Campbell Scientific CR9000X Measurement and Control System - Manual (Page 221)

Section 6. Data Table Declarations and Output Processing Instructions
Calculations:
The calculations performed under the hood by the WindVector
instruction are described below for informational purposes only. NOTE
FIGURE 6.4-2. Input Sample Vectors
In Figure 6.4-2, the short, head-to-tail vectors are the input sample vectors
described by and
s
i
Θ
i
, the sample speed and direction, or by Ue
i
and Un
i
, the
east and north components of the sample vector. At the end of output interval
T, the sum of the sample vectors is described by a vector of magnitude U and
direction
Θu. If the input sample interval is t, the number of samples in output
interval T is N T t = / . The mean vector magnitude is U U N = / .
Scalar mean horizontal wind speed, S:
S=( Σs
i
)/N
where in the case of orthogonal sensors:
S
i
=(Ue
i
2 +Uni 2 ) 1/2
Unit vector mean wind direction, Θ1:
Θ1=Arctan (Ux/Uy)
where
Ux=( Σsin Θ
i
)/N
Uy=( Σcos Θ
i
)/N
or, in the case of orthogonal sensors
Ux=( Σ(Ue
i
/U
i
))/N
Uy=( Σ(Un
i
/U
i
))/N
where U
i
=(Ue
i
2 +Un
i
2 ) 1/2
Standard deviation of wind direction, σ(Θ1), using Yamartino algorithm:
σ(Θ1)=arc sin(ε)[1+0.1547 ε 3 ]
where,
ε=[1-((Ux) 2 +(Uy) 2 )] 1/2
s
n
Θu
s
2
North
U
s
4
s s
3 1
East
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