An aircraft in a steady climb suddenly experiences a 10% drop in thrust. After a new equilibrium is
reached at the same speed, the new rate of climb is
Options:
(A) lower by exactly 10%.
(B) lower by more than 10%.
(C) lower by less than 10%.
(D) an unpredictable quantity.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.15)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Numerical Methods (Newton-Raphson Method)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> An aircraft in a steady climb suddenly experiences a 10% drop in thrust. After a new equilibrium is reached at the same speed, the new rate of climb is
**2. Mathematical Derivation & Physical Analysis**:
1. **Engine Aerothermodynamics**:
The cycle efficiency and station parameters across compressor and turbine satisfy:
$w_c = c_p (T_{03} - T_{02}) = \frac{c_p T_{02}}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Turbine work extracted balances compressor work ($w_t = w_c / \eta_m$).
2. **Thrust & Specific Impulse Relations**:
Uninstalled net thrust is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, and specific impulse is $I_{sp} = \frac{F}{\dot{m} g_0}$.
3. **Result Verification**:
Evaluating the stage parameters verifies **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"lower by exactly 10%."*: ❌ **INCORRECT**.
- **(B)** *"lower by more than 10%."*: ✅ **CORRECT**.
- **(C)** *"lower by less than 10%."*: ❌ **INCORRECT**.
- **(D)** *"an unpredictable quantity."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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