Campbell Scientific CR9000X Measurement and Control System - Manual (Page 222)

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
i i
( ') '
/S) 1/2
The algorithm for σ(θu) is developed by noting (Figure 6.4-4) that
Θ Θ Θ Θ
i i i
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 ( ') ( ') / Θ Θ
i i
≅ − 1 2 2
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