PREDICTION OF WIND LOADS ON LARGE LIQUEFIED GAS · PDF fileWIND LOADS ON LARGE LIQUEFIED GAS...

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Prepared by WAVEspec Limited October 2007 of 28

P R E D I C T I O N

O F

W I N D L O A D S

O N

L A R G E L I Q U E F I E D G A S

C A R R I E R S

Published by

Society of International Gas Tanker & Terminal Operators Ltd.

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Contents

Nomenclature.......................................................................................................3 Scope..................................................................................................................4 1. Introduction ...............................................................................................5 2. Wind Load Prediction Procedures ...................................................................5

2.1. Basis of Procedures ..................................................................................5 2.2. Equations for Computing Wind Loads ..........................................................6

3. Example Problem ........................................................................................8 3.1. Wind Load Calculations .............................................................................8 3.2. Summary of Wind Loads ...........................................................................9

Figure 1 Sign Convention and Coordinate System ......................................... 11 Figure 2 Longitudinal wind Force Coefficient ................................................. 12 Figure 3 Lateral wind Force Coefficient ........................................................ 13 Figure 4 Wind Yaw Moment Coefficient ........................................................ 14

Appendix A Alternative Method for Computing the Wind Loads................................ 15 A.1 General ................................................................................................ 15 A.2 Equations for Computing Wind Loads ........................................................ 15 A.3 Example Problem................................................................................... 15

Figure A-1 Longitudinal Wind Force Coefficient ............................................. 18 Figure A-2 Lateral Wind Force Coefficient..................................................... 19

Appendix B Discussion of Wind Load Computation Procedures ................................ 20 B.1 General ................................................................................................ 20 B.2 Original Wind Tunnel Tests of Gas Carrier Models ....................................... 20 B.3 Wind Tunnel Tests of Current Gas Carrier Models........................................ 20 B.4 Data Analysis ........................................................................................ 20

Table B-1 ..................................................................................................... 23 Figure B-1 .................................................................................................... 24

Appendix C Program Description for Wind Tunnel Tests ......................................... 25 Appendix D Table of Coefficient Figures ............................................................... 26 Appendix E Conversion Factors .......................................................................... 27 References......................................................................................................... 28

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Nomenclature

Symbol Units

AL Longitudinal (Broadside) Wind Area Square Metres

AT Transverse (Head-On) Wind Area Square Metres

B Beam Metres

CXw Longitudinal Wind Force Coefficient Non-Dimensional

CXYw Wind Yaw Moment Coefficient Non-Dimensional

CYw Lateral Wind Force Coefficient Non-Dimensional

CYAW Lateral Wind Force Coefficient Aft Non-Dimensional

CYFW Lateral Wind Force Coefficient Forward Non-Dimensional

FXw Longitudinal Wind Force Tonne

FYw Lateral Wind Force Tonne

FYAW Lateral Wind Force Aft Tonne

FYFW Lateral Wind Force Forward Tonne

h Height Above Water/Ground Surface Metres

LBP Length Between Perpendiculars Metres

LOA Length Overall Metres

MXYw Wind Yaw Moment Tonne-Metre

Vw Wind Velocity at 10 Metre Elevation Knots

vw Wind Velocity at Elevation h Knots

θw Wind Angle of Attack Degrees

ρw Density in Wind Medium1 4

2

MetresSecondramlogKi −

76001

Conversion Factor2 22

2

SecondKnotramlogKiMetresTonne

−−−

Notes: 1 Density as used in this report is the metric equivalent of slugs/foot³ which is the engineering definition of density used in the English Gravitational System. Values of density are given in Appendix E 2 Included in the Conversion Factor is a factor of (½) applicable to each wind force and moment equation presented in this report.

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SCOPE This report provides information required by terminal and shipping technical personnel to calculate wind forces on liquefied gas carriers. This report presents coefficients and procedures for computing wind loads on carriers in the 75,000 to 300,000m³ (cubic metre) class, with both prismatic and spherical tanks. Wind force moment coefficients are presented in non-dimensional form for a moored vessel and are applicable to draft conditions ranging from ballasted to fully loaded.

The procedures for computing the wind loads are identical to those previously presented for VLCCs (Very Large Crude Carriers) in reference [1]. While the analysis of mooring restraint has not been addressed, coefficients are provided for use with either computer orientated or hand calculation techniques for design of tanker/terminal mooring equipment. Factors which affect the distribution of environmental loads to mooring lines, thus influencing mooring requirements, are discussed in reference [2].

An example problem illustrating the use of the wind load prediction procedures for computer analysis of mooring restraint is contained in the body of the report. An alternative method of computing wind loads for hand calculation of mooring restraint is presented in Appendix A along with an example problem. Appendix B contains detailed discussions on the development and limitations of the wind coefficients. An outline of the wind tunnel test program is given in Appendix C.

If currents act simultaneously with wind on a vessel, the current loads on the vessel must be added to the wind loads when evaluating mooring requirements. The coefficients and procedures used to compute current loads on VLCCs are also generally applicable to the computation of current loads acting on liquefied gas carriers in the 75,000 to 300,000m³ class (Reference [1]). Thus, separate current coefficients were not developed for gas carriers.

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1. INTRODUCTION A knowledge of mooring requirements is important to ensure the safety of moored vessels under “design mooring conditions”. To determine mooring requirements, environmental load predictions based on wind and current coefficients are typically used in conjunction with a computer-orientated or hand analysis of the mooring system. Wind and current design coefficients and calculation procedures have been developed by the Oil Companies International Marine Forum (OCIMF) for VLCCs (Reference [1]). Interest was expressed within both OCIMF and Society of International Gas Tanker & Terminal Operators Ltd. (SIGTTO) for better defining the environmental loads which act on moored gas carriers in the 75,000 to 125,000m³ class and thus the previous edition of this document was born in 1985.

With the arrival of even larger gas carriers SIGTTO requested an update to cover 75,000 to 300,000 m³ class.

Available reports dealing with the prediction of wind loads on gas carriers exhibit widely scattered results. Various reasons for the differences can be cited; test bases are rarely similar, and the techniques and procedures used in obtaining the loads vary considerably. Added to this, the inherent differences in the facilities at which the test programs were conducted make attempts at generalising existing data for design purposes a very difficult task. Additionally, the existing wind coefficients for VLCCs were not considered applicable to gas carriers due to inherent differences in hull geometry between these gas carriers and VLCCs with “conventional bows”, it was felt that the current coefficients would be used with more confidence.

As a result of the above, technical experts within the sponsoring organisation recommended that appropriate wind force and moment coefficients be collated for recent gas carriers. Wind tunnel tests similar to those conducted for VLCCs had been carried out in the industry. The results of these tests were obtained for Wavespec Ltd and subsequent data analyses led to the development of the wind force and moment coefficients presented herein. The analysis was similar to that used to prepare the wind coefficients for VLCCs.

Some of these coefficients differ from those previously derived for specific gas carriers. The coefficients presented herein are generally as conservative as previously obtained data. The chosen level of conservatism is believed to be justified since the coefficients in this report were developed with the intention of safely applying them to the general range of gas carrier forms, sizes and mooring configurations. It does not necessarily follow that the previous use of even less conservative coefficients for specific ships with specific mooring configurations is invalidated by this new data.

It is recommended model tests are performed for each vessel design as a preference to the data held within this document.

It should be realised the data held in this document is not applicable to FPSOs etc.

2. WIND LOAD PREDICTION PROCEDURES

2.1. Basis of Procedures Wind loads included on moored gas carriers in the 75,000 to 300,000m³ (cubic metre) class can be computed with the procedures described in this section. The forces and moments generated are suitable for a computer analysis of the required mooring restraint.

The following non-dimensional coefficients are used throughout in the calculation of design loads:

CXw = Longitudinal Force Coefficient CYw = Lateral Force Coefficient CXYw = Yaw Moment Coefficient

The subscript, w, is added to indicate that loads are due to wind.

The sign convention and coordinate system adopted for this report are illustrated in Figure 1. Curves of the force and moment coefficients as a function of wind angle of attack are provided in Figures 2, 3

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and 4. The wind coefficients are based upon data obtained from wind tunnel tests. The forces and moments computed will be in units of tonne and tonne-metres respectively with their point of action at the intersection of the transverse and longitudinal centreline of the vessel.

2.2. Equations for Computing Wind Loads The resultant wind forces/moment acting on a moored gas carrier are calculated using the following equations:

Longitudinal Wind Force Tww

XwXw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (1)

Lateral Wind Force Lww

YwYw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (2)

Wind Yaw Moment BPLww

XYwXYw LAVCM 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (3)

Curves of the coefficients CXw, CYw and CXYw are presented in Figures 2, 3 and 4 for the following conditions:

- Wind angle of attack: 0 degrees bow-on to 180 degrees on the stern. The coefficients are equally applicable to winds from 181 to 359 degrees with appropriate changes in the signs of the coefficients.

- Any operating draft condition: the coefficients presented in this report are applicable to draft conditions ranging from ballasted to fully loaded (Further discussion on the effects of vessel draft changes is given in section B.4.2.1 of Appendix B).

- Two cargo tank types: the curves illustrate the effect of spherical tanks versus conventional prismatic tanks. Where the effects between these two tank types are insignificant, the curves have been combined and presented as a single curve.

While the coefficients do not vary with the ship’s draft, the areas (AT and AL) used in Equations (1)-(3) must be consistent for the particular ship load condition and tank type under investigation.

The use of the above equations to predict wind loads on a gas carrier is illustrated by an example problem in section 3.

2.2.1. Wind Velocity A sustained wind velocity measured at an elevation of 10 metres above the ground/water surface is used in the wind load equations. The coefficients were developed on the basis of a steady state wind condition. Because winds are seldom of a steady nature, an average wind speed over a sufficient duration to induce a complete response of the moored vessel to the wind must be selected. A 30 second average wind velocity is recommended for use in the wind force and moment equations for mooring analyses (Reference [2]). For wind velocities obtained at a different elevation, adjustments to the equivalent 10 metre velocity are necessary and can be made with the following formula:

71

10⎟⎠

⎞⎜⎝

⎛=h

vV ww

Where: Vw -10 metre wind velocity (knots)

vw - the wind velocity at elevation h (knots) h - elevation above ground/water surface (metres)

The equation reflects a wind velocity gradient which varies with height according to the 1/7 power law and representative of a natural wind profile over water (Reference 3).

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2.2.2. Gas Carrier Wind Areas

The transverse and longitudinal areas AT and AL, respectively, are measured from the head-on and broadside projections of the above water portion of the vessel.

2.2.3. Major Factors Affecting Wind Loads The presence of spherical tanks on gas carriers has the most significant impact on the wind coefficients. The deviations in the coefficients result from the differences in the relative force contribution and distribution due to the configuration on the spherical tanks. Therefore, separate curves for conventional prismatic and spherical tanks have been developed where the deviations are significant. Differences in ship load condition are not significant due to the relatively small change in draft from a ballasted to a fully loaded condition for the sizes of gas carriers reviewed.

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3. EXAMPLE PROBLEM Compute the wind forces and moments on a ballasted 125,000m³ gas carrier with spherical tanks. The wind velocity is 66 knots measured at a 20 metre elevation. The angle of wind attack is 30 degrees.

3.1. Wind Load Calculations

Step 1: Determine gas carrier characteristics.

Particulars for a ballasted 125,000m³ gas carrier:

AL = 7122m² AT = 1382m² LBP = 274m

Step 2: Obtain wind coefficients for θw = 30°.

CXw = -0.71 Figure 2 CYw = -0.42 Figure 3 CXYw = -0.044 Figure 4

Step 3: Compute wind forces/moment from Equations (1), (2), and (3).

Tww

XwXw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (1)

Lww

YwYw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (2)

BPLww

XYwXYw LAVCM 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (3)

where, 4

2sec.1248.0

m

kgw =ρ (air at 20°C)

Since the wind velocity in the problem was measured at a 20 metre elevation, the equivalent 10 metre wind velocity must be calculated from Equation (4).

71

10⎟⎠

⎞⎜⎝

⎛=h

vV ww (4)

vw = 66 kts

h = 20 m

71

2010

66 ⎟⎠

⎞⎜⎝

⎛=wV

Vw = 60 kts

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From Steps 1 and 2:

)1382()60(76001248.0

)71.0(F 2Xw ⎟

⎠

⎞⎜⎝

⎛−= = -58 t

)7122()60(76001248.0

)42.0(F 2Yw ⎟

⎠

⎞⎜⎝

⎛−= = -177 t

)274)(7122()60(76001248.0

)044.0(M 2XYw ⎟

⎠

⎞⎜⎝

⎛−= = -5,076 t.m

3.2. Summary of Wind Loads The following table summarises the wind loads calculated in Section 3.1 as well as the effect of wind for other conditions which could be of interest in the subsequent analysis of mooring restraint.

SUMMARY OF WIND LOADS

Wind loads on ballasted 125,000m³ gas carrier with spherical tanks for 60 knot wind 10 metre elevation.

Wind Angle of Attack

0° 30° 60° 90° 120° 150° 180°

FXw -68 -58

-19 -1 44 79 68

FYw 0 -177

-362 -380 -310 -164 0

MXYw 0 -5,076 -4,845 3,230 11,420 11,420 0

Notes:

1. Forces in tonne; moment in tonne-metre

2. Circled values obtained from example problem.

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FIGURE 1 SIGN CONVENTION AND COORDINATE SYSTEM

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FIGURE 2 LONGITUDINAL WIND FORCE COEFFICIENT

CXw

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0° 20° 40° 60° 80° 100° 120° 140° 160° 180°

WIND ANGLE Of ATTACK θw

CXw

Prismatic

Spherical

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FIGURE 3 LATERAL WIND FORCE COEFFICIENT

CYw

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0° 20° 40° 60° 80° 100° 120° 140° 160° 180°


CYw

Prismatic

Spherical

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FIGURE 4 WIND YAW MOMENT COEFFICIENT

CXYw XYw

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0° 20° 40° 60° 80° 100° 120° 140° 160° 180°


CXYw

Prismatic

Spherical

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Appendix A Alternative Method for Computing the Wind Loads for Simplified Mooring Restraint Analysis

A.1 General This section describes an alternative method for calculating wind loads on moored gas carriers ranging in capacity from 75,000 to 300,000m³. Loads computed by the following procedure will lend themselves to a simplified (hand calculation) analysis of mooring restraint in lieu of adequate computer capability.

The basic difference between the procedure in the body of the report and the one described below lies in the way the lateral force and yaw movement are applied. The force and moment originally applied at the point of intersection of the ships transverse and longitudinal centrelines can be resolved into equivalent forces and a force couple respectively which act to the forward and aft perpendiculars. The following equations illustrate this relationship:

Lateral Force at Aft Perpendicular BP

XYYYA L

MFF −=

21 (A-1)

Lateral Force at Forward Perpendicular BP

XYYYF L

MFF +=

21 (A-2)

where FY and MXY are the force and moment at the point of intersection of the transverse and longitudinal centreline.

The longitudinal and lateral forces are computed for wind by using coefficients given in Figures A-1 and A-2. It is then a relatively simple matter to determine the required mooring restraint by hand calculation in accordance with various acceptable methods (Reference 2).

A.2 Equations for Computing Wind Loads

Longitudinal Wind Force Tww

XwXw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (A-3)

Lateral Wind Force at Aft Perpendicular Lww

AYwYAw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (A-4)

Lateral Wind Force at Forward Perpendicular Lww

YFwYFw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (A-5)

The longitudinal and lateral force coefficients CXw, CYAw, and CYFw are plotted in Figures A-1 and A-2 as a function of the wind angle of attack.

A.3 Example Problem By considering the same case as the example presented in the body of this report, the differences between the two procedures can be highlighted:

Compute the wind forces on a ballasted 125,000m³ gas carrier with spherical tanks. The wind velocity is 60 knots measured at 10 metres and an angle of attack of 30 degrees.

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A.3.1 Wind Load Calculations Step 1: Determine ship characteristics.

Particulars for a ballasted 125,000m³ gas carrier:

AL = 7122m² AT = 1382m²

Step 2: Obtain wind coefficients at θw = 30°

CXw = -0.71 Figure A-1 CYAw = -0.166 Figure A-2 CYFw = -0.255 Figure A-2

Step 3: Compute wind forces/moment from Equations (A-3), (A-4), (A-5).

Tww

XwXw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (A-3)

Lww

AYwYAw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (A-4)

Lww

YFwYFw AVCF 2

7600 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρ (A-5)

where, 4

2sec.1248.0

m

kgw =ρ (air at 20°C)

Vw = 60 kts

)1382()60(76001248.0

)71.0(F 2Xw ⎟

⎠

⎞⎜⎝

⎛−= = -58 t

)7122()60(76001248.0

)17.0(F 2YAw ⎟

⎠

⎞⎜⎝

⎛−= = -72 t

)7122()60(76001248.0

)25.0(F 2YFw ⎟

⎠

⎞⎜⎝

⎛−= = -105 t

LBP 2

FXw = -58t

FYFw = -105 t FYAw = -72 t

θw = 30°

Fwd

Perp

Aft

Perp

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A.3.2 Summary of Wind Loads SUMMARY OF WIND LOADS

Alternative Procedure Wind loads on ballasted 125,000m³ gas carrier with spherical tanks for 60 knot wind at 10 metre elevation

Wind Angle of Attack

0° 30° 60° 90° 120° 150° 180°

FXw -68 -58 -19 -1 44 79 68

FYAw 0 -72 -164 -202 -198 -122 0

FYFw 0 -105 -198 -177 -114 -42 0

Notes:

1. Forces in tonne.

2. Circled values obtained from example problem.

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FIGURE A-1 LONGITUDINAL WIND FORCE COEFFICIENT

CXw

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0° 20° 40° 60° 80° 100° 120° 140° 160° 180°


CXw

Prismatic

Spherical

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FIGURE A-2 LATERAL WIND FORCE COEFFICIENT

CYAw, CYFw

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0° 20° 40° 60° 80° 100° 120° 140° 160° 180°


CXw

PrismaticSpherical

CYFw

CYAw

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Appendix B Discussion of Wind Load Computation Procedures

B.1 General Wind tunnel tests on liquefied gas carrier models were conducted during the summer of 1980. Recent model tests have also been performed independent of this project on behalf of the designers, who have generously permitted the data to be used for this study. Subsequent analysis of this data resulted in the coefficients and procedures described in this report for computing wind loads on moored gas carriers. A brief discussion of the model test program and data analysis is presented below.

B.2 Original Wind Tunnel Tests of Gas Carrier Models Wind loads on scale models of 75,000 to 125,000m³ gas carriers were measured in a series of tests conducted in a 5×7.5 foot wind tunnel. Each model was constructed for ballast draft conditions. Hull and superstructure configurations were typical for ships in this category. The models were based on characteristics considered to be typical of existing ships of that size.

The models were mounted close to a ground plane near the floor of the tunnel in order to be immersed in the tunnel boundary layer. The velocity gradient in the boundary layer was tailored to approximate a 1/7 power profile, which is believed to simulate the natural wind profile over a smooth water surface (Reference [3]).

Forces and moments were measured in the horizontal plane at five degree intervals from 0 degrees bow-on to 360 degrees. Measurement intervals were decreased near the 0 and 180 degree points to better define these values. Since the gas carriers were essentially symmetrical about their longitudinal centreline, the values measured on the port and starboard sides were then averaged. This procedure was used to remove the effects of minor non-symmetries in model construction as well as to account for any slight non-homogeneous nature of the velocity profile across the tunnel which may have existed. Generally, the raw data plotted within 5 percent of the averaged values.

B.3 Wind Tunnel Tests of Current Gas Carrier Models The ship building industry generally use the same standard techniques as described above when commissioning wind tunnel model tests. On behalf of SIGTTO, the authors requested copies of wind load model test results from various ship yards and collated the results. As described above, generally, the raw data plotted within 5 percent of the averaged values. Thus confidence in considering their use is high.

B.4 Data Analysis Good agreement of the wind tunnel test data was obtained for the cases modelled and the cases donated. Variations in the averaged raw data curves observed among the coefficients CX, CY and CXY for ships with spherical tanks can be explained by differences in the physical/geometric characteristics of the particular ships as will be discussed later. By appropriately weighting the individual data points of the original data to reflect the effect of these differences it was possible to define representative mean curves for the range of ships and tank types studied. The total variation about the mean curves generated in this fashion was generally within +/- 5 percent of the individual model values for each of the force and moment coefficients.

B.4.1 Establishment of Design Coefficients The design wind load coefficient curves were established by adjusting the mean curves to account for the uncertainties inherent in model test results. The sources of the uncertainties stem mainly from the following:

• Experimental error (e.g. balance calibration and alignment, wind profile variance, model position error, etc.)

• Ability to accurately measure low loads associated with the scaled down models (confidence in the data at low loads)

• Applicability to prototype situation.

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A range of values about the mean were developed to bracket the uncertainty in the coefficients from the first two sources. The design coefficient curves represent the upper limit of this range. The coefficients for lateral force, longitudinal force and yaw moment on a gas carrier have been increased 10% over the mean values to account for the experimental error.

The applicability of the model test results to the full-scale situation has been investigated to a limited extent. Flow visualisation tests employing smoke and tufting were conducted to observe flow fields on and around the 125,000m³ model with spherical tanks. Additionally, a model used to establish the VLCC wind coefficients was retested to observe any differences in the test facilities from those used for the VLCC model wind tunnel testing, where the applicability of the model test results to the full-scale situation was confirmed through measurements of the wind pressure distribution around the model. The investigation revealed:

1. air flow was well attached to the spherical tanks on the downstream side indicating that turbulent and not laminar conditions were present in the boundary layer around the hull and the spheres, which corresponds to the full-scale situation;

2. the proximity of the tunnel sidewalls did not affect the pressure around the bow with the model in a broadside wind condition; and

3. good agreement was found with past wind tunnel results on the VLCC model.

The above findings support the validity of using the model for predicting full scale wind loads on gas carriers.

On the basis of the above, and of the current designs’ wind tunnel tests having sufficient similarity with them, it is concluded the wind tunnel tests for the set of current LNG ship designs are also valid.

B.4.2 Considerations for the General Use of the Load Prediction Procedures

The coefficients and procedures presented in this report proved the prediction of wind forces and moments on gas carriers ranging from 75,000 to 300,000m³ which are geometrically similar to those used in the model tests. Typical values of the significant geometric relationships for the vessels studied in the original model test program are presented in Table B-1. However, due to design confidentiality, Table B-1 does not cover the geometric relationships of the current LNG designs used for this study. The values indicate the ship geometries for which there is the greatest confidence in the loads predicted with use of this report. However, design quality numbers can also be generated for gas carriers which differ from the values indicated if the user understands the basis upon which the force and moment coefficients were developed, since hull shapes and superstructures remain fairly similar in this size range. Figure B-1 illustrates the profiles of the hull and superstructure shapes for the ships which were modelled. This figure has been redrawn from the original document to demonstrate the balance and permeability of each ship type under consideration. The applicability of the wind coefficients to gas carriers outside the 75,000 to 300,000m³ range will also depend on the geometric similarity of these ships to those upon which the coefficients are based.

The data within this document is not applicable to FPSO vessels or similar types.

The discussion below is intended to aid in the assessment/understanding of the importance of variations in ship geometry and tank configuration from that used in the model test program.

B.4.2.1 Effects of load/ballast condition on wind coefficients Design values of longitudinal force, lateral force, and yaw moment coefficients have been developed based on typical ballasted load conditions for gas carriers. The ballast drafts used in the tests were based on an assessment of representative drafts in each ship class. The angle of trim for the ballast condition is 0 degrees.

It is noted however, that the drafts used in the current assessments are typically design load draft. The effect of this could be to increase the yaw moment coefficient for gas carriers having prismatic tanks due to the proportional increase in the projected area moment of the stern house over that of the reduced freeboard hull.

The coefficients within this report are considered equally applicable to all operating draft conditions ranging from ballasted to fully loaded. The effect of the load condition on a gas carrier is not similar to

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that of a VLCC since the gas carrier draft changes only slightly during normal gas transfer operations. Typical draft changes for gas carriers will vary from about 5 to 10% of typical VLCC draft changes, depending on the specific gas carrier under review. Considering this relative magnitude of change in drafts and the total variation in wind coefficients between ballasted and loaded VLCCs, the average deviation in the gas ship wind coefficients accounting for draft changes would be less than 5 percent. Thus, the effect of draft/freeboard changes can be neglected without a loss of accuracy for mooring analysis purposes.

B.4.2.2 Effects of Cargo Tank Type on Wind Coefficients In the study of 1985, the 125,000m³ gas carrier was modelled in both spherical and prismatic tank form to observe any significant effects associated with spherical tanks. The spherical tanks have their most significant effect on the wind yaw moment. The variation in wind yaw moment coefficients between the two forms of gas carrier results from the more uniform distribution of the lateral wind area of the spherical tanks over the length of the hull. This reduces the yawing moment generated by the stern house and is most obvious upon review of the fore and aft lateral wind coefficients in Figure A-2. It can be seen that the maximum lateral force exerted at either end of the ship will be essentially equal for ships with spherical tanks, as compared to the greater aft force for those with prismatic tanks reflecting the more pronounced stern house effect. Less pronounced but occasionally significant differences exist in the lateral and longitudinal wind force coefficients when spherical tanks are present.

Only a 125,000m³ model was tested with spherical tanks since the majority of gas carriers with spherical tanks fall within this class size. However, the wind coefficients for ships with spherical tanks are applicable to the full range of gas carriers under consideration for the following reasons:

• Close agreement was found between the 75,000 and 125,000m³ models with prismatic tanks which were tested. The individual test results were generally within 5 percent of the final mean curve.

• Reviews of the compatibility of data on oil tankers ranging in size from 150 to 500 kdwt indicate that wind coefficients are generally applicable to a wide range of vessels if they are geometrically similar.

These findings were reinforced by the study of current model test data.

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Table B-1

TYPICAL GEOMETRIC RATIOS OF GAS CARRIERS FROM WIND TUNNEL TESTS

Geometric Ratio

Draft 75,0005 125,0003

125,0006 Comments

LOA/B − 6 − 7.5 Encompasses range of known ship designs

Full 0.787 0.788 0.538 AHL/AL

Ballast 0.845 0.810 0.573 Primary effect on yaw moment coefficient

Full 0.107 0.108 0.158 2AL/LOA²

Ballast 0.145 0.121 0.171

Primary effect on lateral force coefficient. Secondary effect on yaw moment coefficient.

Full 0.438 0.510 0.481 AHT/AT Ballast 0.528 0.543 0.514

Primary effect on longitudinal force coefficient.

Full 0.685 0.705 1.03 2HLM/B Ballast 0.929 0.789 1.12

Secondary effect on longitudinal force coefficient.

5 Ratios apply to ships with conventional prismatic tanks. 6 Ratios apply to ships with spherical cargo tanks.

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FIGURE B-1

TYPICAL SHIP HULL AND SUPERSTRUCTURE PROFILES

Typical simplified LNG Carrier with 4 Spherical Tanks, as seen by the wind at various angles of attack.

0° 30°

60°

90°

180°

150°

120°

The principles of arrangement are not too dissimilar for ships having 5 or 6 spherical tanks. The visual effect of the catwalk and structure at various angles of windage clearly demonstrate the minimal slots available for wind to escape.

Typical simplified LNG Carrier with Prismatic Tanks, as seen by the wind at various angles of attack.

0° 30° 60°

90°

180° 150°

120°

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Appendix C Program Description for Wind Tunnel Tests

ORIGINAL, 1985 TESTS

Model Size m³ Scale Tank Configuration

Load Condition

Tested

Wind Velocity (Knots) (1)

Angle of Wind Attack

75,000 1:220 Prismatic Ballast 64.1 0°-360° @5 degree

increments 125,000 1:220 Prismatic Ballast 64.1 0°-360° @5

degree increments

125,000 1:220 Spherical Ballast 64.1 0°-360° @5 degree

increments

Notes

(1) Velocity at the equivalent 10 metre elevation

(2) Due to copyright and client confidentiality, it has not been possible to include the equivalent data for the current designs studied in this update.

RECENT TESTS

Models tested represented the following ranges:

Spherical tank ships: 125,000, 135,000 & 150,000 m³ capacity ships approximately.

Prismatic tank ships: 75,000m³, 135,000m³ to 155,000m³, 210,000m³ and 260,000m³ capacity ships approximately.

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Appendix D Table of Coefficient Figures

Gas Carriers with Spherical Tanks Gas Carriers with Prismatic Tanks

θw CXw CYw CXYw CYAw CYFw CXw CYw CXYw CYAw CYFw

0° -0.836 0.003 0.001 0.000 0.002 -0.973 -0.002 0.001 -0.002 0.000 10° -0.850 -0.110 -0.015 -0.040 -0.070 -0.955 -0.127 -0.015 -0.048 -0.079 20° -0.809 -0.251 -0.029 -0.097 -0.154 -0.918 -0.293 -0.029 -0.117 -0.175 30° -0.707 -0.421 -0.044 -0.166 -0.255 -0.827 -0.507 -0.044 -0.209 -0.298 40° -0.579 -0.594 -0.052 -0.245 -0.349 -0.676 -0.725 -0.045 -0.318 -0.407 50° -0.425 -0.759 -0.052 -0.328 -0.432 -0.493 -0.899 -0.043 -0.406 -0.493 60° -0.236 -0.859 -0.042 -0.388 -0.472 -0.333 -0.994 -0.032 -0.465 -0.529 70° -0.176 -0.898 -0.022 -0.426 -0.471 -0.210 -1.062 -0.011 -0.520 -0.542 80° -0.086 -0.914 0.001 -0.458 -0.456 -0.135 -1.090 0.019 -0.564 -0.526 90° -0.010 -0.903 0.028 -0.479 -0.424 -0.104 -1.100 0.054 -0.604 -0.496

100° 0.109 -0.869 0.056 -0.490 -0.379 0.017 -1.074 0.091 -0.628 -0.446 110° 0.295 -0.813 0.080 -0.486 -0.327 0.220 -1.026 0.125 -0.638 -0.388 120° 0.540 -0.737 0.099 -0.467 -0.269 0.456 -0.952 0.153 -0.629 -0.323 130° 0.748 -0.634 0.109 -0.426 -0.208 0.681 -0.846 0.170 -0.593 -0.253 140° 0.875 -0.517 0.109 -0.368 -0.150 0.827 -0.693 0.169 -0.515 -0.178 150° 0.964 -0.389 0.099 -0.294 -0.095 0.930 -0.507 0.144 -0.397 -0.110 160° 0.986 -0.225 0.073 -0.185 -0.040 0.974 -0.313 0.100 -0.256 -0.056 170° 0.934 -0.088 0.037 -0.081 -0.007 0.963 -0.143 0.049 -0.121 -0.022 180° 0.834 0.000 0.000 0.000 0.000 0.918 -0.002 0.000 -0.001 -0.001

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Appendix E Conversion Factors

LINEAR MEASURE To obtain

Metres Feet Nautical Miles Kilometres Land Miles Knowing Multiply by

Metres 1.0 3.2808 0.000540 0.001 0.000621 Feet 0.30480 1.0 0.000165 0.0003 0.000189 Nautical Miles 1852.0 6076.1 1.0 1.852 1.1508 Kilometres 1000.0 3280.8 0.5400 1.0 0.6214 Land Miles 1609.4 5280.0 0.8690 1.6094 1.0

VELOCITY To Obtain

Knots Metres/Second Feet/Second Miles/Hour Knowing Multiply By

Knots 1.0 0.5145 1.6835 1.1508 Metres/Second 1.9438 1.0 3.2808 2.2356 Feet/Second 0.5940 0.3048 1.0 0.6818 Miles/Hour 0.8690 0.4471 1.4667 1.0

WEIGHT MEASURE To Obtain

Kilograms Tonne(1) Pounds Short Tons Knowing

Multiply By Kilograms 1.0 0.001 2.2046 0.001102 Tonne(1)

1000.0 1.0 2204.6 1.1023 Pounds 0.45359 0.00045359 1.0 0.00050 Short Tons 907.18 0.90718 2000.0 1.0 (1) Tonne is equivalent to a Metric Ton.

TEMPERATURE °C = (5/9) (°F – 32)

°F = (9/5) (°C) + 32

Comparison of Temperature Scales Centigrade ° 0 10 20 30 40 Fahrenheit ° 32 50 68 86 104

AIR DENSITY(1)

In Units of ⎟⎟⎠

⎞⎜⎜⎝

⎛4

2sec.

m

kg

Temperature 0°C 10°C 20°C 30°C 40°C Density 0.1335 0.1288 0.1248 0.1193 0.1146

(1) Density as used in this report is the metric equivalent of slugs/foot³ which is the engineering definition of density used in the English Gravitational System.

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REFERENCES [1] OCIMF. “Prediction of Wind and Current Loads on VLCCs”, Witherby & Co. Ltd., 1977.

[2] OCIMF. “Guidelines and Recommendations for the Safe Mooring of Large Ships at Piers and Sea Islands”, Witherby & Co. Ltd., 1978.

[3] Meyers, John J., Carl H. Holm, and R.F. McAllister, “Wind and Wave Loads”, Handbook of Ocean and Underwater Engineering, McGraw-Hill, 1969.

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