117 



AERO-DYNAMICS. 



AERO-DYNAMICS. 



118 



For the tide-waves produced in the atmosphere, by the attraction o 

 the sun and moon, see PNEUMATICS ; METEOROLOGY. 



As soon as we begin to move, we feel more or less the resistance o: 

 the air. At an ordinary rate of motion this is not very perceptible 

 Ijiit the jockey, who rides at the rate of from thirty to forty miles an 

 hour, feels it sensibly, and is obliged to wear a cap which may cut the 

 wind, as the bow of a ship cuts the water, or otherwise it would be 

 blown off his head, although, iu the common sense of the word, there 

 might be no icind stirring at the time. Whenever we attempt to put 

 any matter in motion, we feel what is denominated pressure, or resist- 

 ma, which is the greater, the greater the quantity of matter which we 

 attempt to move, and the velocity which we attempt to communicate 

 t it. Thus, two violent pressures, of equal force, applied for an 

 instant to weights of ten and twenty pounds, will make the weight ol 

 ten ]N.unds move twice as fast as that of twenty; or, if we would have 

 tin- two move equally fast, we must apply twice as much pressure to 

 the twenty pounds weight as to that of ten pounds. If we now con- 

 i-eive :i number of equal balls placed in a line, along which we move 

 the hand uniformly, so as to set them all in motion one after the other, 

 we might at first imagine that if we move the hand at the rate of two 

 feet hi a second, and afterwards at the rate of four feet in a second, 

 that we exert twice as much force, and encounter twice as much 

 resistance, in the second case, as in the first ; because, we say, we move 

 I'arh ball iu the second case twice as fast as in the first. But there is 

 another consideration : we not only move each ball twice as fast, but we 

 meet with twice as many balls in a second, so that not only the velocity 

 which we communicate in a second is doubled, but also the quantity 

 of matter to which we communicate that velocity is doubled, or, there 

 is four times as much resistance to twice the velocity, as there was to 

 the single velocity. Similarly, at three times the rate of motion, we 

 in. , t with three times as much matter, and communicate to each 

 portion three times the velocity : whence we meet with three times 

 three, or nine times the quantity of resistance. If we transfer this 

 reasoning to the case of a body moving through the air, we should 

 infer, that the resistance is, to speak mathematically, as the square of 

 the velocity : that \, if the velocity be suddenly made ten times as 

 great, the resistance is made ten times ten, or a hundred times as 

 great. And this, which was the first theory proposed on the subject, 

 is sufficiently near the truth for practical purposes, when the velocities 

 :nv not very great; for example, up to eight or nine hundred feet in a 

 second. 



But one or two circumstances have been neglected. (1) The succes- 

 sive particles of air which the moving body strikes, instead of being 

 moved out of the way completely, are forced upon those in front, so 

 that there w a condensation of air before the moving body; which 

 condensation, as we have seen in ACOUSTICS, is propagated onwards at 

 the rate of about 1125 feet in a second. (2) In the meanwhile, the space 

 through which the body moves, or has moved, is, or has been, entirely 

 cleared of air ; and though the air is forced with great rapidity into 

 the vacant space, yet this ia not done instantaneously, as we shall pre- 

 sently see from experiment. Therefore though, when at rest, the 

 atmospheric pressures before and behind the body counterbalance each 

 other, yet, when in motion, there is an increase of the pressure before 

 the body, and a diminution of that behind it; both which circum- 

 stances increase the resistance. 



From theory, tolerably well confirmed by experiment, it appears, 

 that if air of the ordinary pressure be allowed to rush into a rarutnn, 

 or space entirely devoid of air, it will be driven in at first with a 

 velocity of about 1340 feet per second; or, to avoid an appearance of 

 accuracy of which we are not actually in possession, we may say between 

 1300 and 1400 feet per second. If now, instead of rushing into a 

 vacuum, the air which comes through the orifice meeta with other air 

 of a less density, say one-fourth of its own density, the velocity above- 

 mentioned will be diminished in the proportion of 1 to the square-root 

 of'd 1), or of 1 to VfTor of 2 to v/37 or of JOO to 87, 



very nearly. By a similar 

 process any other case may 



be computed. Let us now 



* imagine a ball, a b (Fig. 1), to 

 move forwards in the direction 

 BA, with an initial velocity 

 less than 1000 feet per 



!. Let B be the last point of ita track at which the air has 



completely recovered its former state. The air in the cone Ba6 will not 



have 'entirely recovered ite state, but will all be more or less rarefied ; 



nr> that in addition to the loss of motion arising from communication 



to tlie particles of air, there is a part of the atmospheric pressure on 



'lit of a b, not counterbalanced from behind. The condensation 



t of 06 in propagated [ACOUSTICS] quicker than the ball 



; so that the air in front continues, if not entirely, at least very 



in iu natural state. \Ve cannot say that the canes of air 



ru.-iliing through an orifice into a vacuum, and of air filling up the 



space left by a ball, have any decided similarity ; nor can we say the 



contrary, owing to the very imperfect state of the mathematical 



analysis of this part of the subject. We may however conjecture 



that when the ball moves with a velocity greater than that of sound, 



v condensing the air before it, and leaving a perfect vacuum 



behind it, or nearly so, the resistance will be much greater than the 



PI*. 1. 



theory already stated would lead us to expect. And this proves 

 to be the case at even less velocities than the one just specified ; 

 for though up to 1000 feet per second, or thereabouts, the resistance 

 increases very nearly with the square of the velocity, yet from 

 that point it increases in a much quicker ratio ; so that to a ball 

 moving at the rate of 1700 feet per second, it is three times as great as 

 we should obtain from our first hypothesis. The resistance to an iron 

 ball of twelve pounds weight, moving at the rate of twenty-five feet 

 per second, is equivalent to a pressure of half an ounce avoirdupois ; 

 if we increase twenty-five feet per second to 1700 feet per second, or 

 multiply the first sixty-eight times, the square of which is 68 x 68 or 

 4624, we might, from what has been stated, expect a resistance o 

 4624 half ounces, or 1444 pounds ; instead of which it was found to 

 be 433J pounds ; about three times the preceding, as we said. At a 

 velocity of 1600 feet per second, the resistance was found to be more 

 than twice that given by the_ theory. Without entering further into 

 details, for which the reader may consult the article GUNNERY, to 

 which they particularly apply and also without considering the effect 

 which the different forms of bodies have upon the RESISTANCE (to 

 which we refer), we give some of the conclusions to which Dr. 

 Hutton was led by a long and careful repetition of the experiments of 

 Mr. Robins, his predecessor in the same track. For the method of 

 conducting these experiments, see WHIRLING MACHINE; BALLISTIC 

 PENDULUM. 



1. The resistance is nearly in the same proportion as the surface 

 exposed, but a little greater than this proportion on the larger surface. 

 That is, if we take two bodies of the same figure and material (two iron 

 spheres for example), the surface of the second being twice that of the 

 first, the resistance to the larger sphere is a little more than twice 

 that of the smaller, the velocities being the same iu both. 



2. The round ends and sharp ends of solids suffer less resistance than 

 the flat ends. Thus, the sharp end or vertex of a cone is less resisted 

 than the flat end or base. 



3. Two solids, having the parts presented to, or wliicli push the air, 

 the same, are not equally resisted unless the hinder parts are also the 

 same. 



Though we have hitherto considered the resistance offered to a body 

 moving against still air, and the pressure which is necessary to maintain 

 it at a given velocity, yet the problem is exactly the same, if we suppose 

 the body to remain still, and the air, or as we now call it, the wind, to 

 move against it with the same velocity. Suppose the body to move 

 100 feet in a second, and that the spectator is carried along with- 

 out his knowledge at the same rate. He will, therefore, always be in 

 the same place with respect to the body, and will at the same time 

 imagine that the air or wind is coming towards him at the rate of 100 

 feet per second. The force which, when he imagined the body 

 moving, he called the pressure necessaiy to maintain its velocity, 

 he will now say is the pressure necessary to steady it against the wind. 

 If we suppose both the wind and the body to be in motion, the 

 resistance is variously modified, according to the direction of the 

 motions of the two. I the wind and the body move in the same 

 direction, with the same velocity, there is no resistance ; for no air is 

 displaced by the body. If the wind move 50 feet per second, and the 

 body 100 feet, the pressure on the body is the same as if it were at 

 rest, with a contrary wind of 50 feet per second blowing on it. If the 

 wind and the body move in contrary directions, with velocities of 100 

 feet, the resistance is that of a wind of 200 per second ; and so on. If 

 the spectator move with the body unknowingly, the magnitude and 

 direction which he will assign to the wind is that which will produce 

 such a pressure on the body at rest, as it really sustains when in motion. 

 [APPARENT MOTION.] 



The following well-known table, first given by Mr. Smeaton in the 

 Philosophical Transactions ' for 1 759, and confirmed by the experiments 

 of Dr. Hutton, shows, in pounds avoirdupois, the pressure which 

 different winds will exert upon a square foot of surface exposed directly 

 against them. The first column is a rough representation of the 

 second. 



