task1.txt

# Parameters for Task 1 in the following order from left to right:

# Trajectory number

# Initial velocity (m/s) and direction angle (degree): Umag, theta, phi

# Rotational velocities (rad/s): omgX, omgY, omgZ

# Coefficients of friction and Magnus effect: Cd, Cm

1 35.0 -12.5 76.25 0.0 0.0 0.0 0.3 0.6

2 35.0 -12.5 76.25 0.0 0.0 -14.4 0.3 0.6

3 35.0 -12.5 76.25 0.0 0.0 -28.1 0.3 0.6

4 35.0 -12.5 76.25 0.0 0.0 -42.3 0.3 0.6

5 35.0 -12.5 76.25 0.0 0.0 -56.2 0.3 0.6

6 35.0 -12.5 76.25 0.0 0.0 -70.5 0.3 0.6

task2.txt

# Parameters for Task 1 in the following order from left to right:

# Trajectory number

# Initial velocity (m/s) and direction angle (degree): Umag, theta, phi

# Rotational velocities (rad/s): omgX, omgY, omgZ

# Coefficients of friction and Magnus effect: Cd, Cm

1 35.0 -12.5 76.25 0.0 0.0 0.0 0.3 0.6

2 35.0 -12.5 76.25 0.0 0.0 -14.4 0.3 0.6

3 35.0 -12.5 76.25 0.0 0.0 -28.1 0.3 0.6

4 35.0 -12.5 76.25 0.0 0.0 -42.3 0.3 0.6

5 35.0 -12.5 76.25 0.0 0.0 -56.2 0.3 0.6

6 35.0 -12.5 76.25 0.0 0.0 -70.5 0.3 0.6

Project: Magnus Effects on the Projectile of a Soccer Ball In this project, you are to simulate the effects of spinning on the projectile of a soccer ball. In flight, the motion of the ball is influenced by gravitational, drag and Magnus forces. The Magnus force which results from the spinning motion causes the trajectory to bend. You will examine how different rates and directions of spinning (side-spin and back-spin) affect the motion of the ball. The projectile motion of the soccer ball can be described by the following equations: OUU pA pAr Cnn 2m. pA pAr Cnn 2m OW pA pArr UU) g, WW2 2m OZ (1) The parameters are defined as follows: m 0.4 (kg): mass of the ball r 0.11 (m): radius of the ball (m2) sectional area of the ball p 1.2 (kg/m3): density of air g 9.81 (m/s2): gravity Ca and Cm: Drag and Magnus coefficients, respectively t (s): time X, Y, Z (m): position of the ball in rectilinear coordinate. VW (m/s): velocity components of the ball in the x, y, and z directions, respectively war, wu and w (rad/s): rotational velocity around the x, y and z axis, respectively. Umag (m/s): initial speed of the ball and 0(o): initial kick angles mar-height-position: location where the absolute value of vertical velocity W is smallest landing-location: final position of the trajectory before the ball hits the ground. The initial position of the ball is at X 3 0, Y 0 and Z 0. Some simulation parameters listed above are stored in two data files taskl.txt and task2.txt for two separate tasks.