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 dynamic_pressure(mach, altitude):
"""returns incompressible dynamic pressure."""
rho = Atmosphere(altitude).air_density()
a = Atmosphere(altitude).speed_of_sound()
v = mach * a
q_bar = 0.5 * rho * v**2
return q_bar
def reynolds_number(mach, altitude, x_ref):
"""return reynolds number."""
rho = Atmosphere(altitude).air_density() # [slug/ft^3]
mu = Atmosphere(altitude).viscosity()
a = Atmosphere(altitude).speed_of_sound() # [ft/s]
v = mach * a # [ft/s]
re = rho * v * x_ref / mu # []
return re
def propulsion_weight(aircraft):
"""return engine weight."""
w_p = []
fus = aircraft['fuselage']
w = aircraft['wing']
b = span(w['aspect_ratio'], w['planform'])
length = fus['length']
for ii in range(0, aircraft['propulsion']['n_engines']):
engine = aircraft['propulsion']["engine_%d" % (ii + 1)]
if engine['type'] == 'prop':
t = propeller(engine, [0, 0, 0], 0, 1)
t = (sum(t[0:3]**2))**0.5
rho = Atmosphere(0).air_density()
d = engine['diameter']
a = pi * (d / 2)**2
u_e = (2 * t / (rho * a))**0.5
u_disk = u_e / 2
p = t * u_disk
w_controls = 60.27 * ((length + b) * 10**-2)**0.724
w_prop = 32 * (4**0.391) * (d * p * constants.lbft_s2hp() *
10**-3)**0.782
w_prop_control = 4.5 * (4**0.379) * (
d * p * constants.lbft_s2hp() * 10**-3)**0.759
w_engine = p * constants.lbft_s2hp() / constants.electric_hp_lb()
w_p.append(w_engine + w_prop + w_prop_control + w_controls)
if engine['type'] == 'jet':
w_controls = 88.46 * ((length + b) * 10**-2)**0.294
w_engine = engine['thrust'] / constants.jet_lbt_lb()
d_nac = 0.04 * engine['thrust']**0.5
l_nac = 0.07 * engine['thrust']**0.5
w_nac = 0.25 * d_nac * l_nac * engine['thrust']**0.36
w_p.append(w_engine + w_controls + w_nac)
w_fuel_tank = 1.07 * (aircraft['propulsion']['fuel_mass'] * g)**0.58
w_total = sum(w_p) + w_fuel_tank
return w_total
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_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 c_f_m(aircraft, x, u, engine_out=False):
"""return aircraft body axis forces and moments."""
s = aircraft['wing']['planform'] # [ft2]
altitude = x[-1] # [ft]
a = Atmosphere(altitude).speed_of_sound() # [ft/s]
v = sqrt(x[0]**2 + x[1]**2 + x[2]**2) # [ft/s]
mach = v / a # []
alpha = arctan(x[2] / x[0]) # [rad]
beta = arctan(x[1] / x[0]) # [rad]
weight = array([0, 0, 0, 0, 0, 0])
c_bar = mac(aircraft['wing']['aspect_ratio'], s,
aircraft['wing']['taper']) # [ft]
b = span(aircraft['wing']['aspect_ratio'], s) # [ft]
throttle = u[3] * ones(aircraft['propulsion']['n_engines']) # []
if engine_out:
throttle[0] = 0.01
# get thrust contributions
c_f_m_t = Propulsion(aircraft['propulsion'], x, throttle,
aircraft['weight']['cg']).thrust_f_m()
# get weight contributions
weight[0:3] = aircraft['weight']['weight'] * array(
[-sin(x[4]), cos(x[4]) * sin(x[3]),
cos(x[4]) * cos(x[3])])
q_bar = dynamic_pressure(mach, altitude) # [psf]
s = aircraft['wing']['planform'] # [ft2]
if 'aero_model' in aircraft.keys():
c_aero = nonlinear_aero(aircraft, x, u)
else:
c_aero = linear_aero(aircraft, x, u)
c = array([
-c_aero[0], c_aero[1], -c_aero[2], c_aero[3] * b, c_aero[4] * c_bar,
c_aero[5] * b
]) * q_bar * s
b_2_w = body_to_wind(alpha, beta)
c[0:3] = linalg.inv(b_2_w) @ c[0:3]
c[3:6] = linalg.inv(b_2_w) @ c[3:6]
c = c + c_f_m_t + weight
return 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 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)