A series of full size tests were made by the University of St. Cyr in 1912-1913 with the object of comparing full size aeroplane wings with small scale models of the same wing section. The full size wings were mounted on an electric trolley car and the tests were made in the open air. Many differences were noted when the small reproductions of the wings were tested in the wind tunnel, and no satisfactory conclusions can be arrived at from these tests. According to the theory, and the tests made by the N. P. L., the lift-drag ratio should increase with the size but the St. Cyr tests showed that this was not always the case. In at least three of the tests, the model showed better results than the full size machine. There seemed to be no fixed relation between the results obtained by the model and the large wing. The center of pressure movement was always different in every comparison made.
One cause of such pronounced difference would probably be explained by the difference in the materials used on the model and full size wing, the model wing being absolutely smooth rigid wood while the full size wing was of the usual fabric construction. The fabric would be likely to change in form under different conditions of angle and speed, causing a great departure from the true values. Again, the model being of small size, would be a difficult object to machine to the exact outline. A difference of 1/1000 inch from the true dimension would make a great difference in the results obtained with a small surface.
Plan Form. Wings are made nearly rectangular in form, with the ends more or less rounded, and very little is now known about the effect of wings varying from this form. Raking the ends of the wing tips at a slight angle increases both the lift-drag and lift by about 20 per cent, the angle of the raked end being about 15 degrees. Raking is a widely adopted practice in the United States, especially on large machines.
Summary of Corrections. We can now work out the total correction to be made on the wind tunnel tests for a full size machine of any aspect ratio. The lift co-efficient should be used as given by the model test data, but the corrections can be applied to the lift-drag ratio and the drag. The scale factor is taken at 1.08, the form factor due to rake is 1.2, and the aspect correction is taken from the foregoing table. The total correction factor will be the product of all of the individual factors.
Example. A certain wing section has a lift-drag ratio of 15.00, as determined by a wind tunnel test on a model, the aspect of the test plane being 6. The full size wing is to have an aspect ratio of 8, and the wing tips are to be raked. What is the corrected lift-drag ratio of the full size machine at 14°?
Solution. The total correction factor will be = 1.08 × 1.10 × 12 = 1.439. The lift-drag ratio of the full size modified wing becomes 15.00 x 1.439 = 21.585.
As a comparison, we will assume the same wing section with rectangular tips and an aspect ratio of 3. The total correction factor for the new arrangement is now 1.08 X 0.72 = 0.7776 where 0.72 is the relative lift-drag due to an aspect of 3. The total lift-drag is now 15.00 X 0.7776 = 11.664.
Having a large aspect ratio and raked tips makes a very considerable difference as will be seen from the above results, the rake and aspect of 8 making the difference between 21.585 and 11.664 in the lift-drag. Area for area, the drag of the first plane will be approximately one-half of the drag due to an aspect ratio of three.
Lift in Slip Stream. The portions of a monoplane or tractor biplane lying in the propeller slip stream are subjected to a much higher wind velocity than the outlying parts of the wing. Since the lift is proportional to the velocity squared, it will be seen that the lift in the slip stream is far higher than on the surrounding area. Assuming for example, that a certain propeller has a slip of 30 per cent at a translational speed of 84 miles per hour, the relative velocity of the slip stream will be 84/0.70 = 120 miles per hour. Assuming a lift factor (Ky)=0.0022, the lift in the slip stream will be L = 0.0022 × 120 × 120 = 31.68 pounds per square foot. In the translational wind stream of 84 miles per hour, the lift becomes L = 0.0022 X 84 X 84 = 15.52 pounds per square foot. In other words, the lift of the portion in the slip stream is nearly double that of the rest of the wing with a propeller efficiency of 70 per cent.