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[TowerTalk] Mast Comparison Tables

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Subject: [TowerTalk] Mast Comparison Tables
From: ROBKEL@aol.com (ROBKEL@aol.com)
Date: Mon, 19 Oct 1998 22:16:40 EDT
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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