On 7/20/19 6:35 PM, Richard Smith wrote:
I believe that the rope in the elements, specifically the element tips, is
particular to the Hy-Gain yagis, at least the 20, 15, and 10 meter designs. I
have seen a Hy-Gain yagi, a 5 element 15 meter yagi, with most of its element
tips broken off by regularly occurring, but not huge, winds. The yagi was built
without the rope in the element tips that is shown in the manual for the
antenna.
I replaced the element tips in 1992, with the rope in the tips per the
instructions in the manual, and did not have any element tips break off during
the next 17 years of service at the same location.
Just sharing my experience.
It's a matter of aeolian vibrations - it depends on the wind speed and
the resonant modes of the tube. The mechanical Q of the element is
moderately high (probably in the 50-100 range), and then it depends on
whether the frequency of the wind induced vibrations happens to be close
enough to the resonant mode of the element.
There's probably a special "sweet spot" where it's a problem, and one
can probably design an element so that it almost never occurs.
The other thing is that aeolian vibrations only occur in smooth flow -
if you have a lot of "stuff" up in the air, then you might never see it.
Frequency of vibration is = 3.26 * V(mi/hr) / d(inches) (approximately)
First mode frequency is = Kn/(2*pi) * sqrt( E*I*g/w*L^4)
Kn is 3.52 for the first mode (22.0, 61.7 for second and third)
E is modulus of Elasticity (70 GPa is good for aluminum)
I is the area moment of inertia = pi*(D^4-d^4)/64 for a hollow tube
w is the load per unit length (the weight of the beam)
L is the length.
https://www.amesweb.info/Vibration/Cantilever-Beam-Natural-Frequency-Calculator.aspx
2" (50.8mm) tube with 0.0625 walls has a area moment of 74,400 mm^4
(approx)
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