Lesson 7 · 35 min

From Cut-and-Try to the Design Wheel

The Wrights designed, built and flew their own aircraft. A modern airliner involves thousands of engineers over a decade. This lesson traces how the design process grew, introduces Raymer's design wheel and the phases of design, and shows how the historical data of this module become the first estimate of a new aircraft's weight: the start of the rest of this course.

Learning objectives

Describe how the organization and tools of aircraft design changed from 1903 to today.
Explain Raymer's design wheel and the conceptual, preliminary and detail design phases.
Fit and use a statistical empty-weight trend \(\We/\Wo = A\,\Wo^{\,C}\) from historical data.
Solve the first-estimate sizing equation \(\Wo = (W_{\text{crew}} + W_{\text{payload}})/(1 - \Wf/\Wo - \We/\Wo)\) by iteration, and explain why it is so sensitive.

How the design process grew

1900s
The designer-builder-pilot. The Wrights measured, designed, built and flew. Their method (Lesson 2) was systematic, but it lived in two heads.
1910s
The chief designer and the shop. Wartime firms built dozens of types, often designed by one person with a drawing office, and tested by flying them. Many were built, flown and abandoned within months: design by cut-and-try.
1920s–30s
Engineering departments and research. Stress analysis groups, weight control, and wind-tunnel data from government laboratories such as NACA turned design into engineering. The DC-3 was the product of a team, tested in the wind tunnel before it flew.
1940s
Specialization and speed. War production needed whole design organizations. At Lockheed, Kelly Johnson's small "Skunk Works" team designed and built the XP-80, the first operational US jet fighter, in 143 days in 1943.
1950s–70s
Systems engineering and the computer. Jet programs grew to thousands of engineers; requirements, interfaces and reliability were managed formally. Computers took over structural analysis (the finite-element method) and performance calculations.
1980s–
Digital design and optimization. Computational fluid dynamics, complete 3D digital definition (the Boeing 777 of 1994) and multidisciplinary design optimization let a configuration be analyzed and refined long before anything is built.

Through all of it, one thing did not change: the first estimate of a new aircraft still comes from what earlier aircraft achieved.

The design wheel

Raymer describes design as a wheel rather than a line. Requirements suggest a concept; analysis of the concept shows what it can do; sizing and trade studies show what it would take to meet the requirements; and the results feed back, sometimes into the concept, sometimes into the requirements themselves. Each turn of the wheel refines the design.

Figure 7.1 The design wheel, after Raymer. Select a segment (click, or use Tab and Enter) to read what happens there, with an example from the history in this module.

The phases of design

Conceptual design

What will it look like, weigh and cost, and can it meet the requirements? Many configurations, quick methods, trade studies. The layout is fluid. This course.

Preliminary design

The configuration is frozen in its main features. Specialists in structures, aerodynamics, propulsion and control analyze and test it in depth; the outer shape is defined precisely (lofting).

Detail design

Every part, fastener and wire is designed for manufacture; tooling, production planning, ground and flight testing follow.

History as data: the empty-weight trend

The heart of the first weight estimate is the empty-weight fraction. Within a class of aircraft, \(\We/\Wo\) tends to fall slowly as aircraft get bigger, and Raymer models that with a power law fitted to historical aircraft:

Statistical empty-weight fraction

\[ \frac{\We}{\Wo} = A\,\Wo^{\,C} \qquad\Longleftrightarrow\qquad \ln\frac{\We}{\Wo} = \ln A + C\ln\Wo \]

A straight line on log–log axes, fitted by least squares. \(A\) depends on the units of \(\Wo\) (kg or lb); \(C\) does not. Raymer's Table 3.1 gives \(A\) and \(C\) for many classes of aircraft.

Fitting Loftin's 14 jet transports with a published empty weight gives

\[ \frac{\We}{\Wo} = 1.117\,\Wo^{-0.0698}\qquad (\Wo\ \text{in kg}) \]

Compare it with Raymer's fit for jet transports in his Table 3.1, made from a larger and more recent set of aircraft. The scatter is large: a single fit hides real differences in technology, range and design philosophy. That is exactly why it is only a first estimate.

The first estimate of takeoff weight

Return to the weight build-up of Lesson 1, \(\Wo = W_{\text{crew}} + W_{\text{payload}} + \Wf + \We\). Divide the fuel and empty weights by \(\Wo\) and solve for \(\Wo\):

Sizing equation (Raymer)

\[ \Wo = \frac{W_{\text{crew}} + W_{\text{payload}}}{1 - \dfrac{\Wf}{\Wo} - \dfrac{\We}{\Wo}} \]

The fuel fraction comes from the mission (Breguet, Lesson 6) and the empty-weight fraction from the trend; since the trend depends on \(\Wo\), the equation is solved by iteration.

Example 7.1 — Sizing a jet transport from Loftin's trend

A jet transport must carry \(20\,000\ \text{kg}\) of crew and payload, and its mission needs a fuel fraction \(\Wf/\Wo = 0.35\). Using the trend above, estimate \(\Wo\). Start from a guess of \(100\,000\ \text{kg}\).

Show solution

Guess, evaluate the trend, compute a new \(\Wo\), repeat:

Iteration	\(\Wo\) guess (kg)	\(\We/\Wo\)	New \(\Wo\) (kg)
1	100 000	0.5001	133 400
2	133 400	0.4901	125 100
3	125 100	0.4923	126 900
4	126 900	0.4919	126 500
5	126 500	0.4919	126 500

For example, \(1.117(100\,000)^{-0.0698} = 0.5001\) and \(20\,000/(1 - 0.35 - 0.5001) = 133\,400\ \text{kg}\). The estimate converges to \(\Wo \approx 126\,500\ \text{kg}\), with \(\We \approx 62\,200\ \text{kg}\) and \(\Wf \approx 44\,300\ \text{kg}\).

Figure 7.2 The sizing equation as two curves. The trend (blue) is the empty-weight fraction that history says an aircraft of weight \(\Wo\) will have; the purple curve is the empty-weight fraction the design can afford, \(1 - \Wf/\Wo - (W_{\text{crew}} + W_{\text{payload}})/\Wo\). The design closes where they cross. The points are Loftin's aircraft of the chosen class. Try a technology factor below 1 (for example lighter composite structure) and watch the gross weight fall by much more than the empty weight.

Check your understanding

Key takeaways

Aircraft design grew from one or two people testing their own machines to large organizations with specialist groups, systems engineering and digital tools.
The design wheel: requirements → design concept → design analysis → sizing and trade studies → back to requirements. Design is iterative.
Conceptual design decides the configuration, size and most of the eventual cost; preliminary and detail design follow.
Historical data give the empty-weight trend \(\We/\Wo = A\Wo^{\,C}\), and the sizing equation \(\Wo = (W_{\text{crew}} + W_{\text{payload}})/(1 - \Wf/\Wo - \We/\Wo)\) gives the first estimate of \(\Wo\), solved by iteration.
You have finished the lessons. Try the Practice Lab and the Self-Check Quiz, and explore all of Loftin's aircraft in the Design Trends Explorer.