Explore the trade-off between relative cost and relative mass for the air cylinder of Exercise E8.7, considering
Question:
Explore the trade-off between relative cost and relative mass for the air cylinder of Exercise E8.7, considering the replacement of a mild steel tank with one made, first, of low alloy steel, and, second, one made of filament-wound CFRP. The relevant material properties in the table below. Define a relative penalty function
\[Z^{*}=\alpha^{*} \frac{m}{m_{o}}+\frac{C}{C_{o}}\]
where \(\alpha^{*}\) is a relative exchange constant, and evaluate \(Z^{*}\) for \(\alpha^{*}=1\) and for \(\alpha^{*}=100\).
Data From Exercise E8.7
The air is stored in one or a cluster of cylindrical pressure tanks like that shown here (length L, diameter 2R, hemispherical ends). Most are made of low carbon steel, and they are heavy. The task: to explore the potential of alternative materials for lighter air tanks, recognizing that there must be a trade-off between mass and cost – if it is too expensive, the truck owner will not want it even if it is lighter. The table summarizes the design requirements.
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