Guys,
My original query about just what the K-factor for rotors means and what
it is supposed to protect against received no technical responses.
I dug back into my college physics textbooks to see what I could
determine. Beware, I may be in over my head here.
Here are my conclusions.
Torque limits can come from two places:
1) Starting torque imposed by trying to start the antenna turning in
windy and non-windy conditions
2) Mechanical limits on stopping the antenna when it is turning or being
tossed about in the wind.
The origin of the K-factor has little to do with 1 or 2 but might
instead be due to some limit on the mechanical ability of the rotor
housing to withstand vertical twisting.
First. The normal formula for torque is:
Torque = moment arm x applied force.
However, for torque about the mast axis, the force is not weight but
rather only the forces of the wind. Think of it this way. Take a
wrench and turn a nut that is positioned in the horizontal plane with
the bolt upwards. No matter how hard you push down on the wrench the
nut won't turn. You have to apply the force horizontally. Same way
with the rotor. The only force (besides friction) is the wind force on
the elements resisting the turning. Friction does have a weight term in
it but let's assume that rotors are relatively friction free (at least
in the lower 48 states and above freezing)
.
This wind force is proportional to antenna area and velocity of the wind
raised to some power. The K factor has no stated wind speed associated
with it. It does have the form of the moment arm times something.
The torque required to start or stop a rotating object has the formula
Torque = I x rotational acceleration
I is the rotational moment of inertia and rotational acceleration is
proportional to rpm.
The I factor can be computed for complex objects with odd weight
distributions from calculus
I = integral of moment arm squared * dm
Where dm is the incremental mass at the location of each moment arm
Note that there is an r squared in the formula -- not r like the K
factor has.
The moment of intertia has been tabulated for various objects like
dumbell and pipes.
A 2 element antenna is like a combination of a dumbell and a pipe.
I for the dumbell is the half the boom length * mass of the two elements
I for the boom is the mass of the boom times the length of the boom
divided by 12. For most beams the dumbell component predominates. For
antennas of many elements (some close to the mast), the outer elements
contribute the most to the value of I.
Note: The the full weight of the antenna appears nowhere (at least not
with a multiplier of 1.0) and that the moment arm is not the turning
radius but rather half the boom length. Note there is the square of the
boom length not the boom length to the first power.
IMHO the bottom line. I have't got the faintest idea what the K factor
is and what it is supposed to protect against. It's form suggests that
it is related to wind forces but weight is used instead of wind force.
It appears that it simply might be the force required to break loose
from the housing in up and down drafts. In that case, the housing
should fail and not the guts.
Anybody else got ideas on just what K really is?
Brian/K3KO
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