# Aeronautics

AERONAUTICS, the art of "navigating" the "air." It is divisible into two main branches-aerostation, dealing properly with machines which like balloons are lighter than the air, and aviation, dealing with the problem of artificial flight by means of flying machines which, like birds, are heavier than the air, and also with attempts to fly made by human beings by the aid of artificial wings fitted to their limbs.

Historically, aviation is the older of the two, and in the legends of gods or myths of men or animals which are supposed to have travelled through the air, such as Pegasus, Medea's dragons and Daedalus, as well as in Egyptian bas-reliefs, wings appear as the means by which aerial locomotion is effected. In later times there are many stories of men who have attempted to fly in the same way. John Wilkins (1614-1672), one of the founders of the Royal Society and bishop of Chester, who in 1640 discussed the possibility of reaching the Moon by volitation, says in his Mathematical Magick (1648) that it was related that "a certain English monk called Elmerus, about the Confessor's time," flew from a town in Spain for a distance of more than a furlong; and that other persons had flown from St Mark's, Venice, and at Nuremberg. Giovanni Battista Dante, of Perugia, is said to have flown several times across Lake Trasimene. At the beginning of the 16th century an Italian alchemist who was collated to the abbacy of Tungland, in Galloway, Scotland, by James IV., undertook to fly from the walls of Stirling Castle through the air to France. He actually attempted the feat, but soon came to the ground and broke his thigh-bone in the fall-an accident which he explained by asserting that the wings he employed contained some fowls' feathers, which had an "affinity" for the dung-hill, whereas if they had been composed solely of eagles' feathers they would have been attracted to the air. This anecdote furnished Dunbar, the Scottish poet, with the subject of one of his rude satires. Leonardo da Vinci about the same time approached the problem in a more scientific spirit, and his notebooks contain several sketches of wings to be fitted to the arms and legs. In the following century a lecture on flying delivered in 1617 by Fleyder, rector of the grammar school at Tubingen, and published eleven years later, incited a poor monk to attempt to put the theory into practice, but his machinery broke down and he was killed.

In Francis Bacon's Natural History there are two passages which refer to flying, though they scarcely bear out the assertion made by some writers that he first published the true principles of aeronautics.

The first is styled Experiment Solitary, touching Flying in the Air -"Certainly many birds of good wing (as kites and the like) would bear up a good weight as they fly; and spreading leathers thin and close, and in great breadth, will likewise bear up a great weight, being even laid, without tilting up on the sides. The further extension of this experiment might be thought upon." The second passage is more diffuse, but less intelligible; it is styled Experiment Solitary, touching unequal weight (as of wool and lead or bone and lead); if you throw it from you with the light end forward, it will turn, and the weightier end will recover to be forwards, unless the body be over long. The cause is, for that the more dense body hath a more violent pressure of the parts from the first impulsion, which is the cause (though heretofore not found out, as hath been often said) of all violent motions; and when the hinder part moveth swifter (for that it less endureth pressure of parts) that the forward part can make way for it, it must needs be that the body turn over; for (turned) it can more easily draw forward the lighter part." The fact here alluded to is the resistance that bodies experience in moving through the air, which, depending on the quantity of surface merely. must exert a proportionally greater effect on rare substances. The passage itself, however, after making every allowance for the period in which it was written, must be deemed confused, obscure and unphilosophical. In his posthumous work, De Motu Animalium, published at Rome in 1680-1681, G.A.Borelli gave calculations of the enormous strength of the pectoral muscles in birds; and his proposition cciv. (vol. i. pp. 322-326), entitled Est impossibile ut homines pro priis viribus artificiose volare possint, points out the impossibility of man being able by his muscular strength to give motion to wings of sufficient extent to keep him suspended in the air. But during his lifetime two Frenchmen, Allard in 1660 and Besnier about 1678, are said to have succeeded in making short flights. An account of some of the modern attempts to construct flying machines will be found in the article FLIGHT AND FLYING; here we append a brief consideration of the mechanical aspects of the problem.

The very first essential for success is safety, which will probably only be attained with automatic stability. The underlying principle is that the centre of gravity shall at all times be on the same vertical line as the centre of pressure. The latter varies with the angle of incidence. For square planes it moves approximately as expressed by Joessel's formula, C + (0.2 + 0.3 sin a) L, in which C is the distance from the front edge, L the length fore and aft, and a the angle of incidence. The movement is different on concave surfaces. The term aeroplane is understood to apply to flat sustaining surfaces, but experiment indicates that arched surfaces are more efficient. S. P. Langley proposed the word aerodrome, which seems the preferable term for apparatus with wing-line surfaces. This is the type to which results point as the proper one for further experiments. With this it seems probable that, with well-designed apparatus, 40 to 50 lb. can be sustained per indicated h.p., or about twice that quantity per resistance or "thrust" h.p., and that some 30 or 40 k of the weight can be devoted to the machinery, thus requiring motors, with their propellers, shafting, supplies, etc., weighing less than 20 lb. per h.p. It is evident that the apparatus must be designed to be as light as possible, and also to reduce to a minimum all resistances to propulsion. This being kept in view, the strength and consequent section required for each member may be calculated by the methods employed in proportioning bridges, with the difference that the support (from air pressure) will be considered as uniformly distributed, and the load as concentrated at one or more points. Smaller factors of safety may also have to be used. Knowing the sections required and unit weights of the materials to be employed, the weight of each part can be computed. If a model has been made to absolutely exact scale, the weight of the full-sized apparatus may approximately be ascertained by the formula

$$W' = W\sqrt{\left({S'\over S}\right)}^3,$$

in which W is the weight of the model, S its surface, and W' and S' the weight and surface of the intended apparatus. Thus if the model has been made one-quarter size in its homologous dimensions, the supporting surfaces will be sixteen times, and the total weight sixty-four times those of the model. The weight and the surface being determined, the three most important things to know are the angle of incidence, the "lift," and the required speed. The fundamental formula for rectangular air pressure is well known: P=KV2S, in which P is the rectangular normal pressure, in pounds or kilograms, K a coefficient (0.0049 for British, and 0.11 for metric measures), V the velocity in miles per hour or in metres per second, and S the surface in square feet or in square metres.

The sustaining power, or "lift" which in horizontal flight must be equal to the weight, can be calculated by the formula L=KV2Secosa, or the factor may be taken direct from the table, in which the "lift" and the "drift" have been obtained by multiplying the normal e by the cosine and sine of the angle. The last column shows the tangential pressure on concave surfaces which O. Lilienthal found to possess a propelling component between 3 deg. and 32 deg. and therefore to be negative to the relative wind. Former modes of computation indicated angles of 10 to 15 as necessary for support with planes. These mere prohibitory in consequence of the great "drift"; but the present data indicate that, with concave surfaces, angles of 2 deg. to 5 will produce adequate "lift." To compute the latter the angle at which the wings are to be set must first be assumed, and that of @ will generally be found preferable. Then the required velocity is next to be computed by the formula

$$V = \sqrt{L\over KS\eta\cos\alpha};$$

or for concave wings at +3 deg. :

$$V = \sqrt{W\over 0.545KS}.$$

Having thus determined the weight, the surface, the angle of incidence and the required seed for horizontal support, the next step is to calculate the power required. This is best accomplished by first obtaining the total resistances, which consist of the "drift" and of the head resistances due to the hull and framing. The latter are arrived at preferably by making a tabular statement showing all the spars and parts offering head resistance, and applying to each, the coefficient appropriate to its "master section," as ascertained by experiment. Thus is obtained an "equivalent area" of resistance, which is to be multiplied by the wind pressure due to the speed. Care must be taken to resolve all the resistances at their proper angle of application, and to subtract or add the tangential force, which consists in the surface S, multiplied by the wind pressure, and by the factor in the table, which is, however, 0 for 3 and 32, but positive or negative at other angles. When the aggregate resistances are known, the "thrust h.p." required is obtained by multiplying the resistance by the speed, and then allowing for mechanical losses in the motor and propeller, which losses will generally be 50% of indicated h.p. Close approximations are obtained by the above method when applied to full sized apparatus. The following example will make the process clearer. The weight to he carried by an apparatus was 189 lb. on concave wings of 143.5 sq. ft. area, set at a positive angle of 3 deg. There were in addition rear wings of 29.5 sq. ft., set at a negative angle of 3 deg. ; hence, L= 189=.o.oo5XV2X143.5X0.545. Whence

$$V = \sqrt{189\over 0.005\times 143.5\times 0.545 = 22\hbox{ miles per hour},$$

at which the air pressure would be 2.42 lb. per sq. ft. The area of spars and man was 17.86 sq. ft., reduced by various coefficients to an "equivalent surface" of 11.70 sq. ft., so that the resistances were:- Drift front wings, 143.5X0.0285X2.42 . . . .= 9.90 lb. Drift rear wings, 29.5X(o.o43-0.242X0.05235)X2.42 = 2.17 lb. Tangential force at 3 deg. . . . . . . . . = 0.00 lb. Head resistance, 11.70X2.43 . . . . . = 28.31

Total resistance . . . . . . . .= 40.38

Speed 22 miles per hour. Power = (40.38X22)/375 = 2.36 h.p. for the "thrust" or 4.72 h.p. for the motor. The weight being 189 lb., and the resistance 40.38 lb., the gliding angle of descent was 40.38/189 = tangent of 12 deg. , which was verified by many experiments.

The following expressions will be found useful in computing such projects, with the aid of the table above given:

1. Wind force, F = KV2. 8. Drift, D = KSV2esina 2. Pressure, P = KV2S. 9. Head area E, get an equivalent 3. Velocity, V = sqrt. (W/(KSecosa)) 10. Head resistance, H = EF. 4. Surface S varies as 1/V2. 11. Tangential force, T = Pa 5. Normal, N = KSV2e. 12. Resistance, R = D + H (+ or -) T. 6. Lift, L = KSV2ecsoa. 13. Ft. lb., M = RV. 7. Weight, W = L = Ncosa. 14. Thrust, h.p., = RV/factor.

Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)