Chapter 5, Problem 5.8P

In Problem 1.19 we noted that the Wright brothers, in the design of their 1900 and 1901 gliders, used aerodynamic data from the Lilienthal table given in Figure 1.65. They chose a design angle of attack of 3 degrees, corresponding to a design lift coefficient of 0.546. When they tested their gliders at Kill Devil Hills near Kitty Hawk, North Carolina, in 1900 and 1901, however, they measured only one-third the amount of lift they had originally calculated on the basis of the Lilienthal table. This led the Wrights to question the validity of Lilienthal’s data, and this cast a pall on the Lilienthal table that has persisted to the present time. However, in Reference 58 this author shows that the Lilienthal data are reasonably valid, and that the Wrights misinterpreted the data in the Lilienthal table in three respects (see pages 209—216 of Reference 58). One of these respects was the difference in aspect ratio. The Wrights’ 1900 glider had rectangular wings with an aspect ratio of 3.5, whereas the data in the Lilienthal table were taken with a wing with an ogival planform tapering to a point at the tip and with an aspect ratio of 6.48. The Wrights seemed not to appreciate the aerodynamic importance of aspect ratio at the time, and even if they had, there was no existing theory that would have allowed them to correct the Lilienthal data for their design. (Prandtl’s lifting line theory appeared 18 years later.) Given just the difference in aspect ratio between the Wrights’ glider and the test model used by Lilienthal, what value of lift coefficient should the Wrights have used instead of the value of 0.546 they took straight from the table? (Note: There are two other misinterpretations by the Wrights that resulted in their calculation of lift being too high; see Reference 58 for details.)