Campbell Scientific IRGASON IRGASON Integrated CO2/H2O Open-Path Gas Analyzer - Page 51

Theory of Operation, 11.1 IRGASON Sonic Anemometer, 11.1.1 Wind Speed

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IRGASON® Integrated CO2/H2O Open-Path Gas Analyzer and 3D Sonic Anemometer 11. Theory of Operation 11.1 IRGASON Sonic Anemometer The CSAT3 measures wind speeds and the speed of sound by determining the time of flight of sound between pairs of transducers. However, unlike many other commercial anemometers, it does not use simple threshold detection to determine the ultrasonic times of flight. Instead, it uses advanced digital signal processing techniques to determine the arrival of the transmitted ultrasonic signal. In comparison to other systems, the digital signal processing techniques result in more accurate, lower noise measurements. 11.1.1 Wind Speed Each axis of the sonic anemometer pulses two ultrasonic signals in opposite directions. The time of flight of the first signal (out) is given by: d to = c + ua (1) and the time of flight of the second signal (back) is given by: d tb = c - ua (2) where to is the time of flight out along the transducer axis, tb is the time of flight back, in the opposite direction, ua is the wind speed along the transducer axis, d is the distance between the transducers, and c is the speed of sound. The wind speed, ua, along any axis can be found by inverting the above relationships, subtracting Eq. (2) from (1), and solving for ua. ua = d   1 2  to − 1 tb    (3) The wind speed is measured on all three non-orthogonal axes to give ua, ub, and uc, where the subscripts a, b, and c refer to the non-orthogonal sonic axes. The non-orthogonal wind speed components are then transformed into orthogonal wind speed components, ux, uy, and uz, with the following: u  x   ua   uy  = Aub  uz  uc  (4) where A is a 3 x 3 coordinate transformation matrix, that is unique for each CSAT3 and is stored in ROM memory. 41

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IRGASON
®
Integrated CO
2
/H
2
O Open-Path Gas Analyzer and 3D Sonic Anemometer
11. Theory of Operation
11.1 IRGASON Sonic Anemometer
The CSAT3 measures wind speeds and the speed of sound by determining the
time of flight of sound between pairs of transducers.
However, unlike many
other commercial anemometers, it does not use simple threshold detection to
determine the ultrasonic times of flight.
Instead, it uses advanced digital signal
processing techniques to determine the arrival of the transmitted ultrasonic
signal.
In comparison to other systems, the digital signal processing techniques
result in more accurate, lower noise measurements.
11.1.1 Wind Speed
Each axis of the sonic anemometer pulses two ultrasonic signals in opposite
directions. The time of flight of the first signal (out) is given by:
t
d
c
u
o
a
=
+
(1)
and the time of flight of the second signal (back) is given by:
t
d
cu
b
=
-
a
(2)
where t
o
is the time of flight out along the transducer axis, t
b
is the time of
flight back, in the opposite direction, u
a
is the wind speed along the transducer
axis, d is the distance between the transducers, and c is the speed of sound.
The wind speed, u
a
, along any axis can be found by inverting the above
relationships, subtracting Eq. (2) from (1), and solving for u
a
.
u
d
t
t
a
o
b
=
−
2
1
1
(3)
The wind speed is measured on all three non-orthogonal axes to give u
a
, u
b
, and
u
c
, where the subscripts a, b, and c refer to the non-orthogonal sonic axes.
The non-orthogonal wind speed components are then transformed into
orthogonal wind speed components, u
x
, u
y
, and u
z,
with the following:
u
u
u
A
u
u
u
x
y
z
a
b
c
=
(4)
where A is a 3 x 3 coordinate transformation matrix, that is unique for each
CSAT3 and is stored in ROM memory.
41