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Velocity/volume air calculation

Hi,
If I had something that was 80kg with a surface area of 0.3m2 and I wanted to suspend it in the air with wind, what would be the velocity and volume of air required?
I'm hoping somebody can give me this calc so it can be adjusted to different weights and sizes easily.

Cheers
latitude35s

Quote:

Originally Posted by latitude35s

Hi,
If I had something that was 80kg with a surface area of 0.3m2 and i wanted to suspend it in the air with wind, what would be the velocity and volume of air required?

It really depends on the shape of the object, as different shapes have different amounts of wind resistamce. But to get started:

You want the wind resistance to balance the weight of the object. The formula for weight is

$ W=mg $

and the formula for wind resistance is

$ F_w = \frac 1 2 \rho A C_d v^2 $

where $A$ = surface area that the wind impinges on, $C_d$ is a coefficient of drag (which depends very much on the shape of the object, [/math] \rho[/math] is the density of the air, and $v$ is the air velocity. So setting weight = wind resistance and solving for v:

$ v = \sqrt { \frac {2 mg} {\rho A C_d} } $

For air at sea level $\rho = 1.2$ Kg/m^3. For a boxy shape the coefficient of drag is about equal to 1. You said the surface area is 0.3 m^2; I will assume that this is the area of the face of the object opposing the wind (not the total surface area of the object). So:

$ v = \sqrt { \frac {2 \times 80 Kg \times 9.8 \frac m {s^2}} {1.2 \frac {Kg}{m^3} \times 0.3 m^2 \times 1}} = 66 \frac m s $

Again, this is a rough calculation at best. If you want to see some values for $C_d$ for different shapes see: http://en.wikipedia.org/wiki/Drag_coefficient

Great. Thanks for your help.