This
post is the continuation of Angle of attack windvanes posts
miniserie

*DIY air data boom with angle of attack and angle of sideslip mechanical vanes www.basicairdata.eu*
An
example numeric design will be here presented. 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 those of the main, 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
windvane sizing will be exposed.
Design
process is recursive and require to go forth and back through the
specification, 3D design and performance evaluation phases;
formally to find the best windvane
design
can
be seen as a
multivariable, multiobjective optimization problem. To
avoid a complexity explosion only a basic approach to design
evaluation is presented in
figure F9,3.
Note
that our fast preliminary design is possible
thanks to the
availability of a closed form
math
model for the vane, results and performance evaluation can
be eventually
refined
further
during a
successive
simulation
phase.

Executing
the
Scilab file will return
the following output, that summarize the supplied
example
windvane design parameters

Vane
parameters

Windvane
weight grams 8.00

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
T9.1 Scilab script output*

Consider
the possible model for the main shaft bearing friction in figure
P9.1, let's pretend that the curve is approximate by excess so the
torque values are conservative, to be more general consider also that
torque values are the sum of the torque generated by all the
frictions on the shaft including those derived by the position
sensor.

*Figure
**F**9.1
**General
b**earing
friction model including stiction, **to
carry out a general analysis consider this curve comprehensive of all
the friction caused by bearing and sensors.*

In
table 9.1 is reported the approximate torque generated by the lift of
the fin at the shaft, 5.75e-05
Nm for
a wind blowing at 30 m/s;. The
aerodynamic torque that our vane generate for an alfa of 0,1°
at 30 m/s is
greater than the torque of
0,02e-3 necessary to the
shaft to begin to rotate.
At
30 m/s the
vane will hopefully
correctly rotate to 0,1°
alfa.
differently
if the speed is reduced to the
lower bound of required speed range, in our case10
m/s, the aerodynamic
torque is 0,006e-3Nm
so the windvane will not
rotate to 0,1°;
at the former speed the
static error cannot
be smaller than
0,02/0,006*0.1=3,3e-1.

Given
storque as the static torque required to move the shaft ,statico as
the max static error and N as the vane torque coefficient the
following constrain should be satisfied
by a healthy vane

*E9.1*

Nstatico>>storque,
where N is speed dependent

With
our example numeric
values 0.0036633*0,1/360*6,28>>storque,
storque <<0.0064e-3
In those
cases when it's non possible to reduce anymore the friction it will
be necessary to increase the windvane fin area.
Table
9.1 shown
a low damping
ratio, quite different from
our initial requirement of a value greater than 0,15.
Recalling that
our current model neglects the bearing damping some considerations
should be added for a
correct result
interpretation.
Note
that when wind speed is very high, as friction torque
contribution is
little compared to the
torque generated by the
fin, the behavior of the vane will be essentially those predicted by
the model, so a very low damped response should be expected. At lower
speeds the contribution of friction are not negligible and lead to an
increase in the response damping.

Again
according to Wieringa the damping ratio variation against relative
wind speed is plotted on the following figure valid for the example
vane.

*Figure
**F**9.**2**
**Damping
ratio against **relative
wind speed**,
Dm assumed to be **20**e-**6**
Nms/rad*

To add
damping at higher speeds some mechanism, aerodynamic or mechanical
based, can be employed, the example probe do not use any mean to
compensate for relative wind speed.

Commonly
the choice of the sensor for vane angle is oriented to the use of low
friction devices, hall type sensors have been successfully employed,
see a commercial available typical rotary sensor at this link.
The whole
design process is somewhat recursive, the following figure pictures
at glance a possible design development path.

*Figure
**F**9.**3** **Possible
design process **development
**path*

Inspecting
the figure quickly jump to attention the fact that post design
simulation and testing should be carried out on the vane, although not treated here the design validation is to be considered as a primary design task.

Nice designs,

JLJ