How To Write A Mathematical Model Of Ship Hydrodynamics In An Inland Shiphandlin Simulator Of Smu Insim

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1 Scientific Journals Maritime University of Szczecin Zeszyty Naukowe Akademia Morska w Szczecinie 14, 37(19) pp , 37(19) s ISSN Ship manoeuvrin hydrodynamics in a new inland shiphandlin simulator of SMU InSim Jaroslaw Artyszuk, Lucjan Gucma, Maciej Gucma Maritime University of Szczecin, Faculty of Naviation 7-5 Szczecin, ul. Wały Chrobreo 1, j.artyszuk@am.szczecin.pl Key words: inland ship, hydrodynamics, manoeuvrin, mathematical model Abstract The present paper describes the hydrodynamic modellin solutions, applied in the newly developed shiphandlin simulator at SMU (Szczecin Maritime University) for the inland naviation called InSim. The objective is to provide some uidance on the simulator capability and potential while conductin various research and the crew trainin projects. Introduction The manoeuvrin simulation models (simulators) of sea-oin and inland ships, as used in marine traffic enineerin, belon to the followin two types: non-autonomous; autonomous. The non-autonomous simulation model is an interactive model with a human (operator) input, which mostly works in real time. The simulation with such a model is very sensitive to the operator s knowlede and skills. Additionally, the obtained results are essentially affected by the technical solutions used to simulate the informational (input) environment e.. the bride visual view, and/or the bride equipment display and the control (output) environment. The latter is connected with the emulation of steerin devices, for instance. Nowadays, since the simulation almost entirely has been run by the computers, where everythin must be mathematically (numerically) modelled and prorammed, the advantae of nonautonomous simulation is that we do not have to mathematically model a very complex decision process of a human. On the contrary, the human modellin is absolutely required within the second type of simulation autonomous one. The key element of the computer simulation, if applied to physical phenomena of motion, is the adopted mathematical model (the so-called dynamic model) of the object s motion. For a floatin object, one ets here a hydrodynamic model. The hydrodynamic model of a ship, based on differential equations in a movin frame, operates in a loop, where for iven instantaneous environment disturbances and operator s steerin settins the particular forces and moments are calculated. In the next step, throuh equations interation, the resultin linear and anular velocities, and correspondin displacements, are calculated and forwarded to the simulator s visual system responsible for displayin the ship s smooth movement. The functional diaram of such simulator is presented in the fiure 1, which also served as the framework for developin hardware and software of the latest, independent InSim simulator of SMU, dedicated to inland naviation. The latter is a new area of interest covered by SMU accordin to their lon-term experience and expansion policy. The layout of InSim bride is shown in the fiure. The major merits behind the computer simulation in eneral, and its application for evaluation of vessel traffic safety in restricted waterways in particular (like InSim), are amon others today as follows: hih deree of conformity with reality; mathematical modellin flexibility ensurin fast-built, simple, and adequate models accord- 1 Scientific Journals 37(19)

2 Ship manoeuvrin hydrodynamics in a new inland shiphandlin simulator of SMU InSim in to research objectives, includin the stochastic models; low financial effort in comparison to the physical simulation; time-effectiveness of data collection and processin; solutions can be tested and objectives met without the need to create a real system non- Fi. 1. The functional diaram of InSim simulator Fi.. The photo of InSim simulator with presentation harbour of Szczecin the neihbourhood of Wały Chrobreo Zeszyty Naukowe 37(19) 11

3 Jaroslaw Artyszuk, Lucjan Gucma, Maciej Gucma existin systems can be examined, e.. a maximum ship for the safe operation of iven waterways; virtual extreme loads can be applied on the investiated object, especially those destructive ones. The present study is devoted to hydrodynamic modellin solutions applied in the InSim simulator. They have direct and indirect effects on reliability of simulation results and potential areas of the simulator s application. The software of InSim All procedures for the ship manoeuvrin computation are athered in a self-contained MS Windows DLL library developed usin the C++ lanuae. This basic file mm_model.dll toether with a ship hydrodynamic database file (of.hdb extension) for each ship model forms a packae, referred to as the SMART DLL. An additional nautical area file (of.map extension), which brins a distribution map of various physical phenomena (wind, current, wave, bank, fender, etc.), can also be loaded. Appropriate prorammin interfaces to use the dynamic-link library in C++ or Delphi prorammin environments are provided. The hydrodynamic database files can be supplied in encoded or open format, as to allow in the latter case an input from the authorized user by means of any text editor. These ship specific data files comprise all dimensional and nondimensional model parameters, mostly of eometric or hydrodynamic nature, includin amon others sophisticated multidimensional lookup tables as representin functional relationships. Since the SMART DLL is a purely mathematical library, the user is required to provide a raphical interface within his application for acquirin steerin commands. The crucial procedure of the DLL library, called smm_inout (...), is basically a sinle recursive advance of the ship motion state vector (but extended from the usual one as to combine also the dynamics of steerin devices). This is done throuh a numerical interation of the aforementioned ship motion differential equations. Various numerical alorithms for ODE problems are available within the packae, but the Euler method is still here sufficient and mostly frequently used. If the smm_inout procedure is run inside the PC timer controlled loop, then a real-time mode is achieved. Since the procedure is absolutely very fast, even with lare sizes of the accompanied ship model HDB files, it is thus well suited also for fast-time (offline) modes. The SMART library can be easily replaced with another one, preservin the library functions callin interface, since one of the key features of the InSim simulator is open independent architecture, thus allowin an extension of the simulator to meet various, especially future trainin and/or research the needs. The commercial simulators are mostly prevented from doin even a small modernisation by the user on his own that necessitates placin new simulator upradin orders to the same manufacturer. Mathematical model description of InSim The differential equations of ship manoeuvrin motions in the usual movin frame of reference are as follows: d v x m m m c m 11 m vyz d t c m11 cmm vyz Fx d vy m m m m11 vx z d t c m m v 11 xz Fy dz J z m66 M z d t where: v x, v y, z sure, sway and yaw velocity; t time; m ship s mass (displacement); m 11, m, m 66 added (virtual) masses; empirical (viscosity) reduction factor; c m (1) F x, F y, M z external physical excitations as resultant forces and moment;, c superscripts denotin a ship s round velocity vector components and the water current velocity vector components. The external excitations are modelled within the modules below (the quoted symbols are also used to distinuish particular components of the resultant forces and moment): H hull; P propeller; R rudder; A wind (aerodynamics); WV wave action (of 1 st and nd order); ICE ice interaction; BE bank effect; SS ship-to-ship; LTU lateral thruster unit; FEND fenders; MOOR moorins; 1 Scientific Journals 37(19)

4 Ship manoeuvrin hydrodynamics in a new inland shiphandlin simulator of SMU InSim ANCH anchors; TUG tus. Each of these excitation models consists of a dimensional part (mostly bein a product of certain physical quantities leadin to a proper unit, e.. N or NM) and a non-dimensional part, essentially constitutin a sinle non-dimensional coefficient, bein strictly a constant or a function of multiple parameters. Sometimes, this non-dimensional coefficient (i.e. the multiple variable function underneath) is decomposed into a product or a sum of simpler coefficients (functions) that ives much comfort in storin, such relationships in lookup- -tables. Latter can be easily handled if their dimensions are limited up to three, in which case we have a three-variable functions. However, the two- -dimensional lookup-tables are the best. The above lookup-table approach is just fully implemented in the SMART library in that any analytical formulations for hydrodynamic coefficients, e.. in the form of polynomial expansion, as widely published in the literature, are stronly avoided. The mentioned expansion sometimes serves only as the backround (initial uess) for tunin the non-dimensional coefficients in accordance with the ship s performance in sea trials. The both parts of (semi-empirical) model for iven excitation, dimensional and non-dimensional one, belon to the art of dynamic modellin. Both required a lot of efforts to arrive at the adequate and flexible solution, where all the essential effects / relationships connected with particular excitation are reflected up to the required level of accuracy. For example, an improper choice of dimensional part may sinificantly complicate the non-dimensional coefficient. The dynamic model (1) has to be further supplemented with the known kinematical relationships differential equations of the first order for the chane of the headin anle and the ship s oriin position. Other details on model fittin procedures can be found in [1]. Specific data on Luisa Lynn The main particulars of Luisa Lynn, the first ship bein modelled for InSim simulator, are presented in the table 1. The abovewater side view and the underwater stern view are shown in the fiure 3. The values of thrust and torque coefficients of the propeller, as functions of the advance coefficient and pitch ratio, were taken from available published model tests on CPPs and preserved in the mathematical model. The same was done with the Table 1. Basic data of Luisa Lynn Lenth over all (L) 78.8 m Breadth extreme 8. m Drauht extreme.1 m Trim Displacement (fresh water) 115 t Main enine power/rpm 65 kw/34 rpm Gear none Propeller CPP in half-nozzle, riht-handed, diameter 1.45 m, 3-bladed Stern rudder underhun, dual-blade, maximum anle 57 Bow thruster nominal thrust.5 t (estimated) a) b) Fi. 3. Selected views of Luisa Lynn ; a) source: www. marinetraffic.com, b) source: Rentrans Caro Ltd. (Szczecin, Poland) the owner s archive propeller wake fraction and thrust deduction as functions of forward speed and propeller loadin. Finally, the hull resistance coefficient in deep water, kept, however, constant aainst the speed, was scaled accordinly (also for other non-zero drift and dimensionless yaw values) to reach the known maximum speed of Luisa Lynn, equal to abt. 1.9 km/h. The speed relevant to other settins of the wheelhouse speed control knob is iven in the table. Table. Estimated speed of Luisa Lynn Speed settin [%] Speed [m/s] Speed [kt] Speed [km/h] Zeszyty Naukowe 37(19) 13

5 Jaroslaw Artyszuk, Lucjan Gucma, Maciej Gucma lateral velocity v x [kt] v y [m/s] pomiar trial symul. sim. pomiar trial symul. sim [] drift anle 4 3 [] headin v x [m/s] z [/min] x O [m] yaw velocity track time [s] y O [m] Fi. 4. Turnin circle test (rudder anle 57 PORT, constant throttle) Fi. 5. / zi-za test (constant throttle) Concernin the turnin and yaw checkin ability, determined by means of turnin circle and ziza tests, the combined trial and simulated charts are presented in fiures 4 and 5. The trial data, also as a part of the InSim project, were obtained throuh measurements at sea usin a dedicated hardware and software developed at SMU. The simulated values refer to the model performance after application of a special model fittin procedure, mostly connected with calibratin the hull sway force and yaw moment coefficients (as functions of drift anle and dimensionless yaw velocity), and the rudder-hull interaction factors as well. The displayed in the fiure 4 turnin circle trial data, all except the yaw velocity z, have already included an allowance for the existence of water current at the trial site and refer to the midship position. The current set and drift, 17 (related to ship s initial headin) and.18 m/s accordinly, were herein established on the principle of ettin durin the data recalculation process a constant drift anle at the steady phase of turnin. With reard to stoppin ability the areed sea trial proram only encompassed coastin stop tests, i.e. with settin the propeller to zero pitch. For a riht-handed controllable pitch propeller this leads to the well-known effect of ship s turnin towards the starboard side. This phenomenon is very clear for Luisa Lynn too. The fiure 6 shows the and headin chane for the two conducted runs of such stoppin. Thouh of the same steerin, they reveal some remarkable differences. 14 Scientific Journals 37(19)

6 Ship manoeuvrin hydrodynamics in a new inland shiphandlin simulator of SMU InSim v x [kt] [] pomiar trial no. 'ham1' 1 pomiar trial no. 'ham' symul. simul. headin Fi. 6. Coastin stop performance v x [kt] [] distance 168m (.13 L) time 11s headin 6 to PORT headin Fi. 7. Estimated crash stop behaviour (FULL ASTERN) The reason for such strane behavior can be hardly assessed at this stae of research. It should be added that the water current effect has not been analysed for the coastin stop tests. The final manoeuvrin mathematical model has been essentially fitted aainst the trial No. in the fiure 6 for speed decrease in that the wake fraction, thrust deduction, and the propeller thrust coefficient for zero pitch were tuned in the reions of domain responsible for the coastin stop simulation. The yaw effect of the propeller zero pitch has been however assumed in the middle of the both records, since this has rather little influence on the speed decrease rate, as in the case of Luisa Lynn. The plots in the fiure 7 demonstrate the estimated performance (essentially based on the adopted model test results of the CPP in concern) durin the crash stoppin. Final remarks The presented ship hydrodynamic model, despite the fact that only selected aspects of its have been shown in this paper, is able to interact with any inland waterway infrastructure. The other additional dynamic effects are also included in the model. However, to perform simulation-based safety studies in 3D visual environment provided by InSim, concernin e.. inland ship-bride collisions and related bride protection desin (see [] for examples), we need a detailed raphical and mechanical 3D model of inland waterway infrastructure. This is planned in the near future. Acknowledements The work was carried out within the development project of the Polish overnment: NCBIR R181, entitled Development and construction of an interated interactive simulator for inland ship naviation and manoeuvrin. References 1. ARTYSZUK J.: Modellin and Simulation in Ship Manoeuvrin Safety and Effectiveness Issues. Maritime University, Szczecin 13 (in Polish).. GUCMA L.: Risk Manaement in Ship Collision with Waterway Brides. Maritime University, Szczecin 13 (in Polish). Zeszyty Naukowe 37(19) 15