Aerodynamics of two-dimensional sail wings

Abstract

The purpose of this work is to obtain the exact solution for the profile and characteristics of a two-dimensional sail, immersed in an inviscid incompressible fluid. An experimental investigation was also performed and results are compared with theoretical predictions.

The sail was assumed to be an infinitely flexible, non-porous membrane of zero thickness, fixed at the leading and trailing edges, and stretched under a constant tension T in the sail surface. An aerofoil model was considered where the airflow remains smoothly attached over the entire profile.

All known previous studies have also used the inviscid fluid approximation, but made the further assumptions of small angle of attack and negligible profile slopes. These assumptions enable the use of thin aerofoil theory predictions for pressure distribution and linearisation of the sail equation.

In contrast this investigation obtains the exact solution. An iterative numerical method is devised whereby an initial estimate is made for the profile using thin aerofoil theory. The pressure distribution is then determined using Theodorsen's method and the profile recalculated using the full sail equation, so that tension and pressure forces are balanced. The cycle of redetermining the pressure distribution and profile is repeated until a convergent solution is obtained.

Results are shown for the profile, lift coefficient and centre of pressure, for various angles of attack and states of tension. For sails with non-negligible camber, values of lift coefficient and centre of pressure are found to differ significantly from those predicted by the linear approximations. Previous researchers have established the existence of a critical tension state where the tension force is unable to contain the pressure forces acting on the sail, and predicted that the value of this state (KTc) was independent of angle of attack. However this study indicates that KTc increases with increasing angle of attack. Centre of pressure calculations, for various angles of attack and states of tension, indicate that two-dimensional sails may possess either static longitudinal stability or instability, depending on the tension state. Experimental results for the profile, KTc, lift coefficient and centre of pressure are compared with theory, and areas of agreement and disagreement discussed. Experimental values for the drag coefficient and the lift to drag ratio were obtained and are discussed in detail.