Cost Estimation in Aircraft Design Questions and Answers

Answer: C

Correct answer: 37.5 million dollars

Two hundred units is \( \log_2 200 = 7.64 \) doublings, so:

\[ C_{200} = 200 \times 0.8^{7.64} = 200 \times 0.182 \approx 36\ \mathrm{million\ dollars} \]

which is closest to \( 37.5 \). The distractor \( 51.2 \) applies only three doublings, reaching the eighth unit rather than the two-hundredth. The result - a fifth of the first unit's cost - shows how much of a programme's economics rests on building enough aircraft to descend the curve.

Answer: D

Correct answer: 45 per cent

Take the remainder and express it as a share of the total:

\[ 4.0 - 0.9 - 1.3 = 1.8\ \mathrm{billion} \qquad \frac{1.8}{4.0} = 45\ \mathrm{per\ cent} \]

Even at this share, operation and support is the largest single element. In a real transport programme, measured over thirty years of service, the operating share is usually considerably higher still - which is why a design change that raises acquisition cost to reduce fuel burn is so often worth making.

Answer: A

Correct answer: 16.1 million dollars

Add the fixed charge to the variable cost of the hours flown:

\[ 5.2 \times 10^6 + 4200 \times 2600 = 5.2 \times 10^6 + 10.92 \times 10^6 = 16.1\ \mathrm{million\ dollars} \]

Dividing by the hours gives \( 6200 \) dollars per block hour, of which \( 2000 \) is fixed. Flying 3200 hours instead would raise the total but lower the hourly figure to about \( 5825 \), since the fixed component would be spread further.

Answer: B

Correct answer: 1.71

An exponent less than one means the cost grows more slowly than the weight:

\[ \frac{H_2}{H_1} = 2^{0.777} = 1.71 \]

So doubling the empty weight raises engineering hours by about 71 per cent, not 100. This is an economy of scale in design: a larger aircraft has more structure to analyse but not proportionally more kinds of problem to solve, so the effort per kilogram falls. The same sub-unity exponent appears in the tooling and manufacturing relations.

Answer: C

Correct answer: Both Statement I and Statement II are correct

Both statements are correct and the second explains the first. RDT&E is a one-off expense incurred before the first aircraft is delivered - design, analysis, test articles, ground and flight test - and once spent it does not recur however many aircraft follow.

The charge each aircraft must carry is therefore the fixed sum divided by the quantity built, and it falls as the run lengthens. It is why manufacturers pursue derivatives and export sales so hard: every extra aircraft dilutes a cost already sunk.

Answer: D

Correct answer: Statement I is incorrect but Statement II is correct

Statement I is incorrect. An 80 per cent curve does not mean each aircraft costs 80 per cent of the one before it - that would give an absurdly rapid collapse in cost, with the tenth unit at about a seventh of the first.

Statement II is correct and states the actual definition: the factor applies to each doubling of cumulative output. So the second unit costs 80 per cent of the first, the fourth 80 per cent of the second, the eighth 80 per cent of the fourth - giving \( 0.8^3 = 0.512 \) for the eighth, not \( 0.8^7 \).

Answer: A

Correct answer: Statement I is incorrect but Statement II is correct

Statement I is incorrect. Fuel is the archetypal variable cost: it is consumed only when the aircraft flies, and in proportion to how far and how long.

Statement II is correct and supplies the test that shows why. Fixed costs accrue whether the aircraft flies or not - depreciation, insurance, financing charges, lease payments - and it is that independence from utilisation which defines them. Applying the test to fuel gives the opposite answer, so the two statements cannot both stand.

Answer: B

Correct answer: Both Statement I and Statement II are correct

Both statements are correct and the second explains the first. Fixed costs - depreciation, insurance, financing - accrue with the calendar rather than with use, so flying more hours in the same year spreads the same annual charge more thinly.

Six million dollars over 3000 hours is 2000 dollars an hour; over 4000 it is 1500. Variable costs per hour are unchanged, so the total cost per block hour falls. This is why high utilisation, quick turnarounds and long operating days are central to low-cost operating models.

Answer: C

Correct answer: Both Statement I and Statement II are correct

Both statements are correct and the second explains the first. Fuel, maintenance, crew and fees are incurred continuously over an operating life of twenty-five or thirty years, so their accumulated total dwarfs the one-off development and production spend.

The consequence for design is important: a change that raises acquisition cost but lowers fuel burn or maintenance demand usually repays itself many times over. It is also why operators evaluate aircraft on direct operating cost rather than on purchase price.

Answer: D

Correct answer: Statement I is incorrect but Statement II is correct

Statement I is incorrect. A model calibrated on metal airframes cannot be applied unchanged to composites: the manufacturing processes, learning behaviour, tooling requirements and scrap rates all differ, and composite structures have far fewer parts and fasteners but far more expensive tooling and cure cycles.

Statement II is correct and is precisely why. Parametric relations are regressions fitted to historical programme data, so they carry the technology of that data with them. Applying one outside its calibration range requires explicit adjustment factors, and even then the uncertainty is large.