Ham Radio Roof Tower Calculations

My model IO-810 roof tower is 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.

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-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 (distributed over 4 attachment points) is M = F * D, where D is the distance to the attachment point (base).

For the IO-810, this is approximately  M = 245.76 * 8 = 1966 ft-lbs.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.

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
91218.448.9
9.51.5206.958.4
102196.68.0
10.52.5187.247.6
113178.737.3
11.53.5170.956.9
124163.86.7
12.54.5157.36.4
135151.26.1
13.55.5145.65.9
146140.45.7
14.56.5135.65.5
157131.05.3

Mast Analysis:

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 1.9 inch OD and 1.6 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)
91218.448.926217830833614642
9.51.5206.958.43725111281184820810
102196.68.04718140951500626358
10.52.5187.247.65617167801786631379
113178.737.36434192212046435944
11.53.5170.956.97180214502283740179
124163.86.67862234872500643995
12.54.5157.36.48494253752701647532
135151.26.19072271022885550767
13.55.5145.65.99610287093056653777
146140.45.710109302003215356570
14.56.5135.65.510577315983364259189
157131.05.311004328733500061578

Compare the stress at the reference point to the Yeild Strength of the material to determine if that particular configuration 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.

Mast Choices:

6061-T6 Aluminum is a strong light weight mast material, however it is not as strong as most galvanized steel masts sold by Amateur Radio Dealers. Beware of ordinary steel water pipe! Unless you know the grade of material and it’s yeild 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 yeild strength of 80,000 psi or higher.

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 mast is about $129. Other lengths available.
HRO – US Tower M10, galvanized, reinforced, 10 foot steel mast, 2″ OD x 0.120″ wall is about $129. Other lengths available.
Texas Towers – Universal Tower AM-216, 16 foot long 6061-T6 aluminum 2″ OD x 0.120″ wall mast is about $109.
Penninger Radio – 6061-T6 Aluminum 2″ OD x 0.250″ wall x 10 feet long is about $100. Other lengths available.
Penninger Radio – 6061-T6 Aluminum 2″ OD x 0.125″ wall x 10 feet long is about $62. Other lengths available.
Online Metals – 6061-T6 Aluminum Schedule 80, 1.9″ OD x 0.200″ wall x 8 feet long is about $47. Shorter lengths available.

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 and  Antenna Wind Loading as a Function of Height”, Frank Javanty W9JCC, QEX July/August 2001, pp 23-33

“Tower Tips”  a compilation of many tower tips from various authors

K7NV’s Windload equations

EIA/TIA-222-G Explained