A Study on the Optimal Forebody Forms for Minimum Wave Resistance

최소조파 저항성능을 갖는 최적 선수형상에 관한 연구

A study on the optimization problems to find forebode shapes with minimum wavemaking and frictional resistance was performed. The afterbody was fixed as a given hull and only forebode offsets were treated as design variables. Design variables were divided into the offsets of given hull and small variation from them. For the wavemaking resistance calculation, Neumann-Kelvin theory was applied to the given hull and thin ship theory was applied to the small variation. ITTC 1957 model-ship correlation line was used for the calculation of frictional resistance. Hull surface was represented mathmatically using shape function. As object function, such as wavemaking and frictional rersistance, was quadratic form of offsets and constraints linear, quadratic programing problem could be constructed. The complementary pivot method was used to find the soulution of the quadratic programing problem. Calculations were perfomed for the Series 60 $C_{B}$=0.6. at Fn=0.289. A realistic hull form could be obtained by using proper constraints. From the results of calculation for the Series 60 $C_{B}$=0.6, it was concluded that present method gave optimal shape of bulbous bow showing a slight improvement in the wave resistance performance at design speed Fn=0.289 compared with the results from the ship theory only.

조파저항과 마찰저항이 최소가 되는 선수형상을 구하기 위한 최적화문제에 관한 연구를 수행하였다. 선미부는 기존선형으로 고정하며 선수부만의 offsets을 설계변수로 하였다. 구하고자 하는 최적선형을 기존선형과 이에 대한 미소변화량으로 나누어 조파저항계산시 기존선형에는 Neumann-Kelvin 이론을 적용하고 미소변화량에는 thin ship 이론을 적용하였으며 마찰저항은 ITTC 1957 모형선-실선 상관곡선을 이용하였다. 선체표면을 모양함수(shape function)를 이용하여 근사시켰고, 이로부터 목적함수인 조파저항과 마찰저항은 offsets에 대한 2차식 형태로 표현되므로 선형구속조건을 적용하면 2차계획(quadratic programing)문제를 세울 수 있으며 complementary pivot method를 이용하여 해를 구하였다. 대상선형은 Series 60 $C_{B}$=0.6이고 Fn=0.289에서 최적화하였으며, 적절한 구속조건을 주어서 현실적인 최적선수형상을 구하고자 하였다. 본 방법으로 구한 최적선형은 thin ship 이론만을 이용하여 구한 선형과 비교할 때 설계속도 Fn=0.289에서 약간의 조파저항성능 개선(1.92%)를 가져왔다.