Angle of attack wind vane, or alfa beta construction drawings are available here.

Angle of attack can be measured by mean of a mechanical wind vane. Here below detail drawings for make your own vane, some dimensions can vary from this exposed example.

This kind wind of vane can be used as stand alone unit or integrated into an airdataboom or in a alfa-beta vane.

**Design**

- Wind vanes
- Null seeking devices
- Static-type devices, based exclusively on pressure measurement

Given an airspeed of 20 m/s and a maximum deflection of 20 mm at 10 Hz, the error is:

Another issue to be taken into account is that the motion of the mount at the wind vane mounting point can interact with the wind vane dynamics. To avoid performance degradation it is crucial to maintain the resonant frequencies of the two systems well apart.

The most critical component are the bearing. A Coulomb friction model will be used to describe their static friction.

**Synthesis**

Modeling the dynamics of the wind vane a second-order system as model, we end up with two significant parameters of the system: resonance frequency and damping. Initially, bearing and other sources of friction on the main shaft will be neglected. A known resonance frequency value is used to verify that the wind vane is not excited by other mechanical devices, as depicted in the previous section. Wind gusts are generally an intended source of AoA readings, but we must ensure that their frequency content

does not approach nor exceed the resonance frequency, so as the frequency response of our system has unity magnitude. Damping indicates how faster an excited oscillation decreases with time. The picture AoA 5a illustrates the time response of a second-order system, while varying the value of damping. Our wind vane will be underdamped, hence its damping value will lie withing the (0,1) range.

The following equation defines a second-order transfer function using common notation. Since our vane will be underdamped, the typical time response will be oscillatory, with an exponential time decay term which reduces the oscillation magnitude in time.

(Standard second order transfer function. Transfer function dc gain is equal to one) where is the natural frequency and or zeta is the damping and

is the damped frequency, oscillation in time occur at this frequency.

Inspection of the previous figures reveals that for good system behaviour (fast and stable measurements) we need a high value for both resonance frequency and damping. A SciLab file available for experimenting with parameter values can be found here.

To increase wind vane resonance frequency, much like many mechanical systems, inertia decrease is required. Our wind vane is statically balanced with a fore mass and the overall weight can be decreased by enlarging the distance of the

counterweight and decreasing the distance of the fin from the rotation axis of the vane. On the other hand, using a long fin arm will increase the damping of the system which is an also desirable characteristic, as is also described here, eq.6.

A damped system oscillates at the damped frequency of eq.2, as per figure 5b. When damping is

low, is close to the natural frequency.

Natural frequency should be two times the maximum frequency of the measured quantity, in order to ensure unity measurement gain. Also, as has been said in the previous post, resonance frequency should be lower than , or at least, this is a good first estimate; the more distance

between the two resonance frequencies the better.

In a typical operating scenario

, the vane will have to deal with a constant wind, with gusts superimposed on it.

For design and simulation purposes gust models are available, such as the Dryden, FAR and FAR2 models. Wind gu

st library blocks also exist in many simulation packages.

The Dryden model is based on a stochastic representation of wind gusts.

Using the autocorrelation function spectrum of gusts, it creates a filter that produces time domain signals, once fed with white noise. Neither Dryden nor FAR models intend

to provide a very accurate result. However, they are useful because they provide us with a probable shape of wind gusts and a base for comparison between vane designs. During the preliminary design stages we will use the FAR model and consider the Dryden model during simulations.

The gust model will be used to produce the wind magnitude response on the z-axis. Setting a baseline of zero constant wind, the total wind is assumed to be blowing exactly perpendicular to the ground with upwards direction.

Recalling that wing section

relative speed is equal to the vector sum of groundspeeed and windspeed, it is apparent that in level flight, variation of vertical wind speed will lead to variation in AoA; if vertical speed rises, then AoA increases as well and vice versa.

There is no such thing as correct gust parameters; during the design phase a worst case scenario approach will be applied. This scenario should reflect the airboom intended use and the flight platform on which it will be mounted.

The length of the gust gives us an indication of what is the impact of the vane dimensions on its accuracy. In short, it’s impossible to measure a 10cm gust with a 25cm vane, since given this size, the tip of the vane would be immersed in one gust while the tail still lies in the previous one.

It is also useful to define the minimum steady wind path length required for a stable AoA reading. This parameter has been mentioned by many authors and is usually referred to as the decay resistance. It can be calculated for a given wind vane and is the distance which the instrument should travel into the gust to reach a given percentage of the final AoA value, starting from a different AoA value. A typical wind vane response can be viewed in the followig figure. Compare with a wind tunnel test from 1974 by AMIES T. KARAM, TECNICAL REPORT AFIT TR 74-8 [1].

From table 3 in this reference link, we get the time response of a second order underdamped system to a ramp input; the time domain output is the sum of a ramp, an offset and an oscillating term.

(Equation AoA 3 – Standard second order system unti ramp time response)

*Simplifications:*

- The sensor is ideal: only the mechanical part or primary is under analysis
- Aerodynamic interactions between the different parts of the vane are neglected
- Bearing friction is considered at first negligible, no stiction phenomena. The bearing impact will be accounted for in a secondary phase
- Model is valid only for small AoA values, wind tunnel tests confirm that linear models don’t hold for high AoA values
- Gust models are not expected to be accurate for very low altitudes, about under 100m. At any rate, gust shape is taken as a reference shape for performance comparison purposes
- Windvane support is “stiff enough” and considered as fixed. As was previously discussed, it is imperative that no mechanical interactions occur between these two components. Also any other form of mechanical interaction/resonace with flying components have been checked and/or excluded

*Performance parameters, notation, design goals initial value:*

- Operating speed range, (10m/s,60m/s) Derived from intended use / flying platform specifications
- Operating AoA range, (-30°,+30°) Derived from intended use / flying platform specs
- Vane static measure offset, , , Can be defined according to the appliation requirements
- Vane resonance frequency, , 20 Hz. A higher value reduce sthe ramp tracking error
- Vane Damping coefficient, , >0,15. should be minimized for good ramp response. High damping warrants a fast response to measurement variations
- Decay distance, ,

- Fin aerodynamic center distance from rotation axis
- Counterweight distance from rotation axis
- Angle of attack, AoA. In the reference the greek letter is used for yaw since they are considering a meteorological windvane. For our application as usually denoted we will use the greek letter alpha

- Aspect ratio of the fin , where is the fin fullspan and the fin surface
- Coefficient of lift and drag and

**Numerical Example**

After all the mathematical background has been laid out in the two previous sections, the design procedure based on a numeric example will be discussed. Refer to the following scilab file: it’s a simple script file to evaluate the windvane parameters. For the sake of simplicity, when possible, the nomenclature is that of the common, freely available, reference “Wieringa (1967),Evaluation and Design of Wind Vanes, Royal Netherlands Meteorological Institute, De Bilt” By the end of the post a compact set of equations and a basic procedure for wind vane sizing will have been presented.

**Vane parameters**

- Windvane weight 8.00 grams
- rv lenght 25.00 mm
- rw lenght 6.25 mm

**Vane calculated parameters**

- Fin surface 380.95 mm^2
- Vane inertia 0.000006 kgm^2
- Natural frequency 72.63 rad/s
- Damped frequency 72.60 rad/S
- Damping ratio zeta 0.030
- Decay distance 92.3 [m]

**Shaft at test condition with no friction**

- Relative wind speed 30.00 m/s
- Alfa value 0.10 degrees
- Aerodynamic Torque 5.75e-05 Nm

**Shaft at test condition with viscous friction**

- Viscous friction term Dm 2.000e-05 Nms/rad
- Damping ratio increase due to viscous friction 0.022
- Total damping ratio 0.052

Table 8.1 – Scilab script output

In a different scenario, if the speed is reduced to the lower bound of required speed range, in our case 10 m/s, the aerodynamic torque is 0,6e-5Nm and the windvane will not rotate to 0.1°. At the former speed the static error will not be smaller than 2/0.6*0.1=3.3e-1 deg. This result is obtained with the following reasoning:

### References

*Journal of Aircraft*, vol. 12, no. 3, pp. 190–192, Mar. 1975 [Online]. Available: http://arc.aiaa.org/doi/abs/10.2514/3.44432

*Journal of Applied Meteorology*, vol. 6, no. 6, pp. 1114–1122, Dec. 1967 [Online]. Available: http://journals.ametsoc.org/doi/abs/10.1175/1520-0450%281967%29006%3C1114%3AEADOWV%3E2.0.CO%3B2 [Source]