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. 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?

Data from Problem 1.19 :

For the design of their gliders in 1900 and 1901, the Wright brothers used the Lilienthal Table given in Figure 1.65 for their aerodynamic data. Based on these data, they chose a design angle of attack of 3 degrees, and made all their calculations of size, weight, etc., based on this design angle of attack. Why do you think they chose three degrees?

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TABLE OF NORMAL AND TANGENTIAL PRESSURES Deduced by Lilienthal from the diagrams on Plate VI., in his book "Bird-flight as the Basis of the Flying Art." a Angle. -9⁰ <-80 - 70 <-4° 20 -10....... 0°...... +1°.... +2⁰... +3°..... +4°...... +5°..... +6°...... " Normal. 10⁰..... 11⁰..... 120.. 0.000 13⁰..... 14°..... 15°..... 0.040 0.080 0.1 20 0,160 0.200 0.242 0.286 0.332 0.381 0.434 0.489 0.546 0.600 +7°...... 0.737 0.650 0.696 +8°...... 0.771 +9°...... 0.800 0.825 0.846 0.864 0.879 0.891 0.901 O Tangendal. Angle. +0.070 16° +0,067 17°. +0.064 189 +0.060 19º. +0.055 20° + 0.049 21°.. +0.043 22°. +0.037 23° +0031 24°.... +0024 25°.... +0.016 260.... +0.008 27.. 0.000 28°. -0.007 29⁰. -0.014 30⁰. -0.021 320. -0.028 35⁰. -0.035 40⁰0. -0.042 45°. -0.050 500. -0.058 55° -0.064 60° -0.070 70⁰.. -0.074 80° -0.076 90° 7 Normal. 0.909 0.915 0.919 0.921 0.922 0.923 0.924 0.924 0.923 0.922 0.920 0.918 0.915 a.giz a.g10 0.906 0.896 0.890 0.888 0.888 0.8go 0.900 0.930 0.960 1.000 9 Tangential. -0.075 -0.073 <<- 0.070 -0.065 -0.059 -0.053 -0.047 -0.041 -0.036 -0.031 <<-0.026 -0.021 -0.016 -0.012 -0.008 0.000 + 9010 + 0.016 +0.020 +0.023 +0.026 +0.028 +0.030 +0.015 0.000 Figure 1.65 The Lilienthal Table of normal and axial force coefficients. This is a facsimile of the actual table that was published by Octave Chanute in an article entitled "Sailing Flight," The Aeronautical Annual, 1897, which was subsequently used by the Wright brothers.