Rolling of Ships

Many other reliable experiments have been made on the resist ance of smooth planks from time to time. The results obtained are all in reasonable agreement with Froude's, with the exception of those due to Gebers, in whose experiments particular care was taken to obtain an exceptionally smooth surface and to eliminate parasitic resistance. In general, coatings of varnish and many other compounds give about the same resistance if the surface is reasonably smooth and hard ; and it is assumed that the coefficients for the varnished planks can be applied to the freshly painted ship's surface. Alternative extrapolation of the plank data has been proposed by Baker and also by Gebers. These give ship resistances somewhat less than Froude's, but so far Froude's results are almost universally used with practical success. The subject is continuously under investigation and experimenters are seeking to formulate, if possible, a more rigorous basis for assess ing the skin friction resistance of ships. The plank results are intended for application to a ship with clean surface. After the ship has been some time out of dock the growth of weeds and barnacles causes a considerable increase in skin friction resist ance.

Wave Resistance.

The resistance due to wave making, incon siderable at low speeds, is of importance at moderate speeds and constitutes the greater portion of the total resistance at high speeds. As already stated it is convenient to regard the problem as one of steady motion in a stream flowing past a stationary ship. The stream tubes, originally of uniform width, become broader on approaching the bow of the ship and attain their greatest breadth close to the stem. Near amidships the tubes become smaller and enlarge again near the stern. The changes in size and velocity in the stream tubes lead to corresponding alterations of pressure in accordance with the energy equation, and these altera tions appear as elevations and depressions of the surface forming the statical wave system. If this were a permanent system, no resistance to the motion of the ship would result. But the sur face disturbance is subject to the dynamical laws 'underlying the propagation of waves; and consequently the wave formation differs from the statical wave, the crest lagging astern of the statical wave crest, and the ship is followed by a train of waves whose lengths are appropriate to the speed. The energy in the wave system travels backward relative to the ship at one-half its speed; and the resistance to the ship's motion is due to the stern ward drain of the wave energy which has to be replaced by work done on the ship.

The form of the wave system is not susceptible of complete mathematical investigation ; but the circumstances are approxi mately realized and the conditions considerably simplified when the actions of the bow and stern of the vessel are each replaced by the mathematical conception of a "pressure point." This consists of an infinitely large pressure applied over an indefinitely small region of the water surface ; it is assumed to move forward in place of the ship through still water, or, equally, to be stationary in a uniform stream. The resulting wave system has been investi

gated by many investigators, including Lord Kelvin. Recently the theory has been still further developed ; and it is possible to cal culate the wave resistance of simple ship-shape forms by purely mathematical methods with a fair degree of accuracy. All the results are in agreement in many respects with those of actual observation for ships and models.

The figure, reproduced from Froude's, Trans. I.N.A. 1877, shows the bow-wave system obtained from a model; this is illus trative of that produced by ships of all types.

Two types of waves accompany a ship—(I) diverging waves having sharply defined crests placed in echelon, the foremost wave alone extending to the ship; (2) transverse waves limited in breadth by the diverging crests and reaching the sides of the vessel throughout its length. Since the bow diverging waves are not in contact with the ship, except at the bow, the energy spent in their maintenance travels away from the ship and is lost en tirely. A diverging wave system of similar form but smaller dimensions attends the passage of the stern; and the resistance due to the diverging system of waves is the sum of its components at the bow and stern, increasing with the speed, and depending con siderably on the shape of the bow and stern.

On the other hand the combined transverse bow and stern wave systems produce a stern wave in contact with the ship, and the resistance due to the resultant transverse wave system depends on the phase relation between the waves of the two systems. The effect of the combination on the wave resistance was investigated by Froude (Trans. I.N.A. 1877) by means of experiments on a series of models having the same ends, but in which the length of parallel middle body was varied. At constant speed, curves of residuary resistance on a length base consisted of humps and hollows, the spacing of which was constant for a given speed and approximately equal to the wave length appropriate to the speed ; the amplitude of the fluctuation diminished as the length increased. For a given length the residuary resistance in general increased at a high power of the speed; but it was also subject to a series of fluctuations whose magnitude and spacing increased with the speed. A full analysis was made by R. E. Froude in 1881, and showed that a reduction in resistance occurred when the echo of the bow wave crest coincided with the trough of the stern wave; and conversely that the resistance was abnormally increased when the crests of the two systems coincided. The fluctuation in the resistance was smaller when the length of middle body was greater, owing to the greater degradations of the bow wave sys tem at the stern through viscosity and lateral spreading. With very considerable lengths of middle body, the height of the bow wave system at the stern was insufficient to produce interference or to affect the resistance.