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be taken to resolve all the resistances at their piopei latter factor is given both for planes and for arched angle of application, and to subtract or add the tangential surfaces in the subjoined table : force, which consists in the surface S, multiplied by the Percentages of Air Pressure at Various Angles wind pressure, and by the factor in the table, which is, of Incidence. however, 0 for 3° and 32°, but positive or negative at other angles. When the aggregate resistances aie known, Planes : Duchemin Formula. Wings : Lilienthal. the “ thrust h.p.” required is obtained by multiplying the resistance by the speed, and then allowing for mechanical 2sina Concavity 1 in 12. N = P 1 + sin‘2a losses in the motor and propeller, which losses will generally be 50 per cent, of indicated h.p. Close approximations TanDrift. gential are obtained by the above method when applied to fullLift. Drift. Normal. yjCOSa. Lift. Angle. Normal. rjcosa force. TjSilla. rjsina V 4 sized apparatus. The following example will make the pro+ 0-070 cess clearer. The weight to be carried by an apparatus o-o 0-0 o-o - 9° + 0-067 was 189 ft on concave wings of 143"5 sq. ft. area, set -0-0055 0-0396 0-040 -8° + 0-064 at a positive angle of 3°. There were in addition rear -0-0097 0-0741 0-080 - 7° 0-120 0-1193 -0-0125 + 0-060 wings of 29-5 sq. ft., set at a negative angle of 3°^ carrying -6" 0-160 0-1594 -0-0139 + 0-055 no weight; hence, L = 189 = 0*005 xWxl43 5xO 545. -5° 0-200 0-1995 -0-0139 + 0-049 -4° l i. / 0-005 x 143-5 x 0-545 = 22 miles per hour, at 0-242 0-2416 -0-0126 + 0-043 WTipnpp wnence V V= V -3° + 0-037 -0-0100 0-2858 0-286 -2° 0-332 0-3318 -0-0058 + 0-031 which the air pressure would be 2-42 ft per sq. ft. -1° + 0-024 The area of spars and man was 17*86 sq. ft., reduced 0-381 0-3810 o-o o-o o-o . 0° o-o + 0-016 + 0-0075 0-434 0-434 | 0-000611 0-035 +• 1° 0-035 + 0-0170 + 0-008 by various coefficients to an equivalent sui face of + 2° 0-070 0-070 i 0-00244 0-489 0-489 11*70 sq. ft., so that the resistances were :— + 0-0285 o-o + 3° 0-104 0-104 | 0-00543 0-546 0"545 0-600 0-597 + 0-0418 -0-007 + 4° 0-139 0-139 ! 0-0097 Drift front wings, 143-5 x 0*0285 x 2-42 • • = 9-90 lb. 0-650 0-647 + 0-0566 -0-014 + 5° 0-174 0-173 ! 0-0152 rear wings, 29"5 x (0*043 0*242 x 0-0523) -0-021 = 2-17 ,, 0-696 0-692 + 0-0727 + 6° 0-207 0-206 ' 0-0217 x 2’42 = 0-00 ,, 0-737 0-731 + 0-0898 -0-028 + 7° 0-240 0-238 j 0-0293 Tangential force at 3° -0-035 + 0-1072 0-771 0-763 Head resistance, 11-70 x 2-42 .... — 28 "31 „ + 8° 0-273 0-270 I 0-0381 -0-042 0-800 0-790 + 0-1251 + 9° 0-305 0-300 0-0477 0-825 0-812 + 0-1432 -0-050 10° 0-337 0-332 0-0585 Total resistance . . • • • • = 40-38 ll». 0-846 0-830 + 0-1614 -0-058 11° 0-369 0-362 I 0-0702 -0-064 + 0-1803 0-864 0-845 12° 0-398 0-390 0-0828 0-879 0-856 + 0-1976 -0-070 Speed 22 miles per hour. Power = -4Q |yg 22 = 2*36 h.p. for 13°c 0-431 0-419 0-0971 0-891 1 0-864 + 0-2156 -0-074 14 0-457 0-443 0-1155 0-901 0-870 + 0-2332 -0-076| the “thrust” or 4*72 h.p. for the motor. The weight 15c 0-486 0-468 0-1240 being 189 ft, and the resistance 40*38 ft, the gliding The sustaining power, or “lift,” which in horizontal angle of descent was: 189 = tangent of 12°, which was flight must be equal to the weight, can be calculated _ by the formula : L = KV“S'^cosa, or the factor may be verified by many experiments. The following expressions, some of which have been taken direct from the table, in which the “ lift and the “ drift ” have been obtained by multiplying the normal 7/ given in the text, will be found useful in computing such by the cosine and sine of the angle. The last column projects, with the aid2 of the table above given :— 8. Drift, D = KSV^sina. shows the tangential pressure on concave surfaces which 1. Wind force, F = Ky 2 9. Head area E, get an equivaLilienthal found to possess a propelling component between 2. Pressure, P=KV S. lent. 3° and 32°, and therefore to be negative to the relative 3. Velocity*, y= J K!S7?cosa 10. Head resistance, H = EF. 11. Tangential force, T = Pa. wind. Former modes of computation indicated angles of 12. Resistance, R=D + H±T. 10° to 15° as necessary for support with planes. These 4. Surface S varies as V2 13. Ft. ft, M = RV. were prohibitory in consequence of the great “ drift ’ ; but 5. formal, N = KSV2t7. RV 14. Thrust, h.p., =.factor the present data indicate that, with concave surfaces, angles 6. Lift, L=KSVVosa. of 2° to 5° will produce adequate “ lift.” To compute the 7. Weight, W = L = Ncosa. (o. c.) latter the angle at which the wings are to be set must fii st be assumed, and that of + 3° will generally be found ^Ether.—In the mechanical processes which we can preferable. Then the required velocity is next to be experimentally modify at will, and which therefore we computed by the formula : learn to apprehend with greatest fulness, whenever an v= effect on a body B is in causal connexion with a process A' KS??cosa instituted in another body A, it is usually possible to or for concave wings at + 3°: discover a mechanical connexion between the two bodies which allows the influence of A to be traced all the way W V across the intervening region. The question thus arises =y<F'545KS Having thus determined the weight, the surface, the whether, in electric attractions across apparently empty angle of incidence, and the required speed for horizontal space and in gravitational attraction across the celestial support, the next step is to calculate the power required. regions, we are invited or required to make search for This is best accomplished by first obtaining the total some similar method of continuous transmission of the resistances, which consist of the “ drift ” and of the head physical effect, or whether we should rest content with resistances due to the hull and framing. The latter are an exact knowledge of the laws according to which one arrived at preferably by making a tabular statement body affects mechanically another body at a distance. similar to that shown under the head of balloons, showing The view that our knowledge in such cases may be comall the spars and parts offering head resistance, and apply- pletely represented by means of laws of action at a dising to each the coefficient appropriate to its “master tance, expressible in terms of the positions (and possibly section,” as ascertained by experiment. Thus is obtained motions) of the interacting bodies without taking any an “ equivalent area ” of resistance, which is to be multi- heed of the intervening space, belongs to modern times. plied by the wind pressure due to the speed. Care must It could hardly have been thought of before Sir Isaac
