I'm not at all sure that Cos Theta is a proper formula for the
diminishment of drag as the shapes are turned away from full head on. It
does describe the diminishment of viewed area from a point distant, but
an angled element presents the shape of an ellipsoid to the angled wind
flow. One could make a case that the drag diminishes faster than the
cosine factor. Further, elements built with flex exhibit a "shedding"
effect that reduces their drag in the higher winds.
The complete formula for the drag of a typical yagi, as a function of
its turn to the wind is a right nasty equation, probably better measured
in a wind tunnel and "curved" than computed.
73
-----------------
Guy Olinger
Apex, NC, USA
----- Original Message -----
From: "EUGENE SMAR" <SPELUNK.SUENO@prodigy.net>
To: <towertalk@contesting.com>
Sent: Monday, May 21, 2001 12:17 AM
Subject: [TowerTalk] Angle of maximum wind force on Yagis
> TT:
>
> I just finished putting together an equation to calculate the
angle of
> max wind force on a Yagi. (I couldn't find it in my own TT archives,
and
> wanted to shake the cobwebs out of my forty-something brain. This
isn't
> really that tough, though.)
>
> You'll need to know/calculate the effective area (diameter X
length X
> shape factor of 0.67) of the boom plus the boom-to-mast bracket (no
shape
> factor multiplier) as one term, and the total of all elements X shape
factor
> as another term, in the equation below. (You need the Yagi's assembly
> manual to get these dimensions. All dimensions must be in feet, so
you'll
> have to convert diameters to feet.)
>
> Assuming that zero degrees is where the Yagi is pointed, then
the
> following applies:
>
> Theta(max) = arctan [(Boom plus bracket area )/(element area)].
Theta(max)
> is the angle of maximum wind force on the antenna.
>
> I think we can all (most) agree that there are three other
> angles/directions that also satisfy this equation: one in each of the
other
> three quadrants around the antenna, theta(max) degrees from the boom.
>
> Once you know Theta (the angle), you can calculate the actual
force as
> follows:
>
> F(max) = W[(boom plus bracket area)(sin theta) + (element area)(cos
theta)],
>
> where F(max) is maximum force in pounds exerted by the wind and W is
the
> wind force in pounds per square foot. The remaining terms were
defined
> above.
>
> As an example, say you have a 21.5-foot boom 2M Yagi with 13
elements
> (this is my new/used KLM 144-148-13-LBX.) The effective boom-plus
bracket
> area is 1.91 sqft and the effective element area is 0.464 sqft.
Plugging in
> to the first equation yields Theta(max) as 76.4 degrees. The force at
this
> angle (second equation) from a 70 mph wind is (20.6
psf)(1.91sin(76.4) +
> 0.464cos(76.4)) = 40.5 pounds.
>
> If the example Yagi is facing north, this maximum wind force is
exerted
> on the antenna when the wind comes from 76.4 degrees, that is, from
slightly
> north of east. That's because the wind is almost perpendicular to the
> relatively large boom/bracket area, but it still catches the tiny
elements
> to exert some force on them, too. This max force is not found at
ninety
> degrees (out of the east) because an easterly wind would not _see_ the
area
> of the small element ends (OK - it's there but negligible).
>
> As we agreed above, the three other angles of max force are
slightly
> south of east, slightly north of west and slightly south of west.
(You can
> do the math to determine the exact azimuths.)
>
> As another example, let's say you have a 4-element 15M Yagi on a
short,
> heavy boom. (For this example exact lengths are not needed.) The
ratio
> [boom-plus-bracket area/element area] might be close to unity (one).
>From
> the first equation, arctan 1 equals 45 degrees. In this example the
max
> force occurs at 45 degrees (also at 135 deg, 225 deg and 315 deg.)
>
> The equations assume a few things:
> 1. The wind sees all elements (the wide reflector doesn't hide the
shorter
> DE and Dirs.)
> 2. There is no allowance for turbulence in the vicinity of any
antenna
> component (although the shape factor, I've learned from TT, takes much
of
> this airflow into account. You can ignore shape factor completely if
your
> antenna uses a small boom-to-mast bracket. You decide what small
means.)
> 3. If you use tip-to-tip dimensions for each element, like for
> through-boom VHF elements, the equation ignores the fact that some of
each
> element is hidden inside the boom and not subjected to wind force. If
you
> use the lengths of split elements from the center support to the tip,
there
> is no hidden element length. It's all exposed to the wind force.
> 4. No, I didn't account for the force on hose clamps, taped or
otherwise.
> (Sheesh!)
>
> I want to calculate the force on each of my planned Yagis this
way to
> satisfy myself that I actually have more breathing room in tower
loading
> specs. But that's another discussion entirely.
>
>
> 73 de
> Gene Smar AD3F
>
>
> List Sponsor: Champion Radio Products - We'll be at the Dayton
Hamvention
> with all of our safety equipment and other products. Stop by booth
#559 and
> say hi.
> <A HREF="http://www.championradio.com";>www.ChampionRadio.com</A>
>
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>
>
>
List Sponsor: Champion Radio Products - We'll be at the Dayton Hamvention
with all of our safety equipment and other products. Stop by booth #559 and
say hi.
<A HREF="http://www.championradio.com";>www.ChampionRadio.com</A>
-----
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