Dynamic Longitudinal Modes Questions and Answers

Answer: A

The categories describe what the aeroplane is being asked to do: Category A covers rapid manoeuvring such as air combat or terrain following, Category B gradual manoeuvring such as cruise and climb, and Category C the terminal phases of take-off, approach and landing. Damping and frequency requirements differ between them, which is why a single number cannot settle whether an aeroplane is satisfactory. Speed regime and aeroplane class are separate axes of the specification, and the Levels are the grades of acceptability rather than the phases.

Answer: B

Level 1 means the flying qualities are clearly adequate for the mission, with the pilot's workload no more than satisfactory. Level 2 is where the aeroplane remains adequate but the workload rises or effectiveness falls, and Level 3 is the floor: the aeroplane can be controlled well enough to terminate the flight safely, and no more. Nothing in the definitions refers to the autopilot, and deliberately so, since the levels describe what the pilot faces including the case where the automatics have failed.

Answer: C

The mode lives in the incidence and pitch rate equations, and freezing the speed perturbation is what reduces the quartic to a manageable quadratic. Speed and flight path angle are the phugoid's pair, and the two approximations together cover the full problem. Sideslip and yaw rate, and roll rate and bank angle, belong to the lateral problem, which decouples from the longitudinal one for small perturbations about symmetric flight and so cannot contribute here.

Answer: D

The control anticipation parameter is \( \omega_n^{2}/(n/\alpha) \), so a larger load factor sensitivity in the denominator makes it smaller and the aeroplane feel sluggish: a great deal of load factor eventually arrives, but the initial pitch acceleration that would let the pilot anticipate it does not. This is exactly why the parameter was introduced, since frequency and damping alone would have called the two aeroplanes identical. Higher sensitivity cannot raise the parameter, being in the denominator, and it does not affect stability at all.

Answer: A

Statements 1 and 2 hold. Closing a height loop suppresses the oscillation, and since \( \zeta_{ph} \approx C_D/(\sqrt{2}C_L) \) more drag really would damp it, though no designer would accept the cure. Statement 3 is the trap: a pitch rate damper raises the effective \( M_q \), which damps the short period and does very little for the phugoid, because the phugoid involves almost no pitch rate to feed back. Phugoid damping is improved instead by feeding back speed or height, which is what an autothrottle or an altitude hold does.

Answer: B

A second-order mode is fully specified by its natural frequency and damping ratio, from which the period, the decay rate, the time to half amplitude and the cycles to half amplitude all follow. Peak amplitude describes how hard the mode was excited, not the mode itself, so pairing it with the period leaves the decay unknown. Time to half amplitude gives the product \( \zeta\omega_n \) but cannot separate the two factors. Trim speed and altitude are the flight condition at which the mode was measured, which determines the numbers without being them.

Answer: C

Lanchester's period \( T = \sqrt{2}\pi u_0/g \) contains only true airspeed and gravity, so holding true airspeed fixed leaves the period unchanged, even though the air is a third as dense at the top of the climb. This is a sharp contrast with the short period, whose frequency falls with the square root of density in the same climb, and it is a good check on whether the two formulae are being kept apart. The factors 0.5, 1.4 and 2.0 are all density-driven, and would be right if the phugoid depended on dynamic pressure, which it does not.

Answer: D

Using the shortcut \( T \approx 0.45\,u_0 \), the period is \( 0.45 \times 50 = 22.5 \ \mathrm{s} \), so a little over twenty seconds: brisk enough for a pilot to notice the aeroplane hunting in speed within a few seconds of releasing the stick. 45 s and 90 s belong to aeroplanes trimmed at 100 and 200 metres per second, so they show how much faster a light aeroplane's phugoid is than a jet's. 11 s halves the correct answer. The comparison is the practical reason phugoid handling complaints are more common on fast aeroplanes.

Answer: A

Below minimum drag speed the drag curve slopes the wrong way, so a small speed loss increases the drag and the aeroplane slows further unless thrust is added. That is a speed instability, and it shows up in the phugoid, which is the speed mode; on approach it is the reason speed must be flown attentively or held by an autothrottle. A negative frequency is not a physical statement. Inertia is a mass property unaffected by the drag curve. The elevator remains effective, which is precisely why the aeroplane can still be flown there with care.

Answer: B

Speed is half of the phugoid's energy exchange, so a loop that holds it removes the mode's freedom and damps it. That is why speed-hold and altitude-hold are the two effective cures for a poor phugoid, and why a pitch damper is not. Engines cannot respond in the second or two the short period lasts, and thrust makes almost no moment contribution in any case, so that mode is untouched. Nor is any stiffness added, so the short-period frequency stays where the aerodynamics put it.