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PICList Thread
'Weather Anemometer'
1996\06\04@212726 by Steve Hardy

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This is getting a bit off the subject of PICs, however I can't resist...

Let's do some error analysis on Scott Newell's <spam_OUTnewellTakeThisOuTspamMAJOR.CEI.NET>
result to see how accurately we can measure wind speed (or how large
do we have to build the device for a given accuracy).

Scott's result was

    d       t2 - t1
w = ---  *  ---------
    2       t1 * t2

where d is the transmitter-receiver separation, t1 and t2 are the
measured 'flight times' in each direction, w is the resulting wind
speed (or ether speed if you were Michaelson or Morley).  I have to
admit (pleasant) surprise that this doesn't depend on the speed of sound.

Let us assume that the common 40KHz ultrasonic Rx/Tx is being used.
When detecting the Tx pulse, there is going to be some uncertainty as
to when the pulse is detected.  Since these devices are narrow bandwidth
they resonate hence the Rx level will rise to a peak over several cycles,
then die away once the signal ceases.

The upshot of this is that your Rx circuitry will not be able to do
much better that +/- a few cycles.  Call this uncertainty $t.  Now
assume that the distance d is known accurately.

The biggest error comes about because the (t2-t1) term involves the
difference of 2 very similar quantities.  Thus as a first worst-case
approximation,

     d       t2 - t1 + $t
w1 = ---  *  -------------
     2          t1 * t2

     d       t2 - t1 - $t
w2 = ---  *  -------------
     2          t1 * t2


therefore

$w = w1 - w2 =  d $t / t1 t2   ; $w is uncertainty in wind speed

rearranging in terms of d (which is now the requred distance given
the tolerable error in wind speed, $w, and the measurement uncertainty $t)

d = t1 t2 $w / $t

This is not all that useful a result until we substitute

t1 ~ t2 ~ d/v

where v is speed of sound. Hence substituting into the previous,

d = v^2 $t / $w

Now to plug some numbers in.  Suppose $w = 1 MPH = 0.44 m/s;
$t = 2 cycles of 40KHz = 50us (fairly ambitious); v = 330 m/s.
The required distance between Tx and Rx is therefore 12.4 m = 40.6 ft.
Don't just believe me, check it for yourself.

Perhaps I am overly pessimistic about the accuracy that these detectors
can pick up a pulse - it would be worth experimenting.  Good luck!

If I was going to do this, I wouldn't use 'sonar pulses'.  I would
emit a continuous signal and measure the phase difference between
Tx and Rx.  Since 4 signals are going at once, I would use 4 narrow
band devices at different frequencies.  The device would have a 'zero'
button which would note a reference phase difference when the wind
conditions were known to be zero (put a box over it!).  Put a cage
around the whole contraption so birds wouldn't disrupt the signal.
Use a UPS because readings are meaningless after a power fail.

Regards,
Stephen James Hardy
Canberra Australia

1996\06\07@144444 by Scott Stephens

picon face
Since you probably don't have ceramic cylindrical xducer's used in the
Sensor's Journal article, Consider using piezo buzzers as bi-directional
transucers. Mount 3 or 5 (depending on the basis) in a box, with tubing, cut
to resonance, and bent at right angles at the ends towards each other. This
way, the transucers can be mounted next to the circuitry in an enclosure,
and metal tubing waveguides the sound out of the enclosure. And you can
attach you heater to the pipes. Mount upside-down to keep out rain (and
raindrop noises). Maybe the pipes could be cut to a combination
longitudinal-shear resonance with the ends closed so the pipe itself would
act as a resonant transducer. That would probably only be usefull for high
ultrasound freq. (>40KHz)as ringing in the tranducer would affect pulse
measurments.

A year or two ago, a Circuit Cellar Ink project was a PIC weather station
that featured a PIC as a single-chip weather station & video controller. A
large triangular dial appeared on a TV screen showing the wind direction.
Might make a nice interface.

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