In this python code we are trying to simulate the path of a frisbee that is being shot from a shooter with a certain angle (alpha0). The angle of attack should be the angle at which its being shot, minus the slope of its path. Thus the angle at which the air hits the frisbee. However something goes wrong here, the AoA is not 0 at the beginning, can someone help fixing our code. I suspect that the method of calculating the slope of the path is wrong.
mport numpy as np
import matplotlib.pyplot as plt
t = np.linspace(0,2,1001)
alpha0 = 26*np.pi*(1/180)
v0 = 9.0
vx0 = np.cos(np.rad2deg(alpha0))*v0
vy0 = np.sin(np.rad2deg(alpha0))*v0
x0 = 0.0
y0 = 1.0
g = -9.81
r_disc = 0.12
def Cd_frisbee(alpha):
Cd_0 = 0.18
Cd_alpha = 0.69
Cd = Cd_0 + (Cd_alpha*(alpha - alpha0)**2)
return Cd
def Cl_frisbee(alpha):
Cl_0 = 0.33
Cl_alpha = 1.9
Cl = Cl_0 + (Cl_alpha*alpha)
return Cl
def A_frisbee(alpha):
A = np.pi*(r_disc**2)*(np.sin(alpha))
return A
def a_Drag(Cd,A,vx):
rho = 1.25
m = 0.125
ax = -0.5*(Cd*A*rho*(vx**2))/m
return ax
def a_Lift(Cl, A, vy):
rho = 1.25
m = 0.125
ay = (0.5*(Cl*A*rho*(vy**2))/m) - 9.81
return ay
def numerical(x0, v0, a_func1, a_func2, t):
x = np.zeros(len(t))
y = np.zeros(len(t))
vx = np.zeros(len(t))
vy = np.zeros(len(t))
ax = np.zeros(len(t))
ay = np.zeros(len(t))
alpha = np.zeros(len(t))
dy = np.zeros(len(t))
dx = np.zeros(len(t))
vx[0] = vx0
vy[0] = vy0
x[0] = x0
y[0] = y0
ax[0] = a_func1(Cd_frisbee(alpha0), 0, vx0)
ay[0] = a_func2(Cl_frisbee(alpha0), 0, vy0)
alpha[0] = 0
dy[0] = 0
dx[0] = 0
for i in range(len(t) - 1):
dt = (t[i + 1] - t[i])
x[i + 1] = x[i] + (vx[i] * dt)
y[i + 1] = y[i] + (vy[i] * dt)
vx[i + 1] = vx[i] + (dt * ax[i])
vy[i + 1] = vy[i] + (dt * ay[i])
ax[i + 1] = a_func1(Cd_frisbee(alpha[i]), A_frisbee(alpha[i]), vx[i])
ay[i + 1] = a_func2(Cl_frisbee(alpha[i]), A_frisbee(alpha[i]), vy[i])
dy[i+1] = (y[i + 1] - y[i])
dx[i+1] = (x[i + 1] - x[i])
alpha[i+1] = alpha0 - np.radians(np.arctan(dy[i+1]/dx[i+1]))
return x, y, vx, vy, ax, ay, alpha, dy, dx
x_num = numerical(x0, v0, a_Drag, a_Lift, t)[0]
y_num = numerical(x0, v0, a_Drag, a_Lift, t)[1]
alpha_num = numerical(x0, v0, a_Drag, a_Lift, t)[6]
vx_num = numerical(x0, v0, a_Drag, a_Lift, t)[2]
dy_num = numerical(x0, v0, a_Drag, a_Lift, t)[7]
dx_num = numerical(x0, v0, a_Drag, a_Lift, t)[8]
"""
ax[0].plot(t, x_num, color='green', linestyle='--')
ax[1].plot(t, y_num, color='green', linestyle='--')
ax[3].plot(t, alpha_num, color='green', linestyle='--')
"""
I have used different starting values such as speed etc. and instead of a smooth path i got strange graphs.
If you look at the documentation of np.cos, you will see that it expects the input in radians, not degrees. So you do not want to use np.rad2deg there. The same is true for np.sin.