COMP155/EMGT 155 Golf Ball Dynamics December 1, 2008 There are three forces acting on a golf ball in flight: 1) lift, because of its shape 2) drag, due to air resistance, and 3) gravity. As shown in the figure, lift (CL) is perpendicular to the motion of the ball and drag (CD) is directly opposite the motion of the ball. Gravity (g) always acts downward. These forces act to modify the acceleration of the golf ball, as defined by the following equations: x’’ = - K * v2 * (CDcos(α) + CLsin(α)) y’’ = K * v2 * (CLcos(α) - CDsin(α)) – g where: K is a constant relating ball shape, ball mass and air density CD is the drag coefficient CL is the lift coefficient g is gravity (9.8 m/s2) v is the instantaneous velocity of the ball (m/s) α is the instantaneous angle of flight (radians above horizontal) Values for K, CD and CL can be found at http://simscience.org/fluid/red/golf_exp.html. Problem: Simulate a golf ball to determine: (a) the optimal launch angle for a velocity of 70 m/s, and (b) the optimal launch velocity for a launch angle of 10 degrees. In both cases, “optimal” means the longest horizontal flight on a level surface. figure from http://simscience.org/fluid/red/golf_exp.html gravityCOMP155/EMGT 155 Golf Ball Dynamics December 1, 2008 Golf Ball Coefficents (source: http://simscience.org/fluid/red/golf_exp.html) Challenge Assignment (groups of 2 or 3): Create a golf ball simulation, using the programming and/or simulation environment of your choice. Present simulation in class on December 3. Best simulation: receives a 100% bonus assignment score. Other correct simulations: receive a graded (max 90%) bonus assignment score. Bonus assignment scores will be used to replace lowest score from among regular assignments. Correct simulations must provided reasonable answers to the two problems stated on the previous
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