2. Aerodynamic Module Documentation

2.1. Lifting Line Theory

If \(\theta_0\) is an arbitrary span-wise location:

(1)\[\alpha (\theta_o)=\frac{2b}{\pi c(\theta_o)} \sum_1^N A_n sin(n \theta_o) + \alpha_{L=0}(\theta_o) + \sum_1^N n A_n \frac{sin(n\theta_o)}{sin(\theta_o)}\]

Each equation has \(N\) unknowns (\(A_n\)), so if there are N \(\theta_o\), we have NxN system, which in Einstein notation can be written as:

(2)\[C_{ij}A_{i}=D_{i}\]

where, \(i=0,...,N\), \(j=0,...,N\) and :

(3)\[C_{ij}= \left( \frac{2b}{\pi c(j)} + \frac{n}{sin \theta(i)} \right) sin(n \theta(i))\]
(4)\[A_i=A(i)\]
(5)\[D_i=\alpha(i)-\alpha_{L=0}(i)\]

where \(n=1,3,5,...,N-1\). Since we are considering a symmetric wing, all of the even terms would cancel each other

_images/elliptical_LLT.png

2.2. The code

Current funcionatilities: - Lifting line theory - generate field pressures for Abaqus or other softwares - air properties calculator - Reynolds calculator Created on Mon Jul 20 17:26:19 2015

@author: Pedro Leal

aeropy.aero_module.LLT_calculator(alpha_L_0_root, c_D_xfoil, N=10, b=10.0, taper=1.0, chord_root=1, alpha_root=0.0, V=1.0)[source]

Calculate the coefficients for a Wing. TODO : - Include elliptical wing

  • When alpha_L_0_root = zero, nan!
  • Include non rectangular wings
  • something else?
aeropy.aero_module.Reynolds(height, V, c)[source]

Simple function to calculate Reynolds for a given height.

@author: Pedro Leal Created in Jul 17 2015

aeropy.aero_module.air_properties(height, unit='feet')[source]

Function to calculate air properties for a given height (m or ft).

Sources:

Created on Thu May 15 14:59:43 2014 @author: Pedro Leal

aeropy.aero_module.calculate_moment_coefficient(x, y, Cp, alpha, c=1.0, x_ref=0.25, y_ref=0.0, flap=False)[source]

Calculate the moment coeffcient. Inputs are x and y coordinates, and pressure coefficients (Cp). Inputs can be in a list in xfoil format (counterclockwise starting from the trailing edge, in case necessary, check create_input function from xfoil_module) or dictionaries with ‘upper’ and ‘lower’ keys.

Parameters:flap – if true, also calculates the moment contribution from the trailing edge and the panels in front of the flap (that are not directly in contact with the air)
aeropy.aero_module.pressure_shell(Data, half_span, chord='MAX', air_density=0, Velocity=0, N=10, thickness=0, txt=False, llt_distribution=False, distribution='Uniform', amplifier=1)[source]

Converts pressure coefficient data, usually 2D, into a 3D presurre field that Abaqus understands. Can be used for shells (considers thicknesses), but also for any surface. Can do Lifting Line Theory (LLT), Elliptical, and Uniform distributions.

If chord=’MAX’, the maximum value for vector ‘x’ is used as chord. If data in non-dimensional, use a numerical value.

If txt==True, an output textfile is generated.

aeropy.aero_module.pressure_shell_2D(Data, chord, thickness, half_span, height, Velocity, N, txt=False)[source]

Calculate pressure field for a 2D Shell.