Other structures - Wind Loading of Structures - page 333

14.5 Antennas
14.5.1 Radio telescopes
Wind loads on the antennas of large steerable radio telescopes—usually with dish
reflectors of paraboloidal shape—are of critical importance for several design criteria
(Wyatt, 1964):
• overall strength for safety in extreme winds;
• loads on drive system;
• freedom from oscillations;
• pointing accuracy;
• distortion of the reflector.
The last four of the above conditions are serviceability criteria. Very small tolerances are
required for the operation of these antennas.
The main source of wind loads is the paraboloidal dish itself. If the dish is
impermeable, the pressures acting on it may be assumed to act normal to the surface, with
negligible contributions from skin friction. For a paraboloid, the normal to any point on
the surface passes through the generating axis, at a point 2 f measured along the axis from
that point, where f is the focal length. Therefore, it may be assumed that the resultant
aerodynamic force will act through a point on the axis, distant from the vertex by 2 f plus
half the depth of the dish, d (Wyatt, 1964).
Consider first the case with the wind direction normal to the altitude axis of rotation of
the dish as shown in Figure 14.13. Resolving the aerodynamic forces in body axes
(Section 4.2.2), the force coefficients are given by:
(14.5)
(14.6)
where A is the projected area normal to the dish, given by π(b 2 /4).
Following the arguments in the previous paragraph, the eccentricity, e, of the
aerodynamic force can be closely approximated by (Wyatt, 1964):
(14.7)
Tests in smooth uniform flow (Wyatt, 1964) indicate maximum values of C x of about 1.7
when the angle of attack, a, is about 45°. The transverse force coefficient C Y is
approximately constant with f/d when expressed in the form (f/d)C Y , with a maximum
value of about 0.05, for a equal to about 135°. The transverse force F Y generates a
moment about the vertex equal to F Y ·e.