Research On 4 Degrees Responding Mathematical Model For Ships

When vessels are sailing in the ocean, they may often encounter bad weather and rough sea which will cause fierce rolling. The fierce rolling not only reduces wind resistant ability of vessels but also disturbs the normal work of the equipments carried by vessels. What's more, it will cause damage to the cargos or the vessels, or even causes sea disasters. Therefore, it is particularly important to study on the mathematical model for ship roll. At present, Abkowitz nonlinear mathematical model and the MMG model are well developed and widely used around the world. However, it is very complicated to compute more than 40 hydrodynamic derivatives for Abkowitz nonlinear mathematical model. And in order to get a variety of forces and moments for MMG model, a large number of empirical formulas or charts must be adopted, the process is also extremely complex. So it is very necessary to establish a 4 degrees responding mathematical model for ships which is relatively simple.In the paper, the author innovatively applies compound filtering method to the processing of rolling angle data collected from ship turning tests. And establishes a responding mathematical model for ship roll with analog modeling method and puts forward the concept of the indexes of rolling K1,T1; Then,2 relatively accurate formulas of K1 and T1 are acquired through multinomial regression of 8 ships' K1.T1 statistical data. Finally, a 4 degrees responding mathematical model for ships is got.Firstly, the paper processes the tested rolling data by writing matlab program. and the result is satisfactory. Then, multinomial regression of 8 ships; K1.T1 is done by using SPSS. By observing R and P values, we can find that the data fitting degree of the Regression equations is very good and the precision also meets the requirements. The regression equations have certain practical value.The 4 degrees responding mathematical model for ships established in the paper is simpler than those conventional ship hydrodynamic mathematical models. And the precision also meets the requirements. However, the author uses the analog modeling method when he is establishing the ship rolling model, and simplifies theδ-φresponding mathematical model into a first-order inertial system, so the accuracy of the model is not high. But the model is very concise, because there are only two parameters in it.