260 MANOEUVRING The spiral manoeuvre This is a manoeuvre aimed at giving a feel for a ship's directional stability. From an initial straight course and steady speed the rudder is put over say 15° to starboard. After a while the ship settles to a steady rate of turn and this is noted. The rudder angle is then reduced to 10° starboard and the new steady turn rate noted. This is repeated for angles of 5°S, 5°P, 10°P, 15°P, 10°P and so on. The resulting steady rates of turn are plotted against rudder angle. (a) Figure 10.4 Spiral manoeuvre If the ship is stable there will be a unique rate of turn for each rudder angle. If the ship is unstable the plot has two 'arms' for the smaller rudder angles, depending upon whether the rudder angle is approached from above or below the value. Within the rudder angles for which there is no unique response it is impossible to predict which way the ship will turn, let alone the turn rate, as this will depend upon other disturbing factors present in the ocean. The manoeuvre does not give a direct measure of the degree of stability, although the range of rudder angles over which response is indeterminate is a rough guide. To know the minimum rudder angle needed to ensure the ship turns in the desired direction is very useful. MANOEUVRING 261 The pull-out manoeuvre This manoeuvre 1 is also related to the directional stability of the ship. The rudder is put over to a certain angle and held until the ship is turning at a steady rate. The rudder is returned to amidships and the change in the turn rate with time is noted. For a stable ship the turn rate will reduce to zero and the ship takes up a new steady straight line course. A plot of the log of the rate of turn against time is a straight line after a short transition period. If the ship is unstable the turn rate will riot reduce to zero but there will remain some steady rate of turn. The area under the plot of turn rate against time gives the total heading change after the rudder angle is taken off. The smaller this is the more stable the ship. If the ship is conducting turning trials it will be in a state of steady turning at the end of the run. If the rudder is centred the pull-out manoeuvre can be carried out immediately for that speed and rudder angle. MANOEUVRING DEVICES Rudder forces and torques Rudder forces Rudders are streamlined to produce high lift with minimum drag. They are symmetrical to produce the same lift characteristics whichever way they are turned. The force on the rudder, F, depends upon the cross- sectional shape, area A, the velocity Vthrough the water and the angle of attack a. The constant depends upon the cross section and the rudder profile, in particular the ratio of the rudder depth to its chord length and the degree of rounding off on the lower corners. The lift is also sensitive to the clearance between the upper rudder surface and the hull. If this is very small the lift is augmented by the mirror image of the rudder in the hull. f(a) increases roughly linearly with a up to the stall angle which is typically about 35°. f(a) will then decrease. Various approximate formulae have been proposed for calculating F. An early one was: In this an allowance was made for the effect of the propeller race by multiplying Fby 1.3 for a rudder immediately behind a propeller and 262 MANOEUVRING by 1.2 for a centreline rudder behind twin screws. Other formulations based on the true speed of the ship are: The first two were proposed for twin rudders behind twin screws and the third for a centreline rudder behind a single screw. If wind or water tunnel data is available for the rudder cross section this should be used to calculate the lift and the centre of pressure position. Typically the rudder area in merchant ships is between ^ and ^ of the product of length and draught. Rudder torques To establish the torque needed to turn a rudder it is necessary to find the position on the rudder at which the rudder force acts. That position is the centre of pressure. For a rectangular flat plate of breadth B at angle of attack a, this can be taken as (0.195 + 0.305 sin a) B aft of the leading edge. For a typical rudder section it has been suggested 2 that the centre of pressure for a rectangular rudder can be taken at K X (chord length) aft of the leading edge, where: The open water figure is used for both configurations for a ship going astern. For a non-rectangular rudder an approximation to the centre of pressure position can be obtained by dividing the rudder into a number of rectangular sections and integrating the individual forces and moments over the total area. This method can also be used to estimate the vertical location of the centre of pressure, which dictates the bending moment on the rudder stock or forces on the supporting pintles. Example 10.1 A rudder with an area of 20 m 2 when turned to 35° has the centre of pressure 1.2m from the stock centreline. If the ship speed is 15 knots, and the rudder is located aft of the single propeller, calculate the diameter of the stock able to take this torque, assuming an allowable stress of 70 MN/m 2 . MANOEUVRING 263 Solution Using the simple formula from above to calculate the rudder force and a factor of 1.3 to allow for the screw race: This can be equated to qf/r where r is the stock radius, q is the allowable stress, and/is the second moment of area about a polar axis equal to Jtr 4 /^. Hence In practice it would be necessary to take into account the shear force and bending moment on the stock in checking that the strength was adequate. The bending moment and shear forces will depend upon the way the rudder is supported. If astern speeds are high enough the greatest torque can arise then as the rudder is less well balanced for movements astern. Rudder types The rudder is the most common form of manoeuvring device fitted in ships. Its action in causing the ship to turn has already been discussed. In this section it is proposed to review briefly some of the more common types. Conventional rudders These have a streamlined section to give a good lift to drag ratio and are of double-plate construction. They can be categorized according to the degree of balance. That is how close the centre of pressure is to the rudder axis. A balanced rudder will require less torque to turn it. They are termed balanced, semi-balanced or unbalanced. The other method of categorization is the arrangement for suspending the rudder from the 264 MANOEUVRING hull. Some have a pintle at the bottom of the rudder, others one at about mid depth and others have no lower pintle. The last are termed spade rudders and it is this type which is most commonly fitted in warships. Different rudder types are shown in Figures 10.5 to 10.7. The arrangements are self explanatory. (b) Figure 10.5 Balanced rudders (a) Simplex; (b) Spade MANOEUVRING 265 Figure 10,6 Unbalanced rudder Special rudders A number of special rudders have been proposed and patented over the years. The aim is usually to improve the lift to drag ratio achieved. A. flap rudder, Figure 10.8, uses a flap at the trailing edge to improve the lift by changing aerofoil shape. Typically, as the rudder turns, the flap goes to twice the angle of the main rudder but in some rudders the flaps can be moved independently. A variant is the Flettner rudder which uses two narrow flaps at the trailing edge. The flaps move so as to assist the main rudder movement reducing the torque required of the steering gear. 266 MANOEUVRING Figure 10.7 Semi-balanced rudder Figure 10.8 Flap rudder In semi-balanced and unbalanced rudders the fixed structure ahead of the rudder can be shaped to help augment the lateral force at the rudder. Active rudders These are usually spade type rudders but incorporating a faired housing with a small electric motor driving a small propeller. This provides a 'rudder' force even when the ship is at rest when the hydrodynamic forces on the rudder would be zero. It is used in ships requiring good manoeuvrability at very low speeds. MANOEUVRING 267 The Kitchen rudder This rudder is a two-part tube shrouding the propeller and turning about a vertical axis. For ahead propulsion the two halves of the tube are opened to fore and aft flow. For turning the two halves can be moved together to deflect the propeller race. The two halves can be moved to block the propeller race and reverse its flow. Figure 10,9 Kitchen rudder Vertical axis propeller This type of propeller is essentially a horizontal disc carrying a number of aerofoil shaped vertical blades. As the disc turns the blades are caused to turn about their vertical axes so that they create a thrust. For normal propulsion the blades are set so that the thrust is fore and aft. When the ship wishes to turn the blades are adjusted so that the thrust is at an angle. They can produce lateral thrust even at low ship speed. Lateral thrust units It is sometimes desirable to be able to control a ship's head and course independently. This situation can arise in mine countermeasure vessels which need to follow a certain path relative to the ground in conditions 268 MANOEUVRING Figure 10.10 Vertical axis rudder (a) Construction (b) Operation MANOEUVRING 269 of wind and tide. Other vessels demanding good positional control are offshore rigs. This leads to a desire to have the ability to produce lateral thrusts at the bow as well as the stern. It has been seen that bow rudders are likely to be ineffective because of their proximity to the neutral point. The alternative is to put a thrust unit, usually a contra-rotating propeller, in a transverse tube. Such devices are called lateral thrust units or bow thrust units when fitted forward. Their efficiency is seriously reduced by a ship's forward speed, the thrust being roughly halved at about two knots. Some offshore rigs have dynamic positional control provided by a number of computer controlled lateral thrust units. SHIP HANDLING Several aspects of the handling of a ship are not brought out by the various manoeuvres discussed above. Handling at low speed At low speed any hydrodynamic forces on the hull and rudders are small since they vary as the square of the speed. The master must use other means to manoeuvre the ship, including: (1) Using one shaft, in a twin shaft ship, to go ahead while the other goes astern. (2) When leaving, or arriving at, the dockside a stern or head rope can be used as a pivot while going ahead or astern on the propeller, (3) Using the so-called paddle wheel effect which is a lateral force arising from the non-axial flow through the propeller. The force acts so as to cause the stern to swing in the direction it would move had the propeller been a wheel running on a hard surface. In twin screws the effects generally balance out when both shafts are acting to provide ahead or astern thrust. In coming alongside a jetty a short burst astern on one shaft can 'kick' the stern in towards the jetty or away from it depending which shaft is used. (4) Using one of the special devices described above. For instance a Kitchen rudder, a vertical axis propeller or a lateral thruster. Interaction between ships As discussed in Chapter 8 on resistance a ship creates a pressure field as it moves through the water. The field shows a marked increase in pressure near the bow and stern with a suction over the central portion of the ship. This pressure field acts for quite an area around [...]... natural Figure 11 ,3 (a) Two-node; (b) Three-node; (c) Four-node VIBRATION, NOISE AND SHOCK 2 83 Table 11.1 Typical ship vibration frequencies Shift type Length (m) Condition of loading Frequency . are shown in Figures 10. 5 to 10. 7. The arrangements are self explanatory. (b) Figure 10. 5 Balanced rudders (a) Simplex; (b) Spade MANOEUVRING 265 Figure 10, 6 Unbalanced rudder Special . above to calculate the rudder force and a factor of 1 .3 to allow for the screw race: This can be equated to qf/r where r is the stock radius, q is the allowable stress, and/is . the diameter of the stock able to take this torque, assuming an allowable stress of 70 MN/m 2 . MANOEUVRING 2 63 Solution Using the simple formula from above to calculate the rudder force