# How much wind velocity is required to lift a sphere?

What is the math on how much wind speed is required to lift a given mass in a vertical wind tunnel, assuming a spherical object?

• -1. No research effort. – sammy gerbil Aug 17 '17 at 22:04

The formula for drag force is $$F = \frac{1}{2}*p*v^2*c_d*A$$

• $C_d$ is your coefficient of drag, which is about 0.5 for a sphere. (Independent of size or material)
• $p$ is the density of the air. Approximately $1.225 \frac{kg}{m^3}$ at sea level.
• $v^2$ is your wind velocity, what you need to solve for
• $A$ is the 2-D cross sectional area of the sphere Use $A = \pi * r^2$

Assuming you want your sphere to levitate you want to set $F = m*g$ of the sphere. So in your case you want to solve for $v$.

$$v = \sqrt{\frac{2*mg}{p*c_d*A}}$$