A simple Anemometer
Sometime in the spring of 1996 the odometer of my every-day bicycle stopped working for no obvious reason. When, just as suddenly, it resumed its function again, its place had already been taken over. This was an ideal opportunity to find some alternate uses for an odometer. For a short time I thought about turning it into a digital readout for my turntable but the idea of using it for an anemometer was close behind.
The working-principle of a cup-anemometer is quite simple. On the top (most of the
time, anyway) of the axis there are three or four arms each bearing a cup on the far
end. The axis itself is suspended in a housing on ball bearings and some kind of
signal `generator' at the other end.
To keep things simple I chose the four-armed version. The neccessary cross was easy to fabricate by soldering together two pieces of thin (2mm was sufficiently strong up to now) brass tubing. For the cups I split two ping-pong balls with a jig-saw and didn't have to replace them yet.
The axis consists of a 4mm brass tube seated in appropriately sized ball-bearings.
The impulses for the odometer are caused by a magnet glued orthogonally to the bottom
end of the axis, thus rotating above a reed-contact which is engaged twice per
revolution of the axis. The only thing that still needs to be done now is to connect
the two leads of the reed-contact to the terminals of the odometer and the fun
can begin ...
If you're planning on ever comparing your measured wind speeds to those of the weather report, then you won't be able to avoid a calibration of your anemometer. But don't worry, it's easier than it seems!
It turned out, that the `wheel' circumference I had to enter for my anemometer was fivefold the distance between the centers of the halved ping-pong balls (`D' in the above image).
Or to put it in numbers:
C = 5 * D
A while ago I stumbled acroos the drag coefficients of hollow semi-spheres
and was quite curious as to how close I could approach my calibration (5 * D)
with these. To do this I had to make some rather unrealistic assumptions, but without
these the approximation wouldn't have been possible (without considerable effort).
Assuming a uniform wind (no gusting) of velocity Vw, the speed of the rotating cups (Vr) adjusts in such a way that the forces acting on the open and closed sides of the cups are of the same magnitude. (The cups facing the wind sideways are ignored and I assume that the other two cups rotate with Vr but nonetheless keep their orientation with respect to the wind!!!)
The force on the cup open to the wind turns out to be:
F(o) = x * 1.33 * (Vw - Vr)^2because the direction of rotation reduces the effective windspeed for this cup.
F(c) = x * 0.34 * (Vw + Vr)^2
If I replace the drag-coefficients with the slightly rounder numbers 4/3 rsp. 1/3, let F(o) equal F(c) and solve the equation the result I obtain is:
Vw = 3 * Vr
This means that the cups are turning with a third of the wind speed and the `wheel'circumference I'd have to enter into the odometer is:
C = 3 * pi * Dor:
C = 9.42 * D
Now `9.42' doesn't look much like `5', does it? But I still haven't considered that the magnet causes two impulses per rotation. Comparing `4.71' with `5' gives a totally different picture, the difference between these numbers being below 10%!
Not bad for a homebrew anemometer and a daring
approximation !!!