The model IO-810 roof tower was originally based on the Glen Martin RT-832 roof tower. I have placed a rating of 10 square feet at 80 mph on it, slightly less than what the RT-832 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 back-up 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. EIA-222-F 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/TIA-222-G, 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.
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-810 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 is distributed over 2 pivot points and 2 attachment points. M = F * D, where D is the distance to the attachment point (height of the tower). For the IO-810, this is approximately M = 245.76 * 8ft = 1966 ft-lbs. Now to look at the pullout Force on the bolts at the attachment points. Because there are two, this evenly splits the load (1966 / 2 = 983 ). So M= 983 ft-lbs / 2.5ft (distance between attach and pivot), = a Force of 393 lbs. For a total height of 9 feet (1 foot above the top of the tower), the force (F) should be no more than 218.44 lb. For the same wind speed (80 mph), the area (Ap) is 8.89 square feet.
I have produced the table below for various heights.
| 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 |
To determine the mast strength, begin by placing the antenna attachment point at the top of the thrust bearing and placing the horizontal Force at this point. The Moment at this point is zero because the distance to the reference point (thrust bearing) is also zero. If the antenna attachment point is moved up one foot, the Moment at the reference point created by 8.9 square feet is 218 ft.-lbs. (218.44 lb * 1 foot) This is also the same as 2621 inch-lb. See the table below for the various heights above the thrust bearing.
To calculate the stress at the reference point, we need the Moment of Inertia (I) of the proposed mast. This is calculated from the OD and ID of the hollow tube. You can also find it here.
I = (3.14159 / 64) * (OD^4 – ID^4) where OD and ID are in inches
For a 1.90 inch OD and 1.50 inch ID (schedule 40 tube), I = 0.318
To calculate the stress at the reference point, F = (M * c) / I where c = OD / 2
For the given tube dimensions, F = (M * 0.95) / 0.318
The wind acting on the mast also adds a little more stress, but for simplicity I have omitted this.
See the table below for the various values.
| Total Height (feet) | Height ABOVE tower (feet) | Max Force (lbs.) | Max Antenna area at 80 mph (sq. ft.) | Moment at Thrust Bearing (inch-lb) | 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 Yield Strength of the material to determine if that particular configuration will survive. For 6061-T6 aluminum, a conservative value of yield strength is 35,000 psi. The RED values indicate that 6061-T6 aluminum should not be used for those cases.
6061-T6 Aluminum is a strong light weight mast material. Aluminum masts can be used safely with caution. I would not use an aluminum mast with a wall thickness of 0.150″ or less. Common wall thicknesses of 0.150″ and 0.200″ are common and work well with OD’s of 1.90″ and 2.0″. 6061-T6 is a good, strong aluminum alloy and has a yield strength of 35,000 psi. Normally, I would use a 1.9″ OD x 0.200″ wall 6061-T6 mast with the HF beam mounted just above the thrust bearing. If the wind load of the HF beam is 2 to 5 sq. ft. less than the tower’s limit, then you can also stack a small or medium sized VHF beam or omni a couple feet above the HF beam. If the HF beam is 0.5 to 1 sq. ft. less than the tower’s limit, then you can only stack a short VHF or UHF omni just above the HF beam. Beware of ordinary steel water pipe! Unless you know the grade of material and its yield and tensile properties, it may be weaker than aluminum and will rust if not galvanized. Most galvanized steel mast material sold by Ham Dealers have a yield strength of 70,000 to 80,000 psi or higher. As long as you are shipping 8 ft lengths or less, the shipping cost is reasonable.
Here are some places to find tower masts:
Texas Towers – Texcom Steel masts, galvanized, 87,000 psi typical. A 10 foot long 2″ OD x 0.120″ wall. Other lengths available.
HRO – US Tower M10, galvanized, reinforced, 10 foot steel mast, 2″ OD x 0.120″ wall. Other lengths available.
Texas Towers – Universal Tower AM-216, 16 foot long 6061-T6 aluminum 2″ OD x 0.120″ wall.
Penninger Radio – 6061-T6 Aluminum 2″ OD x 0.250″ wall x 8 feet long. Other lengths available.
Carlson Comm – 6061-T6 Aluminum Schedule 40, 1.90″ OD x 1.50″ ID (.200) wall x 8 feet long is about $120. Shorter lengths available.
“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