Performance Constraint Analysis Questions and Answers

Answer: C

Correct answer: Dividing the design weight by the chosen wing loading

Wing loading is weight per unit wing area, so the area follows by rearrangement:

\[ S = \frac{W}{(W/S)} \]

A design weight of \( 640 \) kN at a wing loading of \( 5.8 \) kN/m\(^2\) therefore needs about \( 110 \) m\(^2\). Multiplying instead of dividing gives a nonsensical figure some thirty times too large. The installed thrust follows in the same way from the other coordinate, \( T = W \times (T/W) \), and these two numbers are the principal output of the whole analysis.

Answer: D

Correct answer: Lower the takeoff constraint

Relaxing the field length requirement means the aircraft may use more runway to reach lift-off speed, so less thrust is needed at any given wing loading. The takeoff line therefore moves downward, enlarging the feasible region and allowing a lower - and cheaper - thrust-to-weight ratio.

The landing constraint is unaffected, since it is set by approach speed and braking rather than by the takeoff run. This is a common trade in practice: an aircraft intended only for long runways can be given smaller engines than one that must operate from short fields.

Answer: A

Correct answer: The thrust for a residual climb rate at altitude

The ceiling constraint expresses the thrust needed to maintain a small specified rate of climb - often 300 feet per minute for the service ceiling - at the required altitude. It matters because thrust lapses steeply with altitude while drag does not fall correspondingly, so the margin between thrust and drag closes as the aircraft climbs.

It is an aerodynamic and propulsive limit, not a structural or pressurisation one, and it concerns climb capability rather than maximum speed. Like the cruise constraint, it must be referred back to sea level static thrust before it can be plotted.

Answer: B

Correct answer: Both are active and size the design

When two constraints intersect at the design point, both are met exactly and neither has margin - both are active, and both size the design. Changing either requirement would move the design point.

This is the normal outcome of good sizing, because the point is placed at a corner of the feasible region to minimise thrust and maximise wing loading, and corners are where constraint lines cross. It tells the designer where sensitivity lies: relaxing either of those two requirements yields an immediate benefit, whereas relaxing an inactive constraint yields none.

Answer: C

Correct answer: Landing field length

Landing field length is essentially independent of thrust-to-weight, because an aircraft lands with the engines at idle. What matters is the approach speed, set by the wing loading and the landing \( C_{L,max} \), and the deceleration available from brakes, spoilers and reverse thrust. The constraint therefore plots as a vertical line.

The other three all depend directly on thrust. Second segment climb sets a gradient with an engine failed, the ceiling sets a residual climb rate at altitude, and takeoff field length requires enough thrust to accelerate to lift-off speed within the runway available.

Answer: D

Correct answer: Downward and to the right

A higher \( C_{L,max} \) in the takeoff configuration lowers the lift-off speed for a given wing loading, so the aircraft needs less runway and less thrust. The takeoff constraint therefore moves downward, and because a higher wing loading can now be tolerated for the same field length, it also moves to the right.

The feasible region grows in both directions, which is why high-lift design is so valuable: better flaps and slats buy either smaller engines or a smaller wing, and improving the landing configuration's \( C_{L,max} \) moves the landing line right as well.

Answer: A

Correct answer: Revisit the requirements or the technology assumptions

An empty feasible region means no aircraft satisfying the stated assumptions can meet all the requirements at once. The honest response is to go back to the inputs: relax a performance requirement, improve an assumption about aerodynamic efficiency, high-lift performance or engine technology, or accept a different configuration.

Choosing a point that violates the fewest constraints is not available, because every line on the diagram represents a customer requirement or a certification rule and neither is optional. Increasing the design weight generally makes matters worse, and ignoring the landing constraint would produce an uncertifiable aircraft.

Answer: B

Correct answer: Early in conceptual design

Constraint analysis is one of the first quantitative steps in conceptual design, done as soon as the requirements are known. It needs only performance requirements and estimates of aerodynamic and propulsive parameters, and it produces the wing area and installed thrust.

Those two numbers are inputs to almost everything downstream - structural layout, fuel volume, weight estimation, engine selection - so deferring the analysis would leave the rest of the design without a basis. It is repeated as estimates improve, but the first pass comes before any structure is drawn, let alone built or flown.

Answer: C

Correct answer: Sea level static, with per-constraint corrections

Thrust-to-weight on a constraint diagram is conventionally referred to the sea level static rating, because that is how engines are specified and selected. Each constraint is then corrected to that datum by dividing the thrust it actually requires by the lapse factor appropriate to its altitude and Mach number.

A cruise requirement of \( T/W = 0.062 \) at 11,000 m where the engine gives \( 0.28 \) of its static thrust corresponds to \( 0.062/0.28 = 0.221 \) at sea level. Without that correction, constraints evaluated at different altitudes could not be plotted on one axis.

Answer: D

Correct answer: A larger wing, with more weight and wetted area

Wing loading is weight per unit area, so a lower wing loading - a point to the left - means a larger wing for the same weight. The penalties follow: more structural weight, more wetted area and hence more parasite drag, and a heavier aircraft that then needs more thrust and more fuel.

The compensation is a lower stalling speed and better field performance, which is why the landing constraint bounds the plane from the right. The design point is pushed as far right as the constraints allow precisely to avoid carrying a larger wing than the requirements demand.