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(1)2019-07-22. Lecture Note of Innovative Ship and Offshore Plant Design. Innovative Ship and Offshore Plant Design Part I. Ship Design Ch. 6 Resistance Prediction. Spring 2019. Myung-Il Roh Department of Naval Architecture and Ocean Engineering Seoul National University Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 1. Contents  Ch. 1 Introduction to Ship Design  Ch. 2 Design Equations  Ch. 3 Design Model  Ch. 4 Deadweight Carrier and Volume Carrier  Ch. 5 Freeboard Calculation  Ch. 6 Resistance Prediction  Ch. 7 Propeller and Main Engine Selection  Ch. 8 Hull Form Design  Ch. 9 General Arrangement (G/A) Design  Ch. 10 Structural Design  Ch. 11 Outfitting Design. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 2. 1. (2) 2019-07-22. Ch. 6 Resistance Prediction. 1. Object of Resistance Prediction 2. Decomposition of Resistance and Methods of Resistance Prediction 3. Resistance Prediction by Holtrop-Mennen’s Method 4. Resistance Prediction by Holtrop-Mennen’s Method for a 3,700 TEU Container Carrier. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 3. 1. Object of Resistance Prediction. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 4. 2. (3) 2019-07-22. Object of Resistance Prediction (1/3) Review) Weight Estimation: Method 4. LWT = Ws + Wo + Wm. L  B  T  CB    (1   )  DWT  Cs  L1.6  ( B  D)  Co  L  B Cm  NMCR There are few data available for estimation of the NMCR at the early design stage. Thus, NMCR can be roughly estimated by ‘Admiralty formula’.. Admiralty formula:. Cad: Admiralty coefficient Vs: Speed of ship [knots] : Displacement [ton] NCR: Required power for service speed. NCR  f ( , Vs ) NCR  C NCR   2/3 Vs 3. Define C ad . NCR .  2/3  Vs 3 Cad. 1 . C NCR. Cad is called “Admiralty coefficient”.. However, NMCR should be estimated more accurately based on the prediction of resistance and propulsion power. 5. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Object of Resistance Prediction (2/3)  Goal: Estimation of NMCR At first, we have to predict total calm-water resistance of a ship.. Ship speed (Vs) Total calm-water resistance (RT(v)). DHP. Then, by using the propulsive efficiency, shaft, and sea margin, required propulsive power can be estimated.. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Propeller Shaft. Propeller. BHP. Diesel engine. 6. 3. (4) 2019-07-22. Object of Resistance Prediction (3/3) 1 EHP (Effective Horse Power). EHP  RT (v) Vs. (In calm water). Resistance Prediction. 2 DHP (Delivered Horse Power). DHP . EHP. (  D : Propulsive efficiency). D. D  O H R O : Open water efficiency  H : Hull efficiency  R : Relative rotative efficiency. 3 BHP (Brake Horse Power). BHP . DHP. T. (. T : Transmission efficiency). Propeller Efficiency Thrust deduction and wake (due to additional resistance by propeller) Hull-propeller interaction. 4 NCR (Normal Continuous Rating). NCR  BHP (1 . Sea Margin ) 100. 5 DMCR (Derated Maximum Continuous Rating). DMCR . NCR Engine Margin. Engine Selection. 6 NMCR (Nominal Maximum Continuous Rating). NMCR . DMCR Derating rate. Engine Data. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 7. 2. Decomposition of Resistance and Methods of Resistance Prediction. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 8. 4. (5) 2019-07-22. Definition of Resistance. Ship speed (Vs) Total calm-water resistance (RT(v)).  Resistance  The resistance of a ship at a given speed is the force required to tow the ship at that speed in smooth water, assuming no interference from the towing ship.  This total resistance is made up of a number of different components, which are caused by a variety of factors and which interact one with the other in an extremely complicated way.. * SNAME, Principles of Naval Architecture – Resistance, Propulsion and Vibration, Vol. 2, 1988 Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 9. Types of Resistance In order to deal with the question more simply, it is usual to consider the total calm water resistance as being made up of four main components. (a) Frictional resistance, due to the motion of the hull through a viscous fluid. (b) Wave(-making) resistance, due to the energy that must be supplied continuously by the ship to the wave system created on the surface of the water.. (c) Eddy(-making) resistance, due to the energy carried away by eddies shed from the hull or appendages. Local eddying will occur behind appendages such as bossings, shafts and shaft struts, and from stern frames and rudders if these items are not properly streamlined and aligned with the flow.. (d) Air resistance experienced by the above-water part of the main hull and the superstructures due to the motion of the ship through the air.. * SNAME, Principles of Naval Architecture – Resistance, Propulsion and Vibration, Vol. 2, 1988 Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 10. 5. (6) 2019-07-22. Dimensional Analysis (1/4) Example) Model propeller test. A model propeller test. A real-ship propeller.  Dimensional Analysis Dimensional analysis is essentially a means of utilizing a partial knowledge of a problem. when the details are too obscure to permit an exact analysis. It has the enormous advantage of requiring for its application a knowledge only of the variables which govern the result. Dimensional solutions do not yield numerical answers, but they provide the form of the answer so that every experiment can be used to the fullest advantage in determining a general empirical solution. * SNAME, Principles of Naval Architecture – Resistance, Propulsion and Vibration, Vol. 2, 1988. 11. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Dimensional Analysis (2/4) Example) Model test in a towing tank. Model test. Design ship.  Application of dimensional analysis to a ship To apply it to the flow around ships and the corresponding resistance, it is necessary to know only upon what variables the latter depends. Applying dimensional analysis to the ship resistance problem, the resistance R could depend upon the following: R   aV b Lc  d g e p f * M: Mass, L: Length, T: Time. (a) Speed, V a b c d (b) Size of body, which may be represented ML / T 2   M / L3   L / T   L   M / LT  by the linear dimension, L. e f   L / T 2   M / LT 2  (c) Density of fluid, ρ (mass per unit volume) (d) Viscosity of fluid, μ  VL  d  gL e  p  f  R  V 2 L2 f  (e) Acceleration due to gravity, g   2  2       V   V   (f) Pressure per unit area in fluid, p non-dimensional term. * SNAME, Principles of Naval Architecture – Resistance, Propulsion and Vibration, Vol. 2, 1988 Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 12. 6. (7) 2019-07-22. Dimensional Analysis (3/4) It is assumed that the resistance R can now be written in terms of unknown powers of these variables :.  VL gL p  R  f , 2, 2 2 2 1/ 2  V L   V V  Writing  for / and remembering that for similar shapes the wetted surface S is proportional to L2, the equation may be written:. VL gL p   f  , 2, 2 1/ 2   SV   V V  R. 2. The 1st term is the Reynolds number Rn. The 2nd term is related to the Froude number Fn. The 3rd term is the Cavitation number σo.. The left-hand side of the equation is a non-dimensional resistance coefficient. Equation states in effect that if all the parameters on the right-hand side have the same values for two geometrically similar but different sized bodies, the R flow patterns will be similar and the value of 1 / 2 SV will be the same for each. 2. * SNAME, Principles of Naval Architecture – Resistance, Propulsion and Vibration, Vol. 2, 1988. 13. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Dimensional Analysis (4/4)  Dimensionless number derived by dimensional analysis to a ship  VL gL p  R  f , 2, 2 2 1/ 2  SV   V V  non-dimensional term * Dimensional Homogeneity Dimensional analysis rests on the basic principle that every equation which expresses a physical relationship must be dimensionally homogeneous.. Dimensionless Number: Rn (Reynolds Number) : A dimensionless number that gives a measure of the ratio of inertial forces to viscous forces. Rn . VL. . V: characteristic velocity of the ship L: length of the ship at the waterline level.  : In 10 degree seawater, 1.35X10-6 In 15 degree seawater, 10-6.  : kinematic viscosity. Fn (Froude Number) : A dimensionless number comparing inertial and gravitational forces V: characteristic velocity of the ship V Fn  L: length of the ship at the waterline level gL g: acceleration due to gravity * Cavitation number: A dimensionless number used in flow calculations. It expresses the relationship between the difference of a local absolute pressure from the vapor pressure and the kinetic energy per volume, and is used to characterize the potential of the flow to cavitate. * SNAME, Principles of Naval Architecture Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 14. 7. (8) 2019-07-22. Decomposition of Resistance (1/3) Rn (Reynolds Number) :. Rn . VL. Fn (Froude Number) :. . Fn . V gL. The concept of resistance decomposition helps in designing the hull form as the designer can focus on how to influence individual resistance components.. Resistance decomposition by Froude Total resistance (RT) = Frictional resistance (RF) + Residual resistance (RR) + Model-ship correlation resistance (RF). Resistance decomposition by Hughes Total resistance (RT) = Viscous resistance (RV) + Wave resistance (RW). 15. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Decomposition of Resistance (2/3) Froude : RT=RF+RR+RF,. Hughes : RT=RV+RW.  Frictional resistance prediction method Frictional resistance is assumed to be a function of the Reynolds number. Frictional resistance (RF): The frictional resistance is usually predicted taking the resistance of an ‘equivalent’ flat plate of the same area and length as follows : . RF  1/ 2   CF  S V. : density of sea water= 1.025 (Mg/m3). C F : frictional resistance coefficient. 2. V [m / s ] :. characteristic velocity of the ship. S [ m 2 ] : wetted surface. The 1957 ITTC (International Towing Tank Committee) line is expressed by the formula: CF . 0.075 (log Rn  2) 2. Rn (Reynolds Number) :. VL. . 3-dimensionalized form using the form factor. Viscous resistance (Rv): RV  1  k  RF  RF. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. k. : form factor. RF : model-ship correlation factor. 16. 8. (9) 2019-07-22. Decomposition of Resistance (3/3)  Wave resistance prediction method The ship creates a typical wave system which contributes to the total resistance. For fast, slender ships this component dominates. In addition, there are breaking waves at the bow which dominate for slow, full hulls, but may also be considerable for fast ships.. The interaction of various wave systems is complicated leading to non-monotonous function of the wave resistance coefficient Cw . The wave resistance depends strongly on the local shape. Tanker (16 knots). RW  f ( L / B, B / T , Cb , Fn , LCB ) Example) Wave resistance formula in the method of Holtrop-Mennen. Wave breaking Wave pattern. 5%. Viscous pressure. 15%. Form effect on friction. 5%. Roughness. 10%. 5%. Ro-Ro (21 knots) 10%. 30%. Wav e resistance. 7.50% 2.50%. 2 n. RW   g  C1C 2C5 exp{m1 F  m4 cos(  F )} d n. 10%. Flat plate friction. Viscous resistance. 60% 40%. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 17. 3. Resistance Prediction by Holtrop-Mennen’s Method. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 18. 9. (10) 2019-07-22. Types of Ship Resistance Evaluation Methods. Ship resistance evaluation methods. Traditional and standard series methods. Taylor Ayre Lap Auf’m Keller Harvald. BSRA series SSPA series Series 60 Coaster series. Regression based methods. Scott Holtrop & Mennen. ⋮. ⋮. Direct model test. 2D extrapolation 3D extrapolation. Computational Fluid Dynamics (CFD). Advanced Navier-Stokes Solution capabilities For 3D flow around ships. ⋮. ⋮. * John Carlton, Marine Propellers and Propulsion, 3rd Edition, Elsevier, 2012. 19. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Resistance estimation by Holtrop-Mennen’s Method - Reason why a statistical method is presented at the initial design stage of a ship (1/2) Model Test for the basis ship. Model Test for the design ship. ? Basis ship. Design ship. As the resistance of a full-scale ship cannot be measured directly, our knowledge about the resistance of ships comes from model tests.. However, at the initial design stage of a ship, the model for the design ship is not provided. Furthermore, the design ship and the basis ship are not preserved geometrical similarity.. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 20. 10. (11) 2019-07-22. Resistance estimation by Holtrop-Mennen’s Method - Reason why a statistical method is presented at the initial design stage of a ship (2/2). Therefore, a statistical method was presented for the determination of the required propulsive power at the initial design stage. This method was developed through a regression analysis of random model experiments and full-scale data. Many naval architects use the method, generally in the form presented in 1984 and find it gives acceptable results although it has to said that a number of the formula seem very complicated and the physics behind them are not at all clear, (a not infrequent corollary of regression analysis).. * Holtrop and Mennen's method, which was originally presented in the Journal of International Shipbuilding Progress, Vol. 25 (Oct. 1978), revised in Vol. 29 (July 1982) and again in N.S.M.B. Publication 769 (1984) and in a paper presented to SMSSH'88 (October 1988), meets all criteria with formulae derived by regression analysis from the considerable data bank of the Netherlands Ship Model Basin being provided for every variable.. 21. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Formula Proposed by Holtrop & Mennen. ① Frictional resistance. ③ Appendage resistance. ⑤ Additional pressure resistance of bulbous bow near the water surface. ⑦ Model-ship correlation resistance. RT  RF (1  k1 )  R APP  RW  RB  RTR  RA Total resistance. ② Form factor of the hull. ④ Wave resistance. ⑥ Additional pressure resistance due to immersed transom immersion. L. T B. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 22. 11. (12) 2019-07-22. 4. Resistance Prediction by Holtrop-Mennen’s Method for a 3,700 TEU Container Carrier. 23. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Resistance Prediction by Holtrop and Mennen’s Method Example) 3,700 TEU Container Carrier Item. Value. Main Dimension LOA LBP LWL Bmld Dmld Td /Ts (design / scantling). 257.4 m 245.24 m 239.26 m 32.2 m 19.3 m 10.1 / 12.5 m. Deadweight (design / scantling). 34,400 / 50,200 MT(metric ton). Displacement Volume at Td. 49,652.7 m3. LCB. -0.531% aft of 1/2LBP. Midship section coefficient (CM). 0.9761. Waterplane are coefficient (CW). 0.7734. Item Transverse bulb area Center of bulb area above keel line Transom area Wetted area appendages Stern shape parameter Propeller diameter Number of propeller blades Clearance propeller with keel line. Value 15.2 m2 5.5 m2 0 m2 317.74 m2 V-shaped 7.7 m 5 0.3 m. Capacity Container on deck / in hold. 2,174 TEU / 1,565 TEU. Ballast water. 13,800 m3. Heavy fuel oil. 6,200 m3. Main Engine & Speed M / E type. Sulzer 7RTA84C. MCR (BHP ⅹ rpm). 38,570 ⅹ102. NCR (BHP ⅹ rpm). 34,710 ⅹ98.5. Service speed at NCR (Td, 15% SM). 22.5 knots (at 11.5 m) at 30,185 BHP. DFOC at NCR. 103.2 MT. Cruising range. 20,000 N.M. Others Complement (Crew). 30 Person. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 24. 12. (13) 2019-07-22. ① Frictional Resistance (1/3). RT  RF (1  k1 )  R APP  RW  RB  RTR  R A. 3,700 TEU Container Carrier Item. Value. V. 22.5 knots. LWL. 239.26 m. v. 1.19. 10. CF : Coefficient of frictional resistance (ITTC 1957 friction formula) CF . 0.075 (log Rn  2) 2. Rn . V L. . Rn is based on the waterline length (LWL). Example 3.700 TEU CTN Carrier). Rn  CF . V  LWL. . . 11.8312  239.26  2.33  109 1.19 106. 0.075 0.075   1.38  10 3 2 (log Rn  2) (log 2.33 109  2) 2 25. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ① Frictional Resistance (2/3). RF . 1 V 2C F Sbh 2. RT  RF (1  k1 )  R APP  RW  RB  RTR  R A. S bh : Wetted surface area of the bare hull ABT : Transverse bulb area. Definition of ABT [L2]: The cross sectional area (full section port and starboard) at the fore perpendicular. Where the water lines are rounded so as to terminate on the fore perpendicular ABT is measured by continuing the area curve forward to the perpendicular, ignoring the final rounding (Reference: ITTC).. A re a A. BT. hB. FP. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Base line. 26. 13. (14) 2019-07-22. ① Frictional Resistance (3/3). RF  S bh. 1 V 2C F Sbh 2. RT  RF (1  k1 )  R APP  RW  RB  RTR  R A. 3,700 TEU Container Carrier. CF=0.001378 ρ=1.025 ton/m3. : Wetted surface area of the bare hull. Item. Value. L (LWL). 239.26 m. T. 10.1 m. B. 32.2 m. CM. 0.9761. CWP. 0.6761. ABT. 15.2 m2. CB. 0.6394. Sbh  L(2T  B) CM (0.4530  0.4425CB  0.2862CM  0.003467 B / T  0.3696CWP )  2.38 ABT / CB In this formula, the hull form coefficients are based on the waterline length (LWL).. Example 3.700 TEU CTN Carrier). Sbh  L(2T  B ) CM (0.4530  0.4425C B  0.2862CM  0.003467 B / T  0.3696CWP )  2.38 ABT / C B  239.26( 2  10.1  32.2). 0.9761 (0.4530  0.4425  0.6394  0.2862  0.9761  0.003467  32.2  10.1  0.3696  0.6761). 2.38  15.2  0.6394.  8, 670.24[m 2 ].  RF . 1 1 V 2CF Sbh  1.025 11.5742 1.38  103  8, 670.24  822.61[kN ] 2 2 27. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ② Form Factor of the Bare Hull (1/3) R  R (1  k )  R T. F. 1. APP. 1  k1  0.93  0.487118  C14 ( B / L)1.06806 (T / L)0.46106 ( L / LR ) 0.121563.  RW  RB  RTR  R A. 3,700 TEU Container Carrier. ( L 3 / )0.36486  (1  CP ) 0.60247. Item. Value. After body form. V-shaped. C 1 4 : The prismatic coefficient based on the waterline length C14  1  0.011Cstern. C stern  25.  10 0  10. Pram stern with gondola V-shaped sections Normal section shape U-shaped sections. Example 3.700 TEU CTN Carrier). Cstern  10. C14  1  0.011Cstern  1  0.011 (10)  0.89. L. T B. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 28. 14. (15) 2019-07-22. ② Form Factor of the Bare Hull (2/3) Types of stern V-shaped U-shaped Bulbous-shaped. Twin gondola stern Pram with gondola. (A) Cruiser sterned vessels. - In the aspect of resistance, V-shaped is better. - In the aspect of propulsive efficiency, U-shaped is better.. (B) Transom sterned vessels (C) Counter sterned vessels 29. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ② Form Factor of the Bare Hull (3/3) R  R (1  k )  R T. F. 1. APP.  RW  RB  RTR  R A. 1  k1  0.93  0.487118  C14 ( B / L)1.06806 (T / L)0.46106 ( L / LR ) 0.121563 ( L 3 / )0.36486  (1  CP ) 0.60247. 3,700 TEU Container Carrier. C14=0.89. L R : Length of run. Item. Value. L. 239.26 m. B. 32.2 m. T. 10.1 m. . 49778. Cp. 0.6794. LCB. -0.531 % (aft). At early design stage, if LR is unknown, it can be obtained by following formula:. LR / L  1  C P 0.06CP  LCB / (4CP  1) LCB : The longitudinal position of the centre of buoyancy forward of 0.5L as a percentage (%) of L. forward : (+), aft : (-). Example 3.700 TEU CTN Carrier) LR  L(1  CP  0.06CP  LCB / (4CP  1))  239.26(1  0.6794  0.06  0.6794  (0.531) / (4  0.6394  1))  73.692[m]. 1  k1  0.93  0.487118  C14 ( B / L)1.06806 (T / L)0.46106 ( L / LR )0.121563  ( L3 / )0.36486  (1  CP )0.60247  0.93  0.487118  0.89(32.2 / 239.26)1.06806 (10.1/ 239.26)0.46106 (239.26 / 73.692)0.121563  (239.263 / 49778) 0.36486  (1  0.6394) 0.60247  1.14. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 30. 15. (16) 2019-07-22. ③ Resistance of Appendages R(1/3)  R (1  k )  R T. R APP  1 / 2 V 2 S APP (1  k 2 ) eq C F. F. 1. APP.  RW  RB  RTR  R A. 3,700 TEU Container Carrier. CF=0.001378 ρ=1,025 kg/m3. Item. Value. V. 22.5 knots. Appendages (SAPP). S APP : The wetted area of the appendages (1  k 2 ) : The appendage resistance factor •Rudder behind skeg: 1.5~2.0. •Hull bossings: 2.0. •Rudder of single screw ship: 1.3~1.5. •Shafts: 2.0~4.0. •Twin-screw balance rudders: 2.8. •Stabilizer fins: 2.8. •Shaft brackets: 3.0. •Dome: 2.7. •Skeg: 1.5~2.0. •Bilge keels: 1.4. 82.74 m2 (rudder) 135 m2 (bilge keel). •Strut bossings: 3.0. The equivalent 1 + k2 value for a combination of appendages is determined from:. (1  k 2 ) eq . (1  k2 )eq .  S (1  k ) S i. 2 i. i.  RAPP . . . S i (1  k 2 ) i. . Si. Si and (1+k2)I is the wetted area of the appendages and the appendage resistance factor for the ith time.. 82.74(1.4)  135(1.4)  1.4 82.74  135. 1 1 V 2 S APP (1  k2 ) eq C F   1.025 11.5742  (82.74  135) 1.4  1.38 103  29.59[kN ] 2 2. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 31. ③ Resistance of Appendages (2/3) Hull appendage. Conventional twin-screw after body hull form. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 32. 16. (17) 2019-07-22. ③ Resistance of Appendages (3/3) Hull appendage. skeg. Twin-screw twin-skeg after body hull form. 33. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ④ Wave Resistance (Low Speed Range) (1/5) R  R (1  k )  R  R  R T. F. - Low speed range: Fn  0.4. 1. APP. 2 n. RW   g  C1C 2 C5 exp{m1 F  m4 cos(  F )} C1  2223105 C 7. 1.07961. (T / B ). C7  0.229577( B / L)0.33333. : when B/L≤0.11. C7  B / L. : when 0.11≤B/L≤0.25. C7  0.5  0.0625 B / L. : when 0.25≤B/L. B. LR=83.148. d n. 3.78613. W. (90  iE ). 1.37565.  RTR  R A. 3,700 TEU Container Carrier Item. Value. L. 239.26 m. B. 32.2 m. T. 10.1 m. CWP. 0.6761. CP. 0.6794. LCB. -0.531 % (aft). . 49,887 m3. iE : The half angle of entrance in degree At early design stage, If iE is unknown, it can be obtained by following formula:   ( L / B ) 0.80856 (1 CWP ) 0.30484 (1C P  0.0225 LCB ) 0.6367    ( LR / B ) 0.34574 (100 / L3 ) 0.16302 . iE  1  89e . B / L  0.135 C7  B / L  32.2 / 239.26  0.135 iE  1  89e{ ( L / B ). 0.80856. (1CWP )0.30484 (1CP  0.0225 LCB )0.6367 ( LR / B )0.34574 (100  / L3 )0.16302.  1  89e{ ( L / B ). 0.80856. (1 0.6761)0.30484 (10.6794  0.0225( 0.531))0.6367 (73.69/32.2)0.34574 (10049887/239.263 )0.16302.  13[deg].  C1  2223105C73.78613 (T / B)1.07961 (90  iE ) 1.37565  2223105  0.1353.78613 (10.1/ 32.2)1.07961 (90  13) 1.37565  0.812 Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 34. 17. (18) 2019-07-22. ④ Wave Resistance (Low Speed Range) (2/5) Meaning of a entrance angle. Water plane area B. A. Aft. Fore A: Angle of entrance of waterline ( iE). B: Angle of run of waterline. iE. : The half angle of entrance is the angle of the waterline at the bow in degrees with reference to the center plane but neglecting the local shape at the stem.. 35. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ④ Wave Resistance (Low Speed Range) (3/5) R  R (1  k )  R  R  R T. F. 1. APP. W. B.  RTR  R A. - Low speed range: Fn  0.4. RW   g  C1C 2 C5 exp{m1 Fnd  m4 cos(  Fn2 )}. 3,700 TEU Container Carrier. C 2 : A parameter which accounts for the reduction of the wave resistance due to the action of a bulbous bow. C2  e. 1.89 C3. C3  0.56 ABT. 1.5. If there is not bulb, C2 is 1.. /{B  T (0.31 ABT  TF  hB )} ABT : Transverse bulb area. Item. Value. B. 32.2 m. T. 10.1 m. TF. 10.1 m. ABT. 15.2 m2. hB. 5.5 m. AT. 0 m2. CM. 0.9761. hB : The position of the centre of the transverse are ABT above the keel line TF : The forward draft of the ship. C 5 : A parameter which accounts for the reduction of the wave resistance due to the action of a transom stern A : The immersed part of the transverse area of the transom C5  1  0.8 AT /( B  T  C M ) at zero speed T. C3  0.56 ABT 1.5 / {B  T (0.31 ABT  TF  hB )}  0.56  (15.2) / {32.2  10.1(0.31 15.2  10.1  5.5)} 1.5. C5  1  0.8 AT / ( B  T  CM ) 1.  0.018. C2  e 1.89. C3. ( 1.89 0.02 ). e  0.78. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 36. 18. (19) 2019-07-22. ④ Wave Resistance (Low Speed Range) (4/5) R  R (1  k )  R  R  R T. F. 1. APP. W. B.  RTR  R A. - Low speed range: Fn  0.4. RW   g  C1C 2C5 exp{m1 Fnd  m4 cos(  Fn2 )} m1  0.0140407 L / T  1.75254 . 1/ 3. 3,700 TEU Container Carrier. / L  4.79323 B / L  C16. C16  8.07981C P  13.8673C P  6.984388CP : when CP≤0.8 2. Item. Value. L. 239.26 m. T. 10.1 m. Cp. 0.6794. . 49,778 m3. Fn. 0.2442. 3. C16  1.73014  0.7067C P. : when 0.8≤CP. d  0.9 m4  C15 0.4e 0.034 Fn. 3.29. C15  1.69385. : when L /  ≤512 3. C15  1.69385  ( L / . 1/ 3.  8.0) / 2.36. : when 512≤ L3 /  ≤1726.91. C15  0.0. : when 1726.91≤ L3 / . m1  0.0140407 L / T  1.75254. 1/3. L3 /   275.152  512. / L  4.79323B / L  C16.  C15  1.694.  0.0140407  239.26 /10.1  1.75254  49778 / 239.26 1/3. m4  C15 0.4e0.034 Fn. 4.79323  32.2 / 239.26  1.25.  1.694  0.4e  0.016.  1.832. 3.29. 0.034 Fn 3.29. 37. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ④ Wave Resistance (Low Speed Range) (5/5) R  R (1  k )  R  R  R T. - Low speed range: Fn  0.4 2 n. RW   g  C1C 2C5 exp{m1 F  m4 cos(  F )} d n.   1.446C P  0.03 L / B   1.446C P  0.36. : when L/B≤12 : when 12≤L/B. F. 1. LR=83.148 C1=1.263 C2=0.778 C5=1 m1=-1.860 d=-0.9 m4=-0.016. APP. W. B.  RTR  R A. 3,700 TEU Container Carrier Item. Value. L. 239.26 m. B. 32.2 m. Cp. 0.6794. . 49,778 m3. Fn. 0.2389. L / B  7.43  12.    1.446C P  0.03L / B  1.446  0.6794  0.03  239.26 / 32.2  0.702.  Rw   gC1C2C5 exp{m1 Fnd  m4 cos( Fn2 )}  1.025  9.81 49778  0.812  0.78 1 exp{1.860  0.23890.9  0.016  cos(0.702  0.23892 )}  406.875[kN ]. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 38. 19. (20) 2019-07-22. ④ Wave Resistance (High Speed Range) R  R (1  k )  R T. F. 1. APP.  RW  RB  RTR  R A. - High speed range: 0.55  Fn. RW   g  C1C 2C5 exp{m1 Fnd  m4 cos(  Fn2 )}. 3,700 TEU Container Carrier. In the high speed, the coefficients C1 and m1 are changed. C1  6919 .3C M. 1.3346. ( / L3 ) 2.00977 ( L / B  2)1.40692. Item. Value. L. 239.26 m. B. 32.2 m. Cp. 0.6794. . 49,778 m3. Fn. 0.2442. m1  7.2035 ( B / L ) 0.326869 (T / B ) 0.605375. 39. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ④ Wave Resistance (Middle Speed Range) - Middle speed range: 0.4  Fn  0.55. RT  RF (1  k1 )  R APP  RW  RB  RTR  R A. RW  ( RW ) at Fn  0.4  (10 Fn  4)  {( RW ) at Fn  0.55  ( RW ) at Fn  0.4 } / 1.5. 3,700 TEU Container Carrier Item. Value. ( RW ) at Fn 0.4. -. ( RW )at Fn 0.55. -. Fn. 0.2442. ( R W ) at F n  0 . 4 : The wave resistance prediction for Fn = 0.4 according to the formula in low speed range. ( R W ) at F n  0 . 55 : The wave resistance prediction for Fn = 0.55 according to the formula in high speed range. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 40. 20. (21) 2019-07-22. ⑤ Additional Pressure Resistance of Bulbous Bow near the Water Surface. RT  RF (1  k1 )  R APP  RW  RB  RTR  R A. RB  0.11e ( 3 PB. 2. ).  Fn i 3 ABT 1.5  g / (1  Fn i 2 ). 3,700 TEU Container Carrier. PB : A measure for the emergence of the bow PB  0.56 ABT /(TF  1.5hB ). Item. Value. ABT. 15.2 m2. TF. 10.1 m. hB. 5.5 m. V. 22.5 knots. g. 9.81 m/s2. ρ. 1.025 ton/m3. Fn i : The Froude number based on immersion of bulbous bow Fn i  V / g (TF  hB  0.25 ABT )  0.15V 2 2.  RB  0.11e( 3 PB )  Fni 3 ABT 1.5  g / (1  Fni 2 ). PB  0.56 ABT / (TF  1.5hB ). 2.  0.56  15.2 / (10.1  1.5  5.5)  1.18.  0.11e( 31.18 ) 1.553 15.21.5 1.025  9.81/ (1  1.552 )  8.33[kN ]. Fni  V / g (TF  hB  0.25 ABT )  0.15V 2  11.574 / (9.81(10.1? 5.5? 0.25 15.2)  0.15  (11.574) 2 )  1.55. In the recent research, it is assumed that RB=0[kN]. 41. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ⑥ Additional Pressure Resistance of Immersed Transom Immersion. RT  RF (1  k1 )  R APP  RW  RB  RTR  R A. RTR  1 / 2 V 2 AT C 6. 3,700 TEU Container Carrier Item. C 6  0.2(1  0.2 FnT ) : when FnT≤5 C6  0. Value. AT. 0 m2. g. 9.81 m/s2. B. 32.2 m. CWP. 0.6761. V. 22.5 knots. ρ. 1.025 ton/m3. : when 5≤FnT. FnT  V / 2 gAT /( B  B  CWP ).  RTR  1 / 2 V 2 AT C 6. ∵. 0.  0[ kN ]. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 42. 21. (22) 2019-07-22. ⑦ Model-Ship Correlation Resistance (1/2) RT  RF (1  k1 )  R APP  RW  RB  RTR  R A 3,700 TEU Container Carrier. R A  1 / 2 V S total C A 2. The model-ship correlation resistance RA is supposed to describe primarily the effect of the hull roughness and the still-air resistance.. C A  0.006 ( L  100 ). 0.16. Item. Value. L. 239.26 m. CB. 0.6394. TF. 10.1 m. V. 22.5 knots. ρ. 1.025 ton/m3. Stotal. 9465.74 m2. 4.  0.00205  0.003 L / 7.5C B C 2 (0.04  C 4 ). C4  TF / L : when TF / L ≤0.04 C4  0.04. : when 0.04< TF / L. TF / L  TF / L  10.1 / 239.26  0.042 Because 0.04 ≤ TF/L. C A  0.006( L  100) 0.16  0.00205  0.003 L / 7.5CB 4C2 (0.04  C4 )  0.006(239.26  100) 0.16  0.00205  0.003 239.26 / 7.50.62414  0.629(0.04  0.04)  0.000312.  RA . 1 1 V 2 Stotal C A  1.025  11.5742  9625.74  0.000312  202.705[ kN ] 2 2 43. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ⑦ Model-Ship Correlation Resistance (2/2) 3,700 TEU Container Carrier. RT  RF (1  k1 )  RAPP  RW  RB  RTR  R A. =822.61. ∴. 1.14. ,. 29.59. ,. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 406.875. & "#$$#$. 0. 0. 202.705. Item. Value. RF. 822.61 kN. (1+k1). 1.14. RAPP. 29.59kN. RW. 406.875 kN. RB. 0 kN. RTR. 0 kN. RA. 202.705 kN. 1,577.21. 1,577.21%&'(. 44. 22. (23) 2019-07-22. Resistance Prediction for a Ship (1/3). Model test of the basis ship. Model test of the design ship. Given. Find. Calculate. Calculate. Resistance of basis ship estimated by Holtrop-Mennen method. Resistance of design ship estimated by Holtrop-Mennen method. 45. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Resistance Prediction for a Ship (2/3). Model test of the basis ship. Model test of the design ship. Given. Find. RT,basis,modeltest RT,basis,Holtrop & Mennen. . RT,design ,modeltest RT,design,Holtrop & Mennen. Calculate. Calculate. Resistance of basis ship estimated by Holtrop-Mennen method ,. ,. & "#$$#$. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Resistance of design ship estimated by Holtrop-Mennen method. 1,557.21%&'( 46. 23. (24) 2019-07-22. Resistance Prediction for a Ship (3/3) Model test of the design ship Model test of the basis ship. Find. Given. Calculate. Calculate. Resistance of basis ship estimated by Holtrop-Mennen method. Resistance of design ship estimated by Holtrop-Mennen method. 47. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Resistance Estimation by Holtrop and Mennen’s Method - Approximation Formula of the Propeller Efficiency (1/4) ①. ②. ③.  D   O  H  R ①. O  [1/ (0.97  0.14 BP )]  k k  [1.11  0.11(( AE / AO ) / 0.6)]  1.11 0.11(0.731/ 0.6)  0.975 BP . n( NCRT R )0.5 V (1  w). CF . 0.075 , (log Rn  2)2. MCR: Maximum Continuous Rating NCR: Normal Continuous Rating) BHP: Brake Horse Power DHP: Delivered Horse Power EHP: Effective Horse Power RT: Total Resistance T: Transmission Efficiency D: Propulsive Efficiency O: Propeller Efficiency H: Hull Efficiency R: Relative Rotative Efficiency t: Thrust Deduction Fraction w: Wake Fraction. 0.2.  MCR  DP  15.4   3   c1 Blade = 5 : C1=1,  nMCR  Blade = 4 : C1=1.05  15.4  (38570[ BHP] /102[rpm]3 )0.2 1  7.936[m] Beware of Unit. 1PS = 0.73575 kW 1BHP = 0.74556 kW ②. H . 1 t 1 w. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. ③.  R  0.98 ~ 1.03. * R: The ratio between a propeller's efficiency attached to a ship (O,B) and in open water (O), that is, R = O,B /O 48. 24. (25) 2019-07-22. Resistance Estimation by Holtrop and Mennen’s Method - Approximation Formula of the Propeller Efficiency (2/4) ①. ②. ③.  D   O  H  R w  c9CV. H . 1 t , 1 w. CV   0.0661875  1.21756c11   TA  (1  CP1 )  L.  0.24558. B L(1  CP1 ). 0.09726 0.95  CP. . 0.11434 0.95  CB.  0.75Cstern CV  0.002Cstern. 239.26 .  14.55  0.003. 10.1  0.24558. . 0.003   0.0661875  1.21756  1.27  (1  0.682)  . 32.2 239.26(1  0.682). . 0.09726 0.95  0.682. . 0.11434 0.95  0.6394. MCR: Maximum Continuous Rating NCR: Normal Continuous Rating) BHP: Brake Horse Power DHP: Delivered Horse Power EHP: Effective Horse Power RT: Total Resistance T: Transmission Efficiency D: Propulsive Efficiency O: Propeller Efficiency H: Hull Efficiency R: Relative Rotative Efficiency t: Thrust Deduction Fraction w: Wake Fraction.  0.75  ( 10)  0.003  0.002( 10).  0.211 c8  BS / ( LDPTA ) c8 =S(7B/TA -25)/(LD P (B/TA -3)) c9  c8 c9  32  16 / ( c8 -24) c11  TA / DP. c8  BS / (LDPTA )  32.2 8670.24 / (239.26  7.936 10.1)  14.55 (∵B/TA  3.19) c9  14.55 (∵c8  14.55) c11  1.27 (∵TA / DP  1.27) CV  (1  k)CF  CA  (1  0.975)  0.001378  0.000312  0.003 CP1  1.45CP  0.315  0.0225LCB  1.45  0.6794  0.315  0.0224  (0.531)  0.682. when B/TA  5 when B/TA  5 when c8  28 when c8  28 when TA / DP  2. c11  0.0833333(TA /D) +1.33333 when TA / DP  2 CV  (1  k )CF  C A CP 1  1.45CP  0.315  0.0225 LCB 3. 49. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Resistance Estimation by Holtrop and Mennen’s Method - Approximation Formula of the Propeller Efficiency (3/4) ①. ②. ③.  D   O  H  R. H . 1 t , 1 w. t. T  RT R R  1 T  T  T T T 1 t. t  0.001979L / ( B  BCP1 )  1.0585c10  0.00524  0.1418D2 / ( BT )  0.0015Cstern  0.001979  239.26 / (32.2  (32.2  0.682))  1.0585  0.13  0.00524  0.1418  7.9362 / (32.2 10.1)  0.0015  (10). MCR: Maximum Continuous Rating NCR: Normal Continuous Rating) BHP: Brake Horse Power DHP: Delivered Horse Power EHP: Effective Horse Power RT: Total Resistance T: Transmission Efficiency D: Propulsive Efficiency O: Propeller Efficiency H: Hull Efficiency R: Relative Rotative Efficiency t: Thrust Deduction Fraction w: Wake Fraction.  0.141 ②. 1 t 1 w 1  0.141  1  0.211  1.09. H . ③. If number of shaft = 1. R  0.9922  0.05908 AE / AO  0.07424(CP  0.0225LCB)  0.9922  0.05908  0.731  0.07424(0.6794  0.0225  (0.531))  1.00 If number of shaft = 2. R  0.9737  0.111(CP -0.0225LCB) - 0.06325Pi / DP. c10  B / L when L/B > 5.2 c10  0.25  0.003328402 / ( B / L  0.134615385) when L/B < 5.2 c10  0.13 (∵ L / B  7.43) * Thrust deduction fraction or coefficient (t): Additional resistance on the hull due to the rotation of the propeller Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 50. 25. (26) 2019-07-22. Resistance Estimation by Holtrop and Mennen’s Method - Approximation Formula of the Propeller Efficiency (4/4) ①. ②. MCR: Maximum Continuous Rating NCR: Normal Continuous Rating) BHP: Brake Horse Power DHP: Delivered Horse Power EHP: Effective Horse Power RT: Total Resistance T: Transmission Efficiency D: Propulsive Efficiency O: Propeller Efficiency H: Hull Efficiency R: Relative Rotative Efficiency t: Thrust Deduction Fraction w: Wake Fraction. ③.  D   O  H  R ①. O  [1/ (0.97  0.14 BP )]  k  [1/ (0.97  0.14 28.62)]  0.976  0.568.  D   O  H  R  0.568 1.09 1  0.62 BP . n( NCRT R ) 0.5 V (1  w). MCR : 38, 570[ PS ]  102[ rpm]  28, 361[ kW ]  1.7[ rps ]. Beware of Unit. NCR : 34, 710[ PS ]  98.5[ rpm ]  25, 522[ kW ]  1.642[ rps ]. 1.642[rps](25522[ kW ]  0.98 1)0.5  11.574(1  0.206)  28.62 51. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. Power Prediction by Holtrop & Mennen Method 1 EHP (Effective Horse Power). EHP  RT (v) Vs. (In calm water). EHP  RT (v)  Vs  1,577.21 11.574  18, 254.7[kW ]  24, 484.5[ BHP] 1PS = 0.73575 kW 1BHP = 0.74556 kW. 2 DHP (Delivered Horse Power). DHP . EHP. D. (  D : Propulsive efficiency). D  O H R O : Open water efficiency  H : Hull efficiency  R : Relative rotative efficiency. DHP . EHP. BHP . DHP. 3 BHP (Brake Horse Power). BHP . DHP. T. (T : Transmission efficiency). 4 NCR (Normal Continuous Rating). Sea Margin NCR  BHP (1  ) 100 5 DMCR (Derated Maximum Continuous Rating). DMCR . NCR Engine Margin. D. T. . 24, 484.5  39, 613.5[ BHP] 0.62. . 39, 613.5  40, 421.9[ BHP] 0.98.  Sea Margin  NCR  BHP 1   100   15    40, 421.9 1    46, 485.2[ BHP ]  100  DMCR . NCR 46, 485.2   51, 650.2[ BHP ] Engine Margin 0.9. NMCR . DMCR Derating rate. 6 NMCR (Nominal Maximum Continuous Rating). NMCR . DMCR Derating rate. Innovative Ship and Offshore Plant Design, Spring 2019, Myung-Il Roh. 52. 26. (27)

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