Another significant item shown in Fig. 3.3-23 is that the maximum temperature has been reduced from the 440°K shown in Fig. 3. 3-22 to 425°K. This is an important reduction in temperature as it provides some margin for an aluminum or graphite/epoxy structure. (The maximum recommended service temperature for these materials is 450° K.) 3.3.2.6 Temperature Difference Between Beam Cap Elements The temperature gradients within the antenna support structure will pose the most severe design condition for maintaining structural flatness. The severity of the problem is indicated by Ref 12 which states that to limit antenna tip deflections to less than 1 arc-min, the temperature difference between the upper and lower caps must be less than 3°K. Some of the temperature gradients and their causes that can exist within the structure are given next. A temperature gradient through the cross section of a standard member will exist tending to give the member a banana shape. Such a gradient is caused by non-uniform heating around the surface of a member. The magnitude of the gradient depends on the material, surface radiation properties and geometry of the element. Figure 3.3-21 shows the triangular shaped geometry to have the smallest temperature difference ( 20° K versus 400° K for the tubular geometry with low inner wall emissivity). However, a much more significant temperature difference that can exist within the structure is between corresponding elements on the upper and lower caps. The cause of the temperature difference is the different views that the two corresponding elements will have of the radiating antenna surface, with the element furthest away effectively receiving radiant energy from a larger portion of the antenna surface below it. For example, 90% of the radiation flux that impinges on a structural element located a distance d above the antenna surface comes from within an imaginary disc of radius 3d on the surface below it. Because the surface has a Gaussian rather than a uniform distribution, the further element will receive a different amount of energy than the closer element. The amount of radiant energy received by the further element may be more or less than that received by the closer element depending on the location of the elements with respect to the center of the antenna. Near the center, the further element will receive less energy, while near the edge it will receive more. The exact amount of energy received by an element and its resulting temperature were calculated using a computer program that was developed to account for the Gaussian waste heat distribution on the antenna surface. As a result of this type of temperature difference, the elements on the lower cap will expand more than those on the upper cap and the antenna will tend to "dish." Naturally if a
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