Rolling of Ships

Similar, but generally less intensified effects are produced if a ship is proceeding along a channel of restricted breadth. In prac tice the matter is generally of small importance, as restrictions are laid down as to the speed at which ships are allowed to use such channels. An extreme case of the effect of shallowness of water sometimes occurs when towing boats or barges at speeds large enough to cause a solitary wave of translation. The re sistance at larger speeds is then often less than at low. Scott Russell was the first to draw attention to this phenomenon and special canal boats have been built to take advantage of it.

Acceleration.

When the speed of the ship is not uniform the resistance is altered by an amount depending on the acceleration, the inertia of the ship and the motion of the surrounding water. The effect may be regarded as equivalent to a virtual increase in displacement ; and in the "Greyhound" experiments Froude found this increase to be about 20% of the displacement. This value is probably approximately correct for all ships of ordinary form.

The action of a marine propeller consists fundamentally of the sternward projection of a column of water termed the pro peller race. The change of momentum per unit time of this water is equal to the propeller thrust which during steady motion is balanced by the resistance of the ship. If we assume that the passage of the ship does not affect, and is uninfluenced by, the working of the propeller, and neglect all losses of energy except that due to the astern motion of the race, it can be shown that the maximum efficiency is 2 V is the speed of the V ± v ship and v the sternward speed of the propeller race relative to the ship. The quantity v— V is termed the slip and v— v V the slip ratio S. It follows that the maximum theoretical efficiency —S • is given by the expression 1— IS In the ideal case then the best result is obtained when the stern ward velocity imparted to the water is small ; that is, when the propeller acts upon as large a body of water as possible. The efficiency will be small if the slip is large. These tendencies are broadly confirmed in practice but they are modified by the losses incidental to the particular form of propulsive agent adopted. These additional losses are caused by friction of the propelling surfaces, rotation or deflection of the propeller race, shock and turbulent flow. The foregoing considerations apply to propulsion by oars, paddle wheel, hydraulic jet and to the screw propeller. The use of oars and paddle wheels is now generally confined to small vessels in sheltered waterways and the hydraulic jet pro peller owing to internal losses and other factors has up to the present not been employed except for rare and special purposes.

Passing reference may be made to propulsion by sails, ships with aerial propellers and the experimental rotor ship. Such ships are relatively few in number and importance.

The screw propeller is by far the most extensively used espe cially for seagoing ships and the remaining remarks herein have reference to this form of propulsion. If v be the apparent speed of advance of the screw propeller, that is the product of the revolutions and pitch ; and V the speed of the ship carrying the propeller, then the slip is v— V and the apparent slip ratio is v v— V .

This notation corresponds to that previously used, v— V being then defined as the absolute velocity of the race. The pitch of the propeller divided by its diameter is termed the pitch ratio.

The

theory of the action of the screw propeller has been the subject of consideration by many investigators. Professor Ran kine in Trans. I.N.A. 1865 assumed that the propeller impressed change of motion upon the water without change of pressure ex cept such as is caused by the rotation of the race. Sir G. Green hill, Trans. I.N.A. 1888 assumed conversely that the thrust is obtained by change of pressure, the only changes of motion being the necessary circumferential velocity due to the rotation of the screw, and a sufficient sternward momentum to equalize the radial and axial pressures. This idea was further developed by R. E. Froude in 1889 who concluded that the propeller probably obtained its thrust by momentarily impressing an increase of pressure on the water, which eventually results in an increase of velocity about one-half of which was obtained before and one-half abaft the screw. A lateral contraction of the race accompanies each process of acceleration. These general conclusions have been in some degree confirmed by experiments carried out by D. W. Taylor (Proceedings of the American Society of Naval Architects, etc., 1906) and by Professor Flamm, who obtained photographs of a screw race in a glass tank, air being drawn in to show the spiral path of the wake. Professor Burnside (Proceedings London Mathematical Society 1918) considered the problem mathemati cally and confirmed some of R. E. Froude's results; he also took into account in a general way the effect of the proximity of the stern of the ship.