def c_l_alpha(aircraft, mach):
"""returns lift curve slope for aircraft."""
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]
downwash = d_epsilon_d_alpha(wing, ht, mach) # []
c_l_alpha_airplane = c_l_alpha_w + c_l_alpha_ht*s_ht/s_w*(1-downwash) # [1/rad]
return c_l_alpha_airplane
def c_l_alpha_dot(aircraft, mach):
"""returns lift 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_l_adt = 2 * c_l_alpha_ht * s_ht / s_w * (x_ac_ht_bar - cg_bar) * downwash
return c_l_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