Performance Constraint Analysis Questions and Answers

Answer: A

Plotting the constraints in these non-dimensional terms makes them independent of aircraft size, so the same diagram serves at any weight. Multiplying back by the design weight then gives the wing area and the thrust required.

Answer: B

Correct answer: The area satisfying every constraint simultaneously

The feasible region is the set of wing loading and thrust-to-weight combinations that satisfy every requirement at once. Each constraint divides the plane into an acceptable and an unacceptable side, and the feasible region is the intersection of all the acceptable sides.

It is not simply the area below all the lines, because some constraints - the landing line, for instance - bound the plane from the right rather than from above. Nor is it a single point: it is generally a region, and choosing within it is the designer's decision. If the intersection is empty, no design meets the requirements as stated.

Answer: C

Correct answer: A line requiring more thrust as wing loading rises

The takeoff constraint rises to the right. A higher wing loading means a smaller wing for the same weight, so the lift-off speed is higher and more distance is needed to reach it - which must be paid for with more thrust if the field length is to be held.

So takeoff bounds the design from below and to the right, and the feasible region lies above the line. A horizontal line would mean the requirement is independent of wing loading, and a vertical line would mean it fixes a wing loading regardless of thrust, which is the character of the landing constraint instead.

Answer: D

Correct answer: A vertical line, since it fixes a maximum wing loading

Landing distance depends on the approach speed and on the braking and reverse thrust available after touchdown, not on installed thrust - an aircraft lands with the engines at idle. The requirement therefore translates into a maximum approach speed, hence a maximum stalling speed, hence a maximum wing loading at the landing configuration's \( C_{L,max} \).

Because no value of thrust-to-weight will help, the constraint is independent of the vertical axis and plots as a vertical line, with the feasible region to its left. It is often the binding constraint on wing area for transport aircraft.

Answer: A

Correct answer: The gradient required with one engine out

The second segment is the part of the takeoff flight path from gear retraction to 400 feet, flown at V2 with the flaps still in the takeoff setting. Certification requires a minimum climb gradient there with the critical engine failed - 2.4 per cent for a twin, 2.7 for a three-engine aircraft and 3.0 for a four.

Because the remaining engines must supply both the drag and the gradient with a substantial thrust loss, this is frequently the constraint that sizes the engines of a twin. It concerns the takeoff climb, not the cruise, the ceiling or the approach.

Answer: B

Correct answer: Matching thrust to drag at the cruise point

The cruise constraint comes from the condition for steady level flight: thrust must equal drag at the cruise altitude and Mach number. Expressed in the diagram's variables, the required \( T/W \) is the reciprocal of the lift-to-drag ratio achieved at that wing loading, corrected for the thrust lapse with altitude.

Because both induced and parasite drag vary with wing loading - one falling and the other rising - the constraint plots as a curve with a minimum, and the wing loading at that minimum is the aerodynamically most efficient cruise point. Field lengths and stalling speed give other constraints entirely.

Answer: C

Correct answer: Downward, since induced drag falls

A higher aspect ratio reduces induced drag, since \( C_{D,i} = C_L^2/(\pi A e) \) falls as \( A \) rises. Less drag means less thrust is needed for the same cruise or climb performance, so both constraints move downward on the diagram and the feasible region grows.

The wetted area does rise somewhat with a longer, more slender wing, and structural weight rises too - real penalties that limit how far aspect ratio is pushed - but they do not reverse the induced drag benefit at the cruise lift coefficients of a transport. The stalling speed is unaffected, so the landing line does not move.

Answer: D

Approach speed follows from wing loading divided by the landing lift coefficient, so a better flap system allows a heavier wing loading for the same field length. This is why high-lift devices earn their weight and complexity.

Answer: A

Correct answer: Combat aircraft

A sustained turn requires the thrust to balance the much larger drag produced at a load factor \( n \), giving approximately \( T/W = n/(L/D) \) at that condition. At \( n = 5 \) with an \( L/D \) of 6 this demands a \( T/W \) of about \( 0.83 \) - an order of magnitude above a transport's cruise requirement, and typically the constraint that sizes a fighter's engine.

Transports, sailplanes and trainers are sized by field length, climb and cruise requirements; none of them manoeuvres hard enough for the turn constraint to bind.

Answer: B

Correct answer: At the lowest thrust and highest wing loading allowed

The design point is normally placed at the corner of the feasible region that gives the lowest acceptable thrust-to-weight and the highest acceptable wing loading. Thrust costs engine weight, purchase price and fuel burn, and a low wing loading means a large wing with more structural weight and more wetted area - so both axes are pushed to their limits.

That corner is where two constraints intersect, which is why a well-sized design usually has two active constraints. The centre of the region would leave performance margin bought at a permanent penalty in weight and fuel.