It was a very windy day today, and there are storm warnings for the sea and coastal region for tonight and tomorrow. On the evidence of a ten-mile walk today, I’ve decided that this would be the perfect occasion to make like Mary Poppins and receive my fifteen minutes of fame (does anyone remember the guy who tied balloons to a garden chair anymore?)
But how large an umbrella and how strong winds would it take to lift, say, a five-foot-five, 160 pound person into the air? Is there a physics formula for it, or should I just experiment with cocktail umbrellas, lumps of clay and a blowdryer until I get it right?
I think you’ll be able to get a ballpark answer by using the drag equation
Fd=cd1/2ρv^2A
Where:
Fd = Force of drag. To start to get lift, you need to have this be equal to your weight (160lb)
cd = coefficient of drag. For a hollow semi sphere opposite stream, cd=1.42
ρ = air density
v = flow velocity (the wind speed)
A = frontal area = pi*(radius of umbrella)^2
Subbing in for air density and customary units, you get the equation
160lb=0.00364v^2A, Where v is in mph and A is in ft^2
So for a gale force wind (40mph), you’d need an umbrella with an opening about 27.5ft^2 (almost 6 feet in diameter) to get lift, if my math is correct.
Note that this assumes that the wind is blowing directly upward (not really likely), so you’re going to have to work out oblique flow angles on your own.
Thanks! Well, that’s somewhat bigger than your average golf umbrella, so I’ll pass. Besides, the gale has abated since yesterday (I might go down to the seashore later and have a look for myself) without anyone coming to harm. Several uprooted trees and damaged power lines in the region, and some parasailing corrugated roofs.
Parasailing is different in that it is done with little wind and you want some control of it. If all you want is being ripped of the face of the Earh under gale winds, a much smaller wing should suffice.
And 6 feet in diameter is well in the range of patio umbrellas. I say grab a camera and go for it.
Your main problem, by the way, if the umbrella doesn’t invert on you, might be holding on to the umbrella. That Mary Poppings must have had arms and hands of steel to hang to that umbrella by one arm in curled position. You might look more like dangling with both hands. And you will definitely need to fix your hair afterwards (if applicable)
