Matematična in fizikalna obravnava idealne vzletne krivulje smučarskega skakalca : diplomska naloga

Flajs, Gašper (author), Kramar Fijavž, Marjeta (mentor), Kokalj, Jure (co-mentor)

Cilj smučarskih skakalcev je, da skočijo čim dlje, na kar vpliva tudi hitrost, ki jo pridobijo na vzletišču. V diplomski nalogi je predstavljeno optimiziranje oblike vzletne krivulje skakalnice z namenom pridobitve čimvečje končne hitrosti na koncu vzletne steze. Za izhodiščno krivuljo smo izbrali krivuljo, ki je kot praktični primer opisana v FIS standardu za projektiranje smučarskih skakalnic. Ključni dejavniki, ki vplivajo na skakalca pri vzletu, so: sila gravitacije, sila trenja in sila zračnega upora. Zaradi kompleksnosti vpliva trenja in vpliva zračnega upora problema optimizacije ni bilo mogoče rešiti analitično. Za numerično optimizacijo smo si pomagali s programskim orodjem Mathematica. Izračunana krivulja je stopničaste oblike. Rezultate optimizirane krivulje smo primerjali z rezultati privzete FIS krivulje, trohoide, cikloide in konstruirane stopničaste krivulje.

• Language: Slovenian
• Keywords: smučarski skoki, vzletna krivulja, optimizacija
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: [G. Flajs]
• Year: 2018
• PID: 20.500.12556/RUL-101666
• UDC: 514:519.862:796.925(043.2)
• COBISS.SI-ID: 8468065
• Publication date in RUL: 24.06.2018

Secondary language

• Language: English
• Title: Mathematical and physical treatment of the ideal take-off curve of the ski jumper : graduation thesis

Abstract

Ski jumpers’ goal is to jump as far as possible which is directly affected by the speed they reach at the take-off. This diploma thesis determines the optimised curve of the in-run slope to obtain the highest final speed at the end of the ramp. The curve described as the practical example in the FIS Standard for the Construction of the Jumping Hills was selected as the basis. The key factors affecting the ski jumper during take-off are the force of gravity, friction force, and air resistance force. Due to the complexity of the influence of friction and air resistance, the problem of the optimisation could not have been solved analytically. Software tool Mathematica was used for the numerical optimisation. The calculated curve takes the form of a step. The results of the optimised curve were compared with the results of the default FIS curve, trochoid, cycloid, and the constructed step curve.

• Keywords: ski jumping, transition curve, optimization