Dayton, October 6, 1901
We have made the experiment of balancing a curved surface against a plane surface 66 percent as large, placed normal to the wind, and find that instead of 5° as called for in Lilienthal's table an angle of 18° was required. The test was made by mounting the surfaces on a bicycle wheel turned over so that its axis was vertical.
The curved surface was 8" X 18" and the plane 8" X 12". The center of pressure of the plane was assumed to be at its center, while that of the curve was assumed to be 1/8 inches in front of the center. The surfaces were mounted so as to bring the centers of pressure at equal distances from the center of the wheel. We found it impossible to get satisfactory results with a natural wind, so we mounted the wheel on a spar projecting in front of a bicycle and made tests in an almost perfect calm. We rode at right angles to the wind so that the natural wind was first on one side and then on the other as the direction of the course was reversed. We found that the difference was only two degrees. The speed was from 12 to 15 miles per hour. We then replaced the curve with a plane of same size, 8" X 18", and found that an angle of 24° was required. We also attempted to measure small angles by the same method but found the pressures to be measured were so small in proportion to the weight of the apparatus, and the variation in relative pressure due to an oscillation of one or two degrees so much greater when measuring the small angles than the larger, that no very satisfactory results could be obtained by this method.
The advantage of the curve over the plane was so much greater than we had expected, that we were led to make an examination of possible sources of error in our Kitty Hawk estimates of the value of Pa/P90 as determined by our kite and gliding experiments and finally located it in the use of the Smeaton coefficient of .005, or .13 metric system. In looking up Langley's experiments we find that his values varied from .07 to .09 or in the neighborhood of 66 percent of Smeaton's value. Approximately the same results were obtained by the Weather Bureau and by Dines. If in our Kitty Hawk calculations we had used a coefficient of .0033 instead of .005 the apparent advantage of our surfaces over the plane as per Duchemin formula would have been much greater. I see no good reason for using a greater coefficient than .0033, for though the Langley value is that of still air, his speed was also measured in still air, and any increase in average pressure due to fluctuations of the natural wind would equally cause the anemometer to overrecord the true velocity, so that the average pressure would always maintain a fixed ratio to the indicated velocity of the wind regardless of fluctuations.
Although the curve was found to be far less effective than Lilienthal's table would indicate, it was so much in excess of the plane that we considered it important to obtain tests of greater exactness at smaller angles and accordingly attached a revolving screw fan to a shaft turning 4,000 revolutions per minute.
In the current thus created we mounted an instrument of the following description. In a square trough which served to keep the current straight, a wind vane mounted on an axis c was placed. The blades of the vane consisted of a plane 1" X 3.25" inclined to one side of the center and a curve 1" X 3.25" inclined to the other side an equal amount. When exposed to the wind the vane took up a position to one side of the line of the wind direction thus showing that the curve required a less angle of incidence than the plane. We obtained the measure of the difference by the following simple method. A sheet of paper was tacked to the trough beneath the vane, and the vane having taken up its position a line was drawn upon it coinciding with the position of the plane, and a second line coinciding with the chord of the curve. The vane was then turned over so as to bring the curve above and the plane below and lines were again drawn to mark the positions of the two surfaces. A record thus taken will appear as shown in figure iii. The line aa indicates the first position of the plane; the line a'a' its second position. Likewise bb represents first position of curve and b'b' its second position. The four lines are all separate observations and their accuracy is easily tested. The angle axb should equal a'xb' and each should equal the angular difference at which the surfaces are mounted on the vane. In a series of records thus made over 50 percent show an error of less than 1/2 of one degree in these angles. Now the angle aya' is double the angle of incidence of the plane, and bzb' is double the angle of incidence of the curve. The fact that the curve and the plane alternately occupy exactly the same position in the wind current eliminates any errors which might other wise result from variations in the force or direction of the wind in different places. An almost infinitesimal error is introduced by the fact that the direction of the vane is inclined from one to two degrees to the direction of the wind, first on one side and then on the other, as the vane is turned over, so that the drifts of the surfaces act at an equal angle to the line of pull, but as the drifts at small angles are very slight and the force is exerted at so small an angle to the line of pull the error hardly exceeds one one thousandth, possibly even less. An allowance of 1/8 inch is made for difference in the position of the center of pressure of the two surfaces.
We find that a curve 1" X 3.25" with a depth of 1 in 9 will balance a plane of equal dimensions when the angles are respectively 4.75° and 9.5°. According to the Lilienthal and Duchemin tables the curve at 4.75° should balance a plane at 24+°, the forces measured in this experiment being lifts instead of normal pressures. However, the Duchemin formula is only true for square planes, and as the surface tested was a narrow rectangle the true lift of the curve at 4.75° is greater than .316, which the formula gives as the lift of a plane at 9.5°. We found in other experiments that decreasing the ratio of lateral to longitudinal dimensions was more costly to the plane than to the curve. Thus with both surfaces in the ratio of 3 to 2 instead of 3.25 to 1 the curve at about 7.5 degrees equaled the plane at 15°, which is in the same ratio as with the 3.25" X 1" surfaces at 4.75° & 9.5°, although the relative advantage of the curve should have decreased as the angles of incidence became greater. We also find that the maximum advantage in lift is obtained with a curvature of about 1 in 9 although with a curvature of 1 in 16 the ratio of angles was 5° to 9°. Experiment further confirmed the correctness of Lilienthal's claim that curved surfaces lift at negative angles: thus a curved surface mounted at a negative angle of some 7° would fly at a positive angle, and when the vane was reversed the same effect was observed, thus showing that the phenomenon was not due to error in estimating the direction of the wind unless the direction of the wind in top of box was different from that below. Will test this point further.
The results obtained, with the rough apparatus used, were so interesting in their nature, and gave evidence of such possibility of exactness in measuring the value of P(tang.a)/P90, that we decided to construct an apparatus specially for making tables giving the value of P(tang.a)/P90 at all angles up to 30° and for surfaces of different curvatures and different relative lengths and breadths. The new apparatus is almost as simple in construction as the vane already used and the values given are lifts in percentages of P90 without extended calculations. I think that with it a complete table from 0° to 30° can be made in thirty minutes, and that the results will be true within one percent. Errors due to variations in the position of the center of pressure are entirely eliminated. The same apparatus will also indicate the line to which the pressure is normal, so that the advantage of one surface over another in ratio of lift to drift can be obtained, and the truth of Lilienthal's tangential determined. We hope to have the apparatus done within a week.
I am now absolutely certain that Lilienthal's table is very seriously in error, but that the error is not so great as I had previously estimated. His glide, with an angle of descent of 6° to 8° at a speed of 10 meters and surfaces of 107 to 161 sq. ft. with a weight supported of 220 lbs. (Moedebeck's book), is still absolutely incredible to me assuming that, as reported, the wind was really still. Even taking the less extraordinary figures of 161 sq. ft. area and 8° angle of descent, the reported lift would still be about double anything that I find reasonable. Subtracting the 2° negative angle from 8° we have an angle of incidence of only 6°, and with a lift of 1.36 lb. per sq. ft. at a speed of 10 meters, P6/P90 would have to be about .8 if we use .087 instead of .13 in estimating pressure. But .8 is nearly four times the Duchemin lift at 6° and at least double what our experiments indicate the lift of surfaces curved 1-15 to 1-18 to be. If the figures 107 sq. ft. area and 6° angle of descent be taken, the disproportion would be still greater.
[P.S.] The error in my last letter in regard to Bretonnière's stork was due to a misunderstanding of a statement of my brother that Bretonnière reported that a stork would descend at an angle of 10° with a speed in still air of 20 meters. I caught it as being miles. Afterward it occurred to me to look up the ratio of wing area and found it in Progress in Flying Machines, p. 47, as 1.4 lbs. per sq. ft. After the letter was dispatched I came upon the statement of Bretonnière myself, and noticed my misunderstanding of the speed and found that he also gave an estimate of wing area and weight differing from that of Mouillard.