To all interested parties,
I've had some requests for expanded comments on the mast comparison I
posted on Thursday.
Notice that there is not a 2" diameter aluminum mast in the comparison.
That is because there isn't a 2" Dia aluminum mast that can be
equivalent to the Texas Towers steel mast.
Even if the mast was 2" solid bar, it would only achieve a safety factor
of 1.0 at the target bending moment. That makes it about 60% as strong
as the baseline mast, and it would weigh about 75 Lbs. So you can reduce
the weight by 20% and reduce the strength by 40% with a 2" solid
aluminum replacement for the steel mast. The solid 2" aluminum mast will
bend twice as much as the steel one.
If you only need to put half as much stuff on the mast, then you're in
great shape.
The basic rule of thumb for using aluminum masts is, If you want to go
aluminum you have to go up in diameter. The lightest mast is the larger
mast. This reduces the available area for antennas to stay within the
tower rating. You can choose to use a purchased bearing at the top or
make a wooden one (as suggested by one contributor).
The increase in mast diameter will require some form of adapter to get
it into many of the popular rotators.
If we were to make a comparison to one of K5RC's masts, 2" Dia x .375
wall @ 110,000 psi yield, we'd need a 3" Dia x .500 wall that has 93% of
the strength of the steel mast, with a 23% weight savings and 2 SqFt
less area for antennas. If you're putting your stuff on a Rohn 100' 110
mph 25G tower, this move just reduced the your antenna capability by
27%. If it is a 100' 110 mph 45G tower you just lost 25% of your
available antenna area.
The aluminum mast can always be lighter. These things don't fly, so the
question is Why?
I understand that the one man tower team has special problems. But these
can be overcome, if one wants to get the maximum antenna population on
the mast.
It should be obvious, from the comparison that low grade steel pipe is
the worst possible choice of materials.
The flexibility advantage proposed by some doesn't contain an ounce of
value. The comparison shows that if we make the aluminum mast as strong
as the steel one, we end up with a stiffer mast, negating the proposed
advantage.
If we make the aluminum mast weaker than the steel one and have it flex
a whole bunch, what do we gain?
Nothing! We have created a weaker mast that flops around, increasing the
dynamic loads, and making our antennas point to the moon instead of at
the horizon. The notion that stiff things break easier than flexible
things is a fairytale when the materials are maleable like steel and
aluminum.
Stiffness and strength are two different things. They both define the
behavior of any mechanical system. But they are not entirely
interdependent!
Let's examine the formula for determining the stress (this is strength)
in a section:
F= (M*C)/I
where F= stress
M = the bending moment (In-Lbs)
C= the radius of the the section (OD/2. units are In)
I = the moment of inertia of the section (a value that describes the
cross sectional distribution of area in the section) (I = PI *(OD^4
-ID^4)/64 units are In^4)
The only variable in this formula that is directly related to stiffness
is I.
>From my last post on the subject, the section stiffness is calculated
from the formula E x I. where E = material elastic modulus, and I =
section moment of inertia.
The variable C is remotely related to stiffness, because it is used to
get the value I, but in the stress formula it appears as a direct linear
component of stress development. If we increase the diameter and reduce
the wall thickness, to maintain the same moment of inertia we get higher
stress.
We can see in the stress formula that the predominant stiffness value,
I, affects stress exactly opposite to the "flexible is better" notion. I
is the denominator in the formula, so a supposed more flexible section
would have a smaller I value. The smaller I creates a higher stress
value. So, the "more flexible is better" notion is nonsense!
As the value C increases the stress goes up linearly with the diameter
increase. The good news is that the linear diameter increase causes an
exponential increase in the I value, which reduces stress far more than
the C value increase. This explains why increasing any section size is
the most effective way of reducing stress, and why aluminum masts need
to be bigger than steel ones.
What is the most fun about this topic is that almost anything can be
made to work for a given set of conditions. That is the easy part.
Figuring out which solution is best, for anyone's personal preferences
can become severely clouded by one's personal prejudice. The mathematics
are very tried and true, please use them to get you past the folklore!
Further questions and discussion are invited.
73, Kurt
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