Performance Constraint Analysis Questions and Answers

Answer: C

Correct answer: Only three

Three pairs are right. Wing area is the design weight divided by the wing loading; installed thrust is the design weight times the thrust-to-weight ratio; and the stalling speed follows from the wing loading and the maximum lift coefficient through \( V_s = \sqrt{2(W/S)/\rho C_{L,max}} \).

The fourth is wrong. Aspect ratio is not obtained from the design point - it is an input to the analysis, chosen beforehand and used in constructing the cruise and climb constraints through its effect on induced drag. Given the wing area and the aspect ratio, the span then follows.

Answer: D

Correct answer: Only three

Three pairs are right. Second segment climb comes from a certification gradient with one engine failed; the ceiling constraint from a residual rate of climb at altitude; and the sustained turn constraint from holding a load factor at constant speed and altitude.

The fourth is wrong. The landing requirement is a field length, which translates into a maximum approach speed and hence a maximum wing loading - it is not a minimum lift-to-drag ratio. Lift-to-drag governs the thrust-driven constraints such as cruise and climb, not landing, which is flown at idle thrust.

Answer: A

Correct answer: Structural fatigue life

Fatigue life is a structural matter, settled by material selection, detail design and inspection intervals. It does not translate into a relation between wing loading and thrust-to-weight, so it cannot be drawn on the diagram at all.

The other three do. Takeoff field length gives a line rising to the right, second segment climb a roughly horizontal line from the engine-out gradient, and cruise speed a curve from matching thrust to drag at the cruise point. The diagram holds only requirements expressible in its two variables.

Answer: B

Correct answer: A shorter landing requirement

A shorter landing requirement tightens the diagram. It lowers the permitted approach speed, hence the permitted stalling speed, hence the maximum wing loading - so the vertical landing line moves left and the feasible region shrinks, forcing a larger wing.

The other three all relax constraints. A longer available runway lowers the takeoff line; a better high-lift system moves the landing line right and the takeoff line down and right; and a higher aspect ratio cuts induced drag and so lowers the cruise and climb lines.

Answer: C

Correct answer: The wing's aspect ratio

Aspect ratio does not follow from the design point - it is an input, chosen beforehand and used in constructing the cruise and climb constraints through its effect on induced drag. Given the wing area that the analysis produces, the aspect ratio then fixes the span.

The other three do follow. Wing area is the design weight divided by the wing loading, installed thrust is the weight times the thrust-to-weight ratio, and the stalling speed follows from the wing loading and the maximum lift coefficient.

Answer: D

Correct answer: The cruise thrust requirement

The cruise thrust requirement comes from matching thrust to drag in steady level flight, so it depends on the lift-to-drag ratio at the cruise lift coefficient. The maximum lift coefficient plays no part, because the aircraft cruises far below the stall.

The other three all depend on \( C_{L,max} \). The stalling speed varies as \( 1/\sqrt{C_{L,max}} \); the landing constraint follows from the stalling speed in the landing configuration; and the takeoff constraint follows from the lift-off speed set by \( C_{L,max} \) in the takeoff configuration.

Answer: A

Correct answer: A thrust-to-weight ratio near 0.28

A thrust-to-weight ratio near \( 0.28 \) is typical of a transport, not a fighter. Transports cruise efficiently at high lift-to-drag ratios and need thrust chiefly for takeoff and engine-out climb, so values around \( 0.25 \) to \( 0.35 \) are usual.

The other three are characteristic of fighters. A sustained turn constraint appears only where hard manoeuvring is required; a thrust-to-weight near unity follows from it, since \( T/W \approx n/(L/D) \) gives large values at high load factor; and a design point set by manoeuvre rather than field length is the natural consequence.

Answer: B

The corner formed by the two active constraints is the economical choice, giving the smallest wing and the least thrust the requirements allow. Both active constraints are then satisfied exactly, with nothing to spare on either.

Answer: C

Correct answer: Both grow by 10 per cent

Holding the design point fixed means holding both ratios fixed, and both physical quantities are proportional to weight:

\[ S = \frac{W}{(W/S)}, \qquad T = W \times \frac{T}{W} \]

A 10 per cent weight growth therefore gives 10 per cent more wing area and 10 per cent more installed thrust. And because a bigger wing and bigger engines are themselves heavier, the growth feeds back into the weight estimate - the spiral that makes late weight increases so expensive and why the sizing loop must be re-converged rather than adjusted once.

Answer: D

Correct answer: It increases, as landing now binds lower

The landing constraint is what sets the maximum wing loading, and shortening the required landing distance moves that vertical line to the left. A lower permitted wing loading means a larger wing for the same weight, so the wing area increases.

Relaxing the takeoff requirement lowers the takeoff line, which reduces the thrust needed but does nothing to the maximum wing loading - the takeoff constraint bounds the diagram from below, not from the right. So the two changes act on different quantities: one buys smaller engines, the other forces a bigger wing.