Lesson 2 · 40 min
Where Requirements Come From
"Design an airplane" is not a design problem. "Carry 150 passengers 5000 km at Mach 0.78 from a 2000 m runway, at a lower cost per seat than today's aircraft" is. This lesson shows who sets numbers like these, what kinds of requirements there are, how to write one that can be checked, and how a few of the most important numbers are worked out from a market, a map and an airport.
Learning objectives
- Name the sources of aircraft requirements and sort requirements into mission, performance, certification, compatibility, economic and environmental kinds.
- Write a requirement that is specific, measurable and verifiable, and distinguish threshold and objective values.
- Estimate seats per aircraft, departures and fleet size from passenger demand.
- Compute great-circle distances between airports, and use them to choose a design range.
- Relate an airport's wingspan limit to the maximum aspect ratio of a wing.
Who sets the requirements
Customers
A military customer states a need and issues a request for proposal (RFP) with numbered requirements. Airlines rarely write formal specifications; instead a manufacturer works with launch customers to agree on the seats, range and economics before committing to a new type.
The market
Market studies forecast traffic on city pairs, the age of fleets that need replacing and what competitors will offer. They decide the size (seats or payload) and the range that will sell the most aircraft, often as a family of sizes.
Regulators and infrastructure
Airworthiness rules (Lesson 4), operating rules such as fuel reserves (Lesson 6), noise and emissions limits, and the airports themselves: runway lengths, gate sizes and wingspan limits.
The manufacturer adds its own requirements: use an engine that exists, share parts with an earlier model, reach a target price, or leave room to stretch the fuselage later. These company requirements can be as decisive as the customer's.
Kinds of requirements
| Kind | Examples |
|---|---|
| Mission | Design payload (150 passengers with bags), design range (5000 km with reserves), cruise Mach number (0.78), cruise altitude; for military aircraft, combat radius, loiter time, weapons carried |
| Field and climb performance | Takeoff field length at maximum weight on a hot day, landing field length, one-engine-out climb gradient, time to climb, initial cruise altitude |
| Maneuver (military) | Sustained turn load factor, specific excess power, acceleration time |
| Certification | The certification basis (FAR or CS Part 25, for example), and everything it implies: safety, structural margins, systems redundancy |
| Compatibility | Wingspan for the airport gates, door sill heights for ground equipment, runway pavement loading, turnaround time, cargo containers |
| Economic | Price, fuel burn per seat, direct operating cost, maintenance cost, dispatch reliability, first delivery date |
| Environmental | Noise at certification points, emissions of nitrogen oxides and carbon dioxide |
Notice that only the first two rows are "aircraft design" in the textbook sense. Real programs are as often won or lost on the others.
Writing a requirement that can be checked
A requirement is only useful if, at the end, someone can show that the aircraft meets it. Good requirements are specific (one thing each), measurable (a number with a unit), state the conditions (weight, altitude, temperature, configuration) and are verifiable by analysis, test or inspection. They are written with "shall".
| Weak | Better |
|---|---|
| The aircraft should have a short takeoff. | The takeoff field length shall not exceed 2100 m at maximum takeoff weight, sea level, ISA + 15 °C. |
| Long range with good fuel efficiency. | The aircraft shall carry 150 passengers at 100 kg each over 5000 km with international fuel reserves. |
| Fit at existing airports. | The wingspan shall be less than 36 m (ICAO aerodrome code C). |
Military requirements often give two values. The threshold is the minimum acceptable; the objective is what the customer would like, if it is affordable. A combat radius might have a threshold of 900 km and an objective of 1100 km. The gap between them is where trade studies (Lesson 7) do their work.
Top-level requirements are then broken down into derived requirements for each part of the aircraft. "Takeoff in 2100 m" becomes, after analysis, a maximum wing loading and a minimum thrust-to-weight ratio (Lesson 4 shows one way), and eventually a maximum lift coefficient for the flap designers to achieve.
From a market to a size
Suppose a market study says a route carries \(Q\) passengers a day in each direction, and the airline wants \(n\) departures a day each way (frequency sells tickets: business travellers want a flight when they need one). With an average load factor \(LF\), the fraction of seats filled, the number of seats each aircraft needs, or the number of departures for an aircraft of a given size, follows from the demand:
Seats and departures
\[ \text{seats} = \frac{Q}{n\,LF}, \qquad n = \frac{Q}{\text{seats}\times LF} \]Round \(n\) up. The fleet needed follows from the time each round trip takes, \(2(t_{\text{block}} + t_{\text{turn}})\), and the hours a day each aircraft can fly.
Example 2.1 — How big, and how many?
A route carries \(1800\) passengers a day each way. (a) With 8 departures a day and a load factor of 0.80, how many seats does each aircraft need? (b) With a 180-seat aircraft instead, how many departures are needed? (c) Each flight takes \(2.5\ \text{h}\) block to block, the turnaround takes \(45\ \text{min}\), and each aircraft can operate \(17\ \text{h}\) a day. How many 180-seat aircraft does the route need?
Show solution
(c) A round trip takes \(2(2.5 + 0.75) = 6.5\ \text{h}\), so each aircraft can fly \(\lfloor 17/6.5 \rfloor = 2\) round trips a day. Thirteen round trips need \(\lceil 13/2 \rceil = 7\) aircraft (plus spares for maintenance).
The airline's choice between (a) and (b) is a real trade: fewer, larger aircraft have a lower cost per seat; more frequent, smaller ones attract more passengers. Market studies of many such routes give the seat count that suits the most airlines.
From a map to a design range
Aircraft fly (approximately) along great circles, the shortest paths on the sphere. For two airports at latitudes \(\phi_1, \phi_2\) (north positive) and longitudes \(\lambda_1, \lambda_2\) (east positive), the central angle \(\theta\) between them and the distance are
Great-circle distance (spherical law of cosines)
\[ \cos\theta = \sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos(\lambda_2 - \lambda_1), \qquad d = R_E\,\theta \]\(R_E = 6371\ \text{km}\) (mean radius of the Earth) and \(\theta\) in radians. One nautical mile is \(1.852\ \text{km}\), about one minute of arc. Airlines and manufacturers quote ranges in nautical miles.
Example 2.2 — Ottawa to London
Ottawa airport (YOW) is at \(45.32^\circ\text{N}\), \(75.67^\circ\text{W}\); London Heathrow (LHR) at \(51.47^\circ\text{N}\), \(0.45^\circ\text{W}\). Find the great-circle distance in km and nautical miles.
Show solution
West longitudes are negative: \(\lambda_2 - \lambda_1 = -0.45 - (-75.67) = 75.22^\circ\).
\[ \cos\theta = \sin 45.32^\circ\sin 51.47^\circ + \cos 45.32^\circ\cos 51.47^\circ\cos 75.22^\circ \] \[ \cos\theta = 0.5562 + 0.4380(0.2551) = 0.6680 \] \[ \theta = 48.09^\circ = 0.8393\ \text{rad}, \qquad d = 6371(0.8393) = 5347\ \text{km} = 2887\ \text{nmi} \]The route bulges north of the straight line on a flat map, toward Ireland: Figure 2.1 shows the curve.
A manufacturer does this for every city pair in its target market and sets the design range to cover the routes that matter, often 90% or more of them, with an allowance for winds, routings and reserves (Lesson 6). Range beyond what the market needs is paid for on every flight in fuel and weight (Lesson 7), so the choice is not "as much as possible".
From an airport to a wingspan
Airports are designed around classes of aircraft. The International Civil Aviation Organization (ICAO) gives each a code letter by wingspan, which sets taxiway widths, separation and gate sizes. An aircraft that is too wide for the code of the gates it must use is a problem for every airline that buys it.
| Code | Wingspan | Examples |
|---|
A span limit is an aspect-ratio limit. Since \(A = b^2/S\), a wing of area \(S\) that must fit span \(b_{\max}\) has \(A \le b_{\max}^2/S\). That matters, because induced drag, and so cruise \(L/D\), improves with aspect ratio. Boeing's answer on the 777X was a folding wingtip: about 72 m in flight, about 65 m (code E) at the gate.
Example 2.3 — The code C box
A narrow-body airliner has a wing area of \(122\ \text{m}^2\) and must fit code C gates. What is the largest aspect ratio it can have?
Show solution
(Strictly, the span must be less than 36 m.) Today's narrow-bodies have aspect ratios a little below this, with winglets that recover some of the induced drag a longer span would have saved. A larger wing area, needed by a heavier stretch, lowers the limit further.
Check your understanding
Key takeaways
- Requirements come from customers (RFPs, launch customers), markets, regulators, airports and the manufacturer itself.
- A good requirement is specific, measurable, states its conditions and can be verified; military requirements give threshold and objective values.
- Seats \(= Q/(n\,LF)\); the fleet follows from block and turnaround times.
- Great-circle distance: \(\cos\theta = \sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda\), \(d = R_E\theta\). The design range covers the important city pairs, with allowances.
- Airport codes limit the span, so \(A \le b_{\max}^2/S\).
- Next, Lesson 3 combines the payload and range requirements in one diagram.