A simplified mast trade-off study
I thought I would make a small contribution to the famous aluminum vs steel
discussion.
In the same vein as Kurt, NI6W, put forth earlier, I propose a 'Figure of
merit' to evaluate the different configurations and materials.
Referring to Leeson's Book (Physical Design of Yagi Antennas) we know the
relation between the maximum permissible resisting moment of a beam (mast) to
be: M = S*Z; where: M= moment in inch*lbs; S = yeild stress in psi of the
material; and Z= the section modulus in inch^3 of the 'beam' (mast).
Leeson provides the Section modulus for hollow cylinders on page 3-4, and I
have calculated a range of values for different wall thicknesses and OD's as
follows: (The larger the 'Z', the stronger the beam (mast) for a given
material)
OD: Thk: ID: Z = Comments
2.00 0.13 1.75 0.33
2.00 0.25 1.50 0.54
2.38 0.15 2.07 0.56 Sch 40 Pipe
2.00 0.38 1.25 0.67
2.25 0.25 1.75 0.71
2.38 0.22 1.94 0.73 Sch 80 Pipe
2.00 0.50 1.00 0.74
2.25 0.38 1.50 0.90
2.50 0.25 2.00 0.91
2.25 0.50 1.25 1.01
2.88 0.20 2.47 1.06 Sch 40 Pipe
2.50 0.38 1.75 1.17
2.50 0.50 1.50 1.34
2.88 0.28 2.32 1.34 Sch 80 Pipe
2.75 0.38 2.00 1.47
2.75 0.50 1.75 1.71
All of the above are tube or pipe sizes as indicated.
Both Aluminum and steel are available in these sizes.
We can now examine the relative mast strength as represented by the maximum
resisting Moment a given configuration can handle without permanent
deformation. Note that this 'figure of merit' is independent of the antenna
configuration, or other assumptions about safety margins, windspeeds, etc.
Those parameters are a function of each individual case, and the individual
concerned must apply the results to his/her antenna configuration, etc.
Here are the 'F-O-M' (in inch-lbs) to go with the sizes above.
The columns reflect standard 6061-T6 Aluminum, the more rare but worth trying
to find 7075-T6 aluminum, and a standard Texas Tower Steel mast and the higher
rated Productivity Resources 110kpsi mast. Of course, the last two are
available only in 2.0x0.25wall and 2.0x0.375wall respectively. The figures for
other steel sizes are for reference only in case you find something like them.
The weights are based on a 20ft mast.
TexTwr
PR
6061 7075 Al Mast Mast Steel
OD Thk. Fy=35k 70k wt. 87k 110k Wt.
2.00 0.13 11375 22751 18 28276 35751 50
2.00 0.25 18791 37583 33 46710 59058 94
2.38 0.15 19622 39244 26 48775 61669 73
2.00 0.38 23294 46589 46 57903 73211 130
2.25 0.25 24816 49633 38 61686 77994 107
2.38 0.22 25581 51162 35 63587 80397 101
2.00 0.50 25771 51542 57 64059 80994 160
2.25 0.38 31408 62817 53 78072 98712 150
2.50 0.25 31698 63396 42 78793 99623 120
2.25 0.50 35411 70822 66 88022 111292 187
2.88 0.20 37241 74483 41 92571 117044 116
2.50 0.38 40799 81597 60 101413 128224 170
2.50 0.50 46731 93462 75 116160 146869 214
2.88 0.28 46851 93702 54 116458 147246 153
2.75 0.38 51469 102937 67 127936 161758 190
2.75 0.50 59742 119483 85 148500 187759 240
I happened to have lucked into a section of 7075-T6, 2.25x0.437wall, with
factory markings, in a scrap yard. It compares favorably with the PR mast,
cost me $80, and weighs 60#. It pays to check those places out. You are also
likely to find the pipe sizes or other thick walled stuff there.
One could also make FOM/$ or FOM/lb or even FOM/$*lbs comparisons, but I don't
think those would be very meaningful.
I hope this is helpful.
Bob, W5LT
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