Raising the landing \( C_{L,max} \) from \( 2.4 \) to \( 2.9 \) allows the limiting wing loading to rise by a factor of
Answer: C
For a fixed approach speed the allowable wing loading scales directly with the lift coefficient, so the factor is \( 2.9/2.4 = 1.208 \). Twenty per cent more wing loading is a substantial return on a better flap system.
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A sustained turn at a load factor of \( 5 \) with a lift-to-drag ratio of \( 6 \) at that condition requires a thrust-to-weight ratio of about
Answer: D
Correct answer: 0.83
In a sustained turn at load factor \( n \), lift is \( nW \) and the drag rises correspondingly, so:
\[ \frac{T}{W} = \frac{n}{L/D} = \frac{5}{6} = 0.83 \]
The lift-to-drag ratio used must be the value at that condition, which is far below the cruise figure because induced drag rises with the square of the lift coefficient. The result - a thrust-to-weight approaching unity - is an order of magnitude above a transport's requirement, and it is why this constraint sizes the engine of a combat aircraft.
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An aircraft's design point sits at \( W/S = 5.5 \) kN/m\(^2\) and \( T/W = 0.30 \). If the weight estimate rises by \( 8 \) per cent with the design point held, the wing area and thrust both rise by
Answer: A
Correct answer: 8 per cent
Both quantities are obtained by multiplying or dividing the design weight by a fixed ratio:
\[ S = \frac{W}{(W/S)}, \qquad T = W \times \frac{T}{W} \]
With the design point held, both ratios are unchanged, so both \( S \) and \( T \) scale in direct proportion to \( W \) - an 8 per cent weight growth gives 8 per cent more wing and 8 per cent more thrust. This linearity is what drives the weight growth spiral: a heavier aircraft needs a bigger wing and bigger engines, which are themselves heavier, and the loop must be iterated to convergence.
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At \( 11000 \) m the thrust available is \( 0.28 \) of the sea level static value. A cruise requirement of \( T/W = 0.062 \) at altitude corresponds to a sea level static ratio of
Answer: B
Correct answer: 0.221
Divide the requirement at altitude by the thrust lapse to refer it to the sea level static datum on which the diagram is plotted:
\[ \left(\frac{T}{W}\right)_{SLS} = \frac{0.062}{0.28} = 0.221 \]
The distractor \( 0.017 \) multiplies instead of dividing, which would say that less sea level thrust is needed than at altitude - the wrong way round, since thrust falls with altitude and the sea level rating must therefore be the larger number. Every constraint evaluated away from sea level needs this correction before the lines can be compared.
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Statement I: The landing constraint plots as a vertical line on a constraint diagram.
Statement II: Landing performance depends on approach speed and braking rather than on installed thrust.
In the light of the above statements, choose the correct answer.
Answer: C
Correct answer: Both Statement I and Statement II are correct
Both statements are correct and the second explains the first. Landing performance depends on the approach speed and the deceleration available from brakes, spoilers and reverse thrust; the engines are at idle throughout the flare and touchdown, so installed thrust plays essentially no part.
Since the requirement is therefore independent of the vertical axis, it translates purely into a maximum wing loading - through the maximum approach speed, hence stalling speed, hence \( W/S \) at the landing \( C_{L,max} \) - and plots as a vertical line with the feasible region to its left.
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Statement I: Second segment climb frequently sizes the engines of a twin.
Statement II: The gradient must be achieved on the remaining engine after a failure at takeoff.
In the light of the above statements, choose the correct answer.
Answer: D
Correct answer: Both Statement I and Statement II are correct
Both statements are correct and the second explains the first. Certification requires a minimum second segment gradient - 2.4 per cent for a twin - to be achieved after the critical engine has failed at takeoff, so the remaining engine alone must supply both the drag and the gradient.
For a twin that means installing roughly twice the required \( T/W \), since half of it is lost with the failed engine. That doubling frequently makes second segment climb the binding constraint, so a twin often carries more thrust in normal operation than its cruise or takeoff performance alone would need.
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Statement I: Raising wing loading always improves the design.
Statement II: A smaller wing has less structural weight and less wetted area.
In the light of the above statements, choose the correct answer.
Answer: A
The benefit named is real, but the landing and takeoff constraints put a ceiling on wing loading and stalling speed rises with its square root. The word always is what makes the assertion false, since every advantage here runs into a limit.
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Statement I: A better high-lift system relaxes both the takeoff and landing constraints.
Statement II: Both constraints depend on the maximum lift coefficient achievable in their respective configurations.
In the light of the above statements, choose the correct answer.
Answer: B
Correct answer: Both Statement I and Statement II are correct
Both statements are correct and the second explains the first. Takeoff distance depends on the lift-off speed, set by the takeoff-configuration \( C_{L,max} \), and landing distance on the approach speed, set by the landing-configuration \( C_{L,max} \).
A better high-lift system raises both, so the takeoff constraint moves down and to the right while the landing constraint moves right. The feasible region grows in both directions, buying either smaller engines or a smaller wing - which is why flap and slat design receives attention out of proportion to the fraction of the flight in which it is used.
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Statement I: An empty feasible region means the design point should be placed where the fewest constraints are violated.
Statement II: Every constraint on the diagram represents a requirement or a certification rule.
In the light of the above statements, choose the correct answer.
Answer: C
Correct answer: Statement I is incorrect but Statement II is correct
Statement I is incorrect. An empty feasible region cannot be resolved by choosing where to violate the fewest constraints, because a violated requirement is a requirement not met and a violated certification rule is an aircraft that cannot be certificated.
Statement II is correct and is exactly why: every line on the diagram represents either a customer requirement or a rule, and neither is negotiable at the designer's discretion. The proper response is to go back to the inputs - relax a requirement with the customer's agreement, or improve an assumption about aerodynamics, high-lift performance or engine technology.
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Statement I: Thrust-to-weight and wing loading on a constraint diagram are dimensionless in wing loading.
Statement II: Working in non-dimensional terms makes the diagram independent of aircraft size.
In the light of the above statements, choose the correct answer.
Answer: D
Correct answer: Statement I is incorrect but Statement II is correct
Statement I is incorrect. Thrust-to-weight is indeed dimensionless, being a ratio of two forces, but wing loading is not - it is a force per unit area, carried in newtons or kilonewtons per square metre, and the diagram's horizontal axis has those units.
Statement II is correct as a general principle: non-dimensional working does make a result independent of scale. It simply does not apply to this axis, which is why two aircraft of very different size have constraint diagrams spanning different ranges of wing loading, and why unit consistency matters so much in these calculations.
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