Chapter 16, Problem 28P

The total drag on an airfoil can be estimated by

$\begin{array}{l}D=0.01\sigma V^2+\frac{0.95}{\sigma }{\left(\frac{W}{V}\right)}^2\\ \text{ friction lift}\end{array}$

FIGURE P16.28

Plot of drag versus velocity for an airfoil.

where $D=\text{drag,}\sigma \text{=}$ ratio of air density between the flight altitude and sea level, $W=$ weight, and $V=$ velocity. As seen in Fig. P16.28, the two factors contributing to dragare affected differently as velocity increases. Whereas friction drag increases with velocity, the drag due to lift decreases. The combination of the two factors leads to a minimum drag.

(a) $\text{If }\sigma =0.5\text{ and }W=15,000$, determine the minimum drag and the velocity at which it occurs.

(b) In addition, develop a sensitivity analysis to determine how this optimum varies in response to a range of $W=12,000\text{ to }18,000\text{ with }\sigma \text{=0}\text{.5}$.