Wind And Current Shape Coefficients For Very Large Crude Carriers
Authors: Benham F.A. , Fang S.S. , Fettersr C.H. 
Published: October 2008

ABSTRACT
This paper describes a research program carried out by the Oil Companies International Marine Forum to develop wind and current shape coefficients for large tankers. A review and comparison of previously developed wind and current force prediction data had revealed wide discrepancies or gaps among the data heretofore in the public domain. The present research effort has resulted in the development of a standardized set of shape coefficients for use by the marine industry to predict forces and moments due to wind and current acting on moored Very Large Crude Carriers.

INTRODUCTION
The ability to accurately predict wind and current forces acting on Very Large Crude Carriers (VLCC's) is necessary in order to determine the tanker mooring equipment and terminal restraint capacity required to safely moor these vessels. Previous reports dealing with the prediction of wind and current loads on tankers 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 generalizing existing data a very difficult task. Furthermore, the majority of existing wind and current force data is for smaller sized ships and its use for predicting forces acting on VLCC's is questionable. Therefore, the Oil Companies International Marine Forum (OCIMF) undertook a research program including wind tunnel tests and current basin model tests to accurately define shape coefficients for wind and current acting on VLCC's. Exxon Research and Engineering Company was selected to manage and perform the data analysis on behalf of OCIMF for this work.
The wind and current shape coefficients have been developed in the form of non-dimensional force and yaw moment coefficients acting on a moored vessel in various draft and under keel clearance conditions. While the analysis of tanker mooring restraint was not directly addressed in this effort, the coefficients developed are applicable for either a computer oriented or simplified hand calculation technique for the design of tanker or terminal mooring equipment.

THEORETICAL DEVELOPMENT
The steady-state dynamic force components of drag, FD, and lift, FL, acting on a body immersed in a fluid can be expressed as follows:(Mathematical equation available in full paper) where CD and CL are the non-dimensional drag and lift coefficients respectively, for the body in question. Since drag and lift are the forces in the direction parallel and perpendicular respectively, to the direction of the fluid flow, they are not very convenient forces to deal with when looking at a tanker mooring problem. Instead, the forces parallel and perpendicular to the tanker longitudinal centerline, Fx and Fy, respectively, are of more interest (see F!gure 1). If one knows FD and FL, from simple geometry the longitudinal and lateral forces Fx and Fy can be obtained as follows:(Mathematical equation available in full paper)