Chapter 7: Anemometry

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Chapter 7 Anemometry Methods of
Measurement wind force heat dissipation speed
of sound calibration exposure wind data
processing Anemometer notes
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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 earths 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.
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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.
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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.
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Wind force The drag force of the wind on an
object, which we have all experienced, can be
written as Fd ½(Cd ?AV2) Cd drag
coefficient, a function of the shape of the
device and of the wind speed. It is
dimensionless and 0lt Cd lt1. 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 ?, 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 VV.
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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.
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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 ViS for
the cup on the right. But, the difference in
drag coefficients dominates, so the cup continues
to turn.
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Figure 7-1. Wind Force acting on cups
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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).
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.
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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.
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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.
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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.
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Figure 7-3
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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.
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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.
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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.
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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.
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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!
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Pitot-Static Tube
Static ports
wind
Stagnation port
P-static
P-stagnation
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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 0.5?V2 p,
thus the differential pressure,
?p(p-stagnation)-(p-static) 0.5 ?V2 . The
calibration equation is
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Pitot-Static Tube The calibration being a
function of atmospheric pressure and temperature
since ?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 high-quality differential pressure
sensor to convert the ?p to a useable signal.
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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!
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Heat Dissipation In a wire operated in the
constant temperature mode, the current I through
the sensor is related to the wind speed by Kings
law 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.
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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.
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