The Ricochet of Spinning Spheres Off Water

Abstract

Liquid impact and ricochet is still attracting researchers interested in the field of hydrodynamics and naval engineering. The ricochet from a water surface experienced by spinning spheres was examined both analytically and numerically. A theoretical analysis was made to quantify the enhancement attained by imparting backspin to the sphere. Numerical simulation of the process was conducted by implementing ABAQUS software. The mathematical analysis and the simulation were built on the assumption that the effects of cavitation, splash, and two phase flow are negligible compared to hydro-dynamical forces of lift and drag. It was proven that both mathematical analysis and simulation were capable of predicting the trajectory of a spinning sphere during its course of entry into the water. Aspects like the critical angle of ricochet and the maximum depth of immersion were extracted from these trajectories and compared with available data. It was found that the analytical and numerical results were generally validated with respect to each other as well as to existing findings. Aluminum () spinning spheres, of radius 10 mm and speed of 10 m/sec, were examined. It was found that a 300 rad/sec backspin improves the critical angle of ricochet from 10.43 to 12.5 deg and increases the maximum depth of immersion from 1.52 to 1.83.  "Magnus Effect" usually acting on a fully immersed spinning sphere, was described and relations estimating the hydrodynamic forces were deduced.

ABSTRAK: Keadaan pertumbuhan bakteria penghasil enzim protease aktif-sejuk terasing daripada sampel Antartika disaring menggunakan satu-faktor-satu-masa (OFAT). Kemudian, enzim protease ini diekstrak pada lewat fasa logaritma untuk ujian enzimatik. Strain yang menunjukkan aktiviti enzim tertinggi telah dipilih bagi tujuan pengoptimuman melalui Kaedah Permukaan Tindak Balas (RSM). Parameter yang dikaji adalah pada suhu pengeraman (4 - 36 °C), media pH (4 – 10) dan kepekatan NaCl (0 - 8 %). Berdasarkan dapatan OFAT, kesemua lapan bakteria menunjukkan kadar pertumbuhan tertinggi pada 20 °C, pH 7 dan 4% NaCl (w/v). Hasil ujian enzimatik menunjukkan enzim protease mentah yang diekstrak daripada SC8 menunjukkan aktiviti yang jauh lebih tinggi (0.20 U dan 0.37 U) daripada kawalan positif (0.11 U dan 0.31 U) pada -20 °C dan 20 °C. RSM ini menunjukkan kadar optimum bagi pertumbuhan SC8 adalah pada 20.5 °C, pH 6.83 dan 2.05% NaCl (w/v) dengan dapatan kadar pertumbuhan bakteria pada 3.70 ± 0.06 x 10⁶ sel/jam. Keadaan pertumbuhan optimum SC8 melalui kajian ini bermanfaat bagi menghasilkan produk protease aktif-sejuk secara besar-besaran pada masa hadapan.