Aerial Locomotion 



27 



APPENDIX A 



DETAHS CONCERNING THE KITE "FROST KING" 



Number of Cells in the "Frost King" 



Num- Number of Number of 

 Layers of cells. ber of cells in cells iu 



rows. each row. eacli layer. 



1st layer i 24 24 



2d layer 2 23 46 



3d layer 3 22 66 



4th layer 4 21 84 



5th layer 5 20 100 



6th layer 6 19 114 



7th layer 7 18 126 



8th layer 8 17 136 



9th layer 9 16 144 



loth layer 10 15 150 



nth layer 11 14 154 



I2th layer 12 13 156 



Total number of cells 1,300 



Dimensions. — Each cell had a side of 25 

 centimeters, so that the roof, or ridge-pole; 

 measured 6 meters, extending laterally across 

 the top of the structure. The oblique sides 

 were 3 meters in length, and the bottom, or 

 floor, formed a square having a side of 3 

 meters. The whole structure constituted a sec- 

 tion of a tetrahedral kite — the upper half, in 

 fact, of a kite having the form of a regular 

 tetrahedron with a side of 6 meters. 



Weight. — The winged cells composing this 

 structure weighed on the average 13.84 gms. 

 apiece, so that the whole cellular part of the 

 structure which supported all the rest, consist- 

 ing of 1,300 winged cells, weighed 17,992 gms. 



In addition to this, the kite carried as dead 

 load stout sticks of wood, which were run 

 through the structure to distribute the strain 

 of the pull upon the strong parts of the frame- 

 work — that is, upon the junction points of the 

 cells. The outside edge of the kite was also 

 protected by a beading of wood. The whole 

 strengthening material weighed 9,702 gms., and 

 the kite as a whole weighed 27,694 gms. (61 

 lbs.). 



Surface. — I estimate the surface of an 

 equilateral triangle having a side of 25 centi- 

 meters as about 270.75 square centimeters ; in 

 which case the silk surface of a single winged 

 cell consisting of two triangles amounts to 

 541.5 square centimeters, and the actual silk 

 surface employed in 1,300 cells equals 70.3950 

 square meters (757.7 sq. ft.). 



The surfaces are all oblique, and if we re- 

 solve the oblique surfaces into horizontal and 

 vertical equivalents (supporting surfaces and 

 steadying surfaces) we find that the resolved 

 horizontal equivalent (supporting surface) of 

 a single winged cell forms a square of which 

 the diagonal measures 25 centimeters, and this 

 is equivalent to a rectangular parallelogram of 



25 X 12.5 centimeters, having an area of 312.5 

 square centimeters. 



Thus an actual silk surface of 541.5 square 

 centimeters arranged as the two wings of a 

 winged cell yields a supporting surface of 312.5 

 square centimeters. 



In kites, therefore, composed exclusively of 

 tetrahedral winged cells each having a side of 

 25 centimeters, the area of supporting surface 

 bears the same proportion to the actual surface 

 as the numbers 3,125 to 5,415; or i to 1.7328. 



Supporting surface i 



Actual surface 



1.7328 



A simple way of calculating the amount of 

 supporting surface in such structures is to re- 

 member that there are 32 cells to the square 

 meter of supporting surface ; therefore the 

 1,300 cells of the kite "Frost King" had a sup- 

 porting surface of 40.6250 square meters (437.3 

 sq. ft.). 



Ratio of Weight to Surface. — The actual silk 

 surface employed in the "Frost King" was 

 70.3950 square meters (757.7 sq. ft.), the 

 weight of the kite was 27,694 gms. (61 lbs) ; so 

 that on the basis of the actual surface, the fly- 

 ing weight was 393.4 gms. per square meter 

 (0.08 lbs. per sq. ft.). 



But, for the purpose of comparing the flying 

 weight of a tetrahedral kite with that of other 

 kites, in which it is usual to estimate only the 

 aeroplane surfaces that are substantially in a 

 horizontal plane, it would be well to consider 

 the ratio of weight to horizontal or supporting 

 surface in this kite. 



The weight was 27,694 gms, (61 lbs.), the 

 resolved horizontal or supporting surface was 

 equivalent to 40.6250 square meters (437-3 sq.- 

 ft.), and the flying weight for comparison with 

 other kites was 681.7 gms. per square meter of 

 supporting surface (0.14 lbs. per sq. ft.). 



The kite, in addition to its own weight,, 

 carried up a mass of dangling ropes and a 

 rope-ladder, as well as two flying cords of 

 manilla rope. The impedimenta of this kind 

 weighed 28,148 gms. (62 lbs.). It also sup- 

 ported a man, Mr Neil IVIcDermid, who hung 

 on to the main flying rope at such a distance- 

 from the cleat attached to the ground that 

 when the rope straightened under the strain 

 of the kite he was carried up into the air to a. 

 height of about 10 meters (over 30 ft.). The 

 weight of this man was 74,910 gms. (about 

 165 lbs.). Thus the total load carried by the 

 kite, exclusive of its own weight, was 103,058' 

 gms. (or 227 lbs.). 



The whole kite, load and all, including the 

 man, therefore, weighed 130,752 gms. (288 lbs.), 

 and its flying weight was 1,857.4 gms. per 

 square meter of actual surface (0.38 lbs. per 

 sq. ft.), or 3,218.5 gms. per square meter of 

 supporting surface (0.66 lbs. per sq. ft.). 



A. G. B. 



