Campbell Scientific CR5000 Measurement and Control Module - Manual (Page 124)

Section 6. Data Table Declarations and Output Processing Instructions
6-30
Calculations:
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
s
i
and
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
Θ
u. 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=(
Σ
s
i
)/N
where in the case of orthogonal sensors:
S
i
=(Ue
i
2 +Uni 2 ) 1/2
Unit vector mean wind direction,
Θ
1:
Θ
1=Arctan (Ux/Uy)
where
Ux=(
Σ
sin
Θ
i
)/N
Uy=(
Σ
cos
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,
σσσσ
(
Θ Θ Θ Θ
1), using Yamartino algorithm:
σ
(
Θ
1)=arc sin(
ε
)[1+0.1547
ε 3 ]
where,
ε
=[1-((Ux) 2 +(Uy) 2 )] 1/2
and Ux and Uy are as defined above.
s
n
Θ
u
s
2
North
East
U
s
1
s
3
s
4