CORS fast; da loom i h many th 1 be acc threads CHAPTER VII. STEAM NAVIGATION. STEAM navigation embraces two main topics of enquiry:the first, what the configuration of a vessel shall be to pass through the water at any desired speed with the least resistance; and the second, what shall be the construction of machinery that shall generate and utilise the propelling power with the greatest efficiency. The second topic has, in most of its details, been already discussed in the preceding pages; and it will now be proper to offer some remarks on the remaining portion of the subject. The resistance of vessels passing through the water is made up of two parts:-the one, which is called the bow and stern resistance, being caused partly by the hydrostatic pressure forcing back the vessel, arising from the difference of level between the bow and stern, and partly by the power consumed in blunt bows in giving a direct impulse to the water; while the other part of the resistance, and the most important part, is that due to the friction of the water on the sides and bottom of the ship. The bow and stern resistance may be reduced to any desired extent by making the ends sharper. But the friction of the bottom cannot be got rid of, or be materially reduced, by any means yet discovered. When a vessel is propelled through water, the water at the bow has to be moved aside to enable the vessel to pass; and the velocity with which the water is moved sideways will depend upon the angle of the bow and the speed of the vessel. When these elements are known it is easy to tell with what velocity the water will be moved aside; and when we know the velocity with which the water is moved, we can easily tell the power consumed in moving it, which power will in fact, be the weight of the water moved per minute multiplied by the height from which a body must fall by gravity to acquire the same velocity. But as nearly all the power thus consumed in moving aside the water at the bow of a vessel is afterwards recovered at the stern by the closing in of the water upon the run, it is needless to go into this investigation further than to determine what amount of power is wasted by the operation, or in other words, what amount of power is expended that is not afterwards recovered. If the vessel to be propelled is of a proper form, each particle of water will be moved sideways by the bow, in the same manner as the ball of a pendulum is moved sideways by gravity, so as to enable the vessel to pass; and when the broadest part of the vessel has passed through the channel thus created, each particle of water will swing backward again until it comes to rest at the stern. There will be no waste of power in this operation, except that incident to the friction of the moving water; just as in the swinging of a pendulum there is no expenditure of power beyond that which is necessary to overcome the friction of the air upon the moving ball. But as the movement of the vessel, however well she may be formed, will somewhat raise the water at the bow, and somewhat depress the water at the stern, there will be a certain hydrostatic pressure required to be continually overcome as the vessel advances in her course, which opposition constitutes the bow and stern resistance; and this, with the friction of the bottom, make up the whole resistance of the ship. Before, however, proceeding to investigate the amount of this hydrostatic resistance, it will be proper to show how accidental sources of loss may be eliminated from the problem by the introduction of that particular form of vessel which will make this resistance a minimum; and I will therefore first proceed to indicate in what way such form of vessel may be obtained. If we take a short log of wood, such as is shown by the dotted lines A B C D E F G, in the annexed figure (fig. 41), and if we proceed to enquire in what way we shall mould this log into a model which shall offer the least possible hydrostatic resistance in being drawn through the water, we have the following considerations to guide us in arriving at the desired knowledge: We shall, for the sake of simplification, suppose that the cross section of the completed model is to be rectangular, or in other words, that the model is to have vertical sides and a flat bottom; for although this is not the best form of cross section, as I shall Fig. 41 F afterwards show, the supposition of its adoption in this case will We first draw a centre line x y longitudinally along the top lines, or ordinates, as they are termed, that we find to be convenient. Now as, by the conditions of the problem, the particles of water have to swing sideways like a pendulum, in order that the resistance may be a minimum, the particle which encounters the stem at x must be moved sideways very slowly at first, like a heavy body moved by gravity, but gradually accelerating until it arrives at b, midway between x and a, where its velocity will be greatest; and this point answers to the position of the ball of the pendulum when it has reached the bottom of the arc, and has consequently attained its greatest velocity. Thereafter the motion, which before was continually accelerated, must be now continually retarded, as it is in any pendulum that is ascending the arc in which it beats, or in any ball which is projected upwards into the air against the force of gravity. When the particle of water has attained the position on the side of the model which is opposite to the midship frame a, it will have come to rest, this being the point answering to the position of the pendulum at the top of its arc, and when just about to make the return beat. Thereafter the particle which was before moved outwards, will now move inward with a velocity, slow at first, but continually accelerating, until it attains the position on the side of the model which is opposite to the frame b, when the velocity again begins to diminish; and the particle finally comes to rest at the stern. A particle of water that is moved in this way will be moved with the minimum of resistance; for since it retains none of the motion in it that has been imparted, but surrenders the whole gradually without impact or percussion, by the time it has come finally to rest, there can be no power consumed in moving it except that due to friction only. Wherever the water is not moved in this manner it will either retain some of the motion, which implies a corresponding waste of power, or heat will be generated by impact, which also involves a corresponding waste of power. That the water may be moved in the same manner as a pendulum is moved, is obviously possi ble, by giving the proper configuration to the sides of the model; and in fact, if an endless sheet of paper be made to travel vertically behind a pendulum, with a pencil or paint we find to be oblem, the pa dulum, in orde le which e slowly at fi re its rel position of Com of the Thera ted, must brush stuck in the ball, the proper form for the side of the model will be marked upon the paper. The curve, however, which is a parabolic one, may be described geometrically as follows: If we compute the height through which a heavy body falls by gravity in any given number of seconds, we shall find that in the first quarter of a second it will have fallen through 12 foot, in the second quarter of a second 34 feet, in the third 93, in the fourth 16, in the fifth 25,25, in the sixth 36,3%, in the seventh 49,495, in the eighth 64}, in the ninth 8137, and in the tenth quarter of a second 100%. The height fallen through, therefore, or the space described by a falling body in a given time, varies as the square of the time of falling; and any body which is to be moved in the same manner as a falling body is moved by gravity, must have the motion imparted to it gradually at the same rate of progression. If, then, we draw a line, x y in fig. 42, and which line we may suppose to be the vertical plane of the keel, then if we form the parallelogram A B C D, with the line x y passing through the middle of it, and make this parallelogram onefourth of the length of the vessel and half the breadth, and divide the line x y into any number of convenient parts or ordinates, say 10, by the vertical co-ordinates numbered from 1 to 10, then if we cause the lengths of these successive and equidistant coordinates, measuring from the line y, to follow the same law of increase that answers to the height through which a body |