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'my math error (was Weather Anamometer)'
1996\06\04@162411 by Scott Newell

I just knew I'd screw up a sign somewhere.  Funny how the signs change once
your post makes it out across the list, isn't it?

Ok, let's assume that we have:

d = distance between ultrasonic sensors.
w = wind speed
v = speed of sound
t1 = time for left to right transit
t2 = time for right to left transit

(I'm gonna do the math assuming a positive wind speed means left to right; a
negative wind speed would then mean the wind is traveling from right to left)

From left to right, we get

d = rate * time
   rate = w + v        ; I'm assuming the wind is also from left to right
d = (w+v) * t1
d/t1 = (w+v)            ; we're gonna use this again, in a minute

Now, from right to left

d = rate * time
   rate = v - w        ; since we're going against the wind (not w-v as before!
d = (v-w) * t2
d/t2 = (v-w)            ; compare to above, this is the important part

Now, we can subtract.

(w+v)  -  (v-w) = 2w
(d/t1) -  (d/t2) = 2w

w = 1/2 ((d/t1) - (d/t2))

or, continuing on,

    1      (d * t2)        (d * t1)
w = ---  *  --------   -    --------
    2      (t1 * t2)       (t1 * t2)

    1       d * (t2 - t1)
w = ---  *  --------------
    2         (t1 * t2)

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

Since you're gonna build the thing, you'll know the distance at compile
time.  Measure the transit time in both directions, and forget about the
speed of sound.


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