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
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