One other complexity is fatigue failure. traditionally, Steel is taken
as having a fatigue limit, below which it can withstand an infinite
number of cycles. Copper and Aluminum do not have such a limit. The
more cycles, the lower level of stress for failure.
A wire antenna "blowin in the wind" can get millions of cycles pretty
easily.
f = So * V/d
So = Strouhal number 0.185 for metric units
V = 5 m/sec (11 mi/hr)
d = 2mm (12 AWG)
f = 0.185 * 5/0.002 = 460 Hz
Time for million stress cycles is 1e6/(460*2) (because the axial load is
at a max twice per cycle of the sinewave) = pretty close to 1000 seconds
- 20 minutes.
There's an even worse situation, when the natural resonance of the wire
happens to align with the aeolian vibration - the Q is pretty high
(internal damping of a wire is about 0.25% - a Q of 200), so the loads
can be dramatically increased.
l (loop length) = 1/(2*f) *sqrt(T*g/w)
loop length is "half a wavelength" of the vibration mode (the distance
between "nodes") (just like a resonant dipole)
T is the tension in Newtons
g is 9.8 m/sec^2 (accel due to gravity)
w is the conductor weight per unit length (kg/m)
Taking our AWG 12 copper wire..19.76 lb/1000 ft = 9 kg/328 meters =0.027
kg/meter
Let's say we've got 50 lbs (225 N) tension.
So, l = 1/(2*460) * sqrt( 225 * 9.8 / 0.027)
= 0.31 meters (1 foot).
yeah, for a 20 or 40 meter dipole that's going to be a pretty high order
mode, so the deflection won't be all that big. But remember that the
frequency is proportional to wind speed. So if the wind is 1 m/s (2
mi/hr), the frequency is about 100 Hz, and now the loop length is more
like 1.5 meters.
So, it's those gentle afternoon zephyrs that will probably afflict your
antenna more than the howling gale.
And I assume that as a responsible ham, everyone will follow the NEC to
the letter, do a complete aeolian vibration analysis, calculate the
loads, test coupons of your antenna wire to destruction, and then,
confirm all the calculations with precision laser measurements of the
span during all wind conditions. <grin>
Oh yeah, and I was talking to someone a while ago who claimed that there
really isn't a fatigue limit for steel, just the slope of the curve is a
lot less than for other metals. So even with copper clad steel, you're
still ultimately doomed.
Perhaps single crystal fibers of fused silica plated with silver would
be best.
On 12/10/19 4:46 PM, jimlux wrote:
On 12/10/19 2:41 PM, Bob Shohet, KQ2M wrote:
Hi Jim,
”A major advantage of using stretched wire is that un-stretched copper
will stretch under tension over years. Before changing to stretched
wire,”
I have seen you mention this a number of times in the past and I have
been meaning to ask you some questions about it.
My non-engineering understanding of wires and stretch is that a given
wire after being subject to variable strength forces over a given
period of time, will stretch only so far before it breaks. Assuming
that that is conceptually correct, let’s say that we have two wires –
Wire A and Wire B. Wire A has been pre-stretched before being put up
and is now compared against Wire B which has just been put up without
being pre-stretched
Wire A will now be smaller in diameter, and probably have a higher
breaking force.
Don't forget that there's a difference between yield (which leads to
deformation) and failure. The load for stretching is above the elastic
limit (above the yield) but below the failure load.
Now we subject both wires to the same forces over the same period of
time. I would expect that going forward Wire A will not stretch as
far as Wire B, but is more likely to break and break sooner under
significant force than Wire B because it has already been
pre-stretched. Wouldn’t this be correct?
Yes, wire A will be "stiffer" (have a higher spring constant in a
"newtons of force per meter of stretch" sense), so for the same load, A
will stretch less.
However, the ultimate failure load for both is probably the same. B will
stretch further before it fails. That is B will pass through the exact
same state as A on the way to failure.
However, there's also a whole thing about "non uniform loads". B, being
softer and stretchier, as it deforms might concentrate the loads at some
point, which would then fail.
When Jim does his "hook it to the bumper and pull til failure", I'm
going to guess that it fails at the end, not in the middle. That's
because the inevitable bends, twists, or wraps to attach it are a stress
concentration of some sort. I doubt he's attaching some thing like a
symmetric mesh cable grip to each end to insure perfectly uniform load.
There's also a work hardening aspect (which is what drawing is doing) -
the softer (B) wire might flex more in the wind, which would cause work
hardening at the ends or attachment points. The work hardened points
have a higher spring constant than the non hardened points, and, so,
take more of the total load. The "load per unit length" is higher on
the work hardened sections (because they're stiffer).
So now you're in the classic "fail at the reinforcing gusset" problem.
If this is not correct, can you please explain why?
Tnx & 73
Bob KQ2M
From: Jim Brown
Sent: Tuesday, December 10, 2019 4:49 PM
To: towertalk@contesting.com
Subject: Re: [TowerTalk] Orion 2800 Rotator Cable Replacement
On 12/10/2019 1:13 PM, john@kk9a.com wrote:
Of course I meant to say "with no issues" in my post. The nylon
coating on
THHN does quickly deteriorate outdoors however I believe that the
nylon's
purpose is to lessen friction and improve chemical resistance.
Neither of
these are issues to me and the PVC underneath is pretty tough.
The 350 ft run to my Yaesu rotator are two 250 ft runs of #14-2 Romex
(plus ground) to the base of the tower, laying on the ground.
Transitioned to something smaller to go 120 ft up the tower. Nine years
so far with no issues.
I've used THHN extensively for wire antennas and radials. My current
favorite for high dipoles is bare #8 that is stretched to make it hard
drawn #9 -- attach one end to a fixed object and the other to the
trailer hitch on the SUV, pull slowing until it breaks.
A major advantage of using stretched wire is that un-stretched copper
will stretch under tension over years. Before changing to stretched
wire, I found that I had to circumcise my 80M dipoles (#10 THHN) every
few years to keep them on frequency. For my fan dipoles, I now use
stretched wire for the longest element that bears the pulling stress and
THHN for the shorter elements that do not.
73, Jim K9YC
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