RE: [TowerTalk] kt34xa torque balancing

[W0UN -- John Brosnahan <shr@swtexas.net>]

Jim Jarvis and I have had a couple of off-line exchanges.  This is
a note I wrote to him to try and make sure we both are talking
about the same thing.   (As my late partner used to say  --
A word is worth a milli-picture!)   And after writing the note I
decided the concept of a single, asymmetrical element might
make the cross-flow principle easier to understand for anyone
who might still be having difficulty.  My apologies to anyone who
is getting bored with all of this.  But it IS an important topic since
the analysis has been done incorrectly by the ham antenna
manufacturers for so many years.  I hope my word picture--
without any mathematics (or drawings!)--makes it all a bit easier
to follow.

--John
---------------------------------------------------------------

Hi, Jim--

I am not sure if we are in agreement or not, but let me show you
the ad absurdum case to make sure we are both talking apples.

Take a 40 ft boom (arbitrary) of 3 inch tubing and attach it to
the mast in the exact center.  Now attach, ala the old Telrex
method, a single element (oh, say a 20M reflector) at one END
of that boom.  (Telrex style element used to greatly reduce any quibble
about mounting brackets, since Telrex ran their elements through
the boom.)

OK, so far?  Only ONE element and it is at the very end of the
boom, 20 ft from the mast.  It LOOKS like a classic weather vane
doesn't it, because of total asymmetry.  BUT it needs NO
torque balancing!

Wind hitting one half of the element (no matter the angle) will produce
a vector force that can be defined as the sum of two vectors -- one 
perpendicular
to the element and one parallel to the element.  The parallel vector
has NO effect on the element--wind has no "stiction".  The perpendicular
vector on one half of the element gets transferred as a force trying to
rotate the element in a counterclockwise direction.  BUT the same wind
on the other half of the element also gets broken down into the same two
vectors and the parallel vector once again can be ignored.  The perpendicular
vector also gets transferred to the boom, but this time in a clockwise
direction.

Or just take your hand and push on one side of the element and see how
the force tries to push on the boom.  Doing the same thing on the other
side with your hand will also push on the boom but in the opposite
direction.  The two forces balance.

In reality it is MUCH more complex but it is not what has typically been
modeled.  For instance, take a 45 degree wind to the element.  The upwind
side will WANT to bend in such a way as to become MORE broadside to
the wind.  And the downwind side of the element will want to bend in such
a way as to become less broadside to the wind -- just due to the fact that
they are attached on opposite ends.  One half is attached to the boom on
the downwind end and one half is attached to the boom on the upwind
end.

But this effect is zero for a completely straight (stiff) element, and only 
plays
a role when the elements are bending a lot on the wind.  And if they bend
more in the wind it is probably because they are thinner -- and have less wind
area to start with.

So, to first order, assuming the elements stay straight under the force of the
wind, then there is NO need to compensate for any elements -- even if there
is only ONE element at one end of the center-mounted boom.

Element flex adds a small extra thing to think about as does any element
projection that has any surface area parallel to the boom, such as the end
cap on traps.  The bodies of the two traps in an element cancel each other
out since they are parallel to the element.  But both upwind ends of any
set of trap end caps will add to the load on the boom.   But once again this
is a pretty small area and the resulting forces are very low.

So, to first order at least, you can ignore the elements and only compensate
the boom if it is off center mounted to the mast.  Or better still, mount 
the boom
in the center and add some weight to one half to balance the boom.

OK?    ;-)

73--John


_______________________________________________

See: http://www.mscomputer.com  for "Self Supporting Towers", "Wireless Weather Stations", and lot's more.  Call Toll Free, 1-800-333-9041 with any questions and ask for Sherman, W2FLA.

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