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Ship Resistance and Propulsion: Practical Estimation of Propulsive Power


Year: 2011
Language: английский
Author: A. F. Molland, S. R. Turnock, D. A. Hudson
Genre: Учебное пособие
Publisher: Cambridge University Press
Edition: 1
ISBN: 978-1107008014
Format: PDF
Quality: Изначально компьютерное (eBook)
Pages count: 563
Description: Ship Resistance and Propulsion is dedicated to providing a comprehensive and modern
scientific approach to evaluating ship resistance and propulsion. The study of propul-
sive power enables the size and mass of the propulsion engines to be established and
estimates made of the fuel consumption and likely operating costs. This book, written
by experts in the field, includes the latest developments from applied research, includ-
ing those in experimental and CFD techniques, and provides guidance for the practical
estimation of ship propulsive power for a range of ship types. This text includes sufficient
published standard series data for hull resistance and propeller performance to enable
practitioners to make ship power predictions based on material and data contained
within the book. A large number of fully worked examples are included to illustrate
applications of the data and powering methodologies; these include cargo and container
ships, tankers and bulk carriers, ferries, warships, patrol craft, work boats, planing craft
and yachts. The book is aimed at a broad readership including practising naval archi-
tects and marine engineers, sea-going officers, small craft designers and undergraduate
and postgraduate degree students. It should also appeal to others involved in transport-
ation, transport efficiency and eco-logistics, who need to carry out reliable estimates of
ship power requirements.

Contents

Index
actuator disc theory, 2, 343
Admiralty coefficient, 308
air cushion vehicles (ACVs), 16. See also
hovercraft
air drag
general, 90
diagram, 50
estimation, 46, 427
reducing, 49
values, 47
air resistance, 9, 28, 45, 88
airwakes, 49
angle of entrance, 322
angle of run, 329
anti-fouling
paints, 55
coatings, 63
anti-foulings, 3
appendage drag
background, 36
data, 41
estimating, 40, 441
high speed craft, 28
scaling, 40
appendages, 10, 426
average c ? data, 200
average hull roughness (AHR),
54
ballast, 27
ballast condition, 450, 460
bank effects, 100
base-ventilating sections, 43
Beaufort number, 57, 93
Bernoulli’s equation, 13, 19, 476
Betz formula, 119
bilge keels, 9, 36, 41, 88
bioinspiration, 255
blade area ratio, 247, 265
blade element-momentum theory (BEMT), 2,
180, 339, 343–366, 469
blade element theory, 2, 346
blockage
corrections, 25, 100, 102
effects, 25, 181
bluff bodies, 41, 45
BMEP, 307, 311
body plan, 27
bollard pull condition, 383, 464
bossings, 36, 41, 43, 329
boundary element method (BEM), 338
boundary layer
general, 19, 35, 39, 109, 168, 181, 477
displacement thickness, 479
inner region, 56, 111
laminar, 478, 480
laminar sub-layer, 51, 111, 478
law of the wall, 111, 342
model, 39
ship, 39, 170
thickness, 37, 39
transition, 478
turbulent, 51, 478, 480
velocity profile, 38, 56, 114
Bowden-Davidson formula, 87
bow thrusters, 45. See also lateral thrust units
box shapes, 50
BSRA series, 23, 90, 189, 192–199
bulb, stern, 332
bulbous bow, 32, 45, 179, 194, 323–328,
426
Burrill chart, 282
buttock slope, 332
calibration, 110, 113
calibration procedure, 25
camber, 276
camber, effective, 352
captive tests, 28
cargo ship, 422
catamaran, 14, 133, 437
catamaran
forms, 99
hulls, 15
529
530 Index
cavitation
general, 2, 41, 248, 270
avoidance, 281
bubble, 270, 273, 277, 466
bucket, 275
Burrill chart, 282
check, 282, 339, 428, 444
criterion, 272
detailed check, 466
erosion, 339
hub vortex, 274
inception, 340
limits, 275
sheet, 270, 273, 277, 466
tip vortex, 274
tunnel, 108, 267, 280
CCD camera, 140
centre of effort, 28
centre of pressure, 16
CFD
general, 37, 90, 119, 136, 140, 167
analysis, 172, 286
flow over superstructures, 49
flow solver, 176
hull form design, 334
predictions of wake, 151
RANS based, 342
software, 177
validation, 2
circulating water channel, 25, 40, 108,
115
climatic design, 57
coatings
self polishing, 54, 55
silicone-based foul release, 54, 55
coefficients
circular, 21, 23
Froude, 21
ITTC, 21
propeller, 266
resistance, 21
slenderness, 21
viscous, 21, 70
wetted area, 21
compensating moment, 27
components of propulsive power, 7
components of ship power, 10
components of ship resistance, 12
concept design, 172
containerships, 60, 331, 424
continuous service rating (CSR), 11, 64, 299
contra-rotating propellers, 2, 249
controllable-pitch propellers, 8, 248, 301, 385
control surface drag, 42
control surfaces, 40
correlation
allowance, 11, 53, 90
factor, 86, 94
line, 78
model-ship, 85
corresponding speeds, 1, 36, 39
costs
construction, 3
disposal, 3
fuel, 3
maintenance, 64
current, 92
curvature corrections, 353
cycloidal propeller. See vertical axis propeller
deadrise angle, 212
density
air, 474
water, 474
detached eddy simulation (DES), 170
diesel, engine, 8, 298
diesel electric, 298
dimensional analysis, 33, 35, 75, 173, 266
direct numerical simulation (DNS), 170
Dirichlet inlet condition, 181
docking, frequency, 56
drag, 28
drift, 24, 51
ducted propeller, 5, 8, 248, 268, 333, 385
ducts, 2
dye streaks, 109
dynamic similarity, 35
dynamometer, 25, 28, 72, 136
economic factors, 3
economics of hull surface finish, 55
efficiency
hull, 10, 369
open water, 7, 10, 369
propeller, 60, 267
propulsive, 3
quasi-propulsive, 9, 10, 256, 369
relative rotative, 10, 145, 155, 369
relative rotative, data, 411–413
transmission, 9
Eggers formula, resistance, 130, 133, 484, 486
Eggers series, 125, 131, 178, 484
electric, 8
emissions, 3
energy dissipation, 12, 17, 109
environmental factors, 3
extrapolation, 26
extrapolation methods, 14
extrapolation, model-ship, 69, 77, 85
extrapolator, 72
fast ferries, 49, 50
fences, anti-ventilation, 17
ferry
catamaran, 437
passenger, 432
passenger/car, 435
twin screw, 429
finite element analysis, 286, 342
finite volumes (FV), 176, 180
fish, 255
five hole Pitôt, 136, 151
Index 531
flow
buttock, 332
continuity of, 18, 475
cross, 37, 43
curvature, 17
curvature corrections, 353
curvature effects, 352
distortion, 49
laminar, 25, 38, 41, 42, 76, 111, 115, 478
measurement, 136
separated, 37, 137
separation, 109, 111, 145, 182, 480
steady, 474
transitional, 76, 115, 478
turbulent, 25, 38, 111, 115, 478
uniform, 474
unsteady, 174
visualisation, 25, 109, 329
foil section, 17
force
normal, 109
pressure, 12
tangential, shear 12, 109
form factor, 40, 70, 79, 87, 89, 141
fouling, 5, 9, 11, 51, 54, 63
fouling, rate of, 63
fractional draught data, 190, 201, 423
free surface, 171, 181
friction formulae, flat plate, 72
friction moment correction, 27
Froude, 1, 69
Froude
circular notation, 21, 23, 76
coefficients, 21
depth number, 26, 93, 97
experiments, 72
friction line, 86, 90
f values, 76
law, 36, 69
number 33, 69
fuel consumption, 7
gas turbine, 8, 297
Gawn propeller series, 377
geosims
general, 33, 40
models, 40
series, 71
tests, 40
geometrically similar forms, 1
Goldstein K factors, 345
golf balls, 480
gravity wave, 133
greenhouse gas emissions, 4
Green’s function, 170, 172, 177
Greyhound, 1
grid, 176
Grigson formula, 79
Havelock, 104
heave, 26, 27, 28
heel, 28, 230
helicopter landing, 49
high speed craft, 26, 28
hollows, resistance curve, 31
hot film gauge, 136
hot film probe, 110
hot wire anemometry, 136
hovercraft, drag, 16
hovercraft lift fan power, 17
Hughes, 78, 114
hull
form, 4
form design, 313
shape, 104
surface pressure, 25
hull parameters, 2
hull parameters, choice, 314
hull resistance, naked, 9
hump, main, 32
hump, prismatic, 32
humps, resistance curve, 31
hydraulic radius, 102
hydrofoil anti-ventilation fences, 17
hydrofoil craft, 16, 481
hydrofoil drag, 17
hydrofoils, 41
hydrostatic force, 16
inclined shaft, 398
induced drag, 15, 19, 109. See also induced
resistance
inflow factors, 349
interference drag, 41, 43
International Maritime Organisation (IMO), 4
International Measurement System (IMS), 230
International Standards Organisation (ISO), 108
International Towing Tank Conference (ITTC),
2, 108, 175
ITTC
coefficients, 21
1957 formula, 53, 78
1957 line, 44
1978 Performance Prediction Method, 54, 87
keels, 16, 40
Kelvin
sources, 177
wave, 29
wave pattern, 98, 126
wave system, 125
wave theory, 30
kites, 4, 257
Kort nozzle. See ducted propeller
KVLCC2 hull form, 180, 183
laminar flow. See flow
large eddy simulation (LES), 170, 338
laser doppler anemometer (LDA), 56, 151
laser doppler velocimetry (LDV), 90, 136, 138,
151
lateral projected area, 48
532 Index
lateral thrust units, 254, 405. See also bow
thrusters
leeway, 51, 230
lift, 28
lifting line theories, 340
lifting-surface method, 3, 338
light emitting diodes (LED), 138
liquid crystals, 115
longitudinal centre of buoyancy (LCB), 315
longitudinal centre of gravity (LCG), 27
longitudinal cut, 133
Lucy Ashton, 40, 72, 122
manoeuvring, 322
margin, engine operation, 64. See also power
margins
mass, machinery, 7
maximum continuous rating (MCR), 11, 64
mean apparent amplitude (MAA), 54
measurement
flow field, 136
non-invasive, 136
skin friction, 25
Melville Jones formula, 119–121
MEMS technology, 110
mesh
generation, 176, 180
quality, 342
resolution, 184
size, 338
metacentric height, 320
midship area, 32
midship coefficient, 317
model
experiments, 80
resistance tests, 2
scale, 25, 108
size, 25
speed, 24
tests, 7, 38
total resistance, 23
models, 52
momentum analysis, 17, 130
momentum theory, 2, 343–345
Mumford’s indicies, 200
Navier-Stokes equations, 168
neutral buoyancy particles, 109
Newton’s second law, 476
noise, 3
nuclear submarine, 296
numerical methods, 166, 191, 277
numerical methods, for propellers, 337
Offshore Racing Congress, 230, 408
open water tests, propeller, 88, 152, 278
optimisation, 172, 185
paint streaks, 37, 109
panel methods, 3
paraffin wax, 25, 74
parametric studies, 172
parasitic drag, 25
particle image velocimetry (PIV), 20, 37, 139, 151
passenger ships, 49
patrol boat, 446
photogrammetry, 137
Pitôt probe, five hole, 136, 151
Pitôt static tube, 13, 24, 56, 151
planing craft, 16, 27, 212, 313, 450, 453
planks, 74
podded propellers, 2, 5, 8, 268, 331, 332, 386–391
pollution, 3
potential
drag, 97, 100
flow, 170
theory, 20
power
components of, 5, 10
delivered, 3, 7, 9
effective, 3, 7, 9
increase, 60, 62
increases, due to wind and waves, 57
installed, 7, 9, 11
margins, 9, 56, 57, 62
margins, service, 63
reserve, 11
thrust, 9
pram stern, 331
pressure, measure, 108
pressure
distributions, 273
gradient, 110, 113
measurements, 117
rake, 119, 121
stagnation, 15
static, 166
transducer, 116
vapour, 270
Preston tube, 109, 111
pre-swirl duct, 256
pre-swirl fins, 2, 256
prismatic coefficient, 32, 317
Prohaska, 80
projected area, 46, 88
projected area, lateral, 48
projected area, transverse, 48
propeller
blades, number of, 369
blade strength estimates, 284–293, 467
boat, 267
boss cap fins, 2, 256
CFD analysis, 286
coefficients, 266
data, presentation, 266
design, 1, 3, 379, 429
efficiency, 61, 267. See also efficiency
-engine matching, 64, 299
finite element analysis, 286, 342
-hull interaction, 4, 7
law, 301
locked, 399
Index 533
off-design, 61, 99, 303–305, 338
off-design calculations, 460–464
open water data, 267
open water tests, 88, 152, 278
scale effect, 85
section data, 352
section design, 2, 350
section thickness, 340
section types, 275
shafting, 23
simple beam theory, 286
strength calculations, 340
strength formulae, 292
stresses, 285, 467
surface finish, 55
theories, 2, 338
tip clearance, 330
tip fins, 2
tip off-loading, 281
propeller geometry
blade area ratio, 247, 265
blade root thickness, 285
blade sections, 262
blade thickness ratio, 265
boss/diameter ratio, 265
camber, section 276
generator line, 261
mass distribution, 293
nose shape, 276
outline, developed, 262
outline, expanded, 262
outline, projected, 262
pitch, 299
pitch, effective, 264
pitch, geometric, 261, 263
pitch, hydrodynamic, 264
rake, 261
rake distribution, 293
skew, 247, 261, 282, 338
sweep, 2
thickness, 276
propulsion, 1
propulsion
engines, 8
layouts, 299
machinery, 11, 57, 296
systems, 7, 172
propulsion plants
diesel, 298
electric, 8, 298
gas turbines, 297
multi-engined plant, 302
steam turbines, 296
propulsor data
cavitating propellers, 391
controllable pitch propellers, 385
ducted propellers, 385
Gawn propeller series, 377
oars, 407
paddle wheels, 270, 405
podded propellers, 386–391
sails, 408–411
supercavitating propellers, 392
surface piercing propellers, 395
vertical axis (cycloidal) propellers, 270, 404
Wageningen propeller series, 371–377
waterjets, 270, 400–404
propulsor types
contra-rotating propeller, 2, 249
controllable-pitch propeller, 8, 248, 301, 385
cycloidal propeller. See vertical axis
propeller
ducted propeller, 248
electrolytic propulsion, 255
kites, 4, 257
Kort nozzle. See ducted propeller
marine propeller, 247
oars, 254
paddle wheels, 253
podded propeller, 5, 251, 268
ram jets, 255
rotors, 257
sails, 253
self-pitching propellers, 399
solar, 257
supercavitating propeller, 5, 248, 268
surface piercing propeller, 5, 248, 268
tandem propeller, 250
vertical axis (cycloidal) propeller, 2, 252
Voith Schneider propeller. See vertical axis
propeller
waterjet propulsion, 252
wave device, 257
wind assisted, 257
wind turbines, 257
Z-drive unit, 250
quasi-propulsive coefficient, 9, 10, 256, 369.
See also efficiency
Rankine source, 172
RANS, 169, 180
RANS
propeller analysis, 342
simulations, 183
solvers, 3, 79
regression analysis, 86, 190
resistance
added in waves, 64
air, 9, 45, 88, 93
calm water, 10
coefficients, 21
components, 12
data, 188
frictional, 1, 12, 21, 28, 41
hull, naked 9
induced, 14, 15, 16, 109. See also induced drag
measurement, 23, 108
pressure, 12, 109, 115
residuary, 1, 35
separation, 38, 47, 51
skin friction, 16, 23, 38, 110, 182
534 Index
resistance (cont.)
spray, 14, 16, 41, 42
still air, 50, 94
test, 24, 26
total, 21, 35, 87
total viscous, 71, 81
transom, 14
viscous, 13, 21, 35, 109, 118
viscous pressure, 70
wave, 13, 21, 35, 37, 70, 97, 100, 123,
486
wave breaking, 14
wave making, 2, 16
wave pattern, 81
wind, 57. See also air drag
resistance regression data
fractional draught, 190, 201
Hollenbach, 190, 205
Holtrop and Mennen, 190, 202–204
Radojcic, 190
Sabit BSRA series, 190, 196
Sabit Series 60, 199
Van Oortmerssen, 190, 220
WUMTIA, 190, 212, 221
resistance series
BSRA, 23, 90, 189, 192–199
Compton semi-planing, 189
Dawson coasters, 189
Delft yacht series, 190, 229
Latiharju, 189
Lindblad twin screw, 189
MARAD, 189
NPL, 27, 189, 210
NTUA, 189, 211
Ridgely-Nevitt trawlers, 189
Robson, 189
Savitsky equations, 189, 212, 216–219, 450,
453
Series 60, 189
Series 62, 189, 212–216
Series 63, 189
Series 64, 27, 189, 208
Series 65, 189
SKLAD, 189
Southampton catamaran series, 189, 223–227
SSPA series, 189
Taylor-Gertler series, 189, 206
tugs, 189
USCG, 189
VWS catamaran series, 189, 227
Zborowski series, 189, 208
Reynold’s averaged Navier-Stokes. See RANS
Reynolds number, 33, 69, 170
Reynolds stress, 136, 138, 169
rise of floor (ROF), 318
risk assessment, passage, 105
roll moment, 28
roll stabilisation, 4
rotors, 4, 257
roughness
general, 11, 51, 63, 309
allowance, 54, 77, 87
criterion, 53
density, 52
form of, 54
hull, 86
levels, 53
location, 52
measured hull, 86
measurements, 87
of surface, 74
values of, 54
rough water, ships in, 2
rough weather, 5
rudders, 9, 16, 17, 36, 40, 42, 43, 329
rudders, twisted, 2, 256
sailing craft, 28
sailing vessels, 16, 26
sails, 4, 253, 408–411
Savitsky equations, 189, 212, 216–219, 450, 453
scaling
general, 1, 12, 34, 108
equation, 35
laws, 7, 14
methods, 69
scale effect, 25, 85
scale effect factor, 40
Schoenherr formula, 76
Schoenherr friction line, 53, 206
seakeeping, 322, 328, 332
sectional area curve (SAC), 318
self-propulsion test analysis, 420
self-propulsion tests, 95, 152–155
semi-displacement craft, 26, 313
separation, flow, 109, 111, 145, 182, 480
shaft brackets, 9, 36, 42, 329
shafting, 9, 17
shafts, 43
shallow draught vessels, 333
shallow water, 2, 5, 26, 63, 82, 93, 97, 103, 126, 133,
179, 482
shear stress, 108, 109, 110, 166, 474
shielding effects, 46, 47
ship resistance, 1, 7
shot blasting, 54
sideforce, 15, 28
Simon Boliver, 72
sink, 23
sinkage, 26, 97, 178
skew, 247, 261, 338
skin friction
general, 37, 97, 110, 339
coefficient, 69
correction, 27, 192
data, 36
drag, 97, 100. See also skin friction resistance
measurement, 25, 110
slamming, 57, 313
slender body theory, 173
Index 535
slip, negative or apparent, 2, 310
slip, true, 310
smooth turbulent line, 52, 76
solar energy, 4, 257
soliton. See solitary wave
sources, 178
speed
critical, 98, 99, 103, 105
loss, 58, 60, 101
loss, percentage, 58
sub-critical, 98, 126
supercritical, 98, 126
trans-critical, 98
spray, 28, 41
spray
drag, 42
rails, 16
root, 28
squat, 103
stabilisation, roll, 4
stabilisers, fin, 9, 36, 42, 43
stability, 314, 320
stagnation pressure, 15
standard series data, 7. See also resistance series
and propulsor data
Stanton tube, 111
steam turbine, 8, 296
stern shape parameter, 82
stern wedge, 330
straight framed ships, 321
strain gauge, 25, 111
Stratford flow, 332
streamline, 475
streamlined, 50
strut drag, 42
struts, 41
supercavitating propellers, 5, 248, 268,
392
superstructure, 28, 45
superstructure, drag, 45, 50
superstructure, streamlined, 47
superstructure, flow over, 49
surface
drift, 51
finish, 55
panel code, 338
panel method, 171, 340
surface piercing propellers, 5, 248,
268
tanker, 423, 460
taper ratio, 234
Taylor, 22
test tank, 23
test tank data, 418
thin ship theory, 177
three-dimensional effects, 14
thrust
deduction, 10, 145, 155, 332, 369
deduction data, 156–162
identity, 95, 154
line, 27
loading, 2
measurements, 53
tip vortex, 342, 358
torque identity, 155
tow fitting, 28
tow force, 27, 28
towing force, 23
towing tank, 23, 108, 121, 166
trade patterns, 54
transducer, load, 40
transducer, pressure, 116
transition, 115
transmission losses, 11
transom immersion, 179
transom stern, 15, 179, 330
transverse
cut, 132
frontal area, 46
projected area, 48
wave interference, 29, 133
waves, 29, 32
trials
BSRA wind correction, 93
conditions, 91
measurements, 91
procedures, 91
ship speed, 90, 464
tributyltin (TBT), 55
trim, 4, 16, 23, 26, 27, 28, 97, 116, 178
trim angle, 16
trimaran, 15
trimming moments, 28
tufts, 37, 109
tug, 189, 305, 448, 462
tunnel stern, 333
Turbinia, 2, 250
turbulence, 145
turbulence
levels, 110
stimulation, 25, 27
turbulence stimulators
sand strips, 25
trip studs, 25
trip wires, 25
turbulent flow. See flow
turnaround times, 54
twin skeg forms, 331
twisted stern, 256
‘U’ forms, 323
‘U’ sections, 329
uncertainty, 26, 108, 141, 166, 173
unsteady flow, 174, 475
unsteady motion, 98
validation, code, 175
‘V’ forms, 323
‘V’ sections, 329
536 Index
velocity
distribution, power law, 39
friction, 111
gradient, 37, 38, 93, 110, 111
gradient effects, 39
perturbation, 19
potential, 170, 484
prediction program (VPP), 230, 408, 455
profile, 38, 109, 110
relative, 46, 50
ventilation, 41, 271
vibration, propeller excited, 369
virtual stern, 179
viscosity
general, 12, 110
air, 474
coefficient of dynamic, 474
coefficient of kinematic, 474
values, 26, 474
water, 474
viscous shear, 19
Voith Schneider propeller. See vertical axis
propeller
Von Karman, 76
Von Karman constant, 56
vortex generator, 41
vortex identification, 343
vortex lattice method, 3
voyage analysis, 55, 57, 306–311
voyage analysis, developments, 311
voyage data, 57
Wageningen propeller series, 89, 371–377
wake
general, 2, 12
adapted propeller, 356–359, 471
analysis, 421
CFD predictions, 151
circumferential, 148, 150
data, 156–162
distribution, 122, 147
effective, 147, 150
fraction, 4, 10, 89, 95, 144, 155, 332, 369
frictional, 146
measurement, 149, 151
nominal, 146
non-uniform, 273
potential, 146
radial, 149
scale effects, 155
surveys, 329
tangential, 162
tangential, effect of, 359
tangential, velocity, 360
traverse, 133
viscous, 342
volumetric mean, 150
wave, 146
warship, 49, 440
wash. See wave wash
water depth, 97
water depth, restricted, 63
waterjets, 2, 5, 8, 252, 400–404
wave
bow, 31
breaking, 101, 122, 141
buoy, 57
components, 124
crest, 30, 114
decay, 104
divergent, 29, 98, 104
diverging, 178
elevation, 20, 121, 484
energy, 105, 179
envelope, 127
gravity, free surface, 133, 168
height, 57, 93, 104
height, maximum, 104
height measurement, 132
orbital paths, 481
orbital velocities, 19, 114
orbit motion, 20, 481
pattern, 12, 109, 124, 133, 179
pattern measurements, 19
period, 482
profile, 27
propagation, 98, 104
properties, 481
shallow water, 482
solitary, 98
sources, 129
speed, 97, 482
stern, 31
theory, 30, 482
transverse, 29, 98, 104, 178
transverse interference, 29
trochoid, 481
trough, 31, 114
wash, 3, 103, 179
wave velocities
induced, 19
orbital, 19
perturbation, 19
subsurface, 20, 145
weather, 9, 11
weather factor, 309
weather margin, 64
weather routeing, 4, 57, 62
weighted power increase, 62
wetted length, 16, 27, 214
wetted surface area
general, 21, 23, 205, 235
displacement ships, 235
planing hulls, 239
running, 27, 28
semi-displacement ships, 236
static, 27
yacht forms, 239
wind
gradient, natural, 50, 93
Index 537
gradient effects, 50
head, 45
induced forces, 51
measurements, 50
resistance, 57
speed, 57, 93
tunnel, 40, 46, 108, 111, 115
tunnel tests, 57, 81
turbines, 4, 257
wireless data transmission, 110
work boat, 448
yacht
model test, 28
performance, 454
resistance estimate, 229–234
yachts, 15, 26, 52
yaw, 16, 28
Z-Drive unit, 25

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