Friday, January 21, 2011

Wind vane calibration


Accurate wind vane calibration is critical, as any small variation will significantly penalize the accuracy of many other results : apparent and true wind angle, VMG, wind direction, etc. By using the procedure described in this post, it is possible to achieve a typical resolution of 1/4 to 1/3 of degree.

The following figure illustrates the interface between the Raymarine transducer and the microcontroller. With a regulated 8.0 V supply, the wind vane produces 2 analog signals (the green and blue wires) varying typically between  2.9 and 5.3 volts. The exact range is influenced by the length of the cable going to the top of the mast. This is why it is necessary to calibrate only after the installation is complete on the boat.



The analog signals can be fed directly to two ADC (analog-to-digital) pins of the microcontroller, as the input pins can tolerate up to 5.5 V. The microcontroller uses a 5 V volt reference to convert the signals to a number ranging from 0 to 1023. All voltages higher than 5 V are reported as 1023.

This is the form of the signals produced when the vane is rotated through a complete turn from 0 (wind from the front of the boat) to 360 degrees, clockwise from above.



The sine waves suggest that the rotation of the vane is translated in a back-and-forth movement of two sweepers on straight-line potentiometers. The output signals do not vary linearly with the angle, as is the case with designs based on circular potentiometers.
What is not apparent in the above figure is that:
·        the voltage amplitudes of the 2 curves are slighthly different;
·        their mean values are slightly different;
·        the phase angle between the two is not exactly 90 degrees.

Rigorous calibration involves the precise mathematical reconstruction of these two curves from a set of measurements taken on the boat during a trial run. To illustrate the procedure, an example with a reduced set of data points is presented here. In this example,we have gathered the following simultaneous green/blue data points (converted voltages) from a trial run on the water:

570/642              530/758              531/812              541/861              558/902
581/940              609/971              643/997              678/1017            879/1021
914/1004            944/983              968/960              987/937              1002/914
1014/892            1022/870            1022/692            1008/660            989/630
965/603              936/576              899/553              856/535              804/526
776/525              747/527              715/535              683/546              651/562
620/585              592/613              569/645              550/679              539/710
534/730

We have discarded all data with a 1023 value, as they are outside the range of measurement. We can now graph these green/blue pairs as X,Y points in Excel.


This may look like a circle, but it is in fact a slightly eccentric ellipse, with its axis slightly tilted, and its center slightly off the main diagonal. The next step is to find the equation of the ellipse that best fits these points. For this step, we use the NLREG software which has a convenient example of fitting an ellipse to data points (http://www.nlreg.com/ellipse.htm)
Using the NLREG software, we obtain the following characteristics for the fitted ellipse:
     Parameter        Final estimate
------------------  ------------------ 
           Xcenter           783.408681     
           Ycenter           782.546036      
         TiltAngle      0.0326530049 radian
              Xdim           254.549343       
              Ydim           257.708809   

We can now define the parametric equation of the ellipse

Note that NLREG has defined the ellipse with the major axis on the Y-axis before rotation (Ydim > Xdim). The parametric equation defines an ellipse on the X-axis before rotation, so we have to use the following relations in order to use it with the NLREG parameters.
     Xc = Xcenter = 783.408681
     Yc = Ycenter = 782.546036
     a = Ydim = 257.708809
     b = Xdim = 254.549343
     ϕ = TiltAngle – π/2 = -1.53814332 radian

The parametric equation gives the position of any point on the ellipse as we sweep around its center from 0 to 360 degrees, beginning near the bottom and going counterclockwise.  This is exactly the correspondance that we are seeking between a vane angle and any pair of green*blue values.

X(t) = 783.408681 + 257.708809 cos(t) cos(-1.5381432) – 254.549343 sin(t) sin(-1.5381432)

Y(t) = 782.546036 + 257.708809 cos(t) sin(-1.5381432) + 254.549343 sin(t) cos(-1.5381432)

The equation reduces to

X(t) = 783.408681 + 8.413472 cos(t) + 254.4136524 sin(t)

Y(t) = 782.546036 - 257.5714342 cos(t) + 8.310324 sin(t)

We can now calculate and plot the fitted ellipse along the original points.

          t[deg]                X(t)                       Y(t)

0             791.8221527      524.9746018
1             796.2610018      525.1588663
2             800.6959359      525.4215335
3             805.1256041      525.7625232
4             809.5486572      526.1817317
5             813.9637478      526.6790313
6             818.369531         527.2542704
7             822.7646647      527.9072739
8             827.1478103      528.6378428
...           ...                          ...
...           ...                          ...
354        765.1825947      525.5169396
355        769.6165261      525.2304464
356        774.0546587      525.0223339
357        778.4956406      524.8926657
358        782.938119         524.8414812
359        787.3807408      524.868796
360        791.8221527      524.9746018

We can also now reconstruct the green and blue signals from the equation results.


We already know that the vane is pointing forward (AWA = 0) when the green signal is at or very near its maximum value. There is a (approximately) 90 degrees offset between the zero angle of the equations and the zero AWA. We will now apply a preliminary offset of 90 degrees to the results of the equation so that we can graph the curves with respect to this nominal AWA. Even if this offset is not exactly 90 degrees, the remaining small adjustment will be merged in the final offset adjustment that we will have to make to correct the alignment of the transducer with the centerline of the boat.


 
We use only the thick lines for calibration, where the values are between the intersection points of 964 and 602. When the green value is outside the red zone, we use the blue curve, otherwise we use the green curve. When we have determined the color of the curve to use, there are 2 possible angles for the same value, which we can separate by noting if the blue value is greater or lesser than the green value.

For efficiency, we precalculate the angle for each thick line value inside the red zone, so that the green (or blue) value defines an index in a lookup table. The lookup tables are stored in the flash memory of the microprocessor.

  Green
G<B
G>B
     Blue
G<B
G>B
602
133.56
222.65
602
222.63
313.68
603
133.24
222.97
603
222.32
313.99
604
132.92
223.29
604
222.01
314.30
605
132.60
223.61
605
221.70
314.60
606
132.29
223.92
606
221.39
314.91
781
88.65
267.56
781
178.50
357.81
782
88.42
267.79
782
178.27
358.03
783
88.20
268.01
783
178.05
358.25
784
87.97
268.24
784
177.83
358.48
785
87.75
268.46
785
177.61
358.70
960
44.18
312.03
960
134.63
41.67
961
43.87
312.35
961
134.33
41.98
962
43.55
312.66
962
134.02
42.29
963
43.23
312.98
963
133.71
42.60
964
42.92
313.30
964
133.39
42.91


This is a lot of work but it has to be done only once and we are rewarded by a resolution varying from 0.23 to 0.32 of a degree, depending on the angle.

Future enhancement considered : add an external 12-bit ADC chip connected through SPI bus to achieve a resolution better than 0.1 degree.



UPDATE :  I am now using a simpler method to calibrate the wind vane. See also here for the related microcontroller code.

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