The W8IO Antenna Site

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.

For a total height of 5.5 feet (1 foot above the top of the tower), the force (F) should be no more than 261.5 lb. For the same wind speed (80 mph), the area (Ap) is 10.6 square feet.

I have produced the table below for a SINGLE ANTENNA mounted at various heights above the IO-45HD roof tower.

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


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 10.6 square feet is 261.5 ft.-lbs. (261.5 lb * 1 foot)  This is also the same as 3138 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)
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.


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