6.21. Frame selection

Written by Marc Budinger (INSA Toulouse), Scott Delbecq (ISAE-SUPAERO) and Félix Pollet (ISAE-SUPAERO), Toulouse, France.

6.21.1. Design graph

The following diagram represents the design graph of the frame selection.

Fig. 6.26 Airframe design graph

The design graphs for the overall drone system can be found in here.

6.21.1.1. Sizing code

import numpy as np

# Specifications
N_arm = 4.0  # [-] Number of arms
N_pro_arm = 1.0  # [-] Number of propellers per arm (1 or 2)

# Reference parameters for scaling laws
sigma_max = (
    280e6 / 4.0
)  # [Pa] Composite max stress (2 reduction for dynamic, 2 reduction for stress concentration)
rho_s = 1700.0  # [kg/m3] Volumic mass of aluminum

# Assumptions
D_pro = 0.3  # [m] Propeller diameter
F_pro_to = 1.0  # [N] Thrust for one propeller during take off

# Design variables
k_D = 0.99  # [-] aspect ratio D_in/D_out for the beam of the frame

# Equations

# Arms selection with propellers size
alpha_sep = 2 * np.pi / N_arm  # [rad] interior angle separation between propellers
L_arm = D_pro / (2.0 * np.sin(alpha_sep / 2.0))  # [m] length of the arm

# Tube diameter & thickness selection with take-off scenario
D_out_arm = (F_pro_to * N_pro_arm * L_arm * 32 / (np.pi * sigma_max * (1 - k_D**4))) ** (
    1 / 3
)  # [m] outer diameter of the arm (hollow cylinder)
D_in_arm = k_D * D_out_arm  # [m] inner diameter of the arm (hollow cylinder)

# Estimation models
M_arms = (
    np.pi / 4 * (D_out_arm**2 - (k_D * D_out_arm) ** 2) * L_arm * rho_s * N_arm
)  # [kg] mass of the arms
M_body = 1.5 * M_arms  # [kg] mass of the body (40% of total mass is the arms)
M_frame = M_body + M_arms  # [kg] total mass of the frame

%whos

Variable    Type       Data/Info
--------------------------------
D_in_arm    float64    0.009126226336644873
D_out_arm   float64    0.009218410441055428
D_pro       float      0.3
F_pro_to    float      1.0
L_arm       float64    0.21213203435596426
M_arms      float64    0.0019158884043039236
M_body      float64    0.0028738326064558853
M_frame     float64    0.004789721010759809
N_arm       float      4.0
N_pro_arm   float      1.0
alpha_sep   float      1.5707963267948966
k_D         float      0.99
np          module     <module 'numpy' from '/op<...>kages/numpy/__init__.py'>
rho_s       float      1700.0
sigma_max   float      70000000.0