


# Propeller selection
*Written by Marc Budinger (INSA Toulouse) and Scott Delbecq (ISAE-SUPAERO), Toulouse, France.*

**Sympy** package permits us to work with symbolic calculation.


```python
from math import pi

from sympy import Symbol
from sympy import *
```

## Design graph 

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




> **Questions:**
* Give the main sizing problems you are able to detect.
* Propose one or multiple solutions (which can request equation manipulation, addition of design variables, addition of constraints) 
* Orientate the arrows
* Give equations order, inputs/outputs at each step of this part of sizing procedure



### Sizing code and optimization

> Exercice: propose a sizing code for the selection of a propeller.



```python
# Specifications
rho_air=1.18# [kg/m^3] Air density
ND_max=105000./60.*.0254 #[Hz.m] Max speed limit (N.D max) for APC MR propellers

# Reference parameters for scaling laws
D_pro_ref=11.*.0254# [m] Reference propeller diameter
M_pro_ref=0.53*0.0283# [kg] Reference propeller mass

# Assumption

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
```

Define the design variables as a symbol under `variableExample= Symbol('variableExample')`


```python
#Design variables
beta_pro=Symbol('beta_pro')#[-] ratio pitch-to-diameter propeller (0.3,0.6)
k_ND=Symbol('k_ND')#[-] undercoefficient max speed propeller (1,1000)
```


```python
#Equations:
#-----
C_t = (4.27e-02 + 1.44e-01 * beta_pro)  # Thrust coef with T=C_T.rho.n^2.D^4 - 0.8 for de-rating of APC catalog
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.))**0.5  # [m] Propeller diameter
n_pro_to = ND_max / k_ND / D_pro # [Hz] Propeller speed 
Omega_pro_to = n_pro_to * 2*pi # [rad/s] Propeller speed

M_pro = M_pro_ref * (D_pro/D_pro_ref)**2. # [kg] Propeller mass

P_pro_to = C_p * rho_air * n_pro_to**3. * D_pro**5. # [W] Power per propeller
T_pro_to = P_pro_to / Omega_pro_to # [N.m] Propeller torque

# Propeller torque & speed for hover
n_pro_hov = sqrt(F_pro_hov/(C_t * rho_air *D_pro**4.)) # [Hz] hover speed
Omega_pro_hov = n_pro_hov * 2.*pi # [rad/s] Propeller speed

P_pro_hov = C_p * rho_air * n_pro_hov**3. * D_pro**5. # [W] Power per propeller
T_pro_hov = P_pro_hov / Omega_pro_hov # [N.m] Propeller torque       
```

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notebooks/10_PropellerSelection.ipynb
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2021-01-28T09:57:42.000Z
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notebooks/10_PropellerSelection.ipynb
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