We know that the vertical anemometer, just like the cup/vane anemometer, works by measuring how fast the cup/fan rotates because of the wind. But how could we possibly know that the fan rotation is due to vertical winds, and not due to the horizontal winds?
Wouldn't the horizontal winds affect the readings of this anemometer? Why, or why not?.
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These anemometers have a characteristic which does not measure horizontal wind, because it isn't affected by any other direction, it is called a cosine characteristic, so vertical speed gives the highest turning speed and then it gets lower with increasing angle to the vertical and it does not turn for horizontal.
TL;DR: The net torque produced on the propeller is zero for horizontal winds and non-zero for vertical winds. In the former, the torque produced by one blade of the propeller gets canceled by that of the radially opposite blade. Similarly, the torque produced due to horizontal winds at any point of a radially symmetric propeller would be canceled by that of a radially opposite point.
Thanks to the point about the cosine characteristic by @trula, I think I understand how the cosine characteristic works (which was the original intention of the question). I am posting this here for community feedback, as well as for others with the same question in mind.
For those who don't know, anemometers are instruments that measure wind speed. Wind speed data is a really big deal for weather forecasters and atmospheric scientists. The accuracy of weather predictions depend on such data.
Coming to the question about vertical anemometers,
Wouldn't the horizontal winds affect the readings of this anemometer?
No, assuming that the wind is acting uniformly across the anemometer. It is impossible to make a table fan/ ceiling fan rotate by a wind parallel to its plane. Of course, you could blow air on one side of the table fan leaves and make it spin, but the wind is not uniform. In normal conditions, atmospheric winds are uniform in the length scales of the anemometer. Of course, there are turbulent winds and eddies, but we ignore them in this discussion.
Why, or why not?
Let's consider a vertical anemometer like the one mentioned in the question.
Let's now just consider two opposite blades.
Now imagine throwing a tennis ball horizontally at both leaves at symmetrically located points about the rotation axis. (These balls represent air molecules in the wind).
Now as the ball hits the left blade, it gets deflected downwards. Look at what happens when the ball is thrown to the opposite blade. It gets deflected upwards.
Drawing the initial momentum and final momentum (shown as arrows drawn with pencil) shows that the momentum imparted on the left blade has two components (shown as arrows drawn with pen), one pointing up and one pointing along the plane of rotation. The component along the rotation plane makes the fan spin clockwise. Let's not talk about the vertical component now, since they don't contribute to the rotation along the vertical axis anyways (but they do act on one other axis, along the junction hook of the fan with the ceiling; this is what makes the fans tilt during winds). The momentum imparted to the right blade has a component upwards. But the second component makes the blades spin anticlockwise. Now if you throw both balls simultaneously to these two blades symmetric to the rotation axis , the angular momentum imparted would cancel out. So the fan won't spin. This is why the horizontal winds cannot affect the rotation of the vertical anemometer. It gets affected only by the vertical wind components.
You can see this by throwing balls again, but this time from the in a vertical direction from the bottom.
This time, both balls are making the fans spin clockwise, and the angular momentum is not getting canceled.
It does not matter what the shape of the blades is; as long as there is a rotational symmetry about the axis of the anemometer, the same argument applies. For every point on a blade where air molecules are hitting, another point on the opposite blade provides the exact nullifying torque.
So you can have cats instead of blades on your anemometer; it would still be functional.
Hope this makes it clear that wane anemometers don't measure just any wind speed. They measure specifically the speed of wind parallel to the plane of rotation of the fan/cup only.
