Resistance and Propulsioin Assignment 2014

Alexander Maclean / Q10846671 / YEP109

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Southampton Solent University

BEng Yacht and Powercraft Design

Resistance and Propulsion

Tow Tank Testing of a Scaled Model

By Alexander D.P. Maclean

Table of Contents

INTRODUCTION ............................................................................................................................................... 1

THE MODEL DATA ............................................................................................................................................ 1

METHOD .......................................................................................................................................................... 2

ANALYSIS OF RESULTS ..................................................................................................................................... 6

APPLYING THE ANALYSIS ................................................................................................................................. 9

CONCLUSION ................................................................................................................................................. 12

APPENDIX OF RESULTS ................................................................................................................................... 13

REFERENCES ................................................................................................................................................... 15


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Introduction On Friday the 21st and 28th of November, two sets of tow tank tests were carried out on 1:15

scale model of a semi-displacement hull form, which has the capability to plane, given the right

conditions. The hull of the vessel has many distinguishing factors that include a deep V forefoot,

immersed transom and a discontinuous skeg.

The aim of these tests was to predict what the resistance of the model would be at full scale,

and also choose a suitable pair of engines for the boat for it to achieve an appropriate service speed

at full scale. The tests carried out in the towing tank involved running the model at varying speeds,

and primarily recording the corresponding total drag resistance to each speed. There were two load

cases tested, with a Lightships test carried out on the 21st and a Full load case being carried out on

the following Friday, the 28th. The results of the total measured drag resistance were then split into

two components, viscous (drag caused by the frictional resistance between the hull and the water,

roughness of the hull and the viscous pressure of the water all combined [2]) and wave drag. The

results seen and calculated went along with the predicted theory which will be explained throughout

the report, along with the method behind the tests and the subsequent calculations.

The Model Data The model as previously mentioned is a 1:15 scale model. The base data of both the model

and full scale data used throughout the report is detailed below in Figure 1. Also detailed below are

the abbreviations for the data. These are shown in the brackets.

Model Full Scale

Scale Factor (SF) 1 15

Length of the Waterline (Lwl) 1.244 m 18.66 m

Wetted Surface Area (A) 0.41 m2 92.25 m2

Density of Fluid (ρ) 1000 kg/m3 1025 kg/m3

Viscosity of Fluid (µ) 1.14 E-03 Ns/m2 1.19 E-03 Ns/m2

Lightship Mass (Δ) 11.4 kg 39.4 T

Full Load Mass (Δ) 12.4 kg 42.9 T

Acceleration due to Gravity (g) 9.81 m/s2 Figure 1: Base data for use throughout the report

Throughout the report, there are many abbreviations used in various formulae that do not

have an associated definite number, unlike the data above. The definitions for these abbreviations

are shown below in Figure 2.

Nomenclature Total Resistance due to Drag V Velocity

Viscous Drag Component Rn Reynolds Number

Wave Drag Component Fn Froude Number

Friction Drag Component Cf Coefficient of Friction

Form Factor Ct Coefficient of Total Drag

Epower Effective Power LCF Longitudinal Centre of Floatation

Indices M Model FS Full Scale

Figure 2: Table of Nomenclature


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Method

Before the tests began, the four pieces of equipment that would be used to measure the

Drag, Side Force, Heave and Trim of the boat all required calibration.

The Dynamometers that would measure the side force (force acting on the side of the

model) and the total drag (total drag resistance of the model) were the first to be calibrated. This

was done by artificially creating a moment using a light pulley and a 2kg weight. The dynamometers

(shown below in Figure 3) work by measuring any slight changes in voltage between a sensor and a

plate. This data is then turned into the two drag components by the computer.

The heave (movement of the vessel up and down) of the vessel was also measured. The

gauge cylinder (shown below in Figure 4) that measures the difference in the vertical movement of

the model was calibrated by using two spacers of known distances.

The final piece of measuring equipment that required calibration before the tests could be

carried out was the device that measures the angle of trim of the model around the LCF. This was

done by using the angle of a known piece of wood at the forward end and aft end of the reader.

Figure 3: The carriage’s two Dynamometers Figure 4: The carriage’s Gauge cylinder

The method used to measure the model’s total drag resistance was relatively simple. The

scale model was attached to a towing carriage via a post and slider. Attached to the post was a cage

which houses the aforementioned measurement equipment. However, in order to get the desired

results, the model first required to be trimmed and aligned to the tow tank and water level

respectively. The two tests that were carried out were at different load cases. Namely, Lightships

and Full load. This meant a different model mass was required in order to test both models. The

difference between the two load cases is detailed in the below in Figure 5.

Lightship Case

Displacement = 11.4kg Model Weight and Fitting = 8.75kg Post and Slider = 1.46kg Ballast = 11.4 - 8.75 - 1.46 = 1.19kg

Full Load Case

Displacement = 12.4kg Model Weight and Fitting = 8.75kg Post and Slider = 1.46kg Ballast = 12.4 - 8.75 - 1.46 = 2.19kg

Figure 5: Detailing of the calculation of the additional ballast to be added to the model


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Once the model was at the correct displacement, it was placed into the water and initially trimmed to the waterline according to two parallel marks at the bow and transom. The model was then attached to the post of the carriage, and subsequently trimmed for the last time. Trimming of the model was achieved by moving the added ballast weight around the hull. Shown to the right in Figure 6 is the final arrangement for the full load condition.

The boat was then aligned to the tank,

so that there were not any adverse side forces acting on the model, that may have affected the results obtained. In order to test that boat was in fact aligned to the tank correctly by eye, calibration runs were carried out. This was done at a nominal speed of 1.22m/s. The measured side force was not to be more than 10% of the total drag measured. In the case of the full load, the measured percentage side force/total drag came in at 0.20012N/3.031N which equates to 6.602%, which is within the limit.

Figure 6: Arrangement of ballast and final set up

The model was then ready to be tested over a number of speeds, increasing from 0.53m/s -

3.747m/s for the Lightships Load case and 0.634m/s - 3.734m/s for the Full Load case. The method

of setting the speed of the carriage to tow the model along at varying speeds comes from a list of

Clock Speeds dictated by the International Tow Tank Conference (ITTC). This set of speeds is

renowned in tow tanks worldwide and all associate members of the ITTC must apply too it when

carrying out test runs. These clock speeds are not directly proportional to speeds measured in m/s.

The results from both load case test runs carried out can be seen in Figures 22 and 23 of the

Appendix section of the document on Pages 13-15. Between each test run, it was vital that the tank

was allowed to settle. This would mean each test run was subject to the same ‘test environment’,

i.e. flat calm water. To aid the damping of the waves, there are planks of wood semi emerged that

run along one side of the tank, and also a large piece of foam at the top end. These help to absorb

the waves, and therefore aid with the settling of the water. At the bottom end of the tank, there is

the ability to artificially create waves using the wave machine if so desired. This machine can also be

set to absorption mode, allowing the tank to settle faster when the wave machine has been in use.


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Analysis of Results With these results, several calculations were then to be carried out which would allow the

results to be scaled from those ascertained at model scale up to what they would be for the full size

boat. All of these calculations are based upon the ITTC1978 Formula which states that:

Where;

Shown below in Figure 7 are the calculated results for a chosen lightships test run. These

involve the use of the numbered equations also shown below in Figure 8. The full results from all the

test runs from both cases can be seen in Figures 22 and 23 in the Appendix section of the document

on Pages 13-15..

Test Speed [m/s]

Fn Fn4 Rn Cf Rf [N]

Rv [N]

Rw [N]

Rt [N]

Ct

12 1.851 0.5298 0.0788 2.02 E6 0.0040 2.8420 4.214 6.481 10.695 0.0152

Equation N/A 1 14 2 3 4 5 6 N/A 7

Figure 7: Example of the results calculated in a Lightships test run

Where the above Equations reference to;

1-

2-

3-

4-

5-

6-

7-

Figure 8: Formulae used in the calculations shown above in Figure 7

In order to calculate the value for the wave drag, the value for the viscous drag component

was required. This in turn required the calculation of , involving the ITTC1957 Formula (shown

above in Figure 8 in Equations 3 and 4 ) and then multiplying this value by the form factor (1+k). The

calculation of the form factor is based upon Prohaska’s plot. This graph allowed (1+k) to be found, as

it is the intercept of the y axis for the plotted equation;

. The Prohaska plots for

the chosen test runs in both load cases are shown below in Figures 9 and 10 respectively.

Figure 9: Prohaska Plot of data used to ascertain a ; value for Lightships (1+K)

Figure 10: Prohaska Plot of data used to ascertain a . value for Full load (1+K)


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All the test run data points in the graph could not be included, for the reason that the

Prohaska plot is based on Fn4, this means that only up to a certain value for Froude Number, can

these results be plotted on a graph which gives a reasonable value for (1+k). Beyond this, the Froude

Number would have to be scaled to the power of 5 or even 6. The data that was selected for use in

the Lightship case was test runs 4, 5, 6, 7, 8 and 9. For the Full load case, the test runs used were; 5,

6, 7, 8 and 9. Using the test runs stated above, this gave a (1+k) value of 1.4826 for lightships and

1.5468 for Full load. From this the value for and subsequently can be worked out for both

load cases.

All the data required to scale the results up to full scale have now been calculated. The

method for scaling the results up too full scale involved scaling each individual component up. The

overall scale factor was 1:15, although this would have to be manipulated in order to calculate

various components. The equations used for scaling certain results from model to full scale are

detailed below;

And,

The other results just use the same equations as detailed in Figure 8, instead, they used the

full scale base data set instead of the model base data set (see Figure 1). Shown below in Figure 11 is

an example of the scaled up results calculated from the chosen Lightships test run in Figure 7. The

full set of scaled test run results for both cases can be seen in Figures 24 and 25 in the Appendix

section.

Test Speed [m/s]

Fn Fn4 Rn Cf Rf [N]

Rv [N]

Rw [N]

Rt [N]

Ct

12 7.1689 0.5299 0.0788 1.15E8 0.0020 4959.8 7353.5 22422 29775 0.0123

Figure 11: Example of the results calculated in the Lightships test run scaled up to full scale from model

From here, a graph of the three resistance components (Viscous, Wave and Total) was

drawn up against Froude Number for both load cases at full scale. These two graphs are shown

below in Figures 12 and 13 respectively.

Figure 12:Lightship Resistance Curves Figure 13: Full Load Resistance Curves

As well as this, a comparative graph was plotted for total resistance against Froude number

between the two load cases at full scale. This graph is displayed overleaf in Figure 14.


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Figure 14: Graph showing the differences in Total Resistance between the two load cases at full scale

From these three graphs it is seen that the resistance components all increase, but as

predicted by theory, the Wave drag component becomes more predominant as Froude number

increases. This happens around a Froude number of 0.35, which happens to be the hull speed of the

vessel. This point is known as the prismatic hump, which is defined as;

The hull waterline length The wave waterline length

Therefore, once the vessel surpasses it’s hull speed, the wave length is shorter than that of

the vessel. This leads to an increase in the wave drag component, and this will continue to increase

sharply until the vessel begins to plane. The vessel begins to plane when it’s speed starts to create

enough lift, creating an angle of attack, which allow the vessel to plane. This begins to happen at a

Froude number of around 0.58 for this hull form. After this, the resistance of the vessel will increase

at a lower rate than what would have been predicted, until the waves created by the hull begin to

superimpose, leading to the wave becoming twice the size, due the concept of superposition [3]. The

theory behind superposition can also partly explain why the wave drag decreases, as at the Froude

number of the range 0.58 - 0.8, the waves created by the bow and the stern of the hull match up at a

cycle of λ/2, and therefore cancel out, lowering the wave drag component. At Froude numbers

outside this range, the waves cycles match up perfectly and superimpose to create larger waves, and

therefore more wave resistance. The resistance will also decrease due to there being less surface

area of the model in the water, due to the lift created when the vessel planes.

There is a set of a data measured that helps back up the point that the vessel is trying to

plane. This is the measured trim angle of the boat, where a positive value meant the bow of the boat

was trimming upwards out of the water. At a Froude number of around 0.44 for both lightship and

Full load cases the trim angle for the vessel becomes positive and begins to increase as Froude


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number and speed increase. The full data set for the measured trim angle can be seen in Figure 26 in

the Appendix section of the document on Pages 13-15.

In terms of the effects of the two sets of results yet to be discussed (heave and side force),

the full recorded results from the test runs are displayed in Figure 27 in the Appendix section on

Pages 13-15.

The side force neglects to have any great affect on the results of interest, but the result it

would affect would be total drag if the model was misaligned. It would be of great interest if the

vessel being tested was a sailing vessel or a large container ship, as side force plays a major factor in

the design of these vessel types. However for the model tested, this was not a key factor. The

positive side force is taken in the Port to Starboard direction. The last results of each run show a

dramatic decrease in Side force (as shown in Figure 27). This is due to the boat naturally self aligning

as a result of the speed and volume of water flowing over the hull.

The heave of the boat measures the sinking or rising of the boat in relation to the carriage. It

can be seen that on the whole, the heave values for the test runs all seem to be negative, which

would suggest that the boat is sinking. When the value for heave is at negative maximum (test run

11 and Froude number 0.53), this is just as the vessel is beginning to plane. After this, the trim of the

vessel increases into positive numbers, and because the trim of the vessel will affect the heave, the

heave also begins to move towards positive numerical results.

Applying the Analysis By applying the data gathered and the calculations carried out, it is possible to predict what

power the vessel will need at full scale to run at a desired speed. Many tests like this one are

predominantly carried out in order to see how the hull form performs at a varying level of speed,

and perhaps even varying sea conditions in more advanced tests. However, using the data collected

over the two load conditions, the power requirement of the tested vessel can be found via the use

of the formula;

This calculation was carried out for both load cases and all test speeds. The values for a

selected range of results are shown below in Figures 15 and 16 respectively. It should be noted that

the column ‘Epower’ shown does not take into account the efficiency of the drive train of the vessel.

For this assignment the efficiency was dictated as 55%. This means that the actual power installed

into the boat, ‘Rpower’, would have to be times as powerful as the initial calculated power

‘Epower’. Also, the power shown in the tables below is the total power required, therefore one

engines required power would simply be half that shown in the table.

Figure 15: Power Calculation for the Lightship Load Case Figure 16: Power Calculation for the Full Load Case


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The service speed of this vessel, if it’s application was to be for Pilot or Patrol boat purposes,

would need to be around the 20 knot mark, with a top speed slightly higher than that. The area of

low wave drag (as previously discussed on Page 8), and it’s associated Froude number and speed

was also taken into account. The end of this area of low wave drag gave a speed of 21knts at full

load, which is a perfect upper boundary for the vessel application and the desired service speed.

For the chosen maximum speed (24 knots), it was found that the required engines were of

around a 600kW power rating each for maximum speed. For these reasons, the suited engine would

be a Volvo Penta D13-900 series engine. This engine is rated at 636kW and is 1.089m wide, taking up

2.203m3 of space per engine [1]. This engine is overpowered as compared to the initial estimate, as to

give a higher torque value at the desired power required for service speed. All of the powering

calculations were based on the full load condition. The difference in weight between the two load

cases roughly equates to a tank of fuel for the boat (around 4100L). Because of the weight

difference, the vessel will have two separate max and service speeds. Although these do not vary

greatly, the two main speeds for the vessel in both load cases are detailed below in Figure 17.

Case Load Service Speed [Knots] Max Speed [Knots]

Lightships 21 24

Full Load 20 23.5 Figure 17: Chosen Service and Maximum speeds along with the Load Case of the vessel

Another important factor to be considered is how well the engine will perform in terms of

fuel consumption. The detailed Specific Fuel Consumption of the engine is 209g/kWh [1], which for a

diesel engine is better than average. Detailed below in Figure 18 are the two differing values for fuel

consumption between the service speed and maximum speed of the vessel.

Service Speed (1900RPM) Max Speed (2200RPM)

Fuel Consumption [Litres/Hour] 98 145 Figure 18: Calculated Fuel Consumption

[1] of the engine at the two main speeds of the vessel

Using this data, it can be said that if the boat was to travel at its service speed of 20 Knots,

then the boat would have a range just over the 800 Nautical Mile mark. This is a good range for the

vessel to have, given that its application may lead to work far offshore.

This data was found by cross referencing the data from the three graphs shown overleaf.

The graph in Figure 19 overleaf shows the required Power vs Speed for the calculated results. This

information is then transferred to the graphs shown on the right and left hand side of the page

overleaf in Figures 20 and 21 respectively. These show the expected power at the crankshaft and

propeller for the engine, and thus a value for fuel consumption can be found by translating the RPM

of the engine at a given prop load down.


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Figure 19: Graph showing the speed of the vessel against the Required power for both load cases

Figure 20: Power Curve for the Volvo Penta D13-900

[1] Figure 21: Fuel Consumption Curve for the Volvo Penta

. D13-900 [1]


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Conclusion With the results, there has to be a certain amount of precaution taken. This is mainly due to

external factors that may affect the results taken for the model. The most predominant of these is

motions on the carriage. Because the carriage runs on rails, when it passes over a joint in the rail, it

causes the whole carriage to vibrate. This vibration will most likely be picked up by the

Dynamometers and may affect the results of drag and or side force produced. Also, the movement

of people on the carriage may upset the results at low speeds and during the calibration of the

equipment used to measure the various components. Therefore it is vital that the whole carriage

does not move during the calibration of the equipment, as if there was to be a slight movement, this

would lead to a discrepancy in the results.

It was important also to note that for scaling the results, the boats must be in a dynamically

similar condition, i.e. the geometry of the full scale must scale exactly to that of the model or vice

versa if the full scale boat had been designed, and the builders or owner wished to test the model.

Overall, the results calculated show that the theory of the ITTC1978 is followed, as it is clearly

seen in Figure 14 on Page 8 of the report that as the speed of the vessel increases, so does the total

drag, and the wave drag component begins to become the majority component out of the measured

components as speed increases as shown in Figures 12 and 13 on Page 7 of the document.

In terms of the calculations carried out and the values obtained for the value of the form

factor (1+k), there are two reasons why they may seem too high (usual (1+k) 1.2). Firstly, the

model is being towed at such low speeds, with the drag only measuring less than 3 Newtons. These

small changes in drag can lead to a scattered Prohaska Plot, and therefore a higher value for (1+k)

value then would be expected. Conversely, it is also important that (1+k) is measured at low Froude

numbers; therefore there is no way that a more sensible value for (1+k) could be obtained without

either increasing the speed of the model (which would increase Froude number, so no good), or

increasing the length of the model. Increasing the length of the model would allow larger values of

drag to be obtained at low speeds, and therefore low Froude Numbers. Secondly, and perhaps more

explanatory, when tested vessels have an immersed transom, and large changes of cross sectional

area over a short distance (as seen in the bow), this can lead to higher (1+k) values being obtained.

In relation to the speeds chosen, the vessel’s most likely application is a pilot or fast patrol

boat. These boats need to have good speed so that they can get to their assigned ship quickly,

whether they are assisting it in an emergency or getting it into a port where a pilot is needed. It is

therefore important that the vessel can maintain a good speed in all conditions. Should the vessels

owners wish the boat to go say 2 knots faster, because of the nature of the resistance curve at this

point, the increase in total power would equate to around 160kW as to achieve the 2 knots extra.

This would impact the vessel, as the bigger engines that would be required will take up more room,

and also weigh a fair bit more, once the additional fuel is carried and also the sheer weight increase

that comes with installing the larger engines.

On the whole, the test results achieved over the two days of testing and the two load cases,

present no significant anomalies. However it could be seen that in the Lightships results (Shown in

Figures 22 and 24 on Pages 13 and 14 respectively) that two values of are negative. This can be

put down to the fact the forces measured are so small, and there may have been a slight jolt or

movement in the carriage, upsetting the data calculated. For this reason, it would be recommended

that before this test is carried out again that each individual test run be done a minimum of three

times, and an average taken from these results. This would help isolate any anomalies (e.g. an

unusually large jolt on the carriage) and give a more reliable set of data results.


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Appendix of Results

Figure 22: Full set of test and calculated data for the model scale ,,mmmH lightships load case

Figure 23: Full set of test and calculated data for the model ,,,?,,? scale Full Load case


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gf

Figure 24: Full set of test and calculated data for the full scale ,. =Designs lightships load case

Figure 25 Full set of test and calculated data for the full ,,,?,,? scale Full Load case


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Figure 26 : Full set of data recorded for Trim ; ; Angle for both load cases

Figure 27: Full set of data recorded for Side Force and ; ; Heave for both load cases

References

1) Volvo Penta Webpage

http://pie.volvopenta.com/ViewFileFrame.aspx?n=221375&r=2013-08-30-17-01-

08&t=PDF1P&a=47704712&p=T416&d=Product%20Bulletins&s=812292&model=D13-

900&transClassId=9&segmentId=13&lang=en-GB

2) Principles of Yacht Design, Larsson and Elisson (2007)

Chapter 5, pages 60-75

3) Principle of superposition

http://en.wikipedia.org/wiki/Superposition_principle

http://pie.volvopenta.com/ViewFileFrame.aspx?n=221375&r=2013-08-30-17-01-08&t=PDF1P&a=47704712&p=T416&d=Product%20Bulletins&s=812292&model=D13-900&transClassId=9&segmentId=13&lang=en-GB



http://en.wikipedia.org/wiki/Superposition_principle

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Resistance and Propulsioin Assignment 2014