Performance Constraint Analysis Questions and Answers

Answer: C

Correct answer: A higher cruise altitude demands more static thrust

The sea level static column rises steadily with altitude - \( 0.161 \) at 9000 m to \( 0.283 \) at 12,000 m - even though the thrust actually required at altitude barely changes, from \( 0.058 \) to \( 0.068 \).

The cause is the lapse factor, which falls from \( 0.36 \) to \( 0.24 \) across the same range. Since the sea level figure is the requirement at altitude divided by the lapse, a shrinking denominator inflates it. Higher cruise altitudes therefore cost engine size, which is the counterweight to the aerodynamic and fuel-burn advantages of flying high.

Answer: D

Correct answer: The thrust saving flattens while weight keeps growing

Compare the two columns. Going from aspect ratio 7 to 9 saves \( 0.014 \) in cruise \( T/W \) for a 9 per cent wing weight penalty; from 11 to 13 it saves only \( 0.004 \) for a further 15 per cent of weight. The benefit is diminishing while the cost accelerates.

This is why aspect ratio is not simply maximised, and why constraint analysis alone cannot choose it: the diagram shows the thrust saving but not the weight penalty, so the choice requires a weight and mission analysis to find where the two balance.

Answer: A

Moving the vertical landing line leftward removes part of the plane that was previously available. The two takeoff rows both open the region up, and a heavier design leaves the non-dimensional lines exactly where they were.

Answer: B

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

Both statements are true and the reason explains the assertion. Landing distance depends on the approach speed and on the deceleration from brakes, spoilers and reverse thrust; the engines are at idle through the flare and touchdown, so installed thrust plays essentially no part.

Being independent of the vertical axis, the requirement translates purely into a maximum wing loading - through the maximum approach speed, hence stalling speed, hence \( W/S \) at the landing \( C_{L,max} \) - and so is drawn as a vertical line with the feasible region to its left.

Answer: C

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

Both statements are true and the reason explains the assertion. The certification gradient of 2.4 per cent must be met on the remaining engine after a failure at takeoff, so a twin must install about twice the thrust that requirement implies - roughly \( 0.21 \) where the surviving engine must deliver about \( 0.107 \).

That doubling frequently pushes the second segment line above the cruise and takeoff lines, making it the constraint that sizes the engines. A twin consequently cruises with more thrust available than it needs, an inefficiency imposed by the engine-out case.

Answer: D

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

Both statements are true and the reason explains the practice. Working in ratios rather than in absolute area and thrust lets the same diagram apply whatever the aircraft's weight turns out to be, which matters because the weight is still only an estimate when the analysis is first run.

The design point is chosen in ratio terms and only afterwards dimensionalised, by dividing and multiplying by the design weight. If the weight estimate then changes, the diagram and the design point stand unaltered and only the resulting area and thrust are recomputed.

Answer: A

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

Both statements are true and the reason explains the assertion. Thrust costs engine weight, price and fuel, so the lowest acceptable \( T/W \) is preferred; wing area costs structural weight and wetted area, so the highest acceptable \( W/S \) is preferred.

Pushing both objectives against their limits puts the design point on the boundary of the feasible region, and specifically where two boundaries meet - a corner. This is why a well-sized aircraft normally has exactly two active constraints, and why those two are where design sensitivity lies.

Answer: B

The reason is correct but the assertion is not: the non-dimensional lines do not move at all, and only the dimensional outcome changes. Confusing a movement of the lines with a change in the dimensional outcome is a common error.

Answer: C

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

Both statements are true and the reason explains the assertion. For a fixed approach speed, the allowable wing loading scales directly with \( C_{L,max} \):

\[ \frac{W}{S} = \tfrac{1}{2}\rho V_s^2 C_{L,max} \]

So a better high-lift system permits a higher wing loading at the same speed, which means a smaller wing for the same weight - the landing line moves right and the wing shrinks. This is why flap and slat development pays for itself despite being used for only a few minutes of each flight.

Answer: D

Correct answer: A is false but R is true

The assertion is false. Constraint analysis cannot determine the optimum aspect ratio, because aspect ratio is an input to it: a value must be assumed before the cruise and climb constraints can be drawn at all.

The reason is true - higher aspect ratio does reduce induced drag and hence the thrust required - but it captures only one side of the trade. The diagram shows the thrust saving and not the structural weight penalty that grows with span, so choosing aspect ratio requires a weight and mission analysis, typically by running the sizing at several values and comparing the results.