def specific_excess_power(aircraft, x, u):
"""calculate specific excess power"""
w = aircraft['weight']['weight'] # [lbs]
v = (x[0]**2 + x[2]**2)**0.5 # [ft/s]
c = c_f_m(aircraft, x, u)
p_s = (c[0]) * v * 60 / w # [ft/min]
return p_s
def takeoff_ground_roll(aircraft, x_0, u_0):
"""return derivatives for aircraft on ground."""
m = aircraft['weight']['weight'] / g
j = aircraft['weight']['inertia']
c = c_f_m(aircraft, x_0, u_0)
c_t, c_g, normal_loads = landing_gear_loads(aircraft, x_0, c, True)
dxdt = nonlinear_eom(x_0, m, j, c_t)
return dxdt
def alpha_stab(x):
u = array([0, x[1], 0, 0.01])
x = array([
speed * cos(x[0]), 0, speed * sin(x[0]), 0, x[0] + deg2rad(gamma),
0, 0, 0, 0, 0, 0, altitude
])
cfm = c_f_m(aircraft, x, u)
return abs(cfm[2]) + abs(cfm[4])
def v_stab(x):
u = array([0, x[0], 0, 0.01])
x_in = array([
x[1] * cos(alpha), 0, x[1] * sin(alpha), 0, alpha + deg2rad(gamma),
0, 0, 0, 0, 0, 0, altitude
])
cfm = c_f_m(aircraft, x_in, u)
return abs(cfm[2]) + abs(cfm[4])
def alpha_stab(x):
u = array([0, x[1], 0, th])
speed = x[2]
x = array([
speed * cos(x[0]), 0, speed * sin(x[0]), 0, x[0], 0, 0, 0, 0, 0, 0,
altitude
])
cfm = c_f_m(aircraft, x, u)
return abs(cfm[2]) + abs(cfm[4])
def aileron_rudder(x):
u = array([x[0], 0, x[1], 0.01])
b2w = body_to_wind(alpha, beta)
v_b = linalg.inv(b2w) @ array([speed, 0, 0])
x = array([
v_b[0], v_b[1], v_b[2], 0, alpha, 0, roll_rate, 0, yaw_rate, 0, 0,
altitude
])
dxdt = c_f_m(aircraft, x, u)
return sqrt(sum(dxdt**2)) / 1000
def obj(x):
u = array([0, x[1], 0, th])
speed = x[2]
x = array([
speed * cos(x[0]), 0, speed * sin(x[0]), 0, x[0], 0, 0, 0, 0, 0, 0,
altitude
])
c_1 = c_f_m(aircraft, x, u)
p_s = (c_1[0]) * speed * 60 / aircraft['weight']['weight'] # [ft/min]
return -p_s
def oei_constraint(x):
v = x[0]
plane['vertical']['control_1']['cf_c'] = x[1]
s = array([
float(v * cos(deg2rad(alpha))), 0,
float(v * sin(deg2rad(alpha))), 0,
float(deg2rad(alpha)), 0, 0, 0, 0, 0, 0, 0
])
u = [0, deg2rad(x[2]), dr, 1]
cfm = c_f_m(plane, s, u, engine_out=True)
return abs(cfm[2]) + abs(cfm[4]) + abs(cfm[5])
def aileron_rudder_speed(x):
u = array([x[0], x[3], x[1], 1])
alpha = x[2]
b2w = body_to_wind(alpha, beta)
v_b = linalg.inv(b2w) @ array([x[4], 0, 0])
x = array([
v_b[0], v_b[1], v_b[2], 0, alpha, 0, roll_rate, 0, yaw_rate, 0, 0,
altitude
])
cfm = c_f_m(aircraft, x, u)
return cfm[1] + cfm[2] + cfm[3] + cfm[4] + cfm[5]
def long_constraint(x):
v = x[0]
plane['horizontal']['control_1']['cf_c'] = x[1]
s = array([
float(v * cos(deg2rad(alpha))), 0,
float(v * sin(deg2rad(alpha))), 0,
float(deg2rad(alpha)), 0, 0, 0, 0, 0, 0, alt
])
u = [0, de, 0, 0.01]
cfm = c_f_m(plane, s, u)
return abs(cfm[2]) + abs(cfm[4])
def sp_constraint(x):
plane['wing']['station'] = x[0]
plane['horizontal']['planform'] = x[1]
plane['weight']['weight'], plane['weight']['cg'] = MassProperties(
plane).weight_buildup(req)
zeta_sp, omega_sp, cap = short_period_mode(plane, s, u)
plane['horizontal']['control_1']['cf_c'] = 0.99
s_r = array([vr, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, alt_to])
cfm = c_f_m(plane, s_r, u_r)
c_t, c_g, normal_loads = landing_gear_loads(plane, s_r, cfm)
c = array([zeta_sp - zeta_req, float(normal_loads[0])])
return c
def nonlinear_eom_to_ss(aircraft, x_ss, u_ss, x_0, u_0, m, j, dx=0.1, du=0.1):
"""aircraft system linearization routine."""
"""return jacobians a, b wrt to x_ss and output matrices c, and d wrt u_ss."""
x = x_0
u = u_0
a = zeros((len(x_0), len(x_0)))
b = zeros((len(x_0), len(u_0)))
for ii in range(0, len(x_0)):
x[ii] = x[ii] + dx
c = c_f_m(aircraft, x, u_0)
dxdt_1 = nonlinear_eom(x, m, j, c)
x[ii] = x[ii] - dx
c = c_f_m(aircraft, x, u_0)
dxdt_2 = nonlinear_eom(x, m, j, c)
ddx_dx = (dxdt_1 - dxdt_2) / (2 * dx)
a[:, ii] = transpose(ddx_dx)
x = x_0
for ii in range(0, len(u_0)):
u[ii] = u[ii] + du
c = c_f_m(aircraft, x_0, u)
dxdt_1 = nonlinear_eom(x, m, j, c)
u[ii] = u[ii] - du
c = c_f_m(aircraft, x_0, u)
dxdt_2 = nonlinear_eom(x, m, j, c)
ddx_dx = (dxdt_1 - dxdt_2) / (2 * du)
b[:, ii] = transpose(ddx_dx)
u = u_0
a_out = a[x_ss, :]
a_out = a_out[:, x_ss]
b_out = b[x_ss, :]
b_out = b_out[:, u_ss]
c_out = identity(len(x_ss))
d_out = zeros((len(x_ss), len(u_ss)))
return a_out, b_out, c_out, d_out
def obj(x):
u = array([0, x[1], 0, th])
speed = x[2]
x = array([
speed * cos(x[0]), 0, speed * sin(x[0]), 0, x[0], 0, 0, 0, 0, 0, 0,
altitude
])
c_1 = c_f_m(aircraft, x, u)
throttle = ones(aircraft['propulsion']['n_engines'])
tsfc = g * speed / (aircraft['propulsion']['energy_density'] *
aircraft['propulsion']['total_efficiency'])
t = Propulsion(aircraft['propulsion'], x, throttle,
aircraft['weight']['cg']).thrust_f_m()
f_s = tsfc * t[0]
p_s = (c_1[0]) * speed * 60 / aircraft['weight']['weight'] # [ft/min]
return f_s / p_s
def rejected_takeoff(aircraft, s_f, x_0, u_0, v_max=350):
"""return derivatives for aircraft on ground."""
v = linspace(5, v_max, 100)
m = aircraft['weight']['weight'] / g
j = aircraft['weight']['inertia']
x = []
for vi in v:
x_0[0] = 0.707 * vi
c = c_f_m(aircraft, x_0, u_0)
c_t, c_g, normal_loads = landing_gear_loads(aircraft,
x_0,
c,
True,
brake=1)
dxdt = nonlinear_eom(x_0, m, j, c_t)
x.append(s_f + (vi**2) / (2 * dxdt[0]))
v = flip(v)
x = flip(x)
return v, x
def v_stab(x):
x = array([x[0], 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, altitude])
c = c_f_m(aircraft, x, u_0)
c_t, c_g, normal_loads = landing_gear_loads(aircraft, x, c)
return float(normal_loads[0])
def v_stab(x):
plane['horizontal']['control_1']['cf_c'] = x[0]
s = array([vr, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
c = c_f_m(plane, s, u)
c_t, c_g, normal_loads = landing_gear_loads(plane, s, c)
return float(normal_loads[0])
def aileron(x):
u = array([x[0], 0, 0, 0.01])
x = array([speed, 0, 0, 0, 0, 0, roll_rate, 0, 0, 0, 0, altitude])
dxdt = c_f_m(aircraft, x, u)
return sqrt(sum(dxdt**2)) / 1000
