Test of MaTS Jack-Up chord in towing tank

Introduction: background and purpose of test 3

Laboratory equipment used 4

2.1 Towing tank 4

2.2 Towing carriage 4

2.3 Electronic equipment 4

2.4 Data analysis software 4

Model 5

3.1 Model as used in de Voorst; model roughness . 5

3.2 Modifications to model 5

3.3 Arrangement of model under carriage 5

3.4 Instrumentation of model: sensors, coordinate

system 6

Limitations to testing 7

4.1 Blockage in tank 7

4.2 Surface waves 8

4.3 Power of carriage propulsion 8

4.4 Structural strength of carriage 8

Test program 9

5.1 Runs made: orientations, speeds 9

5.2 Measurements taken 9

5.3 Video film 9

5.4 Photographs 10

Test execution

6.1 Comments to actual test runs 6.2 Time records of measurements 6.3 Mean values of time records

Analysis of test results 12

7.1 Change of coordinate system 12

7.2 Calculation of drag and lift coefficients 12

7.3 Spectral analysis of chord bound force time

histories 12

Evaluation of test and analysis results 13

8.1 Measurement accuracies ₁₃

8.2 Existence of 3-D effects 13

8.3 Reynolds' dependency ₁₄

8.4 Harmonic force components; possible vortex shedding

effects 14

8.5 Comparison to wind tunnel test results of similar

chord 15

8.6 Wind tunnel testing versus towing tank testing . 16

8.7 Conclusions and recommendations 16

References 18

11 11

11

REPORT ON MaTS JACK-UP CHORD TESTING

1. Introduction: background and purpose of test

The test described in this report is part of a larger scale joint industry project to determine Morison coefficients neces-sary for determination of hydrodynamic loads on lattice type jack-up legs. The project is initiated by Marine Structures

Consultants (MSC) from Schiedam, Holland and administered by the Netherlands Industrial Council for Oceanology (IRO) as a so-called MaTS research project.

The total project is reported in MSC's report SP 8603-1505, dated November 1989 [1] . In the project Morison coefficients are determined for two typical leg chord sections by large scale

(1:2) testing in regular and irregular waves as well as in steady flow. The former part was executed in the large Delta-flume of Deift Hydraulics Laboratory (DHL) in de Voorst, Holland. The results of those tests are reported in an annex to MSC's main report [2] . The steady flow test was performed for one chord type by towing it in the large towing tank at the Ship Hydromechanics Laboratory (SilL) of Deift University of Technology. The results of this test are presented in the fore laying report.

The other chord type was tested for steady flow in a wind tunnel by Marathon LeTourneau Marine Company (MLMC) and made available for the MaTS-project.

Apart from testing the chords also two slightly smaller scale (1:4) leg sections were tested in the DHL-flume, both in regular and in irregular waves. The test results are again

reported in the annex to MSC's report. MSC subsequently analyzed the results and studied the reliability of determination of

hydrodynamic loads on a complete leg section from those on individual members. This again is reported in MSC's report [1].

2. Laboratory equipment used

2.1 Towing tank

SilL possesses two towing basins, the larger of which has been used for the test. This tank has following dimensions:

Length 143 meters

Width 4.2 meters

Depth about 2.5 meters

Water depth 2.0 meters (for this test)

The basin is equipped with a hydraulic wave maker of the flap type, but this is not used for the subject test.

2.2 Towing carriage

Above the towing tank runs a towing carriage of approximate dimensions 8 x 5 meters (see fig. 2.1). This is a new carriage, installed in 1988. The carriage is structurally fabricated out of aluminum. This was done in order to maximize the stiffness within a limited weight to allow the highest speed obtainable by the

carriage. The maximum speed now is around 7 rn/sec. At the same time, however, this material imposes limits to the maximum

allowable local loads on the carriage. As we will see this sets one of the limitations for the test.

2.3 Electronic equipment

The standard electronic equipment on the towing carriage consists of:

- Carriage velocity measuring and control system

- Olivetti M24O personal computer used for data

acquisi-tion

- Asyst software package from Asyst Software

Tech-nologies, Inc

for data acquisition in the time domain. Sampling of the data is done with a frequency of 50 readings per second.

2.4 Data analysis software

The software package Asyst can also be used for data analysis. It allows following relevant treatments of the data time histories:

- Plotting the time tracing

- Determination of mean value in the time period

- Determination of the standard deviation

- Spectral decomposition of the time history

3. Model

3.1 Model as used in de Voorst; model roughness

The chord model used is part of the MSC chord model tested by DHL and described in their report SP 8603 - 1505,

section 1.2.1. The scale of the model is 1 : 1.864. The circular section of the model is roughened by glued-on waterproof

sandpaper resulting in a relative roughness ratio k/D of

9.9 * l0. The model contained a lower and an upper measuring section each with three force transducers. Figure 2 shows the relevant (in view of the model part used; see 3.2) cross section of the model. The model's foot plate was set on top of a founda-tion which was set on the flume bottom. Dowels on the foot plate of the chord model matched with a series of holes in the founda-tion allowing rotafounda-tion of the model to obtain different headings.

3.2 Modifications to model

The total length of the chord model tested by DilL is about 6.5 meters. Given the tank depth at SHL the model had to be shortened and only one measuring section could be used. It was decided to use the lower 2.8 meters of the DilL model containing the lower measuring section. By turning this part the original foundation could be used for attaching of the model to the towing carriage. The foundation and foot plate were provided with new holes allowing bolting together of the two. Figures 3 and 4

respectively show the model and modified foundation (now attach-ment) as used by SilL.

In this set-up the measuring section of the model is located approximately 1.2 meters below the still water line and 0.8 me-ters above the tank bottom.

3.3 Arrangement of model under carriage

The general set up of the model under the towing carriage is shown in figure 3. From a point of the chord model slightly above the measuring section a steel wire was tightened to the towing carriage ahead of the model (relative to the towing direction) in order to reduce the maximum clamping moment transmitted to the carriage. This wire is clearly visible in some photographs such as no. 4.

3.4 Instrumentation of model: sensors, coordinate system The measuring section was equipped with the three force transducers also used at DHL. They were mounted as shown in

figure 5. The force transducers were located at one height. They were of a type allowing the measurement of a force in one

direction only as indicated in fig. 5. They were arranged in such a way that any location of the total force at an other height than the level of the transducers would cause a moment around a horizontal axis that would be kept outside the actual measure-ments. By their arrangement, however, they could measure a moment around the vertical axis through the centroid of the three

transducers, thus permitting the determination of the horizontal location of the resulting total force. The force transducers have a full range of ± 500 N.

The coordinate system as used by SHL differs (unfortunately) from that used by DHL. Figure 5 shows the yawing angle and

transducer numbering used by SHL. Furthermore note that the force transducers are installed in the measuring section, meaning that their orientation with respect to the water flow changes along with the orientation of the complete model.

4. Limitations to testing

4.1 Blockage in tank

Blockage in the tank to some extent influences the water velocity around the model. In order not to influence the (drag) measurements too much the blockage restricts the maximum towing

speed possible.

Towing anything in a tank has the effect to reduce the cross section of the tank aside the model. Consequently the relative speed between model and water is higher than that between

carriage and water in the far field without the presence of a model. Or in other words water has to flow from ahead of the model to behind the model, thus creating a return flow.

In order to be able to make some statement about the speed limitation caused by avoiding an effect of blockage some more will be said about the impact of blockage on the water velocity

along the model.

In the first approach the relation between the water

velocities in the disturbed and undisturbed

condition

is governed by the law of

continuity.

This causes a relative speed between water and model higher than the carriage speed. If the return flow would be homogeneous over the free part of the tank cross section the return flow would have a speed equal to

Vreturn = [(A0 - A1) / A0 )] * Vcarriage

where A0 is the cross section of the water in the tank in the far field and A1 is the lateral area of the model seen in the flow direction.

In this test A0 equals 4.2 * 2 = 8.4 m2. A1 varies from 2 * 0.4 = 0.8 m2 to 2 * 0.338 = 0.68 m2. In other words the

return flow varies from 8 to 9.5% of the carriage speed depending on the orientation of the model.

In the second approach Ratcliffe [3] rather than using this straightforward correction for the velocity, suggests for barges a different correction. He derives a factor

k = 1 + exp (-lOm) with which the model cross section must be multiplied in order to arrive at the correct speed. In this formula rn is the blockage factor, being the 8 to 9.5% mentioned above. Using this formula would result in an increase of relative water velocity of 13 rather than 8% and of 15 rather than 9.5%. As the previous velocity correction already is quite important it

is decided to disregard the correction as suggested by Ratcliffe. Moreover it is unknown to what extent Ratcliffets correction for barges would apply for the chord structure tested.

On the other hand Lapidaire [4] suggests for his tests that blockage ratios below 1.167 will hardly influence the measured drag coefficients. At large blockage ratios the character of the flow around any structure can be significantly altered, thus making simple extrapolations from a non-blocked situation

The return flow will have an effect on the maximum speed allowable for the carriage as well as on several other phenomena

(surface waves, total resistance, vortex generation) are governed by the water velocity along the model rather than the carriage

speed.

Combining all the above it was decided not to let blockage considerations limit the carriage speed in the test. In the evaluation of the test

4.2 Surface waves

When running a model at high speeds relatively high surface waves will be generated. These waves may not become too high for

two reasons:

very high waves may wash over the tank wall and damage the rails for the carriage (corrosion)

high waves will be felt deep under the water surface.

Measuring the Morison coefficients supposes a basically two-dimensional flow. Depending on the depth of the model below the water surface the waves may influence the measurements. Some information on the submergence needed to avoid surface waves to influence the measurements is given for a small

diameter, vertical cylinder by Lapidaire [4] . Although not

comparable in many respects to the SHL tests this informa-tion helped in drawing statements about the effect of

surface waves on the measured drag coefficients.

4.3 Power of carriage propulsion

When towing a model at increasing speeds the resistance and hence the propelling force of the carriage increases. Besides the power needed for constant speed additional power is needed in the acceleration phase. As only limited power is available this may set a limit for carriage speed.

4.4 Structural strength of carriage

The increasing resistance of the model has to be transmitted to the carriage. Partly this is done by the steel wire. A large extent has to be transmitted by clamping the model through its foundation to the carriage. The carriage beams to which the model is connected are fabricated out of aluminum. Although the maximum moment that can be taken by these beams has not been calculated it was felt that this too might set a limit to the maximum speed attainable. In fact when during the testing it was decided not to raise the velocity further this was mainly based upon an instinc-tive appreciation of this last point.

5. Test program

5.1 Runs made: orientations, speeds

Each test run was made by towing the model at a certain

speed ranging from 0.50 m/sec increasing with steps of 0.25 rn/sec up to 2.0 m/sec. Once a steady situation was obtained the signals from the force transducers were registered during 20 or

30 seconds, depending on the carriage speed. This series of runs was repeated for 7 orientations of the model with respect to the relative water velocity. The orientations ranged from 00 in steps of 15° up to 900. Note that the definition of the attack angle (orientation) differs from the one used at DilL. In the present tests zero degrees corresponds to an orientation where the relative water velocity is perpendicular to the tooth rack.

In this way a total of 49 measuring runs has been performed. Separate from those runs some with the same orientation and speed were repeated to allow making of video films and taking of

photos. The visual impression of these latter runs was identical to the actual measuring runs and it is assumed that the visual reporting, as described later, gives a good representation of the actual measuring runs.

An overview of the various test runs is given in appendix 1.

5.2 Measurements taken

During the test runs four signals were sampled 50 times per second and registered digitally by means of Asyst. Those signals originated from the three force transducers and the signal of the carriage speed (which was constant during the actual measure-ments). The recordings are available on diskette.

5.3 Video film

The visual impression of some typical runs is registered on video tape. Total duration about 15 minutes. The tape is avail-able in non-edited form in the VHS-system.

5.4 Photographs

A total of fourteen photographs were taken. An overview of the photos is as follows:

photo no. orientation velocity front/rear

degrees rn/sec 1 2 90 0 f 3 90 1.0 f 4 90 2.0 f 5 90 2.0 r 6 90 1.0 r 7 45 1.0 r 8 45 1.0 f 9 45 2.0 f 10 45 2.0 r 11 0 0 f 12 0 1.0 f 13 0 1.0 r 14 0 2.0 f 15 0 2.0 r

6. Test execution

6.1 Comments to actual test runs

During the SHL tests some of the roughening sand paper progressively came loose. No effect of this on the measuring results could be detected.

6.2 Time records of measurements

Typical examples of time records of the forces measured as acquired using Asyst are given in the upper halves of appen-dices 3 through 23. An explanation of the (Dutch) terms in these is given in appendix 2.

6.3 Mean values of time records

The mean values of the time records of the force transducers is calculated on-line by Asyst during data acquisition. The

7. Analysis of test results

7.1 Change of coordinate system

As mentioned in section 3.4 the force transducers are fixed within the measuring section. The orientation of the measured

forces therefore changes with the orientation of the model.

The following sketch indicates the coordinate system as used by SilL in the towing tank test. Furthermore the formulas to

transform the measured signals into drag and lift forces and moment around the centroid of the cross section are given. Also

the formula for determining the distance b of the resulting total force to the centroid of the section is given. Note that those expressions have a continuous validity in time.

=

FLcivJ

Angle of attack: 1B = 900

-D = (X1 + X2)coscr + Ysina Newton L = -Ycos + (X1 + X2)sina Newton M 80 * (X1 - X2) - 87 * Y Nmm CD D ½pv2A L CL ½pvLA

7.2 Calculation of drag and lift coefficients

The mean values of the signals over the total measuring period are directly given by Asyst. The transformation formulas given in 7.1 for instantaneous values are also valid for the mean values. Dividing the forces by ½*rho*v2*Aref yields the drag and lift coefficients. This has been performed in appendix 1. Note that the results are given on basis of the carriage speed and that no correction has been made for the return flow.

The lift and drag coefficients thus found are plotted in appendix 24 and 25 respectively on basis of the angle of attack, which corresponds to (90° - orientation angle).

Note that the arm for the total resulting force sometimes indicates a quite eccentric total force.

7.3 Spectral analysis of chord bound force time histories

As can be seen from the typical time traces given in appen-dices 3 through 23 some of those show fluctuations with a

magnitude in the order of the mean values. In order to allow an evaluation of those a spectral analysis has been made of each of these typical time traces using Asyst as a tool. Those spectra are shown in underneath the time traces in the appendices.

8. Evaluation of test and analysis results

8.1 Measurement accuracies

Running more than one run with a given carriage speed and model orientation would allow to evaluate any random measuring inaccuracies that might exist. Comparison of force spectra in such situation would be beneficial. Unfortunately no such additional runs have been made.

Any constant value measured would indicate a high measuring accuracy. The time traces of the measurements show fluctuations that do not allow such a conclusion.

The spectral analysis shows whether the fluctuations have a preference for certain frequencies. If so this could indicate

other factors than random measuring inaccuracies. Some of the spectra show clear peaks in the spectral distribution, others do not. The latter cases might indicate a certain amount of random noise in the measurements. We will revert to the peaks in the

spectra.

It may be concluded that measuring inaccuracies can not be excluded.

8.2 Existence of 3-D effects

Four types of deviations from the theoretical two-dimen-sional situation might occur.

The first is that the chord is not a long, slender body of uniform cross section. The teeth are disturbing that picture and will cause water particle movements in vertical direction. This

is the nature of any chord with a tooth rack. The drag and lift forces are then considered as the mean value over the height. As in the test situation the end of the measuring section lays over the tops of two teeth, i.e. in a local plane of symmetry where the local flow may be considered to be two-dimensional, the measured forces will correspond to the drag and lift forces as

defined for such situation.

The second 3-D effect concern the tank wall influence. This is the same phenomena as blockage and return flow. This already was discussed in 4.1. Based upon this a correction to the

velocities considered should be made.

The third 3-D effect is the bottom influence. Hydrodynami-cally this is similar to the wall influence, but it does not cause additional blockage. It is assumed that the effect in the test can be neglected.

The fourth 3-D effect is the influence of the free surface. In particular the surface waves generated might disturb the water flow velocities around the measuring section.

From the photos a surface half wave length can be estimated for speed 2 rn/sec of about 0.5 meters. The theory of deep water waves would in such situation indicate at a depth of 1 meter an amplitude of the wave particle motion of about 2 promille of the wave amplitude. In the maximum test situation wave amplitude was in the order of magnitude of 0.2 meters indicating a marginal free surface effect around the measuring section.

8.3 Reynolds' dependency

Generally it is assumed that the drag coefficient depends on the Reynolds number. Such has been found for smooth circular

cylinder as is shown for instance in fig. 5.1 of the MSC main report. Similarly for chords with tooth racks such dependency on velocity is assumed. See for instance Det Norske Veritas Rules for Mobile Offshore Units Pt.3 Ch.2 Sec.3 D 205, where the drag coefficient for such a chord is related to that of a smooth cylinder. This is one of the reasons why determination of chord drag coefficients is normally done by testing in a wind tunnel.

In the SHL tests following Reynolds numbers were used, based on the reference diameter D 0.4027 meters and on the carriage speed without correction for the return flow.

where the kinematic viscosity of water at the test temperature of

16.5°C is

= 1.098 *

io6

m2/sec.

From the drag and lift coefficients found in the test as shown in appendix 1 no significant dependency on velocity is

clear.

8.4 Harmonic force components; possible vortex shedding effects From the spectra given for the various measuring runs sometimes rather explicit peaks occur at frequencies of around 9.5 rads/sec and, to a lesser extent, at frequencies about 4 or 6 times that value. The occurrence of such peaks does not seem to be related to carriage speed or orientation of the model. This indicates that vortex shedding as cause for these frequency peaks is

unlikely: in that situation frequency is directly related to the relative water velocity.

Carriage speed rn/sec Reynolds number 0.50 0.183 * io6 0.75 0.276 * 106 1.0 0.367 * 106 1.25 0.458 * 106 1.50 0.550 * 106 1.75 0.642 * io6 2.0 0.733 * 106

If vortex shedding occurs the approximate frequency is

v 20

f=0.20-(l

)

D Re

where v is the relative water particle velocity, D the cylinder diameter and Re the appropriate Reynolds number. For a given f, v and Re the corresponding D thus can be derived. In case Reynolds number is large compared to one, the formula may be replaced by £ 0.20 v / D Hz.

We will look to for instance run 1, where a frequency peak occurs at a circle frequency of approx. 9.5 rad/secs or

9.5/2ir = 1.5 Hz. Using the carriage speed for the relative _water velocity (hence not correcting for the return flow) this yields a

corresponding cylinder diameter

D = 0.20 v / £ = 0.20*0.5/1.5 = 0.2 meters. At higher carriage velocities the diameter would be correspondingly higher. Higher

frequencies (like the four or six times that frequency that seem to occur in some of the spectra) would lead to similarly smaller diameters. Although these frequencies relate to circular cylin-ders it is felt that the smallest one, i.e. the 0.2 meters does not represent a diameter recognizable in the test model. Conse-quently it seems unlikely that the frequency peaks found are attributable to vortex shedding.

An other cause for such frequencies can be resonance of the model as attached to the carriage. Alternatively _{a part of the} model, like the measuring section, might resonate relative to the remaining part of the model. Unfortunately no test was performed whereby the model or its parts were brought into vibration and

their eigen frequencies measured. It is therefore impossible to make any conclusive statements about the origin of the frequency peaks, but mechanical vibrations may not be excluded, whereas vortex shedding is unlikely.

8.5 Comparison to wind tunnel test results of similar chord A chord similar to the tested one was tested in a wind

tunnel by MLMC. Only drag forces were measured. Based _{upon those} test results MLMC predicted the drag coefficients for the _{test in} the towing tank. A comparison between the wind and towing tank tests is given by MSC in their report and reproduced in

appen-dix 24. Note that in this comparison the drag coefficients _were calculated based upon the carriage speeds without correction for the return flow. If the latter were to be applied the relative water velocities could be up to 9.5% higher (see 4.1), which

would yield drag coefficients up to 17% lower than now calculated for a flow perpendicular to the tooth rack. For _{a flow parallel} to the tooth rack the return flow increases the relative water velocity by about 8% or the drag coefficient is reduced by about 14%

Whereas the agreement between wind tunnel testing and towing tank

testing as reported by MSC in general was quite good (although for the perpendicular direction the towing tank already found drag coefficients some 15% lower than the wind tunnel) this can change if a correction for the return flow is applied. In that situation the figures for the towing tank become considerably smaller than the wind tunnel tests.

8.6 Wind tunnel testing versus towing tank testing

Comparing the wind tunnel tests as performed by MLMC and the towing tank tests as done by SHL it is found that slightly higher Reynolds numbers have been tested in the wind tunnel, but not to

such extent that it seems impossible to obtain similar Reynolds numbers in the towing tank. The towing tank yielded drag

coeffi-cients that were some 15% lower if related to the carriage speed. If a correction for return flow were to be implemented the

difference may grow to some 30%. It is not known to what extent blockage may have occurred in the wind tunnel test. As no

dependency of the drag coefficient on the Reynolds number was found in the towing tank it is deemed unlikely that this would explain the difference. This notwithstanding the fact that the towing tank tests were performed in a Reynolds regime (based upon the reference diameter) that corresponds to the critical regime of the drag coefficients versus Reynolds number for smooth (if rough the critical regime shifts to lower Reynolds numbers) circular cylinders. In the towing tank case it is felt that a supercritical situation exists.

For the time being it can not be decided whether wind tunnel or towing tank testing yields the more realistic (compared to full scale) drag coefficients. Neither is it possible to compare the costs of wind tunnel and towing tank testing.

8.7 Conclusions and recommendations

8.7.1 Testing of chord sections in the towing tank in order to determine drag coefficients is feasible.

8.7.2 In such tests chords with racks are tested in a

supercritical regime as no influence of the speed on the measured drag coefficients is found (no Reynolds dependency).

8.7.3 Large scale testing (as for instance the 1:2 scale

models as used) may give rise to significant return flows that have to be taken into account.

8.7.4 Without correction for the return flow the drag

coefficients measured are similar to those found by wind tunnel testing for a flow parallel to the tooth rack. For a flow perpendicular to the tooth rack drag coefficients were found in the towing tank some 15% lower than in the wind tunnel.

8.7.5 With correction for the return flow the towing tank yielded drag coefficients consistently lower than the wind tunnel, ranging from 14% for the parallel flow to 30% for the perpendicular flow. Note that it is not known to what extent blockage may have played a role in the wind tunnel testing.

8.7.6 Under small angles of attack (some 15°) lift forces were found of the same order of magnitude as the drag forces. Those lift forces can be attributed to the asymmetry of the chord section relative to the water flow and as such will have the same direction and phase over the water depth. Lift forces at higher angles of attack show a more random character with respect indicating an amount of vortex shedding that can cause phase differen-ces over the water depth.

8.7.7 In several test runs fluctuations of relatively large magnitude were found in the forces measured. It is unlikely that those fluctuations are due to vortex shedding. Mechanical vibrations of the model or parts thereof are the more likely cause. 8.7.8 It is recommended to study the difference in drag found between the test in the towing tank and the wind tunnel.

conditions on cylinder drag in a current"; Fac. of Civil Engnrg. Deift Univ. of Techn. , 1981

9. References

[1] G.H.G.Lagers "Morison coefficients of jack-up legs"; report SP 8603-1505, MSC, Schiedam, november 1989

[2] S.Th.Schuurmans "Wave forces on jack-up legs";

Appendix A to [1], Delft Hydraulics,

1989 [3] A.T.Ratcliffe,

P. J . Fisher,

C. H. C. Mitchell

"An experimental study of the parameters affecting the drag of barges in current and waves"; OTC paper no. 4166, 1981

- lower measuring section

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appendix

RUN Angle Beta Vim Xl X2 Y 0 L Cd Cl

1 0 90 o.so 13.44 13.10 -0.54 28.54 0.54 1.59 0.032 2 0 90 0.75 29.24 30.14 -0.72 59.38 0.72 1.59 0.019 3 0 90 1.00 51.40 S2.36 -3.78 103.76 3.78 1.56 0.057 4 0 90 1.25 82.68 84.36 -5.60 167.04 5.60 1.61 0.054 S 0 90 1.50 118.40 122.20 -7.40 240.60 7.40 1.61 0.049 6 0 90 1.75 163.80 166.56 -9.82 330.36 9.82 1.62 0.048 7 0 90 2.00 216.10 221.60 -13.44 437.70 13.44 1.64 0.050 8 15 75 0.50 16.10 9.80 4.84 26.27 2.03 1.68 0.122 9 15 75 0.75 34.98 23.60 9.73 59.10 5.76 1.58 0.154 10 15 75 1.00 56.90 38.14 17.04 96.21 8.14 1.45 0.122 11 15 75 1.25 89.54 57.84 26.94 149.33 12.12 1.44 0.117 12 15 75 1.50 139.18 69.16 41.24 227.37 18.23 1.52 0.122 13 15 75 1.75 185.94 124.20 55.94 314.05 26.24 1.54 0.129 14 15 75 2.00 241.62 162.78 73.14 409.56 34.02 1.64 0.128 iS 30 60 0.50 15.48 4.16 9.34 21.68 1.73 1.30 0.104 16 30 60 0.75 31.50 9.44 18.62 44.72 4.43 1.19 0.118 17 30 60 1.00 64.32 14.80 33.56 76.64 5.50 1.15 0.083 18 30 60 1.25 81.16 23.12 51.08 115.85 7.90 1.11 0.076 19 30 50 1.50 122.72 36.94 76.52 176.63 13.56 1.18 0.091 20 30 60 1.75 166.40 51.22 102.09 239.51 20.40 1.17 0.100 21 30 60 2.00 222.76 72.12 135.20 322.97 30.35 1.21 0.114 22 45 45 0.60 12.15 -2.38 8.06 12.61 1.22 0.75 0.073 23 45 45 0.75 24.54 -4.46 18.72 27.44 0.96 0.73 0.026 24 45 45 1.00 43.78 -5.82 34.12 50.97 2.72 0.77 0.041 25 45 45 1.25 69.02 -8.28 53.86 81.03 4.85 0.78 0.047 26 45 45 1.50 101.72 -11.20 76.72 118.26 9.76 0.79 0.065 27 45 45 1.75 140.34 -11.46 105.22 165.53 16.73 0.81 0.082 28 45 45 2.00 187.92 -12.80 138.56 221.81 25.86 0.83 0.097 29 60 30 0.50 12.70 -3.38 7.78 11.40 4.18 0.68 0.251 30 60 30 0.75 22.88 -14.80 21.18 22.38 -3.59 0.60 -0.096 31 60 30 1.00 38.84 -29.08 40.58 40.02 -11.84 0.60 -0.178 32 60 30 1.25 60.46 -44.26 63.42 63.02 -17.68 0.61 -0.170 33 60 30 1.50 90.70 -63.48 91.62 92.96 -22.24 0.62 -0.148 34 60 30 1.75 128.24 -81.82 122.88 129.63 -21.24 0.64 -0.104 35 60 30 2.00 178.08 -104.05 149.10 166.13 -10.45 0.62 -0.039 38 75 15 0.50 9.56 -6.25 8.94 9.49 0.87 0.57 0.052 37 75 15 0.75 19.52 -11.34 19.58 21.03 2.83 0.56 0.076 38 75 15 1.00 33.28 -22.32 36.18 37.78 1.22 0.57 0.018 39 75 15 1.25 55.54 -31.84 56.62 60.82 8.24 0.58 0.079 40 75 15 1.50 77.06 -50.76 82.06 86.07 4.17 0.57 0.028 41 75 15 1.75 103.92 -69.30 111.72 116.87 4.63 0.57 0.022 42 75 16 2.00 147.74 -75.50 142.32 156.17 32.94 0.59 0.124 43 90 0 0.50 4.88 -4.64 9.14 9.14 0.24 0.55 0.014 44 90 0 0.76 11.78 -10.10 20.40 20.40 1.68 0.54 0.045 46 90 0 1.00 20.10 -17.98 36.74 36.74 2.12 0.55 0.032 46 90 0 1.26 31.62 -30.60 58.86 68.86 1.02 0.67 0.010 47 90 0 1.50 44.26 -40.44 81.56 81.56 3.82 0.54 0.026 48 90 0 1.76 62.50 -54.18 112.62 112.62 8.32 0.56 0.041 49 90 0 2.00 84.18 -67.66 148.48 148.48 16.62 0.56 0.062

Dutch English

Data van kanaal Data from channel

Run Run

OK OK

Hoekfrequentie Angular frequency

Effectieve waarde van Root mean square value

signaal is

Schatting van statistische Estimation of

momenten statistical moments

53.7 1?. 161. 215. 268:

4.4

8.3 12. 16. Tie (sec) --) xE

Data van kanaal

Run 1

O1(

Effectieve waarde van signaaI is

6.5i33 N.

Schat.t in

van statist ische

omente'n

4229E

2 11:

. 7129E 3 M2 . 1.836E 5

M3: .6471E

6 Ml: .2?Z1E

8 MS: .1262E

1

0 I( Run i

a n aa 1 1 H _(:;i/s) 3 < E 13 appendix t xE N. 't -268. I I F t -215. -161. -17. -53.7 4 i 13 2 13 13 1 13 . 13 r i r J, -i

._J.

1 ._L_ .131313

.JL

Effectieve waarde van signa1 is

5.2799 H

Schatt ing van stat ist ische

momenten

Z7E8E 2 M1 . 1114E 4 M2 . 4903E S

M3 .2285E 7 M1 .i1@9E

9 M5: .SSSSE

10

01< 1bn i.

icaiiaa.I 3

appendix

4 xE 8 _N 273. 1 I I I I 218. 164. 109. 54.6 000 -54.6 -109. -164. -218. 273: 050 _{4.04 8.03 12.0} 0 Tie (sec) --> 16.0 xE 20. 8

Data van 1anaaI 3

Run 1 OR ( H-i.d f >(Ei 2. T I'I I I I I) ill I! 2 i.

80.8

1I38.

.000 10?. 215. 322. 429. :252 4.04 8.03 12.0

TiMe (sec) -->

16.0 20.0 xE 0

Data van kanaal 1 1un 3 ox > r 14 . ) "2 : f ' ad 513(30 OR Run 3 I<anaal 1

Effectieve waarde van signaal is 48.9168 Fl.

Schatting van statistische mornenten

2393E 4 M1 .2584E S M2 .36EiE 6

7898E 7 M4 .2632E 9 M5 . 1@95E 11

F r appendix 5 -4 I - I _L L - J.... I

j_

I .01313 213.13 413(3 613.13 813.13 1130.

Hoekfrequentie (radfs) -->

xEO

xEO -53?. N. I I I I I I I I I -429. -322. -215. -10?.

Data van kanaal 1 Run 5

ox

Effectieve uaarde van signaal Is 7.927 N. Schatt ing van statist ische momenten

M@ .6284E 2 M1 .2@11E 4 M2 .8534E 5

M3 .4249E 7 M4 .2317E 9 M5 .132?E 11-.

OK Bun 5, kanaa.1 1

(H. )2s'.;kd

T 6

000

....-_Y__jk

'L_----J'... I

.000

20.0

40.0

60.0

80.0

100.

Hoekfyeqtu?n tie

C 'ad/s) -->

xEO

appendix xEQ

-537.

N I I I I I I

-429.

-322.

-215.

-107.

000 107. 215. 322. 429.

4.04

8.03

12.0

16.0

20.0

Tiqe (sec)

> xE 0

I 4. xE 0 -1073 -859. -644. -429. -215. .000 -H 215. 429. 644. -_ 859. -1073 050

Data yan kanaal Run 7 OH 'I II, ±L. J I

5L3

30.0 100.

Hoekfrequentie (rad/s) -->

Effectieve waarde vaii siqiaai is 8.7353 N.

Schatt in van statist ische momenten

I1@ .7631E 2 M1 _.1483E 4 r12 .5762E 5

M3 .2716E 7 M4 . 1394E 9 M5 . 7498E 1@

01< &un 7 kanaa 1 1 appendix 7 16.0 20.0 0 4.04 8.03 12.0 Tiiie (sec) -->

ox 4 xE 1092

873.

655.

43?.

218.

-G

218.

437.

655.

--873. (

-192

Data van kanaal 3 Bun 7

25

r _{T 1} 1

3 '1

Effectieve uarcle van siçnai is

1.9i6S N

Schatt in

van statist ische moentei

1668E 3 M1 . M3

. E16E

7 114.

0 IC flu ii 71 n a 1 3

appendix

8 I' II; jI

:1;L') -->

4@1@E

4 r::

. 17@1E 6

443E

(J _M5

225E

₁₁

16.2

8.3

12.

Tite (sec) -->

xE 2

22.2

L. U ata V a kar 1 2 Ft ii ox H I T 1 OI Btn, 8!I ikanaa 1 2

appendix

9 > E 0 2 6 7 2 1 3 1 6 0 1137.

53.4

rvl Im ' f. _.,).i 'r. .,

-53.4

107

-160.

- 213

? 6 7 .-. J... J - . .1_

I

-:30

6.'

i8,

24.0

30.0

.

--)

iiL0

60.0

80.0

1130. 3 0 '3 2 3 .1, 0 . 0 .4

Effect ieve waarde vai sinaa1

Schatt i nq van stat ist i

sche

M .5552E

2 Iii

.825BE

113 .

7e6F

rti-

@3E

Hkf?1tQ

(T4.L7S) ----> xE(3

is

oente

3 MZ B M5

7. SO9

.2102E . 1722E N S i.3 F _L

Fl

)34.

r-427

320

213.

1. 137 13130 -1137

-213.

-- 3 2 0.

F-D.E

ta vai Ianaa I

Run D.1 01< -r -r T

appendix 1

,:

'2

ir

i i---0130 -- 4 L I I ] J .04343

20.0

-10.13 643.0 813.13

(r.1/s)

--fl->

Effectieve waarde van sipaai is

46.6113 M

Schattinq van stat istisrhe

oreiiten

F1 .2173E 4 Mi .Z'SiBE

S Ii2.i58E

6

M3 .1129E 8 M1 .4388E 9 I15 .2:e3iE 11

0J Ftu i I ft. ha na a 1 2

113.

> E13 N

-427.

L L

j.13

i43.l 21.43 T (

e:

-267

L

12..

i6..

...

U'3i1:a van kanka . 2 7 )

01< Rr 1.7,

k.F.naa I 2 I II I 1'I k 1 1h iIVL, '11 i1lIlIi

14 II

\I/IA ? \\i i j 1 _'j I 1O

Hçe.k.freq:uiitie (rt,/) ---->

Effect ieve warde vn s iqna 1

is

21. 83i

Schatt ipg vi tt t 1st i sche

oienteii

1766E 3 M1: . ¶621.E :i h2 . 292 I.E 6

M3

.lth6E

8 M1

i731E

9 M5 .2176E

ii

1 1 F

appendix 11

53 . 4 3g _j yt I' ) . 'r ii IY l Il.I 4

6 '.

-21 .: 26'?

213.

16

17.

H r 1 1

-4 1 .1 >r E 0

-1073

-859.

- 644.

-429.

-215.

000 215. 429. 644. 859. -1073 ___.__L___---'---

_8.03

_12.0

_16.8

_20.0

T i i ( s e -- - > < E 0

Data van kana1 Iun 21 :N.

)2s''.a-20.0

T 16 . 8 8 .

4.08

i-I I. Irl L008 2 0. 4 .

0.

:3 0. 8

Hoe.kfrequer.ie (pad/s) -->

Effect ieve waarde van sinaai is 1i. 1321 N.

chatt ing van statist ische iutenten

1Z7E 3 I11 . 1.574E 4 MZ .

5%9E

5

13 . 291@E 7 M4 . 1534E 9 M5 .8388E ie

O1 Bun 21, 1<anaa 1 1

appendix 12

ioo.

:11

Data van kanraa ]I 2

Pwi 21

oic

4

Effectie'e waarde van sicpiaal is

13.1395 H

Schatt ing van statist ische

ornenten

MFJ -

i?26E

3 M1 -3527E

4 Ii2

. 1449E 6

M3 - 73?2E 7 M4 -

456E

. M5 . 2323E 11

01< Iun 21. k iaal 2

Tt :sec -- > I T

r

T

appendix 13

II - r.J

t-23.

4,. 3

6CL (

i3I. 0

Hcekfrequeirit.ie (a/i) -->

--

16iL

x

-213

267 J_ J L

ir. I

i2.

I J

i6.

)c E (i H 2 6 7 _r 213 -i 6 . 137 -5 3 - 4 1 .' r.

-53.4

(H )-2s/ra:i

1O3. ---i---i---

-

T 1 1 [ N

.L_.i_.L.___±_.._J_._._L_.

:ra53

3'3

12. T i ie ( r ) - )

Data vu

1 4

&ni 21

T F r Y

r

2 4 IL 6

Effectieve waarde vaii siia1 is

16.523 N

Schatt ing van statist ische moe-nten

M

.275E

3 M1 .3966E 4 M2

.131!E

6

r13: .5916E 7 M1 .2913E 9 M5 .1492E 11

01< Iuj n 211 ka n a 1 3

ioekfrequente (ra/) --->

appendix 14

2 I

1G

437.

I

328. 21 3.

-149.

2 1 8

--328.

-437

:1 N

-26 8.

I 1 T

-215.

--161.

-, -1137.

-53.7

268 I

_.___.1_..__i

:13513 6.134 1.2.13 18. 24.13 313.13

(:ec:)

>

I)ata vai'

1 Ru i 24 0 IC

appendix 15

Uue.k.frequen tie

( x'ad/s > --->

Schatt I ny van statist I sche moewt en

i34E

3 I11 . 1E75E 4 M2 .4498E 5

M3 . 1617E 7 M4 .7423E 13 M5 . 3654E

i

01< B 01< J1:u n 24..1a n a a 1 1 8 13 13 . 4 13 . 2 13 . 13 13 II 13 .131313 :

)'s/rki1.

r I 213.13

__j'J.

J 413.13 i -I.

-I 613,13 813.13 11313. .131313 5 3 . 7

i

JJI Jr I ii11'Iji 1137.

-161.

2.15.

ii

>c E

267.

213.

16 3.

107.

53.4

000

--53.4

-107.

-160.

-213.

Data van kanaai Run 24

01<

Effectieve waarde van sigiiaal is 17.6569 N

Scbatt I ng van stat i st I sche momenten

M@ .3118E 3 M1 .873E 4 M2 .3@1SE 6 t13 .11.43E 8 fl4 .4577E 9 fl5 .1947E 11

01< Run 24, kanaal 2

appendix 1

6.01

J23

18.0

24.0

30.0

-->

T

200.

[ 1 ( 0

120.

80. 0

40. 0

Ii

X

-000

H J r, I

.000

20.0

40.0

60.0

80.0

100.

Hoekirequen tie (rd/s) --->

xEO

Fl

24

33.e

1:LKir.? (5h_->

t Vi fli

J:ana

i (H ;

''23'rad

r 4 ) :3 , '3

Hoe frequetie (r'adfs)

---->

-r

Effectieve waai-de van sipiaa1 is

8M576

Schatt inq van statist ische momeirten

6493E 2 M1 . 2186E 4 M2 . i@?2E 6

M3 .4916E 7 M4 .2361E 9 F15 .1183E 11

O} Jun 24

1ana 1 3

appendix 17

N 2 7 3 21

164.

J9.

54 6

-- 54. 6

19

-164

21 T T V I

1 0.

N

273.

-2113. J.. 64. 139.

54.6

0(3(3

-54. 6

-1(39. - 1 6 4 - 2 13. I.

-

. -b 04 43 4 (3 0 (3 1 li.L 4 e4.) -.-- I

Data van Ikanaa 1

3

I1in 25

1)K

E 0

5 00.

44:343

Effectieve warde van sigriaal is

24.4534 N

Schatting van statistische momenten

598@E

3 Ml:

. 2886E S MZz . 1444E 7

M3 .7292E 8 M'1

.3701E

10 M5 .1885E 12

O} Jun 25, kanaal 3

1

I

-. i . I 243.43 40.43 6(3.0 3(3.43 H o 1< f r e L U Efl t i e ( x' a 41 / s ) - >

appendix 18

4: t ' 2 ..

r

T 1 1 1(30. >tEO

:'i N x

-53.4

-10?.

-160.

-213.

Data van 1canaal 2

Run 28

4N )

iLcJ. _---

_r

Schatt mg vav statist ische

rnorneiiter

1684E 3 M1 . 3684E 4 M2 . 1322E 6

t13 .6@40E 7 M1

.388E

9 MS .1668E 11

01< Pin 28, Icauaa 1 2 01< 1 .

80.0'

100.

II o k F re q u i e (

a t /s )

- - > xE 0

appendix 19

xE 0 267. N I I I I I I 213. 160. 10?.

53.4

000 6 . 04 12.0

18.0

24.0

30.0

TiMe (sec) --)

xE 0

IekfeqAentie (rad/s) --->

Effectieve uaarde van signai is

19.5555 N

Schatt i ng van statist i sche

omenten

M@ .3824E

3 Mlz .1?76E

5 M2

.8738E

6

f13 4388E 8 M4 .2224E 1@ M5z . 1 133E 12

01< Bun 32, knaa1 3

appendix 20

)< E 3

273.

218.

J. 6 4

19.

54.6

-54.6

-164.

-218.

-273.

N

-.L.. -f J.

r

..L T 1. iir ( s ... I e ) L.

18.

I . .J..

L.

24.

3.

Date

VEfl J Hun 32 1 i' 3 -L'L'.. 2O3. 1 3 U I U .L 4(L

:3r.O

1

-t68.

1 T 7 V T -21 5 -. 1 6 .1.

-147.

-53.7

2 .

Effectieve waarde vn sigraaJ is

18.31135 N.

Schatt irig

van stat ist i.sche iioirenten

3361.E 3 M1

F13 . 392FJE 8 M4

011 Fu

3), Jniaa]

1

t:.

24.

( er: ) --- )

)Erk?

pY1r

(I. )'2./':d

-..Y

appendix 21

Hoe.kfrequier ('ie (pad/s)

> xEO

1.

. 1519E 5 M2 . 7732E 6 . 213 1@E 1.13 M5 . :1@35E 12 x F4

Data

Iun :3

Oi( 5 3 7

Ja7.

16 .1 15

van Iana43.i

5 lI i: .r 'j

01< r Pat a va n k an a a 1 2 &tn 39 > E 3

26?.

213.

16g.

137.

53.4

-53.4

-1t?.

-16g.

-213

-267.

L _J I _j..

j

6.04

12.

24.cl

r4? Ft _{-- >} M T r i T 2

I

Effect ieve waarde van Schatting van statist

1ft .3965E 3 M1 r13 .452E1E 8 M4 0}( Hun 39, kanaal 2 _J_ J 643.c

Fh)ekfrecuefltie (r'ad/:

signaal is 19.9126 H ische mornenten I

appendix 22

0I 8cLc

iG.

) ---> zE 1822E 5 M2 .9881E 6 228SF 16 F15 .1161E 12 F T

4 I : :

54.6

---27 L i L _{J J} 18. 24. I I M ' ( ( C ) > >( J 'ai knaa1 3' Jun 39 OK A _{s 'y';,1} 1 8

Effectieve waarcle vary sigrta1 is 33.7395 H Schatting vui statistische moiienten

I 138E 4 M1 . .5687E 5 M2 . 2882E 7 F13 . 1468E 9 M4 -7EM@E 1 M5 . 3338E 12

01< Run 39, hanaa 1 3 (3 I [ L I .

Hoei<frequen tie (rd/s) --->

T appendix 23 H 273. _Y

TT

_T 218. -. 164. -.

/.

-'-1O2'L F MOJEL

ft-1QL ₇

VALUtS )J $7-A FLO.f

Chord CD.

model 1 towing tank

model 6 and 7: similar chords in wind _tunnel

appendix 24

00

appendix 25

Cd

Drag Coefficient versus Angle of Attack

75 45 15 90 60 30 0 Angle of Attack 0.4 - 0.2-0 1.6- 1.41.2 - 0.8-