Subtopic: Brayton Cycle with Real Component Efficiencies
Question Statement:
Which of the following design parameters influence the maximum rate-of-climb for a jet-propelled
airplane?
P. Wing loading
Q. Maximum thrust-to-weight ratio
R. Zero-lift drag coefficient
S. Maximum lift-to-drag ratio
Options:
(A) P and Q alone
(B) P, Q, R and S
(C) P, Q and S alone
(D) Q, R, and S alone
AE 10/11
AE (GATE 2014)
- AE
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.53)**
**1. Problem Statement & Parameters**:
- **Module**: Propulsion (2 Mark, MCQ)
- **Topic**: Thermodynamic Cycles of Gas Turbines (Brayton Cycle with Real Component Efficiencies)
- **Organizing Institute**: IIT Kharagpur
- **Problem Statement**:
> Which of the following design parameters influence the maximum rate-of-climb for a jet-propelled airplane? P. Wing loading Q. Maximum thrust-to-weight ratio R. Zero-lift drag coefficient S. Maximum lift-to-drag ratio
**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)** *"P and Q alone"*: ❌ **INCORRECT**.
- **(B)** *"P, Q, R and S"*: ✅ **CORRECT**.
- **(C)** *"P, Q and S alone"*: ❌ **INCORRECT**.
- **(D)** *"Q, R, and S alone
AE 10/11
AE (GATE 2014)
- AE"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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