[TowerTalk] Thrust Bearing, etc: more answers from UST calcs

[Jim Lux]

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.)