AERODYNAMICAL EXPERIMENTS UPON A YACHT'S MAINSAIL. 15 



SPEED BEFORE THE WIND AND WITH WIND ABEAM. 



Let US assume: — . 



1. That your model sail is on a model boat able to sail through the water. 



2. That its stability is such that its heel is negligible. 



3. That the resultants which are in all cases nearly normal to the planes of reference of 

 the sail are for simplicity of calculations actually so. 



4. That the hull resistance is such that an assumed real wind of 15 miles per hour is 

 able to drive the boat "before the wind" at a rate of 7 1/2 miles per hour. (This is a condi- 

 tion I have met in actual sailing.) 



Since the real wind is 15 miles per hour the apparent speed of the wind when "before 

 the wind" is 15 miles per hour minus 7.5 miles per hour, or 7.5 miles per hour. Now the 

 speed of 7.5 miles per hour equals one-half the real speed of wind, and since pressures vary 

 as the square of speed, the pressure equals ( J^ )^ or J4 of 0.913, which is the pressure given 

 in Fig. 14, Plate 8. A speed of 7^ miles per hour is produced by a pressure on the sail of 

 0.228 pound. 



What pressure do we get with wind abeam ? 



If we solve a right-angled triangle where the hypothenuse represents the speed of the real 

 wind as 15, and another side the speed of the boat as 7.5, the third side representing the direc- 

 tion and speed of the apparent wind which is at right angles to the speed and direction of the 

 boat since we assume wind abeam, we shall find that the apparent speed is ±13 miles per 

 hour. 



The diagram for wind abeam (Fig. 9, Plate 8) shows the resultant at 15 miles per hour 

 equals 0.710, but since pressure varies as the square of speed, at 13 miles per hour the pressure 

 equals 0.710 X ( 13/15)^ or 0.528. But the d ive component in a direction parallel to the keel 

 when the sail makes an angle of 45° with the course, as it does in sailing with wind abeam, is 

 iO.7 of 0.528 or 0.3696, which obviously is more than the pressure before the wind (0.228). 



The course nearly before the wind shown by Fig. 39, Plate 10, is not "the one on which 

 the boat will go the fastest." To find out "on what direction of sailing the ship is driven 

 fastest by a sail," it is not only necessary to have the facts which wind timnel experiments give 

 us, but we must combine them with data given us by towing tanks experiments, which will 

 give us hull speeds under different pressures, and then the answer will only be correct for the 

 specific hull considered and for a given speed of real wind. That even this last statement of 

 mine eliminates too many factors will follow from my next criticism. 



The author seems to imply by his calculations where he combines resultant pressure due 

 to angle that sail makes to the wind with the course that the boat is making with the wind, that 

 what determines the efficiency of a sail is the amount of the pressure or force component 

 parallel to the keel (paragraph 2, page 5). This is not strictly true, because the other com- 

 ponent "at right angles to the keel" cannot in practice be overlooked, since it not only "pro- 

 duces leeway" but also produces heel. The efficiency of the sail changes, then, not only with 

 the amount of the keel-parallel component of the resultant, but with the angle the resultant 

 makes with the plane of reference, for in practice Professor Everett's and Eiffel's diagrams 

 show that it is not necessarily normal to that plane. It is a study of changes in the amount, in 

 the direction, and in the point of application of the resultant due to differences in outline (sail 

 plan) of equal areas, and similar changes of the resultant due to differences of curvature for 

 identical sail plans, that will help us most, in my opinion. 



