Expert: Amy - 1/18/2005

Question
I have seen various sites on the internet that talk about making a homemade anemometer using a ping pong ball (0.0025 kg?) supended from a 30 cm thread. See: http://www.enoreo.on.ca/resources/students/anemometer1.htm
Then you have a protractor on top and measure the angle that the wind blows the ball from the vertical. I was wondering how the values for angle vs wind speed or vertical distance the ball goes up vs wind speed can be calculated. I imagine the conservation of energy (potential and kinetic) would be used to calculate this. So I am look for a formula such as Angle = F(Wind Speed) or Distance Ball is raised = F(Wind Speed). I supect the Angle or the distance is a cubic funtion of the wind speed V. When the wind blows on the ball then the string angle is say Theta degrees. Then the ball is displaced L-LxCos(Theta). So the ball now has potential energy of MxGx(L-LxCos(Theta)) where L is the length of the string which in my case is 30cm. So then there is the kinetic energy of the wind which is equal to the mass of the wind times the square of the velocity divided by two. KE = MxVxV/2. The mass of the wind strinking the ball would be the air density x the volume I think. So that's about where I am at. The table below

Speed,   Angle,   Angle,   Height
V (kph), Radians, Degrees, Meters  
0.00,   0.00,   0,   0.0000
9.30,   0.09,   5,   0.0011
13.20,   0.17,   10,   0.0046
16.30,   0.26,   15,   0.0102
19.00,   0.35,   20,   0.0181
21.60,   0.44,   25,   0.0281
24.00,   0.52,   30,   0.0402
26.40,   0.61,   35,   0.0543
29.00,   0.70,   40,   0.0702

I am helping my daughter in grade 5 to do a project relating to wind power. She does not need to know the formula but can do a table lookup like most people do. However I was interested in deriving the formula. I have a math background.

Answer
Hi Ray,
Thanks for writing to me. I have to say that this question is out of my expertise. I've had a hunt around for other people who could help you and I suggest that you try these experts from the general (not science for kids)physics section  in All Experts.

Yamini Nevatia and James Kovalcin.

Good luck,
Amy