In a conventional configuration airplane, the rudder can be used:
Options:
(A) to overcome adverse yaw during a turning maneuver
(B) to overcome yawing moment due to failure of one engine in a multi engine airplane
(C) for landing the airplane in crosswind conditions
(D) for enhancing longitudinal stability
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2024 Q.27)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Thermodynamic Cycles of Gas Turbines** (Turbojet, Turbofan & Turboprop Engine Performance) within the *Propulsion* curriculum (1 Mark, MSQ).
**Problem Statement**:
> In a conventional configuration airplane, the rudder can be used:
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Propulsion. Formulating the mathematical balance relations:
$\text{Analytical State Balance} = 0$
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`A, B, C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"to overcome adverse yaw during a turning maneuver"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(B)** *"to overcome yawing moment due to failure of one engine in a multi engine airplane"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(C)** *"for landing the airplane in crosswind conditions"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(D)** *"for enhancing longitudinal stability"*: ❌ **INCORRECT**. Contradicts governing physical laws.
*Full credit (+1 Marks, 0 Negative Marks) requires selecting all verified choices **`A, B, C`**.*
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, B, C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.
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