Question

Which of the following statements about a general aviation aircraft, while operating at point $Q$ in the $V$-$n$ diagram, is/are true?

• A. The aircraft has the highest turn rate
• B. The aircraft has the smallest turn radius
• C. The aircraft is flying with minimum drag
• D. The aircraft is operating at $C_{L,\max}$

Hint:

On a $V$-$n$ diagram: left curved boundary $\Rightarrow C_L=C_{L,\max}$ (stall). Best turn performance occurs at the corner speed (stall boundary meets $n_{\text{limit}}$), not at an arbitrary low-speed point on the stall curve. Minimum drag lives on the 1-$g$ line near $C_{L,\mathrm{md}}$, not at $C_{L,\max}$.

Answer 1

The Correct Option is D

Step 1: Recall the meaning of the $V$-$n$ (flight envelope) diagram.
The horizontal axis is airspeed \(V\); the vertical axis is load factor \(n=L/W\). The rising curved boundary on the left is the stall limit for positive $n$. On this curve, the wing is just at its maximum lift coefficient \(C_{L,\max}\). Thus every point on this curve satisfies \[ L = \tfrac{1}{2}\rho V^2 S C_{L,\max} = nW \;\Rightarrow\; n = \frac{\tfrac{1}{2}\rho V^2 S C_{L,\max}}{W} \propto V^2. \] Therefore, operating at any point on the positive stall boundary (including $Q$) means the wing is at \(C_{L,\max}\)

Step 2: Evaluate statement (D).
From Step 1, point \(Q\) lies on the positive stall boundary \(\Rightarrow C_L = C_{L,\max}\)
Hence (D) is True. 

Step 3: Check turning performance statements (A) and (B).
For a coordinated level turn at load factor \(n\), \[ \text{turn rate } \omega = \frac{g\sqrt{n^2-1}}{V}, \qquad \text{turn radius } R = \frac{V^2}{g\sqrt{n^2-1}}. \] Along the stall boundary we have \(n = kV^2\) (with \(k=\tfrac{\rho S C_{L,\max}}{2W}\)), so \[ \omega(V)=\frac{g}{V}\sqrt{k^2V^4-1}, \quad R(V)=\frac{V^2}{g\sqrt{k^2V^4-1}}. \] Max \(\omega\) and min \(R\) over the envelope occur at the corner speed where the stall boundary meets the positive structural limit line \(n=n_{\text{limit}}\). Point \(Q\) in the figure is a generic point on the stall curve (at low \(V\)), not necessarily at this intersection.
At very low \(V\) near the 1-$g$ stall, \(n\to 1^+\) so \(\sqrt{n^2-1}\) is small \(\Rightarrow\) \(\omega\) is small and \(R\) is large. As \(V\) increases toward the corner speed, \(\omega\) increases and \(R\) decreases; the best turn performance is reached at the corner, not at a generic point like \(Q\).
Therefore, (A) highest turn rate and (B) smallest turn radius are False for \(Q\) in general (true only at the corner speed). 

Step 4: Check statement (C): minimum drag.
Minimum drag (or minimum \(C_D\)) occurs near the condition \(C_L = C_{L,\mathrm{md}}\) (where \(C_D\) is minimized for the aircraft), corresponding to the speed \(V_{\mathrm{md}}\) on the 1-$g$ line—not at \(C_{L,\max}\). Since at point \(Q\) we are at the stall boundary with \(C_L=C_{L,\max}\), this is far from the minimum-drag condition. \(\Rightarrow\) (C) is False. \[ \boxed{\text{Only (D) is correct: at point }Q\text{ the aircraft is at }C_{L,\max}.} \]