Wind resource and site assessment - Wind Power Generation and Wind Turbine Design - page 53

sound speed and subtracted from the other direction. If the distance of the trans-
ducers is given with s and the velocity of sound with c then the travelling times
can be expressed as

s s

t = and t = (1)

1

2

cu + cu −

These equations can be re-arranged to eliminate c and to express the wind speed
u as a function of t 1 , t 2 and s . The sole dependency on the path length is advanta-
geous, as the speed of sound depends on air density and humidity:

s ⎛ 11 ⎞

u = − (2)

⎜ ⎟

2 ⎝ t t ⎠

1 2

It can be seen that once u is known, c can be calculated and from c the tempera-
ture can be inferred (slightly contaminated with humidity, this is known as the
“sound virtual temperature”). The spatial resolution is determined by the path
length between the transducers, which is typically 10-20 cm. Due to the very fi ne
temporal resolution of 20 Hz or better the sonic anemometer is very well suited for
measurements of turbulence with much better temporal and spatial resolution than
cup anemometry.
The measurement of different components of the wind, the lack of moving parts,
and the high temporal resolutions make the ultrasonic anemometer a very attrac-
tive wind speed measurement device. The major concern, inherent in sonic ane-
mometry, is the fact that the probe head itself distorts the fl ow - the effect of which
can only be evaluated in detail by a comprehensive wind tunnel investigation. The
transducer shadow effect is a particularly simple case of fl ow distortion and a well-
known source of error in sonics with horizontal sound paths. Less well known are
the errors associated with inaccuracies in probe head geometry and the tempera-
ture sensitivity of the sound transducers. The measurement is very sensitive to
small variations in the geometry, either due to temperature variations and/or
mechanical vibrations due to wind. Finally, specifi c details in the design of a given
probe head may give rise to wind speed-dependent errors.

2.2.4 Propeller anemometer
A propeller anemometer typically has four helicoid-shaped blades. This propeller
can either be mounted in conjunction with a wind vane or in a fi xed two- or three-
dimensional arrangement (Fig. 1). While a cup anemometer responds to the dif-
ferential drag force, both drag and lift forces act to turn the propeller anemometer.
Similar to a cup anemometer the response of the propeller anemometer to slow
speed variations is linear above the starting threshold.
Propeller anemometers have an angular response that deviates from cosine. In fact
the wind speed measured is somewhat less than the horizontal component [5]. If a
propeller is used in conjunction with a vane the propeller is in theory on average
oriented into the wind and thus the angular response is not so relevant. However,
the vane often shows an over-critical damping which leads to misalignment and