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Rev #37

Version 8.0

April 2021

Page 90 of 121

7.3

The Aerodynamic Model

The  EKF  uses  the  polar  diagram  of  the  glider  and  a  sideslip  coefficient  to  compute  error
signals.  The sideslip coefficient is calculated from the aerodynamic properties of the glider.
These parameters are internal variables of the EKF and cannot be modified by the user.
The  sideslip  angle  has  a  strong  impact  on  the  performance  of  the  glider.  The  string  is  a
simple  but  key  instrument  for  the  pilot  to  keep  the  sideslip  small.  A  sideslip  causes  an
additional  drag  which  is  particularly  annoying  during  circling  since  it  largely  increases  the
sink  rate.  The  increase  of  the  sink  rate  is  reinforced  when  the  pilot  flies  with  a  large  roll
angle (circle polar).
During circling most pilots fly with the string slightly outside. The EKF calculates the sideslip
angle. The large majority of pilots fly with small sideslip angles of less than 4 degrees.
Before  we  demonstrate  the  effect  by  an  example,  we  recall  some  properties  of  the
conventional  TEK  vario.  Assuming  a  smooth  thermal,  the  TEK  vario  measures  the  actual
climb  rate  of  the  glider,  not  the  air  mass  movement.  If  we  fly  with  a  large  side  slip,  the
glider‘s  climb  rate  is  smaller  than  flying  with  zero sideslip  in  the  same  thermal.  The  Netto
TEK  and  the  Relative  TEK  vario  are  derived  quantities  by  adding  fixed  constants  to  Vario
TEK. These constants are calculated from the polar diagram in still air.
The EKF operates entirely differently: it estimates the climb rate of the air mass (Netto EKF)
from the vertical wind triangle. The sum of vertical wind and vertical true airspeed equals the
vertical  “ground” speed.  The vertical ground speed is the climb rate of the glider. It equals
the reading  Vario  TEK, which is approximately equal to the Netto  TEK subtracting the sink
rate  of  the  polar  diagram.  More  details  can  be  found  in  the  paper  of  the  Segelfliegen
Magazin “Wissen, woher der Wind weht” which can be downloaded from our webpage.
An  example  greatly  helps  to  illustrate  the  details.  Table  summarizes  the  velocities  during
three  circling  segments  of  the  same  flight  by  an  ASG  32.  The  segment  A  has  been  taken
during  right  circling  with  a  roll  angle  of  about  40  degrees.  In  picture  on  next  page  the
average  sideslip  angle  is around  2.7  degrees.  The  glider  climbs  with  1.4  m/s  (2nd  row  in
Table). The Netto EKF equals 2.7 m/s. The sink rate EKF is estimated as -1.0 m/s. According
to the vertical wind triangle, the summation of the Netto EKF and the sink rate EKF equals
1.7 m/s. Due to the short-term averaging, the difference is not exactly m/s as the climb rate.
We next compare this to the readings of the TEK vario. The average Netto values of TEK and
EKF over the segment A are the same. In the 6th row we show the sink rate computed from
the circle polar using the roll angle computed in the artificial horizon of the EKF.