Lilienthal Data Not in Error

by Dr. Richard Stimson

in Dayton Celebration Events

During my visit to Dayton for their “Inventing Flight” celebration, I found presenters consistently attributing the Wrights’ disappointment with the performance of their 1900 and 1901 gliders to errors in the Lilienthal data upon which the brothers had based their glider designs. This is a common fallacy that is repeated in many books on the Wright Brothers.

The truth of the matter is that it was not a problem of Lilienthal errors, rather it was a misinterpretation of his data that was the problem. Here is the story.

A frustrated Wilbur exclaimed to Orville in August 1901, “Not in a thousand years will man ever fly.”

At the time they were on a train returning to Dayton after failing for the second year in a row to achieve the lift for their glider that their calculations predicted. Wilbur recorded in his diary, “Found lift of machine much less than Lilienthal’s tables would indicate, reaching only about 1/3 as much.”

After further thought, Wilbur was cheered by the conclusion that the data they were using might be in error. In a speech on September 18 to the Western Society of Engineers, Wilbur suggested that “the Lilienthal tables might themselves be somewhat in error.” He also questioned the accuracy of the Smeaton coefficient.

Both the Lilienthal data and the Smeaton coefficient are used in the formula for calculating lift.

Otto Lilienthal was a famous German glider experimenter who had published a table containing coefficients of lift in 1895. The coefficient of lift is a multiplying factor that takes into consideration the various angles a wing assumes with regard to the flow of air know as the “angle of attack.” The value of the lift coefficient also varies with the shape of the wing.

The Smeaton Coefficient was used in the calculation of lift at the time of the Wright Brothers. It is a constant number used as a “coefficient of air pressure.” It serves as a multiplying factor used to calculate B122the numerical value of lift in air, as compared to other mediums, such as water or oil.

John Smeaton, an engineer, determined the value of this coefficient was 0.005 in 1759, from his study of windmills. Engineers used this value for 150 years, although others questioned its value and thought it was too high, including the famous early aviation pioneer George Cayley in 1809.

Both Lilienthal, in Birdflight, and Octave Chanute, in Progress in Flying Machines, cited the 0.005 value in their books. This heavily influenced the Wrights in using the same value.

The Wrights would soon find that the 0.005 value was too high. The error was a major cause of their calculation of a lift value that was too high.

However, Smeaton’s coefficient value did not affect the values of Lilienthal’s coefficients of lift.

Note: The Smeaton coefficient is no longer used in modern aerodynamic problems. Problems are formulated differently. My son, who is a graduate aeronautical engineer, had never heard of Smeaton when I first asked him about it.

Smeaton wasn’t the only source of the discrepancy between actual lift and the Wrights’ calculated values. They incorrectly interpreted the Lilienthal tables by not understanding that the table only applied to the one wing shape that Lilienthal used in his study. The wings that the Wrights used in 1900 and 1901 had different aspect ratios as well as differences in the location of the maximum camber of the wing.

The aspect ratio is a measure of the relationship between the length of the wing to the cord (width). The aspect ratio affects the value of the lift coefficient. Lower values of aspect ratio give lower values of the lift coefficient and visa versa within limits.

The aspect ratio for the Wright 1900 glider was 3.5 and the 1901 glider was 3.3. These values were considerably lower than the aspect ratio of 6.8 for the Lilienthal test wing. In other words, the Lilienthal wing was longer and narrower compared to the Wrights’ wing. The lift coefficient from Lilienthal’s tables used by the Wrights should have been reduced by 19% to account for their use of a lower aspect ratio.

Their other problem of interpreting the Lilienthal table had to do with the location of the point of maximum camber (high point on the curved wing).

The Wrights located their maximum camber close to the leading edge of the wing. The Lilienthal test wing was a circular shaped wing with the maximum point located at the middle of the cord. Here again the value coefficient of lift read from the table should have been reduced to account for the difference in location of the maximum camber.

The cumulative impact of the above errors on the calculation of lift amounted to the 1/3 reduction in lift that Wilbur noted for the Kitty Hawk 1900 and 1901 glider flights.

After their disappointing glider performance during the first two visits to Kitty Hawk, the Wrights decided to take a different approach to the problem of calculating lift. Rather than further examining the existing data provided by others, they decided to compile their own.

They built an instrumented wind tunnel and developed their own aerodynamic data by systematically testing some 200 airfoils of widely different shapes and configurations, going well beyond the Lilienthal table.

Shapes included squares, rectangles, and ellipses in configurations such as biplanes and triplanes. They included camber ratios ranging from 1/6 to 1/20 and maximum camber locations ranging from near the leading edge to the 1/2-chord position.

They found that the correct value of the Smeaton coefficient should be 0.003 and developed their own table of lift coefficients (and drag coefficients).

Their airfoil #12 was found to be the most aerodynamically efficient. Its camber was 1/20 and the aspect ratio was 6. This foil was used as a guide in designing their successful 1902 glider and ultimately the successful 1903 Flyer.

The 1902 glider had an aspect ratio of 6.7, about twice that of their previous gliders, and used camber ratios much shallower than Lilienthal test wing.

With his new knowledge and understanding, Wilbur wrote to Chanute in October 1901, “It would appear that Lilienthal is very much nearer the truth than we have heretofore been disposed to think.”

Here is a graph comparing Lilienthal and Wright lift-coefficient data. The Wright data is for their no. 31 wing model. It has the same wing planform shape (see picture at top of graph) and camber ratio (1/12) as Lilienthal’s. The airfoil shape is different. The Wright No. 31 has a parabolic shape and the maximum camber is closer to the front edge.

Although the two model wings are not identical, they are close enough to demonstrate that the Lilienthal data was close to what the Wrights determined using their wind tunnel.

If one compares the data around a 3% angle of attack, which is about what the Wrights were focusing on, the data is almost identical.

It turned out to be fortunate that the Wrights had problems with the determination of lift. It led them into doing research that propelled their knowledge far beyond anyone before them and established the Wright Brothers as the leading aeronautical engineers of their day.

Reference: A History of Aerodynamics by John D. Anderson, Jr.

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