def l_over_d(aircraft, mach, altitude):
"""calculate specific excess power"""
c_d_0 = Aircraft(aircraft, mach).c_d_zero(altitude)
c_l_a = Aircraft(aircraft, mach).c_l_alpha()
ar = aircraft['wing']['aspect_ratio']
l_d = 1 / 2 * (((c_l_a / 2) * ar) / c_d_0)**0.5
return l_d
def trim_aileron(aircraft, v, altitude, p):
"""trim aircraft with aileron and rudder"""
a = Atmosphere(altitude).speed_of_sound() # [ft/s]
mach = v / a
b = span(aircraft['wing']['aspect_ratio'], aircraft['wing']['planform'])
k = b / (2 * v)
c_l_p = Aircraft(aircraft, mach).c_r_roll_rate() # []
c_l_da = Aircraft(aircraft, mach).c_r_delta_aileron() # []
da = -c_l_p * p * k / c_l_da
da = rad2deg(da)
return da
def master_constraint(aircraft, wing_loading, mach, altitude, n, gamma, a_x):
"""master constraint equation for flight."""
"return sea level static thrust to weight ratio"
rho = Atmosphere(altitude).air_density()
rho_sl = Atmosphere(0).air_density()
a = Atmosphere(altitude).speed_of_sound()
v = a * mach
q_bar = 0.5 * rho * v**2
c_d_0 = Aircraft(aircraft, mach).c_d_zero(altitude)
c_l_a = Aircraft(aircraft, mach).c_l_alpha()
t_w = (q_bar * c_d_0 / wing_loading + wing_loading * (n**2) *
(cos(deg2rad(gamma))**2) /
(q_bar * c_l_a) + n * sin(deg2rad(gamma)) + a_x / g) * rho_sl / rho
return t_w
def trim_alpha_de_throttle(aircraft, speed, altitude, gamma, n=1):
"""trim aircraft with angle of attack, elevator, and throttle"""
a = Atmosphere(altitude).speed_of_sound() # [ft/s]
rho = Atmosphere(altitude).air_density() # [slug / ft^3]
mach = speed / a # []
c_l_a = Aircraft(aircraft, mach).c_l_alpha() # [1/rad]
c_l_de = Aircraft(aircraft, mach).c_l_delta_elevator() # [1/rad]
c_m_a = Aircraft(aircraft, mach).c_m_alpha() # [1/rad]
c_m_de = Aircraft(aircraft, mach).c_m_delta_elevator() # [1/rad]
c_l_0 = Aircraft(aircraft, mach).c_l_zero() # []
c_d_0 = Aircraft(aircraft, mach).c_d_zero(altitude) # []
w = aircraft['weight']['weight'] * n # [lb]
q_bar = 0.5 * rho * speed**2 # [psf]
s_w = aircraft['wing']['planform'] # [ft^2]
c_bar = mac(aircraft['wing']['aspect_ratio'], s_w,
aircraft['wing']['taper'])
c_l_1 = w * cos(deg2rad(gamma)) / (s_w * q_bar) # []
t = Propulsion(aircraft['propulsion'], [speed, altitude],
ones((aircraft['propulsion']['n_engines'])),
aircraft['weight']['cg']).thrust_f_m()
a = array([[-c_l_a, -c_l_de, 0],
[c_m_a, c_m_de, (t[4]) / (s_w * q_bar * c_bar)],
[-2 * c_l_1, 0, t[0] / (s_w * q_bar)]])
c_m_0 = Aircraft(aircraft, mach).c_m_zero(altitude)
b = array([[-c_l_1 + c_l_0], [-c_m_0],
[w * sin(deg2rad(gamma)) / (s_w * q_bar) + c_d_0]])
c = linalg.solve(a, b) # [rad]
c[0:2] = rad2deg(c[0:2])
return c
def n_per_alpha(aircraft, x_0):
"""return acceleration sensitivity."""
rho = Atmosphere(x_0[-1]).air_density() # [slug/ft3]
a = Atmosphere(x_0[-1]).speed_of_sound() # [ft/s]
v = sqrt(sum(x_0[0:3]**2)) # [ft/s]
q_bar = 0.5 * rho * v**2 # [psf]
s = aircraft['wing']['planform'] # [ft2]
cla = Aircraft(aircraft, v / a).c_l_alpha() # [1/rad]
n_a = cla * s * q_bar / aircraft['weight']['weight'] # [g/rad]
return n_a
def takeoff(aircraft, wing_loading, s_to, altitude, mu, c_l_max=1.4):
"""takeoff constraint equation."""
"return sea level static thrust to weight ratio"
rho = Atmosphere(altitude).air_density()
rho_sl = Atmosphere(0).air_density()
a = Atmosphere(altitude).speed_of_sound()
q_stall = wing_loading / c_l_max
q_v_avg = 0.5 * q_stall
mach_avg = sqrt(q_v_avg / (0.5 * rho)) / a
c_d_0 = Aircraft(aircraft, mean(mach_avg)).c_d_zero(altitude)
c_l_a = Aircraft(aircraft, mean(mach_avg)).c_l_alpha()
c_l_0 = Aircraft(aircraft, mean(mach_avg)).c_l_zero()
d_w = q_v_avg * (c_d_0 + (c_l_0**2) / c_l_a) / wing_loading
l_w = q_v_avg * c_l_0 / wing_loading
t_w = (1.44 * wing_loading / (rho * c_l_max * s_to * g) + d_w + mu *
(1 - l_w)) * rho_sl / rho
return t_w
def trim_aileron_rudder(aircraft, v, altitude, alpha, beta, p, r):
"""trim aircraft with aileron and rudder"""
a = Atmosphere(altitude).speed_of_sound() # [ft/s]
mach = v / a
b = span(aircraft['wing']['aspect_ratio'], aircraft['wing']['planform'])
k = b / (2 * v)
c_l_b = Aircraft(aircraft, mach).c_r_beta(alpha)
c_l_p = Aircraft(aircraft, mach).c_r_roll_rate() # []
c_l_r = Aircraft(aircraft, mach).c_r_yaw_rate(alpha) # []
c_l_da = Aircraft(aircraft, mach).c_r_delta_aileron() # []
c_l_dr = Aircraft(aircraft, mach).c_r_delta_rudder() # []
c_n_b = Aircraft(aircraft, mach).c_n_beta(alpha) # []
c_n_p = Aircraft(aircraft, mach).c_n_roll_rate(alpha) # []
c_n_r = Aircraft(aircraft, mach).c_n_yaw_rate(alpha) # []
c_n_da = Aircraft(aircraft, mach).c_n_delta_aileron() # []
c_n_dr = Aircraft(aircraft, mach).c_n_delta_rudder() # []
a = array([[c_l_da, c_l_dr], [c_n_da, c_n_dr]])
b = array([[-c_l_b * beta - c_l_p * p * k - c_l_r * r * k],
[-c_n_b * beta - c_n_p * p * k - c_n_r * r * k]])
c = linalg.solve(a, b) # [rad]
return rad2deg(c)
def trim_alpha_de(aircraft, speed, altitude, gamma, n=1):
"""trim aircraft with angle of attack and elevator"""
a = Atmosphere(altitude).speed_of_sound() # [ft/s]
rho = Atmosphere(altitude).air_density() # [slug / ft^3]
mach = speed / a # []
c_l_a = Aircraft(aircraft, mach).c_l_alpha() # [1/rad]
c_l_de = Aircraft(aircraft, mach).c_l_delta_elevator() # [1/rad]
c_m_a = Aircraft(aircraft, mach).c_m_alpha() # [1/rad]
c_m_de = Aircraft(aircraft, mach).c_m_delta_elevator() # [1/rad]
c_l_0 = Aircraft(aircraft, mach).c_l_zero() # []
a = array([[c_l_a, c_l_de], [c_m_a, c_m_de]])
w = aircraft['weight']['weight'] * n # [lb]
q_bar = 0.5 * rho * speed**2 # [psf]
s_w = aircraft['wing']['planform'] # [ft^2]
c_l_1 = w * cos(deg2rad(gamma)) / (s_w * q_bar) # []
c_m_0 = Aircraft(aircraft, mach).c_m_zero(altitude)
b = array([[c_l_1 - c_l_0], [-c_m_0]])
c = linalg.solve(a, b) # [rad]
return rad2deg(c)
def trim_vs(aircraft, altitude, gamma, n=1):
"""trim aircraft with angle of attack and elevator"""
rho = Atmosphere(altitude).air_density() # [slug / ft^3]
mach = 0.3 # [] assume moderate mach number
c_l_a = Aircraft(aircraft, mach).c_l_alpha() # [1/rad]
c_l_de = Aircraft(aircraft, mach).c_l_delta_elevator() # [1/rad]
c_m_a = Aircraft(aircraft, mach).c_m_alpha() # [1/rad]
c_m_de = Aircraft(aircraft, mach).c_m_delta_elevator() # [1/rad]
c_l_0 = Aircraft(aircraft, mach).c_l_zero() # []
w = aircraft['weight']['weight'] * n # [lb]
s_w = aircraft['wing']['planform'] # [ft^2]
a_s = deg2rad(aircraft['wing']['alpha_stall'])
c_m_0 = Aircraft(aircraft, mach).c_m_zero(altitude)
a = array([[-w * cos(deg2rad(gamma)) / (0.5 * rho * s_w), c_l_de],
[0, c_m_de]])
b = array([[-c_l_0 - c_l_a * a_s], [-c_m_0 - c_m_a * a_s]])
c = linalg.solve(a, b) # [rad]
v_s = float((1 / c[0])**0.5)
return v_s
def lateral_stability(plane, mach, alpha):
"""return airplane static lateral stability."""
c_r_b = Aircraft(plane, mach).c_r_beta(alpha)
return c_r_b
def directional_stability(plane, mach, alpha):
"""return airplane static directional stability."""
c_n_b = Aircraft(plane, mach).c_n_beta(alpha)
return c_n_b
def static_margin(plane, mach):
"""return longitudinal static margin."""
c_m_a = Aircraft(plane, mach).c_m_alpha()
c_l_a = Aircraft(plane, mach).c_l_alpha()
sm = -c_m_a / c_l_a * 100
return sm