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For a conventional airplane in straight, level, constant velocity flight condition, which of the following condition(s) is/are possible on Euler angles \((\phi, \theta, \psi)\), angle of attack \((\alpha)\) and the sideslip angle \((\beta)\)?

  • A.\(\phi = 0^{o}, \theta = 2^{o}, \psi = 0^{o}, \alpha = 2^{o}, \beta = 0^{o}\)
  • B.\(\phi = 5^{o}, \theta = 0^{o}, \psi = 0^{o}, \alpha = 2^{o}, \beta = 0^{o}\)
  • C.\(\phi = 0^{o}, \theta = 3^{o}, \psi = 0^{o}, \alpha = 3^{o}, \beta = 5^{o}\)
  • D.\(\phi = 0^{o}, \theta = 5^{o}, \psi = 0^{o}, \alpha = 2^{o}, \beta = 5^{o}\)

Answer: A

The possible set is \(\phi = 0, \theta = 2^{o}, \psi = 0, \alpha = 2^{o}, \beta = 0\).

In straight, level, constant-velocity flight the wings are level (\(\phi = 0\)), the flight path is horizontal so the pitch angle equals the angle of attack (\(\gamma = \theta - \alpha = 0\)), and a conventional airplane flies with no sideslip (\(\beta = 0\)). The heading \(\psi\) can be any constant value. The first set meets every condition.

A 5-degree bank with zero sideslip tilts the lift vector and turns the airplane, and \(\theta = 0\) with \(\alpha = 2^{o}\) would mean a descent, so the second set is neither straight nor level. The third and fourth sets have a 5-degree sideslip with the wings level, which leaves an unbalanced side force, and the fourth also has \(\theta - \alpha = 3^{o}\), a climb. The official key accepts only the first set.

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