Performance Constraint Analysis Questions and Answers

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. Every line on the diagram represents a customer requirement or a certification rule, so none of them is a designer's preference that can be traded away or partially met.

An empty feasible region therefore means the requirements as stated are unachievable under the assumptions made, and the only honest responses are to renegotiate a requirement or to improve an assumption - better high-lift performance, a higher aspect ratio, a more advanced engine. Continuing with a violated constraint would produce an aircraft that either fails to sell or fails to certificate.

Answer: B

Correct answer: 1 and 2 only

Statement 1 is correct: the axes are wing loading horizontally and thrust-to-weight vertically. Statement 2 is correct: the feasible region is the intersection of the acceptable side of every constraint, so it satisfies them all at once.

Statement 3 is false. The design point is normally placed at a corner of the feasible region, not at its centre, because thrust and wing area both carry weight and fuel penalties and are pushed to their limits. A central point would carry permanent performance margin nobody asked for.

Answer: C

Correct answer: 1, 2 and 3

All three are correct. The landing requirement sets a maximum permissible wing loading, so it bounds that axis from above (1). It is essentially independent of installed thrust, because an aircraft lands with the engines at idle and stops on brakes, spoilers and reverse thrust (2) - which is why it plots as a vertical line.

And it moves right when the landing lift coefficient is increased (3), since for a fixed approach speed \( W/S = \tfrac{1}{2}\rho V_s^2 C_{L,max} \), so a better flap system permits a higher wing loading and hence a smaller wing.

Answer: D

Correct answer: 1 and 2 only

Statement 1 is correct: wing area is the design weight divided by the wing loading. Statement 2 is correct: installed thrust is the design weight multiplied by the thrust-to-weight ratio. These two are the analysis's principal outputs.

Statement 3 is false. Aspect ratio does not follow from the design point - it is an assumption fed into the analysis, needed before the cruise and climb constraints can be drawn. Once the wing area is known, the aspect ratio fixes the span, but it is chosen rather than derived.

Answer: A

Correct answer: 1 and 2 only

Statement 1 is correct: the second segment gradient is set by the airworthiness rules, not by the customer. Statement 2 is correct: it is evaluated with the critical engine failed.

Statement 3 is false, and reverses the truth. The required gradient is indeed higher for a four-engine aircraft - 3.0 per cent against 2.4 for a twin - but the twin loses half its thrust to the failure while the four loses only a quarter. The twin's requirement is therefore much harder to meet, which is why second segment climb so often sizes a twin's engines and rarely a four's.

Answer: B

Each line on the diagram traces back to one written requirement, and knowing which is which tells you immediately what to change when a constraint binds. Two of these are certification rules and two are customer requirements.

Answer: C

Correct answer: A-2, B-1, C-4, D-3

Each quantity is matched to how it is obtained. Wing area (A) is the design weight divided by the wing loading (2); installed thrust (B) is the design weight times the thrust-to-weight ratio (1); stalling speed (C) follows from the wing loading and the maximum lift coefficient (4).

Aspect ratio (D) is the odd one: it is an assumption fed into the analysis (3), needed to construct the cruise and climb constraints before any design point exists. Three outputs and one input - recognising which is which is the point of the item.

Answer: D

Correct answer: A-2, B-1, C-4, D-3

Each change is matched to its effect. Better landing flaps (A) raise the landing \( C_{L,max} \) and permit a higher wing loading, so the landing constraint moves right (2). A higher aspect ratio (B) cuts induced drag, so the cruise and climb constraints move down (1).

A shorter landing distance requirement (C) lowers the permitted approach speed and hence the permitted wing loading, moving the landing constraint left (4). A heavier design weight (D) moves no line at all (3), because both axes are ratios - it changes only the area and thrust that a given design point implies.

Answer: A

Correct answer: A-2, B-1, C-4, D-3

Each type is matched to the constraint that usually sizes its engines. A twin-engine transport (A) is sized by second segment climb with one engine out (2), because half the thrust is lost. An air superiority fighter (B) is sized by the sustained turn at high load factor (1), which demands \( T/W \) approaching unity.

A four-engine long-range transport (C) is sized by cruise at altitude (4), since losing one of four engines is a far smaller penalty. A short-field regional turboprop (D) is sized by takeoff field length from a short runway (3), the requirement that defines its role.

Answer: B

Correct answer: Fatigue life of the wing spar

Fatigue life is a structural matter, governed by material choice, detail design, stress levels and inspection intervals. It cannot be expressed as a relation between wing loading and thrust-to-weight, so there is no line to draw for it.

The other three all can be expressed in those variables and are standard constraints: landing field length as a vertical line, takeoff field length as a line rising to the right, and cruise speed at altitude as a curve from matching thrust to drag. The diagram carries performance requirements, not structural ones.