The W8IO Antenna Site

Ham Radio Roof Tower Calculations

(updated 21 April 2021)

W8IO 610 Ham Roof Tower Calculations 

The model IO-610 roof tower has a rating of 10 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-610 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  = 245.8 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-610, this is approximately  M = 245.8 * 6 = 1475 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.

For a total height of 7 feet (1 foot above the top of the tower), the force (F) should be no more than 210.6 lb. For the same wind speed (80 mph), the area (Ap) is 8.5 square feet.

I have produced the table below for a SINGLE ANTENNA mounted at various heights above the IO-610 roof tower.

Total Height (feet) Height above tower (feet) Max. Force (lbs.) Max. Antenna area (sq. ft.) at 80 mph
7 1 210.6 8.5
7.5 1.5 196.7
 8.0
8 2 184.4
 7.5
8.5 2.5 173.5
 7.1
9 3 163.9
 6.7
9.5 3.5 155.3
 6.3
10 4 147.5
 6.0
10.5 4.5 140.5
 5.7
11 5 134.0
 5.4
11.5 5.5 128.3
 5.2

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 8.5 square feet is 210.6 ft.-lbs. (210.6 lb * 1 foot)  This is also the same as 2527 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 = 0.049087 * (13.0321 - 6.5536) = 0.318

For a 2.38 inch OD and 1.94 inch ID (schedule 80 tube), I = 0.049087 * (32.085 - 14.165) = 0.8796

To calculate the stress at the reference point, F = (M * c) / I  where c = OD / 2

For the given 1.9 inch OD 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 for a SINGLE ANTENNA.



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)
7 1 210.6 8.5 2527
 3419
3797
7550
 8037
 14141
7.5 1.5 196.7
 8.0
 3540
 4789
5319
10575
 11260
 19810
8
 2 184.4
 7.5
 4425
 5987
6649
13219
 14074
 24762
8.5
 2.5 173.5
 7.1
 5205
 7042
7821
15550
 16555
 29127
9
 3 163.9
 6.7
 5900
 7982
8865
17626
 18766
 33016
9.5
 3.5 155.3
 6.3
 6522
 8824
9800
19484
 20744
 36497
10
 4 147.5
 6
 7080
 9578
10638
21151
 22519
 39619
10.5
 4.5 140.5
 5.7
 7587
 10264
11400
22665
 24132
 42456
11
 5 134
 5.4
 8040
 10887
12080
24019
 25573
 44992
11.5
 5.5 128.3
 5.2
 8339
 11281
12530
24912
 26524
 46665

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.

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

contact Roger: email to 

rgcox2 (at) gmail.com

Roger Cox, W8IO (ex-WB0DGF) - Spring Lake, MI 49456