Lesson Flying airplane, blowing wind, airspeed, groundspeed etc.

Flying airplane, blowing wind, airspeed, groundspeed etc.

Problem 1

               E x p l a n a t i o n


    (1)  Groundspeed is an aircraft's actual speed and direction of travel over the Earth's surface, 
         calculated by combining the aircraft's true airspeed with the wind's velocity.

         Groundspeed is a vector sum, meaning both the speed and the direction of the wind are considered.     


    (2)  In aviation, airspeed is the speed of an aircraft relative to the air it is flying through.


    (3)  "S65°W" refers to a bearing or direction, meaning South 65 degrees West. 
         This notation indicates a direction starting from South and then rotating 65 degrees towards the West."


               S O L U T I O N


So, S65°W is the direction of  270° - 65° = 205° in the standard coordinate plane.

The direction of the wind "from NW" is 135° + 180° = 315° in the standard coordinate plane.


Thus, we are given two vectors

    the airspeed of the plane = 625*(cos(205°), sin(205°))  km/h;     (1)

    the wind speed vector     = 130*(cos(315°), sin(315°))  km/h.     (2)


Let the groundspeed of the plane be  (x,y).

The groundspeed is the sum of the vectors (1) and (2)


    x = 625*cos(205°) + 130*cos(315°) = 625*(-0.90630778703) + 130*(+0.70710678118) = -474.5184853 km/h;

    y = 625*sin(205°) + 130*sin(315°) = 625*(-0.42261826174) + 130*(-0.70710678118) = -356.0602951 km/h.


So, the groundspeed magnitude is   =  = 593.2509812 km/h.


The angle of the vector with the x-direction of the coordinate plane is


    a =  +  =  +  =  +  =  +  = 

      = 3.14159265 + 0.643732 = 3.78532465 radians = 216.883127 degrees.


ANSWER.  The groundspeed magnitude is about 593.251 km/h.

          The direction of the groundspeed is about 216.883 degrees counterclockwise from positive direction of x-axis,
          or 90 - 36.883 = 53.117 degrees from South to East  (S53.117°W).