Safety factor f
Factor by which the structural strength of the mast
is derated in computing the survival velocity.
Wind loading factor k
From Rohn catalog; pressure of 100 mph wind is
about 40 pounds per square foot, and changes roughly as
kV2.
Maximum stress on mast material S
TV mast is about 60000, specially treated steel
can be even stronger, water pipe is about 30000.
Mast diameter
Outer diameter D and inner diameter d are
used to find the "moment of inertia", or "second moment of area", of
a cylindrical tube,
I = (π/64)(D4 - d4)
and this in turn is used to compute the "maximal bending moment",
i.e. the total torque which, applied to the mast, will make the
stress at the support point equal to the structural strength S
of the material:
M = 2SI/D
If this torque is exceeded, the walls of the cylinder will collapse
at the base.
Mast length
The total length of the mast is used only to calculate its weight,
based on typical steel density. The height of mast above support
h will be used to find the pressure of wind on the mast
itself.
Antennas
An antenna's height above support, h, and its effective
cross-section area, a, are used to find the contribution
of that antenna to the total torque that wind will exert on the
mast. Up to three antennas can be entered.
Velocity calculation
[we will omit the necessary conversions between feet
and inches here to keep the formulas simple]
The torque that wind exerts on the mast is the sum of the torque
caused by wind pressure on the mast itself,
M0 = DkV2h2/2
(this does not take into account any aerodynamic effects caused by
the fact that the mast is round, not square) and the torques from
the three antennas,
kV2h1a1 +
kV2h2a2 +
kV2h3a3
We now assume that this total moment is equal to the maximal
bending moment M = 2SI/D above, and solve for V
to get the failure velocity. To obtain "survival velocity" we
de-rate the stress S by the safety factor f,
i.e. M = 2SI/fD is used instead to solve for V
in the safe range. In general, survival V will be the
failure V divided by the square root of f.