A Generic Mathematical Model for the Maneuvering and Tacking of a Sailing Yacht

2005 ◽  
Author(s):  
J. A. Keuning ◽  
K. J. Vermeulen ◽  
E. J. de Ridder
Keyword(s):  
Mathematical Model ◽  
Present Report ◽  
Full Scale ◽  
Hull Form ◽  
Sailing Yacht ◽  
The Mathematical Model

In the present report an extension of the mathematical model for the tacking maneuver of a sailing yacht, as previously described by the same authors in Reference [1], will be presented. There is a need for such a mathematical model because the tacking maneuver and more in particular the speed loss during such a maneuver, is of interest for handicapping purposes. If this speed loss of a large variety of sailing yachts can be calculated the differences may be incorporated in their respective handicaps. This implies however also that this mathematical model should incorporate only the use of formulations based on “generic” parameters, which describe the hull form and the sail plan of the yacht under consideration. In the present report a more complete description of this model, as available so far, will be presented. The accent is on the hydrodynamic part of the model. As much as possible the results obtained within the Delft Systematic Yacht Hull Series (DSYHS) will be used. In a future report also the aerodynamic part will be more extensively elaborated so that a wider variety of sail plans may be dealt with. A number of simulations with the model have been performed and checked with the results obtained during a series of full scale measurements.

scholarly journals Nurbs modeling for design waterline based on the variation of sectional area curve

2021 ◽  
Vol 3 (SI2) ◽  
pp. SI37-SI46
Author(s):  
Hoa Thị Ngọc Nguyễn ◽  
Ngoc Bich Vu ◽  
Tat-Hien Le
Keyword(s):  
Mathematical Model ◽  
Quadratic Function ◽  
Design Stage ◽  
Sectional Area ◽  
Hull Form ◽  
B Spline ◽  
Preliminary Design Stage ◽  
Form Design ◽  
Hull Form Design ◽  
The Mathematical Model

Hull form design from parent ships transforms the ship's parameters based on the variation of theoretical sectional area curve of the Lackenby method. The correction and modification of the theoretical sectional area curve is essentially the change of ship displacement, hull form coefficients, and the longitudinal center of buoyancy from the parent ships. In the preliminary design stage, the hull form design approach from parent ships minimizes the risks compared to the new design while still retaining hydrostatic and hydrodynamics' advantages. However, the Lackenby method of ship hull form variation uses a linear or quadratic function to shift the sectional area curves, regardless of the ship's hull form faring, especially the curvature's discontinuity the bow, stern, and midship. Therefore, the computer graphic algorithm based on the B-spline function is studied and applied; simultaneously, the mathematical model for the designed waterline is built in the form of a continuous curve instead of the B-spline segments. In this study, the mathematical model for the coastal container ship's design water line is constructed, ensuring continuity and fairing throughout the continuous B-spline curve. The geometry continuity evaluation results are expressed through the parameter curve's curvature and resistance component calculations' performance by computational analysis.

scholarly journals Numerical Simulation of the Ship Resistance of KCS in Different Water Depths for Model-Scale and Full-Scale

2020 ◽  
Vol 8 (10) ◽  
pp. 745 ◽  
Author(s):  
Dakui Feng ◽  
Bin Ye ◽  
Zhiguo Zhang ◽  
Xianzhou Wang
Keyword(s):  
Water Depth ◽  
Full Scale ◽  
Scaled Model ◽  
Hull Form ◽  
Ship Resistance ◽  
Model Scale ◽  
Computational Fluid Dynamics Cfd ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Water Depths

Estimating ship resistance accurately in different water depths is crucial to design a resistance-optimized hull form and to estimate the minimum required power. This paper presents a validation of a new procedure used for resistance correction of different water depths proposed by Raven, and it presents the numerical simulations of a Kriso container ship (KCS) for different water depth/draught ratios. Model-scale and full-scale ship resistances were predicted using in-house computational fluid dynamics (CFD) code: HUST-Ship. Firstly, the mathematical model is established and the numerical uncertainties are analyzed to ensure the reliability of the subsequent calculations. Secondly, resistances of different water depth/draught ratios are calculated for a KCS scaled model and a full-scale KCS. The simulation results show a similar trend for the change of model-scale and full-scale resistance in different water depths. Finally, the correction procedure proposed by Raven is briefly introduced, and the CFD resistance simulation results of different water depth/draught ratios are compared with the results estimated using the Raven method. Generally, the reliability of the HUST-Ship solver used for predicting ship resistance is proved, and the practicability of the Raven method is discussed.

scholarly journals EXPERIMENTAL DETERMINATION OF THE HOLE AXIS DEFLECTION WHEN WORKING WITH A COUNTERSINK WITH CARBIDE BLADES

2020 ◽  
Vol 20 (1) ◽  
pp. 55-62
Author(s):  
I. P. Deryabin ◽  
◽  
A. S. Tokarev ◽  
B. A. Lopatin ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cutting Forces ◽  
Full Scale ◽  
Shape Accuracy ◽  
Full Scale Experiment ◽  
Lateral Displacements ◽  
Scale Experiment ◽  
The Mathematical Model ◽  
Hole Axis ◽  
Theoretical Results

This article discusses the developed mathematicalmodel that takes intoaccount the errors of sharpening and assembling the cutting blades of a countersink tool with carbide blades. This allows you to determine the actual area of the cut sections of the allowance for each blade and calculate the cutting forces acting on them. The resultant cutting forces leads to lateral displacements of the axis of the tool during machining of the hole. The mathematical model makes it possible to determine the errors of processing holes (axis retraction, split and shape accuracy) with a countersink with a carbideblades. To check the adequacy of the mathematical model, fullscale experiments were performed on blanks madeof various materials. The method of conducting a full-scale experiment was developed. Recommended cutting modes and a countersink with three blades are selected. Processing was performed at the MM800 Fanuc processing center. Using modern automation tools – the Renishaw system and additive technologies using the Range Vision Spectrum 3D scanner, the drift of the hole axis was measured after processing with a vertical drill with carbide blades. This device allows you to get the desired result in a very short time. A compact sensor was used to measure the deflection of the hole axis, allowing for very accurate results. Substituting the part processing data into the mathematical model, the calculated values (theoretical) of the hole axis withdrawal during processing for the prototypes are obtained. The theoretical results and the results of the field experiment are compared. Comparing the obtained theoretical results – the results of a mathematical model, and the results of a full-scale experiment, it was concluded that the developed mathematical model is adequate and can be used in production by technologists in the development and computer debugging of technological processes.

Hydrodynamics of Liquid Motion in Straight-Line Capillaries

2019 ◽  
Vol 942 ◽  
pp. 110-120
Author(s):  
Irina Lobanova ◽  
Vladimir Meshheryakov ◽  
Aleksey Kalinichenko ◽  
Anatoly Surzhikov
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Full Scale ◽  
Liquid Motion ◽  
Straight Line ◽  
Capillary Size ◽  
The Mathematical Model

The paper considers the mathematical model of liquid motion in straight-line capillaries. The proposed mathematical model shows the liquid motion in slit-like capillaries, with regard to the density, viscosity and surface tension of liquids, the capillary size, and the angle of capillary inclination to the horizontal. The modeling results are proved by full-scale experiments.

Cutting Technique of Welding Groove for Intersecting of Braces at Small Angle during Liwan 3-1 CEP Jacket Fabrication

2013 ◽  
Vol 328 ◽  
pp. 34-38
Author(s):  
Feng Yan Yang ◽  
Shu Min Li ◽  
Zheng Rong Song ◽  
Tui Deng ◽  
Zeng Bo Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Small Angle ◽  
Full Scale ◽  
Cutting Method ◽  
Transition Section ◽  
Intersecting Pipes ◽  
The Mathematical Model

This paper presents the method to perform cutting of welding groove for intersecting of pipes at small angle during Liwan 3-1 CEP jacket fabrication. The mathematical model of the intersecting pipes as well as the cutting method for transition section have been studied using the principle of geometry, which enables fabrication team to print out the full scale template drawing to guide cutting of welding groove for intersecting of braces at small angle. This method has been fully tested during LW3-1 jacket fabrication which indicated that the welding groove can meet the requirements of AWS D1.1 code and the method can be adopted for future jacket construction.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

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