Expert: Paul Soderman - 2/19/2009

Question
I am attempting to understand how wind will deflect a verticle pole of a given material, diameter and length (i.e. sway angles / deflection).
Can you provide some refererences or calculations that I might use to determine how much "sway" I can estimate?

Answer
Howard
That is a very good question.  Off the top of my head there is a static solution and a dynamic solution.  Statically, we can predict the drag of the pole, but we have to assume a wind distribution because the earth's boundary layer provides a non-uniform wind near the ground.  Then we have to calculate the bending of the pole based on its stiffness.

Dynamically, we have to predict the drag plus a vortex shedding that will induce an oscillation in the pole.

This is an engineering problem that is longer than I can address in this forum.  Following are some ideas.  (If you really need a good answer, I would have to do it as a consulting engineer -  you can contact me at psoderman@gmail.com - not that I'm looking for work).

Drag = CdqS

q = dynamic pressure = rho* V^2 / 2
rho = air density
V = wind speed
S = cross sectional area
Cd = drag coefficient, which can be approximated as 1.0 to first order

All units must be consistent.

The pole bending is found by looking at cantilever beam equations that give deflection as a function of loading and beam geometry, which I would have to look up.

The vortex shedding rate gives an oscillation frequency, but the drag equation above is probably a good load analysis.  The static solution is probably a good first order solution.

I wish I could be more definitive, but I don't have time here.  You might be able to get help on line by searching on pole bending or pole oscillations.  Check out http://www.bobkingsley.co.uk/blog/?p=210  Good luck.

Paul