Lesson 2 · 40 min

The Pioneers: Cayley to the Wright Brothers

For a century, would-be aviators knew what an airplane should look like and still could not build one that flew. The Wright brothers succeeded in four years because they treated flight as a design problem: they split it into parts, measured what they did not know, and tested each part before they built the next.

Learning objectives

Explain Cayley's fixed-wing concept and the three problems every flying machine had to solve: lift, propulsion and control.
Use the lift equation of 1900, \(L = kV^2S\,c_l\), and explain how an error in the Smeaton coefficient \(k\) misled the early designers.
Convert between the historical and the modern lift equation, \(L = \tfrac12\rho V^2 S\CL\).
Describe how the Wrights' wind tunnel, glider tests and control system amounted to the first systematic aircraft design process.

Separating the functions: Cayley's fixed wing

Before 1800, most attempts at flight copied birds: flapping wings that had to lift, propel and steer at the same time. In 1799 the English engineer Sir George Cayley engraved on a small silver disc a different idea: a fixed wing for lift, a separate means of propulsion for thrust, and a tail for stability and control. On the other side of the disc he drew the forces on the wing, resolving the air force into lift and drag.

That separation of functions is the founding idea of aircraft design. It lets each part be designed for one job, and it defines the three problems every flying machine had to solve:

Lift

A wing that supports the weight at a speed the machine can reach, with as little drag as possible.

Propulsion

An engine light enough for its power, and a propeller that turns that power into thrust efficiently.

Control

A way to balance and steer the machine in all three axes, in gusty air, at every speed it flies.

The nineteenth century made progress on the first two and very little on the third. The timeline below picks out the steps that the Wright brothers built on.

1799
Cayley's silver disc. The fixed-wing aircraft concept and the resolution of the air force into lift and drag. In 1804 he flew a model glider with a kite-shaped wing and an adjustable tail, and in 1853 a full-size glider carried a person across a small valley.
1842
Henson and Stringfellow's Aerial Steam Carriage. A patent design with a cambered monoplane wing, a tail, a fuselage and propellers: the layout of a modern airplane, but with no workable engine and no control system. Their steam-powered models never sustained flight.
1866
Wenham and the long, narrow wing. Francis Wenham told the new Aeronautical Society of Great Britain that most lift comes from the front part of a wing, so long narrow wings (high aspect ratio, in modern terms) are better than short wide ones. In 1871 he and John Browning built the first wind tunnel.
1884
Phillips's cambered airfoils. Horatio Phillips tested curved, double-surface wing sections in a wind tunnel and patented them: camber gives far more lift than a flat plate.
1891
Lilienthal's gliders. Otto Lilienthal made some 2000 glides in hang gliders that he balanced by swinging his body, and published tables of the lift and drag of a cambered wing. He died after a crash in 1896, but his tables were the best data available.
1896
Chanute and Langley. Octave Chanute flew a biplane glider braced like a Pratt bridge truss, the structure that biplanes kept for thirty years. Samuel Langley's steam-powered unpiloted Aerodrome No. 5 flew about a kilometer. His full-size piloted Aerodrome failed twice in 1903, in October and on 8 December.
1899
The Wrights' kite. Wilbur and Orville Wright tested wing warping, twisting the wing tips in opposite directions to roll the machine, on a 1.5 m biplane kite.
1900–02
Three gliders at Kitty Hawk. The 1901 glider gave far less lift than predicted. That winter the Wrights built a wind tunnel and tested more than two hundred wing models. The 1902 glider, designed from their own data and given a movable rudder, solved both lift and control.
1903
The Flyer. On 17 December, four powered, controlled and sustained flights; the longest covered 852 ft (260 m) in 59 s.
1905
Flyer III, the first practical airplane. It could bank, turn, circle and fly for more than half an hour, landing where it took off.

The lift equation of 1900

The early designers wrote the lift of a wing in a form that predates the modern dynamic pressure. Following Lilienthal, the Wrights used

The lift equation of 1900 (US units)

\[ \colL{L} = k\,V^2 S\,c_l \qquad (L\ \text{in lb},\ V\ \text{in mph},\ S\ \text{in ft}^2) \]

\(k\) is Smeaton's coefficient, the pressure on a flat plate held square to a wind of 1 mph, and \(c_l\) is Lilienthal's lift coefficient: the lift of the wing as a fraction of that flat-plate force, read from his tables for each angle of attack.

Published values of \(k\) ranged from about 0.0027 to 0.005. The traditional value, which Lilienthal and the Wrights first used, was \(k = 0.005\ \text{lb/(ft}^2\,\text{mph}^2)\). Its origin was an eighteenth-century measurement, and it was far too high. After their disappointing 1901 glider, the Wrights worked back from their own glider measurements and found \(k \approx 0.0033\). The modern value is \(0.00326\).

Connecting to the modern lift equation

Today we write \(L = \tfrac12\rho V^2 S\CL\). In the 1900 units (\(\rho = 0.002377\ \text{slug/ft}^3\) at sea level and \(1\ \text{mph} = 1.467\ \text{ft/s}\)), the dynamic pressure factor is

\[ \tfrac12\rho V^2 = \tfrac12(0.002377)(1.467)^2 V_{\text{mph}}^2 = 0.002557\,V_{\text{mph}}^2\ \ \text{lb/ft}^2 \]

Setting \(kV^2Sc_l = 0.002557\,V^2S\CL\) gives \(\CL = (k/0.002557)\,c_l\). With the correct \(k = 0.00326\), \(\CL = 1.28\,c_l\): the factor 1.28 is simply the drag coefficient of a flat plate square to the flow. Smeaton's coefficient was the flat-plate pressure, \(k = \tfrac12\rho\,(1.28)\), in disguise.

Figure 2.1 The Wrights' problem. Choose a machine, or set the speed, wing area and Lilienthal coefficient \(c_l\) yourself. The bars compare the lift the 1900 equation predicts with \(k = 0.005\) and with the value you choose; the dashed line is the weight to be supported (glider or Flyer plus pilot; the glider weights are approximate). Find the speed at which each bar reaches the weight.

Example 2.1 — How much wind did the 1901 glider need?

The 1901 glider had about \(290\ \text{ft}^2\) of wing; with Wilbur aboard it weighed about \(240\ \text{lb}\). Suppose it flew at a Lilienthal coefficient \(c_l = 0.6\). Find the airspeed needed to support it with \(k = 0.005\) and with \(k = 0.0033\).

Show solution

Set \(L = W\) and solve for \(V\):

\[ V = \sqrt{\frac{W}{k S c_l}} \] \[ k = 0.005:\ \ V = \sqrt{\frac{240}{0.005(290)(0.6)}} = 16.6\ \text{mph}, \qquad k = 0.0033:\ \ V = \sqrt{\frac{240}{0.0033(290)(0.6)}} = 20.4\ \text{mph} \]

The glider needed a wind about 4 mph stronger than its design, at the limit of what the Wrights wanted for safe gliding. The ratio \(20.4/16.6 = 1.23\) does not depend on \(W\), \(S\) or \(c_l\).

The Wrights' design process

The 1901 failure is where the Wrights stopped trusting published data. Their response is a model of engineering design:

Measure what you do not know. In the autumn of 1901 they built a small wind tunnel and two balances, one to measure lift relative to the drag of a flat plate and one to measure the ratio of lift to drag. They tested more than two hundred wing models of different camber, thickness, planform and aspect ratio, and tabulated the results.
Design from your own data. The 1902 glider had a longer, narrower wing (aspect ratio about 6, up from about 3) and a flatter camber, both chosen from the tunnel results.
Test each problem separately. The gliders solved lift and control before any engine was added. In 1902 the Wrights made hundreds of glides and found that warping the wings also turned the glider the wrong way, because the wing with more lift also had more drag (what we now call adverse yaw). A movable rudder, linked to the warping, cured it.
Only then add power. No suitable engine existed, so their mechanic Charles Taylor built a 12 hp aluminum-block engine. The Wrights designed their propellers as rotating wings, using their own airfoil data: a theory of the propeller that did not exist before.

Figure 2.2 The Wright gliders and the Flyer, to scale, seen from above (grid squares are 1 m; one of the two biplane wings is drawn). Spans and chords from NASA Glenn Research Center; the wing area of these biplanes is about \(2bc\). Select one to read its aspect ratio \(A = b/c\) for each wing. Notice the jump from 1901 to 1902.

Example 2.2 — The Flyer by the numbers

The 1903 Flyer weighed about \(341\ \text{kg}\) with its pilot and had \(47.4\ \text{m}^2\) of wing and a \(12\ \text{hp}\) engine. Find its wing loading and power loading. If it flew at an airspeed of about \(13.4\ \text{m/s}\) (30 mph) at sea level, what lift coefficient did it need?

Show solution

\[ \frac{W}{S} = \frac{341}{47.4} = 7.19\ \text{kg/m}^2 = 70.6\ \text{N/m}^2, \qquad \frac{W}{P} = \frac{341}{12(0.7457)} = 38.1\ \text{kg/kW}\ \ (62.5\ \text{lb/hp}) \] \[ \CL = \frac{2W}{\rho V^2 S} = \frac{2(341)(9.81)}{1.225(13.4)^2(47.4)} = 0.64 \]

The wing loading of a modern hang glider and the power loading of a heavy motorcycle. A Boeing 747 has a wing loading 100 times higher (Lesson 1).

Check your understanding

Key takeaways

Cayley's fixed-wing concept (1799) separated lift, propulsion and control. Every aircraft since has had to solve all three.
The lift equation of 1900 was \(L = kV^2Sc_l\). The traditional \(k = 0.005\) overestimated lift by about 50%; the Wrights found \(k \approx 0.0033\) (modern 0.00326).
\(\CL = (k/0.002557)\,c_l \approx 1.28\,c_l\): Smeaton's coefficient is the flat-plate pressure, \(\tfrac12\rho(1.28)\).
The Wrights' method of measuring, designing from their own data and testing one problem at a time is the ancestor of the design process in Lesson 7.
Next, Lesson 3 follows the airplane from a fragile novelty to a weapon of war, and asks why it kept two wings for thirty years.