Campbell-scientific CR9000X Measurement and Control System Manuel d'utilisateur Page 222

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Section 6. Data Table Declarations and Output Processing Instructions
and Ux and Uy are as defined above.
Resultant mean horizontal wind speed, :
U
=(Ue
2
+Un
2
)
1/2
U
Un
U
Ue
FIGURE 6.4-3. Mean Wind Vector
where for polar sensors:
Ue=(
ΣS
i
Sin Θ
i
)/N
Un=(
ΣS
i
Cos Θ
i
)/N
or, in the case of orthogonal sensors:
Ue=(
ΣUe
i
)/N
Un=(
ΣUn
i
)/N
Resultant mean wind direction,
Θu:
Θu=Arctan (Ue/Un)
Standard deviation of wind direction,
σ(Θu), using Campbell Scientific
algorithm:
σ(Θu)=81(1-
U
Cos U / s ; where
ii
(') '
/S)
1/2
The algorithm for σ(θu) is developed by noting (Figure 6.4-4) that
Θ
Θ
Θ
Θ
iii
u
=
=
U
U
i
u
Θ
'
i
Θ
s
i
FIGURE 6.2-3. Standard Deviation of Direction
The Taylor Series for the Cosine function, truncated after 2 terms is:
Cos ( ') ( ') /ΘΘ
ii
≅−12
2
6-38
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