GATE 2022 AE – Question 45
For a conventional airplane in straight, level, constant velocity flight condition, which of the following condition(s) is/are possible on Euler angles (φ, θ, ψ), angle of attack (α) and the sideslip angle (β)?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (A) $(\phi,\theta,\psi,\alpha,\beta)=(0,2,0,2,0)^\circ$; (C) $(0,3,0,3,5)^\circ$
Explanation
In **straight, level, constant-velocity (steady) flight** the flight path angle $\gamma=0$. The relation between the Euler pitch angle $\theta$, the angle of attack $\alpha$ and the flight path angle is
$$\gamma=\theta-\alpha\quad(\text{for zero bank, }\phi=0).$$
So for level flight with no bank, $\theta=\alpha$. A steady sideslip $\beta$ does not change this relation.
Check the options $(\phi,\theta,\psi,\alpha,\beta)$:
- **A. (0, 2, 0, 2, 0):** $\theta=\alpha=2^\circ$. ✓
- **B. (5, 0, 0, 2, 0):** a bank of 5° with no turning force would make the aircraft slip or turn, so a constant-velocity straight flight is not possible. And $\theta\neq\alpha$. ✗
- **C. (0, 3, 0, 3, 5):** $\theta=\alpha=3^\circ$, with a steady sideslip of 5°. ✓
- **D. (0, 5, 0, 2, 5):** $\theta\neq\alpha$, which would give a climb. ✗
Answer **A and C**.