TECHICAL Series MATHEMATICS • INFORMATICS • PHYSICS Series PHILOLOGY Series ECONOMIC SCIENCES Sereies EDUCATIONAL SCIENCES Series LAW AND SOCIAL SCIENCES Series
The Construction of Intersection Points between a Straight Line and an Ellipsoid
(Construcţia punctelor de intersecţie dintre o dreaptă şi un elipsoid)
Vol LXII • No. 1/2010
Lavinia S. Stanciu, Nicoleta F. Rizea
Universitatea Petrol - Gaze din Ploieşti, Bd. Bucureşti, 39, Ploieşti
e-mail: laviniastanciu@yahoo.com, nicoletarizea@yahoo.com

 Keywords   ellipsoid, straight line, intersection points.

 Abstract
In this paper, the drawing of the intersection between a straight line and an ellipsoid, using auxiliary graphic constructions, is presented. This kind of intersection demands many preparatory steps and auxiliary graphic drawings, as the finding of the tangent planes. The draft has been obtained using both the means offered by the descriptive geometry and the AutoCAD program. So, a very precise construction of the intersection points coordinates is guaranteed. Ellipsoidal shells are used in the chemical and petrochemical industry, as ellipsoidal heads for: pressure vessels, heat exchangers, posts etc. On these heads, some fittings can be installed and their axes can have various angles to the horizontal or vertical axis.

 Rezumat
In această lucrare este prezentată intersecţia dintre o dreaptă şi un elipsoid, folosind construcţii grafice auxiliare. Acest tip de intersecţie necesită mai mulţi paşi pregatitori şi construcţii grafice suplimentare, cum ar fi găsirea unor plane tangente. Epura a fost obţinută utilizând atât mijloacele oferite de geometria descriptivă, cât şi programul AutoCAD. Astfel, este obţinută o construcţie foarte precisă a coordonatelor punctelor de intersecţie. Învelişurile elipsoidale sunt utilizate în industria chimică şi petrochimică sub denumirea de funduri şi capace elipsoidale. Echipamentele tehnologice din a căror componenţă fac parte acestea sunt: vase sub presiune, schimbătoare de căldură, coloane, amestecătoare etc. Pe aceste capace elipsoidale sunt montate racorduri având diverse unghiuri de incidenţă. Axele acestor racorduri pot fi asimilate dreptei de intersecţie din lucrarea prezentată.



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