Optimal Ship Forms for Minimum Wave Resistance

1981 ◽  
Vol 25 (02) ◽  
pp. 95-116
Author(s):  
Chi-Chao Hsiung
Keyword(s):  
Linear Inequality ◽  
Inequality Constraints ◽  
Wave Resistance ◽  
Ship Hull ◽  
Towing Tank ◽  
Ship Model ◽  
Linear Inequality Constraints ◽  
Merchant Ship ◽  
Programming Techniques ◽  
Hull Forms

By introducing a set of "tent" functions to approximate the ship hull function, the Michell integral for wave resistance is reduced to a standard quadratic form in terms of ship offsets. With linear-inequality constraints of the type 0 ≤ H(x, z) ≤ B;C ≤ Hx(x,z) ≤ D(where H(x,z) is the hull function and B, C, D are constants), we are able to find various optimal ship forms of minimum wave resistance by applying quadratic programming techniques to the problem. Three optimal forms have been chosen among a number of computed results for tests in the ship-model towing tank. All three models have afterbodies identical with that of Series 60, Block 60, a standard merchant ship hull of good quality. Although the experimentally determined residuary resistance is in no better agreement with the theoretically predicted results than is usual in such comparisons, the order of "goodness" of the hull-forms as predicted and as measured was the same for Fn ≥ 0.36 and also for 0.20 ≤ Fn ≤ 0.26.

Optimal Ship Forms for Minimum Total Resistance

1984 ◽  
Vol 28 (03) ◽  
pp. 163-172
Author(s):  
Chi-Chao Hsiung ◽  
Dong Shenyan
Keyword(s):  
Quadratic Form ◽  
Numerical Scheme ◽  
Linear Inequality ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Frictional Resistance ◽  
Wave Resistance ◽  
Total Resistance ◽  
Linear Inequality Constraints ◽  
Quadratic Programming Method

A numerical scheme is developed by using the "tent" function to compute the hull surface area and then the ship frictional resistance in a quadratic form in terms of ship offsets. Combining with the wave resistance, a total ship resistance formula is derived in a standard quadratic form. With a set of linear-inequality constraints, the optimal solution of ship offsets for minimum total resistance can be obtained by applying a quadratic programming method to the problem. Computations have been carried out for three conditions which have exactly the same constraints as those required to obtain the optimal forms for minimum wave resistance shown in an earlier work [1].3 The optimal forms found for minimum total resistance also have either bow or midship bulbs. The new optimal bulbs have a relatively small size, higher vertical slope to the baseline, and less curvature at the tip of the bulb.

Experimental Study of a Tanker Ship Squat in Shallow Water

2014 ◽  
Vol 66 (2) ◽  
Author(s):  
Mohammadreza Fathi Kazerooni ◽  
Mohammad Saeed Seif
Keyword(s):  
Experimental Study ◽  
Shallow Water ◽  
Experimental Approach ◽  
Model Tests ◽  
Ship Hull ◽  
Experimental Results ◽  
Shallow Waters ◽  
Towing Tank ◽  
Ship Model

One of the phenomena restricting the tanker navigation in shallow waters is reduction of under keel clearance in the terms of sinkage and dynamic trim that is called squatting. According to the complexity of flow around ship hull, one of the best methods to predict the ship squat is experimental approach based on model tests in the towing tank. In this study model tests for tanker ship model had been held in the towing tank and squat of the model are measured and analyzed. Based on experimental results suitable formulae for prediction of these types of ship squat in fairways are obtained.

Resistance of a Ship Undergoing Oscillatory Motion

2010 ◽  
Vol 54 (02) ◽  
pp. 120-132
Author(s):  
Lawrence J. Doctors ◽  
Alexander H. Day ◽  
David Clelland
Keyword(s):  
Finite Depth ◽  
Mean Value ◽  
Wave Resistance ◽  
General Effect ◽  
Towing Tank ◽  
Ship Model ◽  
Average Value ◽  
Unsteady Effects ◽  
Oscillatory Cycle ◽  
Resistance Tests

In this paper, we describe extensions to the research of Doctors et al. (Doctors, L. J., Day, A. H., and Clelland, D., 2008, Unsteady effects during resistance tests on a ship model in a towing tank, Journal of Ship Research, 52, 4, 263–273) and Day et al. (Day, A. H., Clelland, D., and Doctors, L. J., 2009, Unsteady finite-depth effects during resistance tests in a towing tank, Journal of Marine Science and Technology, 14, 3, 387–397) in which the oscillations in the wave resistance during the constant-velocity phase of a towing-tank resistance test on a ship model were measured and predicted, in the cases of relatively deep and relatively shallow water. In the current study, the ship model was towed with a harmonic velocity component superimposed on the usual constant forward velocity. This work constitutes a first step in the understanding of the unsteady hydrodynamics of a racing shell (rowing boat). We show here that the unsteady wave resistance varies considerably from the traditional (steady) average value. Indeed, the wave resistance is frequently negative during part of the oscillatory cycle. However, the general effect is an increase in the temporal mean value of the wave resistance; this suggests that every effort should be made to reduce the unsteadiness of the motion. We also demonstrate that the unsteady wave-resistance theory provides an excellent prediction of the measured effects summarized here. These predictions are often within a few percent of the measured values of the resistance.

scholarly journals Mathematical model for determining rational machining conditions for flat grinding with the wheel periphery on machines with a rectangular table

2018 ◽  
Vol 224 ◽  
pp. 01112
Author(s):  
Dmitriy L. Skuratov ◽  
Dmitriy G. Fedorov ◽  
Dmitriy V. Evdokimov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Linear Inequality ◽  
Inequality Constraints ◽  
Machining Time ◽  
Functional Parameters ◽  
Linear Inequality Constraints ◽  
Machining Quality ◽  
Machining Conditions ◽  
Grinding Operations

A mathematical model is presented for determining the rational machining conditions for flat grinding operations by the rim of a wheel on machines with a rectangular table consisting of a linear objective function and linear inequality constraints. As the objective function, the equation, determining the main machining time, was used. And constraints which are related to the functional parameters and parameters determining the machining quality and the kinematic capabilities of the machine were used as inequality constraints.

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