THE AERODYNAMICS OF SAILS 



Jerome H. Milgram 



Massachusetts Institute of Technology 



Cambridge, Massachusetts 



INTRODUCTION 



The general nature of the aerodynamics of sails is similar to that of low- 

 speed aircraft, for the most part. However, there are a few significant differ- 

 ences. It is the purpose of this paper to discuss the fundamentals of these 

 differences and, to a limited extent, how these differences affect the design of 

 sails. As in the case of aircraft, the best starting point here is the lifting line 

 theory for a single lifting line. One difference between the lifting line theory 

 for sails and the lifting line theory in an unbounded free stream is that there is 

 a boundary beneath the lifting line in the sail problem which represents the hull 

 and the sea. Another difference is that sails operate in a wind gradient that is 

 significant over the entire span of a sail, whereas on most aircraft the wind 

 gradient is usually significant only near the root of a wing. 



For a vessel carrying two sails, much can be learned from the theory of 

 two interacting lifting lines. This is, of course, similar to the biplane theory 

 for aircraft, and some generalizations drawn from aircraft theory can be ap- 

 plied to a sailing rig. Because of the various limitations of the biplane theory, 

 however, as well as the fact that, for sails, the lifting lines are skewed to each 

 other if one of the sails is set on a stay, detailed results from the theory of two 

 lifting lines must be obtained by numerical methods. 



When boundary layer effects are examined, the situation relating to sails is 

 much more complicated than most other applications, because, for the most 

 part, sails operate at relatively large lift coefficients. For example, a typical 

 wing or propeller blade might have a lift coefficient of about 0.4, whereas a 

 typical sail would have a lift coefficient of about 1.4. Most boundary layer ef- 

 fects are determined by the chordwise pressure distribution, since the flow is 

 usually almost wholly chordwise. This is shown in Fig. 1 which is a photograph 

 of sails having tufts to indicate the flow direction in a wind tunnel. Two other 

 frequent effects are also indicated. These are the local leading-edge separation 

 on the mainsail near the head of the jib due to a poor match between the sails, 

 and the local trailing-edge separation near the head of the mainsail due to the 

 large local lift coefficient in this region. 



LIFTING LINE THEORY FOR A SINGLE SAIL 



Two of the main differences between the aerodynamics of sails and the aero- 

 dynamics of most other low- speed lifting surfaces are that a sail operates in a 



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