( 394 ) 



No. LVIII. 



On the best angles for the sails of a windmill. By John Garnet t of 

 New Brunswick, N. Jersey. 



Read January 30th, 1809. 



The angle of weather, or that angle which the section of the 

 vane, at a given distance from the centre of motion, makes 

 with* the plane of its motion, will depend on its proportionate 

 velocity to that of the wind ; some mean velocity of which is 

 generally assumed, to which the interior mechanism of the mill 

 is adapted ; supposing this at 121. feet per second, which would 

 be called afresh gale, the Dutch mills, with the sails of 30 feet 

 radius, make about 13 revolutions per minute ; in this case, the 

 extremity of the vane moves with nearly three times the velo- 

 city of the wind, and consequently, at 10 feet distance with 

 the same velocity as the wind ; at 20 feet with twice the ve- 

 locity, being in a direct proportion to the distance from the 

 centre. 



As different angles of weather have been given by several 

 writers, as Parent, De Moivre, Maclaurin and Simpson, Smea- 

 ton &c. and lately by Mr. Hall Gower, which have been 

 copied in the modern treatises on mechanics, as Gregory, 

 Grey &c. where errors may be of considerable consequence, I 

 will endeavour to shew the true principles, and give a very 

 simple construction which will give the angle of weather on 

 either hypothesis. 



Let the line WV represent the wind's direction and velo- 

 city ; SV, the direction and velocity of any section of the vane 

 whose angle of weather is required ; then WS will be the rela- 

 tive direction and velocity of the wind to that part of the sail ; 

 and the angle WSV, will be the limit of the angle of weather; for, 

 at this angle, the wind's relative direction being parallel to WS, 

 can have no effect, and at any greater angle the vane would 

 be a back sail ; the angle of weather therefore must be less than 

 WSV ; suppose it CSV; then WSC will be the relative angle of 

 incidence of the wind on the plane SC ; from W draw WC per- 

 pendicular to the plane SC, and from C draw CM perpendicular 



