6.15. Propeller selection

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

6.15.1. Design graph

The following diagram represents the design graph of the propeller’s selection. The max thrust is assumed to be known here.

Fig. 6.18 Propeller design graph

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

6.15.1.1. Sizing code

import numpy as np

# Specifications
rho_air = 1.18  # [kg/m^3] Air density
ND_max = 105000.0 / 60.0 * 0.0254  # [Hz.m] Max speed limit (N.D max) for APC MR propellers

# Reference parameters for scaling laws
D_pro_ref = 11.0 * 0.0254  # [m] Reference propeller diameter
M_pro_ref = 0.53 * 0.0283  # [kg] Reference propeller mass

# Assumptions
F_pro_to = 15.0  # [N] Thrust for 1 propeller during Take Off
F_pro_hov = 5.0  # [N] Thrust for 1 propeller during hover

# Design variables
beta_pro = 0.33  # pitch/diameter ratio of the propeller
k_ND = 1.2  # slow down propeller coef : ND = NDmax / k_ND

# Equations

# Estimation models for propeller aerodynamics
C_t = 4.27e-02 + 1.44e-01 * beta_pro  # Thrust coef with T=C_T.rho.n^2.D^4
C_p = -1.48e-03 + 9.72e-02 * beta_pro  # Power coef with P=C_p.rho.n^3.D^5

# Propeller selection with take-off scenario
D_pro = (F_pro_to / (C_t * rho_air * (ND_max / k_ND) ** 2.0)) ** 0.5  # [m] Propeller diameter
n_pro_to = ND_max / k_ND / D_pro  # [Hz] Propeller speed
Omega_pro_to = n_pro_to * 2 * np.pi  # [rad/s] Propeller speed

# Estimation model for mass
M_pro = M_pro_ref * (D_pro / D_pro_ref) ** 2.0  # [kg] Propeller mass

# Performance in various operating conditions
# Take-off
P_pro_to = C_p * rho_air * n_pro_to**3.0 * D_pro**5.0  # [W] Power per propeller
T_pro_to = P_pro_to / Omega_pro_to  # [N*m] Propeller torque
# Hover
n_pro_hov = np.sqrt(F_pro_hov / (C_t * rho_air * D_pro**4.0))  # [Hz] hover speed
Omega_pro_hov = n_pro_hov * 2.0 * np.pi  # [rad/s] Propeller speed
P_pro_hov = C_p * rho_air * n_pro_hov**3.0 * D_pro**5.0  # [W] Power per propeller
T_pro_hov = P_pro_hov / Omega_pro_hov  # [N*m] Propeller torque

%whos

Variable        Type       Data/Info
------------------------------------
C_p             float      0.030596
C_t             float      0.09022
D_pro           float      0.3204517851291232
D_pro_ref       float      0.2794
F_pro_hov       float      5.0
F_pro_to        float      15.0
M_pro           float      0.019730354665561008
M_pro_ref       float      0.014999
ND_max          float      44.449999999999996
Omega_pro_hov   float64    419.3214365967957
Omega_pro_to    float      726.2860328884217
P_pro_hov       float64    36.262832648239105
P_pro_to        float      188.42720571935266
T_pro_hov       float64    0.08647979684164854
T_pro_to        float      0.2594393905249455
beta_pro        float      0.33
k_ND            float      1.2
n_pro_hov       float64    66.73707937877482
n_pro_to        float      115.59201223279518
np              module     <module 'numpy' from '/op<...>kages/numpy/__init__.py'>
rho_air         float      1.18