ReferenceDesign Requirements and Mission Profiles

Formula Sheet

Every key result from the module in one place. SI units, with knots and nautical miles where the industry uses them. Historical segment fractions are from Raymer, Table 3.2; regulations are summarized for conceptual design.

Fits on one page of Letter or A4. For a digital copy, choose “Save as PDF” as the printer.

Process and requirements

  • Conceptual design: requirements → sketch → first weight estimate → \(\TW\), \(\WS\) → layout → analysis → sizing and trades → baseline. Then preliminary (frozen configuration), detail (every part).
  • Rubber engine: \(T = (\TW)\,\Wo g\), divided among \(N\) engines.
  • Good requirement: specific, measurable, with conditions, verifiable ("shall"). Threshold = minimum acceptable; objective = desired.

Market and fleet

\[ \text{seats} = \frac{Q}{n\,LF}, \qquad \text{round trip} = 2(t_{\text{block}} + t_{\text{turn}}) \]

Great circle (\(R_E = 6371\ \text{km}\))

\[ \cos\theta = \sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda,\ \ d = R_E\theta \]
  • ICAO code by span: A < 15, B < 24, C < 36, D < 52, E < 65, F < 80 m; \(A \le b_{\max}^2/S\). \(1\ \text{nmi} = 1.852\ \text{km}\), \(1\ \text{kt} = 0.5144\ \text{m/s}\).

More in Lesson 1 and Lesson 2

Payload–range

Range for payload \(P\) (Breguet, fixed reserve)

\[ R = \frac{V}{C}\frac{L}{D}\ln\frac{\text{TOW}}{\text{OEW} + P + W_{\text{res}}} \] \[ \text{TOW} = \min(\text{MTOW},\ \text{OEW} + P + W_{\text{fuel,max}}) \]
  • OEW = empty + crew and operating items; ZFW = OEW + payload \(\le\) MZFW; TOW = ZFW + fuel \(\le\) MTOW.
  • A: \(P_{\max}\) at MTOW. B: full tanks at MTOW, \(P_B = \text{MTOW} - \text{OEW} - W_{\text{fuel,max}}\). C: full tanks, no payload (ferry).
  • Between A and B: \(W_{\text{land}} = \text{MTOW}\,e^{-R/[(V/C)(L/D)]}\), \(P = W_{\text{land}} - \text{OEW} - W_{\text{res}}\).

More in Lesson 3

Certification and performance

Landing (Part 25)

\[ V_{\text{REF}} \ge 1.23\,V_{SR},\ \ s_{\text{field}} = \frac{s_{\text{land}}}{0.6}\ (\times 1.15\ \text{wet}) \] \[ \left(\frac{W}{S}\right)_{\text{land}} \le \frac{\tfrac12\rho V_{SR}^2 C_{L_{\max}}}{g} \]

Engine-out climb

\[ \frac{T}{W} = \frac{N}{N-1}\left(\frac{1}{L/D} + G\right) \]

Second segment \(G\) = 2.4, 2.7, 3.0% for 2, 3, 4 engines; final 1.2, 1.5, 1.7%; approach climb 2.1, 2.4, 2.7%; landing climb 3.2% (all engines).

  • Takeoff field length: the greater of the balanced field (engine failure at \(V_1\)) and 1.15 × all-engines distance to 35 ft. Approach categories: C to 140 kt, D to 165 kt. Ceilings: service 100 ft/min, cruise 300 ft/min.

More in Lesson 4

Mission profiles

Timeline

\[ t_c = \frac{h}{\overline{RC}},\ d_c = \overline{V}t_c,\ \ d_d = \frac{h}{\tan\gamma_d},\ \ d_{\text{cr}} = R - d_c - d_d \]

Mission fraction

\[ \frac{W_x}{W_0} = \prod\frac{W_i}{W_{i-1}}, \quad \frac{\Wf}{\Wo} = 1.06\left(1 - \frac{W_x}{W_0}\right) \]
  • Historical: takeoff 0.970, climb 0.985, landing 0.995. Cruise \(e^{-RC/(V\,L/D)}\); loiter \(e^{-EC/(L/D)}\). Radius = one way: out and back.

More in Lesson 5

Reserves and winds

Endurance (jet, at \(\LDmax\))

\[ E = \frac{1}{C}\frac{L}{D}\ln\frac{W_{i-1}}{W_i} \]

Still-air distance

\[ d_{\text{air}} = d_{\text{ground}}\frac{V}{V - w}\ \ (w > 0\ \text{headwind}) \]
  • IFR: alternate + 45 min. US international: 10% of flight time + alternate + 30 min hold at 1500 ft. ICAO: 5% contingency + alternate + 30 min final reserve. Loiter: \(C \approx 0.4/\text{h}\) (high bypass).
  • Design range = great circle + routing + winds, at the design payload; reserves carried as fuel.

More in Lesson 6

Trade studies

Weighted score; takeoff weight and growth factor

\[ S_j = \sum_i w_i s_{ij}, \qquad \Wo = \frac{W_{\text{crew}} + W_{\text{payload}}}{1 - \Wf/\Wo - \We/\Wo} \] \[ \frac{\Delta\Wo}{\Delta W_{\text{payload}}} = \frac{1}{1 - \Wf/\Wo - \We/\Wo} \]

More in Lesson 7

Common mistakes

  • Degrees in \(d = R_E\theta\). \(\theta\) must be in radians.
  • West and south are negative. Use signed coordinates for \(\Delta\lambda\).
  • \(V_{\text{REF}}\) as the stall speed. Divide by 1.23 first; knots to m/s.
  • Forgetting \(N/(N-1)\). The climb rule is with one engine out.
  • Burning the reserve. It stays in the landing weight.
  • Minutes with \(C\) per hour. 30 min is 0.5 h.
  • Radius as range. A radius is flown out and back.