Scientiic Journals Maritime University o Szczecin Zeszyty Naukowe Akademia Morska w Szczecinie 1, 3(1) z. pp. 186 19 1, 3(1) z. s. 186 19 Sea waves models used in maritime simulators Piotr Zwolan, Krzyszto Czaplewski Polish Naval Academy 813 Gdynia, ul. Śmidowicza 69, e-mail: p.zwolan@amw.gdynia.pl, krzyszto@czaplewski.pl Key words: navigation, simulation systems, manoeuvring, sea waves Abstract The modern simulation sotware includes an impact o orces acting on the ship hull. One o the most signiicant orces is sea waves acting. The mathematical model allows simulation o ship motions in irregular sea wave area, both at deep and shallow waters. The wave surace model enables simulation o the wave elevation in compliance with wave spectrum occurring in various conditions. The paper presents general description o the sea wave model used in maritime simulators. An example o such simulators is used at the laboratory o the Naval University o Gdynia, where it is operated basing on NT-Pro sotware by Transas Marine. The latest version o simulation sotware gives a possibility to select the wave spectrum. Selection o the waving type, depending on sea area location, makes the ship movement more reliable. This is an important element in testing the ships behavior process. Introduction The research carried out in the latter hal o the last century on ormation and proceeding sea waves, resulted in describing a variety o their mathematic models. They have been constantly developed and improved. While studying sea waves phenomenon, scientiic centres suggested application o several wave spectrum models, dependent on a number o parameters considered (e.g. in the wind unction, waving area or its requency). Models o waves are very useul i the measurement data are lacking, however they may be subject to geographic and seasonal limitations. The models: Bretschneider, ITTC, Pierson Moskowitz, Neumann, Philips or JONSWAP were worked out or dierent water areas (as or example the North Sea), thereore applying thereo is not a universal issue, in addition, it is limited by speciic restrictions. Development o the models is strictly connected with various science domains and industry branches. One o the examples is development o navigation and manoeuvre simulators; in particular, their weather models [3]. Implementing the diversiied wave models to their environment contributes to increasing possibility o applying simulation methods and o the level o the tests results credibility. In the irst part o the paper a general characteristics o some wave models applied in the navigation and manoeuvre simulator, located at the Naval Academy in Gdynia is presented, whereas in the second part, the results o the simulation tests aimed at determining dierences in a behaviour o the selected real vessel s model, aected by action o various sea wave models. This paper describes indings o the initial analysis and assessment o the vessel s simulation model under inluence o various sea wave spectra. Selected sea wave models A majority o sea waves is induced by wind operation. Such waves are called wind-waves. On studying sea waves the research teams worked out a series o mathematic models o waves. Most ocean waves spectra may be described in a orm o the standard ormula, which has to be applied only in case waves heights are known [1]: A exp B S (1) The above dependence is a general orm o the ocean wave model. On conducting the studies carried out world-wide at various water areas, the scientists worked out more detailed models. While 186 Scientiic Journals 3(1) z.
Sea waves models used in maritime simulators selecting the wave model to apply in the research process, it is necessary to take into consideration also the ollowing aspects and questions: Is the considered water area limited with any coastline which prevents ull development sea? Are the sea waves under a process o ormation or degradation? The water area depth; waves on deep water areas dier rom those on shallow waters. Surace currents aecting waves characteristics. Below, three models o waves are presented, implemented to an environment o the simulator, based on Navi Trainer sotware by Transas Marine. Pierson Moskowitz Spectrum One o the most simple wave s spectra was worked out by Pierson and Moskowitz (196). The scientists had assumed that waves begin their action in equilibrium with wind under condition o long lasting wind blowing over a large area. It is a concept o ully developed sea. To achieve a spectrum o the ully developed sea, they used measurements o waves, carried out with a use o accelerometers located onboard o British weather observing vessels, sailing on the North Atlantic. The spectrum is dependent on one o input parameters and a wind speed, wave height or peak period may stand or it. Due to the limitations they can be applied or investigations perormed at an unlimited water area. Having the collected results analyzed, the spectrum was worked out and described, applying the below mentioned relation [1]: A exp B S () πu B or g JONSWAP spectrum A g π (3) B p or g B () π H S.81,.7 () To work out wave s spectrum or limited and shallow water areas, at the beginning o the seventies the Joint North Sea Wave Project was perormed. To carry out the survey, along the German Coast there were located research stations. In eect o analysis o data rom more than measurements, the scientists discovered that the wave s spectrum is not ully developed. However, in view o its characteristics, it is oten used or purpose o studies and analyses reerring to coastal navigation at limited water areas. The spectrum is two- -parameter and dependent on two input parameters, which are a modal requency and ampliication coeicient. It is described in the ollowing dependence () [1]: S g π exp p p exp p (6) p = /T p (7) spectral peak or modal requency o the JONSWAP spectrum (7);. 1.76 U (8) F g is the wind speed at the height o 1. m above the sea; Bretschneider spectrum.7 p (9).9 p Bretschneider spectrum also called a modiied, two-parameter Pierson Moskowitz spectrum, worked out basing on research, carried out at the North Ocean. A dierence between the original Pierson Moskowitz s spectrum consists in a act that Bretschneider s spectrum is unction o the both wave height and peak period []: A exp B S (1) H S p A (11) 16 p B (1) Inluence o waving on vessel behaviour To veriy the sea waves mathematical models, implemented to the simulator s environment, a series o manoeuvring trials were carried out. The ollowing are general structure parameters o the vessel, a model o which was used or the research. Zeszyty Naukowe 3(1) z. 187
:: ::3 ::6 :: ::3 ::6 :: ::3 ::6 Piotr Zwolan, Krzyszto Czaplewski Table 1. Structural parameters o the vessel used in examinations Mine hunter Displacement 3. t Bow drat.1 m Engine 8 kw Stern drat.1 m Length 8. m Height o eye 7. m Breadth 8. m Max speed 9. m/s The vessel used or examinations was a mine hunter, owned by the Polish Navy. Due to its small draught and dimensions it is susceptible to waving and strong winds. The simulations were carried out at various water areas and with consideration o respective thereto waves spectra. Each o trials was carried out at the identical hydrometeorological conditions (wave height = 1.7 m). While the trials discussed below were on, the wave was acting toward starboard side o the vessel heading north (KR = ). Conducting the trial was aimed at comparing the waves mathematical models inluence on the vessel s handling parameters, roll and sway, in particular. Considering a large number o wave models to choose and the extensive research material, the paper was ocused on comparison o three models. Results o the carried out tests are presented below. Ship s rolling While manoeuvring trials perormance there were recorded vessel s rolling; the diagrams are presented below. Basing on the collected materials 8 analysis it can be stated that the most intense rolling, reaching 13 degrees, occurred in a time o the course, when the vessel was a subject to Jonswap spectrum waves. Also the ship s rolling requency is the highest or Jonswap spectrum. According to the results o the presented test specimen, within 1 minute the vessel rolled 1 times toward the same direction. In a time when the vessel was subject to acting o two other spectra, 13 rolls occurred. The more extensive rolling was caused by the wave o Jonswap spectrum characteristics, which is more steep and shorter than the ocean waves, which became a basis or the other examined wave spectra. 1 1 Fig.. JONSWAP Spectrum roll angle 1 1 6 - - -6 Fig. 1. Pierson Moskowitz Spectrum roll angle Fig. 3. Bretschneider Spectrum roll angle 188 Scientiic Journals 3(1) z.
:: ::3 ::6 :: ::3 ::6 :: ::3 ::6 :: ::3 ::6 :: ::3 ::6 Sea waves models used in maritime simulators 1. 1 -. -. -.6 -.8. Fig. 6. JONSWAP Spectrum sway BRETSCHNEIDER JONSWAP PM. Fig.. Summary compilation o ship s rolling Ship s sway In a time o carrying out the second series o tests the vessel s sway / drit induced by waves was recorded. The tests results presented below prove that the most intense sway o the vessel, reaching 3 m, was caused by a wave o Bretschneider s spectrum. The wave o Jonswap spectrum induced a sway o.7 m instead. Thus it may be stated that the vessel is a subject to much more intense sway being aected by a long ocean wave -. -. -.6 -.8. Fig. 7. Bretschneider Spectrum sway. -.1 -. -.3 -. -. -.6 -. -.8 -. -.6. BRETSCHNEIDER JONSWAP PM Fig.. Pierson Moskowitz Spectrum sway Fig. 8. Summary compilation o the vessel s sway data Zeszyty Naukowe 3(1) z. 189
Piotr Zwolan, Krzyszto Czaplewski Conclusions In eect o the simulation tests results analysis and comprising speciic vessel movement parameters on one diagram (Figs and 8), it is possible to present a dierence in behaviour o a vessel aected by activity o sea waves o various spectra. The opportunity o applying various sea waves spectra is an essential aspect or the research process. In spite o the act that works over waves models have been carried out or some dozens years, the sotware or navigational simulators was completed with the above models not beore last years. The collected results and perormed analysis allow to state, that urther tests and simulation trials on the subject would provide us with more detailed inormation about implementation o sea waves spectra into navigation and manoeuvre simulators environment. The results obtained on the research prove, that the simulation sotware is broadly applicable in studies and tests conducted in diversiied hydrometeorological conditions. Anyhow, the present stage o research gives no answer or the question are the implemented models o sea waves activity adequate to the waves truly occurring at speciic water areas in any type o hydrometeorological conditions. A problem o determination o the waves simulation models adequacy level and analysis o behaviour o vessels simulating models in comparison to the real ones behaviour at sea area are to be a subject o the successive research o the authors. Reerences 1. KINSMAN B.: Wind Waves (their generation and propagation on the ocean surace). Prentice-Hall, Inc., Englewood Clis, New Jersey, 196.. MICHEL W.H.: Sea Spectra Revisited. Marine Technology, vol. 36, No., Winter, 1999. 3. The Specialist Committee on Waves, Final Report and Recommendations to the 3 rd ITTC International Towing Tank Conerence,. Others. Transas Marine, Navi-Trainer Pro Ship Motion Model, Sankt Petersburg 11.. Transas Marine, Navi-Trainer Pro Ship Mathematical Model, Sankt Petersburg 11. 19 Scientiic Journals 3(1) z.