At 06:17 PM 3/26/2006, Michael Tope wrote:
>----- Original Message -----
>From: "Jim Lux" <firstname.lastname@example.org>
> > That't the cool thing about that java calculator.. it does all the nice
> > slow speed, low Re stuff, without you having to slog through figuring out
> > what the Re is and looking up the Cd for the cylinder, etc.
> > And, the annoying thing I've found is that the cases of real interest to
> > non-airplane designers are those low speed cases: things like 2" pipes in
> > 50 mi/hr winds, or whip antennas on a car, etc... and that's just where
> > the
> > big discontinuity in the curve is.
> > What's great is to put in a reasonably slow speed (say, 88 ft/sec) and
> > then
> > step through diameters of cylinders and see how the Cd changes,
> > dramatically, with pretty small changes. A diameter of 0.1 ft gives you a
> > Cd of around 1, but a diameter of 0.5 ft gives you something like 0.2..
> > Here's an interesting little table (calculated for 88 ft/sec = 60 mi/hr):
> > dia(ft) Re Cd lb/linear ft
> > 0.05 27,200 1.011 0.46
> > 0.1 54,500 1.007 0.91
> > 0.15 81,800 1.005 1.36
> > 0.2 109,000 0.997 1.80
> > 0.25 136,000 0.952 2.15
> > 0.3 163,000 0.853 2.31
> > 0.35 191,000 0.700 2.21
> > 0.4 218,000 0.492 1.78
> > 0.45 245,000 0.231 0.94
> > 0.5 273,000 0.180 0.81
> > What's fascinating is that a pipe 6" in diameter has about the same drag
> > force as a pipe 1" in diameter, and a pipe that's 3" in diameter has more
> > than twice the drag as either.
>Are you saying that the java calculator algorithm breaks down
>in that speed range (~60 mile/hour), or are you saying that the
>drag coefficient really does wander that much across the pipe
>diameter range of 1" to 6" for winds speeds that are of interest
>to tower designers?
The Cd really does change that much over that range. There's a big change
in how the flow works in that range of 10,000<Re<1,000,000.
> Per Leeson, I've been faithfully using a Cd
>of ~0.67 for round members on all my tower calcs. If what you
>say is true, perhaps I need to be a lot more careful. Or is the
>dramatic reduction in Cd for the larger diameter pipes only valid
>over a narrow range of wind speeds such that in practice you
>couldn't make the projected area of a mast larger in order to
>lower the overturning moment transferred to the structure
>underneath it. Stated another way, what does the Cd value look
>like as a function of wind speed for say the 6" diameter pipe that
>has a Cd of 0.18 at 60 mi/hr? Such widely varying drag coefficients
>might suggest large diameter thin-wall masts are better than small
>diameter thick wall masts with the same section modulus due to
>lower drag coefficients, but only if the lower drag coefficient were
>valid over a fairly wide range of windspeeds.
Cd varies as a function of Re, which in turn scales as Windspeed and
diameter (that is, if the velocity doubles, the Re doubles...if the
diameter doubles the Re is halved)
So, yes, big thin wall tubes ARE actually better.
I ran the numbers at 60 mi/hr, while "survival" numbers are often run at 80
or 100 or more (depending on wind zone). That increases the Reynolds
number, so you're more likely to be above the critical value (around
150,000, it looks like)
Also, for "building permit" purposes, they tend to not use actual
aerodynamic calculations, but some sort of conservative "rule of thumb".
Here's a question about the Leeson analyses: Are they to calculate loads
on the elements to determine if the element will fail, or to calculate
loads on the tower, to see if the tower will fail?
I ran some numbers and generated a plot for varying sizes all at 60
mi/hr. Next I'll run a fixed size at varying wind speeds. It's a bit
tedious because you have to enter the numbers in the webpage and hit
calculate for each data point. I've sent an email to the author of the
macro or Matlab .m file, which would make generating some useful curves easier.
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