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at the Admiralty, is the most satisfactory that has yet been offered. This gentleman supposes a screw, whose blade makes one complete turn only in the length, to be divided by planes all perpendicular to the axis of the screw, and at small intervals from one another, so that the surface of the screw is divided into a great number of sectoral or fan-like areas oblique to the axis, and following one another in succession from one end of the screw to the other. Now, the water in which the screw turns being supposed at rest, a vertical lamina of water, which is acted upon by the first of these sectors, is, by the pressure of the posterior surface in the revolution of the screw, pressed with a certain force towards the a/ifer-part of the screw; the water thus receding is acted upon by the second sectoral portion of the screw in its revolution, and impelled aftward, but with less force than before, on account of the retiring movement of the water: a part of this water is acted upon by the third sectoral portion of the screw in its revolution, and still impelled aft, but with a force further diminished by the greater retiring movement of the water, and so on, to the end of the screw.
3l. Thus, the pressive force of the screw on the water, and, consequently, the reaction of the water, by which the ship is propelled forward, go on diminishing; and the slip, or recession of the water, goes on increasing with the length of the screw. The diminution of the power of motion on this account is probably very small when the velocity of the screw's rotation is small; and, in that case, an entire screw with one turn in its length may have some advantages; but, when the velocity of rotation is great, it is probable that the propelling power of the after-Tpsxt of the screw becomes so small as to permit its removal without diminishing in a sensible degree the speed of the ship; in fact, experience has shown that, with high velocities of rotation, one-third or one-fourth of an entire convolution of the blade is sufficient to produce the full effect of the moving power.
32. In what has been said it is supposed that the water has immediate access to the screw, and that the particles pressed by it are free to move aftward; but neither of these suppositions is correct. From the position of the screw, in an aperture close under the ship's counter, the water, which is divided by the body of the ship, subsequently flows obliquely towards the screw; and, again, the water, after being pressed by the screw, is broken by the stern-post and rudder, where, being arrested, part of it is forced forward in the direction of the ship's motion: on both these accounts the power of the screw must be in some degree modified; in some cases, indeed, the slip has been found to be negative, that is, the actual speed of the ship has been greater than the theoretical speed, or that which is due to the power of the engine.
33. From such considerations, and from repeated experiments, it has been determined that the best form which can be given to a screw is that of two halves of a spiral feather, placed on opposite sides of the axle of the screw in reverse positions: these, while they occupy only half the space in length which they would otherwise require, are found, with equal surface, more efficient than the continuous spiral formerly in use.
The two sectors, or fan-shaped blades, composing the present screw, have generally what is called a uniform pitch; that is, they constitute two equal and similar figures, one on each side of a plane perpendicular to the axle and bisecting the length or pitch of the original screw, supposed to be of one complete turn: each blade occupying exactly half that length. But some screws have been made which occupy much less of the length, and with what is called an increasing pitch : thus, imagining a vertical plane perpendicular to the axle to divide the whole pitch in the ratio of 11 to 12, the forward fan occupies half the shorter portion and the aftward fan half the longer portion; consequently, the extent of the interval between the extremities of the two blades, if measured on a line parallel to the axle, is half the entire pitch of the complete screw. This is Mr. Wood
croft's construction: in that of Mr. Atherton the two fans are equal and similar to one another, but each is formed so that the parts about the axle are portions of spirals, of smaller pitch than those of the parts about the extremities, the pitch increasing gradually from the axle towards the periphery.
34. In a manner similar to that which has been used in finding the propulsive effect of water on a common paddle-wheel, may be found the effect of water on the blades of a screw in giving motion to a vessel. Thus,
let C D be a horizontal line parallel to the keel of the ship or to the screw-axle, and let Z C be at right angles to it in a plane passing through C D, perpendicular to the radius or arm of a screw blade; also let A B in the same plane be the intersection of the plane with the anterior surface of the blade. Imagine A B at present to be a straight line; and let it be observed that the vertical plane in which any point, as C, in A B revolves about the screw-axle is perpendicular to that axle, and to the horizontal line C D.
Now, let the velocity of the point C, by the revolution of the screw-blades about the screw-axle, be represented by V, and be supposed to act in the direction Z C; and let the horizontal velocity of C, by the forward movement of the vessel, be represented by V, in the direction C D; also let the angle ZOB=0: then Z C D being a right angle, V cos. 6 is the velocity of the ship resolved perpendicularly to A B, and Y sin. 6 is the velocity of the blade also resolved perpendicularly to AB; consequently V sin. 6 — V cos. 6 represents the relative velocity of the paddle and ship in the same direction. It follows that (V sin. 6 — V cos. 6)2 V cos. 6 expresses the efficient momentum of the water, in the horizontal direction, in propelling the vessel. Representing V by n V, the expression becomes
Vs (sin. 6 — n cos. fff cos. 6,
and this quantity is to be a maximum.
Making its differential equal to zero, and reducing, we have
tan. 0 = 3-£ ± i (9 ft8 + 8)*.
Assuming V' = §V, or n=|, we have 0=67° 57' or 139° 27'.
When the angle Z C B (= 6) is 67° 57', the motion of A B, resolved vertically, is upwards, or towards Z; in the other case the blade has the position A' C B', and its motion is downwards. If n were diminished, the first value of 6 would become less: now the velocity of a point, as C, on the blade being greater as it is farther from the screw-axle, the value of n being then less, the value of the angle Z C B would be diminished; which shows that A B, instead of being a straight line, should be a curve such that a tangent to it at any point should make a smaller angle with a line perpendicular to the radius of the blade, than is made by a tangent at a point nearer the screw-axle.
35. A propeller, whether it be a wheel or a screw, should be so constructed and applied as, by its action, to disturb the water as little as possible in directions which do not tend to propulsion. This condition, as already observed, Art. 14, is very imperfectly fulfilled in the common radiating paddle-wheel, the boards of which being fixed in the direction of radii, press the water down in entering, and raise it in emerging. A considerable portion of the force of the engine is thus absorbed, and there is formed a negative wave, which is attended with a vibration of the vessel.
36. These defects have been somewhat obviated by an invention which was patented by Mr. Galloway in
1829, by which the paddle-boards are made to turn or feather, so as to enter, pass through, and emerge from the water in positions the most advantageous for propelling a vessel with less of the vibration and loss of power which arise from the action of the radiating paddles. The machinery on each side of the vessel consists of two wheels, both of which are affixed to the main axle, but are not concentric, and the feathering motion of the board is produced by affixing a short arm to one face of each paddle-board at an angle of 120 degrees with its plane, the boards turning on horizontal axles, which pass through the extremities of the radii of one of the two excentric wheels. A rod is connected at one end, by a joint, with the extremity of that short arm, and at the opposite end, also by a joint, with the excentric part of the axle. By the revolution of the double wheel the rod makes a constantly varying angle with the short arm which is attached to the paddle board, and this causes a corresponding variation in the angle which the paddle-board makes with the radii of the wheel, so that by a due adjustment of the length of the rod the board is made to enter and leave the water at an angle of about 30 degrees with a vertical line, this being the angle at which, in general, the reaction of the water against the board is the most favourable for propelling the vessel.
37. This improvement has tended greatly to increase the speed of paddle steamers, and the best sea-going vessels are now fitted with feathering paddles. Such paddles have been applied to her Majesty's yacht, 'Victoria and Albert,' and others; and they are particularly applicable to that description of vessel, as well as to packets, which are employed in short passages, and in which the load line, or draught of water, does not much vary; but for vessels employed on foreign voyages, and particularly for ships of war employed on cruising services, which are necessarily of considerable duration, they are not convenient: vessels so employed being at first deeply laden, and subsequently much lightened, it would become necessary to have