SUAVE  2.5.2
An Aerospace Vehicle Environment for Designing Future Aircraft
Full_Linearized_Equations

Modules

 Supporting_Functions
 

Functions

def SUAVE.Methods.Flight_Dynamics.Dynamic_Stability.Full_Linearized_Equations.lateral_directional.lateral_directional (velocity, Cn_Beta, S_gross_w, density, span, I_z, Cn_r, I_x, Cl_p, J_xz, Cl_r, Cl_Beta, Cn_p, Cy_phi, Cy_psi, Cy_Beta, mass)
 
def SUAVE.Methods.Flight_Dynamics.Dynamic_Stability.Full_Linearized_Equations.longitudinal.longitudinal (velocity, density, S_gross_w, mac, Cm_q, Cz_alpha, mass, Cm_alpha, Iy, Cm_alpha_dot, Cz_u, Cz_alpha_dot, Cz_q, Cw, Theta, Cx_u, Cx_alpha)
 

Detailed Description

Function Documentation

◆ lateral_directional()

def SUAVE.Methods.Flight_Dynamics.Dynamic_Stability.Full_Linearized_Equations.lateral_directional.lateral_directional (   velocity,
  Cn_Beta,
  S_gross_w,
  density,
  span,
  I_z,
  Cn_r,
  I_x,
  Cl_p,
  J_xz,
  Cl_r,
  Cl_Beta,
  Cn_p,
  Cy_phi,
  Cy_psi,
  Cy_Beta,
  mass 
)
This calculates the natural frequency and damping ratio for the full linearized dutch 
roll mode along with the time constants for the roll and spiral modes   

Assumptions:
    X-Z axis is plane of symmetry
    Constant mass of aircraft
    Origin of axis system at c.g. of aircraft
    Aircraft is a rigid body
    Earth is inertial reference frame
    Perturbations from equilibrium are small
    Flow is Quasisteady
    Zero initial conditions
    Neglect Cy_p and Cy_r
    
Source:
    J.H. Blakelock, "Automatic Control of Aircraft and Missiles" Wiley & Sons, Inc. New York, 1991, p 118-124.
    
Inputs:
    velocity - flight velocity at the condition being considered                          [meters/seconds]
    Cn_Beta - coefficient for change in yawing moment due to sideslip                     [dimensionless] (no simple relation)
    S_gross_w - area of the wing                                                          [meters**2]
    density - flight density at condition being considered                                [kg/meters**3]
    span - wing span of the aircraft                                                      [meters]
    I_z - moment of interia about the body z axis                                         [kg * meters**2]
    Cn_r - coefficient for change in yawing moment due to yawing velocity                 [dimensionless] ( - C_D(wing)/4 - 2 * Sv/S * (l_v/b)**2 * (dC_L/dalpha)(vert) * eta(vert))
    I_x - moment of interia about the body x axis                                         [kg * meters**2]
    Cl_p - change in rolling moment due to the rolling velocity                           [dimensionless] (no simple relation for calculation)
    J_xz - products of inertia in the x-z direction                                       [kg * meters**2] (if X and Z lie in a plane of symmetry then equal to zero)
    Cl_r - coefficient for change in rolling moment due to yawing velocity                [dimensionless] (Usually equals C_L(wing)/4)
    Cl_Beta - coefficient for change in rolling moment due to sideslip                    [dimensionless] 
    Cn_p - coefficient for the change in yawing moment due to rolling velocity            [dimensionless] (-C_L(wing)/8*(1 - depsilon/dalpha)) (depsilon/dalpha = 2/pi/e/AspectRatio dC_L(wing)/dalpha)
    Cy_phi  - coefficient for change in sideforce due to aircraft roll                    [dimensionless] (Usually equals C_L)
    Cy_psi - coefficient to account for gravity                                           [dimensionless] (C_L * tan(Theta))
    Cy_Beta - coefficient for change in Y force due to sideslip                           [dimensionless] (no simple relation)
    mass - mass of the aircraft                                                           [kilograms]

Outputs:
    output - a data dictionary with fields:
    dutch_w_n - natural frequency of the dutch roll mode                                  [radian/second]
    dutch_zeta - damping ratio of the dutch roll mode                                     [dimensionless]
    roll_tau - approximation of the time constant of the roll mode of an aircraft         [seconds] (positive values are bad)
    spiral_tau - time constant for the spiral mode                                        [seconds] (positive values are bad)

Properties Used:
    N/A         

◆ longitudinal()

def SUAVE.Methods.Flight_Dynamics.Dynamic_Stability.Full_Linearized_Equations.longitudinal.longitudinal (   velocity,
  density,
  S_gross_w,
  mac,
  Cm_q,
  Cz_alpha,
  mass,
  Cm_alpha,
  Iy,
  Cm_alpha_dot,
  Cz_u,
  Cz_alpha_dot,
  Cz_q,
  Cw,
  Theta,
  Cx_u,
  Cx_alpha 
)
This calculates the natural frequency and damping ratio for the full 
linearized short period and phugoid modes        

Assumptions:
    X-Z axis is plane of symmetry
    Constant mass of aircraft
    Origin of axis system at c.g. of aircraft
    Aircraft is a rigid body
    Earth is inertial reference frame
    Perturbations from equilibrium are small
    Flow is Quasisteady
    Zero initial conditions
    Cm_a = CF_z_a = CF_x_a = 0
    Neglect Cx_alpha_dot, Cx_q and Cm_u
    
Source:
    J.H. Blakelock, "Automatic Control of Aircraft and Missiles" Wiley & Sons, Inc. New York, 1991, p 26-41.
    
Inputs:
    velocity - flight velocity at the condition being considered                                          [meters/seconds]
    density - flight density at condition being considered                                                [kg/meters**3]
    S_gross_w - area of the wing                                                                          [meters**2]
    mac - mean aerodynamic chord of the wing                                                              [meters]
    Cm_q - coefficient for the change in pitching moment due to pitch rate                                [dimensionless] (2 * K * dC_m/di * lt/c where K is approximately 1.1)
    Cz_alpha - coefficient for the change in Z force due to the angle of attack                           [dimensionless] (-C_D - dC_L/dalpha)
    mass - mass of the aircraft                                                                           [kilograms]
    Cm_alpha - coefficient for the change in pitching moment due to angle of attack                       [dimensionless] (dC_m/dC_L * dCL/dalpha)
    Iy - moment of interia about the body y axis                                                          [kg * meters**2]
    Cm_alpha_dot - coefficient for the change in pitching moment due to rate of change of angle of attack [dimensionless] (2 * dC_m/di * depsilon/dalpha * lt/mac)
    Cz_u - coefficient for the change in force in the Z direction due to change in forward velocity       [dimensionless] (usually -2 C_L or -2C_L - U dC_L/du)
    Cz_alpha_dot - coefficient for the change of angle of attack caused by w_dot on the Z force           [dimensionless] (2 * dC_m/di * depsilon/dalpha)
    Cz_q - coefficient for the change in Z force due to pitching velocity                                 [dimensionless] (2 * K * dC_m/di where K is approximately 1.1)
    Cw - coefficient to account for gravity                                                               [dimensionless] (-C_L)
    Theta - angle between the horizontal axis and the body axis measured in the vertical plane            [radians]
    Cx_u - coefficient for the change in force in the X direction due to change in the forward velocity   [dimensionless] (-2C_D)
    Cx_alpha - coefficient for the change in force in the X direction due to the change in angle of attack caused by w [dimensionless] (C_L-dC_L/dalpha)

Outputs:
    output - a data dictionary with fields:
        short_w_n - natural frequency of the short period mode                                            [radian/second]
        short_zeta - damping ratio of the short period mode                                               [dimensionless]
        phugoid_w_n - natural frequency of the short period mode                                          [radian/second]
        phugoid_zeta - damping ratio of the short period mode                                             [dimensionless]
    
Properties Used:
N/A