# How size of objects lifted by the wind depends on the speed of the wind?

What are the sizes of the objects that could be picked up and flown by tornados, depending on the tornado's speed?

To put it another way, assuming turbulent flow and object density much higher than that of air, what is the dependency of the maximal size of the flying object on the speed of the wind around it? Assume the objects are of similar shapes and densities.

My naive estimate is like this: denote characteristic size of the object $l$, denote wind speed $v$, then the weight of the object $mg=const\cdot l^3$, and the force of the wind $f=const\cdot l^2\cdot v^2$. Therefore $l\sim v^2$. Is this estimate correct for the above conditions?

• I think the title of yet question should be modified so that future users will be able to locate this question more easily on search. – Gaurav Jan 16 '15 at 15:29
• Drag or lift force is $F \propto \rho A v^2$ where $\rho$ is air density, $A$ is frontal area of object and $v$ is wind speed. Equate this with $W=\rho_{body} g A \ell$ for a cylindrical body and see what comes out. – ja72 Jan 16 '15 at 19:35

Force per unit area is proportional to $v^2$.
Weight per unit area is proportional to $l$.
So yes, if you double $v$, you have to quadruple $l$.