def aerodynamic_center(wing):
"""return lifting surface aerodynamic center."""
c_bar = mac(wing['aspect_ratio'], wing['planform'], wing['taper']) # [ft]
y = y_mac(wing['aspect_ratio'], wing['planform'], wing['taper']) # [ft]
x = x_mac(y, wing['sweep_LE']) # [ft]
x_ac = wing['station'] + x + c_bar / 4 # [ft]
return x_ac
def parasite_drag(wing, mach, altitude):
"""return parasitic drag coefficient of the lifting surface."""
s_wet_s = 2 + 2 * (wing['airfoil_thickness'] / wing['aspect_ratio']
) + 2 * wing['airfoil_thickness'] # []
c_bar = mac(wing['aspect_ratio'], wing['planform'], wing['taper']) # [ft]
c_f = friction_coefficient(mach, altitude, c_bar) # []
c_d_0 = 1.25 * c_f * s_wet_s # []
return c_d_0
def c_l_pitch_rate(aircraft, mach):
"""returns lift curve of elevator wrt pitch rate."""
wing = aircraft['wing']
s_w = wing['planform'] # [ft^2]
c_bar = mac(wing['aspect_ratio'], s_w, wing['taper']) # [ft]
cg_bar = aircraft['weight']['cg'][0] / c_bar # []
ht = aircraft['horizontal']
s_ht = ht['planform'] # [ft^2]
c_l_alpha_ht = c_l_alpha_wing(ht, mach) # [1/rad]
x_ac_ht = aerodynamic_center(ht) # [ft]
x_ac_ht_bar = x_ac_ht / c_bar # []
c_l_q = 2 * c_l_alpha_ht * s_ht / s_w * (x_ac_ht_bar - cg_bar)
return c_l_q
def c_m_alpha_dot(aircraft, mach):
"""returns pitch moment curve of elevator wrt alpha rate."""
wing = aircraft['wing']
s_w = wing['planform'] # [ft^2]
c_bar = mac(wing['aspect_ratio'], s_w, wing['taper']) # [ft]
cg_bar = aircraft['weight']['cg'][0] / c_bar # []
ht = aircraft['horizontal']
s_ht = ht['planform'] # [ft^2]
c_l_alpha_ht = c_l_alpha_wing(ht, mach) # [1/rad]
x_ac_ht = aerodynamic_center(ht) # [ft]
x_ac_ht_bar = x_ac_ht / c_bar # []
downwash = d_epsilon_d_alpha(wing, ht, mach) # []
c_m_adt = - 2 * c_l_alpha_ht * s_ht / s_w * downwash * (x_ac_ht_bar - cg_bar) ** 2
return c_m_adt
def c_m_delta_elevator(aircraft, mach):
"""returns pitching moment curve of elevator wrt deflection angle."""
wing = aircraft['wing']
s_w = wing['planform'] # [ft^2]
c_bar = mac(wing['aspect_ratio'], s_w, wing['taper']) # [ft]
cg_bar = aircraft['weight']['cg'][0] / c_bar # []
ht = aircraft['horizontal']
s_ht = ht['planform'] # [ft^2]
c_l_alpha_ht = c_l_alpha_wing(ht, mach) # [1/rad]
downwash = d_epsilon_d_alpha(wing, ht, mach) # []
x_ac_ht = aerodynamic_center(ht) # [ft]
x_ac_ht_bar = x_ac_ht / c_bar # []
tau = aircraft['elevator']['chord_ratio']
c_m_de = - c_l_alpha_ht * s_ht / s_w * (1 - downwash) * (x_ac_ht_bar - cg_bar) * tau # [1/rad]
return c_m_de
def c_m_alpha(aircraft, mach):
"""returns pitching moment curve slope for aircraft."""
wing = aircraft['wing']
s_w = wing['planform'] # [ft^2]
c_bar = mac(wing['aspect_ratio'], s_w, wing['taper']) # [ft]
cg_bar = aircraft['weight']['cg'][0] / c_bar # []
x_ac_w = aerodynamic_center(wing) # [ft]
x_ac_w_bar = x_ac_w / c_bar # []
ht = aircraft['horizontal']
s_ht = ht['planform'] # [ft^2]
c_l_alpha_ht = c_l_alpha_wing(ht, mach) # [1/rad]
downwash = d_epsilon_d_alpha(wing, ht, mach) # []
c_l_alpha_w = c_l_alpha_wing(wing, mach) # [1/rad]
x_ac_ht = aerodynamic_center(ht) # [ft]
x_ac_ht_bar = x_ac_ht / c_bar # []
c_m_alpha_w = c_l_alpha_w * (cg_bar - x_ac_w_bar) # [1/rad]
c_m_alpha_ht = c_l_alpha_ht * s_ht / s_w * (1 - downwash) * (x_ac_ht_bar - cg_bar) # [1/rad]
c_m_alpha_airplane = c_m_alpha_w - c_m_alpha_ht # [1/rad]
return c_m_alpha_airplane
def c_m_zero(aircraft, mach, altitude):
"""baseline lift coefficient."""
wing = aircraft['wing']
s_w = wing['planform'] # [ft^2]
c_l_alpha_w = c_l_alpha_wing(wing, mach) # [1/rad]
ht = aircraft['horizontal']
s_ht = ht['planform'] # [ft^2]
c_l_alpha_ht = c_l_alpha_wing(ht, mach) # [1/rad]
vt = aircraft['vertical']
s_vt = vt['planform'] # [ft^2]
c_bar = mac(wing['aspect_ratio'], s_w, wing['taper']) # [ft]
cg_bar = aircraft['weight']['cg'][0] / c_bar # []
z_cg = aircraft['weight']['cg'][2]
x_ac_w = aerodynamic_center(wing) # [ft]
x_ac_w_bar = x_ac_w / c_bar # []
x_ac_ht = aerodynamic_center(ht) # [ft]
x_ac_ht_bar = x_ac_ht / c_bar # []
c_l_0_w = c_l_alpha_w * (deg2rad(wing['incidence'] - wing['alpha_zero_lift'])) # []
c_m_0_w = c_l_0_w * (cg_bar - x_ac_w_bar)
epsilon = 2 * c_l_0_w / (pi * wing['aspect_ratio']) # [rad]
c_l_0_ht = c_l_alpha_ht * s_ht / s_w * (deg2rad(ht['incidence'] - ht['alpha_zero_lift'] - epsilon)) # []
z_w = (z_cg - wing['waterline']) / c_bar
z_ht = (z_cg - ht['waterline']) / c_bar
z_vt = (z_cg - vt['waterline']) / c_bar
z_f = (z_cg - aircraft['fuselage']['height'] / 2) / c_bar
c_m_0_w_d = - parasite_drag(wing, mach, altitude) * z_w
c_m_0_ht_d = - parasite_drag(ht, mach, altitude) * s_ht / s_w * z_ht
c_m_0_vt_d = - parasite_drag(vt, mach, altitude) * s_vt / s_w * z_vt
c_m_0_f_d = - parasite_drag_fuselage(aircraft, mach, altitude) * z_f
c_m_0_ht = c_l_0_ht * (x_ac_ht_bar - cg_bar)
c_m_0 = (wing['airfoil_cm0'] + ht['airfoil_cm0'] + c_m_0_w + c_m_0_ht
+ c_m_0_w_d + c_m_0_ht_d + c_m_0_vt_d + c_m_0_f_d) # []
return c_m_0