TMR7 Experimental Methods in Marine Hydrodynamics
Guide to scaling of resistance and prediction of full scale power
Ship data are found later in this document. Values of some coefficients used in the resistance
and power prediction are given here. There is also an enclosure with formulas used in the
resistance and power prediction. What you find here is a guide on how to use those formulas.
In this analysis it is recommended to use Excel or a similar tool.
For all speeds tested do as follows:
Calculate total resistance coefficient CTm
Calculate residual resistance coefficient CR, using CBDm=0, 1+ko=1.0699, m=1.075•10-6 m2/s
Calculate full scale total resistance coefficient CTs, using CA=-0.228E-03. CBDs=0,
s=1.187•10-6 m2/s
Calculate full scale resistance RTs – now you are done calculating full scale resistance!
The open water test has been given to you as part of the model data. You will need to
interpolate in the open water diagram as part of the analysis of the propulsion test. This can be
done manually on a printed diagram, or it can be done by in a spreadsheet or Matlab. A
description of how to do this in Excel follows.
Import the open water curve into Excel (or similar). Create third-order polynomials of J as
function of KT, and KQ as function of J. You can do this by creating a graph with the curve,
add a trend line, select polynomial as type of trend line, and select “display equation on
graph”. Make sure you show enough numbers for the parameters in the equation, for instance
by right-clicking the equation and selecting scientific with four digits as number format.
For each speed in the propulsion test do as follows:
Calculate J, KT, and KQ. from the propulsion test results.
Enter the open water diagram with KT found from the propulsion test, and read off the
corresponding J-value. This J-value is called J0. This can be done with KT-J regression
Read off the KQ-value corresponding to J0. It is called KQ0. This can be done with a J-KQ
regression.
Calculate thrust deduction t, wake fraction w and relative rotative efficiency R.
Find J* from the open water diagram by entering the open water diagram with the following
RTs
KT

(you can make a KT/J2-J regression to make this
2
J
nprop    (1  t )  D 2  Vs2  (1  ws ) 2
simpler).
Find KQ for J* from the open water diagram (by using the regression for KQ as function of J).
Calculate RPM from J*
Calculate PD and PB from KQ. Use a mechanical efficiency m=0.97 for calculating PB.
2
TOWING TESTS
SHIP RESISTANCE
ENCL.
APPENDIX 1
REPORT
601622.00.01
DATE
2003-04-10
REF
M2375J
The hull model is towed by the carriage at which the total resistance is measured at different speeds.
The hull model is equipped with a rudder and a trip-wire at station 9 ½ (19). The conversion from hull
model (m) into ship (s) is made by using the form factor method. In this method it is assumed that the
total resistance can be divided into two parts, represented by the viscous resistance and the residuary
(due to vorticity, wave making and wave breaking) resistance (CR). The viscous resistance is
determined by multiplying the frictional resistance (CF) with a constant form factor (ko), which is
identical for model and ship. Further, it is assumed that the residuary resistance (CR) is identical for
model and ship.
MODEL (m):
Total resistance coefficient:
CTm 
m
2
C Fm 
Residuary resistance coefficient:
C Rm
Frictional resistance coefficient:
Total resistance:
Effective power:
V  Sm
 C Fm  (1  k o )  C Rm  C AAm  C BDm
2
m
0.075
(ITTC – 57 correlation line)
(log Rnm  2) 2
 CTm  (1  k o )  C Fm  C AAm  C BDm
Frictional resistance coefficient:
SHIP (s):
Total resistance coefficient:
RTm
CTs  C Rm  (C Fs  C F )  (1  k o )  C A  C AAs  C BDs
0.075
C Fs 
(log Rns  2) 2
RTs  CTs 
s
2
RTs  Vs
PE 
1000
 Vs2  S s
CB
(TAP  TFP )  B
LW L
Form factor:
ko  0.6  75 3 where
Air resistance coefficient:
C AA  0.001 
Transom stern resistance coefficient:
C BD
Roughness allowance:
2
C F  110.31  ( H  Vs ) 0.21  403.33  C Fs
AT
S
0.029  ( S B / S ) 3 / 2

(C F )1 / 2

Where H = hull surface roughness in (10-3 mm). H=150 .
and
Vs = ship speed in m/s
Only CF values > 0 are used


PROPULSION TESTS
ENCL.
APPENDIX 2
REPORT
601622.00.01
DATE
2003-04-10
REF
M2375J
The hull model is supplied with a propelling machinery and a driving propeller. The rate of
revolution is regulated until the model is free relatively to the attached towing carriage. In order to
obtain turbulent flow around the model, a trip wire is placed at station 9½ (19). To compensate the
difference between the frictional resistance of the model and the frictional resistance of the ship,
converted to model scale, the model is unloaded with a towing force in the direction of motion.
The towing force (FD) is calculated by the formula:
FD  C S 
m
2
 Vm2  S m
C s  C Fm  (C Fs  C F ) (1  k o )  C A  (C BDm  C BDs )
During the tests, the following parameters are recorded:
Propeller thrust
Propeller torque
Rate of revolution
Model speed
T
Q
n
V
Thrust and torque measured during propulsion and open water tests are expressed nondimensionally as:
KT 
T
  n2  D4
and
KQ 
Q
  n2  D5
In the open water diagram KT and KQ are presented as functions of the advance coefficient (J). By
entering the open water diagram with the thrust coefficient (KT) measured during the propulsion
test, corresponding JO and KQO-values are obtained which are used to estimate wake fraction,
relative rotative efficiency, hull efficiency and quasi-propulsive coefficient.
JO
V
nD
Wake fraction:
w  1
Relative rotative efficiency:
R 
Hull efficiency:
H 
Quasi-propulsive coefficient:
 D  O   H   R
Thrust deduction fraction:
t  1
K QO
KQ
1 t
1 w
(O = propeller efficiency in open water)
RT  FD
(note: T is total thrust – sum of all props.)
T
OPEN WATER TESTS
ENCL.
APPENDIX 3
REPORT
601622.00.01
DATE
2003-04-10
REF
M2375J
The propeller model is driven by a dynamometer at which thrust, torque and rate of revolution are
recorded. The immersion of the propeller shaft is ≥ propeller diameter.
Test procedure:
The rate of revolution is kept constant and by varying the speed, we get the variation of the
advance coefficient (J). At each advance coefficient exact rate of revolution, (n), propeller thrust,
(T), and torque, (Q), are recorded. The results are presented dimensionless as:
J
VA
nD
, advance coefficient
KT 
T
  n2  D4
, thrust coefficient
KQ 
Q
  n2  D5
, torque coefficient
O 
KT  J
K Q  2
, propeller efficiency in open water
PERFORMANCE PREDICTION
ENCL.
APPENDIX 4
REPORT
601622.00.01
DATE
2003-04-10
REF
M2375J
The performance prediction is based on the assumption that the thrust deduction fraction, t, the
wake fraction w and the relative rotative efficiency, R, are free from scale effects.
From the total resistance of the ship, RTs, and the thrust deduction fraction, t, the following
relation is established:
RTs
KT
(nprop is number of propellers)

2
J
nprop    (1 t )  D2 Vs2  (1 ws )2
For each speed, the intersection point of the KT – J2 curve given above with the open water
diagram is found. The advance coefficient J* at this point gives the rate of revolution:
RPM 
60  (1  ws ) Vs

D
J*
The corresponding torque coefficient KQ, and the relative rotative efficiency, R, gives the
delivered power:
PD (kW )  nprop 
2
RPM 3 KQ
   D5  (
) 
1000
60
R
The calculation is repeated for different speeds giving the speed/power curve for the actual pitch
ratio. An extrapolation of the open water diagram gives speed/power curves for different pitch
ratios. The final pitch ratio and speed/power curve is found by interpolation for the actual RPM
and power.
Finally the brake power and merit coefficient are calculated:
PB (kW ) 
C ADM 
PD
M
 2 / 3  Vs3
PB
(VS in m/sec.)
LIST OF SYMBOLS
ENCL.
APPENDIX 5
REPORT
601622.00.01
DATE
2003-04-10
REF
M2375J
Symbol
Title
Dimensions
AE
AO
AT
B
c
CA
CAA
CADM
CADX
CB
CBD
CD
CF
CF
CL
CM
CP
CR
CS
CT
CTA
CV
d
D
FD
Fn
g
J
K0
KQ
KT
KTD
KTP
LOA
LPP
LWL
n
nprop
P
PB
PD
PE
PS
Expanded blade area
Disc area
Transverse projected area of ship/model above the waterline
Breadth moulded
Chord length
Empirical correlation coefficient determined from trial analyses
Air resistance coefficient
Merit coefficient
Admirality coefficient
Block coefficient
Transom stern resistance coefficient
Drag coefficient
Frictional resistance coefficient
Roughness allowance
Lift coefficient
Midship section coefficient
Prismatic coefficient
Residuary resistance coefficient
Towing force coefficient
Total resistance coefficient
Appendage resistance coefficient
Viscous resistance coefficient
Hub diameter
Propeller diameter
Towing force
Froude number
Acceleration due to gravity
Advance coefficient
Form factor
Torque coefficient
Thrust coefficient
Duct thrust coefficient
Propeller thrust coefficient
Length overall
Length between perpendiculars
Length of waterline
Rate of revolution
Number of propellers
Propeller pitch
Brake power
Delivered power at propeller
Effective power
Shaft power
L2
L2
L2
L
L
L
L
LMT-2
LT-2
L
L
L
REVS.T-1
L
L2MT-3
L2MT-3
L2MT-3
L2MT-3
LIST OF SYMBOLS
ENCL.
APP. 5 cont.
REPORT
601622.00.01
DATE
2003-04-10
REF
M2375J
Symbol
Title
Dimensions
Q
R
Rn
RT
S
SB
t
t
T
T
TD
TP
V
VA
w
Z

D
H
M
0
R





Torque
Propeller radius
Reynolds number
Total resistance
Wetted surface
Area of transom stern below the waterline
Max. thickness of a propeller section
Thrust deduction fraction
Draught moulded
Thrust
Duct thrust
Propeller thrust
Speed of ship or model
Speed of advance of propeller
Wake fraction
Number of blades of a propeller
Angle of attack
Propulsive efficiency or quasi-propulsive coefficient
Hull efficiency
Mechanical efficiency
Propeller efficiency in open water
Relative rotative efficiency
Linear scale ratio
Kinematic viscosity
Mass density of water
Displacement volume
Displacement mass
L2MT-2
L
LMT-2
L2
L2
L
L
LMT-2
LMT-2
LMT-2
LT-1
LT-1
L2T-1
ML-3
L3
M
PRINCIPAL HULL DATA
HULL MODEL NO.:
Loading condition:
Draught AP/FP:
Setup:
M2375J
Design WL
6.500 / 6.500
m2375j0s10
ENCL.
i)
REPORT
846001.20.01
DATE
2004-06-21
REF
M2375J
Model Scale:
25.676
SHIP
MODEL
[m]
Symbol Unit
——————————————————————————————————————————————————————————————
Length overall
Length on designed waterline
Length betw. perp.
Breadth moulded
Breadth waterline
Depth to 1st deck
Draught at LPP/2
Draught at FP
Draught at AP
Trim (pos. aft)
Rake of keel
Rise of floor
Bilge radius
LOA
LWL
LPP
B
BWL
D
T
TFP
TAP
t
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
[m]
140.019
134.600
131.300
22.700
22.700
26.002
6.500
6.500
6.500
0.000
0.000
0.000
3.000
5.453
5.242
5.114
0.884
0.884
1.013
0.253
0.253
0.253
0.000
0.000
0.000
0.117
——————————————————————————————————————————————————————————————
Water density
Shell plating thickness
Shell plating in % of displ.
s
[kg/m3]
[mm]
[%]
1025.87
0.00
0.50
998.62
0
0.00
——————————————————————————————————————————————————————————————
Volume displacement
Displacement
Prismatic coefficient*
Block coefficient*
Block coefficient based on LWL
Midship section coefficient
Longitudinal C.B. from LPP/2
Longitudinal C.B. from LPP/2*
Longitudinal C.B. from AP
Wetted surface
Wetted surf. of transom stern
Transverse area above water


CP
CB
CBLW
CM
LCB
LCB
LCB
S
AT
AV
[m3]
[t]
[-]
[-]
[-]
[-]
[m]
[% LPP]
[m]
[m2]
[m2]
[m2]
11094.3
11438.2
0.5887
0.5727
0.5583
0.9727
-5.833
-4.442
59.817
3826.45
10.38
692.00
0.655
0.655
0.5887
0.5727
0.5583
0.9727
-0.227
-4.442
2.330
5.804
0.016
0.233
——————————————————————————————————————————————————————————————
Remarks:
*Refers to LPP
Hydrostatic corrections included
CBLW, is based on naked hull displacement
Appendages:
Twin propeller shaft with V
-bracket,twin spade rudders, one
bow tunnel thruster with pressure
relief opening.
Turbulence stimulator: Sand strip at station 19.5
ShipX (RepGen version 2.0.15) 28-Sep-04 13:48:27
OPEN WATER TEST
PROPELLER MODEL No.:
P1284
ENCL.
ii)
REPORT
846001.20.01
DATE
2016-02-15
REF
M2375J
Model Scale:
25.676
SHIP
MODEL
Symbol Unit
——————————————————————————————————————————————————————————————
Propeller diameter
Pitch ratio at r/R = 0.7
Blade area ratio
Number of blades
Chord/Diameter ratio
Thickness/Chord ratio
Hub diameter ratio
D
P/D0.7
AE/A0
Z
c/D0.7R
t/C0.7R
d/D
[mm]
[-]
[-]
[-]
[-]
[-]
[-]
4500
1.220
0.525
4
0.3549
0.0574
0.298
175.26
1.220
0.525
4
0.3549
0.0574
0.298
——————————————————————————————————————————————————————————————
TEST CONDITIONS
Propeller revolutions
Water temperature
Average Reynolds no. at 0.75R
n
T
Rn
[Hz]
[°C]
[-]
12.48
17.80
0.79·106
——————————————————————————————————————————————————————————————
No scaling is applied to the results
J
(-)
KT
(-)
KQ
(-)
0
(-)
KT/J2
(-)
————————————————————————————————————————————————————————————————
0.000
0.090
0.182
0.274
0.365
0.454
0.546
0.637
0.729
0.821
0.911
1.002
1.096
1.189
0.619
0.578
0.533
0.488
0.447
0.404
0.359
0.316
0.275
0.230
0.187
0.142
0.092
0.035
0.0996
0.0928
0.0858
0.0790
0.0731
0.0673
0.0613
0.0556
0.0503
0.0440
0.0376
0.0306
0.0227
0.0133
0.000
0.089
0.180
0.269
0.354
0.434
0.509
0.576
0.635
0.684
0.723
0.738
0.702
0.503
-1.000
70.891
16.137
6.519
3.359
1.960
1.204
0.777
0.517
0.342
0.226
0.141
0.076
0.025
————————————————————————————————————————————————————————————————
Setup:
p1284s1
Open water test file:
p1284c1_frip_1 (Cs)
ShipX (RepGen version 2.0.16) Sep 26, 2005 3:47:48 PM
OPEN WATER DIAGRAM
ShipX (RepGen version 2.0.16) Sep 26, 2005 3:47:49 PM
ENCL.
iii)
REPORT
846001.20.01
DATE
2016-02-15
REF
M2375J