3. Aerodynamic Module Documentation¶
3.1. 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
3.2. The code¶
Created on Mon Jul 20 17:26:19 2015
@author: Pedro Leal
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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?
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aero_module.Reynolds(height, V, c)[source]¶ Simple function to calculate Reynolds for a given height.
@author: Pedro Leal Created in Jul 17 2015
