Recommended Procedures and Guidelines ITTC Quality

ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 1 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

ITTC Quality System Manual

Recommended Procedures and Guidelines

Procedure

Preparation, Conduct and Analysis of Speed/Power Trials

7.5 Process Control

7.5-04 Full Scale Measurements

7.5-04-01 Speed and Power Trials

7.5-04-01-01.1 Preparation, Conduct and Analysis of Speed/Power Trials

Updated / Edited by Approved

Specialist Committee on Performance of 28th ITTC 2017 Ships in Service of the 28th ITTC

Date 04/2017 Date 09/2017

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Table of Contents

7.6.1 Ship’s track and speed over ground 1. PURPOSE ...... 5 ...... 13 2. DEFINITIONS ...... 6 7.6.2 Torque ...... 13 7.6.3 Wind ...... 13 3. RESPONSIBILITIES ...... 7 7.6.4 Water depth ...... 14 3.1 Shipbuilders’ responsibilities ...... 7 7.6.5 Waves ...... 14 3.2 The Trial Team’s responsibilities ..... 7 7.6.6 Density and temperature ...... 14 7.6.7 Current ...... 14 4. TRIAL PREPARATIONS ...... 8 4.1 Installation & Calibration ...... 8 8. CONDUCT OF TRIAL ...... 14 4.2 S/P trial agenda and pre-trial 8.1 Initiation ...... 14 meeting ...... 9 8.2 Trial trajectory ...... 15

5. SHIP CONDITION ...... 9 8.3 Run duration and timing ...... 15 5.1 Displacement ...... 9 8.4 Trial direction ...... 15 5.2 Trim ...... 10 8.5 Steering ...... 15 5.3 Hull &propeller ...... 10 8.6 Approach ...... 15 8.7 Power settings ...... 16 6. TRIAL BOUNDARY CONDITIONS 10 8.8 Number of speed runs ...... 16 6.1 Location ...... 10 8.8.1 ‘Iterative’ method ...... 16 6.2 Wind ...... 10 8.8.2 ‘Mean of means’ method ...... 16 6.3 Sea state ...... 11 8.8.3 Sister ships ...... 16 6.4 Water depth ...... 11 8.8.4 Additional runs due to limiting wave height ...... 16 6.5 Current ...... 11 8.9 Test sequence ...... 17 7. TRIAL PROCEDURES ...... 12 9. DATA ACQUISITION ...... 17 7.1 Parameters that shall be recorded . 12 9.1 Acquisition system ...... 17 7.2 Primary parameters ...... 12 9.1.1 System requirements ...... 17 7.3 Secondary parameters ...... 12 9.1.2 Location ...... 18 7.4 General information ...... 13 9.2 Manual data collection ...... 18 7.5 Model test information ...... 13 9.3 Sign convention ...... 18 7.6 Scope and conduct of the measurements ...... 13 10. ANALYSIS PROCEDURE ...... 19 10.1 General Remarks ...... 19 ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 3 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

10.2 Description of the Analysis : PROPULSIVE Procedure ...... 19 EFFICIENCY CORRECTION BASED 10.2.1 Resistance data derived from the ON LOAD VARIATION TESTS ...... 36 acquired data ...... 21 D.1. Propulsive efficiency correction ...... 36 10.2.2 Evaluation of the acquired data .. 21 D.2. Correction of shaft rotation rate – 10.2.3 Evaluation based on Direct Power effect of added resistance and of Method ...... 21 shallow water ...... 36 10.2.4 Correction of the measured ship’s speed due to the effect of current 22 : EVALUATION OF WIND 10.2.5 Prediction of power curve from DATA ...... 38 trial condition to other loading E.1. Averaging process for the true wind condition ...... 23 vectors ...... 38 10.3 Calculation methods for resistance E.2. Correction for the vertical position of increase and other corrections...... 23 the anemometer ...... 39 10.3.1 Resistance increase due to the effects of wind ...... 23 : CORRECTION METHODS FOR RESISTANCE INCREASE DUE 10.3.2 Resistance increase due to the TO WIND ...... 41 effects of waves ...... 24 10.3.3 Resistance increase due to water F.1. Wind resistance coefficients by wind temperature and salt content ...... 25 tunnel test ...... 41 10.3.4 Correction of the ship performance F.2. Wind resistance coefficients by CFD .. due to the effects of shallow water...... 41 ...... 25 F.3. Data sets of wind resistance 10.3.5 Correction of the ship’s coefficients ...... 41 performance due to the effects of displacement ...... 26 F.4. Regression formula by Fujiwara et al...... 52 11. PROCESSING OF THE RESULTS .. 26 : CORRECTION 12. REPORTING ...... 29 METHODS FOR RESISTANCE INCREASE DUE TO WAVES ...... 54 13. REFERENCESAND G.1. Simplified correction method for BIBLIOGRAPHY ...... 30 ships with limited heave and pitch during the speed runs (STAWAVE- : GENERAL SHIP AND 1) ...... 54 TRIAL DATA ...... 32 G.2. Empirical correction method with : BEAUFORT SCALE OF frequency response function for ships WIND ...... 33 with heave and pitch during the speed runs (STAWAVE-2) ...... 54 : FORMAT S/P TRIAL LOG SHEET ...... 35 ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 4 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

G.3. Theoretical method with simplified : RAVEN SHALLOW- tank tests in short waves or empirical WATER CORRECTION ...... 71 formula ...... 56 K.1. Calculation of viscous resistance .... 71 G.4. Seakeeping model tests ...... 59 K.2. Shallow-water correction of viscous re-sistance ...... 72 : EFFECT OF CURRENT 60 K.3. Estimate additional sinkage ...... 72 H.1. ‘Iterative’ method ...... 60 K.4. Estimate resulting additional H.2. ‘Mean of means’ method ...... 61 displacement ...... 72 : CONVERSION FROM K.5. Estimate resistance increase caused TRIAL SPEED/POWER TEST by additional sinkage in shallow RESULTS TO OTHER STIPULATED water ...... 72 LOAD CON-DITIONS ...... 63 K.6. Correct measured power ...... 72 : EXTENDED ANALYSIS K.7. Check validity of calculated viscous OF DIRECT POWER METHOD resistance ...... 72 (INFOR-MATIVE) ...... 64 K.8. Limits of applicability: ...... 73 J.1. Propulsive efficiency correction ...... 64 J.2. Application of load variation test NOMENCLATURE ...... 74

results ...... 70

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Preparation, Conduct and Analysis of Speed/Power Trials

• the trial procedure, • the execution of the trial, 1. PURPOSE • the measurements required, The primary purpose of speed-power trials is • the data acquisition and recording, and to determine ship performance in terms of speed, • the processing of the results. power and propeller revolutions under prescribed ship conditions, and thereby verifying The contracted ship’s speed and the speed the satisfactory attainment of the contractually for EEDI shall be determined for stipulated con- stipulated ship’s speed and power and to provide ditions which are defined at specific draughts the ship’s speed and power for the calculation of (contract draught and EEDI draught) and usu- the Energy Efficiency Design Index (EEDI) as ally for ideal environmental conditions i.e. no required by IMO. wind, no waves, no current, deep water.

The present Recommended Procedure con- Normally, such stipulated conditions are not cerns the preparation and execution of speed- experienced during the actual trials. In practice, power trials, as well as the method of analysing certain corrections for the environmental condi- the results. It has been defined by the 27th and tions, such as water depth, wind, waves, current the 28th ITTC Specialist Committee on the Per- and deviating ship draught from specified formance of Ships in Service. In this work the draught have to be considered. For this purpose, Committee took into account: not only the shaft power and ship’s speed are measured, but also relevant ship data and envi- • ITTC 7.5-04-01-01.1 &.2, 2014, ronmental conditions shall be recorded during the speed-power trials. • ISO 19019, 2002, • ISO 15016, 2015, In case it is physically impossible to meet the • Sea Trial Analysis JIP, 2006; (Boom, 2008). conditions in these Guidelines, a practical documented approach mutually agreed among The descriptions for the calculation methods Owner, Verifier and Shipbuilder can be allowed. of the resistance increase due to wind and waves, as well as guidelines for analysis and speed cor- The applicability of these Guidelines is lim- rections are based on relevant research results ited to commercial ships of the displacement and modified from ITTC 7.5-04-01-01.2/2005 type. to meet the IMO EEDI requirements. All trial procedures and measurements shall • The purpose of this document is to define be conducted in such a way that the speed at and specify: Contract power and the speed at EEDI Power • the responsibility of each party involved, are derived within 0.1 knots and the shaft power • the trial preparations, within 2%. • the vessel’s condition, • the limiting weather and sea conditions,

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2. DEFINITIONS • Ship’s speed: speed that is realised under the stipulated conditions. “Contract Speed” • Brake power: power delivered by the output refers to the contractual conditions agreed. coupling of the propulsion machinery before “EEDI Speed” refers to the conditions spec- passing through any speed reducing and ified by IMO. The ship’s speed during a transmission devices. speed run is derived from the headway dis- • Contract power: shaft power that is stipu- tance between start and end position and the lated in the newbuilding or conversion con- elapsed time of the speed run. tract between Shipbuilder and Owner. • Sister ships: ships with identical main di- • Docking report: report that documents the mensions, body lines and propulsor system condition of the ship hull and propulsors built in a series by the same Shipbuilder. (available from the most recent dry-dock- • S/P trials: speed-power trials to establish a ing). speed-power relation of the vessel. • Double run: two consecutive speed runs at • Speed run: ship’s track with specified head- the same power setting on reciprocal heading, distance and duration over which ship’s ing. speed and shaft power are measured. • EEDI: Energy Efficiency Design Index as • S/P trial agenda: document outlining the formulated by IMO. scope of a particular S/P trial. This document • EEDI power: shaft power that is stipulated contains the procedures on how to conduct by the EEDI regulations. the trial and table(s) portraying the runs to be • Ideal conditions: ideal weather and sea con- conducted. dition; deep water of 15°C，no wind, no • Trial baseline: the track of the first S/P run. waves and no current. • The Trial Leader is the duly authorised • Owner: party that signed the newbuilding or (Shipbuilder’s representative) person re- conversion contract with the Shipbuilder. sponsible for the execution of all phases of • Parties involved: Shipbuilder, Ship Owner the S/P trials including the pre-trial prepara- and EEDI Verifier. tion. • Power setting: setting of engine throttle and • Trial log: for each speed run, the log con- propeller shaft speed for fixed pitch propel- tains the run number, the times when the lers and setting of the pitch angle for control- speed run starts and stops, and the data as de- lable pitch propellers scribed in Section 9.2 and Appendix C of • Propeller pitch: the design pitch, also for these Guidelines. controllable pitch propellers. • The Trial Team consists of the Trial Leader, • Running pitch: the operating pitch of a the Owner’s representative, the appointed CPP. persons responsible for the S/P trial measurements and if required, the Verifier. • Shaft power: net power supplied by the pro- • pulsion machinery to the propulsion shafting Verifier: third authorized party responsible after passing through all speed-reducing and for verification of the EEDI. other transmission devices and after power for all attached auxiliaries has been taken off. • Shipbuilder: ship yard that signed the newbuilding or conversion contract with the Owner. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 7 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

3. RESPONSIBILITIES • It is the Shipbuilders responsibility that all ship data relevant for the S/P trials prepara- 3.1 Shipbuilders’ responsibilities tion, conduct, analysis and reporting are made available to the Trial Team prior to the The Shipbuilder is responsible for planning, S/P trials. This data shall include the infor- conducting and evaluating the S/P trials: mation requested in Appendix A as well as the results of the model tests for this ship at • The Shipbuilder is responsible for appoint- trial draught and trim, EEDI draught and ing an authorized Trial Leader. trim and contract draught and trim. • The Shipbuilder is responsible for that speed • The Shipbuilder is responsible for the over- and shaft power measurements and analysis all trial coordination between the ship's crew are conducted by persons acknowledged as and Trial Team. A pre-trial meeting between competent to perform those tasks, as agreed the Trial Team and the ship’s crew shall be between the Shipbuilder, the Owner and the held to discuss the various trial events and to Verifier. resolve any outstanding issues. • The Shipbuilder has to provide all permits • The Shipbuilder has to arrange for divers to and certificates needed to go to sea. inspect the ship’s hull and propulsor if nec- • The Shipbuilder is responsible for ensuring essary. that all qualified personnel, needed for operating the ship, all engines, all systems and The Trial Leader maintains contact with the equipment during the sea trials are on board. Trial Team on the preparation, execution and re- • The Shipbuilder is responsible for ensuring sults of the S/P trials. that all regulatory bodies, Classification So- ciety, Owner, ship agents, suppliers, subcon- 3.2 The Trial Team’s responsibilities tractors, harbour facilities, departments or- ganising the delivery of provisions, fuel, wa- The Trial Team is responsible for correct ter, towing, etc., needed for conducting the measurements and reporting of the S/P trials ac- sea trials, have been informed and are avail- cording to this document and for the analysis of able and on board, when required. the measured data to derive the ship’s speed and • It is the Shipbuilder’s responsibility that all power at the stipulated conditions. safety measures have been checked and that all fixed, portable and individual material The Trial Team is responsible for the follow- (for crew, trial personnel and guests) is on ing: board and operative. • It is the Shipbuilder’s responsibility that • Conducting inspection of ship including hull dock trials of all systems have been executed and propeller condition. and all alarms, warning and safety systems • Providing, installing and operating all re- have been checked. quired trial instrumentation and temporary • It is the Shipbuilder’s responsibility that an cabling. inclining test has been performed and/or at • Providing the ship master and Owner’s rep- least a preliminary stability booklet includ- resentative with a preliminary data package ing S/P trials condition has been approved, and preliminary analysis before debarking. in accordance with the SOLAS Convention. • Providing a final report after completion of the trials in accordance with Chapter 12. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 8 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

4. TRIAL PREPARATIONS Shaft torque shall be measured by means of permanent torque sensor or strain gauges on the The success of the S/P trials largely depends shaft. The measurement system shall be certi- on the preparations. In this chapter, the most im- fied for power measurements on a test shaft with portant steps are summarised. a bias error smaller than 1% so that an overall bias error smaller than 2% (on board of the ac- 4.1 Installation & Calibration tual ship) can be achieved.

Assembling of all trials instrumentation in Alternative shaft torque measurement de- the configuration that will be used on the ship. vices with a certified accuracy equal to or better Testing of the instrumentation system on mal- than the above figures are acceptable. functioning or any other complications. As part of the S/P trial preparation, the tor- Apart from the obvious signals such as shaft sion meter’s zero torque readings shall be deter- torque, rpm and DGPS, it is important to check: mined since there is a residual torque in the shaft, which is resting on the line shaft bearings. The 1. Gyrocompasses torsion meter zero setting is to be done accord- 2. Anemometer system ing to its maker’s instructions. If not specified 3. Speed log system otherwise, the zero torque value is determined 4. Propeller pitch (of each propeller) with the ship at rest by turning the shaft ahead 5. Ship’s draught measurement system (if avail- and astern and taking the mean of these two able) readings as the zero value. 6. Water depth measuring system The shaft material properties e.g. the G- Prior to the S/P trials all shipboard signals Modulus shall be fully described and docu- that will be recorded during the S/P trials shall mented by the Shipbuilder. If no certificate based on an actual shaft torsional test is availa- be calibrated after the instrumentation has been 2 installed. For this purpose, the sensors shall be ble, the G-Modulus of 82,400 N/mm shall be cycled throughout the full operating range of the used. The shaft diameter used in the power cal- system. culation shall be derived from the shaft circum- ference measured at the location of the torsion This is accomplished by: meter. In the case of controllable pitch propeller(s) the drilling diameter must to be taken into • Slewing the gyrocompasses account (to be supplied by Shipbuilder). • Changing the propeller pitch When shaft torque measurement is not possible, an alternative power measurement method Prior to departure on S/P trials, the ship’s recommended by the engine manufacturer and draught measurement system (if available) approved by Owner and Verifier is acceptable. needs to be verified by directly reading all draught marks, seawater temperature, specific As part of the pre-trial calibration for a ship density and the internal draught system at the equipped with controllable pitch propellers, the same time. procedure shall be as follows: The shaft power will be derived from torque and rpm. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 9 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

1. Prior to dock-out the oil distribution The S/P trial agenda is a document prepared mechanism showing the Propeller Pitch by the Shipbuilder, outlining amongst others the shall be checked for zero pitch; scope of a particular Speed/Power trial. This 2. Check zero pitch reading in the measure- document contains the procedures on how to ment system against the mechanical conduct the trial and table(s) portraying the runs reading in the oil distribution box; to be conducted. It outlines the particular re- 3. Determine the maximum ahead pitch, sponsibilities of the Trial Leader, Trial Team, design pitch, and maximum astern pitch ship’s crew/ Shipbuilder, and the Owner’s rep- and then adjust the ship indicators to re- resentative. The scope of the S/P trials shall be flect the measurements. Determine the in line with this document. corrections to account for changes in pitch due to shaft compression as thrust Preferably before the sea trials start, but at increases and temperature effects on the the latest when the trial area is reached and the Propeller Pitch control rod. environmental conditions can be studied, agree- 4. Verify the weight of the propulsor and ment between the Trial Team, Shipyard and hub from the manufacturer’s specifica- Ship Owner and Verifier shall be obtained con- tions for making thrust measurement cerning the limits of wind forces, wave heights corrections. and water depths up to which the trials shall be performed. Agreement shall be obtained con- An important deliverable of this stage is a cerning the methods used to correct the trial data. document describing the test set-up including The measured data, analysis process and the re- evidence of the calibrations that have been car- sults shall be transparent and open to the Trial ried out. Team.

It is important to note that there are two stages to consider in performing instrumentation 5. SHIP CONDITION checks, viz. the pre-trial check procedures and the post-trial check to verify the calibration re- 5.1 Displacement sults. The difference between the ship's actual displacement and the required displacement shall 4.2 S/P trial agenda and pre-trial meeting be less than 2% of the required displacement. If Before departure, a pre-trial meeting shall be model test results are used for the analysis of the held to fix the S/P trial agenda. During this S/P trials, the deviation of the actual displace- meeting two items shall be addressed. ment during the S/P trials shall be within 2% of the displacement used during the model test. • Approval of the S/P trial agenda, The ship’s draught at the perpendiculars, • Approval of the procedures and the conse- midships port and starboard, trim and displace- quential correction methods to be used to ment are obtained immediately prior to the S/P calculate the trial speed and to deliver the trial by averaging the ship draught mark read- speed trial report i.e. this Recommended ings. In the event that reading the draught marks Procedure. is unsafe or provide an inaccurate result, dis- ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 10 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

placement determination shall be conducted ei- The objective during the S/P trial is to minimize ther by reading the internal draught measure- the number of influencing factors. ment system or by evaluating all tank soundings. Although there are correction methods for Displacement shall be derived from the certain deviations from the contract condition, Bonjean data or using quadratic equations with these methods are only valid up to certain limits. hydrostatic data, taking into consideration the hog/sag using the draught data (forward, aft and In order to arrive at reliable S/P trial results at half length) and the density of the water. the boundary conditions shall not exceed the values given in this chapter. The ship shall be brought into a loading condition that is as close as possible to contract con- 6.1 Location dition and/or the condition at which model tests have been carried out. The loading condition High wind and sea state in combination with shall be confirmed at zero ship’s speed. a heading deviating from head waves and following waves, can require the use of excessive 5.2 Trim rudder deflections to maintain heading, and thus cause excessive fluctuations in propeller shaft The trim shall be maintained within very torque, shaft speed and ship’s speed. narrow limits. For the even keel condition, the trim shall be less than 0.1% of the length be- The S/P trial shall be conducted in a location tween perpendiculars. For trimmed trial condi- where the environmental conditions are ex- tions, the forward draught shall be within ± 0.1 pected to be constant and to have only the small- m of the ship condition for which model test re- est possible impact on the vessel in order to sults are available. avoid unexpected environmental effects in the S/P trial results.

5.3 Hull &propeller This means that the speed trial range shall be located in a sheltered area (i.e. limited wind, The ship shall have clean hull and propel- waves and current). Furthermore, the area shall ler(s) for the sea trial. Hull roughness and ma- be free from hindrance by small boats and com- rine growth can increase the resistance of the mercial traffic. ship significantly but are not corrected for in S/P trials. Therefore, it is recommended that the hull and propeller(s) be carefully inspected before 6.2 Wind the sea trial, and cleaned as needed and as per coating manufacturer's recommendation. The During the S/P trial the wind speeds shall not dates of last docking and hull and propeller be higher than: cleaning are to be recorded in the S/P trials report.

6. TRIAL BOUNDARY CONDITIONS

During the S/P trial, there are many conditions that deviate from the contract condition. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 11 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

• Beaufort 1 number 6, for vessels with 6.4 Water depth LPP>100 m or • Beaufort number 5, for vessel with LPP≤100 There are correction methods that compen- m sate for shallow water (see 10.3.4). However, it is preferable to avoid the corrections by a suitable choice of the S/P trial location. If the water depth in the S/P trial area is less than the larger of the values obtained from the following two formulae, shallow water correction may be applied:

V 2 h = 3 B ⋅T and h = 2.75 S (2) M g

where h water depth [m], B ship’s breadth [m], Figure 1. Limits for allowable wave height TM draught at midship [m], ship’s speed [m/s], G acceleration of gravity [m/s2]. 6.3 Sea state 𝑉𝑉s The value of water depth to be used for cor- The total significant wave height H1/3, derived from the significant wave heights of local rection shall not be less than the larger value obtained from the following two formulae: wind driven seas (wind waves) HW1/3 and swells

HS1/3, by V 2 h = 2 B ⋅T and h = 2 S (3) 2 2 M H1/3= HW1/3+HS1/3 (1) g shall �satisfy the following criteria: Furthermore, areas with significant variations in the bottom contours shall be avoided.

H1/3 1.5 when the wave height is derived The actual water depth during each speed run from visual observations, shall be read from the ship’s instruments and ≤ 𝑥𝑥 documented in the trial log. H1/3 2.25 when the wave spectrum encountered during the S/P trials is measured, ≤ 𝑥𝑥 6.5 Current with = /100, Ideally S/P trials shall be conducted in a lo- PP cation where current speed and direction are es- See section𝑥𝑥 � 𝐿𝐿7.6.5 for definition of “observations” sentially uniform throughout the trial area. respectively “measurements” in this context. In cases of current time history deviating The above limits are illustrated in Figure 1. from the assumed parabolic / sinusoidal trend

1 The Beaufort scale is given in Appendix B. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 12 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

and the change of the current speed within the Table 1 Primary parameters timespan of one double run is more than 0,5 Acceptable measurement Unit knots/hour*timespan, neither of the correction devices methods in Appendix H are applicable. Areas Ship Track DGPS [Latitude, Longitude] where this may occur shall be avoided for S/P or [m] trials. Speed over DGPS [Knots] Ground Shaft Torque Torsion meter with [kNm], or shaft power calibrated permanent 7. TRIAL PROCEDURES torque sensor or strain gauges. Power calculated from 7.1 Parameters that shall be recorded torque and RPM [kW] Shaft RPM Pick-up, optical sensor, In this chapter, an overview is given of the ship revs counter [RPM] parameters that influence the trial speed. All Propeller Pitch Bridge replicator Time GPS Time [hh:mm:ss] these parameters shall be measured as accu- Water depth Ship echo sounder + [m] rately as possible and recorded. nautical charts Ship heading Gyro compass, or [deg] For this purpose, a split has been made be- compass- DGPS Relative wind, Ship anemometer, [m/s], tween primary and secondary parameters. For speed and dedicated trial [knots], each of the parameters the preferable measure- direction anemometer [deg] ment methods are given. Height, period and Wave measuring device [m], direction of wind such as wave buoy, radar, [sec], waves and swell or lidar. Observation by [deg] 7.2 Primary parameters multiple Marinners. Bow acceleration Calibrated acceleration [m/s2] (for wave corr gauges The primary parameters to be measured dur- method G.1)) ing each run and the accepted measurement de- Date [YYYY- vices are given in Table 1. MM-DD] Table 2 Secondary parameters It is recommended to record the wave height, wave direction and period, absolute wind speed Acceptable measurement Unit devices and direction at station(s) in the vicinity of the Date [YYYY- speed trial site. MM-DD] Seawater density Salinity sensor, [kg/m3] Conductivity Density 7.3 Secondary parameters Temperature (CDT) sensor Seawater temperature Thermometer, CDT sensor [ºC] The secondary parameters listed in Table 2 Air temperature Thermometer [ºC] Air pressure Barometer [hPa], shall be measured and recorded at the trial site [mBar] at least once during the S/P trial. Sea trial area Geographical position by [Latitude, DGPS Longitude] Draughts, fore, Physical observation and / [m] amidships and aft at or calibrated draught zero speed gauges

Displacement According to draught [metric readings and water density tons] Torsion meter zero Torsion meter with kNm setting calibrated torque sensor or strain gauges ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 13 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

7.4 General information scale. In case different empirical coefficients are used for the different draughts, these shall be Prior to the trial, the data specified in Appen- documented in full detail and documentation dix A shall be recorded, based on measurements must include justification by means of full scale where applicable. S/P trial data for the specific ship type, size, loading condition, model test facility and evalu- 7.5 Model test information ation method. Refer to Guideline on the use and the determination of CA- and CP-correlation fac- The quality and accuracy of model tests play tors used in ITTC Recommended Procedures a large role in the outcome of full scale S/P trials. (2017). For some ship types, sea trials are normally carried out in ballast condition, whereas the con- The model test report shall be transparent tractual condition normally is defined in loaded and give sufficient information to enable the au- design condition. For the conversion from bal- thorized party to check the model test results. last trial results to loaded condition, the differ- This means that in the model test report, the ence between the ballast and loaded model test measured data, the predicted full scale data and curves is used. Therefore, an accurate model test a detailed description of the extrapolation and validated consistent extrapolation method to method and the coefficients used have to be full scale is required. given.

For the analysis of the S/P trials, i.e. to in- 7.6 Scope and conduct of the measure- clude the effect of the propeller loading in non- ments ideal conditions on the propulsion efficiency and rpm, it is required that the model tests data include the results of propeller load variation 7.6.1 Ship’s track and speed over ground measurements as defined in [used in ITTC rec- The ship’s position and speed shall be meas- ommended procedures 7.5-04-01-xx (2017)]" ) ured by a global positioning system such as or Appendix D.3. DGPS. The DGPS system shall operate in the Based on ITTC recommendations, the model differential mode to ensure sufficient accuracy. tests shall be conducted according to the follow- Position and speed shall be monitored and ing criteria: stored continuously.

Model tests shall be conducted at the con- 7.6.2 Torque tract draught and trim, the EEDI draught and trim as well as the trial draught and trim. The calibration of the torque measurement shall not be altered during the S/P trials. Model tests shall be conducted according to the ITTC Recommended Procedures for Re- 7.6.3 Wind sistance and Propulsion Model Tests (2017), including load variation tests. The ship’s own sensor or a dedicated trial anemometer is to be used. The anemometer shall For all draughts and trims, the same methods, be as clear as possible from the superstructure. procedures and empirical coefficients shall be used to extrapolate the model scale values to full ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 14 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

7.6.4 Water depth height, period and direction into relevant equation (see section 10.3.2). Measuring the water depth can be done by using the ship echo sounder. It is important that 7.6.6 Density and temperature the echo sounder is calibrated before the speed run in combination with the check of the water The local seawater temperature and density depth given on the charts and that the vessel’s at the trial site shall be recorded to enable the draught is taken into account. Continuous re- calculation of the ship’s displacement and cor- cording of water depth is recommended. rections with regard to viscosity. The water temperature shall be taken at sea water inlet level. 7.6.5 Waves Air temperature and pressure shall be measured at the trial location using a calibrated thermom- The wave spectrum can be derived either by eter and barometer. measurements or by observations. 7.6.7 Current Wave measurements Current speed in the direction of the ship’s Preferably, the spectrum of waves induced heading shall be derived as part of the evaluation by local wind and swell originating from remote of each run, either using the ‘Mean of means’ wind, shall be measured during the S/P trials. method (Appendix H-2) or the ‘Iterative’ The spectrum is derived from a spectral analysis method (Appendix H-1). See also section 10.2.4. of the measured wave elevation as a function of time. For this purpose, wave buoys in the speed trial area or ship born equipment such as wave 8. CONDUCT OF TRIAL radar or lidar can be used. The wave measurement equipment shall be calibrated and the ac- On the day of and during the S/P trial, a num- curacy shall be validated and documented. ber of prerequisites shall be met in order to arrive at reliable trial results. In this chapter, an The directions of the waves and swells may overview is given of the minimum requirements. be derived from visual observations. Measure- ment of directional wave spectrum is preferable. 8.1 Initiation Wave observations Prior to the S/P trials, the weather forecast In case the wave spectrum encountered dur- shall be studied. ing the S/P trials is not measured, the wave height, direction and period shall be derived Whenever possible, the runs at EEDI power from visual observations by multiple experi- shall be conducted in daylight to enable a clear enced mariners, including the Owner’s repre- visual observation of the wave conditions. For sentative and the Verifier. In addition to the trials in which the encountered wave spectrum wave observations, wave now- or hind- cast data and the wave direction (both wind waves and provided by an experienced and independent swells) are derived by measurements, these runs weather office may be used. The wave spectrum may also be conducted without daylight. is then obtained by entering the observed wave ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 15 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

It is important to check that the engine plant 8.3 Run duration and timing configuration during the S/P trial is consistent with normal ship operations. The S/P trial duration shall be long enough to accommodate a speed/power measurement Prior to the S/P trials, the following actions within the required accuracy. The run duration shall be taken at the vessel's zero speed through shall be the same for all speed runs with a mini- the water: mum of ten (10) minutes. The speed runs for the same power setting shall be evenly distributed 1. draught reading as described in section in time. 5.1 and calculation of displacement, 2. measurement of wind speed and direc- 8.4 Trial direction tion, 3. zero setting of shaft torque meter, The speed runs shall preferably be carried 4. measurement of water temperature and out by heading into and following the dominant density. wave or wind direction, depending on which effects the ship’s speed most. 8.2 Trial trajectory Consequently, once the heading for the The S/P trial runs need to be conducted over speed run and the reciprocal heading for the re- the same ground area. For each base course, turn run are fixed, the selected heading shall be each speed run will be commenced (COMEX) maintained very precisely throughout the S/P at the same place (within reason). trial. However, if the ’Mean of means’ method is used for current correction, the trial direction can be changed between each power setting according to change of weather condition.

8.5 Steering

An experienced helmsman or adaptive auto- pilot will be required to maintain heading during Figure 2 Trial trajectory of one double run each speed run. Minimum rudder angles are to be used while maintaining a steady heading. Modified Williamson turns or similar types of manoeuvre will be executed between each During the speed run, the maximum single run to return the ship to the reciprocal heading amplitude of rudder angles shall be not more on, or parallel to, the trial baseline. Parallel than five (5) degrees. means within one ship length of the trial baseline (see also 8.6). This procedure is used to 8.6 Approach avoid different sea states or different wind conditions. Engine throttles, rpm setting(s) or pitch The S/P trial approach shall be long enough setting(s) shall not be moved during this period. to ensure a steady state ship’s condition prior to The rudder angle used in this manoeuvre shall commencement (COMEX) of each speed run. be such that ship’s speed loss and time loss are During the approach run, the ship shall be kept minimised. on course with minimum rudder angles. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 16 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

No fixed approach distance can be given. In • Two (2) double runs (at the same power set- order to verify that the vessel reached the steady ting) below the EEDI/Contract power, ship’s condition the measured values of shaft ro- • Two (2) double runs (at the same power set- tation rate, shaft torque (if available) and ship’s ting) around the EEDI/Contract power, speed at the control position shall be monitored. • Two (2) double runs (at the same power set- When all three values are stable the ship's con- ting) above the EEDI/Contract power. dition shall be deemed "steady". Two (2) double runs compensate for the ef- 8.7 Power settings fect of current and second order current variations. In order to obtain sufficient accuracy, the A minimum of three (3) different power set- time intervals between each run at the same tings are required. These shall be adequately dis- power setting shall be more or less the same tributed within the power range of 65% MCR (time interval deviation of 25% between single and 100% MCR. runs is acceptable).

8.8 Number of speed runs 8.8.3 Sister ships

All S/P trials shall be carried out using dou- If the results of the S/P trials of the first ship ble runs, i.e. each run shall be followed by a re- of a series are acceptable, sister ships may be turn run in the exact opposite direction per- subjected to a reduced speed trial program. The formed with the same engine settings. runs shall comprise at least:

8.8.1 ‘Iterative’ method • One (1) double run below EEDI / Contract power, When the current correction is carried out • One (1) double run around EEDI / Contract using the ‘Iterative’ method (Appendix H.1), the power, runs shall comprise at least: • One (1) double run above EEDI / Contract power. • One (1) double run below EEDI / Contract power, Additional runs – sister ships • Two (2) double runs (at the same power setting) around EEDI / Contract power, If ‘Mean of means’ method is used for sister • One (1) double run above EEDI / Contract ships and a current variations of above 0.2 knots power. within a double run are encountered, one (1) additional double run at that power setting shall be The EEDI / Contract power runs shall be conducted. conducted not as the first or the last power setting in the trial sequence. 8.8.4 Additional runs due to limiting wave height 8.8.2 ‘Mean of means’ method For the first of a series or a sister ship at any When the current correction is carried out power setting, when the wave height is around using the ‘Mean of means’ method (Appendix the limiting conditions and significant wave-in- H.2), the runs shall comprise at least: duced ship motions are observed then one (1) ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 17 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

additional double run at that power setting shall shall always be to record as many parameters as be conducted. possible by means of the measurement computer in order to increase the level of accuracy of the 8.9 Test sequence S/P trials.

1. Fixing of speed run heading (see section 9.1 Acquisition system 8.4); 2. Navigating through the approach dis- The acquisition system shall record time his- tance on direct course; tories of the measurements described in chapter 3. Prepare all measurements to start; 7.2 to assure quality control and to provide in- 4. Start speed run. Control levers shall re- formation that will allow for the development of main unchanged, maximum rudder an- uncertainty analysis. gle shall not be more than 5 deg. port and starboard. After agreed duration (mini- 9.1.1 System requirements mum of 10 minutes) stop speed run. De- termine the achieved speed and power; The data acquisition system shall: 5. During S/P trial run make environmental observations; • Record all available parameters simultane- 6. Turn ship with small rudder angles to ously. navigate the counter run covering the • Perform a time trace recording with a sam- same geographical track as the first run; pling rate of at least 1 Hz. 7. Repeat steps 2 to 6. • Display time traces of the trial parameters specified in section 7.2. • Calculate statistics (mean min, max, stand- 9. DATA ACQUISITION ard deviation). During the speed/power trial, accurate recording of the speed and power relationship is At the end of each run, the data acquisition of great importance. system shall be able to present all recorded time histories to evaluate the quality and consistency Apart from this, an accurate quantification of of the acquired trial data and be stored for sub- the boundary conditions is necessary since the sequent graphical presentation. ship’s speed and powering characteristics are extremely sensitive to conditions such as hull Furthermore, the acquisition system shall and propeller condition, ship displacement, present the following values for each of the shallow water effects, sea state and wind veloc- measured data: ity. Consequently, these factors shall be monitored and documented to the greatest possible 1. Trial start time extent. 2. Number of samples taken 3. Maximum value During the S/P trials, two types of data ac- 4. Minimum value quisition shall be used: Automated acquisition 5. Average value by means of a data acquisition system (measure- 6. Standard deviation ment computer), and manual recording of infor- 7. Trial end time mation by means of a log sheet. The objective ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 18 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

Filtering of the run data is recommended to avoid “spikes” in the recorded time histories. Chauvent’s criterion that provides a ratio of maximum acceptable deviation to precision index as a function of the number of readings, (N) is to be used. Readings are automatically re- jected from use in the data analysis when they fall outside of the selected mean value band- width.

9.1.2 Location The data acquisition system shall be located Figure 3. Sign conventions on the bridge.

9.2 Manual data collection

For those parameters that cannot be measured and recorded automatically by means of the data acquisition system, manual data collection is required using a log sheet (see Appendix C).

The log sheet is important for two aspects:

1. Firstly, to complete the dataset. 2. Secondly, to provide a backup for the au- Figure 4. Sign convention for wind directions tomated measurements and give a written overview of the measurements. The wind direction is defined as the direction from which the wind is coming. It is important that the parameters that are Zero (0) degrees on the bow and positive to star- varying in time is recorded every few minutes board (clockwise). so that the average can be determined over the run period. Input parameters: ψ Heading of the ship [deg] 9.3 Sign convention VWR Relative wind speed [m/s] ψWR Relative wind direction relative to the The sign conventions to be used for wave bow, ship fixed; 0 means head winds and wind direction are presented in Figure 3, [deg] Figure 4 and Figure 5. VG Measured ship’s speed over ground [knots]

Computed parameters:

ΒWT True wind angle in earth system [deg] VWT True wind speed [m/s] ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 19 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

10.2 Description of the Analysis Procedure

The analysis of speed/power trials shall con- sist of

• evaluation of the acquired data • correction to ship power for resistance increase due to wind, waves, water temperature and salt content • correction to ship’s speed at each run for the effect of current • correction to ship’s speed at each run for the effect of shallow water • correction to ship power for displacement • presentation of the trial results

Figure 5.Sign convention for wave directions Details of the methods are given in the following chapters. For wave and wind corrections The wave direction is defined as the direc- the methods depend on the level of information tion relative to the ship's heading from which the which is available to the conducting party of the wave fronts are approaching. speed/power sea trials. The analysis and correction method to be followed is prescribed below Input parameters: and summarized in Table 3. ψ Heading of the ship [deg] HW1/3 Significant wave height (wind waves) Evaluation [m], For the evaluation the Direct Power Method HS1/3 Significant wave height (swell) [m], in combination with the propulsive efficiency α Angle between ship heading and wave correction based on load variation tests (refer to direction relative to the bow; 0 means ITTC 7.5-02-03-01 (2017)) shall be used. head waves [deg] VG Measured ship’s speed over ground Wind Correction [knots] In calculating resistance increase due to wind, four methods can be used, depending on whether there are wind tunnel measurements 10. ANALYSIS PROCEDURE available or not:

10.1 General Remarks If wind tunnel measurements are available:

This section describes the methods to ana- • Wind resistance coefficients from model test lyse the results of speed/power trials as con- are used (Appendix F.1). ducted according to the previous sections. The method to be used depending on situation and If CFD simulations are available: available data is given in Table 3. • Wind resistance coefficients from simulations are used (Appendix F.2). ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 20 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

If wind tunnel measurements or simulations • Under the condition that heave and pitch are not available: motions are small, the direct correction wave method based on wave reflection prescribed • Wind resistance coefficients from standard in Appendix G.1 or G.2 shall be used. data set (Appendix F.3) • In case significant heave and pitch is observed during the trials, the empirical formu- or lation of the response function prescribed in Appendix G.2, shall be used for the analysis. • Regression formula by Fujiwara et al. (Ap- This empirical transfer function covers both pendix F.4). the mean resistance increase due to wave reflection and the motion induced added re- are(is) used. sistance.

Wave correction

In calculating resistance increase due to waves, the following procedure shall be used:

If ship’s geometry cannot be made available to Verifier:

Table 3. Evaluation method to be followed. The numbers identify the method by the chapters or Appendix in which the methods are described.

Evaluation / Correction Method Condition Air Temp. & Water Displ. & Evaluation Waves Wind Current Resistance Density Depth Trim Heading Yes H.1 changed between power no H.1 or H.2 settings

Load Yes D Variation Test No D available

G.1 or Included in heave No No G.2 method 10.3.3 10.3.4 10.3.5 and pitch Ship geome- Yes G.2 try G.1 or available to Yes Verifier G.2,G.3 Full Seakeeping G.4 Model Tests available Dataset of Wind Tunnel Tests E.1/E.2 wind re- /CFD sistance coef- Data set E.3 ficients No E.4 Available

ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 21 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

10.2.2 Evaluation of the acquired data Provided that the ship geometry is available to Verifier The evaluation of the acquired data consists of the calculation of the resistance value • The theoretical method with tank test in associated with the measured power value sep- short waves or empirical formula as pre- arately for each run of the speed trials. scribed in Appendix G1, G2 or G.3 shall be used. The reason that the associated re- • In the case transfer functions of added resistance/power shall be calculated for each run sistance in waves derived from seakeeping is that a careful evaluation shall consider the tank tests are available for the specific ves- effects of varying hydrodynamic coefficients sel at the relevant draught, trim, speed with varying propeller loads. The recom- range and relative wave direction, these mended correction methods except for the ones shall be used in combination with the wave used for current effect, for shallow water effect spectrum (Appendix G.4). and for displacement and trim are applicable to resistance values. Shallow water 10.2.3 Evaluation based on Direct Power To correct for shallow water effect the Method method proposed by Raven (2016) and specified in Appendix K shall be applied to the To derive the speed/power performance of ship’s speed measured during each run. the vessel from the measured speed over ground, power and rpm, the Direct Power 10.2.1 Resistance data derived from the ac- Method is to be used. In this method the meas- quired data ured power is directly corrected by the power increase due to added resistance in the trial The resistance values of each run shall be conditions. The analysis is based on the deliv- corrected for environmental influences by esti- ered power. mating the resistance increase ΔR as, More details are given in Appendix D. ∆R = R + R + R (4) AA AW AS The delivered power in the trial condition is derived by: with

RAA resistance increase due to relative wind = (5) (see Appendix E and F), Dms Sms S RAS resistance increase due to deviation of 𝑃𝑃when the𝑃𝑃 measured𝜂𝜂 power is shaft power water temperature and water density (see section 10.3.3), = (6) RAW resistance increase due to waves (see Dms Bms M Appendix G). 𝑃𝑃when the𝑃𝑃 measured𝜂𝜂 power is brake power with

PSms shaft power measured for each run ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 22 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

ηS shaft efficiency (0.99 for conventional VS ship’s speed through water [m/s], see shaft) 10.2.4 PBms brake power measured for each run , overload factors derived from load var- ηM transmission efficiency iation model test (Appendix D) 𝑛𝑛 𝑣𝑣 𝜉𝜉 𝜉𝜉 speed correction due to shallow water The corrected delivered power PDid is ob- [m/s], determined according to 10.3.4. tained as follows (under condition Δ𝑉𝑉 The extended analysis in Appendix J, > 0): Dms ∆𝑅𝑅𝑉𝑉S 𝑃𝑃 − which is included informatively, is useful for 𝜂𝜂Did model test correlation purposes since it in- 1 P = volves the full-scale wake fraction. Did 2 2 ∆RV  ∆∆RV  RV 10.2.4 Correction of the measured ship’s −+S − SS + ξ PPDms  Dms  4 PDms P η ηη speed due to the effect of current Did  Did  Did (7) The ship's speed through water (VS) is the measured speed over the ground (VG) corrected VS ship’s speed through water [m/s], see for the current speed (VC) at each run, VS=VG-VC. 10.2.4 ηDid propulsion efficiency coefficient in The current correction can be achieved by ideal condition, from model test. two (2) different methods: either the ‘Iterative’ ξP overload factor derived from load vari- method or the ‘Mean of means’ method. The ation model test. details are given in Annex H. ΔR resistance increase due to wind, waves and temperature deviations [N] (eq. 4 ). a) ‘Iterative’ method

PDid is the power in ideal conditions, i.e. no Based on the assumption that the current wind, waves or other disturbances. For shallow speed varies with a semi-diurnal period, a cur- water a speed correction is applied according rent curve as a function of time is created. In to 10.3.4. Deviations in displacement are cor- the same process a regression curve represent- rected for according to 10.3.5. ing the relationship between the ship’s speed through the water and corrected power is de- The correction of the propeller frequency termined. The current curve and the regression of revolution is also carried out considering curve are created in one process. The regres- load variation effect (Appendix D). The cor- sion curve has no relation with the rected shaft rate nid is speed/power curve from the tank tests.

nms nid = (8) The analysis of the direct power method as PPDms− Did Δ V ξξnv++1 described in Appendix D shall be repeated af- PVDid S ter the value of VS has been derived by the current correction analysis. with nms measured propeller frequency of revo- b) ‘Mean of means’ method lution [1/s], ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 23 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

Based on the assumption that for a given 1 2 RAA= ρψ A C DA( WRref) AV XV WRref + power setting, the current speed varies para- 2 bolically, the influence of current is accounted (9) 1 2 for by applying the ‘Mean of means’ method − ρ AC DA(0) AV XV G for each set of runs with the same power set- 2 ting. (Principles of Naval Architecture, 1988) with

‘Mean of means’ method gives one cor- AXV area of maximum transverse section rected ship’s speed for each power setting as exposed to the wind [m2], described in Appendix H.2. Therefore, for CDA wind resistance coefficient each power setting, the values of corrected power and corrected propeller rate of revolu- Note: CDA = -CX for method F.3 tions shall be combined and averaged to derive VG measured ship’s speed over ground the final results. [m/s], VWRref relative wind speed [m/s] at reference 10.2.5 Prediction of power curve from trial height, 3 condition to other loading condition ρA mass density of air [kg/m ], ψWRref relative wind direction at reference For dry cargo vessels it is difficult to con- height; 0 means heading wind. duct speed trials at full load condition. For such ships speed trials are performed at ballast By nature, the wind speed and direction condition and the power curve is converted to vary in time and therefore these are defined by that of full load or of stipulated condition using their average values over a selected period. the power curves based on the tank tests for these conditions. For speed/power trials it is assumed that the wind condition is stationary i.e. that the speed The tank test results shall be provided by and direction are reasonably constant over the the Shipbuilder. These tank test results shall be duration of each run. The average speed and obtained in full compliance with the require- direction during the run are then determined ments given in Section 7.5. for the duration of each measurement run.

The conversion method to be followed to The wind speed and direction are usually convert the trial results for trial condition to re- measured by the on-board anemometer, posi- sults for the contractual or stipulated condition tioned mostly in the radar mast on top of the is given in Appendix I. bridge. Both wind speed and direction at this location may be affected by the geometry of 10.3 Calculation methods for resistance the vessel in particular the shape of the super- increase and other corrections structure and the wheel house. The true wind vector for each speed-run is 10.3.1 Resistance increase due to the effects found from the speed and heading of the vessel of wind and the measured wind speed and direction. By averaging the true wind vectors over both The resistance increase due to relative wind speed-runs of the double run, the true wind is calculated by: ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 24 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

vector for the run-set at vertical position of an- α angle between ship heading and com- emometer is found. The wind speed as meas- ponent waves; 0 means heading waves, ured by the anemometer shall be corrected for VS ship’s speed through the water, the wind speed profile taking into account the E directional spectrum. vertical position of the anemometer and the reference height for the wind resistance coeffi- If the directional spectrum is measured at cients (normally 10 m) according to Appendix sea trials by a sensor and the accuracy is con- E.2. This averaged true wind vector is then firmed, the directional spectrum is available. If used to recalculate the relative wind vector for the directional spectrum is not measured it is each speed-run of the set. This procedure is ex- calculated by the following relation: plained in detail in Appendix E.1. E = Sη(ω)G(α) (11) The wind resistance coefficient shall be based on the method according to Appendix F. with G angular distribution function. 10.3.2 Resistance increase due to the effects Sη frequency spectrum. of waves The standard form of the frequency spec- The most reliable way to determine the de- trum and the angular distribution function are crease of ship’s increase of resistance in waves assumed for the calculation. is to carry out sea keeping tests in regular waves of constant wave height, at different For ocean waves the modified Pierson- wave lengths and directions and at various Moskowitz frequency spectrum of ITTC 1978 speeds, and according to ITTC 7.5-02-07-02.2. is used:

Irregular waves can be represented as lin- Afw  Bfw  Sη (ω) = exp−  (12) ear superposition of the components of regular ω 5  ω 4  waves. Therefore, the mean resistance increase in short crested irregular waves RAW is calcu- with lated by linear superposition of the directional wave spectrum E and the response function of 2 H W1/3 mean resistance increase in regular waves Afw = 173 (13) T 4 Rwave. 01

2π ∞ ω α 691 Rwave ( , ;VS ) = RAW = 2 E(ω,α)dωdα (10) Bfw 4 (14) ∫0 ∫0 2 ζ A T01 with Other spectra can be used if appropriate for the specific location and environment, given RAW mean resistance increase in short that it can be supported by public references. crested irregular waves, Rwave transfer function of mean resistance in- For the angular distribution function the crease in regular waves, cosine-power type shown in formula (15) is ζA wave amplitude, generally applied; e.g. s=1 for wind waves and ω circular frequency of regular waves, s=75 for swells are used in practice. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 25 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

22s 2Γ+ (s 1) 2s 1 2 G()α= cos (αθ− ) (15) RT0= ρ 0 SV S C T0 (19) 2π Γ+ (2s 1) m 2

ππ where for −≤−αθm ≤ 22 CF frictional resistance coefficient for actual water temperature and salinity, where CF0 frictional resistance coefficient for ref- s directional spreading parameter, erence water temperature and salinity, Γ Gamma function, ΔCF roughness allowance associated with θ primary wave direction; 0 means head- Reynolds number for actual water tem- m perature and salinity, ing waves. ΔCF0 roughness allowance associated with Reynolds number for reference water For wind waves and swells, RAW is calculated for each run with the relevant wave temperature and salinity, height, period and direction. CT0 total resistance coefficient for reference water temperature and salinity, The resistance increase due to waves shall RAS resistance increase due to deviation of be determined by tank tests or formulae shown water temperature and water density in Appendix G. [N], RF frictional resistance for actual water temperature and salt content [N], 10.3.3 Resistance increase due to water tem- RF0 frictional resistance for reference water perature and salt content temperature and salt content [N], RT0 total resistance for reference water tem- Both water temperature and salt content, perature and salt content [N], affect the density of the sea water and thus the S wetted surface area [m2], ship resistance. Usually, speed trials are cor- VS ship’s speed through the water [m/s], rected to a sea water temperature of 15°C and a density of 1026 kg/m³. The effects of water water density for actual water temperature and salt content [kg/m3], temperature and density that differs from these S 𝜌𝜌ρ values are calculated as follows: 0 water density for reference water temperature and salt content.  ρ∆  CC+  S F0 F0 CF, CF0, ΔCF and ΔCF0 are derived according RRAS= T0  −−11 RF  − (16)  ρ∆0  CCFF+  to ITTC Recommended Procedures 7.5-02-03- 01.4, latest version, using the same roughness with kS for ideal and actual condition.

1 2 10.3.4 Correction of the ship performance RF= ρ∆ SS SV( C F+ C F) (17) 2 due to the effects of shallow water. 1 R= ρ∆ SV2 ( C+ C ) (18) Within the restrictions on water depth stip- F02 0 S F0 F0 ulated in section 6.4, the results of speed/power trials in restricted water depth ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 26 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

may be corrected according to the Raven Shal- where low Water Correction Method (2016) for P1 power corresponding to displacement which the calculation procedure is specified in volume 1, Appendix K. P2 power corresponding to displacement ∇ If agreed among builder, owner and verifier, volume 2, then the corrections for power on shallow wa- 1 displacement volume during the ∇ ter may be derived from propulsion model tests speed/power trial, ∇ for the specific vessel on deep and shallow wa- 2 displacement volume used in the tank ter corresponding with the water depth during test. ∇ the speed/power trials. Such model tests have to be conducted in a towing tank with suffi- 11. PROCESSING OF THE RESULTS cient width for which results have been validated with full scale trials on shallow water. After completion of the S/P trials the meas- The recommended basin width is: ured data shall be processed in the following sequence, also illustrated in Figure 6: • blockage (midship sectional area / tank cross section) < 2.0%, 1. Derive the average values of each • 2.0 model lengths for FnH <= 0.5 measured parameter for each speed • 2.7 model lengths for 0.5 < FnH < 0.7 run. The average speed component in the heading direction is found from the Extrapolation of the model test results to DGPS recorded start and end positions full scale shall be done using the ITTC Recom- in the heading direction of each speed mended Procedure 7.5-02-03-01.4 including run and the elapsed time; the form factor, with the form factor deter- 2. Correct ship’s speed for current by mined for the water depth considered. For deep ‘Mean of means’ method in case of two and shallow water, the same methods, proce- double runs (Appendix H) or mean dures and empirical coefficients shall be used speed in case of one double run. (If ‘It- to extrapolate the model scale values to full erative’ method is used, this is the ini- scale(Raven 2012). tial speed.); 3. Derive the true wind speed and direc- 10.3.5 Correction of the ship’s performance tion for each double run by the method due to the effects of displacement described in Appendix E; 4. Derive the resistance increase due to If the displacement of the vessel at the wind (Appendix F); speed/power trial differs from the specified 5. Derive the resistance increase due to displacement within the limits mentioned in waves (Appendix G); section 5.1, the following equation, based on 6. Derive the resistance increase due to the Admiralty formula, shall be applied to the effect of water temperature and salinity power values: (10.3.3); 7. Correct power using the Direct Power 2/3 Method (Appendix D);  ∇2  PP21=   (20) 8. Correct ship speed for current if ‘Itera- ∇  1  tive’ method is used. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 27 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

9. If ‘Iterative’ method is used, repeat item 7; 10. Correction of power for the difference of displacement from the stipulated contractual and EEDI conditions (10.3.5); 11. Correction of speed for the effect of shallow water (10.3.4); 12. Correction of propeller revolution; 13. Use the speed/power curve from the model tests for the specific ship design at the trial draught. Shift this curve along the power axis to find the best fit with all corrected speed/power points according to the least squares method. When more than three (3) power settings, all above 50% MCR, are measured, it is acceptable to use a polyno- mial curve of degree one less than the number of power settings, fitted to the corrected points using least squares method. 14. Intersect the curve at the specified power to derive the ship’s speed at trial draught in ideal conditions; 15. Apply the conversion from the trial condition to other stipulated load conditions according to 10.2.5 and appendix I; 16. Apply corrections for the contractual weather conditions if these deviate from ideal conditions.

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Preparation Conduct

Measured data VG, Pms, nms

Correction of ship’s speed for current by ‘MoM’ or mean

Correction of power for resistance increase Wave data

‘Iterative’ method No Wind data for current correction?

Yes Water temperature, Water density Correction of ship’s speed for current

Correction of power for resistance increase using revised ship’s speed

Speed and power evalua- Water depth tion

Correction of power Displacement for displacement

Final performance

Figure 6. Flowchart of speed/power trial analysis

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wind direction, wind velocity, air temperature, water temperature, water density etc. 12. REPORTING S/P trial agenda. This shall give a complete In the trial report, an overview of the trial and chronological order of the trial programme conditions and all corrections that have been (both planned and actual) with specification of applied to arrive at the contract speed and the the duties of the different recording/monitor- EEDI speed shall be given. ing stations on board.

The trial report shall contain all relevant in- Trial Results of each speed run formation to carry out the data analysis. It shall be written in such a way that all results can be • Date and Time at start of speed run reprocessed. • Run number • The trial report shall contain the following Ship’s position sections: • Ship’s heading • Run duration Trial Report Summary comprising details • Mean values of measured ship's speed of • Mean value and standard deviation of torque (per shaft) A) Ship particulars (including trial draughts • Mean value and standard deviation of shaft and displacement) rpm (per shaft) B) Propeller details • Mean value and standard deviation of shaft C) Engine data power (per shaft) D) Details of hull appendages and rudder • Relative wind speed and direction • Significant wave height, mean period and Contract conditions including contract direction speed, power, and displacement. • Mean water depth

EEDI conditions including EEDI speed, Analysis and Correction methods. The power and displacement. analysis and correction of the measured trial data shall be conducted in compliance with Description of Instrumentation describing these Guidelines. the instrument set-up, calibration procedure, data acquisition interfacing details, location of Conclusions. Speeds and powers on the sensors (e.g. strain gauges on shaft, anemome- contractually specified point and in the EEDI ter etc.), etc. condition, derived from the S/P trial analysis, have to be reported. Description of Trial Site. This will give information on geography, distance from land, water depth etc.

Environment Parameters. This shall list the measured/observed environmental conditions at the site during S/P trials such as wave height, wave period, wave direction, air pressure, ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 30 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

13. REFERENCESAND BIBLIOG- ITTC Powering Performance Committee, "An RAPHY Updated Guide For Speed/Powering Tri- als", Report of the ITTC Powering Perfor- Boom et al., "Speed/Power Performance dur- mance Committee, Appendix I, 21st ITTC, ing Trials and In-Service" Proceedings 1996. SNAME, Athens, September 2008. ITTC 7.5-04-01-01.2;“Recommended Proce- Boom, H.van den, Huisman, H. and Mennen, dures and Guidelines for Speed/Power Tri- F.:”New Guidelines for Speed/Power Tri- als”, 23rd ITTC 2002. als” SWZ/Maritime, Jan./Feb.2013; ITTC “Recommendations and Guidelines for BSRA,"BSRA standard method of Speed Trial Resistance & Propulsion Model Tests”, Analysis", Report NS 466, 1978. 23rd ITTC, 2002.

Deng Rui, Li Chao, Dong Guoxiang, etc. "Op- Japan Ship Research Association, "SR208: timization of the superstructure and fore- New Speed Trial Analysis Method", Re- castle fairing of a multi-purpose ship" port of the SR208 Committee, 1993. OMAE 2017-61256. JTTC, "A proposal for a standard method of Fujiwara, T., Ueno, M. and Ikeda, Y.: "A New speed trial analysis", Bull. SNAJ, No.262, Estimation Method of Wind Forces and 1944. Moments acting on Ships on the basis of Physical Component Models", J. JTTC, "A tentative guide for the operation of JASNAOE, Vol.2, 2005. speed trials with large vessels", Bull. SNAJ, No. 442, 1966. Hansa Int. Maritiem Journal 150th Year, No. 4, April 2013, Hansa-online.de/STA-JIP.pdf. Kaiser, M., Ph.D. (2016), Results of aerody- namic model tests for Handy Size Bulk ISO 15016;”Guidelines for the assessment of Carrier, Technical Report No. RH-2016/T- speed and power performance by analysis 104E, CTO.S.A. of speed trial data”, 2002. Maruo H., "On the increase of the resistance of ISO 19019; “Guide for Planning, Carrying out a ship in rough seas (2nd report)", J. SNAJ, and Reporting Sea Trials”, 2002. Vol. 108, 1960.

ITTC Performance Committee, "ITTC guide Ministry of Transport, "Guaranteed speed for measured-mile trials", Report of the specifications and the analysis procedure", ITTC Performance Committee, Appendix I, Notification No. 174, Japan, 1955. 12th ITTC, 1969. Principles of Naval Architecture, Volume ITTC Performance Committee, "Hull Rough- II,Section II, Ship Standardization Trials; ness", Report of the ITTC Performance published by SNAME 1988. Committee, 19th ITTC, 1990. Raven, H.C.: “A Computational Study of Shal- low-Water Effects on Ship Viscous Re- ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 31 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

sistance”, 29th Symposium on Naval Hy- SRAJ, "A Study of ship speed trials", No. 2 drodynamics, Gothenburg, Sweden, Au- Standardization Panel, , Res. Rep. No. 12R, gust 2012. 1972.

Raven, H.C.: “A New Correction Procedure Taniguchi, K. & Tamura, K., "On a new for Shallow-Water Effects in Ship Speed method of correction for wind resistance Trials”, Proceedings of PRADS2016, Co- relating to the analysis of speed trial re- penhagen, 2016. sults", 11th ITTC, 1966.

Sea Trial Analysis JIP; “Recommended Prac- Tsujimoto, M, Kuroda, M. and Sogihara, N., tice for Speed Trials”, 2006, Public docu- “Development of a calculation method for ment from www.marin.nl. fuel consumption of ships in actual seas with performance evaluation”, Proceedings The Ship Testing and Trial Trip Committee of of OMAE 2013, OMAE2013-11297, 2013. the Association of Ship Technical Societies in Norway, "Standardization code for trials World Meteorological Organization: Manual and testing of new ships", 2nd Edition, 1971. on Codes, International Codes, Volume I.1, Part A-Alphanumeric Codes, WMO-No. SNAME, "Code for Sea Trials", 1989. 306 (1995 edition). ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 32 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

: GENERAL SHIP AND TRIAL DATA

Hull condition Last date of cleaning hull Hull appendages and Rudder Geometry Type Rate of Movement during speed trials Wind fetch Height of anemometer above waterline Transverse Projected area above the waterline including superstructures at trial draught Lateral projected area above the If F.3 method is used waterline including superstructures at trial draught Propeller(s) Type (FPP/CPP) Pitch (FPP) Direction of rotation Number of blades Shaft(s) G modulus Diameter (inside) Diameter (outside)

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: BEAUFORT SCALE OF WIND

Velocity equivalent at a standard height of 10

Specifications metres above open flat ground Probable Probable Descriptive wave wave term Mean veloc- height* in height* in m s-1 km h-1 m.p.h. Land Sea Coast ity in knots metres feet Beafort number Beafort

0 Calm <1 0-0.2 <1 <1 Calm; smoke rises vertically Sea like a mirror Calm - - 1 Light air 1-3 0.3-1.5 1-5 1-3 Direction of wind shown by Ripples with the appearance of Fishing smack just 0.1 ¼ smoke drift but not by wind scales are formed, but without has steerage way (0.1) (¼ ) vanes foam crests 2 Light 4-6 1.6-3.3 6-11 4-7 Wind felt on face; leaves Small wavelets, still short but of smacks which then 0.2 ½ breeze rustle; ordinary vanes more pronounced; crests have a travel at about1–2 (0.3) (1) moved by wind glassy appearance and do not knots break 3 Gentle 7-10 3.4-5.4 12-19 8-12 Leaves and small twigs in Large wavelets; crests begin to Smacks begin to ca- 0.6 2 breeze constant motion; wind ex- break; foam of glassy appear- reen and travel about (1) (3) tends light flag ance; perhaps scattered white 3–4 knots horses 4 Moderate 11-16 5.5-7.9 20-28 13-18 Raises dust and loose pa- Small waves, becoming longer; Good working 1 3½ breeze per; small branches are fairly frequent white horses breeze, smacks carry (1.5) (5) moved all canvas with good list 5 Fresh 17-21 8.0-10.7 29-38 19-24 Small trees in leaf begin to Moderate waves, taking a more Smacks shorten sail 2 6 (8½) breeze sway; crested wavelets pronounced long form; many (2.5) form on inland waters white horses are formed(chance of some spray) 6 Strong 22-27 10.8-13.8 39-49 25-31 Large branches in motion; Large waves begin to form; the Smacks have double 3 9½ breeze whistling heard in telegraph white foam crests are more ex- reef in mainsail; care (4) (13) wires; umbrellas used with tensive everywhere (probably required when fishing difficulty some spray) 7 Near gale 28-33 13.9-17.1 50-61 32-38 Whole trees in motion; in- Sea heaps up and white foam Smacks remain in 4 13½ convenience felt when from breaking waves begins to harbour and those at (5.5) (19) walking against wind be blown in streaks along the di- sea lie to rection of the wind 8 Gale 34-40 17.2-20.7 62-74 39-46 Breaks twigs off trees; gen- Moderately high waves of All smacks make for 5.5 18 erally impedes progress greater length; edges of crests harbour, if near (7.5) (25) begin to break into the spindrift; the foam is blown in well- marked streaks along the direction of the wind 9 Strong 41-47 20.8-24.4 75-88 47-54 Slight structural damage High waves; dense streaks of - 7 23 gale occurs (chimney pots and foam along the direction of the (10) (32) slates removed) wind; crests of waves begin to topple, tumble and rollover; spray may affect visibility 10 Storm 48-55 24.5-28.4 89-102 55-63 Seldom experienced inland; Very high waves with long over- - 9 29 trees uprooted; considera- hanging crests; the resulting (12.5) (41) ble structural damage oc- foam, in great patches, is blown curs in dense white streaks along the direction of the wind; on the whole, the surface of the sea takes on a white appearance; the tumbling of the sea becomes heavy and shock- like; visibility affected 11 Violent 55-63 28.5-32.6 103-117 64-72 Very rarely experienced; Exceptionally high waves (small - 11.5 37 storm accompanied by wide- and medium-sized ships might (16) (52) spread damage be for a time lost to view behind the waves); the sea is completely covered with long white patches of foam lying along the direction of the wind; everywhere the edges of the wave crests are blown into froth; visibility affected 12 Hurricane 64 and 32.7 and 118 and 73 and - The air is filled with foam and - 14 45 over over over over spray; sea completely white with (-) (-) driving spray; visibility very seri- ously affected ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 34 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

* This table is only intended as a guide to show roughly what may be expected in the open sea, remote from land. It shall never be used in the reverse way; i.e., for logging or reporting the state of the sea. In enclosed waters, or when near land, with an off-shore wind, wave heights will be smaller and the waves steeper. Figures in brackets indicate the probable maximum height of waves. (ref World Meteorological Organization, 1995)

State of the sea

Code Descriptive terms Height* figure in metres 0 Calm (glassy) 0 1 Calm(rippled) 0 – 0.1 2 Smooth(wavelets) 0.1 – 0.5 3 Slight 0.5 – 1.25 4 Moderate 1.25 – 2.5 5 Rough 2.5 – 4 6 Very rough 4 – 6 7 High 6 – 9 8 Very high 9 – 14 9 Phenomenal Over 14

Notes:

(1)*These values refer to well-developed wind waves of the open sea. While priority shall be given to the descriptive terms, these height values may be used for guidance by the observer when reporting the total state of agitation of these resulting from various factors such as wind, swell, currents, angle between swell and wind, etc.

(2) The exact bounding height shall be assigned for the lower code figure; e.g. a height to f4 miscoded as 5.

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: FORMAT S/P TRIAL LOG SHEET

Speed - Power Trials Log Form

Ship name: Date:

Ship Environment Propeller shaft Measurement location:

Tfwd m Tair ⁰ C outer dia D1 mm Lat

Taft m Twater ⁰ C inner dia D2 mm Lon

3 2 Displacement tons ρwater kg/m steel type N/mm Description Height of anemometer above water line: m

Relative wind Wind driven waves Swell Propeller PS Propeller SB

Forward Speed Run No. Time Heading UKC Speed Direction Height Direction Period Height Direction Period Torque Power Revs Torque Power Revs / Return (SOG)

[-] [-] [F / R] [deg] [kn] [m] [kn] [m/s] [deg] [m] [deg] [s] [m] [deg] [s] [kNm] [kW] [RPM] [kNm] [kW] [RPM]

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: PROPULSIVE EFFICIENCY The propulsive efficiency is assumed to CORRECTION BASED ON LOAD vary linearly with the added resistance accord- VARIATION TESTS ing to:

η∆R Dms =ξ + D.1. Propulsive efficiency correction P 1 (D-3) ηDid Rid The ship’s propulsive efficiency is affected by the added resistance. This has to be taken where into account when correcting the power. ξP overload factor derived from load variation model test, according to ITTC The delivered power corrected to ideal con- Recommended Procedure 7.5-02-03- dition is derived by 01.4（2017） Rid resistance in ideal condition PPDid= Dms − ∆ P (D-1) This leads to the expression for the cor- with rected delivered power: ΔP correction of delivered power due to   the increased resistance and the ∆RVS P Dms PPDid=−− Dms 1 ξP  (D-4) changed propulsive efficiency ηDid  PDid 

ΔP can be written as: This is expressed explicitly as:

∆ηRVS  Dms  1 ∆PP=+−Dms 1  (D-2) PDid = ηηDid  Did  2 ∆RV P −+S with Dms η (D-5) Did PDms delivered power derived from shaft 2  ∆∆ power or break power measured on RVSSRV +− PPDms  +4 Dms ξP ηη board for each single run [W],  Did  Did VS ship’s speed through the water [m/s], which can be obtained by the ‘Iterative’ method or the ‘Mean of means’ method, D.2. Correction of shaft rotation rate – ef- Δ resistance increase from relative wind, fect of added resistance and of shal- waves and deviation of water tempera- low water 𝑅𝑅 ture and water density for each run. The value is computed according to section With the PDid found as described above the 10.3 in these Guidelines, [N], correction on shaft rate is: ηDid propulsive efficiency coefficient in ideal condition obtained from standard ∆∆n PPDms− Did V = ξξn + V (D-6) towing tank test and interpolated to the nPid Did VS speed VS, ηDms propulsive efficiency coefficient dur- where ing sea trial. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 37 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

∆nn=ms − n id (D-7) with nm measured shaft rate [1/s], nid corrected shaft rate [1/s], ξn, ξv overload factors derived from load variation model test, ΔV speed correction due to shallow water [m/s], determined by equation (K-10) and Pd-Vs curve from model test.

From this follows that the corrected shaft rate nid is:

nms nid = (D-8) PPDms− Did ∆ V ξξn ++V 1 PVDid S

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: EVALUATION OF WIND V= V22 +− V2 VV cosψ (E-2) DATA WT WR G WR G WR

−1 VVWRsin (ψψ WR +−) Gsin ( ψ) ψ WT = tan E.1. Averaging process for the true wind VVWRcos(ψψ WR +−) Gcos( ψ) vectors for VWRcos(ψψ WR +−) VGcos( ψ) ≥ 0 The true wind vectors in each run are found VVsin (ψψ+−) sin ( ψ) ψ = tan −1 WR WR G +180 from the ship’s speed over ground and heading WT VVcos(ψψ+−) cos( ψ) and the measured relative wind speed and di- WR WR G for V cos ψψ+−V cos ψ < 0 rection. By averaging the true wind vectors WR( WR ) G ( ) over both runs of the double run, the true wind (E-3) vector for the run-set is found. This runs-set averaged true wind vector shall be used to re- where: calculate the relative wind vector for each run V measured ship’s speed over ground of the set. G [m/s];

VWR mean value of the measured relative wind velocity at the vertical position of the anemometer in [m/s];

VWT true wind velocity at the vertical position of the anemometer in [m/s]; ψ ship’s heading in [degrees];

ψ WR mean value of the measured relative wind direction at the vertical position of the anemometer [degrees]; ψ WT true wind direction at the vertical position of the anemometer [degrees].

The true wind velocity and direction are corrected by an averaging process over both runs of the double run.

2 VVWT( i)cosψψ WT( i) + WT( i+1)cos WT( i+1)     2  V ' = WT(i/i+1) 2 VVsinψψ+ sin  Figure E-1 True wind vectors and relative wind vec- + WT( i) WT( i) WT( i+1) WT( i+1) tors.    2  The true wind velocity and direction at the (E-4) vertical position of the anemometer are calculated by: ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 39 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

ψψ+ '1− VVWT( i)sin WT( i) WT( i+1)sin WT( i+1) The true wind velocity VWT( i) , true wind di- ψ WT(i/i+1) = tan VVWT( i)cosψψ WT( i) + WT( i+1)cos WT( i+1) rection ψ WT(i) , relative wind velocity VWR( i)

for VWT( i)cosψψ WT( i) +≥V WT( i+1)cos WT( i+1) 0 and relative wind direction ψ WR(i) can then be ψ ' = ' ' ' ' WT(i/i+1) replaced by VWT( i) , ψ WT(i) , VWR( i) and ψ WR(i) .

VVWT( i)sinψψ WT( i) + WT( i+1)sin WT( i+1) = tan −1 +180 VVcosψψ+ cos WT( i) WT( i) WT( i+1) WT( i+1) E.2. Correction for the vertical position of

for VWT( i)cosψ WT( i) +V WT( i+1)cosψ WT( i+1) < 0 the anemometer (E-5) The difference between the vertical position of the anemometer and the reference V ' = WR( i) height is to be corrected by means of the wind (E-6) '2 2 ' ' speed profile given by formula (E-8). =VWT( i) ++ VG(i) 2 VVWT( i) G(i) cos(ψψ WT(i)− (i) )

1 ''ψψ−  Z 9 '1− VWT( i)sin ( WT(i) (i) ) ref ψ = VVWTref= WT   (E-8) WR(i) tan ''  Za  VVG(i) +−WT( i)cos(ψψWT(i) (i) ) +''ψψ −≥ for VG(i) VWT( i)cos( WT(i) (i) ) 0 where '' VWT( i)sin (ψψWT(i)− (i) ) ψ '1= − + VWTref true wind velocity at the reference WR(i) tan '' 180 VVG(i) +−WT( i)cos(ψψWT(i) (i) ) height [m/s];

'' VWT true wind velocity at the vertical posi- for VG(i) + VWT( i)cos(ψψWT(i) −< (i) ) 0 (E-7) tion of the anemometer in [m/s]; Zref reference height for the wind resistance where: coefficients in [m];

' Za vertical position of the anemometer in VWT averaged true wind velocity at the vertical position of the anemometer [m/s]; [m]. ' VWR corrected relative wind velocity at the The reference height for the wind re- vertical position of the anemometer sistance coefficients, ref is selected as the cor- [m/s]; responding height for the wind resistance coef- ' 𝑍𝑍 ψ WT averaged true wind direction at the ver- ficient from wind tunnel tests (normally 10m). tical position of the anemometer [de- The relative wind velocity at the reference grees]; ' height is calculated by: ψ WR corrected relative wind direction at the vertical position of the anemometer V= V22 ++ V2 VV cos(ψψ−) [degrees]; WRref WTref G WTref G WT ()i run number. (E-9) The relative wind direction at the reference height is calculated by: ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 40 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

ψψ− −1 VWTrefsin( WT ) ψ WRref = tan VVG+− WTrefcos(ψψ WT )

for VG+ V WTrefcos(ψψ WT −≥) 0

ψ WRref = (E-10)

VWTrefsin(ψψ WT − ) = tan−1 +180 VVG+− WTrefcos(ψψ WT )

for VG+ V WTrefcos(ψψ WT −<) 0 where:

VWRref relative wind velocity at the reference height [m/s];

VWTref true wind velocity at the reference height in [m/s];

ψ WRref relative wind direction at the reference height [degrees];

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: CORRECTION METHODS For the use of these coefficients the vessel FOR RESISTANCE INCREASE DUE type, shape and outfitting shall be carefully TO WIND evaluated and compared with the geometry of the vessel from the data set. The data provided For calculating the resistance increase due are limited to the present-day common ship to wind one of the following methods are to be types. For special vessels such as tugs, supply used: ships, fishery vessels and fast crafts, the geometry of the vessel is too specific to make use of the available database. Wind tunnel results for F.1. Wind resistance coefficients by wind the specific ship type are required. tunnel test Table F-1 Ship type for the wind resistance data set If wind resistance tests for the specific, or Ship type LC Superstructure Vessel Reference similar, vessel have been performed in a qual- Tanker con- WT L normal 280kDWT ified wind tunnel, the wind resistance coeffi- ventional bow (Boom 2013) Tanker con- WT B normal 280kDWT cients derived by these measurements shall be ventional bow (Boom 2013) used to compute the wind resistance of the ves- Tanker cylin- WT B normal 280kDWT sel in the trial condition. The coefficients drical bow (Boom 2013) CFD LNG carrier A prismatic integrated 125k-m3 should be derived based on projected frontal (Boom 2013) prismatic extended CFD area. LNG carrier A 138k-m3 deck (Boom 2013) CFD LNG carrier A spherical 125k-m3 (Boom 2013) Container WT F.2. Wind resistance coefficients by CFD L with containers 6800TEU ship (Boom 2013) Container without containers, WT L 6800TEU Wind resistance coefficients derived from ship with lashing bridges (Boom 2013) Container WT a CFD viscous flow solver is acceptable pro- B with lashing bridges 6800TEU ship (Boom 2013) vided that the CFD code and the user have Container without lashing WT B 6800 TEU demonstrated verification and validation ship bridges (Boom 2013) CFD Car Carrier A normal Autosky against qualified wind tunnel results for similar (Boom 2013) ships using ITTC Recommended Procedures Ferry/Cruise WT A normal 7.5-03-01-01 and with a required uncertainty ship (Boom 2013) General Cargo WT A normal of the derived RAA corresponding to 2% on the ship (Boom 2013) total power. The simulation corresponding to Handy size WT B Cranes (Kaiser 2016) the actual speed trial case has to use the same bulk carrier Handy size WT B No cranes grid structure, grid density, degree of geomet- bulk carrier (Kaiser 2016) rical resolution and modelling (e.g. turbulence Multi-purpose L With containers 19000D WT carrier WT car- (Deng,2017) models and boundary conditions) as used for rier the validation demonstration. Multi-purpose B With partly contain- 19000D WT carrier ers WT car- (Deng,2017) rier

F.3. Data sets of wind resistance coefficients LC = Loading Condition WT = Wind tunnel L = Laden CFD = CFD computations B = Ballast Data sets of the wind resistance coefficient A = Average

CX are available for certain ship types shown in Table F-1. These are based on projected frontal area and wind speed at 10 m reference height. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 42 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

280 KDWT TANKER CONVENTIONAL BOW

1.5 Angle Cx [-] Ballast of Laden attack Ballast Laden 1.0 [°] 0 -0.86 -0.96 10 -0.76 -0.93 20 -0.62 -0.85 0.5 30 -0.45 -0.73 40 -0.32 -0.62 ]

- 50 -0.21 -0.47 0.0 60 -0.13 -0.34 Cx [ 70 -0.06 -0.17 80 -0.04 -0.06 -0.5 90 0.02 0.05 100 0.08 0.14 110 0.19 0.22 120 0.29 0.29 -1.0 130 0.38 0.40 140 0.47 0.53 150 0.56 0.66 -1.5 160 0.61 0.75 0 30 60 90 120 150 180 170 0.66 0.79 angle of attack [°] 180 0.63 0.77

280 KDWT TANKER CYLINDRICAL BOW 1.5 Angle Cx [-] of Ballast attack Ballast 1.0 [°] 0 -0.86 10 -0.75 20 -0.62 0.5 30 -0.45 40 -0.27 ]

- 50 0.00 0.0 60 0.31 Cx [ 70 0.47 80 0.48 -0.5 90 0.29 100 0.18 110 0.18 120 0.29 -1.0 130 0.37 140 0.47 150 0.56 -1.5 160 0.61 0 30 60 90 120 150 180 170 0.65 angle of attack [°] 180 0.63

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LNG CARRIER 1.50 Angle Cx [-] of Prismatic integrated Prismatic attack integrated 1.00 [°] 0 -1.02 10 -0.99 0.50 20 -0.93 30 -0.83 40 -0.67 ]

- 50 -0.48 0.00 60 -0.30

Cx [ 70 -0.14 80 -0.03 -0.50 90 0.05 100 0.11 110 0.24 120 0.41 -1.00 130 0.56 140 0.68 150 0.79 -1.50 160 0.88 0 30 60 90 120 150 180 170 0.92 angle of attack [°] 180 0.91

LNG CARRIER 1.50 Prismatic extended deck Angle Cx [-] of Prismatic Spherical attack extended Spherical 1.00 [°] deck 0 -0.81 -1.11 15 -0.79 -0.79 0.50 30 -0.93 -0.70 45 -0.55 -0.56 60 -0.27 -0.37 ]

- 75 -0.12 -0.12 0.00 90 -0.20 0.30 Cx [ 105 0.00 0.58 120 0.19 0.83 -0.50 135 0.80 0.61 150 1.06 0.79 165 1.03 0.96 -1.00 180 0.60 0.74

-1.50 0 30 60 90 120 150 180 angle of attack [°]

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6800 TEU CONTAINERSHIP

2.0 Angle Cx [-] Laden without containers, with lashing bridges of Without containers attack with lashing bridges 1.5 Ballast without containers, with lashing bridges [°] Laden Ballast 0 -1.01 -0.97 15 -1.11 -1.06 1.0 30 -1.11 -0.90 45 -0.95 -0.79 0.5 60 -0.74 -0.65 ]

- 75 -0.46 -0.46 90 -0.13 -0.25 Cx [ 0.0 105 0.28 0.12 120 0.77 0.49 135 1.09 0.91 -0.5 150 1.18 1.04 165 1.19 1.08 180 0.94 0.93 -1.0

-1.5 0 30 60 90 120 150 180 angle of attack [°]

6800 TEU CONTAINERSHIP 2.0 Angle Cx [-] Laden with containers of Ballast Laden attack without with 1.5 Ballast without containers, without lashing bridges [°] containers containers 0 -0.86 -0.67 15 -0.89 -0.76 1.0 30 -0.69 -0.66 45 -0.68 -0.40 0.5 60 -0.60 -0.25 ]

- 75 -0.46 -0.21 90 -0.28 -0.26 Cx [ 0.0 105 0.04 -0.04 120 0.41 0.36 135 0.81 0.69 -0.5 150 0.99 0.90 165 1.00 0.85 180 0.89 0.67 -1.0

-1.5 0 30 60 90 120 150 180 angle of attack [°]

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CAR CARRIER 1.50 Angle Cx [-] Average of 1.00 attack Average [°] 0 -0.52 15 -0.50 0.50 30 -0.40 45 -0.20 ] - 60 -0.07 0.00

Cx [ 75 -0.04 90 0.12 105 -0.28 -0.50 120 0.17 135 0.68 150 0.90 -1.00 165 0.86 180 0.76 -1.50 0 30 60 90 120 150 180 angle of attack [°]

CRUISE FERRY 1.50 Angle Cx [-] Average of attack Average 1.00 [°] 0 -0.69 15 -0.73 30 -0.69 0.50 45 -0.34 50 -0.24 ]

- 60 -0.26 0.00 75 0.00 Cx [ 85 0.19 90 0.04 -0.50 95 -0.03 100 -0.04 110 0.10 120 0.24 -1.00 140 0.57 155 0.84 160 0.82 -1.50 170 0.73 0 30 60 90 120 150 180 180 0.67 angle of attack [°]

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GENERAL CARGO

1.50 Angle Cx [-] Average of attack Average 1.00 [°] 0 -0.60 10 -0.87 0.50 20 -1.00 30 -1.00 ]

- 40 -0.88 0.00 50 -0.85 Cx [ 60 -0.65 70 -0.42 -0.50 80 -0.27 90 -0.09 100 0.09 -1.00 110 0.49 120 0.84 140 1.39 -1.50 150 1.47 0 30 60 90 120 150 180 160 1.34 170 0.92 angle of attack [°] 180 0.82

Angle Cx [-] HANDY SIZE BULK CARRIER of Heavy Ballast, attack Ballast, 1.50 No [o] No Cranes Cranes Heavy Ballast, No Cranes 0 -0.68 -0.59 1.00 Ballast, No Cranes 10 -0.67 -0.63 20 -0.66 -0.56 30 -0.62 -0.55 0.50 40 -0.58 -0.50 50 -0.45 -0.36 ] - 0.00 60 -0.31 -0.21

Cx [ 70 -0.13 -0.06 80 -0.10 0.01 -0.50 90 -0.13 0.00 100 -0.05 0.02 110 0.08 0.04 -1.00 120 0.21 0.09 130 0.39 0.28 140 0.57 0.44 -1.50 150 0.65 0.56 0 30 60 90 120 150 180 160 0.71 0.61 Angle of attack [°] 170 0.71 0.64 180 0.80 0.64

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Angle Cx [-] HANDY SIZE BULK CARRIER of Heavy Ballast, attack Ballast, 1.50 Cranes [o] Cranes 0 -0.75 -0.71 Heavy Ballast, Cranes 1.00 10 -0.91 -0.84 Ballast, Cranes 20 -0.94 -0.89 30 -0.87 -0.82 0.50 40 -0.80 -0.70 50 -0.59 -0.49 ] - 60 -0.34 -0.23 0.00 70 -0.18 -0.12 Cx [ 80 0.02 0.01 -0.50 90 0.11 -0.02 100 0.10 0.02 110 0.22 0.12 -1.00 120 0.44 0.36 130 0.65 0.55 140 0.78 0.71 -1.50 150 0.81 0.76 0 30 60 90 120 150 180 160 0.85 0.79 Angle of attack [°] 170 0.82 0.80 180 0.70 0.68

Angle Cx [-] MULTI-PURPOSE CARRIER of With partly With attack containers containers 1.50 [°] 0 -0.81 -0.84 With partly containers 15 -0.76 -0.93 1.00 With containers 30 -0.71 -0.96 45 -0.59 -0.76 0.50 60 -0.47 -0.52 75 -0.22 -0.33

] 90 0.04 -0.14 - 0.00 105 0.44 0.23

Cx [ 120 0.83 0.64 135 0.92 0.81 -0.50 150 1.00 0.97 165 0.94 0.81 180 0.89 0.62 -1.00 130 -0.81 -0.84 140 -0.76 -0.93 150 -0.71 -0.96 -1.50 160 0 30 60 90 120 150 180 -0.59 -0.76 170 -0.47 -0.52 Angle of attack [°] 180 -0.22 -0.33

Figure F-1 Wind resistance coefficients for various ship types.

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Figure F-2 Ship types

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= CDA ψ = WR 90(deg.) F.4. Regression formula by Fujiwara et al. 1 = + CCDA ψµψµ=−=+90(deg.) DA 90(deg.) 2 ( WR WR ) A general regression formula based on model tests in wind tunnels for various ships where has been developed by Fujiwara et al (2005). AOD lateral projected area of superstructures etc. on deck, CCDA= LFcosψ WR AXV area of maximum transverse section  1 2  exposed to the winds, +−CXLIsinψ WR sin ψψWR cos WR (F-1)  2  AYV projected lateral area above the water- 3 line, sinψψWR cos WR+ C ALF sin ψ WR cos ψ WR B ship breadth, with CDA wind resistance coefficient, CMC horizontal distance from midship section to centre of lateral projected area for 0≤<ψ WR 90(deg.) AYV, hBR height of top of superstructure (bridge ACYV MC CLF=++ββ 10 11 β12 (F-2) etc.), LBOA LOA hC height from waterline to centre of lateral projected area AYV, AAYV XV LOA length overall, CXLI=++δδ 10 11 δ12 (F-3) LOA h BR BhBR μ smoothing range; normally 10(deg.), ψWR relative wind direction; 0 means head-

ABOD ing winds. CALF=++εε 10 11 ε12 (F-4) ALYV OA The non-dimensional parametersβij, δij and εij used in the formulae are shown in Table F- for 90<≤ψ 180(deg.) WR 2.

AAYV XV B Table F-2 Non-dimensional parameters CXLI=++++δδ 20 21 δ22 δ23 LhOA BR AYV LOA (F-5) j A +δ XV i 24 0 1 2 3 4 BhBR 1 0.922 -0.507 -1.162 - - βij - B hAC OD 2 -0.018 5.091 3.011 0.341 C =+++ββ β β + 10.367 LF 20 21 LLL22 23 2 OA OA OA (F-6) 1 -0.458 -3.245 2.313 - - δij AXV - - +β24 2 1.901 40.310 5.481 B2 12.727 24.407 1 0.585 0.906 -3.239 - - εij AOD 2 0.314 1.117 - - - CALF=εε 20 + 21 (F-7) AYV

for ψ WR = 90 (deg.) ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 53 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

The system of co-ordinates and the sign conventions and explanation of the input parameters are shown in Fig F.2

AOD AYV AXV center of AYV

HBR upper deck

CMC HC

LOA B

midship

Figure F.2 Input parameters for regression formula by Fujiwara

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B beam of the ship [m] HW1/3 significant wave height of wind waves : CORRECTION METHODS [m], FOR RESISTANCE INCREASE DUE LBWL length of the bow on the water line to TO WAVES 95% of maximum beam as shown in Figure G-1 [m], All method mention below shall satisfy the ρ significant wave height criterion stated in Sec- s water density for actual water tempera- tion 6.3. ture and salt content [kg/m3], g acceleration of gravity [m/s2].

G.1. Simplified correction method for ships with limited heave and pitch during the speed runs (STAWAVE-1) 95%B LBWL Specifically for speed trial conditions with present day ships a dedicated and practical method has been developed by STA-JIP (Boom, 2013) to estimate the added resistance in waves with limited input data. Figure G-1 Definition of LBWL Speed trials are conducted in low to mild STAwave-1 has been extensively validated sea states with restricted wave heights. In short for the following conditions: head waves the encounter frequency of the waves is high. In these conditions the effect of 1. Heave and pitch during speed/power wave induced motions can be neglected and trial are small (vertical acceleration at the added resistance of the vessel is dominated bow <0.05g). by the wave reflection of the hull on the water- 2. Head waves. Wave directions within 0 line. The water line geometry is approximated to ±45 degrees from bow are corrected based on the ship beam and the length of the as head waves . bow section on the water line (Figure G-1).

Formula G-1 estimates the resistance in- G.2. Empirical correction method with fre- crease in head waves provided that heave and quency response function for ships pitch motions are small. The application is re- with heave and pitch during the stricted to waves in the bow sector, within +/- speed runs (STAWAVE-2) 45 deg. off the bow. For wave directions outside this sector no wave correction is applied. The empirical method STAWAVE-2 (Boom, 2013) has been developed by STA-JIP 1 2 B to approximate the transfer function of the RAWL= ρ s gH W1/3 B (G-1) 16 LBWL mean resistance increase in heading regular waves by using the main parameters such as where ship dimensions and speed, see Figure G-2. For this purpose, an extensive database of sea B beam of the ship [m] ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 55 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

keeping model test results for a large popula- 11.0 forω < 1 = tion of ships has been used to derive parametric b1  (G-7) −8.50 elsewhere transformation functions.

Rwave 14.0 forω < 1  −2.66 ff(Fn,Cb) (Fr, CB) d1 =   L  (G-8) −566PP elsewhere   B 

f(L/B) f (Fr, CB) and f(Fn,Cb) Added resistance 1 f (Lpp, B) R= ρ gB ζ2 αω() (G-9) AWRL 2 S A 1

2 1 1/2 1/4 1/8 Wave length / Ship Length wave length / ship length π 2 I 2 (1.5kT ) α (ω) = 1 M f (G-10) 1 π 2 I 2 (1.5kT ) + K 2 (1.5kT ) 1 Figure G-2 Parametric transfer function of mean re- 1 M 1 M sistance increase in regular waves. 0.769  V  fC= 0.692 S  +1.81 (G-11) This empirical transfer function wave co- 1B vers both the mean resistance increase due to  TgM  wave reflection AWRLand the motion𝑅𝑅 induced resistance AWML. where: 𝑅𝑅 CB block coefficient, =𝑅𝑅 + RRwave AWRL R AWML (G2) VS ship’s speed in m/s

k yy non-dimensional radius of gyration in where, lateral direction, LPP ship length between perpendiculars, R= 4ρζ g22 B / Lr () ω (G-3) AWML S A PP aw TM draught at midship, I1 modified Bessel function of the first with kind of order 1, K1 modified Bessel function of the second raw ()ω = kind of order 1,

bb11b ωω1 −−1.50 exp( 1 ) a1 Fr exp( 3.50Fr) with the following restrictions: d1 (G-4) 1. 50m≤≤LmPP 400 , L L 2. 4.0<

6. wave direction within 0 to ±45deg. 50m ≤ L 1. PP , from bow. L 4.0<

∞ RVwave (;ω S ) 1 RAWL = 2 Sdη ()ωω (G-12) for τ ≥ ∫0 2 ζ A 4

m3 ∞ 2 RAWM =4πρ S −+ Hm1() ( ∫∫−∞ m ) G.3. Theoretical method with simplified 4 2 (G-14) tank tests in short waves or empirical (mk++τα ) ( mk cos ) 0 dm formula 4 22 ()m+− k00τ mk Applying the theoretical method, the mean resistance increase in regular waves Rwave is 1 for τ < calculated from the components of the mean 4 resistance increase based on Maruo's theory

RAWM and its correction term which primarily mm32∞ 2 RAWM=4πρ S −++ Hm1() is valid for short waves RAWR. ( ∫∫∫−∞ mm) 41 2 (G-15) (mk++0τα ) ( mk cos ) RRwave= AWM + R AWR (G-13) dm 4 22 ()m+− k00τ mk where with RAWM: mean resistance increase in regular waves based on Maruo's theory (Maruo, ω V 1960), which is mainly induced by ship τ = E S (G-16) motion. g RAWR: mean resistance increase due to wave ω 2 reflection for correcting RAWM. k = (G-17) RAWR should be calculated with high g accuracy because the mean resistance increase in short waves is predominant g k = (G-18) one. 0 2 VS This theoretical method is valid for all ship ωω= + α types with the following restrictions: ESkV cos (G-19) ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 57 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

k (1− 2τ + 1− 4τ ) αT effect of draught and encounter fre- m = 0 (G-20) 1 2 quency, ζA wave amplitude.

k0 (1− 2τ − 1− 4τ ) m2 = (G-21) with 2 22 π I1 () kTe deep k (1+ 2τ + 1+ 4τ ) αT = (G-26) m = − 0 (G-22) π 22I()() kT+ K2 kT 3 2 11e deep e deep

= +Ω α 2 k (1+ 2τ − 1+ 4τ ) kke (1 cos ) (G-27) m = − 0 (G-23) 4 2 ωV Ω= S imx (G-28) H1 (m) = ∫ σ(x)e dx (G-24) g L 2 αβ++ β where ∫sin( ww) sin dl 1  = I g gravitational acceleration, Bf  (G-29) B +−sin2 (αβ) sin βdl H1(m) function to be determined by the distri- ∫ ww II bution of singularities which represents periodical disturbance by the ship, where VS ship’s speed through the water, α encounter angle of incident waves (0 I1 modified Bessel function of the first deg. means head waves), kind of order 1, ρS density of fluid, K1 modified Bessel function of the second ω circular wave frequency, kind of order 1, ωE circular wave frequency of encounter. k wave number, Tdeep draught; for a trim condition Tdeep is the The expression of RAWR is given by Tsu- deepest draught, jimoto et al. (2013). The calculation method βw slope of the line element dl along the introduces an experimental coefficient in short water line and domains of the integra- waves into the calculation in terms of accuracy tion (I&II ) are shown in Figure G-3. and takes into account the effect of the bow shape above the water.

1 2 aft fore II RAWR= ρζ S g A BB f αTU(1+ C Fr ) (G-25) X 2 G α βw I waves where Y B ship breadth, Bf bluntness coefficient, Figure G-3 Coordinate system for wave reflection. CU coefficient of advance speed, Fr Froude number, The coefficient of the advance speed in oblique waves CU(α) is calculated on the basis ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 58 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

of the empirical relation line shown in Figure of advance speed CU is determined by the least G-42, which has been obtained by tank tests of square method through the origin against Fr; various ship types following to the procedures see Figure G-6. in the next paragraph. When CU(α=0) is ob- 70 tained by tank tests the relation used in oblique CU waves is shifted parallel to the empirical rela- 60 tion line. This is illustrated in Figure G-5 for 50 both fine and blunt ships. 40 30

head waves bow waves 20 |CU | quartering waves empirical line 80 10 70 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 60 Bf 50 Exp. in heading waves empirical relation relation used in oblique waves 40

30 70 CU 20 60 10 50 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 40 |B | 30 f 20

Figure G-4 Relation between the coefficient of advance 10 speed on added resistance due to wave reflection and the bluntness coefficient for conventional hull form 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Bf above water. Exp. in heading waves empirical relation relation used in oblique waves The aforementioned coefficient CU(α=0) is determined by tank tests which should be car- Figure G-5 Shift of the empirical relation in oblique ried out in short waves since RAWR is mainly waves (upper; for fine ship Bf < 58 / 310 , lower; for effected by short waves. The length of short blunt ship Bf ≥ 58 / 310 ). waves should be 0.5LPP or less. The coefficient

2The empirical relation line in Figure G-4 was obtained as follows. CU is derived from the result of tank tests and RAWM, In calculating RAWM the strength of the singularity σ is as formula (G-30). calculated by the formulation of slender body theory as for- mula (D-30) and the singularity is concentrated at depth of EXP CVPTM. 1Rwave () Fr− RAWM () Fr CU = −1 (G-30) 1  ∂  1 2 σω=−− Fr ρζg BB α iE VSr{ Z()() xBx} (G-31) 2 s A fT 4π  ∂x  with with EXP B(x): sectional breadth, Rwave : mean resistance increase in regular waves meas- CVP: vertical prismatic coefficient, ured in the tank tests. t : time, TM: draught at midship, x: longitudinal coordinate, Zr: vertical displacement relative to waves in steady motion. ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 59 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

αU=CUFr (ii) BB(α = 0) ≥ and BB(α = 0) ≥ f fc f fs

FBSf=68 − 310 (α ) (G-36)

FCCU=(α = 0) (G-37)

Fr 58 68 − C (α = 0) where B = and B = U . fc 310 fs 310 ship’s speed in the sea trial conditions in this range G.4. Seakeeping model tests Figure G-6 Relation between effect of advance speed Transfer functions of the resistance in- (αU=CUFr) and Froude number Fr. crease in waves (Rwave) may be derived from the tank tests in regular waves. The tank tests The tank tests should be conducted for at have to be conducted for the specific vessel ge- least three different Froude Numbers Fr. The ometry at the trial draughts and trim, and at Fr should be selected such that the speeds dur- contractual draughts if required. A minimum ing the sea trials lie between the lowest and the of two different ship’s speeds VS covering the highest selected Fr. speed range tested in the speed/power trials have to be tank tested. When tank tests are not carried out, the coefficient of advance speed in head waves CU(α As trials are not always conducted in head =0) is calculated by the following empirical re- seas and following seas, the tank tests should lations, formulae (G-31), shown in Figure G-4. not only comprise head and following waves The formulae are suitable for all ships. but also the relevant oblique wave conditions.

+ A maximum interval of incident wave angle C (α) = sgn(B (α))⋅ C (| B (α) |) U f U f (G-32) shall be 30° for head to beam seas (0°-90°) but may be larger for beam to following seas (90°- with 180°).

+ CU( B f (α ))= Max[ FFCS , ] (G-33) These tests shall be performed for a combination of circular frequency of regular waves (ω), angle between ship heading and incident (i) BBf (α = 0) < fc or BBf (α = 0) < fs regular waves (α) and ship’s speed through the water (VS) based on the following: A minimum FC==−(α 0) 310 B ( αα ) −= B ( 0) SU { f f } of 5 wave lengths in the range of 0.3LPP or less (G-34) to 2.0LPP. The test set-up and procedure shall follow ITTC 7.5-02 07-02.2.

FCCU=Min[ (α = 0),10] (G-35) ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 60 of 76 Effective Date Revision Preparation, Conduct and Analysis of Speed/Power Trials 2017 05

speed through the water and its power corrected in accordance with clause 10.2.3 and is : EFFECT OF CURRENT defined as follows:

Considering the nature of currents, the cur- Stage 1: first approximation of ship’s speed rent speed shall be estimated from the meas- through the water ured ship’s speed at each run. q P(VS ) = a + bVS P = a + bV (H-2) There are two methods to account for the p effect of current: S Therefore: • The ‘Iterative’ method, where the current P(V ) − a - speed is assumed as a semi durational phe- V = q S V = (H-3) S b p nomenon. P a S • � b The ‘Mean of means’ method, where the where: current speed is assumed to vary parabolically within a given power setting. P(VS) is the regression curve, VS is the ship’s speed through the water in knots. H.1. ‘Iterative’ method and unknown factors a, b and q. In the ‘Iterative’ method, the current speed is assumed to vary with, inter alia, the semidi- The initial value of VS shall be taken as the urnal period. A current curve is determined as mean of the measured ship’s speeds V’G of a a function of time as follows: double run. As a first approximation of the regression curve representing the relationship 22ππ between ship’s speed and power, a mean curve = + ++ VVC C,C cos tVC,S sin tVtVC,T C,0 is derived by determining the unknown factors, TTCC a, b and q of formula (H-2) by fitting the for- (H-1) mula (H-2) to combinations of the initial value of VS and averaged corrected power P’id by the where: ‘least squares’ method. VC is the current speed in knots, TC is the period of variation of current The ship’s speed on the mean curve at the speed, corrected power for each run is calculated as t is the time for each run. the updated ship’s speed through the water VS VC,C, VC,S, VC,T,VC,0 unknown factors from the formula (H-3) applying the coefficients obtained as described above. The most dominant period is the lunar sem- idiurnal period of 0,517 53 day (12 hours, 25 Stage 2: calculation of current velocity minutes and 12 seconds). Current speed at the time for each run V’C

The ship’s speed through the water VS is de- is calculated by subtracting the updated ship’s rived from a regression curve (H-2) which rep- speed through the water VS from the measured resents the relationship between the ship’s ship’s speed over the ground VG. ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 61 of 76 Effective Date Revision Preparation, Conduct and Analysis of Speed/Power Trials 2017 05

VC′ =VG −VS (H-4) This method assumes that the current speed varies parabolically over the time, and the fol- A current speed curve is obtained by deter- lowing formula is used to account for the cur- mining the unknown factors VC,C, VC,S, VC,T and rent effect: VC,0 of formula (H-1) by fitting the formula (H- V + 3V + 3V +V 1) to the combinations of time and current V = G1 G2 G3 G4 (H-6) speed obtained from formula (H-4) by the S 8 ‘least squares’ method. where: The current speed on the current curve at VS is the ship’s speed through the water in the time for each run VC is calculated as the up- knots, dated current speed from the formula (H-1) VG1 is the measured ship’s speed over the and applying the coefficients obtained as de- ground on the first of four runs in knots, scribed above. VG2 is the measured ship’s speed over the ground on the second of four runs in Stage 3: calculation of ship’s speed through knots, the water VG3 is the measured ship’s speed over the ground on the third of four runs in knots, The ship’s speed, corrected for current V’S, is calculated by subtracting the updated current VG4 is the measured ship’s speed over the ground on the fourth of four runs in speed VC from the measured ship’s speed over knots. the ground VG. Assuming that the current speed varies par- V ′ =V −V (H-5) S G C abolically, a current curve is defined as a quadratic function of time. The updated regression curve representing the relationship between ship’s speed and = 2 − + power is obtained by determining new factors VC VC,2t VC,1t VC,0 (H-7) of formula (H-2) by fitting the formula (H-2) to the combination of ship’s speed obtained where: from formula (H-5) and corrected power by the ‘least squares’ method again. VC,0, VC,1 and VC,2 are unknown factors.

The ship’s speed through the water at the If two double runs, i.e. four runs, are conducted, the following relationship is derived corrected power for each run VS is recalculated as the updated one from the formula (H-3), and for each run from formula (F.7). the processes of Stage 2 and Stage 3 are then 2 2 VVVttVttV= +( +∆ 3) − ( +∆ 3) + (H8) ′ − G1 S{ C,2 C,1 C,0} repeated until ∑(P(VS )i Pidi ) is minimized.

2 VG2 = VS − {VC,2 (t + ∆t) −VC,1(t + ∆t) +VC,0 } (H-9) H.2. ‘Mean of means’ method 2 VVVttVttVG3= S +{ C,2 () −∆ −C,1 () −∆ + C,0} If the ‘Mean of means’ method is used, two (H-10) double runs shall be performed at each power setting. ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 62 of 76 Effective Date Revision Preparation, Conduct and Analysis of Speed/Power Trials 2017 05

2 t is the start time of the first speed run of VVVttVttVG4= S −{ C,2 ( −∆ 3) −C,1 ( −∆ 3) +C,0} a power setting, (H-11) Δt is half of the elapsed time between two successive runs. where:

VS is the ship’s speed through the water in The current speed is accounted for by sub- knots, stituting the above four formulae from (H-8) to VG1: is the measured ship’s speed over the (H-11) for the formula (H-6). The ship’s speed ground on the first of four runs in knots, through the water is the ‘Mean of means’ of the VG2 is the measured ship’s speed over the two double runs. ground on the second of four runs in knots, The propeller shaft speed and power shall VG3 is the measured ship’s speed over the be averaged over the two runs of each double ground on the third of four runs in knots, run and then over the other double runs for the VG4 is the measured ship’s speed over the same power setting. ground on the fourth of four runs in knots,

, ,

Converged?

DPM

Refer to Section 11.

Figure H-1 Flow chart of the ‘Iterative’ method ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 63 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

defined in formula (I-1). The adjusted power at the stipulated condition (PFull,S) shall be calcu- : CONVERSION FROM TRIAL lated by formula (I-2). SPEED/POWER TEST RESULTS TO OTHER STIPULATED LOAD CON- PTrial,Pi DITIONS αPi = (I-1) PTrial,Si For dry cargo vessels it is difficult or unfea- sible to conduct speed trials at full load condi- PFull,Pi P = tion. For such cases speed trials at ballast condi- Full,Si α Pi (I-2) tion are performed and the result of the speed trials is converted to that of full load/stipulated where condition using model tank test results. PTrial,P predicted power at trial condition by tank The power curve at full load/stipulated con- tests, dition is obtained from the results of the speed PTrial,S power at trial condition obtained by the trials at trial condition using the power curves speed trials, predicted by model tank tests. The tank tests PFull,P predicted power at stipulated condition should be carried out at both draughts: trial con- by tank tests, dition and another stipulated condition. PFull,S power at stipulated condition, αP power ratio. Using the speed/power curve obtained by the i index of each power setting. speed trials at trial condition as described in chapter 10 and 11, the conversion on ship’s Figure I-1 shows an example of the conver- speed from trial condition to the other stipulated sion to derive the resulting ship’s speed at full condition to be carried out by the power ratio αP load condition (VFull,S) at 75%MCR.

Figure I-1 Example of conversion from trial condition to other stipulated load condition at 75% MCR

ITTC – Recommended 7.5-04 -01-01.1 Procedures and Guidelines Page 64 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

J.1. Propulsive efficiency correction

: EXTENDED ANALYSIS OF The ship’s propulsive efficiency is affected DIRECT POWER METHOD (INFOR- by the added resistance. This has to be taken into MATIVE) account when correcting the power.

The delivered power corrected to ideal con- The propulsive efficiency coefficient, ηD, is dition, PDid, is derived by calculated as follows:

PPDid= Dms − ∆ P (J-1) 1− t ηD= ηη OR (J-3) 1− wS with

PDms delivered power derived from shaft where:

power or brake power measured on ηO propeller open water efficiency, which is board for each single run [W], derived from propeller open water char- ΔP correction of delivered power due to the acteristics of the actual propeller, con- increased resistance and the changed sidering the propeller load, propulsive efficiency [W]. ηR relative rotative efficiency, t thrust deduction factor, The correction of delivered power, ΔP, can wS full-scale wake fraction. be written as: The self-propulsion factors relative rotative   ∆ηRVS Dms efficiency, ηR, thrust deduction factor, t, and ∆PP=+−Dms 1  (J-2) ηηDid  Did  model wake fraction, wM, are obtained from model self-propulsion tests. Between full-scale with wake fraction, wS, and model wake fraction, wM, it is generally assumed that there is the follow- ΔR Resistance increase [N], which is de- ing relationship: rived from the data measured during sea trial, 11−=−wSM( we) i (J-4) VS ship’s speed through the water [m/s], which can be obtained by the ‘Iterative’ with: method or the ‘Mean of means’ method, ηDid propulsive efficiency coefficient, ηD , in ei: scale correlation factor of the wake frac- ideal condition, tion. ηDms propulsive efficiency coefficient, ηD, during sea trial. Calculation of ηDms

The propulsive efficiency coefficients, ηDid The propulsive efficiency coefficient in the and ηDms obtained as outlined in the following trial condition, ηDms, is obtained as follows, by sections. rewriting the formula (J-3):

1− tms ηDms= ηη Oms Rms (J-5) 1− wSms

where:

ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 65 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

ηOms propeller open water efficiency in the Rid resistance in the ideal condition [N], trial condition, which also can be derived from the ηRms relative rotative efficiency in the trial measured data during sea trial. condition, tms thrust deduction factor in the trial condi- The self-propulsion factors in the ideal con- tion, dition, ηRid, tid and wMid, are obtained from stand- wSms full-scale wake fraction in the trial con- ard self-propulsion test and interpolated to the dition. speed, VS.

Each self-propulsion factor in the trial con- The deviations of the self-propulsion factors dition, ηRms, tms and wMms, is obtained by adding ΔηR, Δt and ΔwM are considered as the functions the deviation of each factor between the trial and of ΔR/Rid. The details of the functions are de- the ideal condition, ΔηR, Δt and ΔwM, to each scribed in Appendix J.2. factor for the ideal condition, ηRid, tid and wMid, respectively, as follows: It is acceptable that ΔηR, Δt and ΔwM are set to zero, because these values are negligibly η= η + ∆η( ∆RR/ ) (J-6) small in comparison with the deviation of ηO due Rms Rid R id to the load variation effect. = + ∆∆ tms t id t( RR/ id ) (J-7) Propeller efficiency ηO and full-scale wake fraction wS are determined using propeller open wMms= w Mid + ∆∆ w M ( RR/ id ) (J-8) water characteristics for the ship's fitted propeller, i.e. curves of thrust coefficient, torque coef- where: ficient and load factor, according to the following procedure. ηRms relative rotative efficiency in the trial condition, Thrust coefficient, torque coefficient and tms thrust deduction factor in the trial condi- load factor can be written as follows: tion, wMms model wake fraction in the trial condi- 2 KTT= aJ ++ bJ T c T (J-9) tion, ηRid relative rotative efficiency in the ideal 2 K= aJ ++ bJ c (J-10) condition, QQ Q Q tid thrust deduction factor in the ideal con- 2 dition, τ P =++aTT bJc// T J (J-11) wMid model wake fraction in the ideal condition, where: ΔηR(ΔR/Rid) deviation of relative rotative effi- KT thrust coefficient, ciency corresponding to ΔR/Rid, KQ torque coefficient, Δt(ΔR/Rid) deviation of thrust deduction fac- 2 τP load factor equal to KT/J , tor corresponding to ΔR/Rid, J propeller advance coefficient, ΔwM(ΔR/Rid) deviation of wake fraction corre- aT, bT, cT factors for the thrust coefficient sponding to ΔR/Rid, curve, ΔR resistance increase [N], which is derived aQ, bQ, cQ factors for the torque coefficient from the data measured during sea trial, curve. ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 66 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

These factors, aT, bT, cT and aQ, bQ, cQ are JK η = msT ms (J-15) obtained by fitting the formula (J-9) and (J-10) Oms 2π KQms to the propeller open characteristics data for the ship’s fitted propeller with the least square where: method. Jms propeller advance coefficient in the trial The torque coefficient in the trial condition, condition, KQms, is calculated by the following formula: KTms thrust coefficient in the trial condition, KQms torque coefficient in the trial condition. P K =Dms ×η (J-12) Qms 35 Rms The speed of flow into propeller, VA, is: 2πρSnD ms = (J-16) where: VA JnD ms ms PDms delivered power in the trial condition where: [W], 3 Jms propeller advance coefficient in the trial ρS water density [kg/m ], condition, nms measured propeller shaft speed [rev./s], D propeller diameter [m], nms measured propeller shaft speed [rev./s], D propeller diameter [m]. ηRms relative rotative efficiency in the trial condition. And the full-scale wake fraction in trial condition, wSms, is: The propeller advance coefficient, Jms, is determined with the following formula derived from the formula (J-10): VA 1−=wSms (J-17) VS 2 −−bQ b Q −4 ac QQ( − K Qms ) J ms = (J-13) where: 2aQ VA speed of flow into propeller [m/s], VS ship's speed through the water [m/s]. where:

KQms torque coefficient in the trial condition. In addition, the total resistance in the trial condition, Rms, is also estimated using the load The thrust coefficient in the trial condition, factor in the trial condition, τPms. KTms, is obtained as follows, by rewriting the formula (J-9): The load factor in the trial conditon, τPms, is:

=++2 K KTTms aJbJc ms T ms T (J-14) τ = Tms Pms 2 (J-18) J ms where: where: Jms propeller advance coefficient in the trial condition, Jms propeller advance coefficient in the trial condition, Therefore, the propeller efficiency in the KTms thrust coefficient in the trial condition. trial condition, ηOms, is: ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 67 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

Then, the total resistance in the trial condi- ηRid relative rotative efficiency in the ideal tion, Rms, is: condition, tid thrust deduction factor in the ideal con- 2 22 dition, Rms=−−τρ Pms(11 t ms)( w Sms) S VD S (J-19) wSid full-scale wake fraction in the ideal con- where: dition.

τPms load factor in the trial condition, The self-propulsion factor in the ideal condi- tms thrust deduction factor in the trial condition, ηRid, tid and wMid, is obtained from standard tion, self-propulsion test and interpolated to the speed, wSms full-scale wake fraction in the trial con- VS. dition, ρS water density in kilograms per cubic me- The full-scale wake fraction in the ideal con- tre, dition, wSid, is calculated by the following for- VS ship's speed through the water in metres mula obtained by rewriting the formula (J-4): per second,

D propeller diameter in metres. 11−=−wSid ( weMid ) i (J-20)

The total resistance in the ideal condition, Rid, The scale correlation factor of wake fraction, is obtained by subtracting the resistance increase, ei, included in the above formula is obtained us- ΔR, from the total resistance in the trial condi- ing the full-scale and model wake fractions in tion, Rms: the trial conditions:

RRid= ms − ∆ R (J-22) 1− w e = Sms (J-21) i 1− w where: Mms ΔR resistance increase [N], which is derived where: from the data measured during sea trial. wMid model wake fraction in the ideal condition, The total resistance in the ideal condition, Rid, is also used when the self-propulsion factor in wSms full-scale wake fraction in the trial con- the trial condition are calculated with the formu- dition derived from the formula (J-17), lae (J-6) to (J-8). wMms model wake fraction in the trial condition derived from the formula (J-8).

Calculation of ηDid The load factor in the ideal condition, τPid, is The propulsive efficiency coefficient in the calculated by the following formula: ideal condition, ηDid, is obtained as follows, by R rewriting the formula (J-3): τ = id (J-23) Pid 2 22 (11−−tid)( w Sid) ρ S VD S 1− tid ηDid= ηη Oid Rid (J-5) 1− wSid where:

Rid resistance in the ideal condition [N], where tid thrust deduction factor in the ideal con- ηOid propeller open water efficiency in the dition, ideal condition, ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 68 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

wSid full-scale wake fraction in the ideal con- where: dition, 3 VS ship's speed through the water [m/s], ρS water density [kg/m ], wSid full-scale wake fraction in the ideal con- VS ship's speed through the water [m/s], dition, D propeller diameter [m]. Jid propeller advance coefficient in the ideal condition, The propeller advance coefficient, Jid, is de- D propeller diameter [m]. termined as follows: Applying the analysis process in Figure J.1, −−2 − −τ bbTT4( a TPid ) c T the value of VS, and thus the values of ηRid, tid Jid = (J-24) Mid 2(aT −τ Pid ) and w are known after the analysis of the current velocity. where: Additionally, the value of ΔR/Rid, and thus τPid load factor in the ideal condition, the values of ΔηR, Δt and ΔwM are known after the extended analysis. Therefore, this analysis Once Jid can be obtained, the thrust coeffi- shall be repeated after the value of VS is obtained cient in the ideal condition, KTid, and the torque by the current analysis. coefficient in ideal condition, KQid, are also obtained as follows, by rewriting the formula (J-9) For the evaluation described above, the and (J-10): mean value of VG for double run or 'Mean of means' value of VG for two double runs shall be 2 KTTid=++ aJbJc id T id T (J-25) used as the initial value, and the values of ΔηR, Δt and ΔwM are set to zero. 2 KQQid=++ aJbJc id Q id Q (J-26)

Therefore, the propeller efficiency in the ideal condition, ηOid, is:

JKidT id ηOid = (J-27) 2π KQid where:

Jid propeller advance coefficient in the ideal condition, KTid thrust coefficient in the ideal condition, KQid torque coefficient in the ideal condition.

The correction for the propeller shaft speed

Finally, the corrected propeller shaft speed, nid, is derived as follows:

VwS(1− Sid ) nid = (J-28) JDid ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 69 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

VG, PDms, nms and ΔR

VS For trial condition

ηRid(VS) = ( ) + DPM VS is set as a mean value of measured VG in each Double Run = ( ) + tid(VS) Rms Rid S R Initial values of ΔηR, Δt, ΔwM are set as zero 𝜂𝜂 = 𝜂𝜂 (𝑉𝑉 ) +∆𝜂𝜂 ms id S wMid(VS) 𝑡𝑡 𝑡𝑡 𝑉𝑉 ∆𝑡𝑡 Current correction 𝑤𝑤Mms 𝑤𝑤Mid 𝑉𝑉S ∆𝑤𝑤M = × DPM VS, ΔηR, Δt, ΔwM are obtained from the result of the above process 2 𝑃𝑃Dms 𝑄𝑄ms 3 5 Rms 𝐾𝐾 S ms 𝜂𝜂 𝜋𝜋𝜌𝜌 𝑛𝑛 𝐷𝐷 Current correction Final “VS” is determined 4 = 2 −𝑏𝑏𝑄𝑄 − �𝑏𝑏𝑄𝑄 −2 𝑎𝑎𝑄𝑄�𝑐𝑐𝑄𝑄 − 𝐾𝐾𝑄𝑄ms� 𝐽𝐽ms = 𝑎𝑎𝑄𝑄 = + + 𝑉𝑉A 𝐽𝐽ms𝑛𝑛ms𝐷𝐷 2 𝐾𝐾𝑇𝑇ms 𝑎𝑎𝑇𝑇𝐽𝐽ms 𝑏𝑏𝑇𝑇𝐽𝐽ms 𝑐𝑐𝑇𝑇 = = 1 = 2 𝐾𝐾𝑇𝑇ms 𝐽𝐽ms 𝐾𝐾𝑇𝑇ms 𝑉𝑉A 𝜏𝜏Pms 2 𝜂𝜂Oms − 𝑤𝑤Sms 𝐽𝐽𝑚𝑚𝑚𝑚 𝜋𝜋 𝐾𝐾𝑄𝑄ms 𝑉𝑉S ms = (1 )(1 ) 2 2 2 𝑅𝑅 𝜏𝜏Pms − 𝑡𝑡ms − 𝑤𝑤Sms 𝜌𝜌S𝑉𝑉S 𝐷𝐷 =

𝑅𝑅id 𝑅𝑅ms − ∆𝑅𝑅 R id ( ) Δη (ΔR/R ) = + 1 = + ( ) = Δt(ΔR/Rid) Rms Rid R id 1 𝜂𝜂 𝜂𝜂 ∆𝜂𝜂 ∆(𝑅𝑅⁄𝑅𝑅 ) ms = + Dms Oms Rms − 𝑡𝑡 ΔwM(ΔR/Rid) 𝑡𝑡ms 𝑡𝑡id ∆𝑡𝑡 ∆𝑅𝑅⁄𝑅𝑅id 𝜂𝜂 𝜂𝜂 𝜂𝜂 − 𝑤𝑤Sms 𝑤𝑤Mms 𝑤𝑤Mid ∆𝑤𝑤M ∆𝑅𝑅⁄𝑅𝑅id 1 = For ideal condition = (1 )(1 ) 1 𝑅𝑅id − 𝑤𝑤Sms Pid 2 𝑖𝑖 𝜏𝜏 2 2 𝑒𝑒 Mms − 𝑡𝑡id − 𝑤𝑤Sid 𝜌𝜌S𝑉𝑉S 𝐷𝐷 − 𝑤𝑤 4( ) = 2(2 ) 1 = (1 ) 𝑇𝑇 𝑇𝑇 𝑇𝑇 Pid 𝑇𝑇 𝑖𝑖𝑖𝑖 −𝑏𝑏 − �𝑏𝑏 − 𝑎𝑎 − 𝜏𝜏 𝑐𝑐 𝐽𝐽 Sid Mid 𝑖𝑖 𝑎𝑎𝑇𝑇 − 𝜏𝜏Pid − 𝑤𝑤 − 𝑤𝑤 𝑒𝑒 = + + = 2 2 id 𝑇𝑇id 𝑇𝑇id 𝑇𝑇 id 𝑇𝑇 id 𝑇𝑇 Oid 𝐽𝐽 𝐾𝐾 𝐾𝐾 𝑎𝑎 𝐽𝐽 𝑏𝑏 𝐽𝐽 𝑐𝑐 𝜂𝜂 𝑄𝑄id = + + 𝜋𝜋 𝐾𝐾 2 𝑄𝑄id 𝑄𝑄 id 𝑄𝑄 id 𝑄𝑄 1 𝐾𝐾 𝑎𝑎 𝐽𝐽 𝑏𝑏 𝐽𝐽 𝑐𝑐 = 1 − 𝑡𝑡id 𝜂𝜂Did 𝜂𝜂Oid𝜂𝜂Rid − 𝑤𝑤Sid = + 1 ∆𝑅𝑅𝑉𝑉𝑆𝑆 𝜂𝜂Dms ∆𝑃𝑃 𝑃𝑃Dms � − � 𝜂𝜂Did 𝜂𝜂Did Propeller shaft speed (1 ) Corrected delivered power = = S Sid id 𝑉𝑉 − 𝑤𝑤 𝑛𝑛 Did Dms 𝐽𝐽id𝐷𝐷 𝑃𝑃 𝑃𝑃 − ∆𝑃𝑃 ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 70 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

2 J.2. Application of load variation test results  ∆∆RR ∆ηRR= ξ  + ζ R (J-25) In order to determine each component of  RRid  id propulsive efficiency coefficient ηD, propeller 2 open water tests, resistance and self-propulsion  ∆∆RR tests are carried out at trial draught and evalu- ∆ξt =tt  + ζ (J-26) RR ated according to the tank's normal procedures.  id  id In addition, a self-propulsion test with load var- 2 iation effect may be carried out at the trial  ∆∆RR ∆ξw = + ζ (J-27) draught and, as a minimum, one speed close to ww   RRid  id the predicted EEDI speed (75% MCR). This speed shall be one of the speeds tested in the where: normal self-propulsion test. ΔηR deviation of the relative rotative effi- The self-propulsion test with load variation ciency, effect includes at least 4 self-propulsion test Δt deviation of the thrust deduction factor, runs, each one at a different propeller shaft ΔwM deviation of the wake fraction, speed while keeping the model's speed constant. ΔR resistance increase in newtons, The propeller shaft speed is to be selected such Rid resistance in the ideal condition in new- that: tons,

∆R and ξR, ξt, ξw, ζR, ζt and ζw are unknown factors ≈−[ 0.1, 0,0.1,0.2] (J-29) R and determined by fitting the formulae (J.25), 0 (J.26) or (J.27) to the results of the load variation where: tests with the 'least squares' method.

3 ρS ∆λRFF=( DM − ) (J-30) ρM where: ΔR resistance increase [N], Rid full scale resistance at the actual speed from resistance test [N], FX external tow force measured during load variation test [N], FD skin friction correction force same as in the normal self-propulsion tests [N], λ scale factor, 3 ρS water density in full scale [kg/m ], 3 ρM water density in the model test [kg/m ].

Each self-propulsion factor obtained from the procedure mentioned above shall be expressed as a function of ΔR/Rid as follows: ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 71 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

: RAVEN SHALLOW-WATER K.1. Calculation of viscous resistance CORRECTION A) The flat plate friction coefficient is found The computation of the power correction for from the ITTC 57 line: trials conducted in shallow-water consists of two parts: 0.075 CF = 2 (logRe − 2) 1. The first is a correction for the increase 10 (K-1) of the viscous resistance in shallow wa- VL e = S PP ter. This requires to estimate the magni- ν tude of the viscous resistance in deep water at equal speed. Its increase in shal- where low water is found from the formula Re Reynolds number given in Raven 2016. ν kinematic viscosity for sea water at the 2. The second is a correction for the re- temperature measured [m2/s]. sistance increase caused by the additional dynamic sinkage in shallow water. B) The form factor 1+k is found from the ex- This correction is based on a constant pression by Gross&Watanabe: Admiralty coefficient. += + 2 1/2 The input required to the computation are: 1k 1.017 20 CB( BL / PP) ( T M / B) (K-2)

LPP length between perpendiculars [m] B breadth [m] c) The roughness resistance is found from the Townsin’s formula: TM draught at midship [m] CB block coefficient [-] 2 1 AW water plane area [m ] 1  k 3 − S wetted surface hull (at the zero speed tri- ∆C =0.044s −+ 10Re 3 0.000125 F   2  LWL  als condition) [m ]  h water depth [m] (K-3) ηDid propulsion efficiency coefficient in ideal condition, from model test [-] with a minimum of 0.0. VS ship’s speed through water as derived

from the previous steps in the trial eval- LWL can in this case be approximated as LPP. uation process [m/s] PDshallow trial power corrected and aver- Here is the ‘Average Hull Roughness’ or aged through the previous steps in the Mean Apparent Amplitude. The value to be used s trial evaluation process but not corrected for delivery𝑘𝑘 trials and EEDI trials is 0.00015 m. for shallow water [W]

The power correction is computed according d) The viscous resistance coefficient thus be- to the following steps: comes:

CVF=1.06 C( 1 ++ kC) ∆ F (K-4)

The viscous resistance in deep water is: ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 72 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

1 K.4. Estimate resulting additional displace- R= C ρ VS2 (K-5) Vdeep V2 S S ment with The additional displacement due to sinkage is computed as: density of the sea water, for actual tem-

s perature & salt content [kg/m³] 𝜌𝜌 δ∇ = d( sinkage) AW /∇ It is noted that the viscous resistance coeffi- with the restriction (K-8) cient is multiplied by a factor 1.06, to incorpo- δ∇ ≤ 0.05 rate the relevant part of the correlation allowance. I.e. the displacement increase due to additional sinkage is limited to 5% of the displacement. For larger sinkages the correction is based K.2. Shallow-water correction of viscous re- on the maximum displacement increase of 5% sistance of displacement. The viscous resistance is corrected according to K.5. Estimate resistance increase caused by additional sinkage in shallow water 1.79 T ΔRR= 0.57 M (K-6) V Vdeep ( h ) Assuming constant Admiralty coefficient, the resistance increase caused by additional sinkage is estimated as: K.3. Estimate additional sinkage 2/3 Rsink =(1 + δ∇ ) (K-9) The increase of the dynamic sinkage due to shallow water is found from the formula given in Raven 2016: K.6. Correct measured power d( sinkage) = The power corrected for sinkage effect and for shallow-water effect on viscous resistance is: ∇ Fr22 Fr (K-7) = 1.46 h − hd L 2 22 PΔ RV PP 11−−Frh Frhd Dshallow V S PDdeep = − (K-10) rsink ηDid with a minimum of 0.0 and with

V K.7. Check validity of calculated viscous re- Fr = S hd sistance 0.3gLPP Finally, we confirm that the calculated deep- VS water viscous resistance from step K.1, is less Frh = gh than the total resistance deduced from the deep- water power as found in step K.6: and P η R ≤ Ddeep Did (K-11) ∇=L BT C Vdeep PP M B VS ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 73 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

If this constraint is not satisfied, is reduced to this upper limit, and the procedure is Vdeep redone starting with step K.2. 𝑅𝑅

K.8. Limits of applicability:

Water depth and ship’s speed as stipulated in section 6.4.

ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 74 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

NOMENCLATURE Fr Froude number [-] Frh Depth Froude number [-] AE/AO blade area ratio [-] 2 Frhd Depth Froude number deep water [-] AX transverse area above water [m ] G angular distribution function [-] AM: midship section area under water [m²] g gravitational acceleration [m/s²] AR rudder area 2 h waterdepth [m] AT submerged area transom [m ] 2 hANEMO height anemometer above water [m] AW water plane area [m ] hR rudder height[m] AXV area of maximum transverse section exposed to the wind [m²] HS1/3 sum of significant wave height of swell B ship breadth [m] and wind waves[m] HS1/3 significant wave height of swell [m] Bf bluntness coefficient [-] HW1/3 significant wave height of wind waves bR: rudder span[m] C coefficient for starboard and port rudder [m] [-] I1 modified Bessel function of the first kind of order 1[-] CDAjj measured wind resistance coefficient at wind tunnel [-] J propeller advance ratio [-] KQ propeller torque coefficient [-] estimated wind resistance coefficient [-] KT propeller thrust coefficient [-] CDA(ψWR) wind resistance coefficient 𝐶𝐶̂𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 K1 modified Bessel function of the second CB block coefficient kind of order 1[-] CF frictional resistance coefficient for ac- k circular wave number [rad/s] tual water temperature and salt content k form factor [-] kS hull roughness CF0 frictional resistance coefficient for refer- kyy non dimensional longitudinal radius of ence water temperature and salt content gyration [% of LPP] [-] LCB longitudinal centre of buoyancy forward CM midship area coefficient [-] of midship [% of LPP] Cnmargin rpm margin in percent rpm at NCR [%] LBWL distance of the bow to 95% of maximum CPA prismatic coefficient of aft part (from breadth on the waterline [m] midship to A.P.)[-] LPP length between perpendiculars [m] CSEAMAR sea margin in percentage NCR LWL length at waterline [m] [%] MCR maximum continuous rating [kW] CT0 total resistance coefficient for reference NCR nominal continuous rating [kW] water temperature and salt content,[-] nMCR rpm at MCR [rpm] CU coefficient of advance speed [-] nNCR rpm at NCR [rpm] CV viscous resistance coefficient [-] NP number of propellers [-] CVP vertical prismatic coefficient [-] NS number of ships[-] CWA water plane area coefficient of aft part Nψ number of wind directions[-] (from midship to A.P.)[-] n: measured rate of revolution of propeller CWL prismatic waterline coefficient [-] at each run CX Wind resistance coefficient nC corrected rpm (RPMC) [rpm] D diameter of the actual full scale propeller th n(i) propeller frequency of revolutions at (i) [m] run [rpm] D depth, moulded, of a ship hull [m] n(i+1) propeller frequency of revolutions at d(sinkage) increase of the dynamic sinkage (i+1)th run [rpm] due to shallow water [m] P propeller pitch at 0.7 R[m] E: directional sea spectrum [m2s] ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 75 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

PB break horse power [kW] VS ship’s speed (VS) [knot] PD delivered power at propeller [kW] VSC. corrected ship’s speed (VSC) [knot] PDshallow trial power averaged and cor- VWR apparent wind speed, relative wind ve- rected for all effects but for shallow wa- locity [m/s] ter [W] VWRref relative wind velocity at the reference PDdeep trial power averaged and corrected for height [m/s] shallow water [W] ' VWR corrected relative wind velocity at the P/D pitch/diameter ratio at 0.7R[-] vertical position of the anemometer [m/s] PS ship shaft power [kW] VWT true wind velocity [m/s] PSC Corrected ship power (PSC) [kW] V ' averaged true wind velocity at the verti- RAA resistance increase due to relative winds WT [N] cal position of the anemometer [m/s] RAS resistance increase due to deviation of VWTref true wind velocity at the reference height water temperature and water density [N] [m/s] RAWL mean resistance increase in short crested w wake fraction [-] irregular waves [N] wm mean wake fraction RAWM mean resistance increase in regular Z number of propeller blades [-] (4) waves based on Maruo's theory [N], a vertical position of the anemometer in [m] RAWR mean resistance increase due to wave re- ref reference height for the wind resistance flection for correcting RAWM [N] 𝑍𝑍 coefficients in [m] Re Reynolds number [-] 𝑍𝑍α: wave direction relative to bow, angle be- RT total resistance in still water [N] tween ship heading [deg] and incident RT0 resistance for reference water tempera- regular waves; 0 means head waves. ture and salt content [N] αT: effect of draught and encounter fre- RVdeep viscous resistance in deep water quency [-] Rwave mean resistance increase in regular β drift angle [deg] waves [N] βw slope of the line element dl along the wa- Rsink resistance increase caused by additional ter line [deg] sinkage [N] βWR apparent wind direction relative to bow S wetted surface hull [m2] [deg] 3 Sη frequency spectrum for ocean waves displaced volume [m ] [m2s] Δ displacement [t] 2 SAPP wetted surface appendages [m ] ΔC𝛻𝛻 F roughness allowance associated with TA draught at aft perpendicular [m] Reynolds number for actual water tem- Tdeep for a trim condition, the deepest draught perature and salinity [-] [m] ΔR resistance increase [N] TF draught at forward perpendicular [m] ΔRV viscous resistance increase due to shal- TM draught at midships [m] low water [N] 3 t thrust deduction fraction [-] Δref reference displacement [m ] tAref reference air temperature [°C] ΔVS decrease of ship’s speed due to shallow tSref reference sea water temperature [°C] water [knot] VFM mean current velocity [m/s] Δτ load factor increase due to resistance in- th VG′(i+1): ship’s speed over the ground at (i+1) crease [-] run [m/s] δ rudder angle [deg] VG ship’s speed over ground [m/s] δn correction factor for RPM (DRPM) [-] VKN ship’s speed over ground [knot] ITTC – Recommended 7.5-04-01-01.1 Procedures and Guidelines Page 76 of 76 Preparation, Conduct and Analysis of Effective Date Revision Speed/Power Trials 2017 05

δPA power correction factor for wind (DPWIN) [kW] δPt power correction factor for temperature (DPTEM) [kW] δPρ power correction factor for density (DPDEN) [kW] δPΔ power correction factor for displacement (DPDIS) [kW] δVH speed correction factor for depth (DVDEP) [knot] δ∇ additional displacement due to sinkage [-] ζA wave amplitude [m] ηR relative rotative efficiency by use of the thrust identity [-] ηS mechanical efficiency in shafting(s) and gear box(es) [-] ηDid propulsion efficiency coefficient in ideal condition, from model test [-] ν kinematic viscosity for sea water at the temperature measured [m2/s] density of the sea water, for actual temperature & salt content [kg/m³] s 𝜌𝜌ρA mass density of air [kg/m³] ρWSref sea water density according to contract [kg/m3] 3 ρWS sea water density [kg/m ] ρ0 water density for reference water temperature and salt content[kg/m³] ψ heading of ship; compass course [deg] ψWR relative wind direction [deg] ' ψ WR corrected relative wind direction at the vertical position of the anemometer [deg]

ψ WRref relative wind direction at the reference height [deg] ψWT true wind direction the vertical position of the anemometer [deg] ' ψ WT averaged true wind direction the vertical position of the anemometer [deg] ξp ξn, ξv overload factor derived from load variation model test [-] ω circular frequency of incident regular waves [rad/s]