[TowerTalk] Mast Comparison Tables

[ROBKEL@aol.com]

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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