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.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)
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Anemometer calculations

 Posts: 1885
 Joined: Sat Feb 21, 2009 12:41 pm
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 Location: Devon UK
Re: Anemometer calculations
Gina
Sorry, no banner  weather station out of action. Hoping to be up and running with a new homemade one soon.
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 hans
 Posts: 171
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 Weather Station: wh1080 /ws4000(alecto) XPsp2
 Operating System: Windows XP SP3
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Re: Anemometer calculations
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.
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.

 Posts: 1885
 Joined: Sat Feb 21, 2009 12:41 pm
 Weather Station: Nothing working ATM  making one
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 Location: Devon UK
Re: Anemometer calculations
While checking out 1wire I came across that first formula on the HobbyBoards site for their anemometer kit. Here's the PDF http://www.hobbyboards.com/catalog/links/windads/ADS%20Anemometer%20User%20Manual.pdf and here's their hardware  familiar, what???
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Gina
Sorry, no banner  weather station out of action. Hoping to be up and running with a new homemade one soon.
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 Posts: 35
 Joined: Sun Dec 05, 2010 12:39 pm
 Weather Station: Fine Offset
 Operating System: Vista SP2
 Location: Woking surrey
Re: Anemometer calculations
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!
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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