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Anemometer calculations

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Charlie
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Anemometer calculations

Postby Charlie » Sun Dec 12, 2010 12:24 pm

I’m playing at building my own weather station and I have most of the sensors sorted out, but how to calibrate the anemometer escapes me. It’s easy to make something that spins in the wind and electronically count revolutions, but how do you map those revolutions to actual wind parameters? Does anybody know the relationships? Most sensors seem to be a horizontal axis “wheel” with 3 cups. Cup area is a variable, but apart from resistance to starting, does it matter? How about the diameter of the “wheel”? Is the circumference related to wind run?
A magazine article I read a few years back suggested an empirical calibration by strapping the prototype to the roof of your car and driving at fixed speeds on a calm day while someone records the counts, but I have to think there is a method less prone to error… and hopefully some basic relationships were worked out long ago!

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Re: Anemometer calculations

Postby steve » Sun Dec 12, 2010 12:37 pm

I think the main factor is the diameter of the wheel. If you liken it to the wheels of a car travelling along a road, then for a given speed, smaller wheels will make more rotations in a given time than larger wheels.

You can work out the theoretical relationship between wind speed and revolutions for a given diameter/circumference; for example an anemometer with a diameter of 10cm will make about 3 revolutions per second with a wind speed of 1 m/s. I think :). But I also think that you would have to calibrate it empirically - somehow.
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Charlie
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Re: Anemometer calculations

Postby Charlie » Sun Dec 12, 2010 12:55 pm

So you are suggesting that, ignoring friction, you simply assume the cup is travelling at the same speed as the wind. In your example, the wind molecules move 1 meter in 1 second, hence so does the cup. Since the cup is on the circumference of a circle (which = pi * d) then for a cup to travel 1 meter on a 10 cm diameter wheel will make 3 revolutions (or within 5% anyway).
That makes perfect sense. So then the size of the cup is all about overcoming the friction in the bearings (and resistance caused by the other cups). I suspect there is little you can do about the friction in the bearings, but there must be a formula to account for the resistance of the other 2 cups?

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Re: Anemometer calculations

Postby wd40 » Sun Dec 12, 2010 1:50 pm

I think this might solve your problem. I stumbled cross this on the Davis site. For 12 bucks, it would give you a good base.

http://www.davisnet.com/weather/products/weather_product.asp?pnum=07903S

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Re: Anemometer calculations

Postby steve » Sun Dec 12, 2010 2:58 pm

I was going to mention the fact that you can get alternative smaller cups for the Davis stations, depending on the max wind speeds that you expect. I don't know whether the diameter of the whole assembly is different, or just the cups, but presumably these cups rotate at a slower rate for a given wind speed - you have to tell the console that you're using them.
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Re: Anemometer calculations

Postby Gina » Sun Dec 12, 2010 4:54 pm

I'm thinking of making my own anemometer (some time in the future) and was wondering about the calibration. First off I considered putting both it and the F.O. anemometer near to each other and roughly calibrating the new one with the F.O. one. Now this is probably a case of "the blind leading the blind" but it would be a start. I very much doubt you can just assume the cups velocity is the same as the velocity of the wind at right angles to the spokes - only that it must be some factor lower. I'm sure there must be a formula that someone has worked out for this. I presume you've tried Google et. al.? I haven't yet.
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Re: Anemometer calculations

Postby Gina » Sun Dec 12, 2010 5:10 pm

I have now and not found anything useful :(
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Re: Anemometer calculations

Postby mcrossley » Sun Dec 12, 2010 6:01 pm

From Wikipedia...

"... the ratio of the speed of the wind and that of the cups, the anemometer factor, depends on the dimensions of the cups and arms, and may have a value between two and a little over three."

http://en.wikipedia.org/wiki/Anemometer

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Re: Anemometer calculations

Postby Ned » Sun Dec 12, 2010 8:25 pm

Even when set by some theoretical model, the instrument should be calibrated in a known working environment. So if you are able to borrow or even hire an anemometer as used by air conditioning engineers and using a steady air stream from a fan, so much the better.
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Re: Anemometer calculations

Postby Charlie » Mon Dec 13, 2010 11:54 am

mcrossley wrote:From Wikipedia...

"... the ratio of the speed of the wind and that of the cups, the anemometer factor, depends on the dimensions of the cups and arms, and may have a value between two and a little over three."

http://en.wikipedia.org/wiki/Anemometer

This is an interesting article.
Now if they had included the actual formula, instead of "depends on the dimensions of the cups and arms", the question would have been answered.
At any rate, assuming the article is true, then a 3 cup anemometer will be linear, so calibrating against a fan with a couple speeds should be sufficient. It would be nice however, to simply be confirming the math, rather than trying to experimentally derive it! (Especially since, according th the article, it does exist)

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Re: Anemometer calculations

Postby Gina » Mon Dec 13, 2010 12:25 pm

Charlie wrote:This is an interesting article.
Now if they had included the actual formula, instead of "depends on the dimensions of the cups and arms", the question would have been answered.
At any rate, assuming the article is true, then a 3 cup anemometer will be linear, so calibrating against a fan with a couple speeds should be sufficient. It would be nice however, to simply be confirming the math, rather than trying to experimentally derive it! (Especially since, according th the article, it does exist)
Yes, exactly what I was thinking! There is a formula, it may not be very accurate but better than nothing. I want to know what it is too.
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Re: Anemometer calculations

Postby hans » Mon Dec 13, 2010 4:12 pm

here are a few:

WS=1.25C/T

WS=wind speed in miles per hour
C=counts
T=time interval over which counts are measured(seconds)

or

To determine wind speed in miles per hour (mph), use this formula: calculate the circumference of your anemometer by multiplying the diameter (or distance between opposing scoops) in feet times pi (or 3.14). Multiply this number times the number of revolutions per minute to get the number of feet per minute (fpm) one scoop travels. By multiplying rpm by 60 (minutes per hour) and dividing this number by 5280 (feet per mile), you will get an approximate wind speed in miles per hour.

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Re: Anemometer calculations

Postby Gina » Tue Dec 14, 2010 3:33 pm

While checking out 1-wire I came across that first formula on the HobbyBoards site for their anemometer kit. Here's the PDF http://www.hobby-boards.com/catalog/links/wind-ads/ADS%20Anemometer%20User%20Manual.pdf and here's their hardware - familiar, what??? :lol:
Screenshot-11a.png
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Re: Anemometer calculations

Postby hans » Tue Dec 14, 2010 4:59 pm

small world :D

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Re: Anemometer calculations

Postby brassing » Sat Dec 25, 2010 1:23 pm

I posted the post below on the Fine Offset forum when I hadn't realised there was a similar thread here so I am reposting here.

It seems that the Fine Offset measures wind speed over 24 2 s intervals during its 48 s reporting period. The maximum of these measurements is reported as the gust speed. If you examine the gust speeds you see that they are all multiples of 0.34 m/s (or the equivalent in other units). Thus 0.34 m/s must presumably correspond to 1 pulse from the anemometer in 2 s. Since the anemometer has only one magnet and one sensor it gives one pulse per rev. The diameter of the anemometer is 140 mm (at the cup centres) so a bit of maths shows that at 0.34 m/s wind speed the cups are rotating at Pi x 140 / 2 /1000 m/s = 0.22 m/s.

I know very little about anemometer theory (just what I found in 30 min web research) but it seems the ratio of wind speed to cup speed is known as the anemometer factor and for 3 cup anemometers it varies between 2 and just over 3. The figures above give an anemometer factor of 0.34 / 0.22 = 1.56 which is well outside the expected range.

Either the Fine Offset anemometer is unusually efficient or there is something wrong with my logic. Does anyone have any idea where the discrepancy comes from?

(I have to admit that the value of 2 to just over 3 is found on various websites but without any source. The wording is almost identical on each site which indicates a single primary source, which might well be unreliable.)


Following on from that post I have a couple of further points:

The formula WS = 1.25 C/T mph quoted above by hans from the Hobbyboards site for an anemometer that appears identical to the Fine Offset one leads to an anemometer factor of 1.27 which must surely be wrong - much too low. Maybe the photo of the anemometer is wrong and the one they sell has a smaller rotor.

I have a datasheet for a Vector Instruments R30 rotor for their A100 anemometer (http://www.windspeed.co.uk/ws/index.php ... &Itemid=48). This is an instrument grade anemometer intended for professional use. It quotes a "Rotal Calibration" of 47.8 rpm / m/s. The rotor has a diameter of 106 mm (across the cup centres). If you do the sums on this you find that 1 rev/s corresponds to 0.333 m/s cup speed and to 1.26 m/s wind speed. This gives an anemometer factor of 3.77 which is a bit higher than the Wikipedia range of 2 to just over 3. The rotor is a 3 cup design with conical rather than hemispherical cups. I don't know what difference that makes but you might expect cup design to make a significant difference. If the cups were replaced by flat plates the anemometer would not turn at all. The anemometer depends on the asymmetry of the cups so the degree of asymmetry will affect the anemometer factor.

I hope I have got the maths right. Someone might like to check!


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