Ham Radio Roof Tower Calculations
(updated 5 April 2020)
W8IO 45HD Ham Roof
Tower Calculations
The model IO-45HD roof tower has a rating of 13 square feet at 80 mph.
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 IO-45HD tower, set V = 80 mph and Ap = 13.0 square feet. Our Force equation becomes as follows.
F = 0.00256 * 80 * 80 * 13.0 * 1.0 * 1.2 * 1.25 = 319.5 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 IO-45HD, this is approximately M = 319.5 * 4.5 = 1438 ft-lbs.
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 very strong mast.Total Height (feet) | Height above tower (feet) | Max. Force (lbs.) | Max. Antenna area (sq. ft.) at 80 mph |
5.5 | 1 | 261.5 | 10.6 |
6 | 1.5 | 239.6 |
9.75 |
6.5 | 2 | 221.2 |
9.0 |
7 | 2.5 | 205.4 |
8.3 |
7.5 | 3 | 191.7 |
7.8 |
8 | 3.5 | 179.7 |
7.3 |
8.5 | 4 | 169.1 |
6.8 |
9 | 4.5 | 159.7 |
6.5 |
9.5 | 5 | 151.3 |
6.1 |
10 | 5.5 | 143.8 |
5.8 |
Total Height (feet) |
Height ABOVE tower (feet) |
Max Force (lbs.) |
Max Ant area at 80 mph (sq. ft.) |
Moment at Thrust Bearing (inch-lb) |
STRONGEST
Stress at Thrust Bearing based on 2.38" OD x 1.94" ID (0.220" wall) I=0.8796 (pounds per square
inch - psi) | STRONG Stress at Thrust Bearing based on 2.00" OD x 1.25" ID (0.375" wall) I=0.66555 (pounds per square inch - psi) |
Stress at Thrust Bearing based on 1.9" OD x 1.6" ID (0.150" wall) I=0.318 (pounds per
square inch - psi) |
WEAKER Stress at Thrust Bearing based on 2" OD x 1.76" ID (0.120" wall) I=0.3144 (pounds per square inch - psi) |
WEAKEST
Stress at Thrust Bearing based on 2" OD x 1.875" ID (0.0625" wall) I=0.1787 (pounds per
square inch - psi) |
5.5 | 1 | 261.5 | 10.6 | 3138 | 4245 | 4715 | 9374 |
9980 |
17560 |
6 | 1.5 | 239.6 |
9.75 |
4313 |
5835 | 6480 | 12885 |
13718 |
24135 |
6.5 |
2 | 221.2 |
9.0 |
5308 |
7181 | 7975 | 15857 |
16883 |
29703 |
7 |
2.5 | 205.4 |
8.3 |
6162 |
8336 | 9259 | 18408 |
19599 |
34482 |
7.5 |
3 | 191.7 |
7.8 |
6901 |
9336 | 10369 | 20616 |
21950 |
38618 |
8 |
3.5 | 179.7 |
7.3 |
7547 |
10210 | 11339 | 22546 |
24004 |
42233 |
8.5 |
4 | 169.1 |
6.8 |
8116 |
10980 | 12194 | 24246 |
25814 |
45417 |
9 |
4.5 | 159.7 |
6.5 |
8623 |
11666 | 12956 | 25760 |
27427 |
48254 |
9.5 |
5 | 151.3 |
6.1 |
9078 |
12281 | 13640 | 27120 |
28874 |
50800 |
10 |
5.5 | 143.8 |
5.8 |
9490 |
12839 | 14259 | 28351 |
30184 |
53106 |
Compare
the stress at the reference point to the Yeild Strength of the material
to determine if that particular configuration (height, Antenna Area, OD, ID) will survive.
For
6061-T6 aluminum, a conservative value of yeild strength is 35,000 psi.
The RED
values indicate that 6061-T6 aluminum must NOT be used for those cases.
Also, you may want to avoid aluminum in cases that are marginal. For values in RED,
high-strength galvanized steel must be used. For values marked with an
"X", that particular mast OD and ID should not be used - either with
aluminum or galvanized steel.
Helpful References:
"Match your Antenna to your Tower", Roger Cox WB0DGF, Ham Radio Magazine, June 1984
"Practical Application of Wind-Load Standards to Yagi Antennas: Part 1", Stuart E. Bonney K5PB, QEX Jan/Feb 1999, pp 46-50
"Practical Application of Wind-Load Standards to Yagi Antennas: Part 2", Stuart E. Bonney K5PB, QEX Mar/Apr 1999, pp 44-49
"Tower Tips" a compilation of many tower tips from various authors
contact Roger: email to
rgcox2 (at) gmail.com
Roger Cox, W8IO (ex-WB0DGF) - Spring Lake, MI 49456