Studies of Modulus-limited Design

Case study 1 a tel SCOPE mirror - involving the selection of a material to 

Optimum combination of elastic properties for the mirror support 

Consider the selection of the material for the mirror backing of a 200-inch (5 m) diameter telescope. We want to identify the material that gives a mirror which will distort by less than the wavelength of light when it is moved, and has minimum weight. We will limit ourselves to these criteria alone for the moment - we will leave the problem of grinding the parabolic shape and getting an optically perfect surface to the development research team. 

At its simplest, the mirror is a circular disc, of diameter 2a and mean thickness f, simply supported at its periphery (Fig. 7.2). When horizontal, it will deflect under its own weight M when vertical it will not deflect significantly. We want this distortion (which changes the focal length and introduces aberrations into the mirror) to be small 

You will find the formulae for the elastic deflections of plates and beams under their own weight in standard texts on mechanics or structures (one is listed under Further Reading at the end of this chapter). We need only one formula here it is that for the deflection, 8, of the centre of a horizontal disc, simply supported at its 

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The modulus is calculated as the chord value between 0.0005 ( = 0.05%) and 0.0025 (= 0.25%) strain to agree with Part 1 of ISO 527. However, the EN Aerospace series still uses load-based criteria (c.f. allowable strain design limits used) to determine the modulus (i.c.. between 0.1 and 0.5 of the maximum load). The specimen preparation details are given now in a "normative annex, prior to development of a separate standard on this aspect, as proposed in a CEN study item. The remaining differences between various versions of the tensile test to be tackled in the next revisions arc given in Table 4. 

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