600 I N W I N diary fan with its gearing, acting on a toothed wheel fixed to the cap. Relation between the Velocity of the Wind and its Pressure on Sur faces. When a flat thin plate is exposed normally to the wind, the pressure 011 its front surface is increased and that on its back sur face somewhat diminished. The resultant total pressure per square foot in the direction of the wind is given approximately by the equation ^ = -005 i- 2 (1) iff is in miles per hour, or ^=0023 v" (la) if v is in feet per second. Thus, winds at velocities of 5, 10, and 20 miles per hour would give a pressure of | ft, ft, and 2 ft respect ively on each square foot of a surface normal to the wind, and these may be considered ordinary working velocities for windmills. In storms the velocity of the wind may reach a much greater value. Pressures of 28 or 30 ft per square foot have been frequently regis tered by anemometers, and at exceptionally exposed stations press ures of 50, 80, and even 90 ft per square foot have been recorded. These pressures, which are useless for working the windmill, must, nevertheless, be reckoned with in deciding on its structural strength. Pressure on Surfaces Oblique to the Wind. The variation of press ure with inclination of surface is only known experimentally. Let R be the direction of the wind, making an angle 6 with the ^ normal to the surface, supposed to be at rest. Then, if p is the pressure per square foot of sur face when the wind is normal to the surface, the resultant normal pressure on the oblique surface is n=p 2c * e >f , ft per square foot (2). r l + cos j But the windmill sail moves in a direction perpendicular to the wind. Hence, if v is the velocity of the wind and u that of the sail, the relative velocity is VV J + v and the direction of relative motion can be found as follows. Let aa be the plane of rotation of the sail. The inclination 6 of the sail to the plane of rotation is called the angle of weather, and is the same as the angle the wind makes with the nor mal to the sail. Set off ob = v, bc = u, then oc is the relative velocity, and this makes an an^le = tan~ 1 - with the direction of the wind v and an angle + with the normal to the sail. Hence for the moving sail Before replacing p by its value in (1) another consideration re quires attention. The sail generally moves faster than the wind ; it is not a thin-edged plane, but presents a not inconsiderable surface at right angles to its direction of motion, and thus creates resist ance. Of the whole pressure of the wind a part only is effective, the rest being used to overcome the resistance of the sail. It will be assumed that the effective pressure driving the sails is only, for v in feet per second, ^ = 001 v 2 ft per square foot, and, therefore, the effective normal pressure on the sails is, for the relative velocity Vtf- + M 8 , w= -001(1* + t* s ) i ~~-- The component of this in the direction of motion of the sail is n sin 0. Consequently the useful work of the sail expressed in foot-pounds per square foot is 01 ]1 Husin0 = -001(v 2 + w 2 )% r^~ - r. By dividing the sail sec (0 + 0) + cos (0 + 0) into strips and introducing the known values of u, v, and the work done is easily found. Best Angle of Weather. The best angle of weather is that which " a maxmum - Tllis the VC1 7 simple rule = 67^ - |0. Given the velocity of the wind and that of the tips of the sails, the value of is easily found for any point of the sail, and thence 0. Thus, for 2-5 2-0 64 1-5 57 1-0 45 0-5, = 72 68 J 64 57 45 27 = 13i 16i 19 24 33 Q 471. Horse-Power of Windmills. For the older kinds of windmills the following rule derived from some experiments by Coulomb may be used. Let ?i = no. of sails, A area of each sail in square feet, v velocity of wind in feet per second ; then the horse-power of the mill is nAi? , this assumes the speed of the tips of the sails to be about 2 to 3 times the wind velocity. For American wheels Wolff gives the horse-power which may be expected for an aver age of 8 hours per day as follows : Diameter of Wheel iu Feet. Velocity of Wind in Miles per Hour. Horse-Power of Mill. Revolutions of Wheel per Minute. 8J 10 16 16 0-04 0-12 70-75 60-65 12 16 0-21 55-60 14 16 0-28 50-55 16 16 0-41 45-50 18 16 0-61 40-45 20 16 078 35-40 25 16 1-34 30-35 Further information will be found in Ranldne, The Steam Engine and other Prime Movers ; Weisbach, The Mechanics of Engineering ; and Wolff, The Wind mill as a Prime Mover. (W. C. U.) WINDSOR, 1 a parliamentary and municipal borough of Berkshire, England, 21 miles from London by the Great Western Railway, situated on the right bank of the Thames, is chiefly remarkable for its royal castle. The town itself 2 is of no special interest, in spite of its great antiquity. In 1276 Edward I. made Windsor a free borough. In 1302 it began to send representatives to parliament, though at irregular intervals, and from the time of Henry VI. it returned two members till 1867, when they were reduced to one. The town is presided over by a mayor, aldermen, and councillors, who were incorporated by a charter of Edward IV. The town-hall was built in 1686 by Sir Plan of Windsor. Christopher Wren, but was much altered in 1852. The Thames is crossed here by a bridge resting on three granite piers (1823). The parish church of St John the Baptist was rebuilt in 1822; the other two churches are also modern. The town was formerly celebrated for the number of its inns, of which " The Garter " and " The White Hart " were the chief. The former vas the favourite inn of Shakespeare s Sir John Falstaff, and is frequently men tioned in the J ferry Wives of Windsor. In 1650 the town contained 70 inns, many of which were very picturesque half-timbered buildings ; but none of these now exist. In 1 The name is said to be derived from Windelsora (A.S. windel, " to wind," and or, a " shore," from the winding course of the Thames). 2 In official documents the town is called New Windsor, to dis tinguish it from its parent settlement Old Windsor, which is now a village prettily situated about two miles to the south-east of Windsor
Castle.