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Regardless of the soil that your tower is sited upon, the total mass of
the concrete must exceed the weight of the tower, the antenna's fixed
upon and the estimated wind force that the tower will see. This is so
that the center of gravity of the tower/antenna system is below ground
level.

That's not how the design works..
Consider an extreme example.. you have a big tripod of a tower. The CG
is well above ground level, yet it still won't tip over.
Or, you have 4 towers that stick out horizontally resting on the ground,
and a 5th one sticking up (like clown feet sticking out). Again, the CG
is above ground, but it won't tip.



For a guyed tower, the base is there to keep the bottom of the tower
from sinking into the soil, or from moving sideways. A wide flat pad or
a deep pillar both do this, although the wide flat pad might be better
from the "floatation" standpoint, as long as the bending forces in the
concrete aren't too high.

Consider the case where the base of the tower sits on rock, with a pier
pin or similar to resist the shear loads.


For an unguyed tower, it's a bit different. The base has to prevent
rotational motion. There's a bending moment applied to the concrete,
which in turn pushes on the soil on the sides and bottom of the
foundation (and, obviously, the concrete itself has to take the loads).







Thirty yeas ago my local radio club installed a new tower. The tower was
180 feet tall with a 4 bay antenna. We had a hole 10feet on a side dug
and filled with concrete. When the tower did fall it bent in two about
80 feet up and folded over. The base formed the bottom of the
replacement tower and is still in service.


Folding in the middle somewhere is the most common failure mode for
unguyed towers (after just falling intact), for the same reason that
pencil points break the way they do, and tall chimneys don't fall
intact. When it starts to fall, the whole thing is basically rotating,
so the top end winds up with very high acceleration, and the bending
forces get very high. It's a rotational inertia thing.

For guyed towers, it depends where the guys are, and whether the tower
is failing by bending loads or by buckling under compression loads.




Dave WD9BDZ