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wind (and at the same time perpendicular to the axis of the
tube). The passenger now rotates the tube approximately 45°,
top end forward. The person holding the tube will now clearly
feel a force that pushes the tube backward (drag force), but at
the same time tries to lift (cross force) the tube. The resulting
force of these two components (the drag and cross force) is a
force that is always perpendicular to the direction of the tube.
If the tube is inclined with the bottom end forward, the force
will try to push the tube downward.”
This means that the direction of the force developed by
the wind on an object exposed to the wind is not necessarily
the same as the wind direction. There are some specific
conditions where the two directions are the same, such as the
case where a flat object is broadside to the wind direction. If
you put a plate (1 meter2) on top of a tower, and have the wind
hit the plate at a 45° angle, it will be clear that the push
developed by the wind hitting the plate will not be developed
in the direction of the wind, but in the direction perpendicular
to the plane of the flat plate. If you have any feeling for
mechanics and physics, this should be fairly evident.
To remove any doubt from your mind, D. Weber states
that Alexandre Eiffel, builder of the Paris Eiffel tower, used
the cross-flow principle for calculating his tower. And it still
stands there after more than 100 years.
Now comes a surprise: Take a Yagi, with the wind hitting
the elements at a given wind angle (forget about the boom at
this time). The direction of the force caused by the wind
hitting the element at whatever wind angle, will always be
perpendicular to the element. This means that the force will be
in-line with the boom. The force will not create any bending
moment in the boom; it will merely be a compression or
elongation force in the boom. All of this, of course, provided
the element is fully symmetrical with respect to the boom.
This force in the boom should not be of any concern, as
the boom will certainly be strong enough to cope with the
bending moments caused by wind broadside to the boom.
These bending moments in the boom at the mast attachment
plate are caused only by the force created by the wind on the
boom only (by the same “cross-flow” principle) or any other
components that have an exposed wind area in-line with
the boom.
If the mast-to-boom plate is located in the center of the
boom, the wind areas on both sides of the mast are identical,
and the bending moments in the boom on both sides of the
mast (at the boom-to-mast plate) will be identical. This means
there is no mast torque. If the areas are unequal, mast torque
will result. This mast torque puts extra strain on the rotator,
and should be avoided. Torque balancing can be done by
adding a boom dummy, which is a small plate placed near the
end of the shorter boom half, and which serves to reestablish
the balance in bending moments between the left and the right
side of the boom.
This may seem strange since intuitively you may have
difficulty accepting that the extreme case of a Yagi having one
element sitting on one end of a boom would not create any
rotating torque in the mast, whatever the wind direction is.
Surprisingly enough, this is the case. You cannot compare this
situation with a weathervane, where the boom area at both
sides of the rotating mast is vastly different. It is the vast
difference in boom area that makes the weathervane turn into
the wind.

Fig 13-4 shows the situation in theory, and what’s
likely to happen in the real world. At A and B the wind only
sees the element (the boom is not visible), and if the element
is fully symmetrical with respect to the boom, there will be
no torque moment at the element-to-boom interface. Hence
this is a fully stable situation. At C the situation where the
boom is facing the wind is shown. The element is invisible
now and as the boom is supposed to be wind-load balanced,
the boom by itself creates no torque at the boom-mast
interface. At D we see that the cross-flow principle only
creates a force in-line with the boom. This means that this
example still guarantees a well-balanced situation, and the
structure will not rotate in the wind.
But let’s be practical. The wind blowing on the long
flexible elements of a Yagi will make the elements bend
slightly, as shown in Fig 13-4E. In this case now it is clear that
the pressure induced by the wind on side (a) of the element will
be much greater than on side (b) as side (a) now faces the wind
much more than side (b). In this case the antennas will tend to
rotate in the sense indicated by the arrow.
Taking all of this into account it seems to be a good idea
not only to try to achieve full boom (area) symmetry but full
element (area) symmetry as well. Leeson came to the conclu­
sion that he prefers to balance in the element plane by offset-

Fig 13-4—Analysis of the influence of the wind on the
mast torque for a single element sitting on the end of a
boom. In all cases, A through D, no mast torque is
induced. Only in case E, where the element is deformed
by the wind, will mast torque be induced. See text for
details.

Yagis and Quads

Chapter 13.pmd

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