## Monday, July 1, 2013

### Angle of Attack Wind Vanes

I will introduce the measurement of angle of attack by mean of wind vanes, in successive posts I will tackle design and practical issues, modelization and finally model cross validation

Angle of attack measurement refer to everything it's necessary to get the angle between the airspeed vector and the zero lift line of our wing at a determined point, it's the angle used to calculate the wing section lift and it's often indicated with the greek letter alfa; AOA vanes can be called also alfa vanes.

AOA usually change all over the aircraft, so it's necessary to take this into account. To visualize this behavior think to a wing with some geometric twist, our measure at the wing root and the real mid wing AOA will differ by the geometric twist term. Usage of this measurement can be sought in a FPV scenario or during a parameter identification flight. In full size airplanes AOA is used, even on small private GA planes, to provide a warning indication as the vehicle approach to a stall. The intended use impact over the choice of AOA sensor type and desired performances. There are many different types of AOA measurement devices the most common are :

-Wind vanes

-Null seeking devices

-Static type devices, based exclusively on pressure measurement

For a general description of this typologies please take a look to naca-tn-4351

I will focus on a classical mass balanced wind vane design though it can be less attractive than pressure based units nor closed loop null seeking devices. Making and calibrating a good wind vane is at reach for a DIY maker, have a look to my own DIY wind vane here below that exposes the main components of the system look the figure AOA.2 for a render of the vane assembly.

Figure AOA.1 Miniature DIY Wind Vane detail, JLJ and GC
Caption 1 Counter weight, 2 Fin, 3 Main rotation shaft, 4 Bearings,
5 Potentiometer, 6 vane body

Important as the instrument itself is to define what our equipment is intended to measure, for an appropriate design it's needed to write down some specifications; I will proceed to focus on some common aspect of design and after that I will propose some specifications. A lot of bibliography can be found regarding specifically weather vanes, in line of principle it's a valuable resource but uncomfortable source for design requirements.
There are two main macroscopic differences between weather vane application and alfa vanes, range of speeds and vane support. Weather vanes are firmly fixed to a support, so if correctly designed they don't have to deal with vibration issues that usually degrade the measurement quality. Imagine a wind vane fixed on the free side of cantilever beam. In such a configuration, that recall those of nose mounted airbooms, the whole structure will start to oscillate, for example purposes we consider a planar oscillation (ref eq. 36)

Given $$h$$, $$\dot{h}$$ as the height of the wind vane fixation point and his speed and $$u$$ as the wind speed it's possible to find the error angle caused by beam deflection at a time instant $$edf(t)=\frac {\dot{h}}{u}$$
Given a speed of 20m/s and a maximum deflection of 20mm at 10 Hz we get
$$edf =\frac {2\pi 10Hz 20e-3m} {20 m/s}=0,0314 radians or 1.8 degree$$
Another aspect of cantilever mount is that the motion at the wind vane fixation point can interact with wind vane dynamics, to avoid performance hindering is crucial to maintain the two system resonance frequencies well apart. Since the boom have not a simple geometry the calculation of the vibration modes is not realistic using a closed form formula, indeed is necessary to build a 3d model and carry on a FEM modal analysis or do some lab test, refer figure AOA,4 for the first mode representation of the probe. There is a valid Open FEM package named Elmer that can be freely downloaded and can handle dynamic analysis.

Figure AOA.2 Miniature DIY Wind Vane 3D model, JLJ and GC

Generally the stiffer is our air boom the higher is the first resonance frequency value, the higher the better, in fact this frequency limit wind vane resonance frequency maximum value and hence the maximum frequency that can handle our wind vane. As a rule of the thumb if the air boom assembly moves under a slight pressure of your hand at ground you will get some vibration correlated problem in the air, to be more accurate if you dispose of a dynamic numerical analysis be sure that your boom first resonance/mode frequency is far from desired wind vane operating range; an offset of minimum 0,3*FirstModeFrequency between the two frequencies is often a good conservative value. Generally you can neglect higher frequencies because the impact in vibration motion decrease with mode frequency/mode number, for best performances check anyway that no other vehicle components excite any of the low to mid frequencies boom modes.

Let's proceed to examine wind vane behavior, refer to figure AOA.1.
The critical component for account for are the bearings, a Coulomb friction model will be used to cope with the static friction. The phenomenon of static friction or stiction consist in the torque that is necessary to start to move a bearing at rest, that is a value superior to the torque needed to keep rolling the bearing once the movement started, this situation is depicted in figure AOA.4. This non linearity lead to some trouble when using numerical integration algorithms, first effect to be detected is a longer integration calculation time. The presence of such friction can generate limit cycles and solution collisions, in other word the solution can be non steady/cyclic or converge to a terminal value that yield a non zero static tracking error.

Figure AOA.3 Modal analysis on the probe, first mode frequency is 106Hz. The probe is fixed at the root. The Maximum deflection at the tip 3 is 25 mm, 16 mm at the 2 windvane fixation point and 0 mm at the root 1.

Figure AOA.4 Bearing friction model including stiction

Analysis can be really neat if the model is write down as a Filippov system, a nice sliding bifurcation arise.
Many articles are available on the wind vane topic, take for reference