Campbell Scientific CR5000 Measurement and Control Module - Manual (Page 125)

Section 6. Data Table Declarations and Output Processing Instructions
6-31
Resultant mean horizontal wind speed, U :
U =(Ue 2 +Un 2 ) 1/2
FIGURE 6.4-3. Mean Wind Vector
where for polar sensors:
Ue=(
Σ
S
i
Sin
Θ
i
)/N
Un=(
Σ
S
i
Cos
Θ
i
)/N
or, in the case of orthogonal sensors:
Ue=(
Σ
Ue
i
)/N
Un=(
Σ
Un
i
)/N
Resultant mean wind direction,
Θ Θ Θ Θ
u:
Θ
u=Arctan (Ue/Un)
Standard deviation of wind direction,
σσσσ
(
Θ Θ Θ Θ
u), using Campbell Scientific
algorithm:
σ
(
Θ
u)=81(1- U /S) 1/2
The algorithm for
σ
(
θ
u) is developed by noting (Figure 6.4-4) that
Cos U / s ; where
i i
( ' ) '
Θ Θ Θ Θ
i i i
u
= = −
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
U
Un
Ue
s
i
Θ
'
i
Θ
u
U
i
U