Specifications
Appendix B. Measurement Names and Meanings
B-6
Resultant mean wind direction, 4
4
u:
4u=Arctan (Ue/Un)
Standard deviation of wind direction,
V
(
4
u), using Campbell Scientific
algorithm:
V(4u)=81(1-
U
/S)
1/2
The algorithm for V(Tu) is developed by noting (FIGURE B-3) that
Cos U / s ; where
ii
(') '4444
iii
u
FIGURE B-3. Standard Deviation of Direction
The Taylor Series for the Cosine function, truncated after 2 terms is:
Cos ( ') ( ') /44
ii
#12
2
For deviations less than 40 degrees, the error in this approximation is less than
1%. At deviations of 60 degrees, the error is 10%.
The speed sample may be expressed as the deviation about the mean speed,
ss'S
ii
Equating the two expressions for Cos (T‘) and using the previous equation for
s
i
;
12
2
(')/ /(')4
iii
UsS
Solving for
(')4
i
2
, one obtains;
(') / (')'/ '/44
iiiii
U S sS sS
22
22 2
Summing
(')4
i
2
over N samples and dividing by N yields the variance of 4u.
Note that the sum of the last term equals 0.