A Catechism of the Steam Engine · Chapter 26Resistance of Vessels in Water
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533. Q.--How do you determine the resistance encountered by a vessel moving in water?
A.--The resistance experienced by vessels moving in water varies as the square of the velocity of their motion, or nearly so; and the power necessary to impart an increased velocity varies nearly as the cube of such increased velocity. To double the velocity of a steam vessel, therefore, will require four times the amount of tractive force, and as that quadrupled force must act through twice the distance in the same time, an engine capable of exerting eight times the original power will be required. 1
534. Q.--In the case of a board moving in water in the manner of a paddle float, or in the case of moving water impinging on a stationary board, what will be the pressure produced by the impact?
A.--The pressure produced upon a flat board, by striking water at right angles to the surface of the board, will be equal to the weight of a column of water having the surface struck as a base, and for its altitude twice the height due to the velocity with which the board moves through the water. If the board strike the water obliquely, the resistance will be less, but no very reliable law has yet been discovered to determine its amount.
535. Q.--Will not the resistance of a vessel in moving through the water be much less than that of a flat board of the area of the cross section?
A.--It will be very much less, as is manifest from the comparatively small area of paddle board, and the small area of the circle described by the screw, relatively with the area of the immersed midship section of the vessel. The absolute speed of a vessel, with any given amount of power, will depend very much upon her shape.
536. Q.--In what way is it that the shape of a vessel influences her speed, since the vessels of the same sectional area must manifestly put in motion a column of water of the same magnitude, and with the same velocity?
A.--A vessel will not strike the water with the same velocity when the bow lines are sharp as when they are otherwise; for a very sharp bow has the effect of enabling the vessel to move through a great distance, while the particles of water are moved aside but a small distance, or in other words, it causes the velocity with which the water is moved to be very small relatively with the velocity of the vessel; and as the resistance increases as the square of the velocity with which the water is moved, it is conceivable enough in what way a sharp bow may diminish the resistance.
537. Q.--Is the whole power expended in the propulsion of a vessel consumed in moving aside the water to enable the vessel to pass?
A.--By no means; only a portion, and in well-formed vessels only a small portion, of the power is thus consumed. In the majority of cases, the greater part of the power is expended in overcoming the friction of the water upon the bottom of the vessel; and the problem chiefly claiming consideration is, in what way we may diminish the friction.
538. Q.--Does the resistance produced by this friction increase with the velocity?
A.--It increases nearly as the square of the velocity. At two nautical miles per hour, the thrust necessary to overcome the friction varies as the 1.823 power of the velocity; and at eight nautical miles per hour, the thrust necessary to overcome the friction varies as the 1.713 power of the velocity. It is hardly proper, perhaps, to call this resistance by the name of friction; it is partly, perhaps mainly, due to the viscidity or adhesion of the water.
539. Q.--Perhaps at high velocities this resistance may become less?
A.--That appears very probable. It may happen that at high velocities the adhesion is overcome, so that the water is dragged off the vessel, and the friction thereafter follows the law which obtains in the case of solid bodies. But any such conclusion is mere speculation, since no experiments illustrative of this question have yet been made.
540. Q.--Will a vessel experience more resistance in moving in salt water than in moving in fresh?
A.--If the immersion be the same in both cases a vessel will experience more resistance in moving in salt water than in moving in fresh, on account of the greater density of salt water; but as the notation is proportionably greater in the salt water the resistance will be the same with the same weight carried.
541. Q.--Discarding for the present the subject of friction, and looking merely to the question of bow and stern resistance, in what manner should the hull of a vessel be formed so as to make these resistances a minimum?
A.--The hull should be so formed that the water, instead of being away driven forcibly from the bow, is opened gradually, so that every particle of water may be moved aside slowly at first, and then faster, like the ball of a pendulum, until it reaches the position of the midship frame, at which point it will have come to a state of rest, and then again, like a returning pendulum, vibrate back in the same way, until it comes to rest at the stern. It is not difficult to describe mechanically the line which the water should pursue. If an endless web of paper be put into uniform motion, and a pendulum carrying a pencil or brush be hung in front of it, then such pendulum will trace on the paper the proper water line of the ship, or the line which the water should pursue in order that no power may be lost except that which is lost in friction. It is found, however, in practice, that vessels formed with water lines on this principle are not much superior to ordinary vessels in the facility with which they pass through the water: and this points to the conclusion that in ordinary vessels of good form, the amount of power consumed in overcoming the resistance due to the wave at the bow and the partial vacuity at the stern is not so great as has heretofore been supposed, and that, in fact, the main resistance is that due to the friction.
[1] This statement supposes that there is no difference of level between the water at the bow and the water at the stern. In the experiments on the steamer Pelican, the resistance was found to vary, as the 2.28th power of the velocity, but the deviation from the recognized law was imputed to a difference in the level of the water at the bow and stern.