Aerodynamics of Teardrop Wingmasts

Aerodynamics of Teardrop Wingmasts

Thomas E . Speer, Des Moines, Washington, USA

ABSTRACT

The two-dimensional flow about a teardrop-shaped wingmast and sail combination is explored using Drela’s XFOIL airfoil design and analysis tool.  The key flow features, consisting of laminar separation bubbles, separation bubbles at the mast/sail junction, and trailing edge separation are described.  A method of designing a wingmast shape based on a reference airfoil is presented, and a family of wingmast designs based on the Clark Y airfoil is analyzed.  Systematic variations in mast size, mast rotation, angle of attack and Reynolds number are presented to show the effects of the principal design and operational considerations.

NOTATION

c                              chord, ft

C_d                            drag coefficient,  d/(q c)

C_l                             lift coefficient,  l/(q c)

C_p                            pressure coefficient,  Dp/q

d                              drag per unit span, lb/ft

l                               lift per unit span, lb/ft

p                              pressure, lb/ft²

p_a                            ambient pressure, lb/ft²

p_t                             total pressure, p + q, lb/ft²

q                              dynamic pressure, ¹/₂rV², lb/ft²

V                             air velocity, ft/sec

Vo                           freestream velocity, ft/sec

r                             air density, slug/ft³

INTRODUCTION

The aerodynamics of sails alone, and the aerodynamics of round masts plus sails have been studied for some time, both in theory and in the lab.  Likewise, rigid wing rigs can benefit from the body of knowledge aimed at aircraft high lift configurations.  But there’s very little information on wingmast-sail combinations.  I’ve used XFOIL (Ref. 1) to calculate the characteristics of wingmast-sail airfoils, and I’m beginning to appreciate just how remarkable this combination is.

This paper concerns itself with teardrop-shaped wingmasts.  These masts can be rotated independent of the sail so that the lee side can be made a smooth contour on each tack.  There are other  types of wingmasts, using parabolic (Ref. 2) and elliptical (Ref. 4) sections.  The flow around the blunt trailing edges of these sections cannot be calculated by XFOIL because the surface contours are too severe.  Since these alternate wingmast shapes could not be compared on an equal basis, this paper only includes results for the teardrop masts.  However, most of the flow features of these other masts are also exhibited by the teardrop masts, such as separation bubbles spanning the mast/sail junction.

Before I get into the aerodynamics, a cautionary note about the limitations of the methods I’ve used.  The theoretical methods in XFOIL are strictly two-dimensional.  That is, they apply to the cross section of a shape that is infinite in length and rigid.  A real soft sail is inherently a three dimensional, flexible problem, since we all know that the shape of the sail is affected by the tensions up and down the sail, as well as the tension in the streamwise direction.  So you really have to combine the material strains and the aerodynamics of the whole rig to get the true picture.  But two-dimensional flow isn’t a bad approximation and it has a lot to say about the cross section shape.  The other limitation is that XFOIL can only handle a limited amount of separated flow.  The wingmast calculations in this paper stress XFOIL to its limit.  XFOIL has been shown to be reasonably accurate at calculating the effects of laminar separation bubbles on conventional airfoils, and less accurate with regard to estimating maximum lift.  To estimate these characteristics properly would require a Navier Stokes code.  However, one can see the key flow characteristics in the XFOIL results, making them qualitatively correct, and the trends are probably well represented even if the absolute results are somewhat in error. Large oscillations in the drag polars indicate poor convergence in XFOIL, and while the data are highly suspect they are presented to show XFOIL’s limitations.

…read more at: Aerodynamics of Teardrop Wingmasts