The Aerodynamics of Sails 



Experiments on Thin, Highly Cambered, Two- Dimensional Sections 



Although vast amounts of data have been taken for sections common to air- 

 plane wings (Abbott and Von Doenhoff, 1959), very little data has been taken for 

 thin, highly cambered sections. Data 

 for circular arc sections with camber . i.8 



ratios between 0,02 and 0.10 were . , g 



taken and reported by Wallis (1961). . 



His sections were of uniform thick- 

 ness, with a thickness-to-chord ratio 

 of 0.02. The lift was measured on a 

 circular arc section with a camber 

 ratio of 0.10 by the author. This sec- 

 tion had a thickness ratio of 0.04 and 

 a faired thickness form with sharp 

 edges. The data for this foil and the 

 10 percent foil of Wallis is shown in 

 Fig. 9. Thin airfoil theory predicts an 

 ideal angle of attack of zero degrees 

 with a lift coefficient of 1.25 for these 

 sections. At zero degrees Wallis 

 measured a lift coefficient of 0.90 and 

 the author measured 0.94. The dis- 

 crepancy is due to boundary layer 

 thickness near the trailing edge. When 

 this is taken into account, theory pre- 

 dicts an ideal angle of attack of 1.8° 

 and a lift coefficient of 1.07 at this 

 angle. This is in excellent agreement 



with the experiments. The drag measurements of Wallis show the profile 

 drag coefficient to be 0.022 at ideal angle of attack. 



1.4 



1.2 



0.8 



0.6 



0.4 



0.2 



0.0 



-0.2 

 -8 



0.06 



0.04 



0.03 



0.02 



0.01 



0.00 



4 8 12 

 ANGLE OF ATTACK 

 - WALLfS 



16 



o MIL6RAM 



Fig. 9 - Experimental results 

 for a thin section with a cam- 

 ber ratio of 0.10 (Reynolds 

 number = 3 x 10^) 



A series of four highly cambered sections were tested with and without 

 masts by Herreshoff (private communication). His sections are shown in Fig. 

 10 and his results are shown in Figs. 11a through lid. The figures show the 

 ideal angle of attack and lift coefficient at this angle predicted by the thin air- 

 foil theory in the absence of boundary layer effects. In the cases without a 

 mast, the flow separates, so that the thin airfoil theory cannot be used for a 

 lift prediction. With a mast, however, the effect of the displacement thickness 

 forward reduces the effective camber and lift sufficiently to prevent flow sepa- 

 ration. Taking the boundary layer into account, the thin airfoil theory predicts 

 an ideal angle of attack of 1.76° with a lift coefficient of 0.85, for Herreshoff s 

 Number One foil with a mast. This is in good agreement with experiment. It 

 is worth noting that at ideal angle of attack the measured drag coefficients 

 were about 0.05 without a mast and 0.06 with a mast. The drag coefficients 

 measured by Herreshoff are higher than those representative of the sections, 

 because there were many structural members protruding from the pressure 

 sides of the airfoils. 



1421 



