Guy:
Thanks for the comments. I agree that flexible elements (Skyhawk) are
likely to shed wind by bending a little,thereby reducing the actual force on
the element/mast/tower. Would it be safe to say, though, that the equation
I posed (first equation) is the MAXIMUM force likely to be encountered,
given the assumptions I laid out in my posting? I'm satisfied that it is.
73 de
Gene Smar AD3F
-----Original Message-----
From: Guy Olinger, K2AV <k2av@contesting.com>
To: EUGENE SMAR <SPELUNK.SUENO@prodigy.net>; TowerTalk
<towertalk@contesting.com>
To: <towertalk@contesting.com>
Date: Monday, May 21, 2001 2:22 AM
Subject: Re: [TowerTalk] Angle of maximum wind force on Yagis
>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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>
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>
-----
FAQ on WWW: http://www.contesting.com/FAQ/towertalk
Submissions: towertalk@contesting.com
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