Vol. 5, No 2, 2007 pp. 121 - 137
UDC 797.4:51.519.8
Scientific Paper
THE MATH MODELING OF THE STAGES OF RESULT DEVELOPMENT IN HIGH PROFILE ELITE SWIMMERS FOR THE 50m, 100m, 200m, 400m AND 1500m FREESTYLE
Tomislav Okičić1*, Dejan Madić1, Milivoj Dopsaj2, Miodrag Đorđević3
1Faculty of Sport and Physical Education, University of Niš
2Faculty of Sport and Physical Education, University of Belgrade
3Faculty of Natural Sciences, University of Niš
* E-mail: okicictomislav@ffk.ni.ac.yu, okicictomislav@yahoo.com
Abstract. The modern theoretical concept of sport training concentrated on achieving top sport results is based on a principle of perennial directional training that includes sports, preparation and competition. The given perennial process is based upon functional entireties of educational-directional training of the same sort, i.e. based on specific entireties divided into preparation periods. Every mentioned part, despite being functionally connected to the other parts, consists of differently designed training purposes called stages. The purpose of this research is to determine the models based upon which we could evaluate the stages of result development for the men’s 50, 100, 200, 400 and 1500m freestyle. This research has been carried out using data from secondary sources and it belongs to the category of chronobiological research. The sample consisted of 41 top male swimmers who won medals, that is, entered the finals at World and European Championships or at the Olympics during the last decade (Olympic size pool). This way, the research sample was categorized as consisting of swimmers with elite competition achievements. The modeling was performed using a mathematical method applying fitting of the polynomial degree function of the basic form n degree y = a0 + a1x + a2x2 + ... anxn. Two patterns have been calculated: 1) the given patterns in the change of the results at competitions in relation to the swimmers’ age 2) the pattern in the trend of change of the results at competitions in relation to the swimmers’ age within the tested discipline. The results showed that a reliable model, through which the given patterns are described, could be defined for every freestyle discipline. This enabled, in the first place, the measuring of the observed phenomenon and its description using the universal language of mathematics, and secondly, it opened the possibility of control and correction of applied training procedures that all trainers use when they want to compare the obtained model with the one they are applying.
Key words:  sport training technology, training stage models, math modeling, swimmers, free style
MATEMATIČKO MODELOVANJE ETAPNIH NIVOA RAZVOJA REZULTATA VRHUNSKIH PLIVAČA NA 50, 100, 200, 400 I 1500 METARA SLOBODNIM STILOM
Moderni teorijski koncept sportskog treninga, orijentisanog na postizanje vrhunskih sportskih rezultata, zasniva se na principu višegodišnje trenažno-takmičarsko-sportske usmerenosti primenjenog trenažnog rada. Dati višegodišnji proces organizaciono je zasnovan na funkcionalnim celinama istorodnog edukativno-trenažnog usmerenja, odnosno na posebnim celinama podeljenim na periode pripreme, od kojih svaki za sebe, iako povezan funkcionalno, ima projektovan različiti trenažni cilj nazvanim – etape. Cilj ovog istraživanja je utvrđivanje modela na osnovu kojih bi se mogla vršiti procena etapnog razvoja rezultata u plivanju na deonicama od 50, 100, 200, 400 i 1500m slobodnim stilom kod muškaraca koji predstavljaju populaciju najboljih vrhunskih plivača. Istraživanje je izvršeno pomoću podataka iz sekundarnih informacionih izvora i pripada kategoriji hronobioloških istraživanja. Sirovi uzorak obrađenih rezultata sastojao se od 41 vrhunskog plivača muškaraca koji su bili osvajači medalja, odnosno finalisti na Svetskim i Evropskim prvenstvima, ili Olimpijskim igrama u poslednjoj deceniji (bazen olimpijskih dimenzija). Na taj način uzorak ispitanika bio je kategorisan kao - sportisti plivači sa elitnim takmičarskim dostignućem. Modelovanje je izvršeno pomoću matematičke metode primenom metode fitovanja polinomijalnom stepenom funkcijom n -tog stepena opšteg oblika: y = a0 + a1x + a2x2 + ... anxn. Izračunate su dve zakonitosti i to: 1) data zakonitost promene takmičarskog razultata u funkciji uzrasta plivača, i 2) zakonitost promene trenda takmičarskog razultata u funkciji uzrasta plivača na ispitivanoj disciplini. Rezultati su pokazali da je za svaku distancu bilo moguće definisati pouzdan model kojim su opisane date zakonitosti, što je omogućilo kao prvo, merenje posmatranog fenomena i njegovo opisivanje univerzalnim jezikom matematike, a kao drugo, obezbedilo je mogućnost kontrole i potrebne korekcije primenjivanih trenažnih postupaka svih trenera koji, dobijeni model žele uporediti sa sopstveno primenjivanim.
Ključne reči: tehnologija sportskog treninga, etapni modeli, matematičko modelovanje, plivači, slobodni stil.