EXTRAPOLATION METHOD

1. Assignment No.: 1
METHOD OF EXTRAPOLATION FOR OBTAINING THE
PROTOTYPE RESISTANCE
 The method of extrapolation is on the basis of ITTC 78 prediction method
using Froude’s law of scaling.
 Resistance and effective power for the given excel values with and
without blockage correction for the prototype.
PRINCIPAL PARTICULARS OF THE VESSEL
Particulars Prototype Model
LOA 33.5 m 2.5 m
LBP 30.8 m 2.29 m
LWL 32 m 2.39 m
Breadth 10 m 0.75 m
Depth 4.7 m 0.35 m
Draft 3.75 m 0.28 m
Displacement 641 t
Wetted surface area of model 389.65 m2
2.17
Scale of model 1:13.4
speed(ship) 9 knots
Vs 4.6296 m/s
speed(model) 2.46 knots
VM 1.265424 m/s
resistance(m) RTM 20.1 N
Symbols used are as follows:
 = Geometric scale of model
RTS = Prototype resistance in Newton
RTM = Model resistance in Newton
VS = Prototype speed in m/s
VM = Model speed in m/s
SS = Wetted surface of prototype
SM = Wetted surface of model
SW = Density of sea water at prediction temperature of 25o
C

2. FW = Density of fresh water at prediction temperature of 25o
C
CTS = Coefficient of total resistance of prototype
CTM = Coefficient of total resistance of model
CRM = Residuary resistance coefficient of model
CRS = Residuary resistance coefficient of prototype
CFoM = Coefficient of equivalent flat plate resistance of model
CFoS = Coefficient of equivalent flat plate resistance of prototype
RnM = Reynolds’s number of model
RnS = Reynolds’s number of prototype
LM = Waterline length of model
LS = Waterline length of prototype
FW = Kinematic viscosity of fresh water for model
SW = Kinematic viscosity of sea water for prototype
R = (1+k) = Form factor
Physical data and constants:
Density of sea water at 250
C, SW = 1025 kg/m3
Density of fresh water at 250
C, FW = 997 kg/m3
Viscosity of sea water at 250
C, SW = 0.9425  10-6
m2
/s.
Viscosity of fresh water at 250
C, FW= 0.8929  10-6
m2
/s.
RTS = CTS  0.5 SW  VS
2
 SS
CTS = CFoS + CRS+ 0.0004 (correlation allowance)
CRS = CTM - CfoM
CTM = RTM / (0.5  FW  VM
2
 SM)
CFoM = 0.075/(log RnM - 2)2
The addition of correlation allowance of 0.0004 is as per standard practice.
Method of calculation of prototype resistance using model resistance data:
RTS = CTS  0.5S  VS
2
 SS
VS = VM
CTS = CFoS +CRS
CRS = CRM

3. CRM = CTM – CFoM
CTM = RTM(N) / (0.5  FW  VM
2
 SM)
CFoM = 0.075/(log RnM - 2)2
CFoS = 0.075/(log RnS - 2)2
RnS = VSLS/SW
RnM = VMLM/FW
Following the above scheme, it is possible to extrapolate the model resistance RTM (in
Newton) at model speed VM (in m/s) to prototype resistance RTS (in Newton) at
corresponding ship speed VS.
Procedure for sample calculation for prototype resistance
Calculation is performed as follows:
Prototype speed, Vs = From 7 to 16.5 at an interval of 0.25 per student
Form Factor, ff = 1.24
Model scale, λ = 13.4
Waterline length of model, LM = 2.39 m
Waterline length of prototype, LS = 32 m
Speed of the model = Scale it from prototype speed
Blockage correction = Tank dimension ((L) 82.0m x (B) 3.2m x (D) 2.5m)
Corrected model speed, VM = Model speed + Speed correction
= 1.26542 m/s
Speed of the prototype, VS = (VM ×  )
= 9 knots
Wetted surface area of model, SM = 2.17 m2
Wetted surface area of prototype, SS = (SM × λ 2
)
= 389.65 m2
RTM (N) = 20.1 N
Total model resistance coefficient,
CTM = RTM (N)/ (FW  VM
2
 SM 0.5)
RnM = VMLM / FW
Frictional resistance coefficient of model,
CFoM = 0.075 / (log10RnM – 2)2

4. CRM = CTM - (ff  CFoM)
RnS = VSLS/SW
CFoS = 0.075 / (log10RnS – 2)2
Correlation allowance = 0.0004
With correlation allowance,
CTS = (ff  CFoS) + CRM +0.0004
RTS = CTS  0.5  SW  VS
2
 SS
Effective power = RTS  VS
Result obtained is plotted in a graph.
 RTs Vs Vship
 Power Vs Vship
Graph 1: RTs Vs Vship
0.00
100.00
200.00
300.00
400.00
500.00
600.00
6.0 8.0 10.0 12.0 14.0
Rts(kN)
Vship (knots)
with blockage correction
without blockage correction

5. Graph 2: Power Vs Vship
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
4000.00
6.0 8.0 10.0 12.0 14.0
P(kW)
Vship (knots)
with blockage correction
without blockage correction

6. Assignment 2:
EFFECTIVE WAKE FRACTION
Find the wake fraction for the given ship data
 PROPELLER DATA
OPEN WATER
Propeller type B series
Propeller diameter 0.120 m
RPS 20
Density 1025 kg/m3
Direction Anti-clockwise
Result:
S.NO.
Model speed
(m/s)
Thrust
(N)
Torque (N-
m)
J KT KQ 10KQ h
1 0 23.5 0.44 0.000 0.276 0.043 0.431 0.000
2 0.08 23 0.43 0.033 0.271 0.042 0.421 0.034
3 0.16 22.2 0.42 0.067 0.261 0.041 0.412 0.066
4 0.24 21.5 0.41 0.100 0.253 0.040 0.402 0.099
5 0.32 20.7 0.4 0.133 0.243 0.039 0.392 0.130
6 0.4 19.6 0.39 0.167 0.231 0.038 0.382 0.158
7 0.48 18.9 0.39 0.200 0.222 0.038 0.382 0.183
8 0.56 17.8 0.38 0.233 0.209 0.037 0.372 0.206
9 0.64 17 0.36 0.267 0.200 0.035 0.353 0.237
10 0.72 15.85 0.35 0.300 0.186 0.034 0.343 0.256
11 0.8 14.4 0.34 0.333 0.169 0.033 0.333 0.266
12 0.88 13.05 0.31 0.367 0.153 0.030 0.304 0.291
13 0.96 12.4 0.3 0.400 0.146 0.029 0.294 0.311
14 1.04 11.3 0.28 0.433 0.133 0.027 0.274 0.329
15 1.12 9.8 0.27 0.467 0.115 0.026 0.265 0.319
16 1.2 8.75 0.26 0.500 0.103 0.025 0.255 0.317
17 1.28 7.7 0.25 0.533 0.091 0.025 0.245 0.309
18 1.36 6.3 0.24 0.567 0.074 0.024 0.235 0.280
19 1.44 4.6 0.23 0.600 0.054 0.023 0.225 0.226
20 1.52 3.6 0.22 0.633 0.042 0.022 0.216 0.195
21 1.6 2.4 0.2 0.667 0.028 0.020 0.196 0.151
22 1.68 0.7 0.19 0.700 0.008 0.019 0.186 0.049

7.  Graph 1: Open Water Characteristic plot
DATA FOR FINDING WAKE FRACTION
BEHIND SHIP
Propeller type B series
Propeller diameter 0.120 m
RPS 20
Density 1025 kg/m3
Direction Anti-clockwise
Dynamometer calibration constant 13.94 N/V
Result
S.NO. Model
speed
(m/s)
Reading
(volt)
Thrust J KT
1 0 1.88 26.207 0.000 0.308
2 0.2 1.76 24.534 0.083 0.289
3 0.3 1.71 23.837 0.125 0.280
4 0.4 1.65 23.001 0.167 0.271
5 0.5 1.6 22.304 0.208 0.262
6 0.6 1.53 21.328 0.250 0.251
7 0.7 1.46 20.352 0.292 0.239
8 0.8 1.38 19.237 0.333 0.226
9 0.9 1.31 18.261 0.375 0.215
10 1 1.21 16.867 0.417 0.198
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800
KT,KQ,&h
J, ADVANCED RATIO
OPEN WATER CHARACTERISTIC PLOT
KT
KQ
h

8. 11 1.1 1.11 15.473 0.458 0.182
12 1.2 1.02 14.219 0.500 0.167
13 1.3 0.94 13.104 0.542 0.154
14 1.4 0.83 11.570 0.583 0.136
15 1.5 0.75 10.455 0.625 0.123
16 1.6 0.7 9.758 0.667 0.115
 Graph 2: Behind Ship - Plot for KT
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.000 0.200 0.400 0.600 0.800
KT
J, ADVANCED RATIO
BEHIND SHIP - PLOT for KT
KT Vs J (OPEN WATER)
KT Vs J (BEHIND SHIP)