
ZENO
®
-3200 USER MANUAL
Coastal Environmental Systems (206) 682-6048 Page D-11
x
y
usx
vsy
ii
ii
iii
iii
sin ;
cos ;
;
;
giving x
i
and y
i
, the unit vector components corresponding to east and north respectively, and u
i
and v
i
, the
wind speed vector components. The vector components are summed over the averaging period, and the
vector averages are computed at the end of the averaging interval:
X
N
x
Y
N
y
U
N
u
V
N
v
i
i
N
i
i
N
i
i
N
i
i
N
1
1
1
1
1
1
1
1
;
;
;
.
The X, Y, U and V terms are available as outputs 8 and 9. These are used to compute the vector average
wind speed (S
V
), vector average independent wind direction (
VI
), vector average component wind
direction (
VC
), outputs 1, 2 and 12 respectively:
U
V
X
Y
VUS
VC
VI
V
arctan
arctan
22
When the arctangent is taken, the result is calculated to provide a full four-quadrant result with the range
0-360.
The (scalar) average wind speed S
S
, output 3, is computed from the speed measurements alone:
S
N
s
Si
i
N
1
1
.
The average wind speed is always larger than the vector average wind speed. However, S
S
is usually
only a few percent greater than S
V
and it serves as a backup measurement if the compass or vane fails and
S
V
is invalidated.
The standard deviation of the wind direction
, output 6 (also known as sigma-theta), is based on the
time series of wind direction measurements,
i
.and the average wind direction,
V
. A formal definition
of
is:
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