Python Magnus Effect

Python script to demonstrate the Magnus Effect.

# © 2019 TheFlyingKeyboard and released under MIT License 
# theflyingkeyboard.net

import math
import matplotlib.pyplot as plt
from pylab import rcParams

rho = 1.225
radius = 0.0635
spin = 100
omega = (2 * math.pi * spin) / 60.0
c = math.pi * math.pow(rho, 2) * math.pow(radius, 3) * omega
mass = 0.136

y = 1.8288
x = 0.0
time = 0.0
precision = 0.01
v0x = 40.0
v0y = 0.0
gravity = 9.81
sy = 1.0

plotX = []
plotY = []

while sy > 0:
    time += precision
    vx = (1.0 / (1.0 - math.pow(time / mass, 2) * math.pow(c, 2))) * (v0x + c * v0y * (time / mass) - c * gravity
                                                                    * math.pow(time, 2) / mass)
    vy = (v0y + (time / mass) * c * vx) - gravity * time

    sx = x + v0x * time + 0.5 * (c / mass * vy) * math.pow(time, 2)
    sy = y + v0y * time + 0.5 * (((c * vx) - mass / gravity) / mass) * math.pow(time, 2)

    plotX.append(sx)
    plotY.append(sy)

rcParams['figure.figsize'] = 16, 9
plt.gca().xaxis.grid(True)
plt.gca().yaxis.grid(True)

plt.xlabel("X")
plt.ylabel("Y")

plt.plot(plotX, plotY)

plt.show()