Chapter 7: Anemometry
Methods of Measurement:
wind force
heat dissipation
speed of sound
calibration
exposure
wind data processing
Anemometer notes
Wind Measurement
The function of an anemometer is to measure some or all
components of the wind velocity vector.
It is common to express the wind as a two-dimensional
horizontal vector since the vertical component of the wind
speed is usually small near the earth’s surface.
Sometimes it is important to consider the vertical
component of the wind and then the wind vector is three
dimensional.
The vector can be written as orthogonal components (u, v,
and w) where each component is the wind speed
component blowing in the North, East, or vertically up
direction.
Wind Measurement
The vector can be written as a speed and a direction.
In the horizontal case, the wind direction is the direction from
which the wind is blowing measured in degrees clockwise
from the north.
The wind vector can be expressed in three dimensions as
the speed, direction in the horizontal plane as above, and
the elevation angle.
Standard units for wind speed are m s-1 and knots (nautical
miles per hour).
WMO standard is 10 min average.
Methods of measurement
What would the ideal wind sensor be like?
The ideal wind-measuring instrument would respond to the
slightest breeze yet be rugged enough to withstand hurricane
force winds.
It would respond to rapidly changing turbulent fluctuations,
have a linear output, and exhibit simple dynamic performance
characteristics.
It is difficult to build sensors that will continue to respond to
wind speeds as they approach zero or will survive as winds
become very large. Thus a variety of wind sensor designs and
within a specific design type, a spectrum of implementations
have evolved to meet our needs.
Wind force:
The drag force of the wind on an object, which we have all
experienced, can be written as
Fd= ½(Cd ρAV2)
Cd = drag coefficient, a function of the shape of the device and of the
wind speed. It is dimensionless and 0< Cd <1.
The dependence of the drag coefficient on wind speed is weak over a
wide range of wind speeds and is therefore often assigned a value that
is a function of shape alone.
The air density ρ, has units of kg m-3 the cross-section area of the
sensor A in in m2 while V is the wind speed, m s-1.
For some sensors, the wind speed must be taken as a vector quantity
and then V2 is replaced by V|V|.
Cup and Propeller Anemometers
Cup anemometer turns in the wind because the drag
coefficient of the open cup face is greater than the drag
coefficient of the smooth, curved surface of the back of the
cup.
Cup and Propeller Anemometers
Cup anemometer turns in the wind because the drag
coefficient of the open cup face is greater than the drag
coefficient of the smooth, curved surface of the back of the
cup (7-1).
Before the cup anemometer starts to turn, the effective wind
speed is just Vi.
Then as the cup wheel rotates, the effective speed is the
relative speed Vi-S for the cup (on the left in Fig 7-1) and
Vi+S for the cup on the right.
But, the difference in drag coefficients dominates, so the
cup continues to turn.
Figure 7-1. Wind Force acting on cups
R
S
S
Vi + S
Wind Speed, Vi
Cup and Propeller Anemometers
The raw output of a cup or propeller anemometer is the
mechanical rotation rate of the cup wheel (and supporting
shaft).
Speed
Cup/Prop
Shaft Rotation
Frequency
The static sensitivity, nearly constant above the threshold
speed, is a function of the cup wheel or propeller design.
Threshold Speed: is defined as the wind speed that first
moves the cup. This is the anemometers threshold. Most
are on the order of ~0.2 – 1 m s-1.
Cup and Propeller Anemometers
Typical values of static sensitivity are 30-60 rpm/m s-1 for
cups and 180-210 rpm/m s-1 for propellers.
A propeller always rotates faster than a cup wheel in the
same wind.
While a cup wheel responds to the differential drag force,
both the drag and lift forces act to turn a propeller.
The shaft of an anemometer is coupled to an electrical
transducer which produces an electrical output signal,
typically a DC voltage proportional to shaft rotation rate and
therefore to wind speed.
Cup and Propeller Anemometers
The shaft of an anemometer is coupled to an electrical
transducer which produces an electrical output signal,
typically a DC voltage proportional to shaft rotation rate and
therefore to wind speed.
An AC transducer may be used which produces an AC
voltage with amplitude and frequency proportional to
rotation rate.
Another option is an optical transducer that generates a
series of pulses as an optical beam is interrupted. The pulse
rate is proportional to rotation rate.
Cup and Propeller Anemometers: Threshold
Cup and propeller anemometers are linear over most of
their range, with a notable exception at the lower end of the
range.
Since anemometers are driven by wind force which is
proportional to the square of the wind speed, there is very
little wind force to overcome internal friction when the wind
approaches zero.
This wind speed, called the threshold wind speed, below
which the anemometer will not turn.
The starting threshold for wind speed slowly increases from
zero is much higher than the stopping threshold.
Cup rotation rate (Hz)
Figure 7-3
1
2
3
4
Wind Speed Tunnel (m/s)
5
Cup and Propeller Anemometers: Threshold
This is because the running friction is much less than static
friction.
Despite this, the lower range limit is often defined to be
zero.
The upper limit is the maximum wind speed the
anemometer can sustain without damage.
Wind Vane
A wind vane is a flat plate or airfoil that can rotate about a
vertical shaft and, in static equilibrium, is oriented along the
wind vector.
There is usually a counter weight to balance the vane about
the vertical shaft.
The most common electrical transducer is a simple pot
(potentiometer) mounted concentrically with the vertical
shaft to convert azimuth angle (0° - 360°) to a voltage
proportional to that angle.
The only source of static error is misalignment of the vane.
While it is fairly easy to align a vane to true North, human
error frequently causes misalignment.
Wind Vane
A vane uses a combination of the lift and drag forces on the
vane to align itself with the wind vector.
Since the vane has a moment of inertia and aerodynamic
damping, there is a dynamic misalignment error due to the
changing wind direction. See Equation 7.7.
Wind Vector
R
Vane
Vertical axis of rotation
Wind Vane
The ideal wind vane would have the following characteristics:
Low friction bearing
Statically balanced (using counterweight)
Maximum wind torque and minimum moment of inertia
Damping ratio  0.3
Low threshold wind speed (0.5 m/s)
Rugged design capable of wind speeds up to 90 m/s.
(hurricane survival)
Maintenance requirements are simple:
Verify low bearing friction
Verify mechanical integrity (check for bent vane arm)
Verify alignment to North
Verify proper operation of transducer.
Pitot-Static Tube
The pitot-static tube is actually a pair of concentric tubes.
The stagnation port, at the end of the tube, is a blunt
obstacle to airflow and therefore the drag coefficient is unity.
The static port is located at a point far enough back along
the tube to have no dynamic flow effects at all, so the
pressure observed there is just the ambient atmospheric
pressure.
The pitot-static tube must be oriented into the airflow. A
typical tube will tolerate misalignment errors up to ±20°.
But it is this alignment problem that makes them virtually
unsuitable for atmospheric work!
Pitot-Static Tube
Static ports
wind
Stagnation port
P-static
Vi
Pitot-Static
P-stagnation
P-static
P-stagnation
Pitot-Static Tube
They are ideal for wind tunnels and are frequently used to
calibrate other anemometers.
p-static = p, the ambient atmospheric pressure
p-stagnation = 0.5ρV2 + p, thus the differential pressure,
Δp=(p-stagnation)-(p-static) = 0.5 ρV2 .
The calibration equation is
V
2p
p
 2 RT

p
Pitot-Static Tube
The calibration being a function of atmospheric pressure
and temperature since ρ=p/RT. Since R is the gas constant
of dry air, humidity will have an effect, but less than 1%.
The Pitot-Static probe is inexpensive but requires highquality differential pressure sensor to convert the Δp to a
useable signal.
Heat Dissipation
Hot-wire and hot-film anemometers are used to infer the
wind speed from the cooling of a heated wire or film, which
is dependent on the mass flow rate (speed and density of
the flow) past the sensing element.
The response speed of wires and films is a function of the
thermal mass of the element.
Hot wires are the fastest conventional wind sensors
available since they can use very fine platinum wires (down
to 5 μm)!
Frequency response is 10-100 Hz!
Heat Dissipation
In a wire operated in the constant temperature mode, the
current I through the sensor is related to the wind speed by
King’s law:
I2  A B V
Where A and B are constants. The equation is applicable
above some threshold flow rate that can be as great as 5
m/s.
Hot-wire and hot-film anemometers are expensive and
power hungry.
Definitions
Distance constant: is the distance air flow past a rotating
anemometer during the time it takes the cup wheel or
propeller to reach 63.2% of the equilibrium speed after a
step change in the input wind speed. =Vi
Starting Threshold of a cup or propeller anemometer is the
lowest wind speed at which the anemometer, initially
stopped, starts and continues to turn and produces a
measurable signal.
Wind run is the average of the scalar wind speed. Direction
is ignored.