II* 



A BUG DYNAMICS. 



AERO-DYXAM 



lift 



For the method of obtaining these remit* see ANEMOMETER. 

 Let u suppose the square foot of surface to be placed obliquely, no as 

 to make MI angle ABC (rig. 2), with the direction A a of the wind. Let 

 u B represent the velocity of the wind per 

 second. Then, if D I be drawn perpen- 

 dicular to B c [COMPOSITION OF VBLOi-mis] 

 the wind which strike* the plnne at B doe* 

 not strike it directly with its whole velocity. 

 but only with the velocity UK; it being 

 the same thing as if we supposed the wind 

 K ^^K to be carried directly against the plane with 



^^ the velocity D K, and at the same time 

 hifted on the surface from c towards B with the velocity E B. ThU 

 but will only make different i "articles of air strike the point B, but not 

 with different forces. Tlii.- line D E is in trigonometry proportional 

 to the tint of the angle D B E. Again, if we draw E r perpendicular to 

 D B, the whole of the velocity DEM not in the direction of the wind, 

 A B, but only the port of it D r ; the other component, r E, being 

 employed in moving the plane in a direction perpendicular to that of 

 the wind. Thu line, D F, which represent* the efeetire velocity of the 

 wind in the direction A B, u, as the r/uare of the sine of the angle 

 D B E, since D T = D E sin D E F = D E sin D B E and D K = D n sin D B E. 

 The line, D r, is a third proportional to D B and D E, so that if we 

 suppose the wind to move at the rate of 100 feet in a second, and 

 the plane to be BO inclined that the wind strikes it directly with 

 only 80 feet of velocity, we have, for the real effective velocity 

 100 : 80 : : 80 : 64, or we nni.it consider this plane an resisting a 

 wind of only 64 feet of velocity. This theory is liable to the objections 

 of the former one, as it does not allow for any condensation, but 

 supposes the particles to disappear after they have struck the plane. 

 Nevertheless, it is found in practice to answer well enough win u the 

 plane is not very oblique to the wind. For the mathematician, we 

 may state that the following empirical formula is found from Smeaton's 

 experiments to be much nearer the truth, which, as he will see, is 

 nearly equivalent to the square of the sine of the angle of inclination. 

 when the latter is nearly a right angle. Let the angle of inclination ui 

 the surface lie 0, and the velocity of the wind V, then the effective 

 velocity is 



V sin 8 ' 8C co> - nearly. 



Every meteorological observatory is furnished with an instrument 

 called an anemometer, which registers the direction, the duration, and 

 the force of the wind. Hitherto it has not been possible to obtain 

 sufficient data for accurately determining the mean monthly or annual 

 direction and force at a large number of different stations, by reason 

 of the costliness of the apparatus required. Meanwhile, it ha* been 

 the practice to assume that the force of all winds may be regarded, on 

 the average, as measured by the frequency of their occurrence. Kiinit/. 

 and Dove have computed the mean annual force and direction, and 

 their monthly variarion.s, for many stations in Kurope and America, of 

 which the following Table is a syno|wis : 



F.ngUnd 



France and Holland 

 Germany . 



Denmark . 

 Sweden . 

 KMtorn Europe . 

 N. of United SUtet . 



Direction. 

 8 66' \V 

 g U \\ 

 S 76' \V 



- U \v 

 8 77" W 

 N 87' W 



- M w 



Force. 

 0-198 

 0-135 

 0-177 

 0-170 

 0-218 

 0-167 

 0-18! 



The mechanical means by which these result* are obtained will be 

 described under ANEMOMETER; but we may here state the value of 

 those recorded results in furnishing the iulei/rui of the wind for each 

 point of the compass ; or, in other words, the entire quantity of wind 

 which has blown from each ]Hiint during a given |>eri<>d. If the force 

 of the wind were constant, the integral would be obtained by multi 

 plying the length of time that the wind blows by the rate at which it 

 travels. The integral is proportional to both these quantities taken 

 jointly, just as the area of a rectangle in proportional to its length aw! 

 breadth taken jointly. If we were to construct a figure the length ol 

 which should represent the duration of the wind, and its breadth the 

 force, the Utter being a constantly varying quantity, the breadth of the 

 figure must vary, in order that it* area may represent the integral of tin 

 wind correctly. The result* furnished by Mr. Osier's anemometer enable 

 ui to construct such a figure ; but in Dr. WheweU's anemometer the 

 integral is represented limply by the depth which the pencil descends. 

 Whewell's instrument is so far defective that it makes no attempt to 

 record the time during which each wind blows, the times of its rA>t >/<< 

 or its fnrce at any given moment ; but only the order of its changes ol 

 direction and the integral or entire quantity that blows from each 

 point, or rather from each rhumb of 1 1 J : this U known by the length o 

 the pencil-mark in each vertical division of the cylinder measure* 

 vertically and not following the windings of the track, for these must 

 be neglected so far as they are confined to one rhumb, the centre o: 

 which corresponds with one of the ]>ointa of the cmnpaiM. Hence, any 

 wind which doe* not deviate from any one of those points more than 

 el*, if the cylinder be divided into 82 parU, or 11 J if it be divide, 

 into 16 parts, is regarded as blowing exactly from that point ; which is 

 a serious defect common to wind-registers. But, supposing that we are 



u possession of the lengths of line described by the pencil in each 

 li vision of Whewell's cylinder during a certain , li lengths or 



roportionate one* may be hud down in their proper older with 

 Unctions so as to form a crooked line expressive of all the quantities 

 md change* of the wind for that particular place ami |>eriod. This is 



ailed the till* of the wind. l''or example, fag nt, the type 



Fig. S. 



of all the wind that blew over Plymouth during August and j 

 September 1843. If the two ends of this line be joined by a straight 

 line we shall get the direction of the raiillaal or average effect of all 

 the winds which blew over Plymouth during that |>erio<l, which, in 

 the case before us, i about N. 23 E. or about equivalent t :i >s. \V 

 wind. Tliis average direction is not, necessarily, the /<rm7i/.</ dii 

 or the direction in which the wind most commonly blow- : -in..- tl,.- 

 prevailing winds may be gentle and the greater force of those from the 

 opposite quarter may more than compensate for their shorter duration, 

 so that the average direction with resi>ect to time and intensity, con- 

 sidered jointly, may ditl'er greatly from the average direction as regards 

 time alone. In England, however, both these averages have nearly the 

 same direction : the time average is equivalent to a wind blowing from 

 some jK.int between S. and \V.. and the true average, however variable 

 on a comparison of the resultants of different months or seasons, 

 exhibits in the tyjie for a whole year a general northward dir< 

 mostly eastward from the starting point. Whewell's instrument 

 the mean direction for three years nearer N. than K., whil- 

 to Osier's, it is nearer E. than N. ; but when it U ron-idenil tli.it in 

 Wh.'H ell's instrument the velocity of the fly does not bear a constant 

 ratio to that of the wind, but is more than proportionally quicker in a 

 quick than in a slow wind, while the distance which the \*> . 

 i proportional to the revolutions of the fly, the traces of the pencil 

 cannot correctly represent the integral* of the wind. In fact, it i 

 necessary to drirc the instrument by means of a clock, lea\inu tin 

 direction or regulation, of the instrument to the wind, as in Osier's 

 instrument. 



It will be seen by reference to Fig. 3, in the article ANKMOMKTKR. 

 that the upper pencil makes a trace on the register paper which i.-pre 

 sent* the pressure of the wind, while the trace made by the middle 

 pencil represents it* direction. Now the ordiuates of the upper trace 

 are pro|>ortional to the wind's velocity ; or in other words, the ord 

 at any two different moments should bear the same ratio to each other, 

 a* did the velocities of the wind at those two moment-. Hence, the 

 total amounts of wind passing over the instrument dining dill'ereni 

 period-, will U- proportional to the areas of the portions of curve ' 

 during those periods, and it is only by mc.imiring and comparing these 

 areas that we can obtain the proportion of the integrals of wind during 

 different periods of time. To draw a type of the wind by Osier's 

 instrument, such as is so easily done by W hewell's, the period- 

 be BO divided that during each period the direction of the wind m>\ 

 have been confined w ithin certain limit*, such as two rhumbs (22)), or 

 one rhumb (11J*). To do this that part of the register-japer devoted 

 to direction must be divided by 16 or 82 longitudinal lim-.-. .-!ich tliat 

 when the vane points to any one of the 16 or 32 principal point . 'lie 

 direction i>enctl may rest midway lietween two of tin- .-n. I , 



noting all the points where the pencil-track intersects these lines, and 

 from every such intersection raising a perjicndicular to the top of the 

 paper, MOO ]T|HMidiculars will divide the upper curve, or that of force, 

 into portions each of which may be regarded as belonging to one \\ in.l 

 only; for during its description the wind did not deviate more than 

 6| or 11J (according as we use 32 or only 10 pointa) on either sid. of 

 a certain point. By ascertaining the areas of these different portions, 

 and drawing lengths of line proportional to them, placing those lines in 

 their proper direction and in their proper order, we obtain a morn 

 correct type of the wind than by the method previously described. 

 'Ph.- integrals of the wind have not only a relative, but also an absolute 

 value. If the pressure-plate be correctly graduated, as by whirling it 

 through the air at known rates of velocity, and noting the several 

 amounts of compression in the spring, we get similar results to those 



