Lesson 7 · 40 min
From Requirements to a Concept: Trade Studies
With the requirements written and the mission drawn, the designer needs a concept, usually several, and a fair way to choose between them. Then comes the question every customer should ask and few do: what does each requirement cost? This lesson closes the design wheel of Lesson 1, from the requirements back to the requirements.
Learning objectives
- Generate alternative configurations with a morphological chart, and explain how requirements favour one layout over another.
- Rank concepts with a weighted decision matrix, and test how sensitive the ranking is to the weights.
- Estimate the cost of a range or payload requirement in takeoff weight, and explain the range wall and the growth factor.
- Build a requirements compliance matrix, and explain when to go back to the customer.
Generating concepts
Conceptual design begins with a sketch, and a designer should draw several. A morphological chart keeps the options honest: list each design choice and its alternatives, then build concepts by picking one option from each row.
| Choice | Options |
|---|---|
| Wing position | Low · mid · high |
| Wing | Cantilever, moderate aspect ratio · strut-braced, high aspect ratio · blended wing body |
| Tail | Conventional · T-tail · V-tail · canard |
| Engines | Turbofans under the wing · turbofans on the aft fuselage · turboprops on the wing · open rotors at the tail |
| Number of engines | 2 · 3 · 4 |
| Landing gear | Wing-mounted main gear · fuselage pods |
Requirements prune the chart quickly. A short, rough-field requirement favours a high wing (ground clearance for propellers and flaps, an easy cargo floor) and turboprops. Fuel burn favours high aspect ratio and high bypass, both limited by the span box and the ground clearance. A strong noise requirement favours engines shielded by the airframe. History (Module 1) is also a filter: a configuration that has been tried and abandoned many times needs a very good reason to be tried again.
Choosing: the weighted decision matrix
Concepts are compared against criteria drawn from the requirements: fuel burn, cost, field performance, technical risk. Each criterion gets a weight \(w_i\) (the weights add to 1) and each concept a score \(s_{ij}\) on each criterion, say 1 (poor) to 5 (excellent). The total for concept \(j\) is
Weighted score
\[ S_j = \sum_i w_i\,s_{ij}, \qquad \sum_i w_i = 1 \]A Pugh matrix is a simpler version: each concept is marked better (+), the same (0) or worse (−) than a reference concept on each criterion.
Example 7.1 — Three concepts for a new narrow-body
Concept A is a conventional low wing with underwing turbofans; B has open rotors at the tail; C has a strut-braced, high-aspect-ratio wing. The team scores them (5 is best; for risk, 5 means least risk):
| Criterion | Weight | A | B | C |
|---|---|---|---|---|
| Fuel burn per seat | 0.40 | 3 | 5 | 4 |
| Acquisition cost | 0.25 | 4 | 2 | 3 |
| Field performance | 0.10 | 3 | 3 | 4 |
| Technical risk | 0.25 | 5 | 2 | 3 |
Which concept ranks first? How sensitive is the answer?
Show solution
A ranks first, but by a small margin over C. Raise the weight on fuel burn from 0.40 to just over 0.5 (as a rise in fuel prices might) and the ranking turns over completely, to B, then C, then A: Figure 7.1 shows where the lines cross. A ranking that changes with a small change in the weights is a signal to study the leading concepts in more depth rather than to declare a winner.
The cost of a requirement
Every requirement costs something. The most useful currency in conceptual design is takeoff weight, since cost, fuel burn and engine size all grow with it. Combine the sizing equation of Module 1 with the mission fuel fraction of Lesson 5:
Takeoff weight as a function of design range
\[ \Wo = \frac{W_{\text{crew}} + W_{\text{payload}}}{1 - \dfrac{\Wf}{\Wo} - \dfrac{\We}{\Wo}}, \qquad \frac{\Wf}{\Wo} = 1.06\left[1 - 0.970(0.985)(0.995)\,e^{-R\,C/(V\,L/D)}\right] \]Treat \(\We/\Wo\) as fixed for a first look, or use a statistical trend (Module 3 does it properly). The range enters only through the fuel fraction.
Example 7.2 — What does 1000 km more range cost?
A jet transport carries \(18\,000\ \text{kg}\) of crew and payload, cruises at \(850\ \text{km/h}\) with \(L/D = 16\) and \(C = 0.55/\text{h}\), and has \(\We/\Wo = 0.50\). Find \(\Wo\) for a design range of \(5000\ \text{km}\) and of \(6000\ \text{km}\).
Show solution
A 20% longer range costs 14% more takeoff weight, about 9.7 t, with a bigger wing and bigger engines to match, on every aircraft built. If only a few routes in the market need the extra 1000 km, the customer should hear that number before insisting on it.
The growth factor
The same equation prices every kilogram added to the aircraft. With the fractions held fixed, \(\Wo\) is proportional to the crew and payload, so
Growth factor (fixed fractions)
\[ \frac{\Delta\Wo}{\Delta W_{\text{payload}}} = \frac{1}{1 - \Wf/\Wo - \We/\Wo} = \frac{\Wo}{W_{\text{crew}} + W_{\text{payload}}} \]In Example 7.2 at \(5000\ \text{km}\), the growth factor is \(1/0.2632 = 3.8\): a requirement that adds \(500\ \text{kg}\) of fixed equipment (a bigger galley, a new avionics suite) adds about \(1900\ \text{kg}\) to the takeoff weight once the wing, engines and fuel have grown to carry it. That is the weight snowball of Module 1 seen from the requirements side. (The empty-weight fraction in reality falls slightly as the aircraft grows, which tempers the factor a little.)
Closing the loop: the compliance matrix
At each turn of the wheel, the team checks the design against every requirement in a compliance matrix: the requirement, the value the current design achieves, how it was shown (analysis, test, inspection), and the margin. For the narrow-body of Lessons 3 and 4 it might begin:
| Requirement | Required | Current design | Shown by | Status |
|---|---|---|---|---|
| Range, 150 passengers at 100 kg, reserves | at least 5000 km | 6048 km (Example 3.2) | Analysis | Met, +21% |
| Approach category | C (\(V_{\text{REF}} \le 140\ \text{kt}\)) | \(\WS\) set to 556 kg/m² at landing (Example 4.1) | Analysis | Met by design |
| Wingspan | under 36 m (code C) | \(A \le 10.6\) at 122 m² (Example 2.3) | Inspection | Met by design |
| Second-segment climb, one engine out | 2.4% gradient | \(\TW \ge 0.248\) needed (Example 4.2) | Analysis | Engine not yet chosen |
A large margin is not good news: the 21% range margin above means the aircraft is carrying fuel capacity and weight it does not need for the requirement, so either the requirement can grow (a selling point) or the design can shrink. A requirement that cannot be met at an acceptable weight goes back to the customer with its price attached. That conversation, informed by trades like Example 7.2, is the arrow from "sizing and trade studies" back to "requirements" in Figure 1.1.
Check your understanding
Key takeaways
- A morphological chart lists the options for each design choice; requirements and history prune it to a few concepts.
- Weighted decision matrix: \(S_j = \sum w_i s_{ij}\). Always check how sensitive the ranking is to the weights.
- Requirements cost takeoff weight: \(\Wo\) rises faster and faster with design range, up to a range wall set by the technology.
- Growth factor \(= 1/(1 - \Wf/\Wo - \We/\Wo) = \Wo/(W_{\text{crew}} + W_{\text{payload}})\): every added kilogram costs several at takeoff.
- A compliance matrix tracks every requirement; requirements that are too expensive go back to the customer, with their price.
- This completes the module. Try the Practice Lab and the Self-Check Quiz; Module 3 turns the mission profile into a full first estimate of the takeoff weight.