9-Manoeuvring - Rudders & Propellers (2012)

Manoeuvring – Rudders & Propellers MANOEUVRING – RUDDERS & PROPELLERS MODULE Note: These notes are drawn from those issued by Dr Jonathan Duffy to students of JEE329 Seakeeping & Manoeuvring at the Australian Maritime College Dr Duffy has used edited extracts from the main reference books for the subject and which are listed at the end of the module Rudders – In General All ships must possess some means of directional control Typically, a rudder is fitted at the stern of the ship to achieve a certain level of directional control It is important to note that the rudder acts as a servo-system causing the hull to develop a drift angle, which in turn develops hydrodynamic forces and moments on the hull that cause the ship to turn When the rudder is deflected a lateral force is generated that creates a moment to turn the ship This turning action causes the ship to develop an angle of attack with respect to its motion through the water, which in turn develops hydrodynamic forces and moments on the hull that augment the rudder moment and cause the ship to turn Rudders are fitted near the stern as the side force produced by the rudder has the largest lever arm from the centre of rotation to provide the largest possible yawing moment to the ship Also, by placing the rudder behind the propeller means that the water velocity over the control surface is increased, hence increasing the effectiveness of the rudder Rudder Geometry − Definitions Typical rudder geometry is shown in Figure Some definitions for the study of rudders are as follows: Mean span: average of the spans of the leading and trailing edges of the rudder Mean chord: average fore and aft distance between the leading edge and the trailing edge Aspect ratio: the ratio of the mean span to the mean chord Profile area: the projected (or plan form) area Taper ratio: the ratio of the tip chord to the root chord Sweepback angle: the angle between the quarter chord line and a line perpendicular to the centerline of the ship Manoeuvring – Rudders & Propellers Angle of attack: angle between the mean chord line and the hydrodynamic inflow direction Lift: is the component of the resultant force on a rudder that is perpendicular to the hydrodynamic inflow direction (see Figure 48) 𝐿𝑖𝑓𝑡 Lift coefficient (𝐶𝐿 ): 𝐶𝐿 = 2𝜌𝐴 𝑉 (63) Drag: is the component of the resultant force on a rudder parallel to the hydrodynamic inflow direction (see Figure 2) Lift coefficient (𝐶𝐷 ): 𝐶𝐷 = 𝐷𝑟𝑎𝑔 2𝜌𝐴 𝑉 (64) Centre of pressure: is the point on the rudder through which the resultant force may be considered to act (approximately chord line for deep unrestricted water) Camber: the maximum distance between the chord line and the mean line, which lies half way between the outer surfaces of a foil ROOT SECTION centreplane axis of rotation hull line centreplane root chord root thickness CR/4 trailing edge leading edge CoP mean thickness mean geometric chord mean span quarter chord line tip thickness tip chord PROFILE CT/4 EDGE PROFILE Figure Terms used to describe rudder geometry Manoeuvring – Rudders & Propellers normal force, F total resultant force  lift, L drag, D rudder stock  ambient stream velocity axial force CoP Figure Lift and drag on a rudder 2.1 Types of Rudder Examples of typical rudders are shown in Figure Spade rudders are commonly installed on ferries and ro-ro ships With this type of rudder the rudder stock is subjected to high bending moments, especially when the rudder height is large and the ship speed is high The balanced rudders typically have reduced bending moments compared to spade rudders, but are not as effective as spade rudders for an equivalent area Figure Various rudder fin arrangements (Saunders 1965) (taken from Lewis 1989) Manoeuvring – Rudders & Propellers A schematic of a flap rudder is shown in Figure This type of rudder consists of a moveable rudder with a trailing edge flap activated by a mechanical or hydraulic system, thus producing a variable flap angle as a function of rudder angle Flap rudders produce a much larger lift compared to a conventional rudder of the same shape, size and area Figure Flap rudder 2.2 Rudder (Steering) Motor When a rudder command is given it will take some time for the rudder rate to increase to its maximum and then it will decrease gradually to zero as the required rudder angle is reached When designing a ship it is important to ensure that the rudder can be turned at a rate sufficient to allow adequate manoeuvrability of the ship In a ship-handling simulator the rudder turn rate is modelled mathematically and most models apply a constant rudder turning rate Care must be taken to ensure that when the rudder angle reaches desired rudder angle it does not oscillate Flow Over the Rudder The water velocity over the rudder is generated by its movement through the water, but may also be significantly influenced by the ship and propeller ahead of it For example, the increase in water velocity over the rudder due to the propeller can significantly increase the force and moment produced by the rudder If the rudder is well clear of the influence of the ship and propeller then it will experience the following water flow over it: Manoeuvring – Rudders & Propellers X direction: 𝑢 Y direction: 𝑣𝑙𝑜𝑐𝑎𝑙 = 𝑣 + 𝑟𝑥 When the rudder is sufficiently close to be influenced by the ship hull and propeller there will be three additional effects on the water velocity over the rudder: The ship wake, which reduces the water velocity to the speed of advance 𝑢𝑎 The propeller race increasing the water velocity over the rudder The angle of the flow into the rudder in a turn To determine the rudder forces and moments we must know the flow velocity and direction over the rudder The points above are discussed in greater detail below 3.1 Effect of Wake The effect of the ship’s wake can be determined in the usual way, i.e.: 𝑢𝑎 = 𝑢(1 − 𝑤) (65) Where 𝑤 is the wake fraction 3.2 Effect of Propeller Race The effect of the propeller race depends upon the proportion of the rudder in the propeller wash, which will depend on whether the rudder is located immediately behind the propeller (not the case for twin screw, single rudder ships) and on the relative size of the propeller diameter and rudder span When dealing with the propeller race it is also necessary to consider four different possible combinations of propeller thrust direction and ship direction: Ship going ahead, thrust ahead Ship going ahead, thrust astern Ship going astern, thrust astern Ship going astern, thrust ahead For the case with ship going ahead, thrust ahead the rudder is experiencing the full effect from the flow from the propeller in addition to the influence of the forward speed of the vessel, modified by the hull wake One possible empirical representation of this is given by Renilson (2003) as follows: 𝑢𝑟𝑢𝑑𝑑𝑒𝑟 = 𝑢𝑎 + 𝑘𝑝𝑟 𝑢𝑎2 + 𝑇 0.5𝜌𝐴 − 𝑢𝑎 𝑝 (66) Where Manoeuvring – Rudders & Propellers 𝑘𝑝𝑟 is the propeller race factor, an empirically determined factor which is a function of the proportion of rudder behind the propeller 𝑇 is the propeller thrust 𝐴𝑝 is the area of the propeller Note that this is only one possible empirical representation of this effect If the thrust, T, is zero the flow velocity over the rudder is 𝑢𝑎 , and if the speed of the ship is zero the flow velocity over the rudder is dependent on the thrust from the propeller If the value of 𝑘𝑝𝑟 is zero (for example if the propeller is not directly ahead of the rudder) then the thrust will not influence the flow velocity over the rudder at all For the two cases with the thrust astern the propeller’s influence on the flow over the rudder will be very complex due to the thrust being astern As the effect is likely to be small it may well be adequate to ignore it (Renilson 2003), giving the following: 𝑢𝑟𝑢𝑑𝑑𝑒 𝑟 = 𝑢𝑎 (ship going ahead) (67) 𝑢𝑟𝑢𝑑𝑑𝑒𝑟 = 𝑢 (ship going astern) (68) A possible empirical representation for the case with the ship going astern, thrust ahead is given by Renilson (2003), as follows: 𝑢𝑟𝑢𝑑𝑑𝑒𝑟 = 𝑢 + 𝑘𝑝𝑟 𝑇 0.5𝜌𝐴𝑝 (69) Note that this is only one possible empirical representation It can be seen that it does satisfy the boundary conditions if either the thrust or the ship speed are zero 3.2 Effect of Flow Angle to the Rudder In a Turn When a rudder angle is applied the ship develops a drift angle, 𝛽 This drift angle causes a cross flow at the end of the ship in the vicinity of the rudder, which leads to a decrease in the effective inflow angle to the rudder The effects of the propeller and hull upstream from the rudder typically straighten the flow, which leads to an increase in the effective flow angle to the rudder The influence of these two effects counter one another and they must be known in order to predict the flow over the rudder It is worth noting that in a 35 degree rudder angle turn the effective rudder angle can be as low as 10 -15 degrees due to the effects outlined above (Renilson 2003) Lift & Drag Characteristics of a Rudder A rudder in a flow will experience a lift and drag force, as illustrated in Figure Once the water speed over the rudder and its effective angle of attack are known, the lift and drag on the rudder can be determined from the lift and drag characteristics of a lifting surface Manoeuvring – Rudders & Propellers with the same aspect ratio, plan form and cross section shape This information is provided for a wide range of lifting surfaces in a variety of publications When calculating the lift and drag characteristics of a rudder the gap between the rudder and the hull should be considered Lewis (1989) states the following: “A control surface of infinite aspect ratio has the same flow pattern in all planes perpendicular to the span.” In other words, there is no flow component along the span and the flow over any section of the control surface is strictly two-dimensional However, in the case of a finite aspect ratio, cross flow does occur over the root and over the tip from the high-pressure side to the low pressure side, thus causing the flow over all sections to be three-dimensional This cross flow increases with decreasing span, and causes a concomitant decrease in the lift generated by the rudder for any given angle of attack The preceding physical picture leads to the concept of effective aspect ratio If the root section of a control surface is sufficiently close to the hull that all cross flow over the root is prevented, the lift coefficient developed by that control surface for any given angle of attack is identical to that of a control surface of twice its geometric aspect ratio Figure shows this doubling effect by projecting a “mirror image” of a control surface flush against a ground-board In computing the lift generated, the area of control surface to use is that bounded by the solid lines, but its effective aspect ratio is 2𝑠 𝑐 rather than 𝑠 𝑐.” Figure Control surface against ground-board (Lewis 1989) There will usually be a gap between the root of a ship’s rudder and the hull, which will constrain the flow somewhat, but will permit some leakage Determining the effective aspect ratio in such cases is difficult, however a value of about 1.8 times the geometric aspect ratio is often accurate enough (Renilson 2003) The other consideration is that the shape of the hull usually will result in an increasing gap as the rudder is put over This is difficult to account for and is usually neglected Manoeuvring – Rudders & Propellers The lift coefficient is typically a linear function of the hydrodynamic inflow direction Typical curves for lift coefficient are shown in Figure Figure Example of typical lift coefficient curves for a rudder as a function of hydrodynamic inflow direction It can be seen from Figure that the lift coefficient decreases at a certain angle of attack This is where stall occurs, which is illustrated in Figure It is important that a rudder does not operate at hydrodynamic inflow angles sufficient to cause stall as the effectiveness of the rudder can be severely reduced once stall occurs Once the above factors have been considered the lift and drag coefficients as functions of angle of attack can be obtained The lift and drag can then be obtained for the desired angle of attack as follows: 𝐿𝑖𝑓𝑡 = 𝜌𝑢𝑟𝑢𝑑𝑑𝑒𝑟 𝐴𝑟𝑢𝑑𝑑𝑒𝑟 𝐶𝐿 (70) 𝐷𝑟𝑎𝑔 = 𝜌𝑢𝑟𝑢𝑑𝑑𝑒𝑟 𝐴𝑟𝑢𝑑𝑑𝑒𝑟 𝐶𝐷 (71) Manoeuvring – Rudders & Propellers Figure Rudder stall 4.1 Rudder Forces & Moments Once the lift and drag have been obtained it is necessary to convert them to side force From Figure 48 it can be seen that the sway force on the rudder is: 𝑌𝑟𝑢𝑑𝑑𝑒𝑟 = ± 𝐷𝑟𝑎𝑔 × 𝑠𝑖𝑛𝛿𝐸 + 𝐿𝑖𝑓𝑡 × 𝑐𝑜𝑠𝛿𝐸 (72) The yaw moment due to the rudder can then be calculated using: 𝑁𝑟𝑢𝑑𝑑𝑒𝑟 = 𝑌𝑟𝑢𝑑𝑑𝑒 𝑟 × 𝑥𝑟𝑢𝑑𝑑𝑒𝑟 (73) Where 𝑥𝑟𝑢𝑑𝑑𝑒𝑟 is the distance from the centre of pressure of the rudder to the origin From Figure 48 it can be seen that the surge force on the rudder is: 𝑋𝑟𝑢𝑑𝑑𝑒𝑟 = 𝐿𝑖𝑓𝑡 × 𝑠𝑖𝑛𝛿𝐸 − 𝐷𝑟𝑎𝑔 × 𝑐𝑜𝑠𝛿𝐸 (74) 4.2 Rudder Size & Effectiveness When designing a new ship it is necessary to establish if the proposed rudder is adequate to provide the level of manoeuvrability desired A method that can be used as a first step without Manoeuvring – Rudders & Propellers requiring calculation of the rudder forces and moments was developed by Det Norske Veritas (DNV Rules 1975) to assess the minimum rudder area, as follows: 𝐴𝑅 = 𝑑×𝐿𝐵𝑃 100 + 25 𝐵 𝐿𝐵𝑃 (75) Where 𝐴𝑅 = rudder area 𝑑 = draught 𝐿𝐵𝑃 = length between perpendiculars 𝐵 = beam Another approach to determining whether a rudder is adequate is by comparing the forces and moments produced by the rudder with the forces and moments produced on the hull when it is moved in the horizontal plane Strictly the forces and moments on the hull should be due to a combination of sway velocity and yaw velocity, but for simplified studies the sway force and yaw moment due to sway velocity can be compared separately to the sway force and yaw moment due to yaw velocity Therefore the steps to assess the effectiveness of a rudder in a simplified manner are:    Calculate the side force produced by the rudder and the yawing moment due to the rudder Compare the rudder sway force and yaw moment to the sway force and yaw moment on the hull due to sway velocity to determine the ability of the rudder to hold the hull at a given angle of attack and thus cause the ship to turn Compare the rudder moment to the rotational inertia of the ship to assess the ability of the rudder to start rotating the ship A more in depth approach to determine whether a rudder design is adequate is to obtain the hydrodynamic coefficients for the hull and rudder by either conducting model scale experiments or through using theoretical approaches and use these coefficients as input to a simulation program to enable assessment of the ship’s performance Propellers 5.1 Propeller Thrust & Torque When numerically simulating ship manoeuvring the propeller thrust and torque can be represented using conventional propeller theory It is usual to non-dimensionalise thrust and torque as follows: 𝑇 𝐾𝑇 = 𝜌 𝑛 𝐷 𝑄 𝐾𝑄 = 𝜌 𝑛 𝐷 (76) (77) The speed of advance is non-dimensionalised as follows: 𝑢 𝐽 = 𝑛𝐷𝑎 (78) 10 Manoeuvring – Rudders & Propellers Propeller Asymmetry Effects When a ship has an odd number of propellers substantial forces and moments can be exerted on a ship travelling in a straight line due to propeller asymmetry effects The propeller asymmetry effects can be exaggerated in shallow water Thus, in order to sail a straight course, such ships must carry a small rudder angle, and a small drift angle, also known as neutral angles The forces induced by an odd number of operating propellers can be categorized as follows:   Direct (forces on the ship from the propeller) Indirect (modification of flow around the ship’s hull) 6.1 Direct Propeller Asymmetry Effects – Ship Travelling in a Straight Line The first direct propeller effect is due to the upward flow into the propeller due to a typical hull shape in the stern region Let us consider a right handed propeller (rotating clockwise when viewed from the stern) Due to the upward flow into the propeller the force on the starboard side blade in the horizontal position is greater than that on the port blade As a result the centre of pressure moves off the centreline of the propeller to the starboard side causing the ship to turn to port The second direct effect is due to the wake field typically being stronger for the top blade and that the flow is typically more sideways for the top blade due to the hull geometry forward of the propeller The result is that the ship hull experiences a net force to port causing a turn to starboard 6.2 Indirect Propeller Asymmetry Effects – Ship Travelling in a Straight Line The first indirect effect is due to the change in pressure distribution around the stern region due to the operating propeller The flow speed around the propeller is increased The reduction in pressure due to the propeller action is less on the port side than on the starboard side for a right handed propeller This effect is small and causes the ship to turn to port The major indirect effect of the propeller is on the rudder The loading on the blades is higher in the upper region of the propeller causing a higher tangential flow velocity onto the rudder behind the upper blades The lateral force to starboard caused by the tangential flow from the propeller onto the higher part of the rudder is larger than the force to port caused by the tangential flow from the propeller onto the lower part of the rudder The result is that the ship turns to port It should be noted that the above effects are for forward straight line motion In a turn additional forces act due to the change in angle of attack of the propeller blades 6.3 Propeller Transverse Thrust The transverse thrust from the propeller can be a very important factor in manoeuvring a ship at low speeds and for realistic simulation this must be modelled accurately 11 Manoeuvring – Rudders & Propellers For the simplest case the transverse thrust can be taken to be a linear function of ahead thrust and can therefore be obtained as follows: 𝑌𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑒 = 𝑌𝑇 𝑇 (79) Note that for a controllable pitch propeller which does not reverse when the thrust is reversed the direction of the side force will not change The yawing moment due to transverse thrust from the propeller can be obtained as follows: 𝑁𝑝𝑟𝑜𝑝𝑒𝑙𝑙𝑒𝑟 = 𝑌𝑇 𝑥𝑝 𝑇 − 𝑦𝑝 𝑇 (80) Where 𝑥𝑝 is the distance from the origin to the propeller and 𝑦𝑝 is the transverse distance from the propeller to the ship centerline Note that this assumes the shafts are parallel For single screw ships 𝑦𝑝 is usually zero Acknowledgements The primary reference sources used for these notes are acknowledged below   Renilson, M.R., 2003, Ship Manoeuvring, Lecture Notes, Australian Maritime College Lewis, E (Ed), 1989, Principles of Naval Architecture, Volume III, Motions in Waves and Controllability, SNAME, New York References Clarke, D., Gedling, P., Hine, G., The Application of Manoeuvring Criteria in Hull Design using Linear Theory, TRINA, 1982 Crane, C.L 1979, Manoeuvring trials of 278,000 DWT tanker in shallow and deep waters, SNAME Transactions, vol 87 Lewis, E (Ed), 1989, Principles of Naval Architecture, Volume III, Motions in Waves and Controllability, SNAME, New York Renilson, M.R., 2003, Ship Manoeuvring, Lecture Notes, Australian Maritime College 12 ... Manoeuvring – Rudders & Propellers Figure Rudder stall 4.1 Rudder Forces & Moments Once the lift and drag have been... 10 Manoeuvring – Rudders & Propellers Propeller Asymmetry Effects When a ship has an odd number of propellers substantial forces and... drag on a rudder 2.1 Types of Rudder Examples of typical rudders are shown in Figure Spade rudders are commonly installed on ferries and ro-ro ships With this type of rudder the rudder stock is