Jim
The non-linear character of the numbers you have chosen are characteristics
of the so-called "drag bucket." Note in the description of the calculator
that the author has used a parabolic algorithm to represent the drag bucket
for Reynolds Numbers between 100,000 and 250,000. This phenomenon has long
been known and results from a favorable pressure gradient delaying the
transition from laminar flow to turbulent flow to a point farther aft of the
leading edge. This is true, of course, only for very smooth surfaces as
roughness will induce boundary layer energies that accelerate the transition
to turbulent flow. Note that turbulent flow is usually associated with
Reynolds numbers beginning at about 530,000 and fully developed turbulent
flow is generally regarded to occur at Reynolds Numbers of 10,000,000 to
20,000,000. In the author's background he states that the flow transition
begins at about Re = 230,000. Since the Reynolds Number is the velocity (V)
in feet per second times the distance from the leading edge (x) divided by
the kinematic viscosity of the fluid (nu = 15.8E-5 ft squared per sec at 60
degrees F) the x value is the width of the pipe even though Re will of
course be zero at the stagnation point where V=0 and increase as the air
flows over the surface. It is also interesting to note that using the
formula D=CdqS where q= the dynamic pressure in psf= sigma Vsquared/295
(sigma is 1.0 at sea level and V in knots) and S is the surface frontal
area, the force per unit length comes out almost the same at 0.829 lbf/ft
for the 6 inch tube. For my purposes I would probably use the traditional
method and ignore the drag bucket so that the results carried a built in
safety factor. I would also add some roughness to the factor to take into
account ice and other surface imperfections.
Regards
Bill
W7VP
----- Original Message -----
From: "Jim Lux" <jimlux@earthlink.net>
To: "Michael Tope" <W4EF@dellroy.com>; "Bill" <w7vp@comcast.net>;
<NPAlex@aol.com>; <towertalk@contesting.com>
Sent: Sunday, March 26, 2006 8:19 PM
Subject: Re: [TowerTalk] Wind loading comment misdirected? W7VP
> At 06:17 PM 3/26/2006, Michael Tope wrote:
>
>>----- Original Message -----
>>From: "Jim Lux" <jimlux@earthlink.net>
>>
>> > 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.
>> >
>>
>>Jim,
>>
>>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
> javascript to ask if I can copy it and turn it into something like an
> Excel
> macro or Matlab .m file, which would make generating some useful curves
> easier.
>
>
>
>
>>Thanks,
>>
>>Mike W4EF...............................
>>
>>
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