WingMotion.mpos = MechMotion.mpos
WingMotion.dt = dt
WingMotion.run()
"""
Define elements along equivalent axis (P_1)
"""
Nele = 100
P_1 = np.zeros((len(theta),Nele,3))
Woc = np.linspace(0,1,Nele*(WingInit.fOC/(WingInit.fCD+WingInit.fOC))+1)
Wcd = np.linspace(0,1,Nele*(WingInit.fCD/(WingInit.fCD+WingInit.fOC))+2)
for i in range(len(theta)):
C = rotx(np.radians(-90),(roty(np.radians(-90),np.array([WingMotion.wpos.front.C[0,i], WingMotion.wpos.front.C[1,i], WingMotion.wpos.front.C[2,i]]))))
D = rotx(np.radians(-90),(roty(np.radians(-90),np.array([WingMotion.wpos.front.D[0,i], WingMotion.wpos.front.D[1,i], WingMotion.wpos.front.D[2,i]]))))
DC = D-C
for j in range(len(Woc)-1):
P_1[i,j] = Woc[j] * C
J_a = j+1
for j in range(len(Wcd)-1):
P_1[i,j+J_a] = C + Wcd[j] * DC
#print P_1[0,:,1][0]
def bet(P_1,V0_1,Vi_1,Vflap_1,J_a,Twist,Pitch,Chord,PLE,Polar,rho,dt):
""" Blade Element Theory according to B. Parslew
in general for state matrices:
i - moment in time, where 0 is the first moment and end the last moment in time
j - blade element, where 0 is the shoulder hinge-element and end is the wing tip-element
k - vector component, where 0 is the x-, 1 the y- and 2 the z-component
"""
Phi = np.zeros_like(Twist)
V_4 = np.zeros_like(P_1)
dV_4 = np.zeros_like(P_1)
F_5 = np.zeros_like(P_1)
F_4 = np.zeros_like(P_1)
F_1 = np.zeros_like(P_1)
l = np.zeros_like(Twist)
d = np.zeros_like(Twist)
m = np.zeros_like(Twist)
aoa = np.zeros_like(Twist)
daoa = np.zeros_like(Twist)
cl = np.zeros_like(Twist)
cd = np.zeros_like(Twist)
cm = np.zeros_like(Twist)
w = np.zeros_like(Chord)
wy = np.zeros_like(Twist)
S = np.zeros_like(Twist)
Vflap_1[np.abs(Vflap_1) < 1e-8] = 0
for i in range(len(P_1)):
for j in range(len(P_1[i])):
# Calculate wing element elevation angle
if j <= J_a:
dz = P_1[i,J_a,2]
dy = P_1[i,J_a,1]
Phi[i,j] = np.arctan(dz/dy)
else:
dz = P_1[i,-1,2]-P_1[i,J_a+1,2]
dy = P_1[i,-1,1]-P_1[i,J_a+1,1]
Phi[i,j] = np.arctan(dz/dy)
# Calculate local flow velocity
V_4[i,j] = roty((Twist[i,j]+Pitch[j]), rotx(-Phi[i,j],(V0_1 + Vi_1 + Vflap_1[i,j])))
V_4[np.abs(V_4) < 1e-12] = 0
# Calculate angle of attack
aoa[i,j] = np.arctan(-V_4[i,j,2]/V_4[i,j,0])
# Find cl,cd,cm from polars with linear interpolation
cl[i,j] = np.interp(np.degrees(aoa[i,j]),Polar[j,0],Polar[j,1])
cd[i,j] = np.interp(np.degrees(aoa[i,j]),Polar[j,0],Polar[j,2])
cm[i,j] = np.interp(np.degrees(aoa[i,j]),Polar[j,0],Polar[j,3])
# Calculate element width
if j < len(P_1[i])-1:
wy[i,j] = P_1[i,j+1,1]-P_1[i,j,1]
else:
wy[i,j] = P_1[i,j,1]-P_1[i,j-1,1]
# Calculate element surface area
S[i,j] = Chord[j] * wy[i,j]
# Calculate aerodynamic forces
l[i,j] = 0.5 * rho * np.linalg.norm(V_4[i,j])**2 * S[i,j] * cl[i,j]
d[i,j] = 0.5 * rho * np.linalg.norm(V_4[i,j])**2 * S[i,j] * cd[i,j]
m[i,j] = 0.5 * rho * np.linalg.norm(V_4[i,j])**2 * S[i,j] * cm[i,j]
# Force vector in Blade Element local axes
F_5[i,j] = np.array([-d[i,j], 0, l[i,j]])
# Force vector in Blade local axes
F_4[i,j] = roty(aoa[i,j],F_5[i,j])
"""
Add mass effect and rotate to stroke plane axes
"""
for i in range(len(P_1)):
for j in range(len(P_1[i])):
# Add mass effects
if i==0:
daoa[i,j] = (aoa[1,j]-aoa[0,j])/dt
dV_4[i,j] = (V_4[1,j]-V_4[0,j])/dt
elif i < len(P_1)-1:
daoa[i,j] = (aoa[i+1,j]-aoa[i-1,j])/(2*dt)
dV_4[i,j] = (V_4[i+1,j]-V_4[i-1,j])/(2*dt)
else:
daoa[i,j] = (aoa[i,j]-aoa[i-1,j])/dt
dV_4[i,j] = (V_4[i,j]-V_4[i-1,j])/dt
F_4[i,j,0] = F_4[i,j,0] - 0.25 * rho * np.pi * Chord[j] * S[i,j] * V_4[i,j,2] * daoa[i,j]
F_4[i,j,2] = F_4[i,j,2] + 0.25 * rho * np.pi * Chord[j] * S[i,j] * dV_4[i,j,2]
# Tranform to Stroke Plane Axes
F_1[i,j] = rotx(Phi[i,j],roty(-(Twist[i,j]+Pitch[j]),F_4[i,j]))
return F_1