Towers and Wind Load

[TowerTalk] I have a crank-up tower rated at 30 sq. ft. for a 50 mph wind. I have 20ft. of chrome-molly mast with 4 ft. in the tower. I want to de-rate the wind load for 70 mph. How do I do this and what effect does the mast have on the wind loading limits of the tower? I want to put 8 sq.ft. near the top of the mast and 8.5 sq. ft. at the top of the tower. Can I do this, or am I dancing with disaster?

To which W6OLD wrote: Pay for a PE to work the numbers for you, Henry. If you will be going for a building permit, you'll have to do that anyway.

That would be the safe/correct way to go. But, to give you a ballpark guess, I'll go though a couple equations that everyone could apply to their particular case.

Let's start with the 50 MPH vs. 70 MPH.

New wind load = old wind load * (old wind speed)^2 / (new wind speed)^2
= 30 * 50^2 / 70^2

= 15.3 sq.ft

By that quick calculation, your 8 + 8.5 sq.ft would be over the rating.

I was going to go into the calculation about the mast height, but it may be too much for most of the readers. On second thought, it reduces pretty nicely. This applies to self-supporting and crank-up towers, not guyed towers. I won't explain it, but will give you the equation:

W = rated wind load
w1= wind load antenna 1
w2= wind load antenna 2
h = tower height
m = mast length (or how far above tower top that antenna 2 is mounted)
d = mast diameter, in feet (ie. 2" / 12 = 0.16666)

W*h >= w1*h + w2*(h + m) + (0.67*d*m)*(h + m/2)

So, if we were to assume that 15.3 sq.ft. is the rating at 70 MPH (remember, that is a close estimate...get a PE to verify), and a 8.5sq.ft. antenna at the top of a 70'(?) tower. How big of antenna can we put 16 feet (20' mast, 4' in tower) above the tower on a mast?

15.3 * 70 >= 8.5 * 70 + X*(70 + 16) + (0.67*0.1666*16)*(70 + 16/2)
1071 >= 595 + X*(86) + 208
268 >= X*86
3.1 >= X

So, as a ROUGH ESTIMATE, you could only have a 3.1 sq.ft antenna at the top of the mast. Notice that 3.1 + 8.5 is nowhere near the 15.3 number. So, you could put up a 4 el 10M beam.

Now remember, I'm not a PE. These equations are to help you get close to an antenna/tower configuration that might work. It is not intended for a final check. Once you get in the ballpark of what might work, then take all that to a PE. These equations are to save you a few extra trips to the PE office. Choosing antennas/towers is a very iterative process. By the very nature of the ham, we are experimenters. We always like to try something different. If we had to check each idea with a PE, it could become very costly.

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Chad Kurszewski, WE9V