Project Cyclops, A Design... - Department of Earth and Planetary ...

side of the dish and shade on the other, for example,
cause deformations proportional to dish size and these
account for the line marked "Thermal Limit." Finally
the strength of materials sets a size above which the dish
will collapse under its own weight. This is marked
"Stress Limit" in the figure, and represents a dish 600 m
in diameter. Also shown on the figure are points
corresponding to a number of existing and proposed
telescopes. Notice that three of these points exceed the
gravitational limit. In the case of the proposed 440-ft
NEROC (or CAMROC) telescope (point 13), this is
achieved by compensation, that is, by mechanical change
in the length of certain structural members as a function
of elevation angle. In the case of the Bonn 100-m
telescope (point 11) and to a much greater degree in the
proposed 300-ft NRAO design (point 14), the gravitational
limit is exceeded by making use of the principle
of homologous
design.
In homologous design, the object is not to eliminate
deflections by making the structure as stiff as possible
everywhere, but to allow greater deflections in certain
regions than would normally be present in conventional
design. Adding this compliance makes it possible to
control the deflections so that, under changing direction
of the gravity vector, the paraboloidal surface deforms
into a new paraboloid. The new surface may be simply
the old surface shifted and tilted slightly, and the feed is
repositioned accordingly. In this case, the deflections
merely produce an elevation angle error as a function of
elevation angle, which may be removed by calibration.
Thus the gravitational limit shown in Figure 8-2
applies only to "conventional" designs and may be
exceeded by active structures or structures designed by
modern computer techniques. We conclude that dishes
100 m or more in diameter operable down to 3-cm
wavelength are well within the present state of the art.
However, it should be noted that the application of the
homologous design principle to date does not seem to
yield a configuration well suited for quantity production.
This is not a criticism of the procedure, for the
homologous design approach has been used to date
only for "one of a kind" antennas. If this design
technique were to be useful for Cyclops, further study is
needed to assure that the design evolved using homology
exhibits the required features for mass production
efficiencies.
Some of the techniques for the design of the back up
structure are listed in Appendix G. The backup structure
cannot be designed independently of the base, since the
positions of load support points, and the force vectors
and torques introduced at these points, must be known.
OPTIMUM
SIZING
In an array, the total area can be obtained with a
certain number of large dishes or a larger number of
smaller ones. We would like to choose the dish size so
that the total cost is minimized. Following an analysis
by Drake we let the cost per element be
where
d = dish diameter
a = a constant
c = adx + b (5)
b = fixed cost per element, that is, cost of receivers,
control equipment, IF transmission and delay
circuit, etc.
To realize a total equivalent antenna area, A, we need a
number of dishes
4 A
n - (6)
rrd2
where r/ is the efficiency of utilization of the dish
surface. Thus, the total cost is
4A
nC = _ (ad x-2 + bd-2) (7)
rt77
Differentiating equation (7) with respect to d, we find
that nC is a minimum when
that is, when
2
ad x = _ b (8)
X-2
2
Structural cost -- _
x-2
fixed channel cost (8a)
The optimum size thus depends heavily on x, that is,
upon the exponent that relates the structural cost _ to
the diameter. If x > 2 there will be an optimum size
given by equation (8). If x _