Ultimately, it's kind of like EM modeling of an antenna.
You can start with a dipole model.
You can then go to a method of moments code.
Then you can go to a monte carlo or systematic variation of parameters to
assess the sensitivity to things like errors in element length or angle.
Something that is available today, that wasn't 10-15 years ago, is cheap
computational horsepower "in the cloud", which makes running multiple cases
simultaneously easier. You're just paying for compute seconds, so whether it's
100 instances running for 30 seconds, or one instance running for 3000 seconds,
the cost is about the same. (and if you're using the "free" tier of AWS, the
cost might be zero - you get 750 hours/month, for a year) AWS pricing is kind
of complex, though. But if you ran spot instances, instances are something
like $0.02/hour, so running 100 instances for a minute is less than a nickel.
So running that Monte Carlo is feasible for an amateur - although I don't know
that any of the NEC front ends can do this with cloud instances.
I ran a whole series of these kinds of analyses for a couple applications
(computing interactions and pattern disruptions from non-ideal position
orientation for the "stands" at OVRO-LWA) over a couple days, using 12 nodes on
a big cluster at JPL. I did a similar thing modeling various arrangements of
128 dipoles in an array on the Lunar surface. There's sort of a tradeoff
between running iterations on the same node, and spreading it out. The latter
has more "moving data around" time.
Typical models had 600 segments, 414 frequencies, and a 2200 second run time.
Each configuration about 5 seconds of "fill" time (computing the interaction
matrix) and 50 milliseconds solve. So the dominant time is computing the big
mutual admittance matrix. And that does lend itself to some optimization. The
fill time varied a lot with the frequency step - probably because of
segmentation issues. The 400 frequency steps were log spaced. Some of the
other models had more segments, so took longer to evaluate. Typical run times
for a single case (length of segments, frequency) was around 30-100 seconds, so
running 144 cases takes several hours, single threaded. But on the cluster, it
was a 2-3 minute effort.
What would be useful is for someone to build some "runnable" versions of NEC
that are configured for the compilers and libraries on AWS. That actually took
more time for me than actually running the models. You get your Fortran source,
and then you have to go make sure that the right libraries are supported, and
the IO isn't weird. Turns out the trickiest part is the internal timing calls
that produce the " RUN TIME = 71.061" and
- - - MATRIX TIMING - - -
FILL= 1.093 SEC., FACTOR= 0.006 SEC.
because every OS and compiler does it slightly differently.
Bringing it back around, though, someone who's ambitious could take the FEM
models, and run the statistical analyses and models that are described below,
without it taking days and days of computing.
On Mon, 25 Sep 2023 09:13:11 -0700, JVarney <jvarn359@gmail.com> wrote:
Dave, W6NL/HC8L wrote: "Thanks [to N7WS] for the link to the very
detailed Weber papers. They clarify the issue. ."
Yes, but as you alluded to, K5IU's analysis is only true in a
world where the wind is of constant speed, horizontal, all flows
are laminar, and the tower and antennas are statically fixed.
Analyzing towers and antennas with simple stick models, statics and
trigonometry are mathematically correct but badly miss the mark on
what happens in the real world. Not only is the wind highly
variable, but towers and antennas are very flexible and have
"geometric non-linearities," meaning the wind forces they
experience change as a function of their bending.
The current building code (TIA-222-H) requires a first-order
finite element analysis. The only second order non-linearity
that is required to be considered is the P-delta effect,
where bending moments increase as a function of tower
lean over. That's a much better approximation than simple statics
but still isn't quite right.
A few years back I discussed with Kurt K7NV (SK) about his
YagiStress program and how using simple statics don't model
antenna elements very well. We agreed there is no program readily
available that takes geometric non-linearities into account.
The finite element program I use for tower analysis can't do
it out of the box. The solution would require a time step
analysis where the wind force and drag are adjusted for each
model node as a function of its displacement.
Recently I read a paper(1) that gives an idea what is needed to
properly model the responses of a tower/antennas to the wind. It
involves "stochastic finite element" analysis where the wind is
described in a time series data set with variations in wind
velocity, azimuth and elevation. The simple brute force way is
to then run those wind numbers as a Monte Carlo against a finite
element structural model of the tower/antenna system. You end up
with a response spectra of stresses and displacements.
Because towers/antennas are flexible structures that behave in
a non-linear way, how they respond to a 100 mph gust is going
to depend on what happens in the time periods just prior to
the arrival of the gust because, on a windy day, it is already
in motion seeking equilibrium and has a mix of potential and
kinetic energy in flux. And so in some cases the tower will
be in a favorable position to handle that gust, in others, it
will not.
Therefore one cannot say a tower or antenna is rated for
exactly 100 mph. Instead, it's a pair of probability curves,
one for the load (the wind) and another for the strength of
the tower system. Then the correct answer is along the lines
of "there's a 95% chance the tower will survive a wind gust
between 95 mph and 105 mph."
So is K5IU right about balancing wind loads and alternating
booms on masts? Yes, but only for the simple assumptions
he made. I think it's highly likely that in a wind storm there
are so many other dynamics going with the tower, mast and
antenna parts moving around that the static balance
will be swamped and disappear. Really the owner of a
tower/antenna system should invest their efforts in making
all mechanical connections as resistant as possible to
dynamics like vibration, oscillations and galloping as possible.
Jim Varney, P.E., K6OK
(1) Szafran, Jacek & Juszczyk-Andraszyk, Klaudia & Kamiński,
Marcin (2020). Reliability Assessment of Steel Lattice Tower
Subjected to Random Wind Load by the Stochastic Finite-Element
Method. ASCE-ASME Journal of Risk and Uncertainty in Engineering
Systems, Part A: Civil Engineering. 6. 10.1061/AJRUA6.0001040.
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