let’s choose some simple geometry, say a box
3 m tall, 2 m wide, and 2 m deep. (Scientists like to work in meters, not
feet! I will convert back into English
units in the end. The weight may be
thought of as acting at the geometrical center of the volume (if the weight is
more or less uniformly distributed and the force from the wind may be thought
of as acting at the center of the face being blown on (as long as the wind has
the the same speed everywhere. What I
can say for sure is that the force of the wind will be proportional to v2 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.