TMR 7 EXPERIMENTAL METHODS IN MARINE HYDRODYNAMICS
Lab test 1 Resistance test with ship model, including set-up
and calibration
Group 1 Roar Christian Håversen Lohne
Eirin Johanne Stangeland Line Fludal Heimstad
Sissel Tjøswold Steinar Skorpa
Ingvild Roti
19-09-2011
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Table of Contents Table of figures ........................................................................................................................................ II
Summary ................................................................................................................................................. 1
Conclusion and recommendations ........................................................................................................... 2
Introduction............................................................................................................................................. 3
Description of the set-up ......................................................................................................................... 4
Model .................................................................................................................................................. 4
Instrumentation, measurement, data acquisition ................................................................................. 5
Calibration ....................................................................................................................................... 5
Sensors ............................................................................................................................................ 5
Collection of data ............................................................................................................................. 6
Environmental conditions .................................................................................................................... 6
Test program ........................................................................................................................................... 7
Results and data analysis ......................................................................................................................... 8
Wave elevation .................................................................................................................................. 11
Uncertainties and error sources ......................................................................................................... 11
References ............................................................................................................................................. 13
Procedure .......................................................................................................................................... 14
Input data .......................................................................................................................................... 15
Results ............................................................................................................................................... 15
Appendix B – Calculation of CR using Hollenbach 98 ............................................................................... 16
II
Table of figures Figure 1: Residual resistance from resistance test and Hollenbach 98 method ......................................... 2
Figure 2 Sketch of model. ......................................................................................................................... 4
Figure 3: Wheatstone bridge .................................................................................................................... 6
Figure 4: Signals from sensors to computer .............................................................................................. 6
Figure 5: Total resistance of the model .................................................................................................... 8
Figure 6: Cr/Fn graph ............................................................................................................................... 9
Figure 7: Interference between bow and stern wave system .................................................................. 10
Figure 8: CR by FN graph from TMR 4220 Naval Hydrodynamics - Ship Resistance ................................. 10
Figure 9: Wave elevation vs time ........................................................................................................... 11
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Summary In this lab, resistance tests for six different model speeds have been performed in a small towing tank.
Setting up the equipment and calibrating the sensors was a part of the assignment. During the tests, the
carriage speed, the resistance of the model, the sinkage fore and aft and the wave elevation was
measured.
The equipment set-up included ensuring that the model had the correct draught. The model was
weighed and extra weights were added accordingly. The weights were placed so that the model had zero
trim and heel. The four sensors were calibrated before the test start-up.
The resistance values obtained from the tests were made dimensionless and the residual resistance
coefficient CR was calculated for each speed. These were then compared to empirical values of CR. ShipX
was used to calculate the full scale ship resistance according to the Hollenbach 98 method. The CR-values
from the model tests and from the empirical formulae were plotted against the Froude number FN.
The graph from Hollenbach 98 gave a smooth curve, while the graph from the model tests was curvier
and gave higher values for a FN between 0.12 and 0.22. For higher FN (i.e. FN > 0.22) the graphs started to
coincide more.
The lack of similarity between the two graphs does not necessarily negate the model test results. The
curvy shape of the model test graph could be due to wave and bow interaction effects in the particular
FN –area. The empirical curve is smooth because it is based on regression of many different model test
results. Due to error sources such as wrong water density, inaccuracy in calibration and set-up, noise in
the wave elevation measurements, inaccurate sensors etc, it cannot be expected that the results from
the model test provide such a smooth curve. In addition, the calculated CR includes more resistance
components than the empirical CR. It is therefore reasonable that the calculated CR has a higher value
than the empirical CR.
2
Conclusion and recommendations The total resistance of a model of an LNG tanker was measured in a towing test, and the corresponding
residual resistances are presented below together with the estimates from Hollenbach 98.
Figure 1: Residual resistance from resistance test and Hollenbach 98 method
The residual coefficient from Hollenbach 98 is generally smaller than the residual coefficient from the
model test. This is most likely due to air and appendix resistance being subtracted from CR in the
Hollenbach 98 method while they are included in the calculated CR from the model test. There is also a
larger degree of uncertainty for the Hollenbach 98 method. A lot of the parameters needed in
Hollenbach 98 were not provided, and therefore had to be estimated.
The model test gives a curvier CR/ FN-curve than Hollenbach 98. This is may be due to interaction effects
between the bow wave and the stern wave. By phasing the bow and stern wave in a correct manner, the
wave crest from the bow cancel the trough from the stern wave. This will reduce the amplitude of the
resulting wave and thus the wave resistance. Hollenbach 98 is based on regression from several model
tests and will therefore provide a smoother curve.
It is concluded that the residual resistance found is reasonable, there is no evidence to suggest
otherwise. However, more runs at higher velocities should be performed to verify that the residual
resistance increases towards a peak around a Froude number of 0.5.
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Introduction
This report describes the test set-up, performance and results from Lab test 1 in TMR7 Experimental
Methods in Marine Hydrodynamics by group 1. Lab test 1 was a ship model resistance test including
model and equipment set-up and sensor calibration. The test was conducted on Thursday 08.09.11.
The aim of this lab was to calculate the residual resistance coefficient of the model and compare this to
existing experimental results. There are several different empirical formulae available for calculating
residual resistance based upon previous model tests. In this case, the Hollenbach 98 method was chosen.
In order to get satisfactory results, the equipment set-up and sensor calibration is of critical importance.
After the model is connected to the tow carriage, there are a few error sources which may affect the
results. For instance, if the model is not at the designated water line, the wetted surface will not be at its
desired value, and hence the results will be wrong.
The model was towed at increasing towing speed, enabling to present the residual resistance as a
function of the Froude number.
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Description of the set-up
Model The model is of an LNG tanker, and the ship and model has the following dimensions:
Symbol Units Ship Model
Length in the waterline LWL [m] 223.6 2.236
Beam B [m] 38.7 0.387
Mean draught T [m] 8.265 0.08265
Trim Trim [deg] 0 0
Wetted surface S [m2] 8915 0.8915
Volume displacement [m3] 46000 0.046
Block coefficient CBLW [-] 0.6432 0.6432 Table 1: Data for ship and model
Before the model tests could start, the model had to be weighed and extra weights had to be added. This
was to ensure that the model had the correct draught during the model tests.
The model has a mass of 16.912 [kg]. From the data above, the mass of displaced water is:
This means that total ballast must be:
Since the weights provided were of different sizes, the total mass added was 29.06[kg].
After the model was correctly ballasted and trimmed, it was connected to the carriage using a force
sensor. There were also two connection points fore and aft to prevent the model from yawing during the
test. This was necessary due to the model not having a rudder. To measure the trim the model was also
connected to two sensors fore and aft by means of a string.
During acceleration and deceleration the model was clamped by a claw to prevent it from becoming
unstable and move too much, and to avoid overloading the sensor. The claw was automatically released
when the carriage had achieved the designated towing speed. When the carriage stopped, the claw was
closed again before the carriage was returned to the start position.
Figure 2 Sketch of model.
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Instrumentation, measurement, data acquisition
Calibration
The first step was to calibrate the sensors to be used for measurements. The sensor for measuring the
towing force was attached to a table by clamps. Then there was carried out zero-measurements with
only the scale hanging from the sensor. The weight of the scale was then subtracted from each of the
other calibration measurements. Weights with increasing mass were used: 0.5[kg], 1.0[kg], 1.5[kg],
2.0[kg] and 2.5[kg]. The force was then plotted against the measured voltage, and a calibration factor of
16.97[N/V] was found by adding a linear trend line in the plot using Excel.
The sensors for measuring sinkage (trim) at fore perpendicular (FP) and aft perpendicular (AP) were then
calibrated. They were clamped to the wall of the towing tank, and a zero-measurement was carried out
with no load. New measurements were then carried out with the string pulled out in 10[cm] intervals
(10[cm], 20[cm], 30[cm] and 40[cm]). The amount of string pulled out was plotted against the measured
voltage, and hence a calibration factor, 0.128[m/V], was found by the same technique as for the towing
force.
The same procedure was used for calibration of the wave sensor. Zero-measurement was made with the
sensor in correct position on the wall of the towing tank. Then measurements with a 5[cm] interval were
carried out, and the calibration factor, 0.0373[m/V], was found.
Sensors
Four linear type sensors were used:
One Wheatstone bridge for the tow force
Two sensors for measuring sinkage (at FP and AP)
One wave sensor
The Wheatstone sensor is based on strain gauges. When the sensor has no loading, there is no difference
in voltage between the strain gauges. When loaded, there is a difference, and this difference is
measured.
The sensors for sinkage fore and aft measured how much string was pulled out at any given time
The sensor for wave rise at the tank wall is made up of two electrical rods about a centimetre apart. The
water will then short circuit the current, and the higher the water is, the less the resistance for the
electrical current.
6
Figure 3: Wheatstone bridge
Collection of data
The measurement system consists of transducers/sensors sending analogue signals via an amplifier
through a filter to an analogue/digital converter. Digital signals are sent to a computer (in this case the
signals were sent wireless) and interpreted.
Figure 4: Signals from sensors to computer
Environmental conditions The tests were carried out in a towing tank that was 20 meters long, 2.5 meters wide and 1.0 meter
deep. No waves were to be present during each run. Even though the water in the tank contained
chlorine, the density to the water was for simplicity set to be 1000 [kg/m3], and the kinematic viscosity
was set to be 1.14 · 10-6 [m2/s].
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Test program
The key features for the resistance test are listed below.
Most of the sensors were calibrated. The two draught sensors, the force sensor and the wave
elevation sensor were calibrated while the towing carriage speed sensor was left unaltered.
Model preparations started. The model was ballasted to stated displacement at waterline 2 (VL2)
with zero trim and heel.
The model was then connected to the towing carriage and draught and force sensors attached to
the model.
Zero reference level was taken for all sensors.
Resistance tests were performed for seven different model speeds (0.6, 0.7, 0.8, 0.9, 1.0, 1.1 and
1.2 [m/s]) with acceleration held constant and length of run equal to 14 meters in the towing
tank.
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Results and data analysis The total resistance of the model was measured for different velocities in the resistance test. After the
first set of runs was completed, it was noted that the resistance/speed curve did not increase steadily as
was expected. It was suspected that the sinkage sensors were influencing the resistance measurement.
Therefore, the test was repeated without the sinkage sensors. However, from Figure 5, it can be
concluded that the sensors did not have any significant influence on the resistance measured. Both
results are included in the analysis.
Figure 5: Total resistance of the model
To validate if the results from the resistance test are reliable, the residual coefficient CR from the
resistance tests were compared with CR found from an empirical method.
The total resistance were made dimensionless in order to calculate the residual resistance coefficient.
This coefficient was found by subtracting the frictional resistance coefficient from the total resistance
coefficient. That means that air resistance or any appendage resistance was not scaled separately, but
instead included in the residual coefficient. The details of this calculation can be seen in Appendix A –
Calculation of CR from resistance test
To validate the calculated CR, an empirical method was used to find the residual resistance for the
particular model. The Hollenbach 98 method was used, which is the newest empirical method that is
available for conventional ships. It gives more accurate results than other empirical methods (Holtrop 84
and Guldhammer & Harvald). Hollenbach’s method is based on model tests and predicts the resistance
9
according to hull parameters, and it distinguishes between mean, maximum and minimum resistance.
Maximum resistance is for poor designs, while minimum is for good lines.
ShipX has been used to calculate the resistance for the ship in full scale according to Hollenbach’s
method. CR should be equal for a model and a full-scale vessel. The ship in this lab is an LNG tanker that
is assumed to have mean resistance referring to Hollenbach’s method. The ship’s scaling parameter is
100 and the velocity is scaled according to Froude’s hypothesis. Necessary lengths are predicted from
the model. See Appendix for input parameters and results.
Figure 6: Cr/Fn graph
In figure 5 the resulting CR/ FN graph is plotted. Hollenbach 98 gives a smooth curve, while the model test
curves are a lot curvier. At an FN of approximately 0.17, CR from the model tests is more than twice the
value of the CR from the empirical calculations. The curves do however coincide at larger Froude
numbers. There are a number of uncertainties and error sources listed on page 11 that may be causing
the different results.
The curvy shape of the model test curves is most likely due to interaction effects between bow wave and
stern wave. By phasing the bow and stern wave in a correct manner, the wave crest from the bow cancel
the trough from the stern wave. This will reduce the amplitude of the resulting wave and thus the wave
resistance. Uncertainties and errors may also have influenced the results.
One would generally expect the CR to increase as the FN increases, up to a certain point (normally about
FN=0.5). The interference can cause both a positive and a negative effect on the CR for different Froude
numbers. This is exemplified in Figure 7 taken from the compendium TMR 4220 Naval Hydrodynamics –
Ship Resistance.
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Figure 7: Interference between bow and stern wave system
A full residual resistance curve for a conventional ship could be expected to look something like the one
seen below in Figure 8. The figure is taken from the compendium TMR 4220 Naval Hydrodynamics – Ship
Resistance. It shows the residual resistance plotted against the Froude number, for a number of
systematically varied ship hulls. The residual resistance has its maximum at a Froude number of 0.5 and
it drastically rises at FN>0.25. At FN =0.3, the curves have a similar behavior to result from the model test.
This gives us confidence that our results may still be correct even though we had expected a smoother
curve.
Figure 8: CR by FN graph from TMR 4220 Naval Hydrodynamics - Ship Resistance
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Wave elevation The following graph shows the time series of the wave elevation.
Figure 9: Wave elevation vs time
As seen from the graph above there are some rectangular shaped measurements from 9.5 seconds.
These are assumed to be due to disturbances. At around 14 seconds, the measurements are more
applicable to the passing wave crest. A negative value on the vertical axis represents a wave rise and vice
versa.
Uncertainties and error sources In the model test no measurements were taken of the water regarding temperature, density and
viscosity. If the temperature was known, table values for density and viscosity could be found.
Instead standard values of ρ = 1000 [kg/m3] and ν = 1.14 × 10-6 [m2 s-1] were assumed. This leads
to inaccurate results for the resistance test. It influences the resistance test results since
necessary ballast weight for the model was calculated based on required volume displacement
multiplied by assumed water density. This value was then compared to the dry weight of the
model and hence ballast weight could be computed.
When the resistance is predicted using Hollenbach’s method in ShipX, it is assumed seawater at
a temperature of 15 C
Exact sensor calibration was hard to accomplish since the draught and wave elevation sensors
were calibrated based on visual estimates. A small error in the force sensor was also present
because it was mounted to a wooden table during calibration. In theory this table is flexible and
can bend during loading of the force sensor when calibrating. But even with inaccurate
calibration measurements the results of the calibrations are still usable. This is because the
calibration results depend on the slope of the trend lines since the sensors are linear.
12
When trim and heel for the ballasted model were measured, the values were taken from the
deck of the model. At this position trim and heel equaled zero, but when looking at the model
connected to the towing carriage a small trim about VL2 could be noted. Due to the difference in
leveling of the model deck and VL2 it was hard to find zero trim and heel. A small trim could
therefore have been present.
The wave elevation measurements contain noise due to wall reflections of the waves radiated
from the model during towing. The first sinusoidal wave profile is thus the most realistic and
correct.
During towing the draught sensors and the force sensor got an angle to the attachment points
which should not be there. The draught sensors should have been vertical and the force sensor
should have been horizontal compared to the attachment points, but with a deviation from this
orientation the draught and force measured have an error.
The draught sensors that were used are new and hence quite stiff. It is therefore possible that
these sensors took up some of the resistance during the towing and caused the resistance
measured from the force sensor lower than expected.
When running the resistance tests the water conditions should be equal for all tests. We may not
have waited long enough for the water to be completely still after the previous test, so varying
water/wave conditions is an uncertainty in the results.
The residual resistance is calculated based on the following equation:
The residual resistance is taken as the total resistance minus the frictional resistance. In reality
also other types of resistance, like air resistance and appendage resistance, should be subtracted
from the total resistance. These types of resistance are here included in the residual resistance
giving it a too large value.
In ShipX, where CR is calculated based on Hollenbach 98, the ship parameters are manipulated to
be similar to the hull used in the model test. Hollenbach takes for instance air resistance and the
presence of a propeller in to account. This reduces the value of CR.
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References
Lecture notes in TMR7, “Instrumentation”, chapter 4, by Sverre Steen and Jan V. Aarsnes
Lecture notes in TMR4220, Naval Hydrodynamics, “Ship Resistance”, by Knut Minsaas and Sverre
Steen
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Appendix A – Calculation of CR from resistance test
Procedure The residual resistance coefficient is calculated using the simplified formula
Where is the total model resistance coefficient found from the model test, is the frictional
resistance coefficient found from the ITTC’57 friction line and is the residual resistance coefficient.
The resistances found from the model tests are given in Newton. In order to make the resistance non-
dimensional, the following relation is applied:
The ITTC’57 friction line gives the following equation for the friction coefficient:
Where is the Reynolds number.
To find a reasonable value for the form factor k, MARINTEK’s standard equation for form factor as given
in chapter 1 in the compendium for TMR 4247 Marin Teknikk 3 was used:
The k found from this equation is generally lower than what is found from model tests. This is because
the equation to a large degree excludes the viscous pressure resistance. However, the formula was
considered to be good enough for this use.
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Input data The values used in these equations are given in Table 2 below.
Symbol Units Ship Model
Length in the waterline
LWL [m] 223.6
2.236
Beam B [m] 38.7 0.387
Mean draught T [m] 8.265 0.08265
Trim Trim [deg] 0 0
Wetted surface S [m2] 8915 0.8915
Volume displacement
[m3] 460000 0.046
Block coefficient CBLW [-] 0.6432 0.6432
Water density Ρ [kg/m3] 1000
Water kinematic viscosity
Ν [m2/s] 1,14E-06
Phi Φ [-] 0,072756
Form factor K [-] 0,058716
1+k [-] 1,058716 Table 2: Data for ship and model, and important constants
Results
With Sinkage
Vm [m/s] RTm [N] CTm [-] RNm [-] 1+k [-] CFm [-] CR [-] FN [-]
1,20 3,41 5,32E-03 2,35E+06 1,058716 3,92E-03 1,16E-03 0,26 1,10 2,88 5,34E-03 2,16E+06 1,058716 3,99E-03 1,12E-03 0,23 1,00 2,54 5,70E-03 1,96E+06 1,058716 4,07E-03 1,39E-03 0,21 0,90 2,25 6,22E-03 1,77E+06 1,058716 4,16E-03 1,82E-03 0,19 0,80 1,81 6,36E-03 1,57E+06 1,058716 4,26E-03 1,85E-03 0,17 0,70 1,37 6,28E-03 1,37E+06 1,058716 4,38E-03 1,64E-03 0,15 0,60 1,01 6,27E-03 1,18E+06 1,058716 4,53E-03 1,48E-03 0,13
Without Sinkage
Vm [m/s] RTm [N] CTm [-] RNm [-] 1+k [-] CFm [-] CR [-] FN [-]
1,20 3,5229 5,49E-03 2,35E+06 1,058716 3,92E-03 1,33E-03 0,26 1,10 2,9720 5,51E-03 2,16E+06 1,058716 3,99E-03 1,28E-03 0,23 1,00 2,5329 5,68E-03 1,96E+06 1,058716 4,07E-03 1,37E-03 0,21 0,90 2,2590 6,26E-03 1,77E+06 1,058716 4,16E-03 1,85E-03 0,19 0,80 1,8054 6,33E-03 1,57E+06 1,058716 4,26E-03 1,82E-03 0,17 0,70 1,3710 6,28E-03 1,37E+06 1,058716 4,38E-03 1,64E-03 0,15
Table 3: Results from resistance test
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Appendix B – Calculation of CR using Hollenbach 98
17
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