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kinematic_sim.py
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kinematic_sim.py
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import math
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider, Button
# v0 = 11 # m/s
# theta0 = 50 # degrees
mass = 280/1000 # kg
diameter = 20/100 # m
r = diameter/2
dt = 0.001 # seconds
# constants
g = 9.8 # m/s
p = 1.225 # kg/m^3
mu = 1.8*(10**-5)
def get_energy(v, w, h):
return .5*mass*v**2 + .5*(2/3)*mass*(r**2)*(w**2) + mass*g*h
def vacuum(v0, theta0, drag_coefficient, spin_coefficient):
v0 = v0 * .3048
theta0 = theta0 * math.pi/180
# Initial Conditions
x = 0
y = 0
vx = v0*math.cos(theta0)
vy = v0*math.sin(theta0)
vacuum_coordinates = []
while y >= 0:
x += vx*dt
y += vy*dt
vx = vx
vy = vy - g*dt
vacuum_coordinates.append([x*3.28, y*3.28])
# print(x, y)
vacuum_coordinates = list(map(list, zip(*vacuum_coordinates)))
# print(x, y)
# print("------------- Vacuum -------------")
# print(x*3.28, y*3.28)
# v = math.sqrt(vx**2 + vy**2)
# print("final v", v, vx, vy)
return vacuum_coordinates
def drag(v0, theta0, drag_coefficient, spin_coefficient):
v0 = v0 * .3048
theta0 = theta0 * math.pi/180
# Initial Conditions
x = 0
y = 0
vx = v0*math.cos(theta0)
vy = v0*math.sin(theta0)
c = (math.pi/16) * p * diameter**2 # kg/m^3*m^2 = kg/m
# print("C:", c)
drag_coordinates = []
while y >= 0:
x += vx*dt
y += vy*dt
# print(vx, vy)
v = math.sqrt(vx**2 + vy**2)
theta = math.atan2(vy, vx)
Fd = c * v**2 * drag_coefficient
# print(v, theta*180/math.pi, Fd)
vx = vx - Fd*math.cos(theta)/mass*dt
vy = vy - g*dt - Fd*math.sin(theta)/mass*dt
drag_coordinates.append([x*3.28, y*3.28])
# print(x, y)
drag_coordinates = list(map(list, zip(*drag_coordinates)))
# print("------------- Drag -------------")
# print(x*3.28, y*3.28)
# v = math.sqrt(vx**2 + vy**2)
# print("final v", v, vx, vy)
return drag_coordinates
def spin(v0, theta0, drag_coefficient, spin_coefficient):
v0 = v0 * .3048
theta0 = theta0 * math.pi/180
# Initial Conditions
x = 0
y = 0
vx = v0*math.cos(theta0)
vy = v0*math.sin(theta0)
c = (math.pi/16) * p * diameter**2 # kg/m^3*m^2 = kg/m
d = 2*math.pi*p*(r)**2/r
b = 4.1*10**-4*2#/4
# print("C:", c)
# print("Constants", b, d)
e = 3*math.pi*mu*r/(2*mass)
# print(e)
w = v0/r
wf = 0*v0/r
ti = 0
tf = 2
spin_coordinates = []
time_elapsed = 0
while y >= 0:
x += vx*dt
y += vy*dt
v = math.sqrt(vx**2 + vy**2)
theta = math.atan2(vy, vx)
Fd = c * v**2 * drag_coefficient
# print(v, theta*180/math.pi, Fd)
energy = get_energy(v, w, y)
# print(energy)
w = w - e*w*dt
Fm = b * v * w * spin_coefficient
# print("magnus", v, Fm/mass*dt)
# print("initial v", v, vx, vy)
vx = vx - Fd*math.cos(theta)/mass*dt + Fm * \
math.cos(theta+math.pi/2)/mass*dt
vy = vy - g*dt - Fd*math.sin(theta)/mass*dt + Fm * \
math.sin(theta+math.pi/2)/mass*dt # + Fm/mass*dt
# v = math.sqrt(vx**2 + vy**2)
# print("final v", v, vx, vy)
# print(x, y)
spin_coordinates.append([x*3.28, y*3.28])
time_elapsed += dt
# break
spin_coordinates = list(map(list, zip(*spin_coordinates)))
# print("------------- Spin -------------")
# print(x*3.28, y*3.28)
# v = math.sqrt(vx**2 + vy**2)
# print("final v", v, vx, vy, w)
# print(time_elapsed)
return spin_coordinates
# The function to be called anytime a slider's value changes
def update(val):
global front_line
global back_line
vel = vel_slider.val
theta = angle_slider.val
drag_coeff = drag_slider.val
spin_coeff = spin_slider.val
distance = distance_slider.val
front_line.remove()
back_line.remove()
front_line = ax.axvline(x=distance)
back_line = ax.axvline(x=distance + 4)
vacuum_data = vacuum(vel, theta, drag_coeff, spin_coeff)
vacuum_line.set_xdata(vacuum_data[0])
vacuum_line.set_ydata(vacuum_data[1])
drag_data = drag(vel, theta, drag_coeff, spin_coeff)
drag_line.set_xdata(drag_data[0])
drag_line.set_ydata(drag_data[1])
spin_data = spin(vel, theta, drag_coeff, spin_coeff)
spin_line.set_xdata(spin_data[0])
spin_line.set_ydata(spin_data[1])
fig.canvas.draw_idle()
fig, ax = plt.subplots(1, 1)
goal_line = ax.axhline(y=6.5)
max_height = ax.axhline(y=18)
front_line = ax.axvline(x=6)
back_line = ax.axvline(x=6+4)
vacuum_line, = ax.plot(*vacuum(35, 60, 1, 1), lw=2)
# plt.subplots_adjust(bottom=0.35)
drag_line, = ax.plot(*drag(35, 60, 1, 1), lw=2)
# plt.subplots_adjust(bottom=0.35)
spin_line, = ax.plot(*spin(35, 60, 1, 1), lw=2)
plt.xlim([-5, 35])
plt.ylim([0, 30])
plt.subplots_adjust(bottom=0.35)
axfreq = plt.axes([0.25, 0, 0.65, 0.03])
vel_slider = Slider(
ax=axfreq,
label='Velocity (ft/s)',
valmin=0.1,
valmax=60,
valinit=35,
)
axfreq = plt.axes([0.25, 0.05, 0.65, 0.03])
angle_slider = Slider(
ax=axfreq,
label='Angle (degrees)',
valmin=0,
valmax=89,
valinit=60,
)
axfreq = plt.axes([0.25, 0.1, 0.65, 0.03])
drag_slider = Slider(
ax=axfreq,
label='Drag Coefficient',
valmin=0.01,
valmax=2,
valinit=1,
)
axfreq = plt.axes([0.25, 0.15, 0.65, 0.03])
spin_slider = Slider(
ax=axfreq,
label='Spin Coefficient',
valmin=0.01,
valmax=2,
valinit=1,
)
axfreq = plt.axes([0.25, 0.2, 0.65, 0.03])
distance_slider = Slider(
ax=axfreq,
label='Distance (ft)',
valmin=0,
valmax=30,
valinit=6,
)
vel_slider.on_changed(update)
angle_slider.on_changed(update)
drag_slider.on_changed(update)
spin_slider.on_changed(update)
distance_slider.on_changed(update)
ax.set_xlabel('Position (ft)')
# plt.plot(vacuum_coordinates[0], vacuum_coordinates[1], drag_coordinates[0],
# drag_coordinates[1], spin_coordinates[0], spin_coordinates[1])
# plt.legend(['vacuum', 'drag', 'spin+drag'])
plt.title(
f"Ball paths")
plt.show()