Rolling of Ships

Air resistance in itself is generally of little importance on a calm day; and the prejudicial effect of wind and rough weather on the speed of ships is largely due to the action of the waves and cur rents and the irregular motions of the ship. The combined effect on the ship's speed is frequently large but indeterminate. Valuable investigations on ships are being made under sea conditions to ascertain quantitative effects and some useful results have been recorded in Trans. I.N.A.

The difference between the total resistance and that due to skin friction is termed the residuary resistance, the principal component of which is the resistance due to wave-making. The action of the waves is such as to distort the stream lines near the hull, and the form of the waves is in turn affected by the frictional wake; it follows that the frictional and wave-making resistances of a ship are to some extent mutually dependent. It is convenient to neglect the interaction of these constituents and treat each independently ; and practical justification for this assumption is furnished by the close agreement between the results of experiments on models and on ships, where the proportion of frictional to total resistance differs greatly.

Wake.

Since the action and the reaction of the water pressure on the hull of a ship are equal and opposite, forward momentum is generated in the water such that the increase of momentum per second is equal to the total resistance. The water participating in the forward movement is termed the wake; and the portion of the wake in the vicinity of the propellers has a considerable effect upon the propulsion of the ship. Experiments on a model were made by Mr. Calvert (Trans. I.N.A. 1893) to determine the wake velocity. The magnitude of the wake was measured at various positions in the length and its maximum velocity was found to be 0.67 times the speed of the model. Abreast the screw the mean velocity ratio over an area of the same breadth as the model and of depth equal to the draught was 0.19 ft. of which about 0.05 ft. was ascribed to frictional resistance. A theoretical investigation by Froude in Reports of the British Association 1874 suggests the approximate extent of the frictional wake and its velocity distri bution based on the equality of the resistance to the momentum added per second. It is to be noted that when a ship is propelled in the ordinary way at uniform speed the momentum generated in the sternward race from the propeller is equal and opposite to that of the forward wake due to the hull ; the motion of the water as a whole thus consists of a circulatory disturbance advancing with the ship but having no linear momentum.

Frictional Resistance.

Practically the whole of the resist ance at low speeds and a considerable proportion of it at higher speeds is due to surface friction. Its magnitude is usually esti mated from the results of experiments made by towing planks coated with various surfaces. The most important of such experi ments were those made in 1871 by Froude in the experiment tank at Torquay, to obtain the laws of variation of resistance with the speed, the length and the nature of the surface. A dynamometric apparatus by which the planks were towed was used to register the resistance ; the planks were given a fine edge at each end to avoid eddy-making and were fully immersed in order that no waves should be formed. For the complete results see Reports of the British Association 1872 and 1874; but the following extract gives a summary, n being the index of the speed at which the resistance varies, A the mean resistance per square foot of sur face over the length stated, and B the resistance per square foot at the after end of the plank; both A and B refer to a velocity of io ft. per second in fresh water.

R

being the frictional resistance, S the area of surface, V the speed, w the density of the water, f a coefficient depending on the nature and length of the surface, and n the index of the speed; the values of f and n are obtained from the above table. The resistance then varies as the density of the water, but is independent of its pres sure; it diminishes as the length of the surface increases on account of the frictional wake which reduces the relative velocity between the water and surface towards the after end. The index n is 1.83 for a varnished surface equivalent to the freshly painted hull of a ship. When applying the data to ships of length greater than 5o ft. the coefficient B denoting the resistance so ft. from the bow, is assumed to remain unaltered at all greater distances astern. The velocity of rubbing is assumed equal to the speed of the ship, any variation due to stream-line action being neglected. The wetted surface S when not directly calculated can be estimated by ap proximate formulae.