[Towertalk] helix windload: an interesting problem

[jljarvis]

Eric, wd3q; Towertalkians:

I'd be interested in knowing if someone pops up with
a real solution to this problem.  Let me suggest a couple
of simple approximations, in the hope that this will
stimulate the more mathematically inclined toward a more
rigorous analysis.

1) First, the simplest approach.  Assume the helix to be
a perfect cylinder.  
	Calculate the end surface area, using Pi r^2.
	Calculate the projected side surface area, L * D
	Take whichever is larger, and multiply it by
	the appropriate lbs/ft^2 for your desired windspeed.
	(100mph=40lbs/ft^2, 70mph=30lbs/ft^2)

   This is WRONG...but it would seem to be a maximum case,
which is what you're REALLY looking for.

2)  If you want to refine that estimate, I believe engineers
use a .70 factor, (PE's, wade in here, pse) to adjust the
calculated projected area of a cylinder for its roundness.  

3)  Depending on the relative diameter and length, and number
of turns in the helix, you might contemplate that maximum wind
load would be a COMBINATION of frontal area and lateral area,
at 45 degrees.  In that case,  multiply each area by .707, and
add the results together.  If that's larger than either surface
alone, use that figure.

4)  If you want to further refine this, you could calculate 
actual projected areas of the tube, still considering the 
frontal, lateral,and angular positions, and looking for the maximum.   

	Calculate the frontal area using Pi r^2 of the outer 
	boundary of the tube, minus Pi r^2 of the inner boundary
	of that tube.

	Calculate frontal area of the boom similarly, along with
	support struts.

	Calculate lateral area, this time assuming that ALL the
	helical tube is exposed to the wind.  Take the length of
	the unwound tubing, times the diameter of that tubing.
	(multiply by .7, or whatever that square/round figure of
	merit is.)  Don't forget the strut areas.  

	Again, compare frontal area to lateral area, to the 45
	degree case, looking for a maximum.
	

Again, all of your results are approximations which are believed
to overstate the load.  

5)  It occurs to me that you might have a rear reflective surface
area to consider, as well.  That's liable to dominate the solution,
so don't forget to add it in.   

This would be a good time for a mathemetician to step in and 
propose a better solution.

Also....has anyone seen a published methodology for calculation
of YAGI windloads?  Allowance for turbulence over downstream
elements?  How does it differ from my spatial approach, above?

I note that The ARRL Antenna Book is silent on the topic.

Jim/N2EA