0.60 0.65 0.70 0.75 0.80 γ 0.54 0.55 0.57 0.58 0.60 0.62 0.64 Where knots V tons andwhere V EHP : , : 1 . 427 3 3 / 2 ∆ ∆ · Θ × (ii) Length correction as suggested by wand G (RINA 1977) ( ) 4 1 2 2 1 10 4 @ @ − − · − x L L L L This correction is approximate where . : ft L (e) Estimation of EHP from series Data wetted surface Area S in 2 m is given as m L m L S · · ∇ ∆ · , , . 2 3 η π · η Wetted surface efficiency (see diagram of Telfer, Nec, Vol. 79, 1962-63). The non-dimensional resistance coefficients are given as · · 2 2 / 1 V S R C R R ρ This can be estimated from services data with corrections. 2 2 / 1 V S R C F F ρ · From ITTC, ( ) 2 10 2 log 075 . 0 − · n F R C Where v VL No s ynold R n · . ' Re : and Viscocity of t coefficien Kinematic v · water fresh for m W F for and water sea for m sec / 10 139 . 1 ., . sec / 10 188 . 1 2 6 2 6 − − × × · ( ) 3 10 004 . 0 8 . 0 0004 . 0 − × − · · · l w A A L C or general in Allowance Roughness C where m in is L l w 2 2 / 1 V S R C C C C T A R F T ρ · + + · Where . tan ce resis hull bare the is R T To get total resistance, Appendage resistance must be added to this: Twin Screw Bossings 8 to 10% A bracket 5% Twin Rudder 3% Bow Thruster 2 to 5% Ice Knife 0.5% If resistance is in Newtons and V is in m/sec, ( ) . 25 . 1 1 . 1 KW to EHP EPH Lrial service × · (f) : Data l statistica from EHP See Holtrop and Mannen, ISP 1981/1984 (given at the end of these notes) (g) Estimation of SHP or shaft horse power QPC EHP SHP service · 10000 0 L N K QPC R H γ η η η − · · Where RPM N · m in L L P B · 84 . 0 · K For fixed pitch propellers 82 . 0 · For controllable pitch propellers can be estimated more accurately later (h) s BHP losses on Transmissi SHP BHP s + · Transmission loss can be taken as follows: Aft Engine 1% Engine Semi aft 2% Gear losses 3 to 4% (i) Selection of Engine Power: The maximum continuous rating (MCR) of a diesel engine is the power the engine can develop for long periods. By continuous running of engine at MCR may cause excessive wear and tear. So Engine manufactures recommend the continuous service rating (CSR) to be slightly less than MCR. Thus CSR of NCR (Normal Continuous Rating) ( ) 95 . 0 85 . 0 to MCR× · Thus engine selected must have MCR as . 95 . 0 / 85 . 0 / s BHP MCR· Thus PEN trial PET service PES (Naked hull HP) Allowance Allowance QPC 0.85 to 0.95 Shafting MCR s BHP SHP (NCR) losses Select Engine 9.0 Seakeeping Requirement 9.1 Bow Freeboard bow F L V γ 0.60 0.70 0.80 0.90 L F bow 0.045 0.048 0.056 0.075 (b) Probability of Deckwetness P for various L F bow / values have been given in Dynamics of Marine Vehicles, by R.Bhattacharya: ( ) t f L 200 400 600 800 ( ) m L 61 122 183 244 L F bow / for P = 0.1% 0.080 0.058 0.046 0.037 1% 0.056 0.046 0.036 0.026 10% 0.032 0.026 0.020 0.015 Estimate bow F check for deckwetness probability and see if it is acceptable. bow F Should also be checked from load line requirement. 9.2 Early estimates of motions natural frequencies effective estimates can often be made for the three natural frequencies in roll, heave, and pitch based only upon the characteristics and parameters of the vessel. Their effectiveness usually depends upon the hull form being close to the norm. An approximate roll natural period can be derived using a simple one-degree of freedom model yielding: t M G k T / 007 . 2 11 · φ Where 11 k is the roll radius of gyration, which can be related to the ship beam using: KB k 50 . 0 11 · , With 82 . 0 76 . 0 ≤ ≤κ for merchant hulls and 00 . 1 69 . 0 ≤ ≤κ generally. Using B 40 . 0 11 ≈ κ . A more complex parametric model for estimating the roll natural period that yields the alternative result for the parameter κ is ( ) ( ) ( ) ( ) ( ) ) / / 2 . 2 0 . 1 2 . 0 1 . 1 2 . 0 ( 724 . 0 2 B D T D C C C C B B B B + − − × + − + · κ Roll is a lightly damped process so the natural period can be compared directly with the domonant encounter period of the seaway to establish the risk of resonant motions. The encounter period in long- crested oblique seas is given by: ( ) ( ) w e g V T θ ω ω π cos / / 2 2 − · Where ω is the wave frequency, V is ship speed, and w θ is the wave angle relative to the ship heading with • ·0 w θ following seas, • · 0 9 w θ beam seas, and • · 0 18 w θ Head seas. For reference, the peak frequency of an ISSC spectrum is located at 1 1 85 . 4 − T with 1 T the characteristics period of the seaway. An approximate pitch natural period can also be derived using a simple one- degree of freedom model yielding: L GM k T / 007 . 2 22 · θ Where now 22 k is the pitch radius of gyration, which can be related to the ship length by noting that . 26 . 0 24 . 0 22 L k L ≤ ≤ An alternative parametric model reported by Lamb can be used for comparison: ( ) ) / 36 . 0 6 . 0 ( / 776 . 1 1 T C T C T B p w + · − θ Pitch is a heavily-damped (non resonant) mode, but early design checks typically try to avoid critical excitation by at least 10% An approximate heave natural period can also be derived using a simple one degree-of-freedom model. A resulting parametric model has been reported by Lamb: ( ) ) / 2 . 1 3 ( 007 . 2 p w B h C T B C T T + + · Like pitch, heave is a heavily damped (non resonant) mode. Early design checks typically try to avoid having , φ T T h · , θ T T h · , 2 θ T T h · , θ φ T T · , 2 θ φ T T · which could lead to significant mode coupling. For many large ships, however, these conditions often cannot be avoided. 9.3 Overall Seakeeping Ranking used Bales regression analysis to obtain a rank estimator for vertical plane seakeeping performance of combatant monohulls. This estimator R ˆ yields a ranking number between 1 (poor seakeeping) and 10 (superior seakeeping) and has the following form: a p v f p v a p w f p w C C L C L T C C R 9 . 15 5 . 23 / 27 . 1 / 378 1 . 10 1 . 45 42 . 8 ˆ − − + − + + · Here the waterplane coefficient and the vertical prismatic coefficient are expressed separately for the forward (f) and the aft (a) portions of the hull. Since the objective for superior seakeeping is high R ˆ , high p w C and low , p v C Corresponding to V-shaped hulls, can be seen to provide improved vertical plane seakeeping. Note also that added waterplane forward is about 4.5 times as effective as aft and lower vertical prismatic forward is about 1.5 times as effective as aft in increasing R ˆ . Thus, V-shaped hull sections forward provide the best way to achieve greater wave damping in heave and pitch and improve vertical plane seakeeping. 10. Basic Ship Method 1. Choose basic ship such that , / L V γ ship type and are nearly same and detailed information about the basic ship is available. 2. Choose B C T B L from empirical data and get ∆ Such that ( ) ( ) new basic w d w d ∆ · ∆ / / . Choose B C T B L . . . etc as above to get new ∆ · B C T B L . 033 . 1 03 . 1 to × 3. Satisfy weight equation by extrapolating lightship from basic ship data. 4. For stability assume ( ) new basic D KG D KG / ) / ( · with on your deletion 5. Check capacity using basic ship method. Use inference equation wherever necessary 10.1 Difference Equations These equations are frequently used to alter main dimensions for desired small changes in out put. For example ρ B C T B L . . . · ∆ Or, · ∆ log + L log + B log + T log ρ log log + B C Assuming ρ to be constant and differentiating, B B C C d T T d B B d L L d d + + + · ∆ ∆ So if a change of ∆ d is required in displacement, one or some of the parameters B C or T B L , , , can be altered so that above equation is satisfied. Similarly, to improve the values of BM by dBM, one can write T B M B / 2 α or T B k M B / 2 × · or T B k BM log log 2 log log − + · Differentiating and assuming k constant T dT B dB BM dBM − ·2 11. Hull Vibration Calculation 11.1 For two node Vertical Vibration, hull frequency is (cpm) N = ] ] ] ∆ 3 L I φγ [Schlick] Where I : Midship m . i. in 2 2 ft in ∆: tons, L : f t φ = 156 , 850 for ships with fine lines = 143, 500 for large passenger lines = 127, 900 for cargo ships ] ] ] ∆ · 3 3 (cpm) L BD N βγ B: breadth in ft and D : Depth upto strength dk in ft. This is refined to take into account added mass and long s .s. decks as, ( ) 2 2 / 1 3 3 1 (cpm) ) 3 / 2 . 1 . C L T B D B C N E + ] ] ] ∆ + · [ Todd] Where D E : effective depth D E : [ ] 3 / 1 1 3 1 / L L D ∑ Where D 1 : Depth from keel to dk under consideration L 1 : Length of s.s. dk C 1 C 2 Tankers 52000 28 Cargo Vessels 46750 25 Passenger Vessels With s.s 44000 20 ( ) ( ) 2 / 1 3 1 2 / 1 ] ] ] + + ∆ Ι · S r T B L N φ Burill Where · φ 2,400,000, I : ft 4 , others in British unit r S : shear correction = ( ) ( ) ( ) ( ) ( ) 1 / 3 2 . 1 / 6 / 9 / 3 5 . 3 2 2 3 + + + + D B L D B D B D B D ( ) [ ] Bunyan where T B C D T L K N B E n 2 / 1 1 6 . 3 ] ] ] + · K = 48,700 for tankers with long framing 34,000 for cargo ships 38,400 for cargo ships long framed n= 1.23 for tankers 1.165 for cargo ships All units are in British unit. T 1 : Mean draught for condition considered T : Design Draught N 3V = 2. N 2V N 4V = 3.N 2V 11.2 Hull Vibration (Kumai) Kumai’s formula for two nodded vertical vibration is (1968) N 2v = 3. 07 * 10 6 cpm L i v 3 ∆ Ι Then I v = Moment of inertia (m 4 ) · ∆ i nt displaceme T B m · ∆ , ` . | + 3 1 2 . 1 including virtual added mass of water (tons) L = length between perpendicular (m) B= Breadth amidship (m) T m = = mean draught (m) The higher noded vibration can be estimated from the following formula by Johannessen and skaar (1980) ( ) ∝ − ≈ 1 2 n N N v nv Then 845 . 0 · ∝ general cargo ships 1.0 bulk carriers 1.2 Tankers N 2V is the two noded vertical natural frequency. n should not exceed 5 or 6 in order to remain within range validity for the above equation. 11.3 Horizontal Vibration For 2 node horizontal vibration, hull frequency is cpm L B D N H H 2 / 1 3 3 2 . . ] ] ] ∆ ·β [Brown] Where · H β 42000, other quantities in British units. v H N N 2 2 5 . 1 · H H N N 2 3 . 2 · H H N N 2 4 3 · 11.4 Torsional Vibration For Torsional vibration, hull frequency is 2 / 1 2 2 5 . 10 3 ] ] ] ∆ + × · L D B I C N p T cpm [Horn] T N node one for C − · 1 , 58 . 1 T N node two for − · 2 , 00 . 3 T N node three for − · 3 , 07 . 4 ( ) 4 2 / 4 ft T ds A I p Σ · (This formulae is exact for hollow circular cylinder) · A Area enclosed by section in 2 ft · g d Element length along enclosing shell and deck ) ( ft · t Corresponding thickness in ) ( ft . : , : , , tons ft D B L ∆ 11.5 Resonance Propeller Blade Frequency = No. of blades × shaft frequency. Engine RPM is to be so chosen that hull vibration frequency and shaft and propeller frequency do not coincide to cause resonance. References 1. ‘ShipDesign and Construction’ edited by Thomas Lab SNAME, 2003. 2. ‘Engineering Economics in ship Design, I.L Buxton, BSRA. 3. D. G. M. Waston and A.W. Gilfillan, some ship Design Methods’ RINA, 1977. 4. P. N. Mishra, IINA, 1977. 5. ‘Elements of Naval Architecture’ R.Munro- Smith 6. ‘Merchant Ship Design’, R. Munro-Smith 7. A. Ayre, NECIES, VOl. 64. 8. R. L. Townsin, The Naval Architect (RINA), 1979. 9. ‘Applied Naval Architecture’, R. Munro-Smith 10. M. C. Eames and T. C. Drummond, ‘Concept Exploration- An approach to Small Warship Design’, RINA, 1977. 11. Ship Design for Efficiency and Economy- H Schneekluth, 1987, Butterworth. 12. Ship Hull Vibration F.H. Todd (1961) 13. J. Holtrop- A statistical Re- analysis of Resistance and Propulsion Data ISP 1984. 14. American Bureau of ships- Classification Rules 15. Indian Register of ships- Classification Rules 16. Ship Resistance- H. E. Goldhommce & Sr. Aa Harvald Report 1974. 17. ILLC Rules 1966. Resistance Estimation Statistical Method (HOLTROP) 1984 R Total = ( ) A TR B W App F R R R R R K R + + + + + + 1 1 Where: · F R Frictional resistance according to ITTC – 1957 formula · 1 K Form factor of bare hull · W R Wave – making resistance · B R Additional pressure resistance of bulbous bow near the water surface · TR R Additional pressure resistance due to transom immersion · A R Model –ship correlation resistance · App R Appendage resistance The viscous resistance is calculated from: S K C v R F v ) 1 ( 2 1 1 0 2 + · ρ …………….(i) Where · 0 F C Friction coefficient according to the ITTC – 1957 frictional = ( ) 2 10 2 log 075 . 0 − n R 1 1 K + was derived statistically as 1 1 K + = ( ) ( ) ( ) ( ) 6042 . 0 3649 . 0 3 12 . 0 4611 . 0 0681 . 1 1 . / / . / . / 4871 . 0 93 . 0 − − , ` . | ∇ + P R C L L L L T L B c C is a coefficient accounting for the specific shape of the after body and is given by C = 1+0.011 Stern C Stern C = -25 for prom with gondola = -10 for v-shaped sections = 0 for normal section shape = +10 for U-shaped section with hones stern R L is the length of run – can be estimated as · L L R / ( ) 1 4 / 06 . 0 1 − + − p p p C LCB C C S is the wetted surface area and can be estimated from the following statistically derived formula: ( ) ( ) B r B wp M B M C A C B C C C B T L S / 38 . 2 3696 . 0 003467 . 0 2862 . 0 4425 . 0 4530 . 0 2 5 . 0 + + − − + + · Where · T Average moulded draught in m · L Waterline length in m · B Moulded breadth in m · LCB LCB ford’s ( ) + or aft ( ) − of midship as a percentage of L · r B A Cross sectional area of the bulb in the vertical plane intersecting the stern contour at the water surface. All coefficient are based on length on waterline. The resistance of appendages was also analysed and the results presented in the form of an effective form factor, including the effect of appendages. ( ) [ ] tot S app S K K K K 1 2 1 1 1 1 1 + − + + + · + Where · 2 K Effective form factor of appendages · app S Total wetted surface of appendages · tot S Total wetted surface of bare hull and appendages The effective factor is used in conjunction with a modified form of equation (i) ( ) K S C V R tot Fo v + · 1 2 2 1 ρ The effective value of 2 K when more than one appendage is to be accounted for can be determined as follows ( ) ( ) ∑ ∑ + · + i i i effective S k S k 2 2 1 1 In which i S and ( ) i k 2 1+ are the wetted area and appendage factor for the i th appendage TABLE: EFFECTIVE FORM FACTOR VALUES 2 K FOR DIFFERENT APPENDAGES Type of appendage ( ) 2 1 of value k + Rudder of single screw ship 1.3 to 1.5 Spade type rudder of twin screw ship 2.8 Skeg-rudder of twin screw ships 1.5 to 2.0 Shaft Brackets 3.0 Bossings 2.0 Bilge keels 1.4 Stabilizer fins 2.8 Shafts 2.0 Sonar dome 2.7 For wave-making resistance the following equation of Havelock (1913) Was simplified as follows: ( ) 2 2 3 2 1 cos 1 − + · n F m w F m e c c c W R d n λ In this equation λ , , , 3 2 1 C C C and m are coefficients which depend on the hull form. L λ is the wave making length. The interaction between the transverse waves, accounted for by the cosine term, results in the typical humps and hollows in the resistance curves. For low-speed range 4 . 0 ≤ n F the following coefficients were derived ( ) ( ) 3757 . 1 0796 . 1 7861 . 3 4 1 90 2223105 − − · E i B T C C with: ( ) ¹ ¹ ¹ ¹ ¹ ' ¹ ≥ − · ≤ ≤ · ≤ · 25 . 0 0625 . 0 5 . 0 25 . 0 11 . 0 11 . 0 2296 . 0 4 4 3333 . 0 4 L B for B L C L B for L B C L B for L B C d = -0.9 ( ) ( ) 5 3 1 1 7932 . 4 7525 . 1 01404 . 0 C L B L T L m − − , ` . | ∇ − · with: ¹ ¹ ¹ ' ¹ ≥ − · ≤ + − · 8 . 0 7067 . 0 7301 . 1 8 . 0 9844 . 6 8673 . 13 0798 . 8 5 3 2 5 p p p p p p C for C C C for C C C C 24 . 3 034 . 0 6 2 4 . 0 − − · n F e C m with: ¹ ¹ ¹ ¹ ¹ ' ¹ ≥ ∇ → · ≤ ∇ ≤ , ` . | − ∇ + − · ≤ ∇ → − · 1727 0 . 0 1727 512 36 . 2 / 0 . 8 69385 . 1 512 69385 . 1 3 6 3 3 1 6 3 6 L for C L for L C L for C ( ) 12 03 . 0 446 . 1 ≤ − · B L for B L C p λ 12 36 . 0 446 . 1 ≥ − · B L for C p λ where E i = half angle of entrance of the load waterline in degrees ( ) ( ) 3 3 2 8 . 6 1551 . 0 32 . 234 25 . 162 67 . 125 , ` . | − + + + − · T T T LCB C C L B i f a p p E where T a = moulded draught at A.P T f = moulded draught at F.P The value C 2 accounts for the effect of the bulb. C 2 = 1.0 if no bulb’s fitted, otherwise ( ) i BT A e C B B BT + · − ν ν 89 . 1 2 where B ν is the effective bulb radius, equivalent to 5 . 0 56 . 0 BT B A · ν i represents the effect of submergence of the bulb as determine by B B f h T i ν 4464 . 0 − − · where T f = moulded draught at FP h B = height of the centroid of the area A BT above the base line ( ) M T BTC A C / 8 . 0 1 3 − · 3 C accounts for the influence of transom stern on the wave resistance AT is the immersed area of the transom at zero speed. For high speed range 55 . 0 ≥ n F , Coefficients 1 C and 1 m are modified as follows ( ) ( ) 4069 . 1 0098 . 2 3 . 346 . 3 . 1 1 2 / 3 . 6919 − ∇ · − B L L C C M ( ) ( ) 6054 . 0 3269 . 0 1 2035 . 7 B T L B m − · For intermediate speed range ( ) 55 . 0 4 . 0 ≤ ≤ n F the following interpolation is used ( ) { ¦ ] ] ] ] − − + · 5 . 1 4 . 0 10 1 04 55 . 0 04 Fn Fn Fn W W n W W R R F R W W R The formula derived for the model-ship correlation allowance C A is ( ) ( ) ( ) ( ) 04 . 0 / / 04 . 0 5 . 7 / 003 . 0 00205 . 0 100 006 . 0 04 . 0 / 00205 . 0 100 006 . 0 2 4 5 . 0 16 . 0 16 . 0 ≥ ¹ ' ¹ − + − + · ≥ − + · − − WL F WL F B WL WL A WL F WL A L T for L T C C L L C L T for L C where C 2 is the coefficient adopted to account for the influence of the bulb. Total resistance ( ) [ ] W W R C k C S R W A F tot T . 1 2 1 2 + + + · ν ρ START Read : owner’s requirements (ship type dwt/TEU, speed) Define limits on L, B, D, T Define stability constraints First estimate of main dimensions D = T+ freeboard + margin No Estimate freeboard Is D >= T + freeboard Yes =LBTCb (1 + s) Estimate form coefficients & form stability parameters Estimate power Change parameters Estimate lightweight No Is= Lightweight + dwt & Is Capacity adequate? Estimate stability parameters No Yes Stability constraints satisfied Yes Estimate required minimum section modulus Estimate hull natural vibration frequency Estimate capacity : GRT, NRT Estimate seakeeping qualities S Shi p desig n cal cul ati ons – Sele cti on of M ai n pa rame ters 1.0 A. The choice of parameters (main dimensions and coefficients) can be based on either of the following 3 ship design categories (Watson & Gilafillon, RINA 1977) Deadweight carriers where the governing equation is ∆ = C B × L × B × T × ρ (1 + s ) = deadweight + lightweight where s : shell plating and appendage displacement (approx 0.5 to 0.8 % of moulded displacement) ρ : density of water (= 1.025 t/m3 for sea water ) and Here T is the maximum draught permitted with minimum freeboard. This is also the design and scantling draught B. Capacity carriers where the governing equation is Vh = C BD . L . B . D ′ = where D ′ = capacity depth in m C m = mean camber = D + Cm + S m 2 = . C [ for parabolic camber ] 3 Vr − Vu + Vm 1 − ss =1 C 2  for straight line camber   where C : Camber at C . L .   = 1 (S f + Sa ) 6  for parabolic shear     S f = ford shear   S = aft shear   c  S m = mean sheer C BD = block coefficient at moulded depth = C B + (1 − C B ) [ ( 0.8 D − T ) 3T ] Vh = volume of ship in m3 below upper deck and between perpendiculars Vr = total cargo capacity required in m3 Vu = total cargo capacity in m3 available above upper deck Vm = volume required for m c , tanks, etc. within Vh [1] S s = % of moulded volume to be deducted as volume of structurals in cargo space [normally taken as 0.05] Here T is not the main factor though it is involved as a second order term in C BD C. e.g. Restrictions imposed by St. Lawrence seaway 6.10 m ≤ Loa ≤ 222.5 m Bext ≤ 23.16 m Restrictions imposed by Panama Canal B ≤ 32.3 m; T ≤ 13 m Restrictions imposed by Dover and Malacca Straits T ≤ 23 m Restrictions imposed by ports of call. Ship types (e.g. barge carriers, container ships, etc.) whose dimensions are determined by the unit of cargo they carry. Restrictions can also be imposed by the shipbuilding facilities. 2.0 Parameter Estimation The first estimates of parameters and coefficients is done (a) from empirical formulae available in published literature, or (b) from collection of recent data and statistical analysis, or (c) by extrapolating from a nearly similar ship The selection of parameters affects shipbuilding cost considerably. The order in which shipbuilding cost varies with main dimension generally is as follows: The effect of various parameters on the ship performance can be as shown in the following table [1] Speed Length Breadth Depth Block coefficient Linear Dimension Ships : The dimensions for such a ship are fixed by consideration other than deadweight and capacity. longitudinal strength. capital cost.78 – 0.89 0.81 – 0.56 – 0. Length Posdunine’s formulae as modified by Van Lammeran : .78  0.88  0.87 Product tankers 0.59 Large bulk carriers 0.79 – 0.60 – 0. dwt as a function of deadweight capacity.86 – 0.1 Primary Influence of Dimensions resistance. transverse stability. longitudinal strength. freeboard displacement.37 – 0.71 – 0. transverse stability Displacement A preliminary estimate of displacement can be made from statistical data analysis.85 0.59 Fishing trawlers 0.2 A. resistance.70 – 0.83 Container ships 0.84 Small bulk carriers 0.50 – 0. resistance.Table: Primary Influence of Dimension Parameter Length Beam Depth Draft 2.69  2.77 – 0. The statistical ratio is given in the ∆ following table [1] Table: Typical Deadweight Coefficient Ranges Vessel Type Ccargo DWT Large tankers 0.45 C arg o DWT or Total DWT C= where Displacement Ctotal DWT 0.50 – 0. hull volume. hull volume hull volume.85 – 0. capital cost. seakeeping transverse stability.63 Ro-Ro ships 0.77 Refrigerated cargo ships 0. freeboard. capital cost. maneuverability. maneuverability. 3 ∗ C Lpp in metres.85 It the block coefficient differs from the value 0.5 for waters and trawler C.5 to 18.5 for single screw cargo and passenger ships where V = 11 to 16.145 Fn . Schneekluth’s Formulae : This formulae is based on statistics of optimization results according to economic criteria.145 Fn within the range 0.LBP (  V  ft ) = C  T   2 + VT  2 ∆ 1 3 C = 23.5 knots = 24 for twin screw cargo and passenger ships where V = 15. Volker’s Statistics :  L   13 − C  = 3. V in m s L→m ∇ → disp in m 3 where C = 0 for dry cargo ships and container ships = 0.5 for refrigerated ship and = 1.3 ∗ V 0. ∆ is displacement in tonnes and V is speed in knots C = 3.5 + 4.5 C = 3.145 + 0.2.5 ∇  V g∇ 1 3 .2 0. LPP = ∆0.48 – 0. if the block coefficient has approximate value of CB = 0.5 Fn ( ) The value of C can be larger if one of the following conditions exists : (a) Draught and / or breadth subject to limitations (b) No bulbous bow (c) Large ratio of undadeck volume to displacement .5 knots = 26 for fast passenger ships with V ≥ 20 knots B. the coefficient C can be modified as follows C B + 0. or length for lowest production cost. 0 + 0.5 to 7.0 m for general cargo ships = L/9 + 12 to 15 m for VLCC.55 ≤ B / D ≤ 2. 2828 m 2.5 (5) Recent ships indicate the following values of B / D .0 for small craft with L ≤ 30 m such as trawlers etc.90 for dwt carries like costers.32 2.5 to 2. such vessels have adequate stability and their depth is determined from the hull deflection point of view.4 Depth For normal single hull vessels 1.Depending on the conditions C is only rarely outside the range 2. (3) D = B−3 m for bulk carriers 1. or B B = L/5 – 14m for VLCC  Dwt  = 10.5 B / D = 1.78  1000   0. The formulae is valid for ∆ ≥ 1000 tonnes.5 m for tankers = L/9 + 6. and Fn between 0. tankers.3 Breadth Recent trends are: L/B = 4.025 (L .0 m for bulkers = L/9 + 6.30) for 30 m ≤ L ≤ 130 m B = L/9 + 4.16 to 0. Statistics from ships built in recent years show a tendency towards smaller value of C than before. bulk carriers etc.5 to 6.8.5 for L ≥ 130.0 m = 4. = 6.65 for fishing vessels and capacity type vessels (Stability limited) = 1. 0 Form Coefficients CB = CP .91 for large tankers = 2.7 to 0. generally 2.m.5 Draught For conventional monohull vessels. depth is governed by L / D ratio which is a significant term in determining the longitudinal strength.66 D + 0.7 for type B freeboard = 0. 3.536  1000   0. L / D determines the hull deflection because b.5 C B ] Draught – depth ratio is largely a function of freeboard : T / D = 0.9 m for bulk carriers Depth – Length Relationship Deadweight carriers have a high B / D ratio as these ships have adequate stability and therefore.75 However.25 ≤ B / T ≤ 3. CM . L / D =10 to 14 with tankers having a higher value because of favourable structural arrangement. B / T can go upto 5 in heavily draught limited vessels.70 for container ships and reefer ships 2.8 for double hull tankers) = 0. beam is independents of depth.1 for Great Lakes ore carriers = 2.8 for B – 60 freeboard T T 2.88 for bulk carriers and = 1.6  dwt  = 4. 290 m = 0.B / D = 1. In such case. For ensuring proper flow onto the propeller B T ≤ [ 9. imposed by waves and cargo distribution.8 for type A freeboard (tankers) ( T / D < 0.625 − 7.5 for ULCC = 1. 48 ≤ CB ≤ 0.14 ≤ Fn ≤ 0.68 Fn where C = 1.and C B = CVP .14  L B + 20  Fn  26    0. V: Speed in Knots and L: Length in feet CB = 0. Ayre’s formulae CB = C – 1.T CVP = 3. and 0. this formulae is frequently used with C = 1.14  L B + 20  2 Fn 3  26    or V gL : Froude Number CB = The above formulae are valid for 0.08 for single screw ships = 1.0 .1 Block Coefficients C B = 0. CWP where Cp : Longitudinal prismatic coefficient and CVP: Vertical prismatic coefficient CP = ∇ AM .69 V L for 0.32 Japanese statistical study [1] gives CB for 0.32 as .5 ≤ V L ≤ 1.09 for twin screw ships Currently.06 It can be rewritten using recent data as CB = 1. L ∇ AWP .15 ≤ Fn ≤ 0.85.18 – 0.7 + 18 tan −1 [ 25 ( 0.23 − Fn ) ] where Fn = A. 70 0.60) − = 1. 5 [ ] −1 [1] Estimation of Bilge Radius and Midship area Coefficient (i) Midship Section with circular bilge and no rise of floor R2 = 2(1 − C M ) B .085 (CB – 0.4 and 0.8584 (iii) Schneekluth’s recommendation for Bilge Radius (R) BC k 2 L ( B + 4) C B Ck : Varies between 0.65 0.976 0. (ii) Midship Section with rise of floor (r) and no flat of keel R2 = 2 BT (1 − C M ) − B .C B = −4.977 + 0.56 = 1 + (1 − C B ) 3. r 0.5 and 0.33 (1 – CM ) B.55 = 0.1 Fn + 46.T. 4 −π =2.7 R= For rise at floor (r) the above CB can be modified as ′ CB = C BT (T − r 2) .987 Recommended values of C can be given as CM = 0.6 and in extreme cases between 0.2 Midship Area Coefficient CB CM = 0.96 0.980 0.6 Fn3 3.T .8 Fn − 39.22 + 27.006 – 0.0056 C B 3.60 0. transom stern schneekluth 1 (17) Schneekulth 2 (17) U-forms hulls Average hulls.1 Intial Estimate of Stability Vertical Centre of Buoyancy. 3.760 CP CWP = 0.36 CM T .860 CP CWP = 0. cruiser stern twin screw.5 − CVP ) / 3 :Moorish / Normand recommend for hulls with C M ≤ 0. many times the bilge radius is taken equal to or slightly less than the double bottom height.262 + 0.V Equation CWP = 0.95 CP + 0.3 Water Plane Area Cofficient Table 11.025 Applicability/Source Series 60 Eames. KB [1] KB = ( 2.4292 r 2 } / BT ] From producibility considerations.444 + 0.17 (1.471 + 0.175+ 0.875 CP CWP = 0.810 CP CWP = CP 2/3 CWP = ( 1+2 CB/Cm ½)/3 CWP = 0.262 + 0.(iv) If there is flat of keel width K and a rise of floor F at B 2 then. CM = 1 − {F [( B 2 − K 2 ) − r 2 / ( B 2 − K 2 ) + 0.0.520 CP CWP = CB/(0.0 4.551 CB) CWP = 0.90 – 0.9<CM T Regression formulations are as follows : KB = 0. small transom stern warships (2) tankers and bulk carriers (17) single screw.9 T KB −1 = (1 + CVP ) :Posdumine and Lackenby recommended for hulls with 0. cruiser stern twin screw.CP)1/3 CWP = (1+2 CB)/3 CWP = CB ½ .180 + 0. Riddlesworth (2) V-form hulls 4. for trapezium reduced 4% (17) Normand (17) Bauer (17) McCloghrie + 4% (17) Dudszus and Danckwardt (17) BM T = BM L = 4.1216 CWP – 0.90 – 0.0372 (2 CWP + 1)3 ) / 12 CI = 1.04 CWP2 ) / 12 CI = (0.KB = (0.0410 CIL = 0.350 CWP2 – 0.87 CWP2 ) / 12 IT ∇ KL ∇ Applicability / Source D’ Arcangelo transverse D’ Arcangelo longitudinal Eames.285 CVP T 4.89 CWP2 ) / 12 CI = (0.2 Metacenteic Radius : BMT and BML Moment of Inertia coefficient CI and CIL are defined as CI = IT LB 3 LB 3 CTL = IL The formula for initial estimation of CI and CIL are given below Table 11.04 (3CWP – 1) CI = (0.70 for normal cargo ships .30 CM – 0.146 CI = 0.405 CWP + 0.10 CB) T KB = 0.0106 CWP – 0.13 CWP + 0.78 – 0.096 + 0.0727 CWP2 + 0.3 Transverse Stability KG / D= 0. small transom stern (2) Murray.VI Equations for Estimating Waterplane Inertia Coefficients Equations C1 = 0.003 C1 = 0.63 to 0. 70 − 45.90 for trawlers and tugs KMT = KB + BMT GMT = KMT – KG Correction for free surface must be applied over this. At even higher speeds the bow must be faired even more resulting in an LCB aft of amidships. initial checks of vessel trim require a sound LCB estimate. resulting in a movement of the LCB aft through amidships.03 KG (assumed). LCB will move aft with ship design speed and Froude number. C B L 100 4.4 C P . Harvald LCB = 9.3 Longitudinal Stability 3 C I L L2 I L CI L L B GM L ≅ BM L = = = ∇ LBT C B T . 4.80 − 38. Like wise. At low Froude number.83 for passenger ships = 0. Then .9 Fn LCB = −13. so the run is more tapered (horizontally or vertically in a buttock flow stern) than the bow resulting in an LCB which is forward of amidships.T . GM’T = GMT – 0. the bow must be faired to achieve acceptable wave resistance.0 Fn ± 0.5 + 19.5 Longitudinal Centre of Buoyancy (1) The longitudinal centre of buoyancy LCB affects the resistance and trim of the vessel. This GM’T should satisfy IMO requirements.8 Schneekluth and Bestram LCB = 8. B. As the vessel becomes faster for its length.= 0. C B C I L L2 C I L L2 B ∇GM L MCT 1 cm = = = 100 LBP 100. In general.T .C B L. Initial estimates are needed as input to some resistance estimating algorithms. the bow can be fairly blunt with cylindrical or elliptical bows utilized on slow vessels. On these vessels it is necessary to fair the stern to achieve effective flow into the propeller. 70  0. Ship type Cargo 20 Cargo cum Passenger 28 Passenger 30 Cross Channe Pass.8 D − T  C B 1 = C B + (1 − C B )    3T  Where C B : Actual block at T.1.1 100 × Steel weight = 18 ∆ Steel weight Estimation – Watson and Gilfillan From ref. 0.0 Lightship Weight Estimation (a) (b) 5. 5. (3). Hull Numeral l1 and h1 l 2 and h2 L ( B + T ) + 0. .70) where Ws Ws 7 ] : Steel weight of actual ship with block C B1 at 0.5( C B1 − 0.85 ∑ l1 h1 + 0. positive forward of amidships.8D : Steel weight of a ship with block 0. Ws = Ws 7 [1 + 0.75 ∑ l 2 h2 in metric units where : length and height of full width erections E= : length and height of houses.Here LCB is estimated as percentage of length. ferry 35 (100 ∆) × Steel weight For tankers. To this Scrap steel weight (10 to 18 %) is added to get gross steel weight.1  dwt  Lightship weight = 1128 (4) 1000   Lightship = Steel Weight + Outfil weight + Machinery Weight + Margin. 5.85 ( D − T ) L + 0. 64 Steel Weight The estimated steel weight is normally the Net steel. 300 350.027 – 0.2 From Basic Ship Value of K 0. 000 6. E 1. Schneekluth Method for Steel Weight of Dry Cargo Ship ∇u = volume below topmost container deck (m3) ∇ D = hull volume upto main deck (m3) ∇ s = Volume increase through sheer (m3) ∇b = Volume increase through camber (m3) s v .051 0.037 – 0. E < 450 250.041 – 0.044 0. E < 1. 000 < E < 15.046 0.000 < E < 2.000 < E < 13. 000 2. 000 800 < E < 1.037 0. 500 3.029 – 0.36 Ship type Tanker Chemical Tanker Bulker Open type bulk and Container ship Cargo Refrig Coasters Offshore Supply Tugs Trawler Research Vessel Ferries Passenger 5. 000 1.029 – 0.500 < E < 40. bL and hL are length. 000 E 5.045 – 0.036 – 0.000 < E < 5. 000 Steeel weight from basic ship can be estimated assuming any of the following relations : (i) Ws ∞ L × weight per foot amidships Ws ∞ L.035 0. 000 5. 500 2.032 0. ( B + D) (iii) To this steel weight.035 0. (ii) Ws ∞ L. B.Ws 7 = K . su = height of s hear at FP and AP Ls n ∇L = length over which sheer extends ( Ls ≤ L pp ) = number of decks = Volume of hatchways  L .032 – 0.900 < E < 2. breadth and height of hatchway .033 – 0. D.032 0. 350 < E < 1.042 0. all major alterations are added / substracted.000 < E < 7. 300 1.037 0.024 – 0.000 1.041 – 0.038 For E 1.000 < E < 15.040 0.037 0.1.029 – 0. 85  0.093 1 + 0.113 to 0.3 t t m3 m3 for 80 m ≤ L ≤ 150 m of passenger ships for 100 m ≤ L ≤ 150 m of refrigerated ships ] m3 Schneekluth’s Method for Steel Weight of container Ships 0.1. C3 = 0.121 C1 = 0.01 − 2.7 CBD L Wst ( ± ) = ∇ u C1 [1 + 0.∇u L B D C BD + Ls B ( su + sϑ ) C 2 + L B b C 3 + ∑ l L bL hL                 =      ∇D ∇s ∇b ∇L CBD = C B + C 4 D −T (1 − C B ) T Where C4 = 0.92 + (1 − C BD )    [ ] Depending on the steel construction the tolerance width of the result will be somewhat greater than that of normal cargo ships.75 C BD ( C M − 0.85) ] D Restriction imposed on the formula : L < 9 .4 for ship forms with marked flame flare C2 = ( C BD ) b 2 3 . The factor 0.116 5.02  D − 0.06( n − D ) ] 4 B [1 + 0.057  D − 12   ( D + 14 )       2  B   1 + 0. and D C1 the volumetric weight factor and dependent on ship type and measured in C1 = 0.002( L − 120 ) 10 −3 2 Wst = ∇ u [ ]  L   30  1 + 0.103 1 + 17( L − 110 ) 2 10 −6 t m3 for 80 m ≤ L ≤ 180 m for normal ships t [0.05 (1.102 to 0.2( T − 0.98) ] [ C1 = 0.25 for ship forms with little flame flare = 0.85 − D ) ] [1 + 0.92 + (1 − C ) ] 2 BD [1 + 0.093 may vary between .1  D      1 2  T  2 1 + 0.033 ( D − 12 ) ] [1 + 0. different double bottom height.75 t / TEU 0.0. Ship type Vessel Vessel Integrated Integrated Length (ft) 20 40 20 40 Fixed 0. higher speeds.1 − 12  D   ) This correction is valid for ships between 100 m and 180 m length (b) No correction for wing tank is needed (c) The formulae can be applied to container ships with trapizoidal midship sections. the lashings weigh : for 20 ft containers 0. higher latchways.5 (  L  L − 10 1 + 0.043 t / TEU 5.4 Steel Weight Estimations : other formulations For containce Ships : .09 and 0 the under deck volume contains the volume of a short forecastle for the volume of hatchways The ratio L should not be less than 10 D Farther Corrections : (a) where normal steel is used the following should be added : δ Ws t ( % ) = 3. These are around 5% lighter (d) Further corrections can be added for ice-strengthening.1.48 t / TEU Detachable 1 t / TEU 0.024 t / TEU 40 ft containers 0. Weight of container cell guides.45 t / TEU 0.7 t / TEU 0.031 t / TEU mixed stowage 0.7 t / TEU - Where containers are stowed in three stacks. Container Cell Guides Container cell guides are normally included in the steel weight. 054 + 0. B.06 ∗  28. 374 pp Wst → steel weight in tonns L pp .009 − 0.7 −  B D     DNV – 1972 where L   0.8   CB   L  Wst = 340 ( LBD 100.00585 − 8.002   + 1   D     [ Ccmyette’s formula as represented by watson & Gilfillan ] Wst → tonnes L. 9 L. D → metres For tankers :  L L    Wst = ∆ α L + α T 1. R. [K.004  ∗ 0. B.675 +  ∗ 0. 712 . 759 .189 ∗    D  . 78  100 L  0. B 0. 72 D 6 2   L 0.939 2  D       [D. Miller] Wst → tonnes 0.3  + 0. 73 x 10 where x = 12 −7 2 L pp B 3 CB [wehkamp / kerlen] Wst = C B3 2 LB 0.97 B αL =  0. D → metres For Dry Cargo vessels Wst = 0. D → are in metres. B. D 0.0832 x e −5.004  ∗ 0.Wst = 0.000)  0. Chapman] 1.007 L1. 274 Z 0.2. Hurrey] 0.07  1.5 C B + 0.42 − 0.035   0. 56  +  ∗ [J.029 + 0.146 − 0. M.215 − 0. valid for a length upto 380 m 5.8 D 2 L L   L − 200   Wst = 4. Corrections may be made as follows: For m/c aft deduct 5% .025  1 +  B B 1800   L L  ∗  2.0252 ∗    100000  Range of Validity : 10 ≤ 5≤ L ≤ 14 D 0.4 ) Wst = 0. ∆  α T = 0.00235 ∗    100000   ∆  α T = 0.1 Machinery Weight Murirosmith Wm = BHP/10 = SHP/17 = SHP/ 30 + 200 + + tons diesel 280 200 tons turbine tons turbine (cross channel) This includes all weights of auxiliaries within definition of m/c weight as part of light weight.2 5.1697 L1.73 + 0. 3 for ∆ < 600000 t for ∆ > 600000 t L ≤7 B 150 m ≤ L ≤ 480 m For Bulk Carriers  B T  ( 0. 62 L 1.0163  D D  [DNV 1972] here Z is the section modulus of midship section area The limits of validity for DNV formulae for bulkers are same as tankers except that is. i Wm (diesel-electric) = 0.19 for frigates and Convetters MCR is in kw and RPM of the engine 5.72 (M CR)0.7 for passenger ships and ferries = 0.69 (MCR)0.3.7 for tankers = 0.1 Wood and Outfit Wight (Wo) Watson and Gilfilla W and G (RINA 1977): (figure taken from [1]) .2 Watson and Gilfillan 0.2.83 (MCR)0.84 Wm (diesel) = ∑12 [ MCRi / RPMi ] + Auxiliary wt .78 Wm (gas turbine) = 0.7 for bulk and general cargo vessel = 0.72 (MCR)0.001 (MCR) Auxiliary weight = 0.3 5.For twin-screw ships add 10% and For ships with large electrical load add 5 to 12% 5. 2. L..40-0.25 t/m2 0. Schneekluth Out Fit Weight Estimation Cargo ships at every type No = K.3. B → meters Where the value of K is as follows (a) (b) (c) Type Cargo ships Container ships Bulk carriers without cranes With length around 140 m With length around 250 m Crude oil tankers: K 0.5.34-0. Basic Ship Wo can be estimated from basic ship using any of the proportionalities given below: 5.45 t/m2 0. B.22-0.3.3.18 t/m2 (d) . Wo → tonnes. L.17-0.38 t/m2 0. 4 for full bossings d: Propeller diameter.6 Dead weight Estimation At initial stage deadweight is supplied.005 do 1. However.5 to 7% Margin on VCG 0.7 for fine and 1. (ii) (iii) (iv) where C = 0. where K = 0. 5.5 to ¾ % ¾ to 1 % 5.005 is for ULCCS and 1. .008) where 1.039 t m 3 Passenger ships with large car transporting sections and passenger ships carrying deck passengers W0 = K ∑ ∇ .01 x d3 tonnes ∆ ext = ∆ ext + ∆ app.4 Margin on Light Weight Estimation Ship type Margin on Wt Cargo ships 1. 5.5% Naval Ships 3.5% Passenger ships 2 to 3.25 t/m2 0.5 to 2.13 x (area)9/2 tonnes Propeller Displacement = 0.With lengths around 150 m With lengths around 300 m Passenger ships – Cabin ships W0 = K ∑ ∇ where 0.5 Displacement Allowance due to Appendages ( ∆ αPP ) (i) Extra displacement due to shell plating = molded displacement x (1.008 for small craft. From this.036 t m 3 − 0. all major alterations are added or substracted.04 t/m2 – 0.05 t/m2 Wo α L × B or W02 = W0 L L 2 B 2 + × 2 L1 B1 Where suffix 2 is for new ship and 1 is for basic ship.17 t/m2 ∑∇ total volume 1n m3 K = 0. Rudder Displacement = 0. 0 Estimation of Centre of Mass The VCG of the basic hull can be estimated using an equation as follows: VCGhull = 0.01D [ 46.135 ( 0.01D [ 46.81 – CB ) ( L/D )2 ].01t / (person x day) 5. 6.7 Therefore weight equation to be satisfied is ∆ ext = Light ship weight + Dead weight where light ship weight = steel weight + wood and out fit weight + machinery weight + margin.008D ( L/B – 6.6 + 0.6 + 0.17t / person WPR : weight of provisions and stores WPR = 0. L ≤ 120 m = 0.135 (0.17 t/(person x day) WC&E : weight of crew of fresh water WC&E : 0.5 ). 120 m < L (1) .81 – CB ) ( L/D )2 ] + 0.Dwt = WC arg o + WHFO + WDO + WLO + WFW + WC & E + WPR Where WCargo : Cargo weight (required to be carried) which can be calculated from cargo hold capacity range × m arg in WHFO = SFC x MCR x speed Where SFC : specific fuel consumption which can be taken as 190gm/kw hr for DE and 215gm/kw hr for 6T (This includes 10% excess for ship board approx ) Range: distance to be covered between two bunkeriy port margin : 5 to 10% WDO : Weight of marine diesel oil for DG Sets which is calculated similar to above based on actual power at sea and port(s) WLO : weight of lubrication oil WLO = 20 t for medium speed DE =15 t for slow speed DE WFW : weight of fresh water WFW = 0. Waston gives the suggestion: LCGhull = . = D + 2.25. .25 + 0. L ≤ 125 m 125 < L ≤ 250 m The longitudinal center of the outfit weight depends upon the location of the machinery and the deckhouse since significant portions of the outfit are in those locations.This may be modified for superstructure & deck housing The longitudinal position of the basic hull weight will typically be slightly aft of the LCB position. The centers of the deadweight items can be estimated based upon the preliminary inboard profile arrangement and the intent of the designer. The vertical center of the machinery weight will depend upon the inner bottom height hbd and the height of the engine room from heel. This approach captures the influence of the machinery and deckhouse locations on the associated outfit weight at the earliest stages of the design. minimum values from classification and Cost Guard requirements can be consulted giving for example: hdb ≥ 32B + 190 T (mm) (ABS) or hdb ≥ 45.35 ( D’-hdb ) Which places the machinery VCG at 35% of the height within the engine room space. D.417 L (cm) Us Coast Guard The inner bottom height might be made greater than indicated by these minimum requirements in order to provide greater double bottom tank capacity. the VCG of the machinery weight can be estimated as: VCGM = hdb + 0.0.50. = D + 1. The remainder of the outfit weight is distributed along the entire hull. meet double hull requirements. The vertical center of the outfit weight is typically above the main deck and can be estimated using an equation as follows: VCGo = D + 1. In order to estimate the height of the inner bottom.15 + LCB Where both LCG and LCB are in percent ship length positive forward of amidships.5% at LCG dh.01(L-125).5% at amid ships) The specific fractions can be adapted based upon data for similar ships.7 + 0. With these known. and 37. 37. or to allow easier structural inspection and tank maintenance. LCGo = ( 25% Wo at LCGM. Bale capacity 0.74 0. 2 1 1 Structurals for F.515 x D above tank top.787 CB at 0. 4 2 1 3 2 to 2 % for d. + extra vol.5 % for deep tanks for FO/BW/PW. due to hatch (m3) coamings. O.742 0. Grain capacity can be estimated by using any one of 3 methods given below as per ref.778 0. bunkers etc. tanks : 2 to 2 % of mid.77 0.90 x Grain Capacity. of structurals. no.85D 0. 2 4 1 to 1. 1 Structurals for holds : 1 to 2% of mid vol. tanks cemented.85D can be calculated for the design ship from the relationship dcu 1 = dT 10.760 0. . C1 = LBP x Bml x Dmld x C C: CB at C capacity coefficient as given below 0.75 0. of C1 can be taken as 0. tunnel. (with heating coils):1% for 2 4 cargo oil tanks 1 1 Structurals for BW/FW tanks: 2 to 2 for d.edcape hatched etc – vol. tanks non-cemented.G.0 Estimation of Capacity Grain Capacity = Moulded Col. of containers below deck (TEU) and above dk.769 0.(without heating coils): 4 4 1 9 2 to 2 % of mid vol.T The C.751 0. MSD by Munro-Smith: 1.b.73 0.: Capacity = C1 + C2 + C3 Where C1 : Grain capacitay of space between keel and line parallel to LWL drawn at the lowest point of deck at side.78 0. Vol.76 0. Grain capacity for underdeck space for cargo ships including machinery space. Tank capacity = Max.b.7. 2365 + 0.548 x camber at midship x B x LBP/ 2 with centriod at 0. are added go get the total grain capacity. of cargo spaces + under dk non-cargo spaces – hatchways. C2 and C3 are calculated on the assumption that deck line. C3 = 0.76 at 0.85 D If DH : Depth of hold amidships and C9 : cintoroid of this capacity above tank top then. From the capacity thus obtained.573 0.12 0.236 X S X B X LBP/2 with centroid at 0. II.565 0. camber line and sheer line are parabolic. + tank top ceiling) Grain capacity below upper deck and above tank top including non cargo spaces is given as: LBDC. C1 × L 2 B 2 Dc 2 − C B 2 L1 B1 D1C BL 2000 2000 3000 3000 4000 4000 5000 5050 6000 6100 7000 7150 8000 8200 Where CB is taken at 0. Under deck capacity of new ship. C9/DH is decreased or increased by 0.08 0.85 D.02. (ft3 ) III.06 0.556 0.002.259S above WL at lowest point of sheer Where S = sheer forward + sheer aft. From basic ship: C1: C2: C2= Under dk sapacity of basic ship = Grain cap.381 x camber at above WL at lowest point of sheer. 1/6(SF + SA)/DH C9/DH 0. non cargo spaces are deducted and extra spaces as hatchways etc.CB/100(ft3) Grain Cap.10 0. 0.C2 : C2 : Volume between WL at lowest point of sheer and sheer line at side. for CB = 0. Capacity Depth DC DC = Dmld + ½ camber + 1/6 (SA + SF) – (depth of d. Both forward and aft calculations are done separately and added. .583 For an increase of decrease of CB by 0.b. . No. EHP for a new ship with similar hull form and Fr.0 Power Estimation For quick estimation of power: (a) (b) SHP 0. AC = ∆ 2/3 V 9 BHP Where AC = AdmiralityCoefficent ∆ = Displacement in tons V = Speed in Knots (c) In RINA. 102) . ∆ in tons.5 = 0. (d) (i) From basic ship: If basic ship EHP is known. RINA. vol 102. Fn ).V in knots. Moor and Small Have proposed L   H ∆1 / 3 V 3  40 + 400 ( K − 1) 2 −12 C B   200  SHP = 1500 − N γ L Where N : RPM H : Hull correction factor = 0. form. vol.9 for welded construction K :To beobtained from Alexander ' s formula L : in ft .can be found out as follows: Breadth and Draught correction can be applied using Mumford indices (moor and small.5813 [ DWT / 1000] 3 V0 Admirality coefficient is same for similar ships (in size.8. Θ B new = basic  n B  b Θ     X −2 / 3  Tn  T  b     Y −2/3 Where x = 0.57 0. The non-dimensional resistance coefficients are given as RR = This can be estimated from services data with corrections.55 0. Nec. 1962-63). L.54 0. (e) Estimation of EHP from series Data wetted surface Area S in m 2 is given as 2π η η = Wetted surface efficiency (see diagram of Telfer. 1/ 2 ρ S V 2 RF 1/ 2 ρ S V 2 CF = S= ∆.75 0. ( log10 Rn − 2) 2 VL v 0.55 0.70 γL γ 0.60 Where Θ= (ii) EHP andwhere ∆ : tons.64 Length correction as suggested by wand G (RINA 1977) @ L1 − @ L2 = 4( L2 − L1 ) x 10 − 4 This correction is approximate where L : ft. ∇ = m 3 . = . Vol.075 Where Rn : Re ynold ' s No.1 2/3 0.50 0.9 and y is given as a function of V / γ L as V 0.62 0. 79.65 0.80 0. L = m CR = CF = From ITTC.60 0.58 0. V : knots ∆ V 3 × 427. 5% SHP = QPC =η 0 η H η R = K − Where N = RPM L = LB P in m . To get total resistance.8 − 0. EPH service = EHPLrial × (1.004 Lw l ) ×10 − 3 where Lw l is in m CT = C F + C R + C A = RT 1/ 2 ρ S V 2 = 0..W .1to 1.139 ×10 −6 m 2 / sec for fresh water C A = Roughness Allowance or C A = ( 0.1.0004 in general Where RT is the bare hull resis tan ce. ISP 1981/1984 (given at the end of these notes) (g) Estimation of SHP or shaft horse power EHPservice QPC Nγ L 10000 8 to 10% 5% 3% 2 to 5% 0.188 ×10 −6 m 2 / sec for sea water and for F .v = Kinematic coefficient of Viscocity and =1. Appendage resistance must be added to this: Twin Screw Bossings A bracket Twin Rudder Bow Thruster Ice Knife If resistance is in Newtons and V is in m/sec.25) KW . (f) EHP from statistical Data : See Holtrop and Mannen. 82 For controllable pitch propellers can be estimated more accurately later (h) BHPs BHPs = SHP + Transmission losses Transmission loss can be taken as follows: Aft Engine Engine Semi aft Gear losses (i) Selection of Engine Power: 1% 2% 3 to 4% The maximum continuous rating (MCR) of a diesel engine is the power the engine can develop for long periods.95 MCR BHPs (NCR) Select Engine 9.85 to 0.95) Thus engine selected must have MCR as MCR = BHPs / 0.84 For fixed pitch propellers = 0. Thus CSR of NCR (Normal Continuous Rating) = MCR× ( 0.1 Seakeeping Requirement Bow Freeboard Fbow losses PET service PES Allowance QPC Shafting SHP . By continuous running of engine at MCR may cause excessive wear and tear.85 / 0.0 9.85 to 0. So Engine manufactures recommend the continuous service rating (CSR) to be slightly less than MCR. Thus PEN trial (Naked hull HP) Allowance 0.K = 0.95. 075 (b) Probability of Deckwetness P for various Fbow / L values have been given in Dynamics of Marine Vehicles.76 ≤ κ ≤ 0.Bhattacharya: L( f t) L ( m) 200 61 Fbow / L for P= 0.046 0. Fbow Should also be checked from load line requirement.1% 1% 10% 0.50 KB . A more complex parametric model for estimating the roll natural period that yields the alternative result for the parameter κ is .058 0. which can be related to the ship beam using: k11 = 0.046 0.026 0. heave.037 0. Their effectiveness usually depends upon the hull form being close to the norm.020 0. by R.00 generally.015 400 122 600 183 800 244 Estimate Fbow check for deckwetness probability and see if it is acceptable. and pitch based only upon the characteristics and parameters of the vessel. 9.V γL Fbow L 0. With 0.007 k11 / G M t Where k11 is the roll radius of gyration.080 0.60 0.036 0. Using κ 11 ≈ 0.056 0.80 0.048 0.90 0.40 B .2 Early estimates of motions natural frequencies effective estimates can often be made for the three natural frequencies in roll.70 0. An approximate roll natural period can be derived using a simple one-degree of freedom model yielding: Tφ = 2.82 for merchant hulls and 0.056 0.045 0.026 0.032 0.69 ≤ κ ≤ 1. 2Th = Tθ . heave is a heavily damped (non resonant) mode. the peak frequency of an ISSC spectrum is located at 4. θ w = 9 0 beam seas. which could lead to significant mode coupling.0 − C B ) ( 2. The encounter period in long. but early design checks typically try to avoid critical excitation by at least 10% An approximate heave natural period can also be derived using a simple one degree-of-freedom model.2 ) / C w p ) Like pitch. Tφ = 2Tθ . Tφ = Tθ . which can be related to the ship length by noting that 0. A resulting parametric model has been reported by Lamb: Th = 2.36 / T ) ) Pitch is a heavily-damped (non resonant) mode.6 + 0. For reference.2 − D / T ) + ( D / B ) ) 2 Roll is a lightly damped process so the natural period can be compared directly with the domonant encounter period of the seaway to establish the risk of resonant motions.85 T1−1 with T1 the characteristics period of the seaway. and θ w = 18 0 • Head seas. For many large ships.724 (C B ( C B + 0. .007 (T C B ( B + 3T + 1. however.2) − 1.24 L ≤ k 22 ≤ 0. An approximate pitch natural period can also be derived using a simple one. Early design checks typically try to avoid having Th = Tφ .degree of freedom model yielding: Tθ = 2.crested oblique seas is given by: Te = 2 π / (ω − (Vω 2 / g ) cos θ w ) Where ω is the wave frequency. and θ w is the wave angle relative • • to the ship heading with θ w = 0 following seas. An alternative parametric model reported by Lamb can be used for comparison: Tθ =1.26 L.776 C −1 w p / (T C B ( 0.κ = 0.1 ( C B + 0. Th = Tθ .2 ) × (1. V is ship speed. these conditions often cannot be avoided.007 k 22 / GM L Where now k 22 is the pitch radius of gyration. B.9. Use inference equation wherever necessary 10.5 times as effective as aft and lower vertical prismatic forward is about 1.5 times as effective ˆ as aft in increasing R . T . Note also that added waterplane forward is about 4. can be seen to provide improved vertical plane seakeeping. ˆ This estimator R yields a ranking number between 1 (poor seakeeping) and 10 (superior seakeeping) and has the following form: ˆ R = 8. Satisfy weight equation by extrapolating lightship from basic ship data. 10. C B etc as above to get ∆ new = L B T C B ×1.42 + 45.03 to 1.1C w p f + 10. For stability assume ( KG / D) basic = ( KG / D ) new with on your deletion Check capacity using basic ship method.27 C / L − 23. Corresponding to V-shaped hulls. ship type and are nearly same and detailed information about the basic ship is available.1 Difference Equations . 4. Since ˆ the objective for superior seakeeping is high R . Choose L B T C B from empirical data and get ∆ Such that ( d w / ∆ ) basic = ( d w / ∆ ) new . 3. 5.9 C v p a Here the waterplane coefficient and the vertical prismatic coefficient are expressed separately for the forward (f) and the aft (a) portions of the hull.5 C v p f −15. Basic Ship Method Choose basic ship such that V / γ L. V-shaped hull sections forward provide the best way to achieve greater wave damping in heave and pitch and improve vertical plane seakeeping. 2.1C w p a − 378 T / L + 1.033. high C w p and low C v p . Choose L . 1.3 Overall Seakeeping Ranking used Bales regression analysis to obtain a rank estimator for vertical plane seakeeping performance of combatant monohulls. Thus. one can write B M α B2 /T or B M = k × B 2 / T or log BM = log k + 2 log B − log T Differentiating and assuming k constant dBM dB dT =2 − BM B T 11.T . Similarly. L : f t φ = 156 . in in 2 ft 2 ∆ : tons.1 Hull Vibration Calculation For two node Vertical Vibration.These equations are frequently used to alter main dimensions for desired small changes in out put. For example ∆ = L. B. to improve the values of BM by dBM. T . 500 for large passenger lines . hull frequency is N = φγ  I   3  ∆ L  (cpm) [Schlick] Where I : Midship m . d ∆ d L d B d T d CB = + + + ∆ L B T CB So if a change of d∆ is required in displacement. or C B can be altered so that above equation is satisfied. 11. log ∆ = log L + log B + log T + log C B + log ρ Assuming ρ to be constant and differentiating. B. C B ρ Or. 850 for ships with fine lines = 143. i. one or some of the parameters L. decks as.400.s 44000 1/ 2 C2 28 25 20 52000 46750   Ι N =φ  3   ∆ L (1 + B / 2T ) (1 + rS )  Burill Where φ = 2.000.s. DE N = C1   3 (cpm)  (1. 3   B .2 L2 ( 3B / D + 1) 3 2 rS : shear correction = ( ) . others in British unit 3. This is refined to take into account added mass and long s .= 127. dk C1 Tankers Cargo Vessels Passenger Vessels With s.5 D 3( B / D ) + 9( B / D ) + 6( B / D ) + 1.2 + B / 3T ) L ∆)  1/ 2 + C2 [ Todd] Where DE : effective depth DE : ∑ D13 L1 / L [ ] 1/ 3 Where D1: Depth from keel to dk under consideration L1 : Length of s. I : ft4 .s. 900 for cargo ships (cpm) N = βγ  BD 3   3 ∆L  B: breadth in ft and D : Depth upto strength dk in ft. 000 for cargo ships 38.23 for tankers 1.2 +  3 Tm    ∆ = displacement   including virtual added mass of water (tons) L = length between perpendicular (m) B= Breadth amidship (m) Tm == mean draught (m) The higher noded vibration can be estimated from the following formula by Johannessen and skaar (1980) N nv ≈ N 2v ( n − 1) ∝ Then ∝ = 0. 07 * 106 Then Iv = ∆i = Ιv cpm ∆i L3 Moment of inertia (m4)  1 B 1.2 Hull Vibration (Kumai) Kumai’s formula for two nodded vertical vibration is (1968) N2v = 3.165 for cargo ships All units are in British unit.700 for tankers with long framing 34.K N= n L   T DE    C B ( B + 3.N2V 11. N2V N4V = 3.845 general cargo ships .6 T1 )  1/ 2 where [ Bunyan] K= 48. T1 : Mean draught for condition considered T : Design Draught N3V = 2.400 for cargo ships long framed n= 1. 0 1. B. other quantities in British units.1. N 2 H =1.3 Horizontal Vibration For 2 node horizontal vibration. D : ft . hull frequency is N2H  D.4 Torsional Vibration For Torsional vibration. . N 2 H N 4 H = 3N 2 H 11. hull frequency is Ip   N T = 3 ×10 C  2  2  B + D L. ∆ : tons.00 for two node.5 N 2 v N 3 H = 2. L  1/ 2 cpm [Brown] Where β H = 42000. N 1 − T 5 1/ 2 cpm [Horn] = 3.2 bulk carriers Tankers N2V is the two noded vertical natural frequency. 11. B 3  = βH  3   ∆.07 for three node . N 2 − T = 4. ∆  C = 1. N 3 − T I p = 4 A2 / Σ ds 4 ( ft ) (This formulae is exact for hollow circular cylinder) T A = Area enclosed by section in ft 2 d g = Element length along enclosing shell and deck ( ft ) t= Corresponding thickness in ( ft ) L.58 for one node. n should not exceed 5 or 6 in order to remain within range validity for the above equation. A. 1979. NECIES.Munro.H. BSRA. Ship Design for Efficiency and Economy. M. E. J. R. 2003.A statistical Re. ‘Merchant Ship Design’. The Naval Architect (RINA). R. I. Engine RPM is to be so chosen that hull vibration frequency and shaft and propeller frequency do not coincide to cause resonance. Gilfillan. References 1. G. 2. ILLC Rules 1966. Munro-Smith 7.Classification Rules 15. Goldhommce & Sr.H Schneekluth. Ship Hull Vibration F. Waston and A. 11. 1977. RINA. Aa Harvald Report 1974.W. Mishra. American Bureau of ships. ‘Concept Exploration. Todd (1961) 13. Ayre. some ship Design Methods’ RINA. Munro-Smith 10. 3. ‘ShipDesign and Construction’ edited by Thomas Lab SNAME. . of blades × shaft frequency. P. ‘Elements of Naval Architecture’ R.An approach to Small Warship Design’. N. D.Classification Rules 16.analysis of Resistance and Propulsion Data ISP 1984. Butterworth. 1977.L Buxton. Eames and T.11. 5. C. M. 17. 14. Drummond. L. ‘Applied Naval Architecture’. 1977.H. IINA. VOl. ‘Engineering Economics in ship Design. 1987. 9.Smith 6. 8. Indian Register of ships. Townsin.5 Resonance Propeller Blade Frequency = No. 12. 4. Holtrop. 64. Ship Resistance. C. R. . (i) C F 0 = Friction coefficient according to the ITTC – 1957 frictional = ( log10 Rn − 2) 2 0.011 C Stern 0.4871c ( B / L ) 1.3649 C Stern = -25 for prom with gondola = -10 for v-shaped sections = 0 for normal section shape = +10 for U-shaped section with hones stern . ( L / LR ) 0.12 1 + K 1 = 0. ( T / L ) 0.6042 .075 1 + K 1 was derived statistically as 3  − 0.Resistance Estimation Statistical Method (HOLTROP) 1984 R Total = R F (1 + K 1 ) + R App + RW + R B + RTR + R A Where: R F = Frictional resistance according to ITTC – 1957 formula K 1 = Form factor of bare hull RW = Wave – making resistance RB = Additional pressure resistance of bulbous bow near the water surface RTR = Additional pressure resistance due to transom immersion R A = Model –ship correlation resistance R App = Appendage resistance The viscous resistance is calculated from: 1 Rv = ρ v 2 C F 0 (1 + K 1 ) S 2 Where …………….93 + 0. (1 − C P )  L / ∇   C is a coefficient accounting for the specific shape of the after body and is given by C = 1+0.4611 .0681 . 06 C p LCB / ( 4 C p −1) S is the wetted surface area and can be estimated from the following statistically derived formula: 0 S = L ( 2T + B ) C M. 1 + K = 1 + K 1 + [1 + K 2 − (1 + K 1 ) ] Where K 2 = Effective form factor of appendages S app = Total wetted surface of appendages S tot S app S tot = Total wetted surface of bare hull and appendages The effective factor is used in conjunction with a modified form of equation (i) Rv = 1 ρV 2 C Fo S tot (1 + K ) 2 The effective value of K 2 when more than one appendage is to be accounted for can be determined as follows S (1 + k 2 ) i (1 + k 2 ) effective = ∑ i ∑ Si In which S i and (1 + k 2 ) i are the wetted area and appendage factor for the i th appendage . All coefficient are based on length on waterline.3696 C wp ) + 2.38 AB r / C B Where T = Average moulded draught in m L = Waterline length in m B = Moulded breadth in m LCB = LCB ford’s ( + ) or aft ( − ) of midship as a percentage of L AB r = Cross sectional area of the bulb in the vertical plane intersecting the stern contour at the water surface.4425 C B − 0.5 ( 0.LR is the length of run – can be estimated as LR / L = 1 − C p + 0.2862 C M − 0. The resistance of appendages was also analysed and the results presented in the form of an effective form factor.003467 B + 0.4530 + 0. including the effect of appendages. 8 for C p ≥ 0.4 2.8 ( ) 2 C 5 = 8. λ and m are coefficients which depend on the hull form.0796 ( 90 − i E ) −1.0 3.4 the following coefficients were derived 3 C1 = 2223105 C 4 .0 2.4 e −0.3757 B with:  C = 0.11 L for 0.3 to 1.8 2. results in the typical humps and hollows in the resistance curves.7301 − 0.7067 C p  m2 = C 6 0. For low-speed range Fn ≤ 0.11 ≤ B ≤ 0.2296 B 0.0625 L  B  d = -0. C 3 .7525 ∇      − 4. The interaction between the transverse waves.7861 (T B ) 1.9 ( ) ≤ 0. C 2 .01404 L with: ( T ) − 1.5 to 2.24 .0798 C p − 13.0 1.7 For wave-making resistance the following equation of Havelock (1913) Was simplified as follows: d Rw = c1 c2 c3 e m1Fn + m2 cos λ Fn−2 W ( ) In this equation C1 . accounted for by the cosine term.034 Fn −3.TABLE: EFFECTIVE FORM FACTOR VALUES K 2 FOR DIFFERENT APPENDAGES Type of appendage Rudder of single screw ship Spade type rudder of twin screw ship Skeg-rudder of twin screw ships Shaft Brackets Bossings Bilge keels Stabilizer fins Shafts Sonar dome value of (1 + k 2 ) 1.25 L for B ≥ 0.3333 L  4  C4 = B  L  C 4 = 0.25 L for 1 3 m1 = 0.9844 C 3  p   C 5 = 1. λL is the wave making length.5 2.8673 C p + 6.7932 B − C 5 L L  for C p ≤ 0.8 1.0 2.5 − 0. 67 B i E = half angle of entrance of the load waterline in degrees ( ) 2 p 3 p )    3 The value C2 accounts for the effect of the bulb.0 if no bulb’s fitted.56 ABT5 i represents the effect of submergence of the bulb as determine by i = T f − hB − 0.P Tf = moulded draught at F. Coefficients C1 and m1 are modified as follows − C1 = 6919.36    ∇ 3  → ≤ 512 ∇ 3 for 512 ≤ L ≤ 1727 ∇ 3 for L 3 for L ∇ ≥ 1727 λ = 1.3269 (T B ) 0.03 L B λ = 1.3 ) 2.36 where ( ) for L for L B B ≤ 12 ≥ 12 6.1551  LCB +  L T  where Ta = moulded draught at A.0 6  → L   1 − 8.3 C M1. ν B = 0.89 BT (ν B + i ) where ν B is the effective bulb radius.25 C + 234.4464 ν B where Tf = moulded draught at FP hB = height of the centroid of the area ABT above the base line C 3 = 1 − 0.446 C p − 0.0  / 2.346 ( ∇ / L. otherwise ABT ν B C 2 = e −1.446 C p − 0. C2 = 1.69385 6   C 6 = − 1.with:  C = − 1. For high speed range Fn ≥ 0.8 AT / ( BTC M ) C3 accounts for the influence of transom stern on the wave resistance AT is the immersed area of the transom at zero speed.3.32 C + 0.69385 +   C = 0.0098 ( L B − 2) 1.2035 B ( L) 0.4069 m1 = −7.P i E = 125.8(Ta − T f  − 162. equivalent to 0.6054 .55 . For intermediate speed range ( 0.4 ≤ Fn ≤ 0.16 0.5  { }    The formula derived for the model-ship correlation allowance CA is C A = 0.W 2 W .55) the following interpolation is used (10 Fn − 0.55 − RWFn04 RW 1  =  RWFn04 + W W 1.006 ( LWL + 100 ) for TF / LWL ≥ 0.006 ( LWL + 100 ) −0.00205  − 0.16 − 0.04 C C 2 ( 0.04 − TF / LWL ) 4 B for TF / LWL ≥ 0.00205 + 0.04 where C2 is the coefficient adopted to account for the influence of the bulb.003 ( LWL / 7.4) RWFn0. Total resistance R 1 RT = ρ ν 2 S tot [ C F (1 + k ) + C A ] + W .5) C A = 0.5 − 0.