Questioning Lilienthal data
At the end of 1901, the Wright brothers were frustrated by the flight tests of their 1900 and 1901 gliders. The aircraft were flown frequently up to 300 feet in a single glide. But neither aircraft performed as well as predicted using the design methods available to the brothers. Based on their measurements, the 1901 aircraft only developed 1/3 of the lift which was predicted by using the Lilienthal data. During the fall of 1901, the brothers began to question the aerodynamic data on which they were basing their designs. Their kite and glider experiments convinced them that the accepted value of the Smeaton pressure coefficient (.005), which is used in both the lift and drag design equations, was in error. The brothers determined that a value closer to .0033 would more accurately describe their flight tests. But this did not account for all of the performance differences. There was still some questions about the lift and drag coefficients which were obtained by Lilienthal and were being used by the Wrights.
Bicycle Wheel Models
The brothers decided to measure the lift and drag coefficients themselves. They first built some small models of a wing and a flat plate and attached them to a bicycle wheel. Here is the configuration that the wheel would assume as it was moved through the air.
Initially the wing model and reference drag plate are located at equal angles b about the centerline of the bike. As the wind strikes the airfoil model it exerts a force to the left as viewed from riders seat. The drag force on the plate is exerted aft (down as viewed from above in the figure). The lift and drag forces generate torques about the hub of the wheel. The lift generates a counterclockwise torque equal to the lift force L times the moment arm s times the sine of the sum of the initial angle b and the angle of rotation a
Tlift = L * s * sin(a + b)
The drag plate generates a clockwise torque equal to the drag force D times the moment arm s times the cosine of the difference of the initial angle b and the angle of rotation a
Tdrag = D * s * cos(b – a)
When the wheel reaches an equilibrium condition, it no longer rotates and the angle a can be measured. The equilibrium condition is that Tlift is equal to Tdrag and then
L * sin(a + b) = D * cos(b – a)
Beginning with this relationship and using some information from high school trigonometry, the brothers were able to relate the deflection angle a to the ratio of the lift and drag. Here’s the math:
They used the Lilienthal data to predict the angle of rotation of the wheel at which the drag of the flat plate would exactly balance the lift of the wing. They attached the wheel to the handles of a bicycle and rode through the streets of Dayton to produce a wind over the models.
Building a Wind Tunnel
The test indicated a much lower value of lift from their model than the lift predicted by the Lilienthal data. But the test conditions were hard to control. So the brothers decided to build a wind tunnel to produce a more controlled environment. They would compare the results they found in the wind tunnel to the performance they had measured during their kite and glider flights.
The wind tunnel tests were conducted from September to December of 1901. At the conclusion of the tests, the brothers had the most detailed data in the world for the design of aircraft wings. They used this data to design the 1902 aircraft which overcame the problems encountered in 1900 and 1901. They also used the data in the design of their propellers for the 1903 aircraft.