First,
let’s choose some simple geometry, say a *v*^{2} where *v* is the speed of the wind.
The proportionality constant is where the geometry of the object comes
in. There is a handy formula which is
approximately true for the force on a sphere of diameter *D *which is in a wind of speed *v*:
. So, suppose we say that the force is about
the same order as that on a sphere of radius 3 m, then approximately.
Now, the wind is trying to tip the tower about the far edge (where the
little “donut” is) and the weight is trying to keep it from tipping. The torques must be the same and then if the
wind is any faster it will tip over. The
torque is force times moment arm and the moment arms are 1 m for the weight and
1.5 m for the wind force. The weight
(500 lb) is about 2200 N (newtons).
Therefore, . Solving, m/s which is about 60 mi/hr.