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Assuming a small umbrella (e.g. http://www.amazon.com/ShedRain-WindPro-Umbrella-Close-Size/dp/B001DL5WN0). What are the factors that need to be considered? I assume where I hold the umbrella might dictate part of the calculation of torque which in turn is dependent on the weight of the umbrella. But what about effects like (a light) wind that can turn the umbrella into a sail and make it seemingly harder to hold?

How would I calculate for example total torque required to hold the umbrella accounting for light wind as well?

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The drag equation en.wikipedia.org/wiki/Drag_equation is the force from the wind and it depends on the shape en.wikipedia.org/wiki/Drag_coefficient –  Martin Beckett Jan 31 '13 at 16:57
That's an interesting question I often ask when I hold an umbrella - except that my perception seems to be the opposite to yours. I usually feel that an umbrella is a wing/aircraft of a sort that seems lighter than it should be. Which way it goes for a normal shape umbrella oriented in the normal upside direction and a horizontal, reasonably large wind speed? Maybe I just know how to manipulate the umbrella so that it feels lighter and you prefer to make your work harder. ;-) –  LuboŇ° Motl Jan 31 '13 at 17:06
I seem to observe that if I hold such that the umbrella generates lift I usually end up getting wet unless I hold the umbrella such that its canopy is very close to the top of my head and it gets some lift while deflecting rain from my head. –  Jon Jan 31 '13 at 17:28

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