Performance Constraint Analysis Questions and Answers

Answer: A

Correct answer: The engines are sized by engine-out climb

The constraint sitting highest at the design wing loading is the one that determines the thrust, and here that is second segment climb. The engines are therefore sized by the certification gradient with one engine failed, and the aircraft carries more thrust in normal operation than its cruise performance alone would require.

This is the usual situation for a twin, because half the installed thrust is lost with the failure. It says nothing about the cruise requirement being impossible - it is simply less demanding - nor about the wing or the landing constraint, which bound the horizontal axis.

Answer: B

Correct answer: Revisit the requirements or the assumptions

An empty feasible region means no aircraft meeting the stated assumptions can satisfy all the requirements simultaneously. Every line represents either a customer requirement or a certification rule, so none may simply be dropped or violated.

The response is to go back to the inputs: negotiate a longer field length or a higher approach speed with the customer, or improve an assumption about high-lift performance, aerodynamic efficiency or engine technology. Removing the second segment constraint is not open to a designer at all, and increasing the design weight generally makes matters worse.

Answer: C

Correct answer: It lowers the thrust-driven constraints

A higher aspect ratio reduces induced drag, since \( C_{D,i} = C_L^2/(\pi A e) \). Less drag means less thrust for the same performance, so the cruise, climb and ceiling constraints all move downward and the feasible region grows.

The landing constraint does not move, because it depends on the maximum lift coefficient and the approach speed, not on drag. The penalty for the higher aspect ratio is structural: a longer, more slender wing is heavier, and that weight growth is what limits how far aspect ratio can usefully be taken.

Answer: D

Correct answer: feasible

The feasible region is the set of wing loading and thrust-to-weight combinations satisfying every requirement at once - the intersection of the acceptable side of every constraint line.

Any point inside it describes an aircraft that meets all the requirements; the designer then chooses among them, normally at the corner giving the lowest thrust and the highest wing loading. If the intersection is empty, no design meets the requirements as stated and the inputs must be revisited. The design point is a single point within the region, not the region itself.

Answer: A

Correct answer: wing loading

Wing loading is the aircraft weight divided by the wing reference area, carried in newtons or kilonewtons per square metre, and it forms the horizontal axis of the constraint diagram.

It governs the stalling speed through \( V_s = \sqrt{2(W/S)/\rho C_{L,max}} \), and hence the field performance, while a higher value means a smaller and lighter wing with less wetted area. That tension - field performance against wing size - is what the landing constraint arbitrates. Thrust-to-weight is the other axis, and aspect ratio and load factor are different quantities entirely.

Answer: B

Correct answer: second

The second segment runs from gear retraction to 400 feet, flown at V2 with the flaps still in the takeoff setting. Certification requires a minimum climb gradient there on the remaining engines after the critical engine has failed: 2.4 per cent for a twin, 2.7 for a three-engine aircraft and 3.0 for a four.

The first segment is from lift-off to gear retraction, the third the level acceleration and flap retraction, and the fourth the final climb in the en-route configuration. The second is the one that most often sizes a twin's engines, because half its thrust is gone.

Answer: C

Correct answer: service

The service ceiling is the altitude at which a specified small residual rate of climb - commonly 300 feet per minute - remains available. It is a practical limit, defining where the aircraft can still climb usefully rather than merely maintain height.

The absolute ceiling is where the rate of climb falls to zero, which is approached only asymptotically and is of little operational use. The cabin ceiling is a pressurisation limit and the structural ceiling a limit on the fuselage, both quite separate from the thrust-and-drag balance the constraint expresses.

Answer: D

Correct answer: installed thrust

The installed thrust follows from the vertical coordinate of the design point:

\[ T = W \times \frac{T}{W} \]

Dividing the weight by the horizontal coordinate gives the wing area in the same way. These two numbers are the principal output of the whole analysis, and the installed thrust is then divided among the engines to give the per-engine rating that must be matched against catalogue engines.

Answer: A

Correct answer: 6.4

The binding constraint at any wing loading is whichever demands the most thrust. Reading across each row: at \( 4.0 \), \( 4.8 \) and \( 5.6 \) the largest value is the second segment figure of \( 0.28 \), which exceeds both the takeoff and the cruise demands. At \( 6.4 \) the takeoff figure has risen to \( 0.31 \) and overtakes it.

So takeoff first becomes binding at \( 6.4 \) kN/m\(^2\). The pattern is typical: the takeoff column rises steadily with wing loading while second segment climb is nearly flat, so takeoff always takes over eventually - and the crossover marks the corner of the feasible region.

Answer: B

Correct answer: 5.0 kN/m\(^2\)

Read down the approach speed column against the \( 70 \) m/s limit. At \( 5.0 \) kN/m\(^2\) the approach speed is \( 68.9 \) m/s, just within it; at \( 6.0 \) it is \( 75.5 \) m/s, well outside. The maximum permissible wing loading therefore lies between the two and is closest to \( 5.0 \).

That value is exactly what the vertical landing constraint would be drawn at. Note how quickly the margin disappears: a 20 per cent increase in wing loading costs almost 10 per cent in approach speed, because the speed varies as the square root of the loading.