An aircraft in steady level flight has a parabolic drag polar $C_D = C_{D,0} + K C_L^2$. At the airspeed corresponding to **minimum power required** $(P_{R,\min})$, the ratio of parasite drag $D_0$ to induced drag $D_i$ is:

(A) $D_0 / D_i = 1 / 3$

(B) $D_0 / D_i = 1$

(C) $D_0 / D_i = 3$

(D) $D_0 / D_i = 1 / \sqrt{3}$

Answer Key:

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### 1. Strategy & Theoretical Principles Power required is $P_R = D \cdot V = \frac{1}{2} \rho V^3 S C_{D,0} + \frac{2 K W^2}{\rho V S}$. Differentiating $P_R$ with respect to velocity $V$ and setting to zero: $$\frac{d P_R}{dV} = \frac{3}{2} \rho V^2 S C_{D,0} - \frac{2 K W^2}{\rho V^2 S} = 0$$ $$\frac{3}{2} \rho V^2 S C_{D,0} = \frac{2 K W^2}{\rho V^2 S}$$ ### 2. Analytical Drag Ratio Notice that the parasite drag is $D_0 = \frac{1}{2} \rho V^2 S C_{D,0}$ and induced drag is $D_i = \frac{2 K W^2}{\rho V^2 S}$. Substituting into the derivative relation: $$3 D_0 = D_i \implies \frac{D_0}{D_i} = \frac{1}{3}$$ Induced drag is exactly three times the parasite drag at the minimum power speed ($C_L = \sqrt{3 C_{D,0}/K}$). ### 3. Distractor Forensics - **Option A (1/3):** Correct ratio for minimum power required. - **Option B (1):** Condition for minimum thrust required (minimum drag $D_{R,\min}$ where $D_0 = D_i$). - **Option C (3):** Inverted ratio ($D_i / D_0$). ### 4. Exam Trap & Standard Reference - **Trap Alert:** At minimum thrust required: $D_0 = D_i$. At minimum power required: $D_i = 3 D_0$ ($D_0/D_i = 1/3$). - **Standard Reference:** Anderson, J.D., *Introduction to Flight*, Chapter 6.

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