The resistance created by the screw itself arises principally from two sources—the resistance to the cutting edge and the tail-edge, and the friction of the surface in contact with the water. The amount of the first may of course be reduced to an unlimited extent by having a fine edge, and practically such edge ought to be much finer than that of the screw of the ‘Archimedes.’
The friction upon the surface will of course materially depend upon the smoothness of that surface, and in the ‘Archimedes’ it was very rough, the iron being corroded at many places, with exfoliations and small holes—the corrosion arising apparently from the galvanic effect produced by the iron and the ship’s copper.
The great number of revolutions required in the screw as compared with those of the paddlewheel, leads a person to assume, without much consideration, that a very high velocity is given to the cutting edges and to the surface of the screw, and consequently that great friction must be produced—this velocity is not, however, nearly so great as it at first appears.
In the present screw of the ‘Archimedes’ the velocity of the extreme point, following its oblique or spiral course, is only about three times that of the vessel, while the average velocity of either of these knife edges or of the surface is not twice that of the vessel.
Now without determining what the actual amount of these resistances may be, we can at once satisfy ourselves that it cannot be very considerable, by comparing it (which we have the means of doing) with the resistance caused by the cutwater and any given portion of the ship’s bottom. The resistance of a knife-edge will be about as the square of the velocity, and if we assume the surface friction to increase in the ratio determined by Colonel Beaufoy—namely, at the 1·75th power, or as the 4th root of the 7th power of the velocity—then the resistance of the knife-edge will be equal to the resistance of a similar edge of about five and a-half times the length of the diameter of the screw moving at the same rate as the vessel, and the surface friction will be equal to that of a piece of the ship’s bottom about six and five-eighth times the area of the screw—or, in the case of the ‘Archimedes,’ the additional power absorbed by the friction of the screw would be about equal to that absorbed by the friction of little more than twice the space of the dead wood which had been cut out to receive the screw—while the knife-edges would be about equivalent to three knife-edges immersed in the water, of the same depth as the ship’s stem.
The actual amount of power absorbed in driving the ‘Archimedes’ screw was probably about twenty horse-power gross, or from ten to twelve nominal horse-power; but I have no doubt that a screw of similar diameter and in good condition would not absorb half that power: and this amount may be still further, and very much reduced, by increasing the relative size of the screw to that of the ship, and thereby reducing the slip, and proportionately reducing the number of revolutions required.
The great extent to which this is capable of being carried will at once be seen when I state that if the ship’s progress were made to be 7 feet instead of 6 feet to each revolution of the screw, which a very slight increase of diameter and pitch of screw would effect, the power absorbed in driving the screw would be diminished in the ratio of the 624 √67 to 724 √77—that is, as 615/4 to 715/4, or about as 3 to 2.
I must repeat here the observation I have previously made, and remind you that these calculations are not introduced as proving, but merely as explaining, that which appears to me proved by the general results of the experiments on the ‘Archimedes’—namely, that the effect produced was, considering all the circumstances, fully proportionate to the power expended, while the experiments and calculations which I have since made also satisfy me that these results may be very much improved upon.
As regards the first of the two heads under which I stated that I proposed to consider the subject, namely, the mere efficiency of the screw as a propeller, I think but one conclusion can be drawn from the results of the experiments quoted, and that is, that as compared with the ordinary paddlewheel of sea-going steamers, the screw is, both as regards the effect produced, and the proportionate power required to obtain that effect, an efficient propeller.
I limit the comparison to the ordinary paddlewheels of sea-going steamers, first, because those are the circumstances which we have alone to consider; and, secondly, because it is possible, by increasing the diameter and breadth of the paddles, which, for the attainment of an adequate object is practicable to any extent in a mere river boat, to render the action of the common paddle all but perfect, and probably more effective than any other propeller.