"A Theory," says Admiral Chapman, in his elaborate Treatise concerning the true Method of finding the proper Area of the Sails for Ships of the Line, "which does not agree with practice, does not deserve the name of a Theory." A charge of this kind Captain Gower appears by no means likely to incur.
It will be necessary first to prove that the deeper a moving body be immersed in the water, the greater resistance will it meet in proportion to the depth. This I think will appear clear from the following considerations:
Let A, B, fig. I, be a tube, open at each end, and immersed perpendicular in water, the upper edge A, being on the surface; and let C, be a solid cylindric body, (made nicely to fit the tube, that water may not pass its sides) of equal weight its bulk of water: to this body let a fine line be attached, to move it upwards, by weights hung on at E. Let us presume the body is immersed in the tube, its bottom being even with the division 16, and that the weight of water contained between each division of the tube is exactly one pound, then the whole weight in the tube, above the bottom of the body, will be 16 pounds; of course, before it can be moved upwards, a weight, or power, of something more than 16 pounds must be applied to the line. However, for the sake of avoiding fractions, we will admit that 16 pounds would be sufficient; then, if the body has moved upwards on division, one pound of water will be delivered at the top of the tube, leaving but 15 pounds weight upon the line; when it has moved up wards another division, 14 pounds only will rest upon the line; and so on, the weight of water to be removed will gradually lessen in proportion as the body rises towards the surface. Again, did the body move horizontally, the weight of water to be removed will still be in proportion to the depth. To explain which, admit that the tubes, F and G, be fixed rectangularly to the perpendicular tube, at the divisions 9 and 16; then, were bodies moved horizontally in these tubes, the weight of water above them to be removed, would remain the same throughout their motion; the body in the tube F, would be continually displacing 9 pounds of water, which is proportional to its depth; and the body in the tube G, 16 pounds of water, which also is proportional to its depth. Admitting that the substance of the tubes is suffered to vanish, leaving only the idea of their shape, still the argument will hold good, for the circumambient water will surely perform the duty of the solid tubes, neither admitting the water displaced to go downwards, nor laterally! Evidently then the body is motion, must give motion to a volume of water to the very surface; and as power and resistance are equal, while a body moves uniformly, it follows — that the deeper a moving body be situated, the greater resistance will it meet in proportion to its depth.
This being admitted, let the certain capacity have, in the first instance, the form of a double cube, as Fig 2, and let it have nearly the specific gravity of water, so that when immersed and drawn horizontally, its upper side, A B, may float even with the surface: with a given velocity, admit that the resistance on the upper half of the front be considered as three, (then since resistance is in proportion to the depth immersed) that on the lower half will be six, making the total resistance on the front equal to nine.
It now remains to give the capacity of Fig. 2. such a shape, that it may meet with less resistance while moving at the same velocity. Suppose that it be cut through the dotted line EC, and that the pieces be placed end to end, forming the shape of Fig. 3; if this be drawn through the water with the same velocity as Fig. 2, then the resistance on its front will be but three; one on the upper half, and two upon the lower. Again: divide Fig. 3 in the direction of the dotted line, and place the pieces end to end, forming the shape Fig. 4; then, with the same velocity, the resistance on its front will be but one; and by thus continuing to spread the capacity lengthwise on the surface of the water, the resistance on the front might nearly be done away.
A resistance will also arise from the adhesion of the water to the sides of the body, which, with the same velocity, will increase with the extension of the surface. In the three figures last given, the touching surface is composed of all the sides, except the upper one; and if we admit that Fig. 2. be two cubic feet, then its surface which touches the water, will be 8 feet; Fig. 3. will 9 feet; and Fig. 4. will be 12½ feet.
Since then the total resistance on the body arises from two causes (the most powerful of which is decreasing in the rapid ratio of 9, 3, 1; while the other, trifling in itself, particularly if the surface be even and glib, is increasing only in the much slower ratio of 8, 9, 12½) it follows, that however small the original resistance of adhesion, and however slow the increase of it be from the augmentation of the surface, yet, as the resistance on the front decreases, in time their powers must be equal. This period then must limit the extension of the capacity, for was it still continued to be increased, the resistance arising from adhesion would preponderate, and consequently the total resistance on the body be increasing, to the detriment of its velocity.
As velocity does not increase proportionally with the decrease of resistance, let us examine. by way of removing any false impressions that might arise, what velocity Fig. 4. will move with, if drawn by the same power as Fig. 2. It must be considered that power and resistance are alike, while a body moves uniformly; therefore, (neglecting the resistance arising from adhesion) one and nine are the powers which maintain these two bodies at the same velocity; viz. a velocity of two. Now, were the power nine applied to the body, Fig. 4, it would move with a velocity of 6; for the velocity will increase as the squareroot of the increased power; and the square-root of the first power, or 1, is to the square-root of the increased power, or 3, as the first velocity, 2, is to the acquired velocity, 6.
Notwithstanding the extension of the capacity of a vessel lengthwise, at the surface of the water, is so material to fast sailing, yet it must not be overdone: it must be kept within such limitations, as shall be consistent with the necessary strength required, and celerity of manoeuvring, for vessels will stay and veer slower in proportion to their length. I have thought proper to confine the limits within five breadths to one length of the keel, giving the hull a midship frame, resembling Fig. 5, which continues the same full half the length. Such a midship form, continuing so great a part of the length of the vessel, will produce considerable stability, as the space C is sufficient to hold the iron ballast, which bend placed below the principal floating capacity of the vessel, must, in effect, give the same stiffness that would arise from its having a deep iron keel. The depth of the under water shape, C, will naturally cause the vessel to be weatherly, and will prevent her from rolling with violence. To such a midship form is attached a bow, well calculated to divide the water, and prevent the vessel from diving; together with a stern sufficiently fine to admit of quick steerage.
Transcribed by Lars Bruzelius
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Copyright © 1997 Lars Bruzelius.