## Subsystem BLwind: wind in Earth's boundary layer

BLwind is a masked subsystem block, contained in the FDC blocklibrary WINDLIB. It calculates velocity components of a horizontal wind along the body-axes of the aircraft, where the wind velocity and direction may change along the flight path as a function of altitude. By default, the wind profile is valid in the Boundary Layer of the Earth. However, BLwind can easily be altered in order to implement wind shears at different altitudes.

The user can specify the wind profile by means of three functions:

1. wind velocity function; expresses Vw as a function of the altitude H,
2. function for the horizontal wind angle; expresses psi_w as a function of H.
3. function for the vertical wind angle; expresses gamma_w as a function of H.

where Vw is the wind velocity [m/s], psi_w represents the wind direction in a horizontal plane[rad], and gamma_w expresses the wind direction in a vertical plane that is aligned with the projection of the wind-vector on the horizontal line. Notice that psi_w should be equal to pi rad if the wind is blowing to the North and that gamma_w is positive for upward blowing wind! In the default setting, the following expressions, taken from ref.[1] have been used:

      Vw(H) = (H^0.2545 - 0.4097)/1.3470     0 <= H <= 300 m
      Vw(H) = 2.8658 m/s                     H > 300 m

      psi_w   = 180 rad for all altitudes

      gamma_w = 0   rad for all altitudes

(The Vw function in BLWIND is automatically truncated above 300 m and below 0 m, which means that the user can only specify the function for altitudes between 0 and 300 m above the Earth's surface.)

Note: if you want to implement a constant wind, use the block Cwind instead.

### Inputvector: x

      x = [V alpha beta p q r psi theta phi xe ye H]'        (states)

     {V    : airspeed [m/s]                                         }
     {alpha: angle of attack [rad]                                  }
     {beta : sideslip angle [rad]                                   }
     {p    : roll rate [rad/s]                                      }
     {q    : pitch rate [rad/s]                                     }
     {r    : yaw rate [rad/s]                                       }
      psi  : yaw angle [rad]
      theta: pitch angle [rad]
      phi  : roll angle [rad]
     {xe   : x-coordinate in Earth-fixed reference frame [m]        }
     {ye   : y-coordinate ''     ''          ''      ''  [m]        }
      H    : altitude above sea-level [m]

The variables which are not actually used by BLwind have been displayed between curly braces.

### Outputvector: ywind

      ywind = [uw vw ww]'

      uw   : wind velocity component along XB-axis [m/s]
      vw   : wind velocity component along YB-axis [m/s]
      ww   : wind velocity component along ZB-axis [m/s]

### References

1. Approach and Landing Simulation, AGARD report 632, Ames, 1975.