def dynamic_pressure(mach, altitude):
"""returns incompressible dynamic pressure."""
rho = air_density(altitude)
a = speed_of_sound(altitude)
v = mach * a
q_bar = 0.5 * rho * v**2
return q_bar
def stall_speed(mach, h, c_l_max, n, gamma):
"""stall speed constraint equation."""
rho = air_density(h)
a = speed_of_sound(h)
v = a * mach
q_bar = 0.5 * rho * v ** 2
w_s = q_bar*c_l_max/(n*cos(deg2rad(gamma)))
return w_s
def reynolds_number(mach, altitude, x_ref):
"""return reynolds number."""
rho = air_density(altitude) # [slug/ft^3]
mu = viscosity(altitude)
a = speed_of_sound(altitude) # [ft/s]
v = mach * a # [ft/s]
re = rho * v * x_ref / mu # []
return re
def master_constraint(aircraft, wing_loading, mach, altitude, n, gamma, a_x):
"""master constraint equation for flight."""
g = gravitational_acceleration()
rho = air_density(altitude)
rho_sl = air_density(0)
a = speed_of_sound(altitude)
v = a*mach
q_bar = 0.5*rho*v**2
c_d_0 = c_d_zero(aircraft, mach, altitude)
c_l_a = c_l_alpha(aircraft, mach)
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 c_f_m(aircraft, x, u):
s = aircraft['wing']['planform']
altitude = x[-1]
a = speed_of_sound(altitude)
v = sqrt(x[0]**2 + x[1]**2 + x[2]**2)
mach = v/a
alpha = arctan(x[2]/x[0])
c_bar = mac(aircraft['wing']['aspect_ratio'], s, aircraft['wing']['taper'])
q_hat = x[7]*c_bar/(2*v)
alpha_dot = 0
d_elevator = u[1]
f_x = force_x(aircraft, mach, altitude, alpha, alpha_dot, q_hat, d_elevator)
f_y = 0
f_z = force_z(aircraft, mach, altitude, alpha, alpha_dot, q_hat, d_elevator)
m_x = 0
m_y = moment_y(aircraft, mach, altitude, alpha, alpha_dot, q_hat, d_elevator)
m_z = 0
c = array([f_x, f_y, f_z, m_x, m_y, m_z])
return c
def trim_alpha_de(aircraft, speed, altitude, gamma):
"""trim aircraft with angle of attack and elevator"""
a = speed_of_sound(altitude) # [ft/s]
rho = air_density(altitude) # [slug / ft^3]
mach = speed / a # []
c_l_a = c_l_alpha(aircraft, mach) # [1/rad]
c_l_de = c_l_delta_elevator(aircraft, mach) # [1/rad]
c_m_a = c_m_alpha(aircraft, mach) # [1/rad]
c_m_de = c_m_delta_elevator(aircraft, mach) # [1/rad]
c_l_0 = c_l_zero(aircraft, mach) # []
a = array([[c_l_a, c_l_de], [c_m_a, c_m_de]])
w = aircraft['weight']['weight'] # [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 = c_m_zero(aircraft, mach, altitude)
b = array([[c_l_1 - c_l_0], [-c_m_0]])
c = linalg.solve(a, b) # [rad]
return rad2deg(c)
def takeoff(aircraft, wing_loading, s_to, altitude, mu):
"""takeoff constraint equation."""
g = gravitational_acceleration()
rho = air_density(altitude)
rho_sl = air_density(0)
c_l_max = 1
a = speed_of_sound(altitude)
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 = c_d_zero(aircraft, mean(mach_avg), altitude)
c_l_0 = c_l_zero(aircraft, mean(mach_avg))
c_l_a = c_l_alpha(aircraft, mean(mach_avg))
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