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Porównanie metod modelowania matematycznego kształtu skorupy jaj kurzych®

Mieszkalski Leszek, Tucki Karol, Grabowska Katarzyna

Postępy Techniki Przetwórstwa Spożywczego

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2022

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nr 2

65--69

PL

W artykule przedstawiono dwie metody matematycznego modelowania powierzchni kształtu skorupy jaja kurzego. Bryłę 3D wg Mieszkalskiego złożono z powierzchni zewnętrznej skorupy, stosując krzywą Beziera, którą obracano według osi Z układu współrzędnych. Model matematyczny bryły 3D opiera się na długości osi długiej i krótkiej jaja oraz na współrzędnych punktów węzłowych i kontrolnych. Wg Prestona podłużny kontur jaja (model 2D) można opisać za pomocą czterech parametrów. Kontur zdefiniowany za pomocą metody Prestona pozwolił na określenie objętości i porównanie jej do wyników opracowań Stonehouse-a i Coulson-a. Wizualizacje modeli 2D i 3D wykonano w programie Mathcad. W proponowanych metodach nie uwzględniono wewnętrznej struktury jaja kurzego.

EN

The article shows two methods for mathematically modelling the surface of the shell of a hen’s egg. The 3D block of Mieszkalski was composed from the outside of the shell using the Bezier curve, which was rotated according to the Z-axis of the coordinate system. The mathematical model of the 3D body is based on the length of the long and short axis of the egg and the coordinates of the nodes and control points. According to Preston, the elongated contour of the egg (model 2D) can be described with four parameters. The contour defined by the Preston method made it possible to determine the volume and compare it with the results of Stonehouse and Coulson. The visualizations of the 2D and 3D models were created with Mathcad. The methods proposed do not take into account the internal structure of the hen’s egg.

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Methodology for the Formation of a New Economic Model for Geological Exploration in Subsoil Use

Kuzina Elizaveta

Rocznik Ochrona Środowiska

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2021

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Tom 23

891--901

EN

In modern realities, there is no unified methodology for the economic assessment of geological exploration in subsoil use. The main research question of this study was to develop a methodology for the new economic model formation for assessing geological exploration in the subsoil use for the mineral resource base rational use. The new methodology can facilitate the assessment of subsoil users of hydrocarbon reserves and resources and government bodies when putting resources and reserves on the balance sheet. In the course of the study, modeling, observation, description, and analysis methods were used. The result of the study was a new economic model for evaluating geological exploration in subsoil use. The main conclusions can be characterized by the optimization of the main indicators of the valuation of mineral raw materials. The basic principles for calculating discounted cash flow, discount rate, payback period and internal rate of return were developed.

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Modelling the concentration and dimensional changes in the structural constituents of vermicular graphite cast iron on cooling within the range of solidus-eutectoid temperature

Kapturkiewicz W., Burbelko A. A., Fraś E.

Archives of Foundry Engineering

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2008

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Vol. 8, iss. 1 spec.

179--182

EN

A mathematical model and a simulation program have been developed to trace changes in the structure of Fe-C alloy on cooling from the solidus temperature to the temperature of eutectoid transformation. A simplified schematic representation of the process can be referred to the cast iron with vermicular graphite. The numerical experiments using the newly developed program have proved a significant effect of the cooling conditions and structure refinement degree (the dimensions of austenite) on the concentration field in austenite and, consequently, on the dimensional changes of graphite within the examined cooling range. The developed methods of modelling the process of transformation enable including the procedure into a complex software operating in a system reproducing in real manner the casting configuration, while the obtained results indicate an important effect of thermophysical parameters and heat transfer process on final alloy structure.