How can I calculate wind speed based on the rotations of a propeller?

December 1, 2021 1:58 PM

Assume the propeller is always directly facing the wind. If I wanted to calculate the wind speed based on the number of rotations of a propeller, is there an equation for that?

At first I was thinking of off-the-shelf propellers, but then realized probably a home made propeller with a defined pitch throughout the entirety of each blade would be the easiest to do calculations?

I'm not sure if there would be simple vector math, for instance, if the blade pitch is 45 degrees. Or maybe there is some way just to use the circumference and length of the propeller along with the number of rotations per time?

posted by czytm to Science & Nature (13 answers total)

Response by poster: Apologies, propeller is probably not the correct term. I'm thinking about the sails on a windmill but using a smaller version attached to a roof, to calculate wind-speed.
posted by czytm at 2:11 PM on December 1, 2021

Response by poster: Ok, sorry to thread-sit, I think my answer is to read more about anemometers.
posted by czytm at 2:16 PM on December 1, 2021

Best answer: Unfortunately propeller aerodynamics is really complex, even more than wings. How accurate do you need it to be? Instead of a propeller, have you considered a cup anemometer? The FAA has a page on building a cup anemometer that may be helpful. The best bet is to just build it and then calibrate it like that page says, by using a car driving at constant speeds.

Note: each part of a propeller blade (or windmill sail) has a different speed through the air, so to get the same angle of attack everywhere you need a twisted blade, like the ones you can buy... and even those are approximations and are only constant at one speed.
posted by phliar at 2:32 PM on December 1, 2021 [3 favorites]

(BTW I'm a pilot, and have been obsessed with aerodynamics ever since I was a kid, and have built many anemometers -- and airplanes! -- over the years.)
posted by phliar at 2:39 PM on December 1, 2021 [2 favorites]

You could determine the curve empirically. Get the propeller, make a crude wind tunnel, and blow different-speed winds at it.
posted by dum spiro spero at 2:47 PM on December 1, 2021 [1 favorite]

Propellers for outboard motors on boats typically have their pitch measured in distance rather than angle, so you can have, say, 17" and 19" propellers—the distance each would travel screwing through an imaginary solid material in one rotation. In such a solid you could easily get speed by multiplying the rate of revolutions by the pitch distance, but as phliar says, neither air nor water are such convenient substances.
posted by Fiasco da Gama at 2:48 PM on December 1, 2021 [1 favorite]

In theory, you can do this by measuring the pitch, as Fiasco da Gama mentions. Unfortunately, you have to allow for slip, as the propellor won't work perfectly and there's always some loss. I think that would be true of any device being driven by the wind because there's always going to be some mechanical drag as well as the blades responding to wind in different ways at different speeds. Things like windmill sails are effectively the same as a propellor.

If you're planning to build a propellor-like device yourself and use it to measure wind speed, I don't think there's an alternative to calculating the wind speed by blowing wind across and measuring the rotations at different speeds. You could do this by mounting it on a car and driving at known speeds, but that may not be accurate enough depending on how finely-grained you want to measure wind speed.

You can possibly use maths to calculate the theoretical wind speed, but that would be an approximation at best.
posted by dg at 3:06 PM on December 1, 2021 [1 favorite]

Best answer: I used to have to care a *lot* about anemometers. I've run large fleets of weather monitoring towers. I've used everything from paper chart recorders, through digital loggers and ultrasonic sensors up to beam sensing technologies like SODAR and LIDAR. I've seen (but never directly used) radiosondes and calibrated kites for calculating wind profiles at different heights.

The challenges of building a prop and calculating its wind performance are considerable. R. M. Young in Michigan make very nice prop anemometers, but even they work from wind tunnel calibrations. Cup anemometers are more common: not because they're better, but their limitations have been really well studied. They're pure drag devices, which have slightly simpler theory than combined lift/drag devices like props. You can buy fairly cheap cup anemometers (like this one: Octopus Wind Speed Sensor Anemometer Three Aluminium Cups) that have a mostly linear response.

There are a couple of types of anemometer (I still can't spell that damn word the first time) for which design theory comes pretty close to actual performance. One is a hot wire anemometer, the other the pitot tube. These aren't direct-reading devices, and aren't exactly easy to make
posted by scruss at 5:45 PM on December 1, 2021 [3 favorites]

Not directly related, but if you're looking at utility scale wind turbines, they spin at a constant speed regardless of the wind speed (above a threshold, which is usually a few miles per hour).
posted by tayknight at 8:01 AM on December 2, 2021

Best answer: I’d suggest attaching your anemometer to a car, then drive on a windless day. You would need a helper, or automatic recording, to make the data points for a speed table.
posted by nickggully at 2:54 PM on December 2, 2021 [1 favorite]

→ utility scale wind turbines ... spin at a constant speed

Not ones built in the last decade or more. Variable speed has been standard outside the USA since the early 2000s. Only GE, with its Kenetech/Enron Wind patent and its fleet of very expensive lawyers, have prevented more efficient turbines being widely deployed in the USA.
posted by scruss at 5:06 PM on December 2, 2021 [1 favorite]

"they spin at a constant speed regardless of the wind speed"

From many days spent watching wind turbines from a hill or a beach, this is not remotely true.
posted by turkeyphant at 12:28 AM on December 3, 2021

Response by poster: Thanks all, calibrating with a car is a great idea. Accuracy isn't super important, this is more for fun to repurpose a small brushless motor for fun.

I also asked my friend how he would make an analog anemometer (thinking along the lines of measuring the voltage of something spinning) and he replied:
> google "windsock"
posted by czytm at 9:54 AM on December 3, 2021 [1 favorite]