Ham Radio Roof Tower Calculations
(updated 17 Feb 2015)
W8IO
Ham Roof
Tower Calculations
My model IO810 roof tower is based on the Glen Martin RT832 roof tower. I have placed a rating of 10 square feet at 80 mph on it, slightly less than what the RT832 has. This was done because of the many unknowns. The major unknown is what the weakest point of the structure is. I estimate that the roof itself may be the weakest point, as there are many variables, including bolt size, deck thickness, shingle composition and thickness, and what was used for backup under the deck. Another unknown includes the method of determining the antenna's effective wind area. An old method, but now considered inaccurate, is to calculate the effective area of the boom and elements separately, then combine the two using the square root of the sum of the squares of each. Also, the antenna effective area often included a 2/3 shape factor for aluminum tubing construction. This has also been replaced with newer, more accurate drag coefficients. EIA222F is likely a good reference for the equations necessary to calculate antenna tower stress. The newest specification for analyzing commercial steel antenna towers is EIA/TIA222G, however this is overkill for most small towers, including roof towers. You can find links to these and other specifications at the bottom of this page.
Maximum Antenna Wind Area based on the Tower:
Here are the equations that I recommend.
The horizontal force exerted at the attachment point of a single antenna, mounted just above the thrust bearing is labelled F.
F = 0.00256 * V * V * Ap * Kz * Cd * Gh
where V = fastest mile wind speed
Ap = projected area
Kz = exposure coefficient
Cd = drag coefficient
Gh = gust response
If we assume that the antenna height is approximately 33 feet above ground, then Kz = 1.0, Gh = 1.25 and for HF and VHF yagi antennas, Cd = 1.2.
For the IO810 tower, set V = 80 mph and Ap = 10.0 square feet. Our Force equation becomes as follows.
F = 0.00256 * 80 * 80 * 10.0 * 1.0 * 1.2 * 1.25 = 245.76 lb.
The Moment at the base (distributed over 4 attachment points) is M = F * D, where D is the distance to the attachment point (base).
For the IO810, this is approximately M = 245.76 * 8 = 1966 ftlbs.
This is as far as I can go, as the analysis of the stress at these attachment points is more complex than what I am familiar with. However, I can work backwards from this point to predict the maximum antenna effective area that can be attached at various heights above the top of the tower, assuming a strong enough mast.Total Height (feet)  Height above tower (feet)  Max. Force (lbs.)  Max. Antenna area (sq. ft.) at 80 mph 
9  1  218.44  8.9 
9.5  1.5  206.95  8.4 
10  2  196.6  8.0 
10.5  2.5  187.24  7.6 
11  3  178.73  7.3 
11.5  3.5  170.95  6.9 
12  4  163.8  6.7 
12.5  4.5  157.3  6.4 
13  5  151.2  6.1 
13.5  5.5  145.6  5.9 
14  6  140.4  5.7 
14.5  6.5  135.6  5.5 
15  7  131.0  5.3 
Total Height (feet) 
Height ABOVE tower (feet) 
Max Force (lbs.) 
Max Antenna area at 80 mph (sq. ft.) 
Moment at Thrust Bearing (inchlb) 
Stress at Thrust
Bearing
based on 1.9" OD and 1.6" ID (0.150" wall) I=0.318 (pounds per square
inch  psi)

Stress at Thrust
Bearing based on 2" OD and 1.76" ID (0.120" wall) I=0.3144 (pounds per square inch  psi) 
Stress at Thrust
Bearing
based on 2" OD and 1.875" ID (0.0625" wall) I=0.1787 (pounds per square
inch  psi)

9  1  218.44  8.9  2621  7830  8336  14642 
9.5  1.5  206.95  8.4  3725  11128  11848  20810 
10  2  196.6  8.0  4718  14095  15006  26358 
10.5  2.5  187.24  7.6  5617  16780  17866  31379 
11  3  178.73  7.3  6434  19221  20464  35944 
11.5  3.5  170.95  6.9  7180  21450  22837  40179 
12  4  163.8  6.6  7862  23487  25006  43995 
12.5  4.5  157.3  6.4  8494  25375  27016  47532 
13  5  151.2  6.1  9072  27102  28855  50767 
13.5  5.5  145.6  5.9  9610  28709  30566  53777 
14  6  140.4  5.7  10109  30200  32153  56570 
14.5  6.5  135.6  5.5  10577  31598  33642  59189 
15  7  131.0  5.3  11004  32873  35000  61578 
Compare
the stress at the reference point to the Yeild Strength of the material
to determine if that particular configuration will survive.
For
6061T6 aluminum, a conservative value of yeild strength is 35,000 psi.
The RED
values indicate that 6061T6 aluminum must NOT be used for those cases.
Also, you may want to avoid aluminum in cases that are marginal.
Helpful References:
"Match your Antenna to your Tower", Roger Cox WB0DGF, Ham Radio Magazine, June 1984
"Tower Tips" a compilation of many tower tips from various authors
contact Roger: email to
rgcox2 (at) gmail.com
Roger Cox, W8IO (exWB0DGF)  Spring Lake, MI 49456