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 




Va S finc y
m Ay y
2
2 1
 
 (7)
2.5.2 Improved estimate of β
In due course it was found that resulting sideslip angles sometimes reached fairly large and unrealistic values, of
up to 10º-20º. To alleviate that effect a more thorough analysis was performed on the linearised yawing equation and
the forces contributing to the side force Y. This equation plus more information is given in Ref. 3.
The first notion to make is that in Eq. (5) it was assumed that only the tail fin would contribute to the side force
as result of a slip angle, however, the fuselage contribution can also be substantial. Thus it was decided to re-write
Eq. (5) as:
m
Y fin Y fus
m
Y
Ay y

    (8)
Here the side force from the fuselage is estimated to be:
  2 .
2
1
sin Va S fus
d fus Y fus  Dfus  c (9)
using the small-angle assumption. Combining the previous equations one can write for the improved estimate for  :
 
 

 


 

d fus c
S fin
S fus
Va S fin c y
m Ay y
impr
 


2
2 1
(10)
Compared to Eq. (7) the coeffi cient in the denominator is no longer cy but is now
d fus c
S fin
S fus
cy 

, which
can be substantially larger than before, hence the sideslip angle will be much less. One could rewrite Eq. (10) as:
impr  K  (11)(a)
where
1
1
1 




cy
cd fus
Stailfin
S fus
K
(11)(b)
However, how much less than 1.0 is not known, as the fuselage “ side” area as well as the isolated fusel age drag
coeffi cient are diffi cult to estimate accurately. At any rate, the inclusion of fusel age drag does give rise to the notion
that a gain correction on the computed sideslip angle could be in order.
By also taking the (linearised) yawing equation of motion into consideration a methodology was developed in
Ref. 3 to estimate the “ corrective” gain value for each aircraft type, which came out in the order of 0.3-0.6. The
result of this was that peak values for turbulent kinetic energy TKE and EDR, for example, much better matched one
another, as the TKE calculation is sensitive and EDR is much less sensitive to the sideslip angle.
7
2.6Other parameters
2.6.1 TKE and windshear
With the above processing, the three components of the wind are determined as per Eq. (1), which in its
components reads in the E-frame:
 
 
  


  


  


  


  


  


 
   

 
 
sin
cos sin
cos cos
Va
Va impr
Va impr
T
be
z
y
x
Vwz
Vw
Vw
b
a
T
be
e e
a
e
w
y
x
e
T
V V V V T V



or
With the wind vector known, the windshear paramet ers such as headwind change and windshear hazard ‘F’ can also
be calculated. The F-factor at time t is calculated as follows:
a
w
w a V
t
t t
g
F t
V k
V e

   
( )
( ) 1  ( ) ( ) (12)
where the vector ea is the unit vector along the airspeed vector and k is the unit vector along the vertical axis
(positive “into” the earth). The definition is such that for a downdraft, i.e. positive component Vwz , the F-factor is
negative as it implies a loss of energy.
The turbulent kinetic energy is computed from the standard deviations in the 3 wind components
where the running mean value Vwx y z , , is computed from:



　
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