Practical Ship Hydrodynamics

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106 Practical Ship Hydrodynamics the incident wave frequency ω. An exception are short following seas which are passed by the ship. The condition for the ship passing the waves is: Fn > 0.4 cos � L An important parameter in this context is: D ωeV ωV D g g � �2 ωV cos g For following sea for cases with cos
Ship seakeeping 107 The procedure to obtain these properties is as follows: Assume we have a record of the wave elevation ⊲t⊳ at a given point for the time interval t D 0 to T. Then is decomposed in a Fourier analysis, i.e. the complex constants OAj are determined in a finite series: ⊲t⊳ D A0 C J� Re⊲ OAje iωjt ⊳ with ωj D j1ω, 1ω D 2 /T jD1 The average wave elevation A0 is of no interest here. The phase angle εj of the complex amplitudes OAj DjOAjje i2j would be different at a different (near-by) location and are therefore also of no interest here. The absolute value of OAj depends on the registration time T. Only the sea spectrum remains as constant and of interest in the above sense: S ⊲ωj⊳ D Average value of j OAjj 2 21ωj The averaging can be done: ž over many records of statistically equivalent seaways (e.g. at various locations spaced by a few kilometres at the same time), or ž over many records of time intervals of the total registration time T, or ž over several (10 to 30) ‘neighbouring’ j OAjj 2 (preferred choice in practice); e.g. for j D 1 to 10, 11 to 20, 21 to 30 etc., an average j OAj 2 can be found as the arithmetic average of ten j OAjj 2 in each case. The ωj in the argument of the sea spectrum S is the (circular) frequency (in the last case the average frequency) on which the average is based. The wave energy per horizontal area in an elementary wave is: E D 1 2 gj OAj 2 gS is thus the average seaway energy per frequency interval and area. Therefore S is also called the energy spectrum of a seaway. It describes the distribution of wave energy over the frequency ω. Its dimension is, e.g., m2 Ð s. The spectrum can be used to reconstruct the time function ⊲t⊳ given earlier in this section: J� � ⊲t⊳ D 2S ⊲ωj⊳1ωj Ð cos⊲ωjt C εj⊳ jD1 (Instead of Re e i˛ we simply write here cos ˛.) We substituted here j OAjj 2 by its average value; this usually has no significant effect. As the phase angle information is no longer contained in the spectrum (and we usually only have the spectrum information to reconstruct a seaway) the phase angles εj are chosen as random quantities equally distributed in the interval [0, 2 ]. This creates various functions ⊲t⊳ depending on the actual choice of εj, but all these functions have the same spectrum, i.e. the same characteristic (non-random) properties as the original seaway.
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Practical Ship Hydrodynamics
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Butterworth-Heinemann Linacre House
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3 Resistance and propulsion .......
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5.4.5 Interaction of rudder and shi
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Preface The first five chapters giv
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1 Introduction Models now in tanks
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Introduction 3 certain investigatio
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Introduction 5 there have been prop
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Introduction 7 is a material consta
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Introduction 9 margin may make a di
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Introduction 11 solution either. Ev
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Introduction 13 in naval architectu
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Introduction 15 ž Finite differenc
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Introduction 17 makes seakeeping pr
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Introduction 19 ship. Inner flow co
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Introduction 21 performed on workst
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Introduction 23 experts, while boun
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Introduction 25 two more decades be
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Introduction 27 Figure 1.3 A cylind
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Introduction 29 resolved by conside
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Introduction 31 ž LSOR (line succe
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Introduction 33 flow direction. CDS
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Introduction 35 equation, i.e. the
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2 Propellers 2.1 Introduction Ships
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Propellers 39 ž rake iG The face o
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KT KQ h 10 . K Q K T Figure 2.3 Pro
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Propellers 43 methods or panel meth
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Propellers 45 This formula can be i
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Propellers 47 power. The earliest l
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Propellers 49 corrected subsequentl
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Propellers 51 flow computations are
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Propellers 53 occurs earlier, as ca
Page 65 and 66: Propellers 55 2.5.2 Open-water test
Page 67 and 68: Propellers 57 the traditional prope
Page 69 and 70: Propellers 59 (model/full-scale shi
Page 71 and 72: Propellers 61 represents the cavity
Page 73 and 74: Resistance and propulsion 63 1. The
Page 75 and 76: Resistance and propulsion 65 3.1.2
Page 77 and 78: Figure 3.3 Double-body flow y Wave
Page 79 and 80: Resistance and propulsion 69 course
Page 81 and 82: Resistance and propulsion 71 limite
Page 83 and 84: Table 3.1 Recommended values for CA
Page 85 and 86: Resistance and propulsion 75 3.2.6
Page 87 and 88: P B ⋅ 10 3 (kW) 40 30 20 10 0 n P
Page 89 and 90: Resistance and propulsion 79 t is t
Page 91 and 92: Resistance and propulsion 81 are no
Page 93 and 94: 3.4 Simple design approaches Resist
Page 95 and 96: Resistance and propulsion 85 of the
Page 97 and 98: Resistance and propulsion 87 non-li
Page 99 and 100: Resistance and propulsion 89 resist
Page 101 and 102: Resistance and propulsion 91 (doubl
Page 103 and 104: Resistance and propulsion 93 only b
Page 105 and 106: Resistance and propulsion 95 resist
Page 107 and 108: Resistance and propulsion 97 1°. S
Page 109 and 110: Ship seakeeping 99 3. Addition of t
Page 111 and 112: Ship seakeeping 101 1. No recording
Page 113 and 114: Ship seakeeping 103 Re denotes the
Page 115: Ship seakeeping 105 the ship axis x
Page 119 and 120: Ship seakeeping 109 If several ω r
Page 121 and 122: a 0.015 0.010 0.005 0 1 2 3 4 5 Uc/
Page 123 and 124: Ship seakeeping 113 The (only stati
Page 125 and 126: Ship seakeeping 115 height H1/3 for
Page 127 and 128: Ship seakeeping 117 using data of B
Page 129 and 130: Ship seakeeping 119 for each strip
Page 131 and 132: Ship seakeeping 121 between near fi
Page 133 and 134: Ship seakeeping 123 wave length of
Page 135 and 136: Ship seakeeping 125 The elements of
Page 137 and 138: Ship seakeeping 127 4.4.3 Rankine s
Page 139 and 140: Ship seakeeping 129 to zero. Then t
Page 141 and 142: Ship seakeeping 131 for commercial
Page 143 and 144: Ship seakeeping 133 Since the spect
Page 145 and 146: Ship seakeeping 135 ž The ωj are
Page 147 and 148: Ship seakeeping 137 changing sea sp
Page 149 and 150: Ship seakeeping 139 The wave impact
Page 151 and 152: Ship seakeeping 141 pressure gauges
Page 153 and 154: v(t) h(x,t) y u(x,t) Figure 4.23 On
Page 155 and 156: Ship seakeeping 145 computations wi
Page 157 and 158: Ship seakeeping 147 4. Derive the p
Page 159 and 160: Ship seakeeping 149 The free consta
Page 161 and 162: 5 Ship manoeuvring 5.1 Introduction
Page 163 and 164: Ship manoeuvring 153 ž yaw rate (r
Page 165 and 166: Ship manoeuvring 155 Table 5.2 Non-
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Ship manoeuvring 157 but also the i
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C y 1.50 1.25 1.00 1.75 0.85 0.80 0
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Ship manoeuvring 161 section. The l
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Ship manoeuvring 163 methods have b
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esistance R is proportional to spee
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Ship manoeuvring 167 accuracy, but
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Ship manoeuvring 169 the difference
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Ship manoeuvring 171 it is importan
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d, y 20° 10° 0° −10° −20°
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Distance Lateral deviation Length o
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Ship manoeuvring 177 also performed
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Ship manoeuvring 179 ž Rudders out
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ehind the leading edge (nose) is: c
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Ship manoeuvring 183 the rudder. In
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Ship manoeuvring 185 attack ˛ of n
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V a /V 0.4 0.3 0.2 0.1 V a /V 2.0 1
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Ship manoeuvring 189 ž Rudder with
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average between VA and V1: � �
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C L (V corr ≠ V A ) C L (V corr =
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Ship manoeuvring 195 hull influence
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Ship manoeuvring 197 - Estimate the
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Ship manoeuvring 199 rudder tip vor
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Ship manoeuvring 201 (1993) uses de
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Ship manoeuvring 203 ž Profiles wi
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Ship manoeuvring 205 The ship perfo
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6 Boundary element methods 6.1 Intr
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C ⊲t1n3 C n1t3⊳⊲t3 xxz C s3 x
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xx D ⊲ 3 x⊲x xq⊳ ⊳/r 2 xy D
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The velocity in the x direction is:
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∂ ∂z Boundary element methods 2
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Boundary element methods 217 2. Thr
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and ⊲ , ⊳ is: r D � ⊲x ⊳
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⊲1⊳ y D � d 2 y d r 2 f ⊲c
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Boundary element methods 223 the so
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2 0 8xz D 2 2 0 8xxz D 2 2 0 8xzz D
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Figure 6.9 Velocities induced by po
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It is convenient to write ϕ as:
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Boundary element methods 231 usuall
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Boundary element methods 233 From t
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with: Boundary element methods 235
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Numerical example for BEM 237 S is
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Numerical example for BEM 239 In ea
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Numerical example for BEM 241 Once
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Numerical example for BEM 243 ž Tr
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Numerical example for BEM 245 that
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Numerical example for BEM 247 is ch
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Table 7.1 Sign for derivatives of p
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z y Figure 7.5 Coordinate system us
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the contour (Fig. 7.5): n� iD1 i
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Numerical example for BEM 255 Let E
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Numerical example for BEM 257 At th
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Numerical example for BEM 259 This
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Numerical example for BEM 261 The i
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Numerical example for BEM 263 The e
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References Abbott, I. and Doenhoff,
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References 267 Morgan, W. B. and Li
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Index Actuator disk, 44 Added mass,
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Practical Ship Hydrodynamics

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