Balıkçı gemilerinin baştan gelen dalgalarda hareketlerinin regresyon analizi ile incelenmesi

Abstract

Bu çalışma, D. J. Doust tarafından verilmiş olan farklı prizmatik katsayılı (CP), 4 (dört) ana gemi üzerine kurulmuştur [1]. Bu gemilerin ofset değerleri, genişliklerinin yüzdesi şeklinde boyutsuz olarak alınmıştır. Bu 4 (dört) ofset grubunun CP'ye göre değişimi kübik tiriz eğrileri ile ifade edilip, istenilen CP değerlerinde ve karakteristik özelliklerde gemiler üretilmiştir. Tüm bu işlemler gemi üretim programı kullanılmak sureti ile, farklı özelliklerde, herbir boy için 27 (yirmi yedi), 20 (yirmi) farklı boy için de toplam 540 (beş yüz kırk) adet hayali gemi üretilmiştir. Üretilen herbir geminin enkesit ve suhattı eğrileri, gemi modelleme programından yararlanılarak çizdirilmiştir. Görüntüsü bozuk olan ofsetlerde de gerekli düzeltmeler yapılıp, yeniden modellenmiştir. Söz konusu 540 (beş yüz kırk) geminin modellenmesinden sonra, herbir geminin hidrostatik değerleri hazırlanan bilgisayar programından bulunarak, Wolf son Unit gemi hareketleri programı için gerekli datalar elde edilmiştir. Bu datalar, herbir geminin yüzdüğü draftındaki hidrostatik değerleri ile eşit aralıklı 20 (yirmi) posta sistemine göre herbir postanın genişlik, yükseklik ve alan katsayısı değerlerini kapsamaktadır. Hidrostatik hesaplamalardan sonra, hareket programı kullanılarak herbir geminin 3, 4, 5, 6, 7 ve 8 Beaufort rüzgar şiddetlerine karşılık gelen deniz durumlarında ve 5, 6, 7, 8, 9, 10 ve 11 knot hızlarında, baştan gelen dalgalarda, düşey hareketleri incelenmiş, herbir geminin 42 (kırk iki) farklı durumu için dalıp-çıkma ve baş-kıç vurma genlikleri hesaplanmıştır. Bu işlemlerden sonra, trovil balıkçı gemilerinin hidrodinamik analizi ve baştan gelen dalgalarda hareketlerini etkileyen parametrelerin analizi yapılmıştır. Bundan yararlanılarak, dalıp-çıkma ve baş-kıç vurma genliklerinin form parametrelerine ve boyutsuz oranlarına bağlı olan regresyon denklemleri kurulmuştur. Dalıp-çıkma ve baş-kıç vurma hareketleri için toplam 240 (iki yüz kırk) adet regresyon denklemi oluşturulmuştur. Uyarlanan bir regresyon programından yararlanılarak, regresyon katsayıları hesaplanmıştır. Sonuçta, elde edilen regresyon katsayıları gemi boyuna ve Beaufort sayısına göre tablolar şeklinde sunulmuştur. Bu tablolardan yararlanılarak regresyon ifadelerinin hesaplanması zor ve zaman alıcı olması sebebiyle ve ayrıca bu çalışmayı pratik bir hale getirmek için, Quicbasic ve Fortran77 programları geliştirilmiş bulunulmaktadır.

The paper entitled " Optimized Trawler Forms " written by D. J. Doust, published at the N.C.I.E.S. in 1962 was taken as a first step in this study. Analysing the resistance and propulsion data for trawler fishing boat forms which were obtained in the National Physical Laboratory by statistical methods and developing the optimum trawler hull forms are the main themes of this paper. The resistance values of the trawler hulls have been expressed in the equation systems containing series of non-dimensional parameters depending on hull shape and dimensions. The new hull forms which give superior performance have been generated, by the solution of these equation sets. As a result, optimized trawler hull form offsets for four different prismatic coefficients (Cp) have been presented in non-dimensional form in the tables. This study has been established on four main ships having prismatic coefficient values (CP) of 0.582, 0.606, 0.625 and 0.649 which was optimized in terms of resistance and propulsion by D. J. Doust [1]. These non-dimensional ship offsets changing with respect to CP have been represented by cubic splines (and for the prismatic coefficient values (CP) ). 27 ships at the same length, 20 ships at different lengths and different properties, totally 540 fictitious ships have been generated by using ship production computer program. The length between perpendiculars (Lpp) and non- dimensional parameters of these generated ships are given as follows : LPP : 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 32, 35, 38, 41, 45 Lpp/B : 4.4, 5.1, 5.8 B/T : 1.9, 2.3, 2.7 Cj, : 0.590, 0.620, 0.650 The second step of this study consists the modelling of ships, hydrostatic calculations, calculation of heaving and pitching amplitudes in head seas. Body plans and water lines of ships have been drawn by using cubic splines passing through the offset values. If the ship lines are not smooth, they are faired and values of the offset are corrected with respect to faired curves. The non-dimensional parameters to be used in regression equations and the input values for ship motion program have been determined for each trawler ship by using the hydrostatic program utilizing cubic spline techniques. In this study, the ship motion program developed by Southhampton University (Wolf son Unit) was used. Data required for the program was based on a 2 0 -station system; the beam, draft, and sectional area coefficients at each station of the ship were used. Wolf son Unit Ship Motion Program has been executed for six different Beaufort numbers (ranges from 3 to 8) and seven different ship speeds (ranges from 5 to 11 knots), totally 42 different conditions, to obtain vertical motions (significant pitch and heave amplitudes) of each trawler ship in head seas. In calculations, the longitudinal centre of gravity (LCG) and longitudinal position of the centre of buoyancy (LCB) for each ship were assumed to have the same value. The ratio of longitudinal radius of gyration to Lpp for pitching has been chosen arbitrarily between 0.23 to 0.25. The third step in this study is to investigate the influences of design parameters to ship motions (heave and pitch). The success of a ship design depends ultimately on its performance in a seaway. However, the prediction of ship motions is a complex problem that ship designers are generally forced to select their hull forms and ship dimensions on the basis of calm water performance without much consideration of the sea and the weather conditions. vi Only sophisticated experimental techniques and computer applications in ship motion theories have made it possible for the designer to consider the seakeeping qualities of his ship at an early stage. The overall seakeeping design can be divided into three areas: 1. Habitability 2. Operability 3. Survivability To assess the above items properly there are three particular considerations in regard to the seakeeping design: 1. Definition or prediction of the seaway in which the ship has to operate. 2. Qualitative or quantitative criteria of various seakeeping qualities of the ship in order for her to perform its mission. 3. Determination of whether the seakeeping criteria can be met by the ship for the particular seaway under consideration. If not, design alternatives must be sought. However, any analysis of the seakeeping design is essentially of the probabilistic nature, since the environmental itself in which the ship operates (i.e., the actual seaway) can be analyzed only in a probabilistic manner by statistical methods. The design parameters to be considered for seakeeping design may be classified into four categories. 1. The first group may consist of only the simplest parameters that must be determined before a hull form is designed (i.e., length, beam, draft, displacement, longitudinal position of centre of buoyancy, speed, etc.) 2. The second group may consist of parameters such as longitudinal moment of inertia, water plane area, and position of the longitudinal centre of flotation, which are likely to have a significant influence. vii 3. The third group can include various other parameters (e.g., angle of entrance, presence or absence of bulbous bow) that might reasonably be expected to have an effect. 4. The fourth group should contain the principal parameters defining a propeller, namely, diameter, pitch, blade area ratio, number of blades, and so on. It is not simple to determine uniquely the influence of various parameters on motions as well as dynamic effects. There is also a probability that a change in a parameter may be advantageous for the motion characteristics while degrading other performance factors. Therefore it is imperative to make series studies systematically, by computer applications, in order to establish the parametric influence in the determination of seakeeping qualities of any design. The fourth step of this study is obtaining and solving the regression equations. The result of the experimental studies which were carried out by D. I. Moor and D. C. Murdey in 1967 and our studies have shown that heave increases with Beaufort number, block coefficient, draft, radius of gyration and speed, and as the centre of buoyancy moves forward; and decreases as length, water plane area coefficient and beam increase. Similarly, pitch increases with Beaufort number, block coefficient, draft and radius of gyration; and decreases as length, water plane area coefficient and beam increase and as the centre of buoyancy moves forward. In addition pitch amplitudes tends to increase for high ship speeds and decrease for low ship speeds. Under these circumstances, the regression equations have been set up for the heave and pitch motions in terms of form parameters. For each Beaufort numbers, six linear equation systems have been obtained. Here the ship speed has been chosen arbitrarily in the range of 5 to 11 knots. Further, these linear equation systems have been solved by regression program. As the fifth step of this study, regression coefficients for the heave and pitch motions which were determined in the previous Step are presented. These regression coefficients change depending on the ship length, Beaufort number and the ship motion type. viii Finally, they are given in the tables. Finding the values of coefficient from the tables, and the calculation of regression expressions both are difficult and take time. For this reason, a computer program was developed for the calculation in Quickbasic and Fortran-77 languages. In this program, the coefficient values which were obtained in the fourth step are arranged as data files which change according to ship motion type and Beaufort numbers. Hence, through the use of the results of this study seakeeping considerations for trawlers can be included into the design cycle during the concept design stage.