On 2/9/13 8:21 AM, Michael Tope wrote:
Jim,
With regard to your comments below, are you assuming laminar or
turbulent flow? I just grabbed my copy of Leeson's "Physical Design of
Yagi Antennas" and he discusses this same issue of a rapid change in
drag coefficient for wind speeds and tubing diameters of practical
interest to antenna builders for the case of turbulent flow.
Turbulent flow.. When I built the spreadsheet that does the
calculations, I assumed turbulent flow, and used those tables: the
airflow over the elements is likely not smooth, having been disrupted by
other elements and environmental effects, and also the elements
themselves are likely not smooth, so the laminar/turbulent transition
would be tripped by hose clamps, bird droppings, surface corrosion,
galvanized surfaces, etc. (relatively few antennas have a "mirror
finish" on them)
Laminar flow is when you have undisturbed air (e.g. clean airplane
wings) and my own experience with trying to get laminar flow (soap box
derby car when I was a kid, airplane wings as an adult, artificial
tornado machines, etc. ) is that it's *really hard* to generate and keep
laminar flow. It just wants to go turbulent.
He then
states "conservative design, however, dictates a less aggressive
choice", referring to the choice between assuming turbulent flow or
laminar flow when doing these sorts of design calculations (for laminar
flow this transition from ~constant drag coefficient to rapidly changing
drag coefficient occurs at much higher wind speeds). UBC and EIA-222 (at
least the versions that were current when his book was published) both
appear to assume laminar flow.
yes.. I agree with Leeson. Interesting that UBC and 222 assume laminar
flow. I find the idea of laminar flow over a typical galvanized strut
somewhat unrealistic, but I admit I haven't looked at that particular
situation.
Leeson presents calculations from both UBC and EIA-222 formulas both of
which show an ~0.6 ratio between cylindrical member and flat-plate
member drag coefficients.
Aha.. that's where the 0.6 comes from.
But if you look at the classic "drag of a cylinder" graph, it starts out
with Cd very high (10 for Re=1) and smoothly comes down to about 1 for
Re <1E5.. then there's the big dip to 0.5-0.6 around 500,000, then it
comes back up to around 0.8 for Re>1E7...
That dip is from the transition to turbulent flow nearer to the front of
the cylinder, so the boundary layer "sticks" to the cylinder longer on
the back side.
What's interesting is that a flat plate (or rectangular box) has a Cd of
about 2 at low Re.. So it's drag is twice the "flat plate area"...
The overall summary is that I think just assuming a Cd of 1 works
(conservative for cylinders), and hoping that the other design margin
takes care of the variation on things like flat bars, angle iron, etc.
If you're designing your tower such that the Cd changing by 20-30%
makes a difference, I think you're kind of on the ragged edge anyway. I
doubt that you know the wind profile from ground to top that accurately,
and that's a square law effect. (actually, assuming the wind at the
ground level is the same as at the top is probably a conservative
assumption.. the wind at the ground is almost always less, because of
the surface drag of the ground, not to mention there's bushes, grass,
trees, houses, etc.)
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