Ham Radio Roof Tower Calculations

(updated 4 Nov 2018)

W8IO
815HD Ham Roof
Tower Calculations

The model IO-815HD roof tower has a rating of 15 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-815HD tower, set V = 80 mph and Ap = 15.0 square feet. Our Force equation becomes as follows.

F = 0.00256 * 80 * 80 * 15.0 * 1.0 * 1.2 * 1.25 = 368.64 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-815HD, this is approximately M = 368.64 * 8 = 2949 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 9 feet (1 foot above the top of the tower), the force (F) should be no more than 327.68 lb. For the same wind speed (80 mph), the area (Ap) is 13.33 square feet.

I have produced the table below for a SINGLE ANTENNA mounted at various heights above the IO-815HD roof tower.

Total Height (feet) | Height above tower (feet) | Max. Force (lbs.) | Max. Antenna area (sq. ft.) at 80 mph |

9 | 1 | 327.68 | 13.33 |

9.5 | 1.5 | 310.42 | 12.63 |

10 | 2 | 294.9 | 12.0 |

10.5 | 2.5 | 280.86 | 11.43 |

11 | 3 | 268.09 |
10.91 |

11.5 | 3.5 | 256.43 |
10.43 |

12 | 4 | 245.75 |
10.0 |

12.5 | 4.5 | 235.92 |
9.6 |

13 | 5 | 226.85 |
9.23 |

13.5 | 5.5 | 218.44 |
8.89 |

14 | 6 | 210.64 |
8.57 |

14.5 | 6.5 | 203.38 |
8.28 |

15 | 7 | 196.6 |
8.0 |

Here is a table below for TWO ANTENNAS, with a 6 SQ FT antenna mounted at the tower top and a second antenna mounted at various heights above the IO-815HD roof tower. The first (lower antenna) produces 147.45 lb. force at the tower top and 1180 ft-lbs moment at the IO-815HD tower base. The maximum Moment at the tower base is 2949 ft-lbs, so we must not exceed 1769 ft-lbs Moment with the second (higher) antenna. (1180 + 1769 = 2949) For these calculations, we ignore the wind area of the mast and we assume the mast is extremely strong.

Total Height (feet) | Height of 2nd Ant. abv tower (feet) | Max. Moment of 2nd Ant. (Ft-lbs.) | Max. Force of 2nd Ant. (lbs.) | Max. 2nd Ant. area (sq. ft.) at 80 mph |

10 |
2 |
1769 |
176.9 | 7.2 |

10.5 |
2.5 |
1769 |
168.5 | 6.8 |

11 |
3 |
1769 |
160.8 | 6.5 |

11.5 |
3.5 |
1769 |
153.8 | 6.2 |

12 |
4 |
1769 |
147.4 | 6.0 |

12.5 |
4.5 |
1769 |
141.5 | 5.7 |

13 |
5 |
1769 |
136 | 5.5 |

13.5 |
5.5 |
1769 |
131 | 5.3 |

14 |
6 |
1769 |
126.3 | 5.1 |

14.5 |
6.5 |
1769 |
122 | 4.9 |

15 |
7 |
1769 |
118 | 4.8 |

15.5 |
7.5 |
1769 |
114 | 4.6 |

16 |
8 |
1769 |
110.5 | 4.5 |

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 13.33 square feet is 327.68 ft.-lbs. (327.68 lb * 1 foot) This is also the same as 3932 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) | 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) |
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) |

9 | 1 | 327.68 | 13.33 | 3932 | 5319 | 5908 | 11747 | 12506 | 22003 |

9.5 | 1.5 | 310.42 |
12.63 |
5588 |
7560 | 8396 | 16694 |
17773 |
31270 |

10 | 2 | 294.9 |
12.0 |
7078 |
9576 | 10635 | 21145 |
22513 |
39608 |

10.5 | 2.5 | 280.86 |
11.43 |
8426 |
11399 | 12660 | 25172 |
26800 |
47152 |

11 | 3 | 268.09 |
10.91 |
9651 |
13057 | 14501 | 28831 |
30697 |
54007 |

11.5 | 3.5 | 256.43 |
10.43 |
10770 |
14570 | 16182 | 32174 |
34256 |
60269 |

12 | 4 | 245.75 |
10.0 |
11796 |
15959 | 17724 | 35240 |
37519 |
X |

12.5 | 4.5 | 235.92 |
9.6 |
12740 |
17236 | 19142 | 38060 |
40522 |
X |

13 | 5 | 226.85 |
9.23 |
13611 |
18414 | 20451 | 40662 |
43292 |
X |

13.5 | 5.5 | 218.44 |
8.89 |
14417 |
19505 | 21662 | 43070 |
45856 |
X |

14 | 6 | 210.64 |
8.57 |
15166 |
20518 | 22787 | 45307 |
48238 |
X |

14.5 | 6.5 | 203.38 |
8.28 |
15864 |
21462 | 23836 | 47392 |
50458 |
X |

15 | 7 | 196.6 |
8 |
16514 |
22342 | 24812 | 49334 |
52525 |
X |

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 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