On the Reciprocal Propelling Powers of Fluids and Certain Rotary Machines Upon Each Other

Downloaded from http://pygs.lyellcollection.org/ by guest on September 27, 2021 116 to the soil those constituents which, as analysis points out to the inquiring mind, become exhausted by such treatment. Could this table be used in conjunction with an analysis of the soils on which his efforts are to be employed, the agricul turist might indeed feel that science had opened to him a prospect of almost boundless improvement in the results of his labour; and it could no longer be said that "Agriculture " owed nothing to Chemistry." At the Evening Sitting, the following Paper was read:— ON THE RECIPROCAL PROPELLING POWERS OF FLUIDS, AND CERTAIN ROTARY MACHINES UPON EACH OTHEU. BY B. BIRAM, ESQ., WE NT WORTH. The object of this communication is to elucidate the principle of action and proper construction of those rotary machines which derive their motion from the oblique impulse of fluids, as in the vertical windmill; or which, on the other hand, are capable of giving motion to fluids by an oblique impulse; being themselves propelled by some other source of power. Since the introduction of steam power, wind, as a prime mover of machinery, has been comparatively little thought of; yet, from the abundant supply which often sweeps over the land, and from the great economy of its application, it is well deserving of consideration. We find, however, that little has been done for a long series of years towards the improvement of this description of power; that nearly the same form of windmill sail is still adhered to which the illustrious Smeaton found to be the best; and that the employ ment of wind for driving machinery, instead of progressing, Downloaded from http://pygs.lyellcollection.org/ by guest on September 27, 2021 117 is, on account of its uncertainty, and from the difficulty occasionally of governing its impetuosity, fast sinking into disuse. Being fully persuaded that this power deserves more the attention of scientific men, after considerable thought upon the subject, and at the risk of being thought presump tuous, I have ventured to question the truth of the conclusion at which Smeaton arrived after his numerous experiments, and now submit, that the shape of sail which he recommends is capable of improvement, and that with properly constructed sails, the whole cylinder of wind in which they may be said to revolve, may he advantageously intercepted, whereby the same area of resisting surface may be presented to the wind, with a reduction of 2-5 ths of the diameter of the sail, or, retaining the same diameter of the sails, the power of the mill may be nearly doubled. I think it will be evident to all who pay attention to the subject, that every portion of the sail should present a pro portionate resistance to the wind, and should recede from its impulse with that velocity which would least interrupt the wind's onward progress. If the object in view were to pro duce rectilineal motion, such, for instance, as the propelling a carriage upon a railway in a right line oblique to the wind's direction, the best form of sail would doubtless be a flat surface, and the angle with the wind uniform throughout: but the circumstances are much altered when a rotary motion is required; in that case the velocity of the sail varies con stantly from the extremity to the axle, whilst the wind continues to act upon the sail with equal velocity throughout the whole area of the revolving circle. In order, therefore, that the sail should present a due resistance to the wind, and on the other hand not disadvantageously intercept its pro gress, that form should be adopted which is the best calculated for securing this object. Downloaded from http://pygs.lyellcollection.org/ by guest on September 27, 2021 118 The sail of a windmill will, of course, be the length of the radius of a circle in which it revolves. The parallelogram FIG. 1. FIG. 2. A B c D, Fig, 2, B represents this D A. raditis ; c B being 5 /. S // the axle^ and the 4 4 •-% leTigtk being di 3 ^S^^"^^* 3 vided into six #^^ ...-• Z equalparts. Let ...fj/.^2 1 ABJJRE^^T. 1, equal c w-A1 the curved line K of the sixth part of a circle, which the periphery of the revolving sail would describe, the chord of its arc would then be equal to the radius A B, Fig. 2, and the chord of the several arcs 5-5, 4-4, 3-3, 2-2, 1-1, Fig. 1, would be respectively equal to the lengths 5B, 4B, 3B, 2B, and 1B, Fig. 2. The periphery of the sail A B. Fig. 1, being placed at an angle with regard to the plane of rotation, the two points would not revolve in the same line, but would describe a cylinder, the depth of which may be said to be D A. Fig. 2 ; and as the length of the lines A B. Fig. 1 and 2, are respectively eqnal to each other, the angle CAB. Fig. 2, would be the angle of the extremity of the sail with the plane of rotation. The sail being considered without fric tion, the tendency of the wind on the oblique plane A B, Fig. 1, (represented by A C, Fig. 2, the arrow denoting the direction of the wind,) would be to cause the sail to revolve from A to B in the time the wind passed from D to A, and as the several other portions of the sail would in the same time each pass through the spaces 5-5, 4-4, 3-3, 2-2, 1-1, the angle which the sail should present at those several points, should be respectively c 5 B, C 4 B, C 3 B, C 2 B, and c 1 B. The form of sail which Smeaton recommends accords in some measure to this principle, inasmuch as the angle of Downloaded from http://pygs.lyellcollection.org/ by guest on September 27, 2021 119 the sail with the plane of rotation increases towards the axis; but it is not clear that he has any rule for determining those angles, more than that they were the angles of those sails with which he experimented, which produced the greatest mechanical effect. The following are the angles which he prescribes :— SMEATON'S CONSTRUCTION. Mid Ex Radius divided into 6 equal parts. dle. tremity Csee Fig. 2) 4 5 6 11 2 3 Angle of the sail with the axis ... 172 71 72 74 77i 83 Angle of weather 1 18 19 18 16 7 CONSTRUCTION HEREBY RECOMMENDED. Weather angle, supposing the ex-ii tremity 7° 37 2011 14 101 Ditto, supposing the middle 18°..Jl 43 26A'Wi 18 13# 11 With sails formed upon Smeaton's plan, I am not surprised that he found the whole cylinder of wind could not be advantageously intercepted; but with properly constructed sails, I am persuaded that he would have arrived at a differ ent conclusion, and that he would also have found, that the angle at which the extremity of the sail might be advan tageously set, would admit of a much more extensive range, where the products of the velocity, multiplied by the weight raised in a given time, would have produced an uniform maximum result. At least, so I have inferred from the following experiments. It is not easy to show the unnecessary obstruction, and consequent loss of power, which the wind encounters from ill-formed sails; but if water be the medium in which the sails are made to revolve, very conclusive evidence of the fact may be exhibited. If in any vessel of water a number of small pieces of paper, bran, or other light body of about the same specific gravity as water be sprinkled, the effect L Downloaded from http://pygs.lyellcollection.org/ by guest on September 27, 2021 120 produced upon the floating bodies by sails at different angles and of diff*erent constructions, will be seen by submerging the sails, and passing them through the water in the direction of the axis. If the sails be formed of the construction hereby recommended, they will revolve without materially disturbing the particles of floating matter; but in proportion as the form differs from this principle, there will be more or less disturb ance of the water, and commotion amongst the bodies floating therein. These experiments in water also clearly establish the law which governs the velocity of revolving bodies, acted upon by fluids on this principle. For let A B, Vig, 3,* represent the plane in which the wheel rotates FIG. 3. upon its axis, and the oblique lines ^ drawn from B, and terminating in the j^ line A c, be the angles ^vhich the extremity of the vanes of variously formed wheels make with the plane of rotation; then supposing A B also to represent a line of the same length as the circumference of the wheel w, JPig. 4, and the angle A B E be that which the extremity of the vane or sail forms with the plane of rotation, the wheel upon being moved through riG. 4. the water in the direction of the axis, would make one revolution in the dis w tance A E, or four in that of its own circumference. If * This diagram, Fig. 3, presents a convenient method of ascertaining the proper angles to be given to vanes or floats at any required distance from the centre of the wheel, the angle at any one distance being given.

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