Wind speed calculation with an anemometer

[tonykart44]

Homework Statement

Hi everyone,

I'm currently in my first year of college and today I tried to calculate the wind speed of a fan by using a home made cup anemometer.

In our experiment we measured the time needed for 10 revolutions, on both of the speed settings of the fan. We then converted that to the number of revolutions per minute.

Then we calculated the circumference of a cup, and converted that to km. (to get the wind speed in km/h)

Homework Equations

Circumference = diameter * Pi

Finally, we multiplied the circumference in km with the number of revolutions per minute and devided this product by 60.

Now when we calculate all this we end up with a wind speed of around 0.0003 km/h .Now somewhere along the road we must have made either an error in calcutation or an error in reasoning, and we just can't find our mistake.

Any help please?

The Attempt at a Solution

These were our results:

https://docs.google.com/open?id=0B61x_UsWB0wpVEdxQnJianRzYjQ

For our experiment we used this article as a guideline:

http://www.scientificamerican.com/article.cfm?id=bring-science-home-wind-speed

 

[TSny]

Hello and welcome to Physics Forums!

Finally, we multiplied the circumference in km with the number of revolutions per minute and divided this product by 60.

If you are converting from revolutions per minute to revolutions per hour, do you need to divide by 60 or multiply by 60?

 

[TSny]

In looking at your data, it seems to me that the circumference given below the speed 2 table has not been converted to km correctly.

 

[tonykart44]

We divided by 60 because the article said so, we didn't really question it because it made sense since there are 60 minutes in one hour.

However when I change it it gives me a more acceptable value of around 1.1 km/h for the lowest speed and 1.4 km/h for the highest speed. If we then take into account that we didn't factor in the friction of our meter and certain statistical errors, this looks like a much more acceptable value.

But I am still wondering, is 1 km/h not a little low? It is just a small table fan but this still appears a little low to me. Do you know of any reliable sources for commercial table fan wind speeds perhaps? (I've not been able to find one myself).

I also converted the second circumference correctly this time.

An updated version of the results:

https://docs.google.com/open?id=0B61x_UsWB0wpT0VWZUtZTnJqVFk

 

[TSny]

To make sure you see that you should multiply by 60 rather than divide by 60, think of a simple numerical example such as 2 revolutions per minute. How many revolutions would there be in one hour?

I would imagine that your anemometer will give significantly low values. Note that when the wind is pushing on one of the cups to make it rotate counterclockwise, say, then the wind is simultaneously pushing on a cup on the other side trying to make it rotate clockwise. The only reason the thing rotates is because the cup is more streamlined in one orientation compared to the other. Even without any friction in the system, I don't see how it would ever rotate at a speed such that the cups are moving at the wind speed.

Here's a link that shows a graph of wind speed vs distance from a fan using a commercial wind speed gauge. He got on the order of 8 m/s for high speed setting of his fan.
http://www.bealecorner.org/best/measure/fan/fanspeed.html

 

[tonykart44]

Ah yes now I understand, so that is why we are getting such low speeds from our anemometer.

Perhaps we can get around this by using a different meter for the wind speed? I know someone suggested also using a Savonius turbine and comparing the results from the two experiments. And now I see why it was turning so much faster than the anemometer.

I know I've been asking a lot of questions now, but I just have one left now.

When we use a Savonius turbine, I assume that our calculations would differ from using an anemometer. So would we in this case use the area or the circumference of the cups (or half cups in this case) for our calculations?

 

[TSny]

I'm not familiar with the Savonius turbine. Looking at the Wikipedia article http://en.wikipedia.org/wiki/Savonius_wind_turbine helped. That's an interesting design. According to the article, it is possible for some wind rotors to rotate such that the outer tip of the rotor moves at up to 14 times the wind speed! Although, for the Savonius design, the tip rotates at approximately the wind speed.

I'm not understanding your question regarding using the area or circumference of the cups. I don't know what specific calculation you are referring to. But it did make me wonder about your calculation for your anemometer. You mentioned that you measured the diameter and circumference of a cup and converted to km. Are you referring to the diameter of the circle that a cup is revolving around, or are you referring to the diameter of the opening of a cup? You would want to use the diameter of the circle that the cup is revolving around as the anemometer rotates, as shown by the red circle in the attachment.

 

[tonykart44]

Of course, we used the wrong diameter for our circle! I can't do the exact measurement right now but I measured the straws we used and if i account for a certain amount overlap where the straws are connected, I think this diameter is approximately 4 times the diameter we used in our original calculation. This gives a wind speed of 4,4 km/h and 5,6 km/h for the lowest and the highest setting respectively.

As for the Savonius turbine, we can calculate our wind speed using the formula given in the wikipedia article. We already measured the RPM for one setting and can also measure our diameter. The only thing that we then have to find is the tip-seed ratio. But if we assume that this is approx. equal to one then we have everything we need to solve for the wind speed.

I just want to say to you that you were awesome during this entire conversation. You basically saved our experiment and with that an entire mornings worth of work! I just want to say that I really appreciate that, thank you very much!

 

[TSny]

Glad to help. Hope you enjoy your project.