An ideal glider has drag characteristics given by \(C_{D} = C_{D_{0}} + C_{D_{i}}\), where \(C_{D_{i}} = KC_{L}^{2}\) is the induced drag coefficient, \(C_{L}\) is the lift coefficient, and \(K\) is a constant. For maximum range of the glider, the ratio \(C_{D_{0}}/C_{D_{i}}\) is
GATE AE - 2023,
Answer: A
For maximum range of a glider the ratio is 1.
A glider has no thrust, so in a steady glide its glide angle satisfies \(\tan\gamma = D/L = C_{D}/C_{L}\). The range from a given height is greatest when the glide angle is smallest, that is, at maximum \(L/D\), or minimum \(C_{D}/C_{L}\).
\[ \begin{aligned} \frac{C_{D}}{C_{L}} &= \frac{C_{D_{0}}}{C_{L}} + KC_{L} \\ \frac{d}{dC_{L}} &: -\frac{C_{D_{0}}}{C_{L}^{2}} + K = 0 \\ C_{D_{0}} &= KC_{L}^{2} = C_{D_{i}} \end{aligned} \]
So zero-lift drag equals induced drag and the ratio is 1. The option 1/3 is the condition for minimum sinking speed (maximum \(C_{L}^{3/2}/C_{D}\)), where the induced drag is three times the zero-lift drag; the option 3 is that relation turned upside down, and 3/2 matches neither. None of them gives maximum range.
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