Practical_Antenna_Handbook_0071639586

C h a p t e r 2 9 : T o w e r s 659
ample, where we are assuming the presence of a steady wind with no gusts, we shall
use a K FLAT of 0.004, as previously discussed.
Example 29.1 A typical HF short-Âboom trap-Âtriband HF Yagi might have a published
effective wind surface area of between 5 and 6 ft 2 . The Cushcraft A-Â4S, for instance, is
specified at 5.5 ft 2 . This figure is determined by the manufacturer from calculations on
both the cylindrical parts (boom, elements, struts, traps, etc.) and the flat plate parts
(brackets, end faces of cylindrical items) at different orientations with respect to the
wind. Next, we use Fig. 29.2 to obtain the impact pressure for a target wind speed. Let’s
suppose that we conclude that 100 mph is a conservative value for the highest wind
speed we expect our tower installation to survive. From the graph or the equation we
obtain P = 40 psf.
Suppose we add 0.5 ft 2 for a rotator housing and other “odds and ends” at the top
of the tower. Then our total wind load (ignoring the tower itself) is 40 (psf) × 6.0 (ft 2 ), or
240 lb of horizontal force. If the antenna is mounted at the top of an 80-Âft tower, for
instance, the total moment arm, measured from the base of the tower, due to the force
of the wind on just the antenna and rotator is calculated from Eq. (29.1) as 19,200 lb-Âft.
Because the bottom of this tower is rigidly held by its base, the tower will resist
overturning. To do that, the moment arm is converted back into a compressive force in the
downwind (or leeward) side of the tube if it’s a single rigid member or in the downwind
leg(s) if it’s a triangular lattice structure. That force can be calculated by working
backward through a second moment arm equation involving the cross-Âsectional
dimensions of the tower. Specifically, we take the distance of any leg or outer wall from
the centerline of the tower and divide that distance into the 19,200 lb-Âft. For a tower
whose legs form a triangle 18 in on a side, the calculation is:
F
COMP
M
=
R
ANT
TOWER
19,200
=
0.866
= 22,170 lb
(29.4)
To put it bluntly, mounting a small HF Yagi antenna atop a freestanding 80-Âft “stick”
has converted a sideward force of 240 lb into a vertical compressive force nearly 100
times greater! Is it any wonder that, while antennas are made of aluminum, towers are
almost always made of steel?
For comparison, the “maximum allowable axial compression in a side rail” (or
tower leg) for Rohn 45 tower sections, very popular with amateurs and business
band users, is slightly less than 8,000 lb. Thus, it is not allowable to put an antenna of
this size on top of 80 ft of freestanding Rohn 45 tower sections. In fact, the tower and
its accessories all have surface areas, so the wind loads of the tower and accessories
on it (rotator, brackets, feedlines, control cables, work platforms, etc.) have to be
added to the antenna wind loading to obtain the total “real-Âworld” moment arm and
force on the tower legs. When that is done, it can be seen that the maximum allowable
height for a freestanding Rohn 45 with no antennas or accessories except perhaps a
small UHF whip might be more like 50 ft, depending on the maximum wind speed
anticipated.