Dayton, August 29, 1901
Your letter of Aug. 22 with photographs enclosed rec'd. Also letter forwarded from Kitty Hawk, and copy of Goupil's pamphlets. Please accept our thanks for same. Our own pictures of glides will be rather poor, I fear, as we had no good gliding days after you left. If you will spare them, we should be glad to have the films of your pictures numbered 2 and 4 after you have taken such prints as you desire. We will try to enlarge them.
The experiment of cutting holes in the surface we did not try, as we thought that we might need the machine further in its present state and did not wish it mutilated till it had served our other uses.
I enclose some estimates of the performance of our machine and also an attempt to apply the same methods to your glides of Aug. 1897. The latter is a little more successful than if calculated according to Lilienthal's table and Herring's estimate of resistances of man and framing, but the performance of the machine at 40 miles relative speed apparently upsets both methods of calculating. I cannot think of any experiment that would be of greater value in the present muddled state of affairs than an actual measurement, both as a kite and in glides under specially chosen conditions, of some other machine than our 1901 model. Do you know whether the machine which Mr. Herring built for Mr. Arnot is still in gliding shape? It is probable, though, that it has been torn down like your own. If so it is a great pity.
As to camping expenses, we find that your stay was so short as to amount only to a visit, and we will prefer to regard you as our guest for the time you spent with us.
[P.S.] Draft for $5.39 a/c groceries enclosed.
|Area of Wings||290||sq.||ft.|
|Area of Rudder||18||"||"|
|Length including rudder||14||"|
|Angle||Meters per sec.||Total Pull|
|(1) July 30||10°||7.5 (6?)||18 lbs.|
|(2) Aug. 6||7°||8||16 "|
|(3) Aug. 6||5°||10||15 "|
|(4) Aug. 16||13°||7 (5.5?)||23 (21?)|
|(5) Aug. 16||7°||11||17 (15 3/4)|
|(6) Aug. 17||5°||12.5||20 (18 1/2)|
Note 1. Tests Nos. 1, 2 & 3 were made before the ribs were trussed down; 4, 5 & 6 were afterward.
Note 2. The wood, wire, &c., used in this trussing added probably 3 lbs. to weight of machine.
Note 3. In tests Nos. 1, 2, & 3 no extra weight was needed to bring the centers of gravity and pressure into coincidence. In tests Nos. 4, 5, & 6 sand was placed on front rudder. This sand was not weighed on Aug. 15th but on Aug. 16th the sand used in test No. 6 was weighed and found to be 8 lbs.
Note 4. The increased pull due to extra weight carried and also to head resistance of materials used in trussing are estimated to amount to 2 lbs. in No. 4, to 1 1/4 lbs. in No. 5, and to 1 1/2 lbs. in No. 6.
Note 5. At large angles the rear edge of the lower surface came so near to the ground as to materially obstruct the free passage of air beneath it. It is probable that about 2 meters per second should be subtracted from the wind velocities in No. 1 and No. 4. At the angle of 5° this source of error almost disappears.
Note 6. The measurements given are subject to the usual chances of error and are not claimed to be absolutely exact. The angles may vary a degree or more, the wind a half meter, the pulls in some cases a pound or more. The more important ones, however, Nos. 2, 3, & 5, were confirmed by repeated tests, on different days, and the wind velocity and pull cannot be greatly in error.
Note 7. It appears that reducing the curvature of the surfaces made the angle for support greater in the flatter surface, by more than a degree, but the dynamic efficiency did not seem to be greatly affected.
Note 8. The total pull at speeds above 10 meters apparently increases faster than would be expected, for it would be reasonable that the increase of head resistance should be almost counterbalanced by the decrease in drift due to the smaller angle at high speed. It is possible that at angles below 5° the drift of curved surfaces remains almost constant.
Note 9. The dynamic efficiency of the unloaded machine appears to be greatest at 10 meters per second. The reasonable assumption would seem to be that at this point drift and head resistance are equal, each being 7.5 lbs.
I consider glide No. 3 of Aug. 8th, 1901, A.M., the most perfect, for purposes of calculation, of all the glides we made, for the following reasons. The hill had exactly the same slope as the glide, and was uniform. Thus the direction of the wind was exactly opposite to the line of motion of the machine. Also in this glide the speed at stopping was equal to that of starting and varied but little throughout the glide.
The data of this glide were as follows:
|Speed wind||11 miles per hr.||Area 290 sq. ft.|
|Speed of machine||13 miles per hr.||Weight 240 lbs.|
|Relative speed||24 miles per hr.||Angle of descent 10°|
Estimated resistance of framing at 22 miles is 7.5 lbs. Resistance of man in horizontal position 1.25 lbs. Total 7.5 + 1.25 = 8.75 lbs. This would amount at a speed of 24 miles to 10.4 lbs. which is equal to 10.4/240 = 1/23 of weight carried, so that a drop of about 2.5° would be required to overcome this resistance.
The normal pressure at 24 miles is 2.88 lbs. while the weight actually supported per sq. ft. was 240 ÷ 290 = .83. Therefore the proportion of normal pressure was .83 ÷ 2.88. We find this lift in the table calculated from the Duchemin formula at about 8.5°. This added to the 2.5° required to overcome the head resistance would make the angle of descent 8.5 + 2.5 = 11° as against an observed drop of a little less than 10°. It is apparent that the difference of angle required for support with our curved surface (7.5°) and that required for a plane (8.5°) is the measure of the superiority of a curve over a plane in lifting power under the conditions specified.
The drift of a plane at this angle is about 1/7 of the lift, making the drift 240 ÷ 7 = 34 lbs., which added to the head resistance 10.4 lbs. makes a total of 44.4 lbs. against an observed total of 240 ÷ 6 = 40 lbs. or counting drifts alone, 34 lbs. against 29.6 lbs., which is the measure of the superiority in economy of power in the curve used over a flat surface under the conditions named.
Since the drift at this speed is 29.6 lbs. and the head resistances only 10.4 lbs. it is apparent that a higher speed would give a flatter angle of descent. I figure that the speed of greatest efficiency would be between 31 and 32 miles per hour, at which speed, drift and head resistance would be about 17.5 lbs. each, making a total of 35 lbs. and the rate of descent 35/240 = 1/7 = 8°.
Glide No. 5, Aug. 8th, P.M., 1901, was made under the following conditions:
Length of glide 366 ft., of which 125 ft. were at an angle of 14° and the remaining 240 ft. at an angle of 7°. By following the surface of the ground closely I raised the speed to about 33 miles per hour at point A, from which place I glided to B at an angle of about 8° with no loss of speed, and then ran out on the flat to C by using up this speed. I do not think it possible with this machine to glide permanently at a less angle than 8° in still air.
According to Lilienthal tables its performance might have been as follows at 17 miles in still air:
|Normal pressure at 17 miles||1.45 lbs.|
|Weight supported per sq. ft.||.83|
.83 ÷ 1.45 = 0.56 + which corresponds to an angle of a little over 3°. The drift at this angle is 1/20 the lift or 12 lbs. in our 240 lbs. machine.
The head resistances of man and machine at 22 miles being 8.75 lbs., the resistance at 17 miles would be 5.2 lbs., making a total pull of 12 + 5.2 = 17.2 lbs. But 17.5:240::1:13.7. Therefore the drop should have been 1 ft. in 13.7 ft. or about 4° angle of descent!
I have also attempted to apply my methods of calculation to the glides given on p. 42, Aeronautical Annual. 1897, but with only partial success.
Data: Wind 22.3 miles per hr. Speed of machine 18 miles. Total 40 miles. Drop 1 in 5.75.
|Normal pressure = 8 lbs. per sq. ft.|
|Weight carried = 1.4 lbs. per sp. ft.|
|Proportion = 1.4/8 = .175|
This lift is found in Lilienthal tables at -4.5° and in the Duchemin at +5°. According to Lilienthal the drift is -.013 and adding the tangential +.052 = +.039. Lift:drift = .175:.039 = 4.5:1. Since the lift or weight carried is 180 lbs. the drift will be 180 ÷ 4.5 = 40 lbs.
Mr. Herring, p. 70, estimates the resistance of framing at 22 miles per hr. at 9.73 lbs. and of the man at 12.1 lbs. or a total of 21.74 lbs.
This at 40 miles per hr. would amount to 72 lbs., making the total head resistances and drift 72 + 40 = 112 lbs. as against an observed resistance of 180 ÷ 5.75 = 32 lbs.
Our estimate of the head resistance is 1/2 that of Mr. Herring, or 11 lbs. at 22 miles, or 36 lbs. at 40 miles. This added to the drift as per Duchemin formula, which at 4 degrees would be 1/14 of 180 lbs., or 13 lbs., makes a total of 49 lbs., which would call for a drop of 180/49 = 1 in 3.6; but as the glides were actually made with a drop of 1 in 5.75 it is evident that (1) we still overestimate the head resistances of the framing & operator, or (2) the men took a good run at the start, or (3) the rising trend of wind furnished the extra power required. We think the last the more probable explanation.
The speed of greatest efficiency would be about 33 miles per hour, at which point the drift and head resistances would be about 21 lbs. each and the ratio of descent 42/180 = 1/4.3; or, 1 ft. to each 4.3 ft.; or 13°.
This figured maximum is less than the actual performance of machine under less favorable conditions, as to speed, than 33 miles per hr.
On the same day, Chanute to Wilbur, August 29, 1901