.1 THE INTERNAL WiillK OF THK WIND. 



If a puff of wind, however, strikes the aeroplane when it has reached the point 

 (' the second part of the trajectory will evidently be modified; the problem is now 

 to find to what height the aeroplane can ascend under these changed conditions, 

 the velocity of the wind being twelve meters per second for example. 



We have seen that the same equations are applicable when the air is in 

 motion, provided that the coordinate axes follow the displacement, for in Bucb 

 a case the air is at rest in reference to the coordinate axes. The trajectory ob- 

 tained under these conditions will not he the trajectory relative to the earth, but 

 that relative to the moving ail'. This offers no dilficulties, however, as the direc- 

 tion of the wind is horizontal and therefore only the abseiss.e arc changed when 

 we pass from the apparent trajectory to the actual one or vice versa 



In this <-asc, as in the preceding, it is necessary to find the position of the 

 point where tin' tangent is vertical (Fig. 6). 



Let CE be the trajectory relative to the moving air, and CD' the trajectory 

 with reference to the earth. To find the ordinate of the point I)' where the tan- 

 gent is vertical it is only necessary to know that of the corresponding point E on 

 the other trajectory. The velocity at C relative to the earth lias been found to be 

 22.1607 m. 



This velocity, however, corresponds to the curve CD'; the velocity at C on 

 the curve C E, that is to say, the velocity at C of the aeroplane compared to the 

 air, is equal to 22.1607 + 12., or 34.1607 m. 



In general, if we consider two points m and n situated at the same altitude, 

 the horizontal component of the velocity at m is equal to the horizontal component 

 of the velocity at n plus the velocity of the wind. As this horizontal component 

 is zero at D', that at E should be equal to the velocity of the wind. Thus, 

 to define the position of the point E on the curve C E we have the condition 

 V cos ft — 12. 



Working tentatively with equation (.'i) we find, after having substituted in it 

 the initial condition- Y 34.1607 and b = {(' being now considered as the 

 origin), that when /? = 5.")" ]', V E =20.9311 in. and consequently: Y cos ft = 

 12.0006 m.' 



Knowing the velocity at E, formula (4) Li'ivcs us the ordinate of this point ; 

 we find in this way that : //,, = 35.594 m. 



This ordinate is also that of the point D'. 



'These values were obtained by giving c the same value a- before : <■ — 7 . sos. In reality, he- 

 tween A and K. that is t" say in the interval where this value of c was used, the minimum 



e 7 80S 



velocity is at A', where V=10; therefore the maximum value for a = =j = j . . = 4° 30' 

 approximately. Thus in no case does thi i reach 7 degrees. 



