Having made these general observations, in order to put our readers in possession of the real state of our information respecting the resistance of fluids, and its applications to the science of naval architec ture, we shall offer a few remarks from Chapman, in order that our readers may become acquainted with the views of a man, who, if he did not possess the highest philosophical qualifications, nevertheless, from the great attention he devoted to naval architec ture, and the efforts he made to blend science as much as possible with its practical details, is entitled to considerable attention.
When a ship is at rest, observes Chapman, the pressure of the water upon each of its extremities is the same; but as soon as it is impelled by any force, the pressure is increased at the end opposite to the impulse, and is diminished at that end where it acts.
Again, if a plane be moved in the water, the resist ance is the most forcible when the direction of the motion is perpendicular to the plane, and becomes less as the plane assumes a position more oblique to of motion. Hence bodies of different forms and convexities, with equal bases, experience differ ent resistances.
It is by no means difficult to estimate the resistance which one body meets with from another, when im pinging on it; but the difficulty becomes prodigiously increased when the object is to determine the effect which any medium produces on bodies moved there in. The effect of the impact of bodies on each other is subject to known mechanical laws; but that of me dia upon solid bodies, is, a:i we have before remark ed, almost unknown.
When a body is at rest in water, every part of it immersed in the water, is subject to a pressure per pendicular to its surface, and the degree of pressure produced is some function of the depth of the part subject to the action of the fluid. This is a fact veri fied by daily experience.
When a ship, Fig. 29, Plate CCCCI,XXXIX, is put in motion in still water, with any velocity. it al ways happens that the water upon the extremity A before the greatest breadth C, rises against this part, above the surface at F. This elevation is perceptible at some distance before the ship in the direction of its course. It also extends laterally towards PQ: but beyond the greatest breadth C, the water falls again, so that between C and B it is below its proper level, until it meets in D the part of the fluid which con stantly follows the ship with the same velocity as it self, in order to fill up the void space which it would otherwise leave behind. But as the water which glides along the side of the ship has already filled this space, there is a collision in the fluid in EE, which produces what is called eddy water. This is a thing most ob servable in small vessels, which draw little water; but in large ships the elevation of the water before is not perceptible till they have attained a velocity of 4 or 5 feet in a second. This water, which is before the
greatest breadth, is driven forward with the ship, and so moves in the same direction; and as it is higher before the greatest breadth than abaft, it flows clown a declivity, so as to acquire a velocity in a direction contrary to that of the ship; and moreover, the greater the velocity of the ship, the greater is this declivity.
All this may be readily observed when a ship is na vigated in a sea but little agitated; but when a vessel sails in a channel where there is not more than three or four times the breadth of the ship between it and the sides of the channel, the effect is much more per ceptible, however small may be the velocity.
Hence it follows that the resistance a ship sailing with a given velocity meets with, is increased on ac count of the water's rising before the greatest breadth, and because the ship has to propel a more elevated body of water before it, than at the commencement of its motion; although this column thus elevated and driven a-head, by acting on the water in the direction of its motion, before the body of the ship gets to the same point, in some degree diminishes the resistance.* Secondly; that the resistance is farther increased, be cause the water is lower behind the greatest breadth, and because this water has, moreover, lost in regard to its pressure against the after part of the ship, a force which depends on the velocity of the ship, and also on that with which the fluid flows along the after part of the ship, in running from the greatest breadth of the ship to the stern post.
We shall now proceed to illustrate the method em ployed for estimating the resistance of ships, by sup posing ACBQ, Fig. 30. to be a body formed of two wedges, joined together at their base CQ, the pres sure of the water on which, perpendicular to the sur face, is denoted by FG, FG.
Suppose, in the next place, the body to move with the velocity F11, in a direction parallel to the middle line AB, from B to A. Complete the parallelogram of forces FGII1, and draw its diagonal IF. Produce the line 1H if necessary, to meet AC or CB in K, and draw KL perpendicular to GI. Then will 1L, which forms a part of the first parallelogram of force, repre sent the resistance which the body receives in the di rection BA; and LI, forming a part of the other pa rallelogram of force, denote the effort of the fluid on the hinder part of the body, and which contributes to help it forward in the direction in which it moves.
Let the form of the entire body be limited to the condition that CAI is perpendicular to AB, and that the latter diagonal is bisected by the former. As slime VG = m, and FIT = n; and let the areas of the planes CE, Cl', and CN be respectively denoted by A, 13, and C.
By similar triangles we have, DC KI I = n .
AC' whence 1K n . + 7/1 AC DC and IL — DC . — m) which is the measure