20
SYSTEM
For a given sound path length,
d
(m), the number of wavelengths,
n
, in still air is
determined with
.
Equation 4
n
c
vd
=
Here
v
is the frequency of the sound (Hz). When the air is moving, the sound speed is the sum
of the wind speed and the speed of sound in still air. The anemometer transmits a sound
pulse in a forward direction, then a similar pulse in the reverse direction. The difference in n
between the two points is computed. If the vector magnitude of the wind in the direction of
the sound is
u
(m/s), then
Equation 5
n
n
c
u
vd
D
-
= +
+
Equation 6
n
n
c
u
vd
D
-
= -
-
for sound traveling with and against the wind. Subtracting the result of
from the
results of
creates
Equation 7
n
n
n
c
u
vdu
2
2
2
D
D
D
=
+
=
-
-
+
Even at the maximum wind speeds for the anemometer,
u
2
is only about 1% of
c
2
, so the
equation can be simplified as shown in
Equation 8
x
vd
c
n
2
2
,
D
This is the basic equation for the anemometer. Delta (
∆
)
n
is proportional to the phase
difference between the forward and reverse sound pulses. The sound comes from a
40 kHz ultrasonic transducer in the head of the anemometer. A sound pulse is transmitted
diagonally across the anemometer, bouncing off a sintered glass disk in the center. The
sound pulse is then received by another transducer in the anemometer head that is
opposite the first. Once the sound pulse is received, the receiver becomes the transmitter
and the process is repeated. Two more sensors, mounted at 90 degrees from the first
two, give the other horizontal component of the wind. The sound travels a total distance
of about 72 mm from transmitter to receiver, but
d
in the equations is just the horizontal
distance, which is 40 mm.
If
u
is the magnitude of the wind vector in the east-west direction (east +) and
v
is the magnitude
in the north-south direction (north +), then wind speed is computed with
.
Equation 9
S
u
v
2
2
=
+
Where the overbar indicates an average of the values sampled every 10 seconds, wind speed
is computed with
Equation 10
( / )
tan
v u
1
i
=
-
