
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 Θu. If the input sample interval is t, the number of samples in output
interval
T
is
NTt
=
/
. The mean vector magnitude is
UUN
=
/
.
Scalar mean horizontal wind speed, S:
S=(Σs
i
)/N
where in the case of orthogonal sensors:
S
i
=(Ue
i
2
+Un
i
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
σσ
σ(Θ
ΘΘ
Θ1), using Yamartino algorithm:
σ(Θ1)=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
Θu
s
North
East
s
s
s
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