8-Manoeuvring - Model & Full Scale Experiments (2012)

Manoeuvring – Model & Full Scale Experiments MANOEUVRING – MODEL & FULL SCALE EXPERIMENTS 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 Introduction Physical model scale experiments may be used to predict the manoeuvring behaviour of a ship There are essentially two different ways of predicting the manoeuvring behaviour of a ship using scale model experiments The first technique is to use a radio controlled free running model and to measure its response to a given rudder input The alternative method is to use a captive model, where prescribed motions are imposed on the model and the forces measured to obtain the coefficients for a mathematical model, which can be used to simulate the response of the ship 1.1 Free Running Experiments Some advantages and disadvantages of using free running model experiments are listed below Advantages   The results are immediate and visual A mathematical model is not required to predict the motion of the manoeuvring ship Disadvantages         Requires a sophisticated model which contains self contained self propulsion gear and radio control equipment The model must have the correct longitudinal moment of inertia If significant heel angles are expected, the model must have the correct GM and the correct transverse moment of inertia The weight of the equipment inside the model can make it difficult to obtain the correct rigid body dynamics and to have sufficient displacement the model must be quite large Due to the requirement of a larger model the model basin must be large Need to measure the exact position of the model in the test basin No insight is given into the individual forces that combine to give the total manoeuvring characteristics Scale effects Manoeuvring – Model & Full Scale Experiments The question of scale effects in manoeuvring is very complex A self-propelled model will require a higher scaled thrust than the full size ship due to the skin friction correction This means that the rudder will be operating in a greater slip stream and will hence produce more force than in the full scale ship, resulting in larger Yδ and Nδ This can be overcome by using a small air fan on the model directed along the longitudinal axis to give the external force required to permit the model to operate at the ship self propulsion speed Because the model is operating at lower Reynolds numbers than the ship there will be a larger skin friction and hence the water flow velocity into the propellers and rudders will be smaller This will result in a less effective rudder and hence lower value of Yδ and Nδ It will be noted that this is the opposite of the previous effect and it is possible that in a single screw, single rudder ship these two effects may cancel out and hence the air fan would not be required 1.2 Captive Model Experiments Some advantages and disadvantages of using captive model experiments are listed below Advantages   Requires a less sophisticated model than for free running experiments The individual forces that combine to give the total manoeuvring characteristics can be investigated Disadvantages      The results are not immediate and visual A mathematical model is required to predict the motion of the manoeuvring ship A large number of experiments are typically required and knowledge of the equations of motion to the desired degree of complexity is necessary A large test basin is required to perform some types of captive model experiments Scale effects Types of Captive Model Experiments 2.1 Rudder Angle Test The model is towed on a straight line in a conventional towing tank The rudder is given a known deflection angle, 𝛿, and the sway force and yaw moment measured This is repeated over the full range of rudder angles (including degrees) and plots of sway force and yaw moment against rudder angle are produced Hence 𝑌𝛿 and 𝑁𝛿 can be found 2.2 Oblique Tow Test The model is towed in a conventional towing tank with a static drift angle β This results in a sway velocity, v, being imposed on the model, since 𝑣 = −𝑉𝑠𝑖𝑛𝛽 A model undergoing an oblique tow test is shown in Figure The process is repeated for a range of drift angles and hence the sway force and yaw moment can be plotted against the sway velocity The results can be used to obtain 𝑌𝑣 , 𝑁𝑣 and the non linear forms 𝑌𝑣𝑣𝑣 and 𝑁𝑣𝑣𝑣 (or 𝑌𝑣 𝑣 or 𝑁𝑣 𝑣 ) It is possible Manoeuvring – Model & Full Scale Experiments to combine the rudder angle tests and oblique tow tests to obtain some of the cross coupling terms such as 𝑌𝑣𝛿𝛿 , 𝑌𝛿𝑣𝑣 , 𝑁𝑣𝛿 𝛿 , 𝑁𝛿𝑣𝑣 Figure Model during an oblique tow test (taken from Lewis 1989) 2.3 Rotating Arm Test The principal purpose of the rotating arm test is to obtain the rotary coefficients For this it is necessary to impose a yaw velocity, r, on the model without imposing a sway velocity This is achieved by towing the model in a circle using a rotating arm In order to perform a rotating arm test a large basin is required The setup is shown in Figure The model is set up on a turntable which can be positioned at any distance from the centre to the outer edge This means that for a constant linear velocity, V, different values of r can be obtained, since: 𝑟= 𝑉 (57) 𝑅 Figure Rotating arm test setup (taken from Lewis 1989) Manoeuvring – Model & Full Scale Experiments Plots of Y and N against r are made to obtain the derivatives of 𝑌𝑟 and 𝑁𝑟 The coefficients 𝑌𝑟𝑟𝑟 and 𝑁𝑟𝑟𝑟 can also be obtained from the non linear section of this plot To obtain the linear derivatives it is necessary to have data over the linear part of the curve, i.e to have data at small enough values of r such that linearity holds Unfortunately, the rotary derivatives tend to be fairly non linear which makes it difficult to identify the linear region From Equation 57 it can be seen that large values of R or very small models are required to obtain small values of yaw velocity The value of R is dictated by the dimensions of the basin and small models are not favourable due to the small magnitude of the measured forces Therefore, it is usually not possible to obtain small values of yaw velocity From the discussion above it can be seen that the rotating arm test is ideal for determining the non linear coefficients The rotating arm can also be used to obtain the sway velocity coefficients by testing with different drift angles and cross plotting the results The rudder angle can also be varied and a combination of cross plots will result in all the linear and non linear coefficients and coupling coefficients involving r, v and 𝛿 being obtained 2.4 Planar Motion Mechanism Using the rotating arm it is possible to obtain all of the velocity coefficients, however, it is a specialized facility which is very expensive and cannot be used for anything else In addition, it is not possible to obtain the acceleration derivatives using a rotating arm In order to obtain the yaw coefficients (as well as the sway ones) in a conventional towing tank the PMM was devised in the late 1950s at the David Taylor Model Basin in America This was originally developed for submarine models but was soon used for surface ships Essentially the idea was to oscillate the model with simple harmonic motion whilst it travelled down the tank For obtaining the sway coefficients the model was oscillated in pure sway and for obtaining the yaw coefficients it was oscillated in pure yaw This is illustrated in Figure Figure Pure sway and pure yaw using a PMM Initially the PMM consisted of two mechanical oscillators; one attached near the bow of the model and the other near the stern This is shown in Figure Manoeuvring – Model & Full Scale Experiments Figure PMM with two mechanical oscillators The oscillators were driven at a prescribed frequency, ω, and amplitude y0 The phase angle between the oscillators determined the type of motion experienced by the model This system permitted small yaw amplitudes and was ideal for testing submarines The equations governing the motion in pure sway, for example, are: 𝑦 = 𝑦0 𝑠𝑖𝑛𝜔𝑡 (58) 𝑣 = 𝑦0 𝜔𝑐𝑜𝑠𝜔𝑡 (59) 𝑣 = −𝑦0 𝜔2 𝑠𝑖𝑛𝜔𝑡 (60) It can be seen that for constant 𝑦0 , 𝑣 and 𝑣 can be varied by varying 𝜔 When this technique was applied to surface craft it was found that the coefficients had considerable frequency dependence Thus, it was necessary to test over a range of frequencies and extrapolate to zero frequency (see Figure 5) The values obtained with the lower frequencies are much less accurate since the forces measured are small (because 𝑣 and 𝑣 or r and 𝑟 are small) and the ordinate is divided by a small number In addition, because of the limited length of the towing tank few cycles can be obtained to average the results over This makes it very difficult to extrapolate results to zero frequency In order to overcome this difficulty larger amplitude PMMs were developed The system of struts was replaced by a single sub carriage which moved in the y direction and mounted a rotating tube which was attached to the model via a strongback This allowed larger amplitudes and hence larger 𝑣, 𝑣, r and 𝑟 values with lower frequencies The setup is illustrated in Figure Manoeuvring – Model & Full Scale Experiments Figure Typical plot of Yv’ against frequency Figure Larger amplitude PMM set up The next development was the computer controlled PMM Here, a computer controlled a separate subcarriage so that the variation in forward speed required by very large amplitudes could be provided This could be used to give arbitrary motion or circular motion tests as well as the standard simple harmonic motion oscillatory testing Arbitrary motion could involve imposing impulse like motions to the model and analyzing the resulting force using fourier techniques to obtain a frequency plot and hence the zero frequency value Manoeuvring – Model & Full Scale Experiments Circular motion testing is similar to that carried out using a rotating arm The model could be towed down the tank with a path similar to the one in the pure yaw PMM experiment except that the path consists of arcs and circles with short joining paths One advantage of the PMM over the rotating arm is the fact that it can be used to simulate large values of R and hence small values of r to obtain the linear coefficients 𝑌𝑟 and 𝑁𝑟 Predicting the Coefficients of Motion We have seen from the preceding section that the hydrodynamic coefficients can be obtained from physical model scale experiments Alternatively, the coefficients can be predicted using theory or empirical formulae Slender body theory may be used to predict the hydrodynamic coefficients The hull is divided into transverse strips and the force on each strip is summed to give the overall forces and moments Low aspect ratio theory can also be used to predict the hydrodynamic coefficients The hull is likened to a very low aspect ratio lifting surface and the forces and moments due to a small drift (or incidence) angle can be calculated One problem with theoretical techniques is that the flow over the stern region is very important and this cannot be predicted easily as the separation and vortex shedding can be affected by small changes In general, the acceleration coefficients can be predicted reasonably well as they are just added mass terms and are independent of vortex shedding, whereas the velocity terms are not There are a number of different empirical methods for obtaining the linear hydrodynamic coefficients The four empirical methods given below are all taken from Clarke (1982) The formulae for the Wagner Smitt method are as follows: The formulae for the Norrbin method are as given below: Manoeuvring – Model & Full Scale Experiments The formulae for the Inoue et al method are as follows: The formulae presented by Clarke are given below: Manoeuvring Trials In order to check that a ship meets specified manoeuvring requirements and to provide data for ship/model correlation of manoeuvring characteristics, manoeuvring trials are sometimes carried out on new ships These may vary between steering gear trials which are simply to ensure that a required rudder rate can be met when steering at full speed, and complex trials involving many standard manoeuvres in deep and shallow water with sophisticated measuring equipment to obtain accurate values of sway and yaw at all times There are three principle standard manoeuvres which can be used to judge the manoeuvrability of a ship travelling at reasonable forward speed These are: Manoeuvring – Model & Full Scale Experiments The Turning Circle The Kempf Zig-Zag The Dieudonne Spiral 4.1 The Turning Circle The turning circle has been described earlier in the notes It involves steadying the ship on a given heading for about a minute and then with a constant engine throttle setting applying a set rudder angle and maintaining this until the ship has travelled through about 360° The path of the ship must be measured and recorded accurately The characteristics of the turning circle are as follows: Advance: The distance the ship travels forward in the direction of the approach course from the instant the rudder is put over until the vessel has made a designated change of heading (e.g 45° for a coasting turn or 90° for a powered turn) Transfer: The distance of the longitudinal centre of gravity of the ship normal to the approach course when the vessel achieves a 90 degree change of heading Tactical Diameter: The distance normal to the approach course in which the ship achieves 180° change of heading Steady Turning Radius: The radius of the steady circular path the ship takes up Steady Drift Angle: Angle between the ship’s head and the tangent to the path on the circle Steady Heel Angle: Heel angle of the ship during the steady part of the turn Rate of Change of Heading: The rate of change of heading during the steady part of the turn Speed on Circle: Speed of the ship during the manoeuvre The first four characteristics are the most important and are shown in Figure The pivot point is also shown in Figure This is of interest because to someone on board the vessel it appears as if it is turning about this point The pivot point is obtained by drawing a perpendicular from the centre of the steady turning circle to the centerline of the ship The position of this point in a steady turn does not vary much with turning radius or even with ship type The turning circle manoeuvre is usually conducted for a number of different speeds and for both port and starboard rudder angles Typically, the turning circle will be similar for different ship speeds It is usual to repeat each turning circle with the opposite rudder (using the same initial heading) and to plot both results together with the wind and current direction and speed superimposed This will highlight whether environmental factors influenced the turning circle Propeller asymmetry effects may also cause the turning circle to vary As with all manoeuvring trials, the turning circle test should be conducted with as little wind, waves and current as possible Manoeuvring – Model & Full Scale Experiments Figure Advance, transfer, tactical diameter and steady turning radius (Lewis 1989) 4.2 The Kempf Zig-Zag While the circle test gives a good indication of the behaviour of the ship in a steady turn it is not particularly suited to judge the immediate response of the ship to the helm (up to about 20°) For this reason the zig-zag test was devised The procedure for this test is to set the ship up on a steady course for about a minute and then to apply the rudder at maximum rate to a given angle, 𝛿1 The rudder angle is held over until the heading has changed by a given angle, α Often 𝛿1 = α1 for convenience The rudder is then deflected at maximum rate to −𝛿1 and held until the ship reaches a heading angle α1 on the other side of the approach course At this point the rudder is again deflected at its maximum rate to 𝛿1 and the procedure is repeated for about cycles The throttle settings remain constant throughout the test An example of the ship’s path while performing a zig-zag test is shown in Figure Figure Typical ship path for a zig-zag manoeuvre 10 Manoeuvring – Model & Full Scale Experiments Typical plots that are obtained from a zig-zag test are shown in Figure Figure Typical plot of results from a zig-zag test (Lewis 1989) The principal characteristics of the zig-zag test are: ● ● ● ● The time to reach the second execute yaw angle The time between successive rudder movements The overshoot yaw angle The overshoot width of path The zig-zag test can be repeated for different values of 𝛿1 and α1, and at different speeds The original Kempf zig-zag manoeuvre used 𝛿1 = α1 = 20°, however with very large tankers there has been some difficulty experienced with the large amount of sea room required to perform the manouevre and the time factors involved For this reason ITTC now recommends using 𝛿1 = 10° and α1 =10° or 𝛿1 = 20° and α1 =10° Because this manoeuvre is dependent on the initial response of the ship to the rudder the rudder deflection rate becomes very important The nondimensional rudder rate is given by Equation 61 𝛿′ = 𝛿𝐿 𝑉 (61) From Equation 61 it can be seen that as V is decreased the non dimensional value of the rudder rate will increase and hence the non-dimensional time that the rudder has to act will be greater Thus, the results of this manoeuvre are very speed dependent 11 Manoeuvring – Model & Full Scale Experiments 4.3 The Dieudonne Spiral Manoeuvre The purpose of this manoeuvre is to evaluate the directional stability of a ship, i.e its ability or otherwise to maintain a straight path with the rudder amidships if there are no other disturbances The spiral as originally proposed by Admiral J Dieudonne The procedure is as follows: The ship is set up on a steady course for about a minute or so Then with a fixed throttle setting the rudder is put over to 15 degrees starboard and the ship is allowed to settle to a steady rate of change of heading When steady this rate is recorded, the helm is eased to 10 degrees starboard and again the rate is allowed to steady and is recorded The helm is then eased to degrees starboard and the steady rate of change of heading again recorded Smaller steps in helm change are taken from degrees starboard through to degrees port and then out to 10 degrees port and finally 15 degrees port with the steady rate of change of heading recorded at each step The whole procedure is then repeated back to 15 degrees starboard helm The results obtained are plotted as heading rate against rudder angle If the ship is directionally stable the plotted curve will be a single valued function passing through or near the origin, depending on whether there is any steering bias If the ship is unstable there is a different appearance to the plotted curve near the zero rudder angle It will be found that the ship persists in turning to starboard when the rudder has been brought back to amidships from a starboard rudder angle and it may still persist to starboard for a few degrees of port helm There is then a sudden jump to port turning as the helm is put further over to port On the reverse procedure the ship continues to turn to port for zero and small starboard helms before suddenly reverting to starboard turning, thus the curve has the appearance of a hysteresis loop The larger the loop the more unstable the vessel and the more difficult is to handle It should be noted that the response of the ship depends on both the directional stability and the rudder effectiveness and it is not easy to distinguish between a vessel with very poor directional stability but effective rudder and one with only marginal stability Typical results from a spiral manoeuvre are shown in Figure 10 Figure 10 Typical results for directionally stable and unstable ships from the Dieudonne spiral manoeuvre 12 Manoeuvring – Model & Full Scale Experiments The results from a spiral test should not vary considerably for different ship speeds as the manoeuvre is essentially made up of sections of steady turning When conducting spiral manoeuvres it is essential to allow the ship to be well settled on its steady turn before recording the turning rate If this is not done an apparent hysteresis loop can appear The Dieudonne spiral test requires a large amount of sea room and time and also tells us nothing about how a ship steers a straight path or does a small turn For these reasons Bech proposed what is known as the reverse spiral in which specified rates of turn are demanded and the rudder is operated to maintain each steady rate Thus, with this test it is possible to specify zero turning rate and find what rudder movement is required to this For unstable ships the rudder cannot stay at zero and will oscillate about a mean of zero or the bias angle This requires a statistical analysis of the rudder movements, but as well as giving information about the area inside the loop it also shows what rudder activity can be expected to maintain the ship on a straight course, even in calm water The reverse spiral also has the advantage of being quicker to conduct Comparative tests have shown that the two methods agree well where results are obtainable from the Dieudonne spiral However, caution must be exercised when conducting the reverse spiral due to its dynamic nature In very large ships the response to helm may be slow and therefore there can be a time lag between the rate of turn and the rudder angle, which could in a severe case mean that the rate of turn achieved and the apparent mean rudder angle not correspond Starting, Stopping & Reversing Starting is defined as the action of accelerating a vessel from rest to a given speed Stopping is defined as the action of decelerating a vessel from a given speed to rest There are three different types of stop:    A crash stop, where the ship is initially travelling at full speed and is required to stop as soon as possible A standard stop, where the ship is gradually brought to rest from a typical harbour speed A coasting stop, where the engines are not used in reverse to stop the ship With the coasting stop the propellers can either be allowed to windmill producing no thrust or they may be locked in a set position Reversing is defined as the action of accelerating the vessel from rest to a given astern speed and then maintaining this speed In general, this section covers manoeuvring where the ship is not travelling at (or close to) self propulsion speed throughout, i.e the action of the propeller or propellers may be being used to assist a manoeuvre Because a large ship has the lowest drag/mass ratio of all earth bound man made vehicles (including aircraft) it requires the lowest power/mass ratio This makes it very difficult for it to change speed and hence starting and stopping times can be very great 5.1 Starting With the starting manoeuvre it is the length of time and the distance travelled from the ‘execute’ to the position where the ship is travelling at the desired speed which is of interest In general, when calculating the acceleration of a ship it is assumed to be travelling in a straight line The value of the force accelerating the ship is the difference between the value of the net thrust and the ship’s resistance Both the thrust and the resistance will be functions of speed Typical 13 Manoeuvring – Model & Full Scale Experiments relationships of the accelerating forces are shown as a function of speed in Figure 11 A typical relationship of the acceleration as a function of speed is shown in Figure 12 Figure 11 Acceleration forces as a function of speed (Lewis 1989) Figure 12 Acceleration as a function of speed (Lewis 1989) The acceleration may be found from: 𝑋 = 𝑅 + 𝑇 = (𝑚 − 𝑋𝑢 )𝑢 (62) Where: X is the force in the x direction R is the resistance (negative for forward speed) T is the net thrust m is the ship mass −𝑋𝑢 is the added mass in surge 𝑢 is the acceleration in the x direction In simulation models it is sometimes assumed that the thrust can be applied instantaneously Although, in reality it does take a finite time for the thrust to build up this is generally small compared to the time taken to increase speed 14 Manoeuvring – Model & Full Scale Experiments 5.2 Stopping Stopping, and in particular stopping distance, is of great importance mainly from the point of view of collision avoidance The distance travelled by a ship, along the path of the ship, in coming to a stop is known as the ‘head reach’ The ‘advance’ is the maximum distance travelled in the direction of the original course The two principal factors which govern the deceleration characteristics of a ship (apart from the mass and added mass) are the resistance of the ship and the reverse thrust available from the propeller The resistance is obviously speed dependant and is the most important factor at high speeds whereas the reverse thrust is taken to be independent of ship speed (contrary to the acceleration case) and is more important at low speeds The resistance, thrust and decelerating force is shown as a function of ship speed in Figure 13 Figure 13 Resistance, thrust and decelerating force as a function of speed (Lewis 1989) 5.3 Coasting With propeller wind-milling: This involves reducing the power to that necessary to cause the propeller to rotate without producing any thrust The ship is slowed down only by the hull resistance With propeller locked: In this case the thrust from the propeller is also zero, however, the ship is slowed down by the hull resistance plus the resistance of the locked propeller The drag of the locked propeller can be as large as that of the hull for slow speed ships and can be as large as three times the drag of the hull for fast twin-screw passenger liners A meaningful characteristic of coasting is the distance travelled until the ship speed has reached a certain fraction of the initial speed 15 Manoeuvring – Model & Full Scale Experiments 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 16 ...Manoeuvring – Model & Full Scale Experiments The question of scale effects in manoeuvring is very complex A self-propelled model will require a higher scaled... performing a zig-zag test is shown in Figure Figure Typical ship path for a zig-zag manoeuvre 10 Manoeuvring – Model & Full Scale Experiments ... basin is required to perform some types of captive model experiments Scale effects Types of Captive Model Experiments 2.1 Rudder Angle Test The model is towed on a straight line in a conventional