Static Longitudinal Stability Questions and Answers

Answer: C

Correct answer: Stability and control authority are separate requirements

The table sets them out as two independent conditions. Stability is about what the aeroplane does when left alone, and it is preserved by keeping the centre of gravity forward of the aft limit. Control authority is about what the pilot can make it do, and it is preserved by keeping the centre of gravity aft of the forward limit. An aeroplane loaded ahead of the forward limit satisfies the first splendidly and fails the second: it is very stable and cannot be flared. Both must be met, and only the range between the limits meets both.

Answer: D

Correct answer: Moving the centre of gravity aft

The neutral point is fixed by the aerodynamic layout - tail size, tail arm and wing geometry - and knows nothing about how the aeroplane is loaded. Enlarging the tail, lengthening the arm and sweeping the wing all move it aft and so increase the margin. Moving the centre of gravity aft leaves \( h_n \) exactly where it was and reduces \( K_n = h_n - h \) directly. It is the only row in which the change is a loading change rather than a design change.

Answer: A

A conventional tail balances the wing's nose down moment with a download the wing must offset. A canard's foreplane carries part of the weight instead, which removes that particular penalty at the cost of other difficulties.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the second explains the first. Static stability is a statement about the sign of the moment immediately after a disturbance, nothing more. Whether the resulting motion converges depends on the damping and the coupling between the modes, which is dynamic stability. A statically stable aeroplane may have a lightly damped or divergent phugoid, oscillating in speed and height with the initial restoring tendency present throughout.

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the second states exactly the difference the first asserts. The aft limit is a stability limit, protecting a minimum static margin so that the aeroplane still returns from a disturbance. The forward limit is a control limit, protecting the elevator\'s ability to produce a nose-up moment at low speed. They come from different equations, they are checked against different conditions, and they can be violated in quite different ways.

Answer: D

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason is the mechanism. On a conventional layout the centre of gravity lies aft of the wing’s aerodynamic centre, so an increase in incidence produces a nose-up moment, and the fuselage adds a further destabilising moment of its own. The tailplane is the only surface working the other way, so it must be sized to overcome both and leave a net negative moment slope.

Answer: A

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason explains the preference. The tail volume ratio is \[ \bar{V}_H = \frac{S_t\,l_t}{S\,\bar{c}}, \] which is linear in the moment arm as well as in the area. Extra arm therefore buys the same stability as extra area but adds far less wetted area and weight in the tail, where weight is most costly to balance.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the link is direct. The tail contribution carries the factor \( (1-\mathrm{d}\varepsilon/\mathrm{d}\alpha) \), which is exactly the statement that the tail sees only part of the aeroplane’s change in incidence, because the wing’s downwash increases at the same time. Downwash appears explicitly in the expression precisely because it dilutes the tail’s effectiveness.

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason is the cause. A conventional tail trims with a download, so the wing must generate that much lift again on top of the weight, and the induced drag of doing so is the trim drag penalty. A canard foreplane trims with an upload instead, carrying part of the weight and relieving the wing rather than adding to it.

Answer: D

Correct answer: A is false but R is true

The reason is sound - a larger static margin does give a steeper restoring moment - but the assertion does not follow from it. Too much stability makes the aeroplane heavy in pitch and sluggish to manoeuvre, demands more elevator and more download to trim, and so costs drag. The margin is chosen as a compromise, not maximised.