PEMODELAN MATEMATIKA DAN SIMULASI NUMERIK LEMPAR LEMBING - Rani Rotul Muhima; Maftahatul Hakimah (Universitas Trunojoyo Madura, 2015)
ABSTRAKLempar lembing merupakan salah satu cabang olahraga atletik. Hasil lemparan dalam lempar lembing tergantung beberapa faktor, antara lain kekuatan, kecepatan, persiapan fisik dan psikologis pelempar. Teknik melakukan lemparan,kondisi cuaca saat melakukan lemparan, jenis lembing yang digunakan, kondisi lapangan juga berpengaruh pada hasil lemparan. Pengembangan model matematikagerak lembing setelah dilempar pada makalah ini bertujuan untuk mengoptimalkan hasil lemparan pelempar lembing. Pengoptimalan hasil lemparan dititikberatkan pada pemilihan kecepatan awal lemparan dan sudut arah lemparan. Model matematika dikembangkan dalam bentukdua dimensi. Tiga paremeter yang dikaji dalam model matematika gerak lembing, yaitu: geometri, massa dan gaya aerodinamika. Persamaan Nonlinear Three Degrees of Freedom (3 DOF) digunakan untuk model matematika gerak lembing. Karakteristik aerodinamika lembing dianalisa menggunakan metode analitik, empiris dan hasil-hasil eksperimen. Karakteristik tersebutdihitung dengan memasukkan geometri umum lembing. Geometri lembing yang digunakan pada makalah ini adalah geometri lembing wanita. Simulasi numerik dari model matematika dilakukan dengan variasi kecepatan awal lemparan dan arah lemparan. Hasil simulasi numerik gerak lempar lembing disajikan dalam bentuk grafik dan diperoleh tinggi maksimumH sebesar 28,62 m dan jangkauan maksimum x sebesar157,476 m pada kecepatan awal V0=40 m/s dan sudut lemparan θ0 = 35 deg.Kata Kunci: gerak lembing, model matematika, aerodinamika, simulasi numerik, 2D.ABSTRACTJavelin throw is one of the sport of athletics. Results in the javelinthrow depends on several factors, such as strength, speed, physical preparation, and psychological thrower. Technical thrower, the weather conditions when making the throw, javelin used species, field conditions also affect the results of the throw. Development of mathematical models of motion javelin after being thrown on the paper aims to optimize the results throw javelin thrower..Optimization of the results focused on the selection of the initial speed of the throw and angle of direction of the throw. The mathematical model of javelin motion developed in 2D. Three parameter were studied in the mathematical model of javelin throw: geometry, mass, and aerodynamic forces. NonlinearThree Degrees of Freedom(3DOF) equations of motion used in the mathematical model of javelin motion. Javelin aerodynamic characteristics were analyzed using the analytical method, emperical and results of the experimental. The characteristic was calculated by including the general geometry of the javelin. Geometri of javelin that used in this paper was the geometry of female javelin. The model was simulated for different initial velocities and throwing angles. The simulation results are presented in graphical form and maximum height H = 28,62 m and maximum rangevalue R = 157,476 m was obtained at the initial velocity V0 = 40 m/s and the pitch angle θ0= 35 deg.Keywords: javelin throw, mathematical model, aerodynamics, numerical simulation, 2D.