Basics of wind measurement technology

1. Basics
Unlike most meteorological quantities, which are scalars, wind speed is a vector. Therefore, to fully determine it, three pieces of information are needed: either the three components or the magnitude and the direction (determined by two angles). However, since the vertical component (at least on average) is usually very small compared to the horizontal components of wind speed, making measuring the vertical component quite difficult, wind speed is usually understood to mean the horizontal component. To determine this, two pieces of information are sufficient: either the two components (NS, WO) or the magnitude and direction. One characteristic of wind that is particularly noticeable at high wind speeds is its gustiness. According to these two components, a distinction is made between the gustiness of the wind direction and the gustiness of the wind speed.

2. Determining the wind direction
The direction of the surface wind can be roughly estimated without special tools. This can be more accurately determined with smoke plumes, provided several chimneys are somewhat distributed in the wind direction. The wind direction is always the direction from which the wind is coming. For a more precise indication and, in particular, for recording the wind direction, wind vanes are used, whose position is transmitted mechanically or electrically (contact, resistance, or rotating field sensors) to the display or recording device. When setting them up, particular care must be taken to ensure that they do not have a preferred position, which would otherwise indicate the direction incorrectly—especially in light winds.
In addition to specifying wind direction according to the four cardinal directions and their subdivisions, it is common, especially in the synoptic service, to specify wind direction in degrees, omitting the units due to the inaccuracy of the determination (gustiness). The following correspond to each other:

The value 00 refers to calm winds.

3.0 Determining the wind speed
Wind speed can also be estimated without any special tools. It is then given either according to the Beaufort scale or in equivalent speed values.
The individual levels of the Beaufort scale are assigned to characteristic effects of wind on land (smoke, trees, etc.) and at sea (waves). The ranges given in the table in ms"1 apply to an anemometer at a height of 6 m. They can be easily converted into other units.

In the synoptic service, wind speed is usually given in knots (= nautical miles/hour).

The obvious method of determining wind speed by marking the air and tracking the movement of the marker is used in aerological wind measurements—apart from occasional measurements of this kind, such as in micrometeorological studies with smoke balls, small balloons, and others. Here, one targets either a transmitter (radio transmitter) attached to the balloon or a reflector (radar), calculates the balloon's path, and from this, determines the magnitude and direction of the wind at the respective altitude. This method of measuring wind using markers can also include estimating wind direction and speed using cloud mirrors.
For most wind speed measurements, indirect methods are used, meaning that the strength of the wind is inferred from the magnitude of the wind's effects. These are primarily dynamic pressure and heat transfer (cooling), which form the basis of the most commonly used wind speed measurement methods. Closely related to heat transfer are the occasionally used mass transfer (evaporation) and the friction that sometimes plays a role in dynamic pressure measurement methods. Finally, sound propagation should be mentioned. Compared to the first two methods mentioned, the methods listed later play a subordinate role.

3.1 The dynamic pressure measurement methods
The most common device for measuring wind speed using the ram-pressure method is the Prandtl Pitot tube. It consists of two tubes pushed inside each other (see drawing). The inner tube is open at the front (pitot nozzle) and sealed off from the outer tube. The outer tube ends in a hemisphere into which the open inner tube opens. Behind the pitot nozzle, the outer tube has an annular slit (annular nozzle) or two or more small holes. According to the laws of aerodynamics, the excess pressure p _s (ram pressure) on a surface perpendicular to the wind is

p _s = 0.5-p _L -v ² . (1)

Where v is the wind speed and p _L is the air density.
The total pressure p ₁ at the tip of the pitot tube is composed of the dynamic pressure p _s and the static air pressure p ₀

p ₁ = p _s + p ₀ (2)

The pressure at the cylinder wall of the outer tube, p2, is, since there is no back pressure there, equal to the static air pressure p0 minus a negative pressure proportional to the back pressure, which is so small that it can be neglected due to the special design of the Prandtl Pitot tube.

p ₂ = p ₀ - (3)

The difference between the two pressures P2 and pi is

Δp = p ₁ - p ₂ = 0.5-p _L -v ² (4)

proportional to the square of the wind speed. If pL is known, then from the pressure difference Δ one can

v=√[(2 •Δp) / p _L ]

V p _l directly calculate the wind speed v.
Compared to the usual air pressure, Δp is small. For 10 °C, 1013 hPa (p _L = 1.25 kg-m _-3 ) one finds

Δp is also often given in mm WS (1 millimeter water column = 9.81 Pa).

The pressure on the pitot tube p ₁ and the pressure on the annular nozzle p ₂ are transmitted via hoses to a differential micromanometer. This essentially corresponds to a communicating tube (U-tube). If p ₁ acts on one side of the fluid in the tube and p ₂ on the other, the fluid in the leg with the lower pressure will rise until the pressure difference caused by the level difference in the fluid is equal to the dynamic pressure Δp. Since Δp is very small, one leg of the micromanometer is inclined. If α is the angle of inclination, ρ _F is the density of the filling fluid, and ΔI is the displacement of the end of the fluid thread at a constant level in the second leg, which is therefore designed as a wide trough, the pressure difference is

Δp = ρ _F -g-ΔI-sin(α). (6)

The movable arm can be fixed at several different angles of inclination. Colored alcohol (ρ _F = 791 kg-m _-3 ) is used as the filling fluid of the micromanometer. For the most sensitive setting of the micromanometer used (sin(α) = 1/25 = 0.04), the numerical equation is found at 20 °C and 960 hPa.

v = 0.7438 √Δl. (7)

It yields v in ms ^-1 , if ΔI is used in mm (alcohol column). Therefore, at low wind speeds (v<0.7 ms ^-1 ), one can hardly expect good measurement values, in contrast to high wind speeds.
The micromanometer described here is not suitable for recording. Ring balances and immersion tubes are primarily used for this purpose. With the latter, the reading can even be linearized by appropriately shaping the immersion bell, into which pi is directed while p2 prevails outside. However, the deflection is also hardly useful for real measurements at v < 1 ms ^-1 . Since Δp can only be calculated with the Pitot tube in equation (5) if the nozzle points in the wind direction (directional deviations of up to ±15° still result in tolerable errors), the Pitot tubes at meteorological stations are coupled to a wind vane.
Externally, a flow probe is very similar to a Pitot tube, except that in this case, air flows through the tube. The air enters the tube at the pitot nozzle, flows through a measuring chamber, and exits the device via the annular nozzle. In the measuring chamber, the flow deflects a pair of vanes (due to the effects of dynamic pressure and friction) against the restoring force of a spring. The deflection, readable using a pointer connected to the pair of vanes, is a measure of the wind speed being measured. Different measuring ranges can be set using nozzles in the flow path.

The effect of dynamic pressure is also the basis for wind indicators using wind plates, which are probably the oldest anemometer in existence and consist of vertically suspended plates that are lifted by the wind. Their deviation from the vertical is a rough measure of wind speed. These are rarely used in practice today. However, tethered cup anemometers, i.e. cup anemometers with many (up to 12) cups that can only rotate about their axis to a limited extent, are still in use today. The torque caused by the dynamic pressure is compensated by a spring, so that the deflection (angle of rotation) is a measure of wind speed. Because of the quadratic relationship between dynamic pressure and wind speed, the angle of rotation is a quadratic function of the wind speed.


3.2 The rotating cup anemometers
Rotating cup anemometers are also based on the dynamic pressure effect, but represent a separate group due to the linear relationship between the primary measurement variable (rotational frequency) and wind speed. They carry a star of three or four, usually hemispherical, cups on a vertical axis. In a flow, they rotate around the axis. Since the cups are in a different position relative to the flow at every moment of the cup's rotation, the temporal progression of the dynamic pressure acting on them is a very complex function.
For simplicity, consider two opposing shells whose arms are perpendicular to the wind. The shell cross has a constant rotational frequency v corresponding to the wind speed v. Where r is the distance of the shell center from the anemometer axis, then u = 2-r-π-v is the orbital velocity of the shell center. Since the shell cross rotates in such a way that the instantaneous velocity of the shell concave towards the wind has the same direction as the wind itself, the relative velocity of the wind to the shell, which determines the dynamic pressure, is given by (vu). On the other hand, the shell convex towards the wind moves against the wind. For this shell, the relative velocity of the wind to the shell is therefore given by (v + u). In both cases, the dynamic pressure is proportional to the square of the relative velocities. In the stationary rotational state considered here, the oppositely directed torques emanating from the two opposing shells must be equal, apart from friction (axis bearing). Otherwise, an acceleration (change in speed) would occur, which contradicts the assumption of steady-state conditions. This torque is the product of the distance from the shell center r and the force acting on the shell due to the dynamic pressure. This force is proportional to the dynamic pressure. However, the proportionality factor f is larger for the concave shell (f1) than for the convex shell (f2).

The equilibrium condition is:

f _i -r• 0.5•p _L •(v - u) ² = f ₂ -r • 0.5 •p _L •(v + u) ² . (8)

This means

V = [(√ f ₁ +&radicf ₂ )/(√f ₁ -&radicf ₂ )]• and

The orbital velocity u of the shells and thus the rotation frequency of the axis of the shell cross v = u/(2-r-π) is proportional to the wind speed v. The proportionality factor in equation (9) has values ​​around 2.6 for conventional shell crosses with hemispherical shells. From this, one finds f ₁ /f ₂ ~ 5. This means that when the shell cross is at rest (u = 0), the force on the concave hemisphere is five times greater than on the convex hemisphere (wind shear).
In the above derivation, the absence of friction was assumed. In reality, of course, friction cannot be neglected, and a friction term must be included in the equilibrium condition equation (8). Although friction is practically unnoticeable at high wind speeds, it causes u = 0 when v > 0 ; this means that the cup cross no longer moves at low wind speeds. In practice, the approach

v = a + bu (10)

proved to be sufficiently accurate, where v < au = 0. a is called the starting velocity, although the cup cross usually starts from rest at a somewhat higher v. For conventional cup crosses, a has values ​​between 0.2 and 1 ms"1, b the value of 2.6 already mentioned above.
Due to friction, cup anemometers cannot measure wind speeds below a at all, and those slightly above a can only be measured incorrectly. Therefore, attempts are being made to reduce a, which is possible through smooth-running bearings, revolution counting with light barriers, reducing the weight of the cups, and other methods. However, this is limited by the necessary robustness of the cup anemometer.
The above equations apply to a time-constant v. When v changes rapidly, i.e., in gusty winds, inertia becomes noticeable. This causes the recorded wind speed to be smoother than the actual wind speed. Furthermore, cup anemometers adapt more quickly to increasing v than to decreasing v (f ₁ <=> 5 •f ₂ ), so that in gusty winds the calculated mean value is higher than the true mean. Despite these disadvantages, cup anemometers are widely used. This is due not only to their ease of recording but above all to the fact that their readings are independent of wind direction.
A frequently used variant of the cup anemometer is the contact anemometer, which is still used today in inaccessible terrain without connection to the public power grid (battery operation). The rotation is transmitted via a worm gear to a contact wheel, which closes an electrical contact after N revolutions. To prevent the contact from becoming stuck (and the battery running out), drop contacts are installed that only close briefly. If n is the contact frequency, the rotation frequency is v = Nn and the orbital speed is u = 2 • r • π •v = 2 •r •π •N •n. Inserted into the anemometer equation (10), this results in

c = 2-rnNb (11)

the equation

v = a + 2 • r • π • v • b = a + 2 • r • π • N• b • n= a + c • n. (12)

The wind path is sometimes specified for an anemometer. It is defined as the distance w that a quantum of air must travel to produce the effect of, for example, N = 50 revolutions of the cup anemometer:

w = (N • v) / v. (13)

For individual measurements, the time between two or more contacts can be recorded. For recording, the contact is used to write a mark on the paper of a chronograph. Conventional chronographs have a drum that rotates once around its vertical axis every hour. At the same time, the pen is lowered by about 1 cm, so that a spiral appears on the paper bearing the contact marks. By reading the time between two contacts (fine evaluation) or counting the contacts every quarter of an hour or hour (rough evaluation), the temporal variation of the wind speed can be obtained using the calibration curve corresponding to equation (12).
Modern cup anemometers are generally equipped with light barriers or inductive pulse generators that emit one or more electrical pulses per rotation of the cup anemometer. By counting these pulses in electronic or electromechanical counters over a specific period of time (usually 10 minutes or 1 hour), temporal averages of wind speed are obtained. The wind speed can be displayed in any desired unit (ms-1, km-h-1, knots) using special digital electronic control circuits (in the simplest case, by interposing electronic scalers) or microprocessors.
A direct reading is possible with cup-shaped hand anemometers, which generate the pointer deflection mechanically using centrifugal action.
If a dynamo is placed on the axis of the cup cross, the generated voltage is proportional to the rotational frequency and thus to v. V can then be read directly from a suitably calibrated voltmeter or recorded with an electric recorder (gust recorder).
Vane anemometers are related to cup anemometers. Here, the wind drives a vane similar to a windmill wheel. The rotational frequency of these anemometers is also proportional to the wind speed. Their initial speed is usually lower than that of cup anemometers. In meteorology, however, they are practically only used as handheld anemometers, as they are direction-dependent and their axis must always point in the wind direction.


3.3 The thermal anemometers
If a body is heated (e.g. electrically), the difference between body temperature and air temperature depends on the heat transfer coefficient ai_ and thus on the wind speed v (see task 2). The sensor is either a thin wire clamped between two tips (hot-wire anemometer) or a thin metal film made of platinum or tungsten applied to a quartz or ceramic body of various geometries (hot-film probe). The heat dissipated by the flow (cooling variable) is a measure of the velocity of the incoming medium. The very complex relationship between particle velocity and heat dissipation generally has to be determined experimentally for the individual probe types, i.e., each sensor is calibrated. For thermal equilibrium, the heat loss (cooling) of the hot wire is equal to the supplied electrical power. For hot-wire and hot-film probes, this relationship can be expressed by the equation

R _v /(R _v -R ₀ ) J ² = a + b • v ^1/n (14)

where R _v is the warm or operating resistance of the probe, R ₀ is the probe resistance at medium temperature, J is the heating current, and v is the flow velocity. The constants a, b, and n (= 2 ... 2.5) depend on the probe shape. With a constant heating current (constant current anemometer), the operating resistance of the probe changes depending on the wind speed.
In the simplest design, the hot-wire or hot-film probe exposed to the air flow is located in one branch of a Wheatstone bridge circuit. The almost constant bridge current heats the probe by Δθ = 100 K to 300 K relative to the air temperature θ _L . The remaining bridge resistors are temperature-independent, so that the temperature or the operating resistance R _v can be measured as a function of the wind speed via the bridge output voltage.
In order to describe the behavior of the hot wire with respect to wind fluctuations, the empirically determined equation (14) must be supplemented by an additional term that takes into account the thermal inertia of the measuring probe. The following approximate equation is found for a hot wire probe:

R _v /(R _v -R ₀ ) J ² = a + b • v ^1/n + C/(R _v -R ₀ )• (dR _v / dt)

Herein is

c = C/(α • R ₀

the modified heat capacity of the wire with its heat capacity C and its temperature coefficient a of resistance. The integration of this differential equation ultimately leads to an equation for the time constant τ, according to which the anemometer has adjusted to the new wind speed value to within 1/e after a sudden change in wind speed.

τ = (R _v • c)/(R ₀ • ( a + b • v ^1/n )) (17)

The time constant τ is proportional to the modified heat capacity and the resistance ratio rv/ro of the probe, where Rv is the long-term average of the sensor's operating resistance at a given average speed. Furthermore, t decreases with increasing wind speed. With a constant-current anemometer, inertia times of the order of 10 ms ^-1 are typically obtained at wind speeds around 10 ms ^-1 .
In contrast to constant-current anemometers, where the bridge current J is constant, in constant-temperature anemometers the amount of heat dissipated is always compensated by a change in the bridge current, so that the probe is held at the set overheating temperature or a specific resistance. In this case, the supplied heating power or - since the bridge resistances are constant - the bridge supply voltage is a measure of the wind speed. In principle, the constant-temperature anemometer consists of a Wheatstone bridge circuit, whose error voltage, caused by the cooling of the probe, is amplified by a servo amplifier and fed back into the bridge circuit in phase. This reheats the probe and automatically compensates for the error voltage. In this operating mode, it can be said that the inertia time characteristic of the anemometer can be reduced by a factor of 0.5 rS. Here, S is the slope of the servo amplifier and r is a variable dependent on the sensor resistance and the overheating ratio. This allows inertia times in the order of 2 -10 µs to be achieved.
In both constant-temperature and constant-current anemometers, the probes respond to any change in heat dissipation, including changes in air temperature. Therefore, high operating temperatures (approximately 200-300 K above air temperature) are desired for the probes to keep the relative temperature error small. However, if the air temperatures differ significantly between calibration and measurement, the influence of temperature must still be taken into account or eliminated using suitable compensation circuits with a temperature sensor.
The nonlinear relationship between the measured variable and wind speed (v - J - ²ⁿ √v, where n can take values ​​between 2 and 2.5 depending on the probe type) no longer poses any difficulties in modern data processing. In devices with optical wind speed displays, the measured value is often linearized using logarithmic amplifiers.
Hot-wire probes are directionally sensitive and have their maximum sensitivity for perpendicular flow. In the angle of attack range of 45° < 0 < 135°, the effective wind speed can be approximated by:

v _eff = v • sin(θ). (18)

This effect is particularly exploited in turbulence studies, for example, when the three-dimensional wind vector and its fluctuations are to be measured using three hot wires arranged perpendicular to each other, like the corners of a cube. Virtually all empirical knowledge about turbulence has been obtained using such devices.

3.4 Ultrasonic anemometer

An ultrasonic anemometer usually consists of four ultrasonic transmitters/receivers placed at the corners of a (virtual, i.e., open) tetrahedron. This device, also mounted on a mast, transmits ultrasonic waves from each of the four sensors to the other three sensors. The wind displaces the sound waves both horizontally and vertically, so that the sound reaches the next sensor with a corresponding time delay. From this delay, the measuring electronics calculates the horizontal and vertical wind speed. The advantages of the ultrasonic anemometer are its higher accuracy, the lack of inertia in the system, and the additional detection of the vertical wind component. Since the speed of sound is strongly dependent on the air temperature, the sound travel time is measured in both directions on each of the two measuring sections. This allows the influence of the temperature-dependent speed of sound on the measurement result to be eliminated by subtracting the reciprocals of the measured travel times. The measuring rate depends on the sound travel time on the measuring sections. With three measurement sections, each 20 centimeters long, measured consecutively in both directions, the total sound propagation time is approximately five milliseconds. This allows for up to 200 measurement cycles per second. A system developed for meteorological measurements is the SODAR, which allows vertical measurements and has the transmitter and receiver on the same plane.