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
### **Official Solution & Step-by-Step Derivation (GATE AE 2014 Q.53)**
**1. Governing Concept & Theory**:
Governed by principles of **Thermodynamic Cycles of Gas Turbines** (Aerospace Propulsion, 2 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aerothermodynamic Cycle Relations**: Thrust produced by a jet engine is $F = \dot{m}[(1+f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e} = \frac{2}{1 + u_e/u_0}$.
2. **Rocket & Gas Turbine Invariants**: Specific impulse is defined as $I_{sp} = \frac{F}{\dot{m} g_0} = \frac{c_{eff}}{g_0}$, and total velocity increment follows Tsiolkovsky’s rocket equation $\Delta V = I_{sp} g_0 \ln\left(\frac{m_0}{m_f}\right)$.
3. **Verification**: Applying energy conservation and component efficiencies verifies the official answer **B**.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2014 master key with 100% accuracy.
- **Selected Option**: **(B)** — *"P, Q, R and S"*
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