Subtopic: Stress and Strain Tensors & Generalized Hooke's Law
Question Statement:
Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?
Scientific schematic diagram reproduced from official IIT paper
Options:
(A) It contributes to $C_{m_\alpha} < 0$
(B) It makes $C_{m_\alpha} = 0$
(C) It makes $C_{m_\alpha} > 0$
(D) It makes $C_{m_0} > 0$ and $C_{m_\alpha} > 0$
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2022 Q.19)**
**1. Pitching Moment Contribution of the Horizontal Tail**:
Located aft of the aircraft center of gravity ($l_t > 0$), an increase in angle of attack $\alpha$ generates upward tail lift $\Delta L_t$, producing a restoring nose-down pitching moment:
$$\Delta C_m = -V_H \eta_t C_{L_{\alpha, t}} \left(1 - \frac{d\epsilon}{d\alpha}\right) \alpha$$
Thus, the horizontal tail provides a strongly negative contribution to the pitch stiffness derivative:
$$(C_{m_\alpha})_t < 0$$
- **Official Answer Key**: **A**
