university of newcastle upon tyne department of naval ... t.e... · department of naval...

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UNIVERSITY OF NEWCASTLE UPON TYNE

SCHOOL OF MARINE TECHNOLOGY

DEPARTMENT OF NAVAL ARCHITECTURE & SHIPBUILDING

A TECHNO-ECONOMIC MODEL OF SHIP OPERATION WITH SPECIAL REFERENCE TO HULL ANDPROPELLER MAINTENANCE IN THE FACE OF UNCERTAINTY

by

TOR E. SVENSEN

VOLUME II

MARCH 1983

A Thesis submitted to the University of Newcastle upon Tyne for the Degree ofDoctor of Philosophy

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SILLERUD, B.O., "The Economic Consequence of Ship Service Speed Reduction",Norweg~an Maritime Research, No.1, 1974.

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WAGLE, B., "A Statistical Analysis of Risk in Capital Investment Projects",Operational Research Quarterly, Vol. 18, 1967.

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Appendix A

A-I INTRODUCTION

-The various methods available for investigating the relationship

between hull roughness and drag have been described in Chapter 1. None of

these methods have on their own provided an entirely satisfactory answer

to the problem. Since Telfer proposed his one third power law

relationship between roughness and drag, the only major improvement until

very recently has been the ITTC correlation formula for hull roughness,

although it is now accepted that this formula includes other model to ship

correlation factors as well. Faced with this uncertain basis for the

economic mqdelling of hull maintenance strategies,a search of ways of

obtaining more information was initiated. This search finally resulted in

an opportunity being created for the undertaking of a full scale

performance monitoring experiment on two sisterships with a known

difference in hull surface condition. Following the successful outcome of

the first experiment, as reported in Reference (82), it was decided to

repeat the monitoring exercise after the two vessels had spent another 12

months in service. The two objectives of this experiment were, firstly to

obtain a confirmation of the results obtained for the two ships in the

previous year and secondly to relate any change in speed performance to

changes in the condition of each ship's underwater hull. Neither of the

vessels were drydocked during the 12 month period between the twoexperiments, and the change in hull condition therefore would reflect a

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change in service only. An additional benefit from a second experiment

was the further evaluation of the monit'oringsystem itself to see whether

some of the procedures could be improved.

In both experiments an independent observer was placed on each ship for

the purpose of continuous data collection and'analysis during the deep sea

passages of a complete roundtrip. Both vessels were on each occasion

making identical voyages between Europe and the Far East at approximately

the same time of the year.

The general principles behind a system for monitoring speed and power

performance have been discussed thoroughly in References (43) and (83).

The basic parameters to be monitored are speed and power. In addition,

corresponding readings of shaft revolutions and fuel consumption are taken

as a measure for checking the consistency of the speed and power data, and

recordings are made of draught, trim and weather for the purp~se ofcorrecting speed and power to a common basis for comparison. Two main

options are availale in the final interpretation of the recorded data. If

the vessel is operating at nearly constant power, the data can be

corrected to a constant power basis, and each voyage will then normally

yield one single average point on the speed-power curve. On the other

hand, if the vessel is operating over a range of powers during its round

voyage, then with an adequate number of data readings, a complete

speed-power curve can be constructed for each voyage and used forcomparison. A third and useful way of presenting the results is to

mile by integrating thecalculate the energy requirement per nautical

power multiplied by the time over the total round voyage and divide by thedistance. Every voyage will then yield a specific energy requirement per

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mile, and one voyage can be compared with the next, provided each voyage

is corrected to the same average speed.

A-2 VESSEL DESCRIPTIONS

SHIP PARTICULARS:Cel!ular type container ships, maximum capacity 2865 TEU, carrying 3 high

on deck.

Overall Length = 288.75 m

Length B.P. 274.32 m

Breadth = 32.26 m

Depth = 24.60 m

Maximum Summer Draught = 13.03 m

Average Operating Draught 11.00 m

Deadweight at max.Summer Draught = 49600 t

Displacement at 13.03 m draught = 73600 t

Displacement at 11.00 m draught = 58900 t

Block coefficient = 0.623

Wetted surface area at 11.0 mdraught

2= 11100 m

Transverse projected area abovewaterline at 11.0 m draught AT

2= 900 m

Design Speed = 26.5 knotsAverage operating speed = 21.0 knots

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MACHINERY:

2 Steam TurbinesDesign Output 29825 kW/40550 HP (metric) each at 136 RPM

Max. Output 32810 kW/44610 HP (metric) each at 140.4 RPM

PROPELLERS:

Diameter = 6200 mm

Pitch = 7500 mm

No. of blades = 5

Approximate Quasi PropulsiveCoefficient in operating range20 - 25 kn = 0.67

A-2.1 UNDERWATER HULL MAINTENANCE HISTORIES

SHIP A:

Coated with a Vinyl Organo-Tin antifouling prior to delivery in

December 1972 and subsequently recoated with the same at guaranteedrydocking in 1973. At normal maintenance drydocking in June 1975 the

complete underwater hull was coated with Intersmooth SPC 1 and was also

recoated with the same at maintenance drydocking in 1977. Due to some

detachment both sides were grit blasted during maintenance drydocking in

June 1979 and the complete underwater hull recoated with Intersmooth SPC4.

Outdocking roughness was measured in June 1979 yielding a result of 136 rmAHR with 149 rm for the flats and 129 rm for the sides.

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SHIP E:

Coated with a Vinyl Organo-Tin antifouling prior to delivery inNovember 1973, and recoated with the same at guarantee drydocking in 1974.During maintenance drydocking in 1976 the underwater hull was coated with

a High· Performance Chlorinated Rubber antifouling and the same

specification was used at normal maintenance drydocking in 1978.

From the above specifications it can be seen that at the time of the

first experiment in July/August 1979, Ship E had been through one

drydocking less than Ship A.

A-3 INSTRUMENTATION FOR MONITORING

Only the ships' own instrumentation was used. The vessels were both

fitted with Jungner AEM-1 torsion meters on each propeller shaft. Priorto the start of the first experiment, a malfunction in one of the torsion

meters on ship A was repaired, and the instruments on both shafts

re-calibrated by the manufacturer. In the case of ship E, no malfunction

had ever occured, and a simple zero check was made at the end of the

voyage. Any relative change in calibration between the instruments on

each shaft could easily be detected during the voyage, and this eliminated

the·need for a zero check before as well ,as after the completion of the

voyage. In the second experiment a zero calibration check was carried out

on both vessels immediately before the start of each voyage by arepresentative of the manufacturer. No significant drift in thezero-point had occured during the 12 month period and this confirmed the

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high reliability of this particular make of instrumentation. Shaft

revolutions were measured using double sets of counters mounted on each

gearbox and with an electronic repeater for each shaft positioned in the

engine control room. Fuel consumption was measured by the use of

flowmeters positioned at the point of fuel entry to each boiler. A double

check on fuel consumption was made by taking readings from the daily

settling tanks. Observed speed over the ground was calculated by the use

of Magnavox MX 1102 satellite navigator, and tog speed was measured using

a Jungner pitot type log. An anemometer was fitted, but its positioning

caused inaccurate readings for certain wind directions, and wind speeds

were therefore recorded on the basis of observation of sea state as

customary. For the purpose of continuous data checking, a power diagram

was used throughout the voyage for plotting difference curves betweenobserved speed, log speed and speed derived from the power diagram. This

enabled errors in power, speed or RPM readings to be spotted quickly and

inaccurate data to be eliminated from the final analysis. Prior to the

monitoring exercise, a series of power diagrams were constructed for a

range of values of apparent wake on the basis of the open water

characteristics of the propellers. The correct diagram to be used and the

corresponding value of apparent wake was hence found, using a trial and

error process with the recorded values of observed speed, power and RPM at

the start of the monitoring exercise.

A-4 EXPERIMENTAL PROCEDURE

The system set up on board was based on a satellite fix to satellitefix recording procedure. The reason behind this, rather than using a

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fixed interval procedure, (eg: watch-by-watch), was to eliminate the

accumulated error introduced in using a dead reckoning position between

satellite fixes. This error can, after two hours, be as much as one mile.

At the time of satellite fix, readings of log speed, RPM, power and fuel

consumption with corresponding temperature were recorded. Time between

satellite fixes could vary between two ana twelve hours, but on average

was 4 to 6 hours. In order to compute a good average value of power

bet~een fixes, a continuous log of power readings was kept in the engine

control room. Recordings were taken every hour in the first experiment

and reduced to every half our in the second experiment. Weather and ship

motion recordings were made on a watch-by-watch basis by deck officers, so

that each inter-fix period could be associated with a particular set of

weather conditions, and corrections could later be made to a standard

basis.for comparison. Only data corresponding to wind strengths less than

and including Beaufort 5 have been used, and no shallow water data or data

including substantial course changes have been included in the final

analysis. The limiting value of Beaufort 5 has been applied in accordance

with the results of Kwon's work, as reported in References (84) and (85).

Kwon concluded that the added resistance due to waves becomes significant

for full form tankers at a fully developed sea state above level 4 on the

Beaufort scale, and for fine form container ships at a level above

Beaufort 5, provided there are no significant ship motions. Draughtreadings were made on departure and .arrival in ports. Recordings were

also made of daily fuel consumption and changes to ballasting condition

for the purpose of calculating draughts on a daily basis throughout thecomplete voyage.

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A-S DATA ANALYSIS

A-S.l PROCEDURE FOR RELATING SPEED AND POWER

In both experiments the two vess~ls were operating over a wide range ofengine power during the voyage, and rather than correcting to a standard

power for comparison, the data have been used to construct a speed-power

curve for each vessel.

Corrections to power have been made for the effect of direct wind

resistance and changes in draught. The wind resistance corrections have

been made on the basis of recent wind tunnel tests for container ships,

[Reference (34)]. From the general wind tunnel test data, a particular

correction curve for the vessel type employed in this experiment wasderived, based on the projected transverse area above the waterline as

calculated from drawings. The curve of resistance coefficient Cx against

angle of relative wind resistance is given in Figure (A-l). When

correcting power to a basis of still air wind resistance, account was also

taken of the change in propulsive efficiency with added resistance. This

correction curve was derived using the open water characteristics of the

propellers and is shown in Figure (A-2). The corrections to power due to

changes in draught were made to a standard draught value of 11.Om. The

required correction curves were derived using the original tank test

results for these ships and were expressed as percentage change in power

per 0.1 m change in draught over a range of speeds. A mean curve wasproduced for every 0.5 m step in draught. The correction curves for

- 374 -

variation in draught are shown in Figure (A-3), and the final tabulatedcorrections to power are given in Column 24 of Tables (A-IS) to (A-21).

Speed over the ground, as calculated from individual position fixes

obtained from the satellite navigator, has been used as the principalmeasure of speed. A basic assumption for fitting a mean speed-power curve

to the corrected set of power date is that with a sufficient number ofinter-fix recordings in both directions on a complete round voyage, the

net effect of ocean currents will be zero. From routing charts the ocean

currents on the roundtrip voyage covered in this experiment were found to

be predominantly "following" on the outward bound part of the voyage and

"against" on the homeward bound part. Hence as long as an equal number of

inter-fix periods are obtained "out" and "home", and both data sets are

equally distributed over the speed and power range included in the

analysis, then this.assumption will be valid.

In the first experiment, the above conditions for averaging out the

effects of ocean currents were satisfied. However, a different situation

arose with the second experiment in which there was not an equal

distribution of outward and homeward bound data over the complete speed

and power range. In the case of Ship A, all the outward bound data were

at relatively high speeds and the homeward bound data at low speeds, while

for Ship E, the low speeds occured outward bound and the higher range

homeward bound.

As a result of this different situation a more detailed examination had

to be made of ocean currents, since an error in the applied current

correction would have significant effect on the slope of the deduced

- 375 -

speed-power curve.

The method adopted was to make use of the pitot log distance reading

and calculate the difference between observed distance and log distance

for each leg of the voyage, and hence obtain the difference between mean

observed speed and mean log speed. This mean difference can, however, not

be used as a measure of average current since the recorded log speed will

neatly always contain a calibration error. This calibration constant is

determined by assuming equal magnitude of average strength of currents on

the outward and homeward bound leg of the voyage. The average net current

bias, with which all the recorded observed speeds are to be corrected, is

subsequently calculated for the total voyage of each vessel.

As a result of this analysis, two sets of measurements of speed through

the water were obtained. In this particular exercise, the observed speed

was considered to be the most accurate and most reliable measurement of

speed and was therefore used as the primary measurement. The log speed

was used to obtain the current corrections as described above and as a

secondary measurement of speed to be used as a ~onsistency check.

This method of correcting for the effects of ocean currents has

Subsequently been applied to the complete data set of each vessel from

both experiments.

- 376 -

A.-5.2 ANALYSIS OF SPEED AND POWER DATA FROM THE FIRST EXPERIMENT

A-5.2·.1 SPEED AND POWER RELATED

For ship A, a total of 90 good weather interfix periods were obtained,

and for ship E the corresponding number was 78. In both cases, the

periods covered a total of approximately 10,000 miles of deep sea passage.

Corrections to power were made for the effect of direct wind resistance

and changes in draught as described in the previous section. Malfunction

of the speed log resulted in only 71 and 70 interfix periods for Ship A

and Ship E respectively being suitable for the calculation of the current

correction. The calculations for the current correction and speed log

calibration are presented in Tables (A-I) and (A-2).

TABLE (A-I) CURRENT CORRECTION SHIP A, FIRST EXPERIMENT

AVERAGETOTAL TIME OBS DISTANCE LOG DISTANCE (OBS SPEED-LOGSPEED)

OUT 182.8 hrs. 3749.1 miles 3670.5 Miles 0.43 knots

HOME 211.6 hrs. 4313.4 miles 4289.1 miles 0.11 knots

0.43-0.11Average net current bias = = 0.16 knots (following out and

2 against home)Log calibration constant = 0.43-0.16 +0.27 knots (Ls e, speed log is

0.27 knots slow)

- 377 -

TABLE (A-2) CURRENT CORRECTION SHIP E, FIRST EXPERIMENT

AVERAGETOTAL TIME OBS DISTANCE LOG DISTANCE (OBS SPEED-LOGSPEED)

OUT 106.0 hrs. 2289.2 miles 2239.4 miles 0.47 knots

HOME 266.9 hrs. 5984.9 miles 5868.7 miles 0.44 knots

0.47-0.44Average net current bias = --------

2= 0.015 knots (ie: negligible)

Log calibration constant - +0.45 knots (ie: speed log is 0.45 knots slow)

After correcting observed speeds for the average net current bias a

mean speed power curve was fitted based on logarithmic regression.

The following equations between speed power were obtained:SHIP A: :1>.07'1

PM= 1.808V with a correlationcoefficient r=0.925

SHIP E: 3.~PEl= 1.882V with correlationcoefficient r=0.926

P = power delivered to the propeller measuredin kW (allowing for 2% loss in shafting).

V = observed speed corrected for average currentbias, measured in knots.

For the .same speeds the difference in power between those two meanlines over the speed range is substantially constant and

= 10.7% [see Figure (A-8)]P~I

- 378 -

Compared with a similar value of 11.4% obtained when currentcorrections were not applied this demonstrates that current corrections

are not critical when recorded data in both current directions show an

equal distribution over the speed/power range.

A-5.2.2 CALCULATION OF DIFFERENCE IN ENERG~ CONSUMPTION USING TORSION

METERS

This method of calculation has been adopted, as explained in theintroduction to this chapter, in order to yield a single representative

number as a measure of performance for comparison purposes between the twoships.

(average power) x (time)represents the energy per nauticalmile to drive the ship.(corrected observed

distance)

Table (A-3) CALCULATION OF ENERGY REQUIREMENT PER MILE, FIRST EXPERIMENT

SHIP A SHIP E

Eo (,Power x Time 9.881 x la kW hr 12.232 x 10 kW hrTotal Distance 10107.9 miles 9759.4 milesTotal Time 488.40 hrs 440.86 hrsAverage Speed 20.70 knots 22.14 knotsAverage Power 20230 kW 27740 kW

3 3Power x Time 0.9776 x 10 kW hr 1.25341 x 10 kW hrDistance mile mile

A higher average speed and power will result in a higher energy

requirement per mile for the same ship, and this is corrected by using theregressed mean speed power curve.

- 379 -

TABLE (A-4) CORRECTION FOR DIFFERENT MEAN SPEED

(Correcting Ship E to the mean speed of Ship A)

Mean Speed 20.70 knots 22.14 knots .Power 22260 kW 27410 kW

3 3Power x Time 1.0754 x 10 kW hr 1.2381 x 10 kW hr

Distance mile mile

333.Hence correction = 1.2381 x 10 -1.0754 x 10 = 0.1627 x 10 kW hr

mile

which is the extra energy consumption per mile due to the higher speed

only. The corrected energy consumption per mile is given in Table(A-5).

TABLE (A-5) ENERGY REQUIREMENT PER MILE FOR SHIP A AND SHIP E

FIRST EXPERIMENT

SHIP A SHIP E

3 3Corrected Power x Time 0.9776 x 10 kW hr 1.0907 x 10 kW hrDistance mile mile

(at 20.70 knots)

In percentage terms this difference is 11.6%, which is in satisfactory

agreement with the mean difference of 10.7% in power between the twospeed/power curves.

A-5.2.3 AVERAGE SPEED AFTER CORRECTING TO A CONSTANT POWER BASIS

In statistical terms a more satisfactory single number representationof the vessel is obtained by calculating the average speed, after first

- 380 -

having corrected each individual speed-power point to a selected standard

power value using the speed-power curve from regression analysis.

Effectively, this is the same as taking the centroid of the data set used

in the regression analysis as a representative number of the completesample, or in other words, transforming the speed and power values into a

logarithmic scale and taking the mean of each. Transformed back into the

normal speed and power scales this will yield a single representative

point for each vessel on e~ch occasion. Using one vessel as basis, the

average speed and power value for the second vessel can subsequently be

corrected to the same basis and the difference in performance between thetwo vessels can be calculated.

The results for Ship A and Ship E in the first experiment are shown inTable' (A-6).

TABLE (A-6) RESULTS FOR SHIP A AND SHIP E AFTER CORRECTING TO A

CONSTANT POWER BASIS, FIRST EXPERIMENT

POWER CORRECTEDSPEED (knots) POWER (kW) TO THE SPEED OF

.. SHIP A

SHIP A 20.723 20150 20150SHIP E 22.100 27270 22350

In percentage terms the difference is 1~.9%. This is in good agreementwith the results obtained from the previous two methods.

- 381 -

A-5.3 ANALYSIS OF SPEED AND POWER DATA FROM THE SECOND EXPERIMENT

A-5.3.l SPEED AND POWER RELATED

For Ship A a total number of 109 good weather interfix periods were

obtained, covering a total of about 10,000 miles of deep sea passage, and

for Ship E the corresponding numbers were 88 good weather interfix periods

and approximately 8,000 miles of deep sea passage. Again, both vesselswere operating over a wide range of engine power, but the distribution of

data over the speed-power range on each leg of the voyage was unequal as

discussed in Section A-5.l. It was therefore essential that the average

net current bias was calculated and corrected for prior to obtaining a

mean speed-power curve based on logarithmic regression techniques.

Malfunction of the speed log resulted in only 105 and 85 of the

interfix periods for Ship A and Ship E respectively being suitable for the

calculation of current correction. The calculation for current correction·and speed log calibration are presented in Tables (A-7) and (A-8).

TABLE (A-7) CURRENT CORRECTION SHIP A, SECOND EXPERIMENT

AVERAGETOTAL TIME OBS DISTANCE LOG DISTANCE (OBS SPEED-LOG SPEED)

OUT 212:.8hrs 4770.8 miles 4670.1 miles +0.48 knots

HOME 234.4 hrs 4766.0 miles 4894.0 miles -0.09 knots

- 382 -

0.488-(0.08)

2= 0.28 knots (following out and

against home)Average net current bias = -----------

L·ogcalibration constant = 0.48-0.28 = 0.20 knots (slow)

TABLE (A-8) CURRENT CORRECTION SHIP E, SECOND EXPERIMENT

AVERAGETOTAL TIME OBS DISTANCE LOG DISTANCE (OBS SPEED-LOG SPEED)

OUT 224.0 hrs. 4327.3 miles 4303.0 miles 0.11 knotsHOME 153.4 hrs. 3547.9 miles 3558.1 miles -0.07 knots

0.11-(0.07)Average net current bias = ----------

2= 0.09 knots (following out and

against home)

Log Calibration constant = 0.11-0.09 = +0.02 knots (i.e. negligible)

After correcting observed speeds for the average net current bias a mean

speed-power curve was fitted, and the following two equations between

speed and power were obtained:

SHIP A: 2.'90PAl= 2.404V with a correlation

coefficient r = 0.920

SHIP E: with a correlationcoefficient r = 0.979

For the same speeds the difference L power between these two meanlines over the common speed range is substantially constant and

= 10.2% [see Figure(A-8)]

- 383 -

A-5.3.2 CALCULATION OF DIFFERENCE IN ENERGY CONSUMPTION USING TORSION

METERS

In Section A-5.2.2 a calculation was made for the energy required per

nautical mile to drive each ship in order to yield a single representative

number for comparison purposes with the data collected in the first

experiment. In order to enable a similar comparison between the two ships

in the second part of the experiment and also to enable a comparison of

the results for the same ship after a period of 12 months, this

calculation was repeated for the new set of data from the second

experiment.

(average power) x (time)represents the energy pernautical mile to drive the ship(corrected observed

distance)

TABLE (A-9) CALCULATION OF ENERGY REQUIREMENT PER MILE, SECOND EXPERIMENT

SHIP A SHIP E

E- l.Power x Time 10.895 x la kW hr 9.244 x la kW hrTotal Distance 10197.4 miles 8059.5 milesTotal Time 479.2 hrs 387.5 hrsAverage Speed 21.28 knots 20.80 knotsAverage Power 22740 kW 23850 kW

3 3Power x Time 1.0684 x la kW hr 1.1469 x la kW hrDistance mile mile

In order make the comparison on the same basis, all values are

corrected to the meanspeedof Ship A in the first experiment of 20.70 knots.

- 384 -

TABLE (A-10) CORRECTION FOR DIFFERENT MEAN SPEED

SHIP A SHIP E

Mean Speed 20.70 knots 21.28 knots 20.70 knots 20.80 knotsPower 20690 kW 22470 kW 22720 kW 23050 kW

Power x Time 0.9993 x 103 1.0558 X 103 1'.0997 X 103 1.1080 X 103distance kW hr kW hr kW hr kW hr

mile mile mile mile

Correction Ship A: 3 3 31.0558 x 10 -0.9993 x 10 = 0.0565 x 10 kW hrmile

3 ~ 31.1080 x 10 -1.0977 x 10 = 0.0103 x 10 kW hrmile

Correction Ship E:

The corrected energy consumption per mile is given in Table (A-II).

TABLE (A-II) ENERGY REQUIREMENT PER MILE FOR SHIP A AND SHIP E,

SECOND EXPERIMENT

SHIP A SHIP E .

3 JPower x Time 1.0119 x 10 kW hr 1.1366 x 10 kW hrCorrected mile mileDistance

In percentage terms this difference is 12.3% between the two ships.

A-5.3.3 AVERAGE SPEED AFTER CORRECTING TO A CONSTANT POWER BASIS

As explained in Section A-S.2.3, a more satisfactory single number

representation of the vessel performance in statistical terms is obtained

- 385 -

from the centroid of the speed/power data when transformed to a

logarithmic scale for use in the linear regression analysis. The results

for Ship A and Ship E in the second experiment are shown in Table (A-12).

For the purpose of comparison with the results of the previous experiment,

the speed and power values have been corrected to the speed of Ship A in

the first experiment using the regressed speed/power curves.

TABLE (A-12)" RESULTS FOR SHIP A AND SHIP E AFTER CORRECTING TO A

CONSTANT POWER BASIS, SECOND EXPERIMENT

POWER CORRECTED TO THESPEED (knots) POWER (kW) SPEED OF SHIP A IN THE

FIRST EXPERIMENTSHIP A 21.267 22420 20750SHIP E 20.626 22490 22800

Iripercentage terms the difference between the two vessels is 9.9%

which is in good agreement with the first method of comparing the

individual speed/power curves and in reasonable agreement with the results

obtained from the calculation of energy requirement per mile.

A-5.4 COMPARISON OF SPEED AND POWER PERFORMANCE RESULTS FOR THE TWO

EXPERIMENTS

"A comparison between the two mean speed/power curves from the first

experiment, as analysed in Section A-S.2 and shown in Figures (A-4) and

(A-5), shows an average difference between the two ships of 10.7%. The

- 386 -

same analysis performed on the data collected 12 months later, as shown in

Section A-S.3 and Figures (A-6) and (A-7), indicatesan average difference

between the two ships of 10.2%. An individual comparision of each vessel

after this 12 month period shows that the performance of Ship A has

deteriorated approximately 2% while Ship E shows an average deterioration

of about 1.S% in power terms, although these rigures are too small for any

conclusions to be drawn about the change in performance of each ship over

the'12 month period.

In the case of Ship A the mean speed/power curves for the two

experiments are parallel, while for Ship E this is not strictly true.

Furthermore, the speed/power curves cover slightly different ranges of

A mean speed/power curve based on logarithmic regression

compromise to obtain a best fit line, since a truenspeed/power curve of the form P = k.V will have a continuously changing

speed and power.

is already a

exponent N with varying speed V, and an attempt to extend the curve beyond

its regression boundaries will introduce errors. It therefore follows

that a single number representation of change in performance evaluated on

the basis of speed/power curves only will not be an entirely accurate andreliable measure.

A simple and more practical method of obtaining a single number for

COmparison purposes is the calculation of energy requirement per mile as

presented in Sections A-S.2.2 and A-S.3.2. In these calculations each

interfix period carried equal weight in the analysis, and the mean

speed/power curve only is utilised in the process of correcting the values

to the same basis of mean speed. If a speed/power curve is not available,

the approximate relationship P = k_Vn can be used.

- 387 -

In Section A-5.2.2 it was shown that based on the calculations ofenergy consumption per mile there was, in the first experiment, a

difference in performance between the two vessels of 11.6%. After a

period of 12 months in service this difference had increased to 12.3% as

shown in Section A-5.3.2. An individual comparison of the results of each

vessel by this method has shown that the performance of Ship A

deteriorated by 3.5% over this 12 month period, while Ship.E deteriorated

by 4.2% over the same period. This method has the advantage of making no

initial assumption about the relationship between speed and power, and the

calculation procedure is simple. An error will, however, be introduced

due to the fact that no account is taken of the gradually increasing rate

of change in the energy requirement per mile with an increasing speed.

The final method, believed in statistical terms to be the most correct,

has yielded a single representative number for each vessel on each

occasion after first transforming the speed and power values to a

logarithmic scale and taking the mean of each. In percentage terms the

difference in performance between Ship A and Ship E in the first

experiment was found to be 10.9%, and in the second experiment the

difference had been reduced to 9.9%. An individual comparison of each

vessel between the two experiments indicated a deterioration of 3.0% forShip A and 2.0% for Ship E.

Clearly, this method is only correct if the linear relationship between

the transformed value of speed and power is true.

- 388 -

A-5.5 STATISTICAL INTERPRETATION OF THE MEASURED PERFORMANCE RESULTS

The performance monitoring experiment has yielded a set of measurements

of the two variables speed and power on the sisterships on two occasions a

year apart. Each set of measurements can be regarded as an independent

group giving a total of 4 groups obtained from the complete experiment.

The data analysis has hitherto been centered around the analysis within

eacH group, and the comparisons made between groups have simply been based

upon the "within group" results in terms of mean values. The regression

lines fitted to each group have been based upon the general linear model

(t - 1, ••••• k , i - 1, ••••• n )

where Speed is the independent variable and takes the transformation X =In(Speed) and Power is the dependent varia.blewith the transformation Y =

In(Power) and Zttrepresents the random residual for each observation. This

residual variable complies with the following 4 assumptions.

1) Expected value of Z~i is zero for all t and i

2) ·AII values of Ztt are mutually independent

3) Variance of Z~[ is constant for all t and i4) The variable Z~, is normally distributed

In the general case with t groups of bivariate observations and

regression lines fitted to each individual group acc0rding to the above

model, an obvious natural extensLon to this analysis is to consider

whether it is possible for a single linear regression line Y = ~ + ~ X torepresent all the t groups of observations. In other words, we have thelinear hypothesis:

- 389 -

Ho (0(1 :Ill 0(2.= •••••• = o(lrl and PI""11>1" •••••• "" ~It. )

The test of th~s hypothesis will yield an answer to the question of

whether all the groups can in fact be represented by a single regression

line, or alternatively, the level of significance at which the null

hypothesis is rejected and the alternat'ive hypothesis of separate

individual regression lines for each group can be accepted. The abovelin~ar hypothesis is most conveniently split into 3 parts where each part

can be tested separately.

(1) Null Hypothesis Ho(l): The regression lines are parallel,~I - p.2. - •• • • • • •• fJlt

Alternative Hypothesis H,(l): The regression lines are notparallel

( 2) Null Hypothesis Ho(2): The group means lie on a straightline, i.e. the residual sum ofsquares for the regression lineon the points [~, (oI.t + ~t.X)] iszero.

Alternative Hypothesis HI (2): The group means does not lie ona straight line

( 3) Null Hypothesis Ho(3): The slope of the regressionline on the group means equalsthe common value of ~I ••••• pit.

Alternative Hypothesis HI (3): The slope of the regression lineon the group means is not equalto the common value of ~I ••••• pit.

The test of each Null Hypothesis is conducted in accordance with the

principles for the analysis of variance where ratios of sums of squares

are compared with the appropriate points on the F- distribution. Thebasic parameters required for the test are set out in the following table:

- 390 -

ANALYSIS OF COVARIANCE TABLE

DEGREESSOURCE OF SUM OF SQUARES MEAN

FREEDOM SQUARE

Common regression1line 1 SG" WO s, SG

Slope of group ~eans weW'" 2vs. Average within 1 SIIIICO=--(Bc- Bm) SIIIIGgroup slope Wo

Residual about linear II

regression - of group k-2 SG""2:nt ['4 -Y-Bm (Xt -X)] SG I (k-2)means ta,

Between within group II. :1slopes k-I S",=~ wi (B~-Bc.) Sw/(k-I)

-\: .. 1

Residual about within IIIgroup - linear regres- N-2k Sit-I [Y~-'4 -Bt (~\-Xt )] Sit.I(N-2k)sian (sep.reg.lines) t·, '''1

II. lit. :l.TOTAL N-I 2 I Cft,- Y)

+-;! ."

The symbols used can briefly be explained as:

and Bt == I.(Ytl -Yt: ). (X~l-Xt ) /Wtl-'

ItW ='wc. L ~-1:.,

II.Be= ['~: Wt Bt;.]Iwc

t...,

It

B", ""2.n~ (Xt -X) • ('4 -Y)ta,

lit

Xt =l.Xt(/ntt=1

It "tY =LLYt,/Nt=, ie,

- 391 -

Sw/(k-1)- Ho(1) is tested by comparing the mean square ratio SR/(N-2k)

with the F distribution with (k-1), (N-2k) degrees of freedom

SG/(k-2)- Ho(2) is tested by comparing the mean square ratio SR/(N-2k)

with the:F distribution with (k-2), (N-2k) degrees of freedom

S~- Ho(3) is tested by comparing the mean square ratio SR/(N-2k)

with the F distribution with 1, (N-2k) degrees of freedom

In all 3 cases a two tailed test must be used because of the way thealternative hypothesis is formulated.

The problem under consideration consists in total of 4 groups ofbivariate observations. However, the primary objective is to examine the

difference in performance between the two vessels on each occasion, and

the comparative study of changes in performance on each vessel from oneoccasion to the next is only a secondary interest. Each analYSisperformed will therefore consist of 2 groups of observations only, and the

test of the second null hypothesis, Ho(2), becomes redundant because theresidual about linear regression of group means is aiWayszero with zerodegrees of freedom. Only tests of Ho(1) and Ho (3) will therefore berequired.

- 392 -

A-5.5.1 TEST OF RESULTS FOR SHIP A AND SHIP E, FIRST EXPERIMENT

Number of observations for Ship A: 90Number of observations for Ship E: 78

TABLE (A-13) ANALYSIS OF COVARiANCE, SHIPS A AND E, FIRST EXPERIMENT,DEGREES OF

SOURCE FREEDOM SUM 0'FSQUARES MEAN SQUARE

Common regression line 1 9.06708

Slope of group means1 {).3493 0.3493vs. average within

group slope

Between within group 1 0.00006 0.00006slopes

Residual about within 164 0.9393 0.000573group - linear reg.

TOTAL 167 10.3557

Null Hypothesis Ho(l): F ratio = 0.00006 .. 0.01050.00573

Null Hypothesis Ho(3): F ratio = 0.3493 = 60.960.00573

From statistical tables: F O.o:l,I, 1&'1 = 10.8 and F ..2.70.20, I, 1(,1f

The null hypothesis Ho(1) is therefore clearly accepted, while the null

hypothesis Ho(3) is rejected at the 0.2% level. In other words, there is

clear statistical evidence that the regression lines on Ship A and Ship E

are parallel, while there is less than 0.2% chance ~'hatthe measureddifference between Ships A and E could have occured by chance only. We

are therefore more than 99.8% confident that there is a true difference inperformance between Ship A and Ship E in the first experiment.

- 393 -

A-5.5.2 TEST OF RESULTS FOR SHIP A AND SHIP E, SECOND EXPERIMENT

Number of observations for Ship A: 109Number of observations for Ship E: 88

TABLE (A-14) ANALYSIS OF COVARIANCE, SHIPS A AND E, SECOND EXPERIMENTpEGREES OF

SOURCE FREEDOM SUM rtF SQUARES MEAN SQUARE


Slope of group means1 0.40945 0.40945vs. Average within

group slope

Between within group 1 0.00007 0.00007slopesResidual about within 193 0.813 0.00421group linear reg.

TOTAL 196 11.4334

Null Hypothesis Ho(l): F ratio ... 0.00007 = 0.01660.00421


From.statistical tables: F = 10.8 and F ,.2.7o.eca, I) 1'13 __ 0.'20) I) In

The null hypothesis Ho(l) is therefore clearly accepted while the nullhypothesis Ho(3) is rejected at the 0.2% level. Again therefore, clearstatistical evidence exists that the regression lines on Ship A and Ship E

are parallel while there is less than 0.2% chance that the measureddifference in performance 'between Ships A and E could have occured by

chance only. We are therefore more than 99.8% confident that there is a

true difference in performance between Ship A and Ship E in the secondexperiment.

- 394 -

A-5.5.3 A COMPARATIVE TEST OF RESULTS BETWEEN THE TWO EXPERIMENTS FORSHIP A

Number of observations for Ship A, first experiment: 90Number of observations for Ship A, second experiment: 109

TABLE (A-15) ANALYSIS OF COVARIANCE, SHIP A, FIRST AND SECOND EXPERIMENTDEGREES OF

SOURCE FREEDOM SUM OF SQUARES MEAN SQUARE.


Slope of group means0.03652vs. Average within 1 0.03652

group slope

Between within group 1 0.00100 0.00100slopes

Residual about within 195 0.94354 0.004839group linear reg.

TOTAL 198 6.88459

Null Hypothesis Ho(l): F ratio = 0.00100 = 0.20670.004839


From statistical tables: F = 6.60.02., '. I'IS

Again, the null hypothesis Ho(l) is clearly accepted while the null

hypothesis Ho(3) is rejected at the 2% level. Clear statistical evidence

therefore exisits that the measured difference in performance between thefirst and the second experiment could not have occured by chance only.

- 395 -

A-5.5.4 COMPARATIVE TEST RESULTS BETWEEN THE TWO EXPERIMENTS FOR SHIP E

Number of observations for Ship E, first experiment: 78Number of observations for Ship E, second experiment: 88

Table (A-16) ANALYSIS OF COVARIANCE, SHIP E, FIRST AND SECOND EXPERI~mNTDEGREE OF

SOURCE FREEDOM SUM rtF SQUARES MEAN SQUARE


Slope of group means0.00545vs. Average within 1 0.00545

group slope

Between within group 1 0.00504 0.00504slopesResidual about within 162 0.80929 0.00500group - liner reg.

TOTAL 165 13.1788

Null Hypothesis Ho(l): F ratio .. 0.00504 .. 1.0080.00500


From statistical tables: F ..10.8 and F ..2 70.002.,I,lb2 0.'20, " '1.2 --!__

The level of significance for an F ratio of unity with 1 and 162degrees of freedom is in fact 64%. Both null hypothesis Ho(l) and Ho(3)

are·therefore accepted and we conclude that the regression lines for ShipE in the two experiments are par~llel, and that there is no significantdifference in the results from the first to the second experiment.

- 396 -

A-6 HULL ROUGHNESS SURVEYS

Prior to the first experiment a hull roughness survey was carried out

on Ship A in drydock, and a weighted value of 136 ~m AHR was found.

The roughness history of Ship E is incomplete, and as a consequence ofthis an underwater roughness survey was performed at the end of the firstvoy~ge. This was the first time that the BSRA hull roughness analyser had

been used under water, and the survey only covered the sides of the

vessel. The AHR of the sides was found to be 384 pm but unfortunately no

measurements could be taken on the flat bottom, and the survey thereforeremains incomplete.

Further development of the underwater

successful,and it was therefore decided to

surveys on both vessels at the end of

measurement technique proved

perform underwater roughness

the second experiment, andsubsequently to compare the measured difference in AHR in more detail.

For Ship A a complete survey covering 96 locations on the hull wasobtained and weighted AHR of 147 pm calculated. An identical survey of

Ship E covering 84 locations yielded a weighted AHR of 452 ~m. The

results of the hull roughness survey for both vessels in the two

experiments are given in Table (A-17). As shown, the weighted AHR of Ship

A has over the 12 month period increased from 136 ~m to 147 pm. This

difference of only 11 pm is less than the stated error bounds of themeasuring instrument, and the conclusion will therefore have to be thatthe AHR of Ship A have remained unchanged over the 12 month period.

- 397 -

TABLE (A-17) HULL ROUGHNESS SURVEYS, SHIPS A AND E, BOTH EXPERIMENTS

EXPERIMENT 1 EXPERIMENT 2SHIP A SHIP E SHIP A SHIP E

\

Slides 129 Jlm (2) 384 pm (1) 134 pm (1) 430 pm (1)

flats 149 11m - 172 pm (1) 493 Jlm (1)Mean AHR 139 Jlm - 153 pm (1) 462 Jlm (1)

.

Weighted AHR (3) 136 11m - 147 pm (1) 452 pm (1).

(1) Underwater survey(2) One side only

(3) For the weighting, the ratio of sides to flat of bottom is takenas: 0.65 0.35

The sides of Ship E show a significant increase in roughness from 384to 439 11m. Unfortunately measurements could not be taken on the flats of

Ship E at the time of the first experiment, and a total AHR can only be

obtained by estimating roughness of the flats on the basis of the

measurements taken 12 months later. It is unlikely that the roughness on

the flats of Ship E will have decreased over the 12 months. If it hasremained unchanged over the period at 493 11m the weighted AHR at the time

of the first experiment would have been 422 11m• On the other hand, if theroughness has increased at the average rate since new over this 12 month

period the roughness of the flats at the time of the first experiment

would have been 450 pm giving a weighted AHR of 400 11m. The estimated AHR

for Ship E during the first experiment is therefore in the region 400 to420 pm, but since this is only an estimate it should also be treated assuch in the following evaluations.

- 398 -

The average hull roughness of a vessel is obtained by calculating the

weighted average of the mean roughness at each measurement location.

Although it is this AHR value that is required for relating hull roughness

to speed and power performance, it does not give a very good description

of what is happening to the hull surface itself over a period of time. In

particular this is true in the case of serf polishing coatings, where a

major part of the surface may experience a reduction in roughness withtime, but because of some areas of:high roughness readings due to damage,the overall result may be that the AHR has increased. A better method for

demonstrating both trends in polishing and roughening is to plot afrequency distribution of the total number of ungrouped data from all

measurement locations. The plots of frequency distributions comparing the

roughness surveys on Ship A and Ship E in the two experiments are shown inFigures (A-9), (A-lO) and (A-II). In Figure (A-II) it can be seen that

the sides of Ship E have deteriorated further over the past 12 months, and

the mean has increased, mainly due to the large increase in values above

500 ~m. In Figure (A-lO) a similar frequency distribution for the sidesof Ship A show that the modal value of the distribution has decreased ,indicating that a major part of the surface has experienced a reduction inroughness. At the same time there has been an increase in high roughnessvalues from damage to the surface, and the overall effect is that the mean

roughness value remains approximately the same as 12 months earlier.

The same development can be seen in Figure (A-9) only moredramatically. The flats on Ship A have suffered Some detachment from theearlier system, and as a result of this the proportion of high roughness

readings (above 500 ~m) has increased from 0.9% to 6.0%. Although a major

part of the surface has experienced a reduction in the local roughness as

- 399 -

indicated by the reduction in modal value, this is not sufficient tooffset the increased proportion of high readings, and as a result the meanroughness value shows an increase.

As a further continuation in monitoring of the hull surface conditionon these two sisterships, another underwater hull roughness survey was

carried out 4 months after the completion of the second monitoringexperiment. Due to repeated failure of the BSRA hull roughness analyserto work underwater, readings were obtained for only about 70r. of the

underwater hull surface. For the sides a total number of 55 measurement

locations were obtained and this constitutes a sufficiently large sample

to enable comparison with the earlier surveys. For the flats, however,

only 16 measurement locations were obtained and greater care should be

taken when comparing this result with the previous surveys. The 55measurement loations on the sides yielded an average roughness value of

123 ~m, while for the flats the corresponding value for the 16 measurementlocations was 176 ~m. This gave a weighted AHR for the complete ship of

140 ~m and served as confirmation of the results obtained 4 monthsearlier.

A-7 POWER AND ROUGHNESS RELATED

The fu~damental relationship:

where ~CF is the increment to the total resistance coefficient due tohull roughness.

h is the average hull roughness.

L is the ship length between perpendiculars.

- 400 -

was first suggested by Telfer, [Reference (86)], and later supported byBowden in his ship-model correlation work, as well as by more recent

prediction methods based upon boundary layer .integration techniques

[Reference (22)]. If this basic relationship is accepted the generallinear equation for~CFcan be written:

:II a where a and b are constants.

For the purpose of evaluating the difference in l::::. C,between tworoughness levels, only the constant "a" will have to be defined.Estimates of the magnitude of "a" can therefore be made if two roughnesslevels and the corresponding difference in resistance or power performanceis known. The difference in power requirement between two roughnesslevels, hiand h~can be expressed:

a x [ (~,t- li't] x

and therefore a = V. (~I)~](assuming QPC remains unchanged)~'S'V3 [(~t-

Using this relationship estimates of "a" have been made from theresults of the of the two performance monitoring experiments. Since thehull roughness survey on Ship E in the first experiment is incomplete only

a probable range of AHR have been given and the calculated values for "a"are subsequently also presented in the form of ian est mated range.Results from all 3 methods of calculating the di·fference .1n performancebetween the two vessels are included, although in statistical terms themethod of calculating the mean on the basis of transforming the speed andpower values to a logarithmic scale is believed to be the most correct.

- 401 -

From the first experiment the estimated values of the constant "a" areas follows:

(i) between 58.2 and 61.4 by direct comparison of the regressedspeed/power curves

(ii) between 63.4 and 66.8 on the basis of calculating the energyconsumption per mile for each vessel

(iii) between 59.3 and 62.5 by comparing values obtained followinga logarithmic transformation of speed and power scales.

The second experiment with complete roughness surveys for both vesselshas:...provided the following set of values for "a":

(i) a = 56.0 by direct comparison of the regressed speed/powercurves

(ii) a = 67.3 on the basis of calculating the energy consumptionper mile for each vessel

(iii) a = 54.3 by comparing mean values obtained following alogarithmic transformation of speed and powerscales

This range of values for the constant "a" clearly does not correspond

with the value of a=105, as suggested by Bowden, but are on the other handin good agreement with the recent results obtained from prediction methods

based upon boundary layer integration techniques. It has been suggested

that the values of ~ CF calculated from Bowden's formula also includesother correl~tion factors. The present study conforms this statement andtentatively suggests that approximately 60% of the values predicted byBowden's formula are due to hull roughness and the remaining 40% due toother unexplained factors.

- 402 -

A-8 DISCUSSION OF RESULTS

A true difference in speed/power performance of between 10% and 12% on

account of under water hull condition only has been shown to exist betweenthe two vessels included in the present study. This difference has

remained practically unchanged over a 12 month period with a slight,although not statistically conclusive deterioration in the performance of

eacH individual vessei over the same time period. The assumption that the

difference in speed/power performance is due to a difference in underwater

hull condition only has been substantiated by the repeated underwater

inspections and hull roughness measurements carried out on the two

vessels. At the time of the first experiment when Ship E had been out of

dock for a period of 14 months, the underwater hull was reported to be

free from macroscopic fouling, and the propellers were also reported to be

free from any marine growth. After completion of the second experiment

both vessels were again examined for the presence of fouling. Ship A was

reported to be clean, while Ship E had a small band of weed fouling justbelow the waterline extending around the complete ship. In terms of area,this fouling covered less than 4% of the total wetted surface area, andthe effects upon performance were assumed negligible. The propellers on

both vessels were reported to be clean, apparently undamaged and ofsimilar surface condition according to visual inspections by divers. All

propellers had some long standing cavitation damage at the tips, but ofsmall extent. The nearly complete absence of hull f Iiou ng on theconventionally coated Ship E after a period of 26 months in service isquite remarkable. The lifetime of the antifouling system, as claimed bythe manufacturer, is only of the order of 18 months, and the system musttherefore be said to have performed extraordinarily well.

. .

- 403 -

Unfortunately, the underwater hull roughness of Ship E after the firstexperiment was incomplete, and from the point of view of relating

differences in hull condition between hhe two vessels to actual measured

differencesin speed and power performance, this first experiment was notentirely successful. Although the findings of the first experiment basedupon an estimated value ofAHR for Ship E are in good agreement with the

results of the more successful second experiment, they should be treated

witH some'caution as a result of their unsatisfactory scientific basis.

The comparision of measured differences in hull roughness with measured

differences in power requirement at constant speed have been made using aconstant propulsive coefficient. This is in accordance with therecommendations in Chapter 1, which concluded that for single screw ships

the added resistance due to roughness would result in a decrease in the

open water efficiency component, while at the same time, the increased

roughness would have the opposite effect of increasing the wake fractionand therefore also the hull efficiency component. The net effect of the

two efficiency changes is therefore that they practically cancel each

other out and the total efficiency remains more or less unchanged. Nodata are available for twin screw ships, but it is belived that thechanges in wake fraction, and therefore hull efficiency will be less thanfor single screw ships. However, as shown in Figure (A-2), the higherpitch ratio propellers on the twin screw container vessel experience only

the change in open water efficiency due to the added resistancecompared with the lower pitch ratio propellers of the single screw vesselsshown in Figure (1.6), and the net effect may be that the total efficiencyremains substantially constant for the twin screw ships as well. In theabsence of further arguments therefore, it appears to be justified to make

- 404 -

use of the results from single screw ships and maintain a constantpropulsive coefficient.

The statistical analysis has shown that a true difference inperformance exists between the two vessels, but no attempt has been madeto quantify the possible experimental. .err.or. Principal sources ofexperimental error are in power readings and speed measurements, but dueto tne method of data analysis, it is impossible to provide an exactquantification of the total expected error. The large data-samplesobtained in each experiment, ranging from a minimum of 78 to a maximum of

109 effectively reduces the random error in the final results to anegligible amount. Instrumental error from the satellite navigator can be

assumed zero when only exact satellite fix positions are used. The randomerrors in the pitot tube log used.for estimating current corrections are

significant, but due to the large data-samples, the final error in thecurrent corrections are expected to be small. Only the power-meterreadings therefore remain as a principal source of error. Tests carriedout by the British Ship Research Association, [Reference (87)], have shown

the instruments used to be of an accuracy at least as good as the

reference instruments employed in the test and therefore within ±2%.Fortunately, the vessels used in this experiment are twin screw with twinsets of instruments, and a continuous check on the relative accuracybetween the two instruments could be made on the basis of accurate rpmre~dings and the propeller characteristics. The relative accuracy wasfound to be within 1% for both vessels on both occasions. In fact, theonly discrepancy observed was a difference of 0.9% in the power readingsfor each shaft at the same rpm for Ship E, but this was later identifiedas being mainly due to a difference of 17mm in pitch between the two

- 405 -

propellers. The instrumental accuracy of the torsion meters is thereforebelieved to be nearer to 1% than the value of 2% quoted by BSRA.

A subjective estimate of the total error limits of the experiment would

therefore be ±2-2.5%.

In conclusion, a further comment is required about the attempt to

reldte the measured difference in performance to a measured difference inroughness. The roughness measurements are based upon a single height

parameter only and as discussed in Chapter 1 , this is not an adequateparameter for describing the relationship between frictional drag and a 3-

dimensional surface texture. Present instrumentation, however, are only

capable of providing a single peak to trough measure of height, and this

is therefore the only parameter on which a comparison between the twovessels could be made.

Recent prediction methods based upon boundary layer integrationtechniques also indicate a certain speed dependence between roughness anddrag, and therefore that the basic relationship

is not quite correct.

Despite the areas of uncertainty outlined above, the experiment has

resulted in a proposed modification to the original corre,lation formula

for hull roughness developed by Bowden as a part of an attempt to separatethe contribution due to hull roughness from other correlation factors.

- 406 -

In addition, the range of roughness values covered in the presentexperiment is approximately twice the range covered in Bowden's work, andthis provides some support to the validity of extrapolating the formula tohigher values of roughness.

Finally, it is of interest to notice that recent work using predictionmethods based upon boundary layer integration techniques have predictedthe 'difference in power performance between Ship A and Ship E in the

second experiment to be approximately 8.2% based upon the measured hullroughness values of 147 and 452 pm, respectively, [Reference (22)].

- 407 -

Clf X 103

876

54

32

FIGURE (A-1)LEVEL OF WIND COEFFICIENT Cx ATDIFFERENT ANGLES OF APPARENT WIND 't.

-1

-2-3-4-5-6-7-8

FIGURE (A-2)EFFECT OF ADDED RESISTANCE~RON PROPELLER EFFICIENCY~.

1 + .!d.!!l~.1.20

1. 15

1. 10

= 0.1325 [1 + ~oRJ + 0.8675

1. 051 + tl

'17!

1.00

0.95

1.0 2.0 3.0

~l 18 0

- 408 -

FIGURE (A-3)PERCENTAGE CHANGE IN POWER REQUIREMENTPER O.lm CHANGE IN DRAUGHT

1.50

0.5

10.5-11.0m

% CHANGEIN POWER

1.00t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1d.0_10.5m 1J.5-12.0m11.0-11.5m

o SHIP SPEED (knots)

19 20 21 22 23 24 25

en -e-~ C\J

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- 409 -

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- 410 -

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- 411 -

FIGURE (A-8)REGRESSION CURVES FOR SPEED AGAINSTPOWER, SHIP A AND SHIP E, FIRST ANDSECOND EXPERIMENT

SHIP E, 1st Experiment3.0~P = 1.882 V

SHIP E, 2nd Experiment2.'3'iP =.3.129 V

18 19 20

SHIP A, 2nd ExperimentP = 2.404 Vl.,,,,

SHIP A, 1st Experiment \~.07'1

P = 1.808 V

SHIP SPEED (knots)21 22 23 24

- lj12 -

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- 413 -

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- 414 -

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- 415 -

TABLE (A-18)

SUMMARY OF MONITORING DATA FOR SHIP A, FIRST EXPERIMENT

Summary of recorded voyage data:Column 1. Inter-fix period identification number.

2. Observed distance between satellite fixes, calculatedon the basis ·ofnavigational position~

3. Time between satellite fixes.4. Observed average speed between fixes •

.5. Average speed as recorded from 'pitot tube log.

6. Average shaft revolutions over inter-fix period.

7. Average recorded shaft power over inter-fix period(metric horse power).

8. Average power delivered to the propellers afterallowing for 2k% shafting losses.

9. Speed from the Power Diagram, based on RPM from column6 and DHP from column 8.

10. Difference between Observed Speed (column 4) and LogSpeed (column 5).

11. Difference between Observed Speed (column 4) and Speedfrom Power Diagram (column 9).

12. Difference between Speed from Power Diagram (column 9)and Log Speed (column 5).

13. Total fuel consumption in tonnes per hour and grammesper shaft horsepower per hour.

14. Draughts, calculated daily.

15. Observed Wind, given by Beaufort number and directionfrom code indicated below.

16. Observed Swell, period, height and direction given bycode.below.

17. Ship motion, pitch and roll, given by codes below.

18. Ocean Current, speed and direction as taken from seasonalcurrent charts.

19. Observed Sea State, given by code below.

- 416 -

Column 20. As column 1.Summary of Corrections made to Data:

21. As column 4.22. Observed Speed (column 4) corrected for average

seasonal current (column 18).

23. As column 8.24. Correction to Power for wind resistance different

from still air condition.

25. Correction to Power for mean draught difference frombasis condition of 11.0m.

26. Power delivered to propellers after corrections tostandard basis.

27. Fuel consumption in tonnes per hour (as column 13).28. Fuel consumption corrected to standard basis as for

power in column 26.

Sw.ell PeriodCode

1 2 sec period2 4 sec period3 6 sec period4 8 sec period5 10 sec period

Swell HeightCode

0 Less than lm1 1 metre2 1 metre3 1l metre4 2 metre

Sea Code0 Calm1 Rippled2 Slight3 Slight/Mod4 Moderate

Pitch & RollCode

0 Total angle 001 Total angle 202 Total angle 403 Total angle 604 Total angle 80

Wind, Swell, CurrentDirection Code

- 417 -

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- 418 -

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19,17

21OBS,

SPEED

:1

4

5

7

8

9

10

21. 92

21,82

21,96

22,00

?2,05

22,01

21.74

21.59

22.06

22.21

21.72

n.ll

21.90

22.38

22.28

21,13

11

1213

14

15

16

18

19

20

21

22

23

24

25

26

27

28

29

32

33

34

35

36

37

38

21.15

20.87

21,07

21.20

20.90

20,66

20.31

2"1.38

20.38

19.2719,05

19.2219.66

39 19.89

19,BO

19,58

13.30

21.85

21. 77

21,89

21.94

19.9S

CORRF:CTED

OBS. SPEW

21.69

21,61

21.73

21.7821.76

21,66

21,80

21.84

21.89

21.85

21.58

21.43

21.90

22,05

21.56

21.95

21. 74

22.22

22.12

20,97

20,99

20.71

20,91

21.04

20.74,

20,50

20.15

21,22

20,22

19.11

18.98

19.06

19,50

19.73

19.64

19.42

19,1-1

19,01

19.'19

18. 'lG

22 23

CHrWIND CORR.

tl ['liP

33500

33500

33500

33600

33700

34000

34100

34000

33400

32900

32900

32800

32400

32600

32500

32600

32500

32500

32500

25700

25700

25400

25400

25200

25500

25500

24900

24600

24300

21000

20900

20900

21000

21000

2'1000

19'70018600

,Ro',OO

'WbOO

';w1on

+ 500

+ 400

300

100

100

100

+ 400

+ 200

+ 300

+ 500

+ 800

+ 800

+ 800

+ 400

+ 600

+ 600

+ 600

400

oooo

+ 500

500

'r 500+ 500

+ ,100

400

,100

+ 400

400

- 421 -

25

DR}\IJSH'r CORH.

tl OHP

CORRP.CTED

DHPFUEL CONS.

27 28

CORRI::CTED

FUF~L COIlS.

700

700

500

900

700

700

900

o

600

100

'lOO

100

o

oo

oo

ooooo

+ 100

+ 100

+ 100

+ 100

+ 100

+ 100

300

300

200

200

200

200

200

200

200

100

oo

o

ooooooo(1

3270,0

32700

32900

32100

33000

33300

33200

34000

34000

33400

33300

32500

32300

32600

32500

33100

32800

32900

33100

26200

26200

26000

25600

25600

25900

25900

24300

24400

2420021000

20900

2'1.400

2',[ sao2150C21500

20100190(lO

'190001~10C

9.474

9.522

9,432

9.451

9.493

'),438

9.276

9,456

9.369

9.373

9.292

9.322

9.316

9,329

9.335

9.307

9.318

9.182

8,040

8,008

7.975

7.975

7,964

8.020

8.063

8.020

7.962

7.368

7.354

7.351\

'J .1,16

7,337

ti.9,16

6,939

,~.HS3

(), S17tJ

9,252

9,300

9,355

9.185

9,259

9.301

9.193

9,275

9.622

9,506

9.485

9.209

9.294

9.316

9.329

9.475

9.402

9.430

9.297

8,194

8.161

8.159

8,036

8.088

8.143

8.187

7,829

7,956

7,930

7.360

7.354

7,527

7,5277.589

7.509

7,074

6,8(;5

'I,OIll.>

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7.11C

20 IRU,l I

_~ __ J_S'_~E_E_'D-l

4647484950

515253

54

55

19. to

56

57

58S960

6164

6566

67'

6869 20.16

20.2521.1121.1620.74

20.5220.44

20.2120.1919.9119.4019.88

'107273747576

77

788485868788

19.1519.15

8990

21

OBS,

18,3918.8318.6023.1823.00

23.1623.6022.4522.0822.4122.1121.31

20.9321.7022.6922.35

20.6621.6220.62

20.3520.13

CORRr;CTED

OBS. SP8ED

22 23

DHP\oJJND corm.

f::., DHP

18.23 .. 400

18.6718.44

23.0222.8423.00

23.4422.2921.9222.25zi ,95

21.15

21.1421.8522.8522,5120.8221.7820,78

20.51

20.2920.32

20.4121.2721.3220.90

20.6820.60

20.3720.3520.0719.5620.0419.31

19.3119.2619. 'J'.'

18.90

19,11

32200309002970029700296002950029900

299002400024400247002290022800

22600

22500

1860019300201100311500

35000

34600326003140030800313003050028800

31100332003600036400320003230032400

32500

3230032300

+ 400+ 400+ 400

+ 400+ 600+ 500+ 100

- 1300- 1600

900

- 1300- 1600

- 1600- 1000- 1000- 1000- 1100

- 1000- 1000- 1300- 1300

- 1000800

800..1100

24

600

700400

800700

900800

700

- 422 -

25

f::., Oil?

+ 1300..1300

+ 1300+ 1300..1200+ 1200+ 1200+ 1200

+ 1200

+ 1500+ 1600+ 1700+ 1700

200

100100500500400

400300300200

100100

100

o

o

200200200

200

CORRECTW

26

DHPFU8L CONS.

27

1900019700208003(,000

36700

36500344003270032000325003170030000

3260034200

364003650030900

3030030600

30700311003120031100293002850028900

284002&600

28600287002270023100

2380022100

21800,:1900218001%00?C600

6.874

7.203

10.0039,895

9.G579.3229.1018.9869.2679.016

8.714

9.2369.679

10.1'.1610.0869.299

9.4079,410

9.4579.5289.3789.3689.0198.8038,783

8.817&.8068.9698.9267.7228.0058.222

".521

28CORHECTr~D

FUEL CONS.

7.0197.3437.343

10.48610.36610.1789.8269.4709.3299.6179.364

9.0699,673

9.965

10.28710.1138.986

8.98G8.899

8.944

9.1819.0669.0568.5618,4548.550

8.467

8.514

8,5878.5747.3117.5il67.9267.295

7.198

7. '136

27 IFU~L:J

~1--:-:-~-:-:~~-2-1-'-1-2--+-2-8-7-0-o~~-~-D-:-:-0--1~--+-4-0-0---~-?-_S-2-0-0--~--8-,647

94 21,19 21,35 28600 500 + 400 28500 8,62698 20,51 20,67 29000 - 1400 + 500 28100 8,649

700 + 300 28700 8,600

20 ;>1HUN OBS.

99

19,7019,13

20,30100102

21,0620,36

103 19,8820,13104

1U5 19,74106107

22CORHEC~~D

oss • SP~r:D

20,4621,?2

20,5220,04

20,2919,9019,8619,29

2890028900241002390024000240002410024200

DHP

- 423 -

Dlll\UGHT CORP.,

25WIND CORIl,

+ 400 + 500+ 700 200

200

200

+ 700

+ 700+ 600 200+ 300 200

200+ 300

26CORIlECTED

DHP

2980024800

8,0217,654

24400 7,4097,6837,8177,7307,650

24500244CO2420024300

21>

C:ORRECTE:D

fUEL. CONS,

8,5008,5978,3838,5428,8847,8107,5617,8407,9457,7617,681

- 424 --

TABLE (A- 19)

SUMMARY OF MONITORING DATA FOR SHIP E, FIRST EXPERIMENT

Column Configuration as for Table (A-18), Except for Swell PeriodWhich is not Included

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ICORRECTED I

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20,86

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20,18

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24,17

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30000

29900

30300

30400

31700

31800

31300

29800

29700

29700

29700

29800

47100IJG900~G'70(1

'182001'11)00

,,;,1200

23 24

WIND CORR,

l:::. OHP

- 428 -

25

DHAUGHT CORR,

l:::. OHP

CORREC:Yf,D

OHP

34(;00+ 900

+ 800

+ 700

+ 200+ 200

+ 900+ 900+ 900

+ 9llP

+ 900+ 900

+ 900

+ 400

+ 500

+ 500

+ 600

- 1400- 1500

+ 200+ 200

+ 400+ EOO

+ 600+ 600

+ 500

- l~;()O

.• 1.)()0

900

200

600

200

300

'iOO

.\)\'0

400

400

40()

300

200

100

+ 500

+ 500

+ 1000

+ 1000

+ 1000

+ 1100

+ 1100

+ 1300,

+ 1300+ 1300

+ 1300

+ 800

+ 800

+ 800+ 800

+ 800

+ 800

+ 800

r 1000

+ 1000+ 1000

+ 1100

+ 1'100+ 2~00+ 2200

+ 2200

+ ~/j{)O

+ :~r.OO

26 27

FUEL CONS.

9,878

34GOO

34600

33700

J4000

3340032600

32600

34500

34500

34800

34700

34700

34800

34600

34200

33500

31300

31200

31700

29800

3"1000

32400

32300

31000

31100

31300

31400

31500

4%00

4%00

49300

45800

9.83'1

9,785

9.654

9,480

9,761

9,565

9,4e6

9,530

9,506

9,527

9,4929,509

9,458

9,703

9,524

9,123

9,000

9,165

9,220

9,458

9,407

9,322

9,063

9,165

9,046

9,081\

9,106

12,320

1~, :l33

12,199

"12,421

"_I_ ,G,.l

11. 940

11. ,)',17

1:i • 9~J;?

28

CORP,E:CTED

FUEL CONS,

10,020

9,980

9,895

9,626

~,G229.564

9,771

9,690

10,073

10.049

D,067

10,140

10,06010,138

10,08110, "199

9,900

9,5109,384

9,964

9,028

9,2549,580

9,6139,421

9,588

9,5949,616

12,963

12,816

12,890

12,8'10

12.642

12.'15)

12.303

12,1.'i9

It:. :>70

20

RUN

NO,

5152535455

56

6364656667

6869707172737475

7677

8081828384858587

88899091

9394

98

SPCF'D

23,38

22,6822,7823,4523,67

23,8623,5522,8021,8822,4023,17

23,04

23,2723,77

24,1222,8623,5023,2622,18

22,6823,0523,12

22,9922,8322,8122,9122,5119,47

20 09

19,95

:~O, ') (~.

21

05S,

20,26

20,2220,20

1<) .: t:....

;~O, \')'j

CORRECTED

OBS, SPEED

22,8222,1822,2822,9523,1723,26

23,0523,8022,8823,4023,6723,54

23,7724,37

24,6223,3624,0023,7622,68

23,1823,55

23,6223,4923,3323,3123,4123,0119,9720,59

20,7620,4520,72

20,7020,6520,2920,68

20,51

;'0 t 12

20,16

22 23

DHP

24

wmo corm,

!!. DIIP

- 429 -

25

DRAUGIlT CORR,

!!. DHP

CCRRCCTE:D

DHP

26 27

FUEL CONS,

28

COI<RECTW

F'UEL CONS,-------------+----.------~-----------~~------------12,396

·1

2·1800

45200~4700444004440044300

44400453004520045600460004620045100

4480045000

4890042600423004200042100

3990040100

39800

39200379003820037900374002760")

26900273002710027000

269002650026200

- 1200- 1300- 1200- 1200

- 1200- 1200

- 1700- 1500- 1700- 1300- 1300- 1100

- 1100- 1100

- 800800

- 1300- 1000

+ 30~)

+ coo

800900300100600

700400600700400400

voo

+ 2800+ 2900+ 2900+ 3000

+ 3000+ 3000

+ 1900+ 2000+ 2100+ 2200+ 2300

+ 2400+ 2400+ 2500+ 2500+ 2600+ 2600+ 2700+ 2800

+ 2700+ 2700

+ 3000

+ 3000+ 3000+ 3000+ 3000+ 3000+ 1800

+ 1800+ 1800+ 1800+ 1800+ ·1800

• 1800

• 18DO+ 1800

• 1900• lC'OO

,. ;_()OO

463004630046100<16200

46100462004550045700460004690047200

45400

46100464004560044300446004460044300

4180042000

4280042200409004120040900404002810027700

28400

.285002t3200

280002790027liOO

2'/tOO

27?OO

:~'} 10n

11,9801~.,92411,94011,978

11,90011.95711,95·112,02011,90312,02Cl12,002

11.828

11.84611.82911,68311,44911,29511,26811,256

10.79510,764

10,91210,59610,72510,59110,57110.4718,5030,360

8,3908,3358,329

8,3648.322

8,065

II·

7,'.108

",725

'1,750.

',.7"12

'l.'l8B

12,34212,387

12,45312,37312,43212,00312,15112,00512,25012,257

12,162

1.2,18312,19012,12711.89611,89511.95211,842

11,29911,264

11.71911,39111.55611,40711,390

9,047

8.907

8.9378.8828,6758, ']\ i

8,8758.('\)7

R,3~7

- 43().-

TABLE (A-20)

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'" 0'"' \'"\1

10

JJ.

12

13

14

15

1617

18

192021

23

24

25

2627

28

2930

31

3233

34

35

36

373R

0:;;

234

5

6

7

89

23.7823.35

21.04

22.97

23.5423.5223.44

23.16

?2.84

n.28

22.0022. 7.~

22.18

22.1223.06

22.84

22.11923.51

23:13

22.41

22.53

22.6922.17

22.70

n.19

22.61?2.36

22.35

22.33

22.10

22.37

22.64

22.70

21.9722.06

22.10

21.90

21.8~

22.7822.56

2?.21

23.23

22.85

22.13

22.25

22.41

21.89

22.42

21.91

22.33

22.0822.07

20.05

21.82

22.09-22.36

22.12

21.69

21.78

21. 82

23.50

23.07

22.76

22.6923.2&

23.24

23.16

22.88

22.56

22.00

21.72

:),? ;?0

-33500

33500

33100

332003330035300

35200

3510035000

35300

35300

35600

33000

32800

32900

3?700

3?COG

'·nell

DHP

~J"11300

'8200

38200

38200

37900

3&50036200

32800

32500

32300

32500

33100

3'3100

33100

33200

33100

33500

33900

33500

- 435 -

~~ I 2G

nr,/,UGHT conn. [' CCHI<I:;cn'D6. DBi-' DHP

-----1-------- _

\-JU11J conr..6 DHP

o+

+

+

+

+

+

+

o+

+

+

+.

+

o

+

+

+

+

+

+

o+

+

+

+

+

+

+

+

19:)0

2)00

1700

100

400

600

1000

800

500

100

100

300

700

500

100

100

100

200

400

300

300400

1100

400

400

400

GOO

400

700

GOO

500

500

700

800

800

+ 37100

+

+

+

+.

+

+

+

+

+

+

+

+

+

+

+

+

+

+.

+

+

+

+

+

+

+

+ 3100

3100+

+ 3100

3100+

+ 3400

+ 3200

+ 32003;>001300

3JOO..

1000

1000

1000

'jOOO

1100

1100

1100

1000

1100

1100

1100

1100

1100

1100

1200

1200

1200

1200

1500

1600

1600

1600

1700

1700

3000

3000

3000

37500

39100

38900

38700

38c'OO

382·00

34600

34100

3350033700

34200

34500

34900

34900

34200

311600

35000

35200

35500

35400

34700

35200

35400

38400

38600

37700

38500

39000

38800

28700

39500

36800

36500

%60036'/00

36900

,6800

J6~IOO.

FilEr.CONSUi-1PTION

10.G99

10,702

10.717

10.522

10.G09

10.287

10.139

1.0.121

9.493

9.360

9.3389.3'12

9.521

9.574

9.522

9.542

9.575

9.617

9.616

9,518

9.523

9.642

9.667

9.705

10.2;9

10.16?

10.139

10.100

10.086

10.102

10.168

9.8389.477

9.414

9.411

9./13'/

9. )8_)

?7 I ;"8

·lCO;d~rCTr:D

[-'ULL CONS.

10.400

10.525

10.765

10.883

10,693

10..60310.696

10.002

9.811

9.G78

9.710

-9.831

9.970

10.017

10.000

9.852

9.883

9.923

10.094

10.074

10.051

10.098

10.237

10.304

1~.403

11.-'129

10.875

11,090

11.122

11.085

11.036

10.95710.545

:0.454

~O.447

10.654

10.579

10.6?1

10.5(,3

10.579

4748

4950

5152535455

56

57585960

61

G2

63S4

65

6667686970

71

73

7475

7677

78

'}9

80

81

()W;.

JPEFD

n,98

19.~519,5(,

19.33

19,69;>0,35<1,7721,19

?1.J9

21. 2619,852C,0320,93

21.232·1,08

21.• 43

21,24

20,96

19,74'20,3520,54

20,25

20,49

19,65

~1

20,6820,5620,0620,0620,65

20,3220,4~1'.', ,18

19.86li1,7S

"19.82

,'C,ilO

coru; EC'EI)OBS, SPEED

,?~. 7018,97

19,2819,0519,4170,07

22.0521.4721.6721. 54

20,1320,3121. 2121,51

21,3621,662'1,7121,52

21,24

20,0220,6320,82

20.5320,9620,8420,3420,3420,9320.77

19,93 .

19,8320,6020,7219,7619,76

.?O,1420,03

;:OO,lfl

326002120021200

2120021200713003130031300'31100

3120031200312003110031200'

30400311003130031200

3120031400

314003140031400

31200311003110029300?92002930029~00

2890028900292002690024800

25100

2~2(l0

25500

.:\_70()

436 -

, ?A I' -0 11 're'I ,:", , )

',.IIND CORR, DP.!\UGHT C01\H, CORf(CCTED

6. DHI' [;:, DHI' DHI'::+--:~-o---::-;---DHI'

o

+

+ 4002400

RI:;: II

NO,

:---~I---+-~-t-j,:;

24001500'1300~SOO10001100 .

').100

1100140018001700

200

200200

17001700

1.70011001300

1300150015001000100015002300

140012001000

'1.100900BOO

900

')00

500

2200+ 2200

+ 2200

+ 2200

+

2200

1100

1100+

+ 1100

+ 1100

+ 1100

+ 1100

+ 1100

+ 1200300300300400

500500

500400400

400400500600600600600

500SCO50C

400300

300

300

cOO.1,10

23'100232002320.023(;00

23900300003000030'/003100030800313003110031300

29000294002920029100

2900029200

29'2002990029700

29500292002910027000276002720026500

2700027200279002650C!

23400

21900

FUrl,CON:,Ul'lP'l'ION

7,4057,3607.134

7,4047,3849.0.)2

9.0648.967

3,9338.9138,9099.045

9,0529,1159,0709,0959,198

9,0999,076

9,1069, :l069,1109,100

9,1659,2338,7238,7068,7218,730

8,3-118,7:>G8,763

8,'18S

8,30J8.335

8,459

CCHJ<r.CTI.:D

l'UEL CONS,

10,5'35

8,lSt)8,O,1?

8.227

8,2688,6748,6958,654

8,877

8,8018,937

9,045

.8,'/02

8,582

8,591

8,470

8.471)

3,6798,6268,G14

8,6166;6518,25E.8,2398,1.087,886

8,2718,233

8.325

8,3G17,8447,91\47,990S,06~.

S,01O

?(!

nUNNO.

connscreoOB:;, srr.eu

DHP WIND CORR,

6. DHP

- 437 -

2S

DRAUGHT CORR,

6 DHP

CORRECTEDCHP

25

FUEL COi~r<CC'rcr)CONSljMP-rION ruct, CO:-lS,

- !I

81

----------------4--------~--------~------------_+----------~--8,623

85

8C87

8889909192

9394959697

9899

100101

II 102-103

ri

104105

106107

108109

20,86

19,6519,3,1

19,1020,01

20,21

20,7920,4420,5729,5020,9820,5920.8620,73

20.3520.2521. 2920.9320.5810.1720.8120.75

20.4919.97

19.3919.22

20,1,9

21.14

21.07:?O.7220,8520,7821.2620,87

21.14

21.01

20.6320,5320.5721.2120.8610,<\521.0921.03

20.7720.25

19.6719.50

19.93_

19.3820.29

2(900

31100301002'j~OO

291;00

28,,00297002910029300

28700

2850029200288002730026600265002660026800

276002620D

2520024900

24900

23~OO24800

+

+

+

o

+ 600,1000

o

800

1900

100'01100700700700500

300700

100500900200200200200

900700700

900

o

o

,300

?OO

300400400400400400300

300

300300200200200200200

200

lOO.

100100100

300300

2580028500

27900;>7900

2790027500286002800028500

28100

27500288002800026200

266002650026600

26400

26600254002440024800

25500

23700

2210024500

9,278

9.1038,91018.9738.8768.9288,8768,655

8.6498,633

8.7298.770

8.2668.0487.9848.00?

8.168

8.3247.8357.6977.611

7,577

7.5727.4937.791

8.51€;

8.450·8.5418,525

8.5428.6048,5478.417

8,4728,336

8.6128.532

7.9408.0487.9848.002

8.048

8.0297.6017.~587.581

7.756

7.2717,1157.699

- 438 -

TABLE (A-21)SUMMARY OF MONITORING DATA FOR SHIP E, SECOND EXPERIMENTColumn Configuration as for Table (A-18)

439 -N -"' __ --"'· __ ... _· -----------.-..-----_ •• _ •• __ ....... _'"' • ,. .. M.~ .. • _

V· ~ ~~ f N I.>

'f! ~~ ~~ c , ....... N ,\",1_______ ..:2_ji- _

C

v-'N ,.,r: ('J

u) u)r-," ...,IJ1 W til t:.J,-I C. .~t-.u~+~------------------------~-..----------------------------.-------------

5 8 ru ~ Lf) If) If'l Lt) In U'J Ul In If) U') If') If) U') If) ifl Lt') lJ) 11'1 Lf't \..f)

J ~:f. ;1· 0 0 0 0 0 0 0 0 0 0 0 0 () 0 0 0 0 Co' 0 0 0 0 () 0 0 0------.--~-.~----------------------------------------_.-----------------------------_._---5H[~o>::

(J".Il ," U)

'.1'\ .0

N

'-- o o o o o o o o oo o o o oN(" o:2I~~----------------------------------.~-,'o.c-~------------------------------------------------------------~--------------'"-cl·Co

~ ~ ~ ~ 0 0 0 0 0 0 0 0 000 0 0 0 0 C 0

rt') 0-1 -eM M , , N N M cl , 0 0 0 ~ M M("J ~.....

I.{') If) L.') e() 0::::', (") LJl tI1 lr) LI1

-------------------_._._--,.., o o oo

r..... M N N C"J '\'-1W cl N N , M N ~ cl , 0 0 0 ~ , ~ " ~ ~ ~ N ~ ~ , ~

______ ~ ~ N N .__'_~ ~__ ~ . . N _

I.·doo

ZH

3:

C)<,N

N N (J)

" ClN

oM

sr~1

oo~ o~ o~ o"

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83 24,86 24,95 57400 0 + 1800 59200 14,719 15,171

- 446 -

Appendix B

TABLES OF RESULTS FROM HULL ROUGHNESS ANALYSIS (CHAPTER 1)

COST AND STATISTICAL INFORMATION FOR CASE STUDIES

(CHAPTERS 3 AND 4 )

- 447 -

TABLE (B-1) AVERAGE HULL. ROUGHNESS FOR NEW SHIPS

SHIP TYPE BUILDING PLACE AHR (1J.ffi)

LPG CARRIER ST. NAZAIRE, FRANCE 140ULCC ST. NAZAIRE, FRANCE 157BULK CARRIER SUNDERLAND, U.K. 113GENERAL CARGO SUNDERLAND, U.K. 135CONTAINER DEVON, U.K. 110CONTAINER DEVON, U.K. 89CONTAINER FEEDER TYNE, U.K. 78CONTAINER DEVON, U.K. 121GENRAL CARGO SUNDERLAND, U.K. 120CONTAINER DEVON, U.K. 100CONTAINER BREMEN, GERMANY 125CONTAINER U.S.A. 124CONTAINER U.S.A. 141CONTAINER U.S.A. 165CONTAINER U.S.A. 131CONTAINER U.S.A. 123CONTAINER U.S.A. 124

- 448-

TABLE (B-2) CHANGE IN ROUGHNESS DURING DRYDOCKING

SHIP TYPE INDOCKING OUTDOCKING CHANGE INAHR (1J.IIl) AHR (1J.IIl) AHR (Ilm)

GENERAL CARGO 470 455 -15VLCC 125 156 + 31VLCC 155 222 +67·GENERAL CARGO- 317 352 +35REFRIG. CARGO 558 575 +17VLCC 397 422 +25CONTAINER 159 166 + 7VLCC 212 225 +13REFRIG. CARGO 544 527 -17PASSENGER 629 638 + 9PASSENGER 669 649 -20GENERAL CARGO 109 138 +29REFRIG. CARGO 513 522 + 9GENERAL CARGO 351 340 -11PASSENGER 152 194 +42GENERAL CARGO 178 214 +36PASSENGER 147 143 -4PASSENGER 145 181 +36CONTAINER 124 138 +14VLCC 128 198 +70REFRIG. CARGO 163 160 -3PRODUCT CARRIER 271 293 +22PRODUCT CARRIER 422 426 + 4CONTAINER 172 168 -4CONTAINER 109 107 -2GENERAL CARGO 253 271 +18CONTAINER 124 133 + 9CONTAINER 158 188 +30CONTAINER 430 379 -51CONTAINER 453 415 -38VLCC 166 183 +17VLCC 113 161 +48CONTAINER 147 153 + 6CONTAINER 156 182 +26BULK CARRIER 130 140 +10·RO RO 345 264 -81CONTAINER 377 342 -35CONTAINER 131 139 + 8CONTAINER 146 191 +45CONTAINER 140 155 +15CONTAINER 164 243 +79CONTAINER 131 150 +19CONTAINER 123 154 +31CONTAINER 124 161 +37

- 449· -

TABLE (B-3) CHANGES IN HULL ROUGHNESS WITH TIME IN SERVICE

AVERAGESHIP TYPE AGE AHR INCREASE IN

AHR IN SERVICE(MONTHS) (!J.IIl) (!J.IIl/MONTH)GENERAL CARGO 158 470 + 1.79VLCC 27 125 -0.91VLCC 42 156 -0.41GENERAL CARGO 51 317 +3.10REFRIG. CARGO 70 655. +7.73VLCC 41 303 +3.27VLCC 63 397 +3.72CONTAINER 33 159 +0.20llLCC 18 183 +3.33REFRIG. CARGO 172 1083 +6.92PASSENGER 227 669 +3.72GENERAL CARGO 12 109 -1.08REFRIG. CARGO 61 639 +8.45GENERAL CARGO 34 351 +6.19PASSENGER 26 152 +0.18

.GENERAL CARGO 15 178 +3.67PASSENGER 34 145 -0.85VLCC 112 351 +1.37VLCC 84 128 -1. 17VLCC 13 135 +0.92REFRIG. CARGO 54 595 +8.56PRODUCT CARRIER 182 376 +0.70PRODUCT CARRIER 22 271 +5.92GENERAL CARGO 83 337 +1.82CONTAINER 74 172 -0.30BULK CARRIER 114 429 +2.18GENERAL CARGO 89 407 +2.62PASSENGER 150 782 +5.45PASSENGER 115 524 +3.12CONTAINER 114 241 +0.15VLCC 121 432 +2.06PRODUCT CARRIER ·82 561 +5.01CONTAINER 16 158 +2.19CONTAINER 14 124 +0.07VLCC 78 609 +6.05GENERAL CARGO 30 253 +3.63VLCC 48 244 +1.66CONTAINER 192 430 +1.11CONTAINER 12 F74 +4.25PRODUCT CARRIER 121 505 +2.81CONTAINER 84 453 +3.43VLCC 122 315 +0.76PRODUCT CARRIER Lf~ 420 +6.47CONTAINER 79 228 +0.52CONTAINER 8Li 125 "I .28PASSENGER 174 800 +4.80GENERAL CARGO 111 820 +6.63CONTAINER 118 534 +3.21BULK CARRIER 123 120 +4.99BULK CARRIER 16 130 +0.44RO RO 98 996 +10.16RO RO 54 345 +3.49CONTAINER 84 317 +2.38RO RO 94 544 +4.11CONTAINER 58 285 +1.83CONTAINER 102 283 +0.67

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- 455 -

Appendix C

TABLES OF RESULTS FROM CASE STUDIES (CHAPTER 3)

- 456 -

TABLE (C-1)

CASE STUDY 2.1SHIP A

PRESENT (INDOCKING) AVERAGE HULL ROUGHNESSPERIOD OF

CALCULATION 200llm 300llm 400p.m 500llm 600llm 7001lffi 800llm

NPV 19.3 -.321.4 -572.6 788.6 982 1156 1315.2 years

PROF/ 0.120 2.001 3.565 4.910 6. 115 7.198 8.188INV

NPV 287.5 805 1241 1622 1963 2273 25584 years PROF/

INV 1.790 5-;012 7.727 10.10 12.22 14.15 15.93

NPV 474.8 1148 1723 2229 2685 3102 34866 years

PROF/ 2.956 7.148 10.73 13.88 16.72 19.32 21. 71INV

NPV 608.5 1399 2078 2681 3226 3726 41898 yearsPROF/ 3.789 8.711 12.94 16.6~ 20.09 23.20 26.08INV

NPV 708.3 1584 2344 3021 3636 4201 472510 yearsPROF/ 4.410 9.863 14.60 18.81 22.64 26.16 29.42INV

NPV = Difference in net present value betweenalternative hull maintenance strategies ($1000)

PROF/INV = Discounted profit to investment ratio

- 457 -

TABLE (C-2)

CASE STUDY 2.1SHIP B (1)


CALCULATION 200~m 300~m 400p.m 500~m 600~ 700~m 800~

NPV 30.1 116.6 186.79 246.4 298.3 344.7 386.62 years

PROF/ 0.335 1.300 2.083 2.747 3.327 3.843 4.311INV

NPV 107.6 254:8 376.4 481 573 655 7304 years PROF/

INV 1.199 2.841 4.197 5.361 6.386 7.306 8.142

NPV 160.7 351.7 511. 5 650 773 883 9846 years

PROF/INV 1.792 3.922 5.703 7.248 8.616 9.851 10.98

NPV 198.5 421.6 610 775 921 1054 11758 years

PROF/ 2.213 4.701 6.804 8.639 10.27 11.75 13.11INV

NPV 226 473 683 868 1033 1183 .132110 years

PROF/ 2.52 5.275 7.620 9.679 11.52 13. 19 14.73INV



- 458 -

TABLE (C-3)

CASE STUDY 2.1SHIP B (2)

PRESENT (INDOCKING) AVERAGE HULL ROUGHNESSPERIOD OF .

CALCULATION 200llm 3001lID 400p.m 500llm 600llID 700llm 8001lID

NPV -89.1 -1.7 '69.2 129.4 182.0 228.8 271.22 years

PROF/ -0.966 -0.018 0.751 1.403 1.974 2.482 2.941INV

NPV -10.8 137.9 260.7 366.2 459.1 542.4 618.14 years PROF/

INV -0. 117 1.496 2.828 3.972 4.979 5.883 6.704

NPV 49.2 235.7 397.0 536.9 660.8 772.5 874.66 years

PROF/ 0.465 4.306 5.832 7.167 8.379 9.486INV 2.556

NPV 81.8 306.2 496.5 662.5 810.5 944.5 10678 years

PROF/ 0.887 3.321 5.385 7.185 8.792 10.24 11.57INV

NPV 108.8 358.0 570.2 756.4 923.1 1074 121310 years

PROF/ 1.180 3.883 6.184 8.204 10.01 11.65 13.16INV



- 459 -

TABLE (C-4)

CASE STUDY 2.1

SHIP C


CALCULATION 200ll-m 300ll-m 400~Lm 500ll-m 600llffi 700ll-m 800llffi

NP,V -282.9 -164.5 ·-69.0 11.5 81.6 143.8 199.82 years

PROF! -0.672 -0.391 -0.164 0.027 0.194 0.342 0.475INV

NPV -176.5 24.5 189.6 330.7 454.4 564.9 665.04 years PROF!

INV -0.419 0.058 0.450 0.786 1.079 1.342 1.580

-NPV -104 156:3 373.0 559.9 724.9 873.1 1007.96 years

PROF!INV -0.247 0.371 0.886 1.330 1.722 2.074 2.394

NPV -52.8 250.9 506.3 728.1 925.1 1103 12658 years

PROF! -0.125 0.596 1.203 1.729 2.197 2.620 3.005INV

NPV 15.7 320.3 604.9 853.4 1075 1275 145910 years

PROF! -0.037 0.761 1.437 2.027 2~553 3.029 3.466INV


PROF!INV = Discounted profit to investment ratio

- 460 -

TABLE (C-5)

CASE STUDY 2.1SHIP D


CALCULATION 200j.lm 300j.lm 400!lm 500j.lffi600j.lffi700j.lffi800j.lffi

NPV -69.6 12.0 77.7 133.2 181.4 224.3 262.92 years

PROF/ -0.503 0.087 0.562 0.963 1.312 1.622 1.901INV

NPV 3.7 142.3 256.0 353.2 l138.3 514.5 583.44 years PROF/

INV 0.027 1.029 1.851 2.554 3.169 3.720 4.218

NPV 53.8 233.2 382.4 511.2 624.8 726.9 819.76 years

PROF/ 0.389 1.686 2.765 3.696 4.518 5.256 5.927INV

NPV 89.2 298.4 474.3 627.2 762.8 885.2 996.98 years

PROF/ 2.645 2.158 3.430 4.535 5.516 6.401 7.208INV

NPV 114.8 346.3 542.3 713.6 866.3 1005 113210 years

PROF/ 0.830 2.504 3.921 5.160 6.264 7.267 8.185INV



- 461 -

TABLE (C-6lCASE STUDY 2.2 SHIP A

OUTDOCKING DIFFERENCE IN NPV.RELATIVE TO AN OUTDOCKING AFTERAHR REBLAST OF 125 f.J.mAFTERREBLAST 2 YEARS 4 YEARS 6 Y;EARS 8 YEARS 10 YEARS

125 f.J.m - - - - -

150 -121.8 -200 -253 -291 -318

175 -232.3 -384 -48.8 -561 -616

200 ,:",333.7 -554 -707 -816 -896

225 -427.8 -714 -913 -1056 -1161

250 -515.6 -864. -1107 -1283 -1414

All NPV values are $1000

TABLE (C-7lCASE STUDY 2.2 SHIP B

OUTDOCKING DIFFERENCE IN NPV RELATIVE TO AN OUTDOCKING.AFTERAHR REBLAST OF 125 umAFTERREBLAST 2 YEARS 4 YEARS 6 YEARS 8 YEARS 10 YEARS

125 f.J.m - - - - -150 -36.7 -59.5 -74.8 -85.5 -93.2175 -69.6 -133.6 -143.4 -164.4 -179.5

200 -99.5 -163.3 -206.9 -237.7 -260.1

225 -127. 1 -209.5 -266.2 -306.5 -335.9

250 -152.6 -252.7 -322.0 -371.5 -407.7


- 462 -

TABLE (C-8)CASE STUDY 2.2 SHIP C

OUTDOCKING DIFFERENCE IN NPV RELATIVE TO AN OUTDOCKING AFTERAHR REBLAST OF 125 f.lmAFTERREBLAST

2 YEARS 4 YEARS 6 ~EARS 8 YEARS 10 YEARS

125 f.lr.l - - - - -,

150 -50.4 -81.7 -102.6 -117.1 -127.6

175 -95.6 -155.4 -196.5 -225.0 -245.5-

200 -136.5 -224.0 -283.3 -325.1 -355.4

225 -174.0 -287.0 -364.3 -419.0 -458.6

250 -208.8 -345.9 -440.2 -507.3 -556.2


TABLE (C-9)CASE STUDY 2.2 SHIP D

OUTDOCKING DIFFERENCE IN NPV RELATIVE TO AN OUTDOCKING AFTERAHR REBLAST OF 125 f.LmAFTERREBLAST

2 YEARS 4 YEARS 6 YEARS 8 YEARS 10 YEARS

125 !J.m - - - - -

150 -34.7 -56.4 -70.7 . -80.8 -87.9

175 -65.8 -107.4 -135.5 -155.0 -169.2200 -94.0 -154.4 -195.4 -224.2 -245.0

225 -119.9 -197.9 -251.1 -288.8 -316.2

250 -1L.3.8 -238.4 -303.4 -349.7 -383.3


- 463 -

TABLE (C-10)

CASE STUDY 2.3

.

PRESENT (INDOCKING) AVERAGE HULL ROUGHNESS.200 j..I.m 300 um 400 um 500 um 600 um 700 j..I.ffi 800 um

.24 rrooths

E-o cl;delay +59.1 -246 -500 -720 -914 -1091 -1252

Cl)cl; Cl..~ HIII ::t: 48 rrooths[xl Cl)a:: delay -203 -725 -1166 -1551 -1895 -2209 -2497[xlE-ocl;H 24 nrnthsCl[xl delay +13.2 -74.8 -146. 1 -206.7 -259.6 -306.8 -349.42 IIIH

Cl..0 H 48 rroothsE-o ::t: -66.4 -215.6 -339.0 -444.9 -538.2 -622.0 -698.0Cl) delay[xl:>HE-ocl; 24 rrooths~ 60.9 -58.2 -154.2 -235.3 -305.8 -368.3 -424.7[xl delaya:: u:> Cl..Cl.. HZ ::t: 48 rronthsCl)z delay -12. 1 -214.1 -380.0 -521.9 -646.2 -757.3 -857.9H

[xlUz 24 rrooths[xla:: delay +26.1 -56.2 -122.5 -178.5 -227.1 -270.3 -309.2[xl Cl[%..[%.. Cl..H HCl ::t: 48 rroothsCl) delay -38.5 -178.0 -292.5 -390.4 -476.2 -541.4 -622.3


- 464 -

TABLE (C- 11)CASE STUDY 3.1

2 YEARS 4 YEARS 6 YEARS 8 YEARS 10 YEARS0H0:::c:r::z PROF/ PROF/ PROF/ PROF/ PROF/t.:J NPV NPV N~V NPV NPVu INV INV INV INV INVrI)

1 17.3 0.175 298.4 1.695 711.9 2.919 1190 3.923 1691 4.760-2 17.3 0.175 181.3 1.030 408.1 1.674 660.6 2.178 919.1 2.586

c:r:fl...H::c 3 -42.8 -0.434 -6.4 -0.037 62.0 0.254 145.3 0.479 234.0 0.659rI)

4 -98.7 t-l -176. 1 -1 -243.9 -1 -303.3 -1 -355.4 -1

1 -31.2 1-0.469 23.7 0.200 120.2 0.733 237.8 1•165 364.1 1.523

2 -31.2 0.469 -11.7 -0.098 28.9 0.176 79.4 0.389 133.4 0.558cofl...H::c 3 -49.5 0.745 -68.0 -0.574 -74.1 -0.451 -73.15 0.359 -68.3 -0.286rI)

4 -66.4 1.000 -118.4 -1.000 -164.1-1.000 -204.0 1.000 -239.1 -1.000

1 -231.9 -0.826 -303.9 -0.607 -300.2 -0.433 -251.8 -0.292 -177.5 -0.176

2 -231.9 -0.826 -253.3 -0.705 -428.0 -0.617 -473.6 -0.549 -500.3 +0.495uc,H...... 3 -257.3 -0.916 -431.3 -0.861 -570.1-0.822 -683.4 -0.792 -777.4 -0.769U5

4 -280.8 -1 .000 -500.9 -693.9 -693.9 -1.000 -863.0 -1.000 -1011 -1.000

1 -60.6 -0.643 -32.5 -0.193 38.15 0.164 131.2 0.453 234.6 0.692

Cl 2 -60.6 -0.643 -66.5 -0.396 -49.7 -0.213 -21.2 -0.073 12.8 O.03ec,H::c 3 -78.0 -0.828 -120.1 -0.71'5-147.5 -0.634 -165.8 -0.573 -178.1 -0.527rI)

4 -94.2 -1.00 o -168.0 -1.000 -232.E -1.00o -289.5 -1.000 -339.2 -1.000


- 465 -

TABLE (C-12)

CASE STUDY 3.2

SHIP A SHIP B SHIP C SHIP C

rIl rIl NPV 307.6 229.6Cl) ..c..c -5.7 35.7Cl: +>+><C C CW o 0>< s s0 o.;r AW 47.8 35.7~ MN -0.9 5.5

rIl rIl NPV 548.4 341.0 291.6 153.6..c..cCl) +> +>Cl: C C<C o 0w s s>< \O.;r AW 125.9 78.3 66.9\0 MN 35.2

rIl rIl NPV 610.7 358.8 314.7..c..c 168.4Cl) +> +>Cl: C C<C o 0w S S>< co.;r AW 197.5 116. 1.;r .;rN 101.8 54.5

(jJ rIl NPV 1042 642.2 540.3 288.2Cl) ..c..cp:: +>+><C C CW o 0>< a sco co.;r AW 190.7 117.5 98.8 52.7.;rN

All NPV and AW values are $1000months denotes drydocking intervals of alternatives 1 and 2 respectively

- 466-

TABLE (C-13)CASE STUDY 5 .

,

SPEED DIFFERENCE IN NPV ($1000)LOSS

SHIP WHENTYPE FOULED 2 YEARS 4 YEARS 6 YEARS 8 YEARS 10 YEARS

5% 260 515 709 893 1.067SHIP A

10% 575 1.142 1.569 1.976 2.361

5% 125 247 341 433 507SHIP B

10% 254 501 692 878 1.029

5% 120 234 338 432 518SHIP C

10% 241 470 679 868 1.040

5% 80 158 230 283 333SHIP D

10% 162 319 464 572 672

- 467 -

TABLES OF RESULTS FROM CASE STUDIES USING THE

DYNAMIC PROGRAMMING MODEL

Path configuration is shown in Figure (2.15c)

Maintenance alternatives are described in Section 3.2.8

Reblast Alternativel - first alternative coating system in Figure (2.15c)

Reblast Alternative2 = second alternative coating system in Figure (2.15c)

IDENT1- ROUGHNESS SCENARIOTABLE FICATION SHIP WITH SECOND ALT.

CODE COATING SYSTEM

C-14 3320 A 1C-15 3321 A 2C-16 3322 A 3C-17 3323 A 4C-18 2320 B 1C-19 2321 B 2C-20 2322 B 3C-21 2323 B 4C-22 4320 C 1C-23 4321 C 2C-24 4322 C 3C-25 4323 C 4C-26 5320 D 1C-27 5321 D 2C-28 5322 D 3C-29 5323 D 4

- 468 -

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-("04 .... _ M......... .. .....

ClI-_N..,

...-- -N,.., ... .,.,uuuuu

_N...., .,,-.or-..CDOO...,...,"" ww"" ......w'"I-

4:...

- 479 -

-tlaN.."MN_Q_-00 TII~'-"'N"'"COM"IIf"M ... --.or...,;)o_-0 -.c. "" ·0 -0 -0 '0 r-, "I I I I I I , I I

.,.<>

'"<><>""....'\ "" ca"'''II">COoM

~.NNI , I

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N

0_

::!~~'?;~"!!r::~~::,,:::«:!r:;~~c;!<:,!:~,::~~:~~':!~~~':'!':!-?'?~

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~ ~ H _ " " b _ " " _

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('>1 NN_M

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- 480 -

g<> <>

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t. .. % :z:

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u ... ~ "- '-NM

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0......*:

- 481

<><>o'.1) t"),"~II'lI""'M""'VJCD"'o-.o-.

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<:>oc>;;;

<>s<n "".,..o .....·r~ ....mo

("I c... u•• "'I" 0" 0'-1" W!.1"1 :n -.0 -.0 \(') "'., Il"lI I/')

",:'l"'Jr"MMI"lF<)Mr"')

_N,.., ... IO-O ......O'IIO-'~=

.... L.l,.. ..... l.Ia.u.u..u.. ..... t.r- .... u..

N..,In.....0u

:"".<n~'"UJ.... g s<!: ;g g <>:= 0 '"0 <.> 0 0 0

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i!i :z: :z: '" :z: z

\;;'".. '"'" :c.... ;C N ... '".... ..

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N o

.......:::>

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_NM"'"tn-()r-................._NMNN.-In

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....<I::cI-

~";:':!":"! ... .,.,

l"lr.,c;-.., to') .....oXq;

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........

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""...

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.,.ceN...

'..N

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- 482 -

Cl,_

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u,.,

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<><:>c-

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g<:>;;;

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0_

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"",_<r....

-NM an-O ..... QlO"o _

Ll..La..u..l La.. ..... La.. .... ~u:;:

e-c,%

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WWlULUW ........~ .... l.&I

- 483 -

sg'" -e- ~ N Q_,

olo")r -, ·,.."'"COOO'-CJ)CO-('4 _

-.0-.0-.0"' ... 0-. ...... ·O,In...;)O<-O-O10(,0000)"''''-0NN C"IN:- .. NN

1" ... .,...00 ~_N'<I~lNo..er-.O~_COO-1fl1r.l'O-OVlIf".IMMJ1''''''''M.-..MMr'"'JM

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Cl....

- 484 -

Appendix D

VARIABLE DESCRIPTIONS AND SAMPLE OUTPUTS

TABLE (D-l) Variable descriptions for deterministic and

dynamic programming model

TABLE (D-2) Description of additional variables in

probabilistic cash flow simulation model

SAMPLE (D-l) Output from deterministic model

SAMPLE (D-2) Output from dynamic programming model

SAMPLE (D-3) Output from probabilistic cash flow

sLmi Lat Lon model

TABLE (D-l)

- 485 -

VARIABLE DESCRIPTION

CODE four digit code number serving as identificationof each case study evaluation

TRl

TR2

TaJ

TR4

TRS

TR6

LIFE

TR7

TR8

TR9

TRlO

trigger for maintenance arternative 2if TRl-l then ON, otherwise OFFif TRl=O in dynamic programming routine, then in-service period prior to first drydocking

trigger for fouling alternativeif TR2=l then ON, otherwise OFF

trigger for propeller deteriorationif TaJal then ON, otherwise OFF

trigger for sensitivity analysisif TR4=l then ON, otherwise OFF

trigger for speed/power operation of alternative 1if TRS=O then constant power operation

TRS-l then constant speed operationTRS 1 then constant optimal speed operation

trigger for drydocking procedure for alternative 1if TR6=O then NO reblast or change in paint system

TR6=l then ONE reblast and/or change in paint syst.TR6 1 then MORE THAN ONE reblast and/or change

in paint systemremainder of ship life or period for whichcalculation is requiredtrigger for speed/power operation of alternative 2- optional values as for TRS

trigger for drydocking procedure for alternative 2- optional values as for TR6

trigger for fouling option with alternative 1if TR9=O then no fouling

TR9=l then fouling with first paint systemTR9 2 then fouling with first and folJ~wing systems

trigger for fouling option with alternative 2- optional values as for TR9

VL

VB

ship speed in laden (or average) condition [knots]

ship speed in optional ballast condition [knots]

POWERL

POWERB

EXPO

ROUGHBASEFUELRATE

AUXTPD

TPDP

QPC

AREAL

AREAB

L

FACTOR

- 486 -

shaft power corresponding to VL [kW]

shaft power corresponding to VB [kW]

exponent to speed/power curve of the form P=kVft

hull roughness corresponding to speed/power description

specific fuel consumption at POWERL [g/kW hr]

daily auxiliary fuel consumption at sea [tonnes/day](given as heavy fuel oil equivalent)

daily fuel consumption in port [tonnes/day]

propulsive coefficient (including transmission losses)

wetted surface area in laden condition [m2]

wetted surface area in ballast condition [m2]

ship length between perpendiculars [m]

multiplication factor used to increase/decrease thepower penalty predicted by the ITTC correlationformula for hull roughness

MAXCARGO

LOADF

SR

MILESDISTLOAD

PTDAYS

OFFH

maximum cargo carrying capacity [tonnes or units]loadfactor

stowage rate (applies to volume carriers only)

length of roundtrip voyage [no miles]

% of roundtrip distance in laden condition [%]number of days in port per roundtrip

number of days off hire per annumCREW

CRCRUPKEEP

UPKCR

fIX

FIXCR

FUEL

FUELCR

crew costs per annum [S1000]

annual escalation in crew costs give as fractionupkeep costs per annum [S1000]

annual escalation in upkeep costs (fraction)

fixed costs per annum [S1000]

annual escalation in "fixed costs (fraction)

fuel cost per tonne (R.V.F.) [S/tonne]

annual escalation in fuel costs (fraction)

PORT

PORTCR

CARGO

CACR

FRATE

FRCR

DR

KSC

- 487 -

port charges per roundtrip [$1000]annual escalation in port charges (fraction)

cargo handling charges [$/tonne or unit]

annual escalation in cargo handling charges (fraction)

freight rate [$/tonne or unit]

annual escalation in freight rate (fraction)

discount rate used in present value calculations(fraction)

inflation rate (fraction)

FIRST ALTERNATIVE :

PAINTCOST1

PAINTCOST2

PAINTCR

DOCKHIRE

CLEANCOST

DOCKCR

ININVEST

cost of first coating system [$/m1]

cost of optional second coating system [$/m1]

annual escalation in coating system costs (fraction)

total daily cost of hire of drydock [$/day]

additional cost of special hull cleaning/preparationprior to application of optional second coating system

annual escalation in docking charges (DOCKHIRE &CLEANCOST) given as fraction

initial single capital investment in year 0 [$1000]NEW1

MINCS1

INCDA1

INCDB1

NEW2

MINCS2

INCDA2

initial AHR with first coating system [pm]

monthly increase in AHR in service with firstcoating system [pm]

slope of regression line for roughness increasein drydock, first system

constant term for roughness increase in drydock,first system

initial AHR with second coating system afte~' reblastor equivalent hull surface treatment [pm]

monthly increase in AHR in service with secondcoating system [pm]

slope of regression line for roughness increasein drydock, second system

INCDB2

DOCKINTI

DOCKINT2

NEXTDOCK

DOCKDAYS

XTRADAYS

NEXTBLAST

BLASTINT

NEXTSURV

SURVINTI

SURVINT2

- 488 -

constant term for roughness increase in drydock,second systeminterval between drydockings with first coatingsystem [months]

interval between drydockings with optional secondcoating system [months]

number of months until next drydocking

number of days in drydock

additional number of days required in drydock forreb1ast or equivalent hull surface treatment

number of drydockings until reb1ast and change ofcoating system (if NEXTBLAST=l then at next dryd.)

number of drydockings between reb1asts or equiv.(i.e. if BLASTINT=2 then at every seconddrydocking following NEXTBLAST)

number of drydockings until next classificationsurvey in drydock

number of drydockings between classification surveysin dock with first coating system(if SURVINTl=l then at every drydocking)

number of drydockings between classification surveysin dock with second optional coating system

NOFOULl

NOFOUL2

SATFOUL

FOULOSS

time period from outdocking free from foulingwith first coating system [months]

time period from outdocking free from foulingwith second optional coating system [months]time period from initial fouling settlement to reachsaturation growth [months]

speed loss with fouling when saturation growth hasbeen reached [knots]

SECOND ALTERNATIVE :

PAiNTCOSTl

1ININVEST

same variable descriptions as for alternative 1

- 489 -

NEW1

1 same variable descriptions as for alternative 1

SURVINT2

PERCHANGE %change in variables in sensitivity analysis

NOFOUL

1 same variable descriptions as for alternative 1

FOULOSS

TABLE (D-2)

VARIABLE DESCRIPTION

CASES number of variables described in terms of aprobability distribution function

PARNUM(l)1to

PARNUM(CASES)

code number of each of the variables described interms of a probability distribution function

DISTPAR(*,l) code number for distribution shape, (1) impliessingle half or part of truncated normal distribution,(2) implies a combination of two truncated halves

DISTPAR(*,2) if code=l then: mean value of normal distributionfrom which truncated part is obtained

if code=2 then: mean value of actual variable

DISTPAR(*,3) if code=l then: limiting ordinate at non-continuousend of distribution

if code=2 then: standard deviation of lower truncatedhalf of normal distribution

DISTPAR(*,4) if code=l then: standard deviation of normaldistribution from which truncatedpart is obtained

if code=2 then: standard deviation of upper truncatedhalf of normal distribution

above sequence for DISTPAR repeated for all CASES

- 490

NSIM number of repeat simulations requiredREPEAT trigger for random number generation

if REPEAT=l then identical sequence of random numbersproduced for every programme run, etherwise startingpoint is random and the following sequence of randomnumbers is non-repeatable

K2 specifies (number+l) of equally spaced groups forhistogram and frequency distribution of the finalnet present value of the ~nvestment

C the negative of the minimum acceptable net presentvalue of the investment, used in calculating thecertainty equivalent assuming a logarithmicutility function

- 491 -

**,~.~·t*~••~**•• **f*~4*~~.****~ *• TECHNO ELONDMIe ANALYSIS *

INrUT-DhTA : TECHNICAL

SHIP SPEEn LADEN CONDITleN: 15.0 I·.nots CORRESPONDING PDWER LADEN: ,~OO kUSHIP SPEED aALl~ST CONDITION: 16.7 knots CORRESPONDING POWER DALLAST: 9400 k~l

EXPONENT TO THE SP;ED/POYER CURVE: 3.216

AHR CORRESPONDING TO SPEED/POWER DATA: 125

SPECIFIC FUEL COHSUHPTICN: 219 g/kUhr

~.Ot/day

ExrONENT TO S. r.c. Clli(VE: O. O~(I

AUXILLIARY FUEL CONSUMPTION: FUEL CONSUMPTION IN PJRT: 5.0 t/day~ETTED SURFACE AREA LADEN: 10500 sq.,.. WETTED SURFACE AREA fALLAST: 7660 sq.~

PROPULSIVE COEFFICIENT: 0.66

S~IP LlNGTH (D.P.): 214.5 M

INPUT-DATA I OPER4TIGNAL

LE~GTH OF ROU~DTR!PI 16380 N.H.DISTANCE LADEN: 64% DISTANCE IN RALlnST: 36 'l:

HUM~ER OF DAYS IN PORT PER ROUNDTRIP: 12.0 d~ysNUH~ER OF DAYS OFF HIRE PER ANNUH: 0.0 days

HAXIHUK CARGO CARRYING CAPACITY: 60000

LOADrhCTOp.: 0.50

INPUT-DATA : FI~ANCI4l

tREY cus: <11C(}O)' 1000 ANNUAL ESCALATION: 10.OXANNUAL ESCALATION: tLOl

ANNUAL ESCALATION: 10.0l:AiiNUAL t:5~ALATiON: 10.0;':

ANNUAL rs GALA TJ ON: :0.0%ANNUAL ESCALATION: 10.0;(

IIPKEfP C(!Sl (~1 000): 500

FIX[!l cesr ($10(00): 1500

PORT CHARGES (PER ROUNDiRIP, $10(0): 45

f'UH cusr ~$nQH"E): 185

fREIGHT RATE ($/TD~NE OR UNIT): 19.00

- 492 -

INPUT-DATA : ALTERNATIVE HULL HAl~TEHA~[r STRATEGIES

Al.TERrlATIVEI

fRESfHT HULL RGUGHNESS (AHR): 50() UM

MONTHLY INCREASE IN AHR IN SER~ICE: i .SS Uti

INCREASE IN AHR IN DHVfOCK:

DRYDOCK INTERVAL VITH PRESENT SYSTEM: 24 lIonthsHEU AHR AFTER ~EFLHST O~ EGUIV.: ISO UII

NEU HONTHLY INC~EASE IN AHR IN SERVICE: 1.85 UII

NEU INCREASE IN AHR IN DRYDOCK:

PRY DOCK INTERVAL YITH HEY SYSTEr.: 24 Months

"EXT DRYDOCKING TO TAKE PLACE IN: o lIonths7 days

5 days

1ST. DRYDOCKING

1ST. DRYDOCKIHGDRYDOCKING

DRYDOCKING

DIIYS IN DRYDOCK:

EXTRA D~YS IH DRYDOCK FOR REBLAST:

HEXT REBLAST TO TAKE PLACE AT:HEXT CLASS. SURVEY TO TAKE PLACE liT:CLASS. SURVEY 10 TAKE PLACE AT EVERY;CLASS. SURVEY UITH NEU SYSTEM AT EVERY:PAINT SYSTEM COST UITH PRESENT SYSTEM: 8.17 '/sq.1I

8.17 $Isq.1IPAINT SYSTEM COSI UITH NEU SYSTEM:ANNUAL ESCALATION OF PAINT S~STEM COST: 10.0%

DAILY COST OF HIRE or DRYDOCK: 12000 •ADDITionAL COST OF RfBLAST OR EGUIV.: 12.02 $/sq.1IANNUAL ESCALATION OF DRYDOCK CHARGES: 10.0%ADDITIO"Al INVESTMENT IN YEAR 0 ($1000): o

INPUT-DATA: MISCELLANEOUS

SHIP LIFE iOR PERIOD OF CALCULATION): 6 yearsCISCOUHT RATE USED IN CALCULATIONS: 17.5%ANNUAL RftTE OF INFLATION: 10.0%I CHANGE IN ~ARIABL£ IN SENSITIVITY ANALYSIS: 10%

% CORllECTIO~ 10 ITTC COr.REI.HION FORMULA: -40%

tt. CALCULATIOMS MADE FOR TUO ALTERNATIVE HULL MAINTENANCE STRATEGIES

.*. THE EFFECT OF HULL FOULING ~OT INCLUDED

...'" THE EFFECT OF PROPELLER ROUGH~ESS ArID FOULING ser I1lCLIJDED••• SENSI1IUITY ANALYSIS ON NAJOH PAK~METERS IS INCLUDED

t.* SI~ULATION OF SHIP OPERATION FOR ALTERNATIVEl BASED ON CONSTANT POUER

tt. SIHULATIOH OF SHIP OPERATIQN FOR ALTERNATIVE~ ~ASED ON CONSTANT POYER

i'lL TERNATl VE2

500 un

I.S5 UI1

-0.094*CAIiRI t37 tiM

24 I'IOnth~

ot ••..'"***

o "Clnths7 daY5

."'*

1ST. DRYDOCI(ING

Dr<YDUCKING

."''''8.17 $/sq.1I

....10.0:1:

12000 $....HI.O%

o

••• HULL ~ArHTENANCE AllERNATIVEl INCLUDES ONE ~r~lAST OR CHANGE IH PAINT SYSTEM••• HULL "AIN1[~ANCE ftLIERNATIVE2 INCLUDES ND REBLAST OR CHANG[ IN P~INT SYSTFM

* Al.1ER~/ATlVt1 - 493 -

1* :SPEE.' 011 n:"f f'v',IEri ON 1ST r.IINUAL NET Ct:5H ·l.)lJ ;*f COSTS

1*1'(EAf< ROUIIDTRIP5 ROU11l'fR1P l~fjll!'I:ITRlf' f'!JtL COSIS EXCUmING :*1 (,LLOCATEII iD

1* IPeR ANNUM IN '(H~ YE(.lR (f(V) nH~tJSI\:iDS ) CAl"lTfi' CHfI[<GlS: * I ,'AINT SYSTEM

It.:-----------------------_ ..._---_ ..__ .._----_-._-_. ..._--._---- .._------_._--_ ..__ .._----_ ..----------------------:*:

6.299 14.04 9':')0 2799 41S 1*: 29<):*:

2 6.1,98 14.89 9400 3186 912 1*1 0:*:

3 6.349 14.81 9400 3440 712 1* f 104:* :

6.4bO 14.78 9J,OO 3860 1047 1*1 0f* I

5 6.320 1~.73 9400 41-'.7 012 :~'I 126:*1

6 6.432 14.69 9400 4675 1215 :*1 0lltq

THE NEr PRESENT VALUE OF THE OPERATING ACCOUNI (EXCLUDING CAPITAL CHARGES) IS ($1000): 2829

THE HET PRESENT VALUE OF TKE COSTS ALLOCATE~ TO T~E PAIHT SYSTEM IS (11000): 375UHICH IS EGUIVALENT TO AN ANNUAL UORTH ESCALATING AT 10 % PER ANNUM OF ($1000): 86

ALL PRESENT VALUE CALCULAlIONS ARE USIUG A DISCOUNT FACTOR OF 17 %

•• ** •••• ** •••••••••• •• ALTERNATIVE 2 *• *

1*1SPEED OH 1ST POUER OH 1ST AHtlUf,L NET CASH flOU 11lFFFRENCE HI :*1 COSTS

1*:YEAR RDUNDTRIPS ROUilDTRIP ROUNlITRlf' FUEL COSTS EXCLUDING NCF llETUEEH :~: ALLOCATE[! TO

:*;PER ANNUM IN TilE YEAR (KU) <T HOUSAIIDS) CAPITAL CHARGES: ALTI AND ALT2 ~* I PAINT SYSTEM

:.;

:*16.236 1~.48 9~00 2855 459 -41 1* : 66

1*12 6.351 14.~6 9400 3203 728 184 :* I 0

;:t:3 6.227 14.45 9~OO J4j6 543 169 1*1 104

:*:t.J~2 14.1,3 9~OO 3877 867 ISO I~: 0f:f;!

5 6.219 14.43 9400 HaJ 644 168 l:f: 126:*1

6 6.334 14.~ 1 9400 4692 1035 180 :* ; 0:*1

-------------------- ______ 0. _____ --------------------- __________________________________________________ •__ • ___________

THE ~ET PRESENT VALUE OF TilE OPEkATI~G ACCOUNT (EXCLUDING CAPITAL CHARGES) IS ($1000): 2388

THE DIFFERENCE IN ~PV hETYEEN THE OPERATING ACCO~NTS OF ALll AND ALT2 IS (fIOOO): 440UHICH IS EOUIVALEIIT TO ,'H M/fIliAL ~QRTU ESC4UilNG AT 10 I fH: ilNI!I!HOF ($1000)1 101

'HE NET PRESENT VALUE OF lHE COSTS Al.LOCA!EB 10 TUE PAl NT SYSTEM IS ('10001: 193"HICH IS EOUIVALEI!T TO MI 1:~I/'iAL ~ORTH ESCA~(;TIHG AT 10 I PEP. r,NNUH OF ($10l'C): 44

THE RATE OF RETURN O~ lHE A~OI';nHAl IHUE~TEE~T C~N ~01 DE CALCULATED

DISCOUNTED PROFIT Ht !~\'FS1~[NT RAiIiJ r~R T!lF INCREi!;::;nAl. INVESTrl::IH IS: 3.11')1

**.~••••*$1.~.*~t**1#*~*'** *~ SENSITIUITY ANALYSIS •

: HPV OF: ALTERN.i (EXCL.

- 494 -

: ilPV OF: AL TERri. 2: (£XCI..

D IFFER£IlCEI~ HPV

:l;APlT,\l CH.):CItPliAl CH.): Ali. 1&2I

BE"iUEEil

: BASIS CONDITION1

I~PROV~ PROPULSION EfFICIEilCY BYIOZ

SPECIFIC FUEL CONSUHP110N DEeR. BY 10l

VOYAGE DIST~NCE DDUBlED (F.R. COMP.)Fuel PRICE INCR. BY 10% (F.R. COMP.)FUEL PRICE INCR. ~Y 10% (NO F.R. COMP.)

FUEL ESC. INCR. BY 10% IF.R. COMP.)

FUEL ESC. INCR. BY lOX INO F.R. CO"P.)• FREIGHT RATE INCR. BY 10%

FREIGHT RATE ESC. IIlCR. BY 10%COST OF PAINT INCR. ~Y 10%HIRE OF DRY DOCK INCR. BY 10%COST OF HULL ~REP. INCR. BY 10%

DOCKINT. OF f.LT.1 IIiCR. BY 12 1I0NTHS

ALL DOCKI"T. INCR. BY 12 KCNTHS 1.1

DAYS IN DRY DOCK INCR. BY 2 FOR ALT.I ,

DAYS IN DRYD. IHCR. BY 2 FOR BOTH ALT.

EXTRA DAYS IN DRY DOCK INCR. BY 2IMPORTANCE 3F ROUGHNESS DEeR. BY 10%

2829 ,

1125

-1247

-2960

3008

7108

2308

827

-41-16

-1256

-98-2972

2957

-19-15-II

168

168

-74

-74

-2833

815

1134

-113

-160

69S7-19-12

oo

138

o-72

o

91

HO

11

-9

72

30

9

61

1251

122o

-3-11168

30

-74

-2

-28-57

PRESENT ~ORTH OF DIFFERENCE BETYEEH ALT. 1&2 AT VARIOUS nISCOUNT RATES

YEAR lOX0%

o o o-39 -37

2 191 16i 1523 169 116 127

130 148 123

168 lJ2 10~

IBO 107.

~FV I ~71- - .•.• _ - ----- .. ._..... - ,. __ .• _ .•- .• - - .• -- - - -- - _ .• _- ••. .•- • __ . - - ...__ ... .' .......,, •• _'''_'0 .... ._. ._ .._

;04

20%

-31

12899

III

68

30%

o o

-32

,,,977

6145

37

401

o·-29

9·1

62

31

22J

ClhiNGE INDIFFERENCEflS XOF BASIS

0.00 1

2.55

-2.04

16.266.812.09 •

13.90

2.74

11.53

27.62·'0.00-0.59"2.56

38.236.83

-16.79

-0.38

-~.3a-12.93

50%

o-27

5035

2216

1;'8

YIELD OFADDITIOr-lP.LINVE5H1EiH

**

**

****

**

.,

....

**••

*.

75%

o-23

60

3119

10

CfltiHGE !NYHLDCOhl'ARED!lITH BASIS

0,00

**

**" 1

I.,,**

**.•*

- 495 -

SM1PLE (D-2)COOt.:; o

••••• DYNAMIC PROGRAHKINB OF DPTIMAL HULL MAINTENANCE STRATEGIES *****

RESULTS OF BACKWARD DYNAMIC PROGRAMMING

DRYDOCKING NUMBER HA) YEAR 0

PATH FROH OPTItiAL ROUTE NPV iSl000)_--------- ------------- --_ ....._-_ ..,._--A 1 :2:2:2:5:5 4174

DRYDOCKING NUMBER 2CEt) YEAR 2

PATH FROM OPTIMAL ROUTE NPV (S1000)_----_ ... _- ------------- --_ ..... __ .,.._---

B 1 :3:3:5:5 3104B 2 :2:2:5:5 3158B 3 :5:7:5:5 3159

DRY DOCKING NUMBER 3(C) YEAR 4 :

PATH FROM OPTIMAL ROUTE NPV (SI000)-_ .... ------ ------------- ------_ ....---C 1 :4:4:4 2171C 2 :2:5:5 2171C 3 :3:5:5 2213C 4 :6:8:10 2216C 5 :7:5:5 2184

DRYDDCKING NUMBER 4(D) YEAR "PATH FROM OPTIMAL ROUTE NPV (S1000)... _--_ ..._-- --,----------- _ ...- ....__ .... _ ....... -

D 1 ;5:5 1348D 2 :5:5 1348II 3 :5~5 1348n 4 ~4:4 1390D 0 :7~9 1391D I:. :S:10 1361II 7 :5:5 1348

nRYIlOCK ING NUHBER S(f) YEAR S

PATH FROM OPTI MAL ROllTE Np!J (S1000)-_ ... _--_ ...- ..._----, ...._-_ ......... _ _ ..... ,-_ ......_-- .._._-E 1 :6 600E 2 :6 600E 3 ~3 607E " :4 632E 5 :5 l:6~E 6 :8 657E 7 :9 641E S : 10 629E 9 :11 618

- 496 -ReSULTS OF FORWARD OYNAMiC PROGRAMMING---------------------------------------DRYfiOCKING NU~iDER 2HI) YEAR 2

PATH TO OPT! Hr-IL f,OUTE NPV (81000)-, .....~--.-...-- -------_ ...._--- ---_._ ..',_-..;...--

n t : 1 918s 2 :2 1016D 3 :3 952

DRYDOCKING NUMBER 3(C> YEAR -4

PATH TO OPTlMtlL ROUTE HPV (S1000)----_._--- ------_ ..... _-_ ....... -----------

C 1 : 1 : t i707C 2 :2:2 2003C 3 :2:3 1907C <1 :2:4 1851C 5 :3:5 1928

DRY DOCKING NUMBER 4<D) YEAR 6

PATH TO OPTH1AL ROUTE HPV (91000).... __ .... __ ...._- ---~.. - ....---- ...-- -----------

D 1 :1:1:1 2387D 2 :2:2:2 2826D 3 :2:3:3 2772D 4 :2:2:4 2784D 5 :2:2:5 2734D 6 12:4:6 2706D 7 :3:5:7 2763

DRYDOCKING HUMBER 5(E) YEAR a

PATH TO OPTII1AL ROUTE NPV (51000)--------- -_._---------- --------- .......E 1 :1:1:1:1 2975E 2 :2:2:2:2 35t8E J :2:3:3:3 3493E 4 :2:2:4:4 3542E 5 :2:2:2:5 3510E 6 :2:2:2:6 3467E 7 :2:2:5:7 3484Ea :2:4:6:8 3438E 9 :3:5:7:9 3480

DRY[lOCKING NUMBEF: 6{F) YEAR 10

PATH TO OPTIMAL ROUTE NPV (51000)-------_ ..... ---_ .... __ ._._---- -------_ ..---

F 1 :1:1:1:1:1 3482F 2 :2:2:2:2:2 4105F 3 :2:3:3:3:3 4100f 4 :2:2:4:4:4 4174F 5 ~2:2;2:5:5 -4174F 6 :2:2:4:4:6 4141F 7 :2:2:4:4:7 4103F 8 :2:2:2:6:9 4124F 9 =2:2:5:7:9 4125FlO :2:4=6:8:tO 4066fit :3:5~7~9:tt 4098

ALTCRkllTlVE 1

MEAN OF DISTRIBUTION- 3127STANDARD DEVIATIDN 2865

SKfUIIESS O.Bl

KURTIlSIS 0.27

"UHBE~ UF CASES 400

C lAS S FREQUENCY

UP TO -1059.8-1059.8 - 176.1

176.1 - Hll.91411.9 - 2647.72647.7 - 3083.63883.6 - 5119.45119.4 - 6355.26355.2 - 7591.17591.1 - 8826.99826.9 - 10062.7

10062.7 - 112ge.511298.5 - 12534.412534.4: 13770.213770.2 AND ABOVE

Al TlRHATIVE 2

MEAN OF DISTRIBUTION- 2607STANDARD DEVIATION • 2823

SKE~NESS 0.81

KURTOSIS 0.20

HUH~ER Or CASES 400

-497 -

*.*~*.~*~*.~¥~**.~*~o.*~*~.~~ *f KONTE-CARLO SIMULATION 0

>I<

~****4~~*••••'.>I<**.'****.*.'

o62845556493332129512o

:**••••••***•••••**.*:••••••• **.** ••••• t ••••• **•••I**.***•••*** •• *.*tI.*••**•• *•••••~*••:*****.*.*** ••* ••:."'*••••*....*:**********:****1***1*

EACH * ~ J OBSERVATIONS

C l n P S FREQUENCY

UP TO-1511.3. 317.9 -B75.4 -

-1511.3-317.9675.4

2068.72068.7 - 3262.0326<.0 - 4455.~4455.4 - 564B.?564B.7 - 6842.06842.0 - 0035.3e035.3 - 122B.69228.6 - 10422.0

10422.0 - 11615.311615.J - 12800.612808.e AND ABOVE

o54e6565(1602735149522o

:****$C************,.*••••***•••••••••• ****.** ••l****.·**tt •• ******:***t~**~*.***.**:*********~****.~***.: ;,j~:r::f;*:t***: ****,t*:J;:f·***1****:***1*

IHCREM[WlftL I~VESTHENT

MEAN OF DI5TRIRUrI0H- 521STANDftR~ DEVIATION' 231

SI(EUN(SS 0.63

KURliiSIS 1.15HUMB~R or CAsrs 400

C LAS S FREQUENCY

UP TO -20.2-20.2 - 122.8122.8 - 265.8265.8 - ~08.8408.8 - S51.B551.8 - 69~.8694.8 - 837.e837.8 - 980.3980.6 - 1123.8

1123.8 - 1266.81266.8 - 1409.B1409.S - !552.91552.8 - 16~5.91695.8 AH~ ABOVE

oB

4277

112784722112Co1o

- 498 -

1$*I*u*$'i<ot'u.

I'.·*.*·**.****~**·.'*u*u*~**.

EACH'" • ~ OBSERVATIONS

(E~TAINTY EourVALfNT OF JNCREMENTAL INV£STKENT 487BASED UPON A HINIH~X TDLERABLE NPV OF -250

SUM OF PROBABILITIES. 1.00000000

university of newcastle upon tyne department of naval ... t.e... · department of naval...

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