Performance Constraint Analysis Questions and Answers

Answer: C

Correct answer: A point just outside it is acceptable

This is the false statement. A point outside the feasible region violates at least one constraint, and every constraint is a customer requirement or a certification rule - so an aircraft designed there either fails to meet its specification or cannot be certificated. There is no tolerance band around the boundary.

The other three are true. The region may be empty if the requirements are too demanding; its corners are formed where two constraints are simultaneously active; and by definition it satisfies every constraint at once.

Answer: D

Correct answer: Increasing the design weight

Increasing the design weight does not relax the landing constraint. The constraint is a limit on wing loading, a ratio, so the line does not move - a heavier aircraft simply needs a proportionally larger wing to stay within the same limit, which is a penalty rather than a relaxation.

The other three all relax it. A better flap system raises the landing \( C_{L,max} \) and moves the line right; a longer landing field and a higher permitted approach speed both raise the allowable stalling speed and so do the same.

Answer: A

Correct answer: The wing's aspect ratio

Aspect ratio is an input, not an output. It must be assumed before the cruise and climb constraints can be constructed, since it determines the induced drag those constraints depend on.

The other three are genuine outputs. The design wing loading is read off the horizontal axis at the chosen design point, the wing area follows by dividing the design weight by it, and the installed thrust follows by multiplying the design weight by the thrust-to-weight ratio at the same point. Choosing aspect ratio well requires running the sizing at several values and comparing.

Answer: B

Correct answer: Wrong: field performance worsens

Raising wing loading is not an unqualified improvement. It gives a smaller, lighter wing with less wetted area and often a better ride in turbulence, but it also raises the stalling speed as \( \sqrt{W/S} \), and with it the takeoff and landing distances - landing distance scaling roughly with the square of the approach speed.

That is exactly why the landing constraint is a vertical line bounding the diagram from the right: it marks the point beyond which better cruise efficiency would cost unacceptable field performance. The trade applies to fighters and transports alike.

Answer: C

Correct answer: It is more demanding for a twin

The second segment requirement is hardest for a twin. Although the required gradient is lower - 2.4 per cent against 3.0 for a four-engine aircraft - the twin loses half its installed thrust when one engine fails, while the four loses only a quarter. The surviving thrust fraction dominates the comparison.

The constraint applies to all multi-engine aircraft, propeller or jet, and is by definition evaluated with the critical engine failed - an all-engines evaluation would defeat its purpose, which is to guarantee a safe climb away after a failure at the worst moment.

Answer: D

Correct answer: Raising the cruise altitude

Raising the cruise altitude increases the installed thrust required, because engine thrust lapses steeply with altitude. The thrust actually needed at the cruise point changes little, but referring it back to the sea level static rating means dividing by a smaller lapse factor, which inflates the number the engine must be sized to.

The other three all reduce the thrust required. A higher aspect ratio cuts induced drag, a lower cruise Mach number reduces wave and profile drag, and reducing parasite drag lowers the total directly.

Answer: A

Correct answer: It must lie where two constraint lines cross

This is the false statement. The design point is usually placed at such an intersection, because that corner gives the lowest thrust and highest wing loading, but nothing requires it. A designer may retreat inside the region to keep margin for weight growth, or move along a boundary to match an available engine rating.

The other three are true: it must lie inside the feasible region, it is usually near a corner of it, and it is dimensionalised using the design weight to give the wing area and installed thrust.

Answer: B

Thrust available at altitude is a fraction of the sea level static value, so recovering the static figure means dividing by that fraction. Mixing reference conditions is one of the commonest errors in constructing the diagram.

Answer: C

Correct answer: It usually sizes the engines of a long-range transport

This is not true of the sustained turn constraint. A long-range transport is sized by cruise, takeoff or engine-out climb; it never manoeuvres hard enough for the turn constraint to bind, and would not be certificated for the load factors involved.

The other three are true. The constraint reflects the large induced drag at high load factor, since lift must be \( n \) times the weight; it is a defining requirement for combat aircraft; and it demands a high thrust-to-weight ratio, roughly \( n/(L/D) \), which at \( n = 5 \) approaches unity.

Answer: D

Correct answer: It is carried out early and refined as better data arrive

Constraint analysis is one of the first quantitative steps of conceptual design, and it is repeated. The first pass uses rough estimates of aerodynamic efficiency, high-lift performance and thrust lapse; as drag build-ups, weight estimates and engine data improve, the constraints are redrawn and the design point revisited.

It does not replace the weight estimate but works with it - the analysis produces ratios, and the weight estimate turns them into an area and a thrust. It applies equally to civil and military aircraft, though different constraints bind in each case.