Science Buddies: "Ask an Expert"

My objective for this project is to determine how much power a pinwheel generates at different orientations of a wind source. My pinwheel has a horizontal axis (6 in) and a wing span of 5.5 inches.
I used a hair drier as a wind source and then faced it at different angles (0,45,90,135,180) from the pinwheel. I attached a load (5 grams) to the pinwheel with a string (24 in) and see how long the pinwheel lift up the load. From each angle, the velocity of the pinwheel's rotation and the time it took to lift the load was different.
My results:
0 degree-17.8sec, 2.4132W, 0.135573P
45 degree-18.9sec, 2.4132W, 0.1276825P
90 degree-21.6sec, 2.4132W, 0.1117222P
135 degree-24.0sec, 2.4132W, 0.10055P
180 degree-27.0sec, 2.4132W, 0.0893777P
Could you explain why my results turned out that way? Thanks.

Toki Mukai - I'm having a little problem visualizing your test setup. You said pinwheel had a horizontal axis. Does that mean the rotating shaft was horizontal and a string was attached to that shaft and to the weight? What was the diameter of the shaft that was winding the string? When you say the wind angle was 0 degrees, does that mean it was in front of the pinwheel and parallel to the shaft? If that were so, it is easy to understand your other angles, including the reference to 135 degrees (45 degrees relative to the shaft, but from the backside of the pinwheel) and 180 degrees ( from behind the pinwheel, parallel to the axis). Do I have the correct visuals here?

What do the other numbers, 2.4132W and 0.135573P refer to? I think the experts are having difficulty understanding the way this was set up and what the measurements were. Sorry to ask so many questions, but I can't assist with the information as presented.

Rick Marz

I believe you are doing our project described at

https://www.sciencebuddies.org/science- ... p025.shtml

Given that, I too am still having some difficulty understanding the numbers in your table. Take for example the first row:

0 degree- 17.8sec, 2.4132W, 0.135573P

where I interpret the entries as:

angle | time in sec | work | power

I see that your numbers for power are derived as work/time,
which is correct. However I do not understand the values you
list for the work.

Work = Force x distance

A 5 gm mass exerts a force = mg, where m is in kg and g = 9.81 m/s²,
hence F = (.005 kg) x (9.81 m/s²) = 0.0491kg m / s² = 0.0491 N.
The distance, assuming that in every case the weight reached the top
of the run of string, is d = 24 inches = 24 x ( 0.0254 inches/m) = 0.6096 m.
Thus

Work = (0.0491 N) x (0.6096 m) = 0.0299 N m = 0.0299 joules.

Finally

Power = Work / time = (0.0299 J)/(17.8 s) = 0.00168 J/s = 0.00168 watt.

Hence, I conclude that the value for the power shown in your table (0.135573) is off by two orders of magnitude.

Nonetheless, the power values, although incorrect, are still all proportional to the correct power, so the variation with angle will be the same as for the correct values. So your experiment shows that the power developed by the pinwheel is greatest at the angle of 0 degrees, dropping 20% at 90 degrees, and dropping another 25% as you swing all the way around to 180 degrees.

I do not see an obvious way to explain this result. That doesn’t mean it’s wrong, it just means I don’t understand exactly what is happening. Did you happen to notice in what direction the pinwheel was rotating in each case? It would be interesting to know if the rotation with the wind at 180 degrees was in the opposite direction than with the wind at 0 degrees (that is, say, clockwise at 180 and counterclockwise at 0). If that were the case, then the pinwheel might be operating somewhat like a paddle wheel. On the other hand, if it always spins the same way, it might be acting like an airplane propeller, where each vane acts as a small wing producing “lift” perpendicular to its long axis, which is a radial direction, with the net force being circular in a sense determined by the pitch angle of each vane. But for that idea, I would expect the maximum power to be developed at 90 degrees. Bottom line: I don’t have a good explanation.

You could explore these two concepts by experiment: a paddle wheel should spin in the direction with the wind if you raise the hair dryer so that the air flow is mainly over the top, then spin the other way if you lower the dryer so that the air flow is mainly over the bottom. If the pinwheel is acting like a propeller instead, then raising or lowering the hair dryer while at 90 degrees would not change the direction of spin. It’s possible that the pinwheel is acting as a mixture of a paddle wheel and a propeller. Predicting the results for moving the height of the air flow would then become difficult, and you would have to come up with a different strategy to determine what’s going on.

Remember though, that the observations are right even if you can’t come up with a simple explanation.

Good luck with your project!