Roll Stabilisation at Anchor: Hydrodynamic Aspects of the Comparison of Anti-Roll Tanks and Fins R.P. Dallinga, Manager Seakeeping Department Maritime Research Institute Netherlands (MARIN) Project 2002, 18-20 November 2002, Amsterdam Abstract Passive anti-roll tanks have become a well established means to increase the comfort of motor yachts at anchor. More recently it became clear that fin stabilizers can also be very usefull in this respect. The present paper describes the hydrodynamic characteristics of both systems and ways to compare the performance. Introduction The present paper describes the inherent characteristics of roll stabilisation by means of active fins or a U-type anti-roll tank, the related design procedure and the way to compare both systems. All of the present work was based on tests with a scale model of a 55 m motor yacht equipped with 40 cm bilge keels, 1 pair 3.8 m active fins and an anti-roll tank with a content of 1.7% of the vessels displacement. Roll stabilisation by means of anti-roll tanks Work by Stigter [1,2] learned that U- type anti-roll tanks, see Figure 1, can be quite effective in the reduction of roll motions. This characteristic, combined with the possibility to disable the tank quickly by closing the air ducts and the expected low noise production, makes it an attractive solutinn fnr mntnr vanhts. Because the tank relies on a resonant response of the tank contents to the motions of the ship, a careful tuning of the natural period of the ship and the tank as well as the internal damping of the tank are important design issues. For a given wing-tank area (which determines the restoring term in the natural period) the height of the connecting duet is the remaining design parameter for the tuning. The "added" mass associated with the high acceleration of the fluid through the narrow duet is an important factor. The internal damping is governed by the vortex shedding at the point where the duet emerges in the wing-tank, the drag of structural elements in the tank and the frictional drag. The first two components are considered as major factors. By nature these elements are non-linear in character (the drag force is more or less proportional to the square of the flow velocity). Because this induces a relatively high tank response at relatively low roll amplitudes this is an interesting characteristic to obtain a high degree of stabilisation in low wave heights. At the same time the relatively low response in extreme conditions prevents impacts at the tank top. Fig. 1 Anti-roll tank Design Figure 2 illustrates the character of the roll response of a stabilised yacht. It shows that a considerable roll reduction is obtained around the roll resonance peak. At the same time the roll in short waves increases slightly. 1
E 2, \ Roll RA c 0 A r ' 0.5 1.0 Wave Freq. [rads] Fig. 2 Roll response with anti-roll tank A consequence of the foregoing is that the entire design starts with a target maximum roll amplitude (the comfort criterron which, if exceeded, will motivate the master to leave the anchoring site). The primary problem in the design is then to establish the internal damping that yields a maximum tank response at that target roll amplitude. A secondary issue is that the magnification in off-resonant conditions should not spoil the behaviour in short wind waves. If the outlet losses are insufficiënt the internal damping can be increased by introducing small drag elements in the duet. Response in irregular waves Figure 3 compares the response of the unstabilised design with that of the optimum tank (optimised for a 2 m wave) in an unfavourable wave condition with a peak period equal to the natural period of roll (8.6 s swell). The unstabilised response shows a very non-linear character that is attributed to the non-linear character of the eddy and bilge keel damping. The stabilized response appears surprisingly linear in character. This suggestion is deceiving; it is attributed to the counteracting effects of an increasing eddybilge keel roll damping contribution and a decreasing contribution of the anti-roll tank. It is concluded that the anti-roll tank is effective over a broad range of wave heights; the reduction of the rms values is around 66% in 0.5 m waves, 63% in 1 m waves and 57% in 2 m waves. Roll stabilisation by means of active fins Earlier work [3] lead to the notion that the dissipated energy is an important measure for the performance of active fins at zero speed. This "work" is the integral of the product of the reaction force M (see Figure 4) from the fins and the roll velocity <j> M Reaction moment acceleration peak deceleration peak drag atstationary vetocity Roll velocity Roti Response Anti-Roll Tank Dissipated energy -PBSS.Ffis -withaftt M.<f> 0 5 1 2 Slgn. Wava hfelght [m] Fig. 4 Roll damping of active fins Fig. 3 Roll reduction anti-roll tank 2
The ftrst acceleration peak is more or less proportional to the acceleration of the fin. Because of the timing (immediately after a zero-crossing of roll, at the moment the velocity is largest) its contribution to the dissipated energy is relatively large, it is limited by the short duration of the first phase. The second stage, the drag at stationary velocity, is more or less proportional to the square of the fin velocity. The fin velocity affects both the magnitude and duration of the reaction moment (a transit from -30 to +30 deg at 50 degs takes around 1.2 s). The third stage, the moment due to the fin deceleration is similar to the first stage, except for the fact that the moment does not oppose the roll velocity. Because of the timing (at around one-quarter roll period, where the velocity becomes small orechanges sign) the negative contribtion to the dissipated energy is relatively small. Design The character of the response of the stabilised ship is shown in Figure 5. It demonstrates that the fin activity reduces the peak response without side effects. This reduces the optimisation to balancing the three contributions to the overall roll damping with the initial acceleration and transit velocity and the related timing of events. Response in irregular waves The fact that the fin forces are independent of the roll response leads to a relatively high damping at low roll amplitudes. This is recognized in the results in irregular 8.6 s swell waves in Figure 6. Roll Response Active fin* 0 5 1 2 Slgn. Wav* H»lght[m] Fig. 6 Roll reduction active fins Rass. fins Actfins It may be concluded that the active fins are particularly effective in relatively low wave heights. In 0.5 m waves they yield a reduction of around 80%. In higher waves the system becomes less effective; in 1 m waves the reduction is 65%, in 2 m waves 36%. Comparison Roll RA D degm * 0 y 0.5 1.0 Wave Freq. [rads] The rather non-linear character of the roll response in all three cases implies that a comparison at the level of the transfer functions can be misleading if these are based on test results with different roll amplitudes. Figure 7 compares results that were derived by interpolating transfer functions on basis of the rms roll. In case of a relatively low roll criterion (0.5 deg rms) the unstabilised response is relatively high. Also the secondary high frequency peak of the response with the anti-roll tank is relatively high; a feature that can be solved by increasing the internal damping. Fig. 5 Roll response with active fins 3
30 Equivalent RAOs (0.5 deg rms) 30 Equivalent RAOs (2.0 deg rms) E 20 f\ { 1 I \ 1 ƒ \ ( e 20 < * 10 \ ' ^."V_ < * 10 0.5 I Vv^ve Frequency rdds No stabilisation Active Fins Anti-RollTank 0.5 I Wave Frequency [rads] No stabilisation Active Fins Anti-RollTank Fig 7: Comparison of Transfer Functions of Roll In case of a less demanding roll criterion (2 deg rms) the response function of the unstabilised ship decreases, in this case the transfer functions of roll of both stabilising systems are very comparable. Figure 8 compares the performance of both stabilisation systems in terms of the rms values in irregular swell waves. It shows that in lower waves the active fins show the lowest response, in higher waves the antiroll tank shows the best performance. Figure 9 indicates these limits for a tough and a relaxed comfort criterion. For the tough criterion (which is an off-design condition with the present tank internal damping) the fins show the best performance. For the relaxed criterion (in rougher seas) both systems show comparable operational limits. Opera! ion al Limit "^ RoO RraponM 3 I, 4- h i 0i 0.5 1 2 AarêO Hl [m] 2.5 -o wlhaflt -* Actrtt» Wtvt Puk Penod i None, 0.5 deg rms ****** Active Fins H-t- ART ' None, 2deg tms K'K Active Fins f»- ART Fig. 8 Comparison of anti-roll tank and active fins Considering the characteristics of the roll response, the roll in the most unfavourable wave condition seems a narrow basis for a judgement. For this reason the interpolated transfer functions were used to establish the operational limits. Fig. 9 Operational limits for two criteria Conclusions The merits of the use of active fins and an anti-roll tank to reduce the roll response of a motor yacht in anchored conditions were established by means of model tests and compared in detail. Considering the results 4
for zero-speed stabilisation it may be concluded that: The comparison is complicated because of the non-linear characteristics in the response. This limits a comparison to a given wave condition {or more accurately, to a given roll amplitude). Taking the 1.0 m swell as the "design" condition the active fins offer a reduction of 65%; the anti-roll tank yields 63%. Both systems may be regarded as effective ways to widen the operational limits of a yacht. For comfort in modest wave conditions active fins seem a very effective solution. In more demanding conditions the anti-roll tank offers the most effective solution. References 1. Stigter, C: The performance of U-tanks as a passive anti-roll device, TNO Report No. 81S, Feb. 1966. 2. Dallinga R.P. and Wieringen, H.M. van: Passenger Comfort on Board Motor Yachts, Project 97, Amsterdam, Nov. 1997. 3. Dallinga, R.P.: Roll Stabilisation of Motor Yachts: Use of Fin Stabilizers in anchored Conditions, Project 99, Amsterdam, Nov. 1999 If comfort in transit conditions is an issue, fins with a high aspect ratio (like applied on ferries) are a much more efficiënt way to stabilise the vessel. Because these fins cannot be used at zero speed, this system must be completed with an anti-roll tank for anchored conditions.