Airfoil toolbox

A list of functions and script used for analysis of airfoils and related data with Matlab.

Disclaimer

This toolbox was mainly developed under Matlab R2018a. The various functions were not tested on older versions. A code compatibility analysis showed no errors, so in theory it should work properly with any other versions of Matlab as well. If for some reason it does not work on your version, please open an issue.

The functions in this repository are intended to be used as a Matlab package (see Matlab documentation for more details).

Documentation

Each function contains a complete description in its preamble. Type help <function> in Matlab command window to print it.

Install and use

Installation

1. Either clone this repository or download a .zip version of the source code.
2. Place the +af_tools/ folder somewhere on your Matlab Path such as:
   • in you current project
   • in a folder that is already in Matlab's path (e.g. /Documents/Matlab/).
   • somewhere else, but then explicitly add it to Matlab's Path.

Remark

Unfortunately, Matlab packages have a few limitations. Hence, you should avoid changing the package name if you do not know what you are doing.

• The + in the folder's name is required for Matlab to treat it as a package.
• Some functions of this package are interconnected (e.g., nacaairfoil calls nacacamber). In that situation, Matlab forces the main function to re-import explicitly all sub-functions before using them, even if they are part of the same package (people have complained about that design choice for quite some time, to no avail). If you rename the package, these links will be broken and Matlab will not find the connected functions.
• All functions that import other functions will have an import line at the beginning. If you rename the package, you must therefore update these imports.

Use

Once the +af_tools/ folder is placed somewhere where Matlab will find it, you can start using its features.

• If you are only interested in a single function of the package, use

import af_tools.<functionName>
functionName(args)

• If you want to import all functions, use

import af_tools.*
xf2mat(args)
nacacamber(args)
...

• If you want to use functions on-the-fly without importing them, call them directly

af_tools.xf2mat(args)

Functions

• All functions can be used as standalone functions and give meaningful output on their own (they are not sub-routines used to perform intermediary tasks).
• All functions can be called without arguments. If that is the case, they will prompt the user to manually enter or select the few mandatory arguments. The rest will be set to default values.

List of functions:

• xf2mat: Aggregates multiple XFOIL or XFLR5 polar results into a single structure.
• formatairfoilcoord: Re-format airfoil coordinates datafile.
• Airfoil generation
  • nacacamber: Generates the coordinates of the camberline for a NACA 4 or 5 digits airfoil.
  • nacaairfoil: Generates the full coordinates of a NACA 4 or 5 digits airfoil.
• Polar manipulation
  • extendpolar: Extends polars to the full range of
    \alpha
    ([-180, 180] deg).
  • findstall: Finds the stall point and returns the corresponding
    \alpha
    ,
    C_l
    and
    C_d
    .
  • findzerolift: Finds the zero-lift angle and the associate
    C_d
    .
  • findcllinearrange: Finds the linear range of the lift coefficient and returns the range and lift slope.
  • plotpolars: Plot various polars.

xf2mat

Aggregates airfoil polars obtained using XFOIL v6.99 of XFLR5 v6.55 into a single Matlab structure.

This function can either aggregate multiple polar files into a single structure (e.g. same airfoil at different Reynolds) or simply convert a single polar data into a Matlab-ready structure.

import af_tools.xf2mat
Polar = xf2mat
Polar = xf2mat(inputFiles, 'autosave', true)
Polar = xf2mat(inputFiles, 'trimAoas', true)
Polar = xf2mat(inputFiles, 'autosave', true, 'trimAoas', true)

The output is a structure with the following fields, where M is the number of angles of attack and N is the number of input files.

formatairfoilcoord

The UIUC airfoil database from the University of Illinois gathers the coordinates for more than 1600 airfoils. Two different standards are used to represent the coordinates of the airfoil:

• Selig: The first line is the name of the airfoil, and each line after that is a set of coordinates. The coordinates are ordered from the trailing edge, along the upper surface to the leading edge and back around the lower surface to trailing edge (e.g., see E205). This format is the most common one.
• Lednicer: The first line is the name of the airfoil, the second one is the number of points on each side and the lines after that are the coordinates. The coordinates are given separately for the upper and lower surfaces, each from the leading edge to the trailing edge (e.g., see Clark Y).

Many engineering tools or application (such as XFOIL) rely on inputs in the Selig format only. This script was therefore created to reformat original data so they can be used easily with other tools.

Even though the Selig format is the default option, the script allows also the user to reformat Selig files in Lednicer form if needed. It also comes with the option to refine the coordinates by adding points with a spline interpolation following the half-cosine rule (more points are the leading and trailing edge). If that option is selected, the airfoil will be defined using 50 points for each surface.

import af_tools.xf2mat
Af = formatairfoilcoord
Af = formatairfoilcoord(inputFiles, 'autosave', true)
Af = formatairfoilcoord(inputFiles, 'overwrite', true)

Airfoil generation

The following functions use the same two main input arguments.

nacacamber

Determines the camber line of a NACA 4 or 5 digits airfoil. The output is ordered from the leading edge to the trailing edge.

import af_tools.nacacamber
[coord, gradY] = nacacamber
[coord, gradY] = nacacamber(digits)
[coord, gradY] = nacacamber(digits, nPoints)
[coord, gradY] = nacacamber(digits, nPoints, 'spacing', 'halfcosine')

nacaairfoil

Generates the full coordinates of a NACA 4 or 5 digits airfoil. The output coordinates follow the most usual order. They start at the trailing edge, along the upper surface to the leading edge and back around the lower surface to trailing edge.

import af_tools.nacaairfoil
[coord] = nacaairfoil
[coord] = nacaairfoil(digits)
[coord] = nacaairfoil(digits, nPoints)
[coord] = nacaairfoil(digits, nPoints, 'spacing', spacing, 'zerote', true)
[coord] = nacaairfoil(digits, nPoints, 'savedat', true)

Polar manipulation

The following functions all share the same main inputs arguments in the exact same order. These arguments can be of two types:

1. Polar: A Polar structure, as the one given by [xf2mat][xf2mat];
2. alpha, cl, cd, cm: Arrays representing the different polars. Some functions only allow the first two or three arrays.

Some functions then extend these inputs by using various optional arguments.

extendpolar

This function extends known

import af_tools.extendpolar
[alphaExt, clExt, cdExt] = extendpolar
[alphaExt, clExt, cdExt] = extendpolar(Polar)
[alphaExt, clExt, cdExt] = extendpolar(Polar, 'method', 'Viterna')
[alphaExt, clExt, cdExt] = extendpolar(Polar, 'limit', 'stall')
[alphaExt, clExt, cdExt] = extendpolar(alpha, cl, cd, 'method', 'Viterna')

plotpolars

Plots the following polars:

import af_tools.plotpolars
plotpolars
plotpolars(Polar)
plotpolars(alpha, cl, cd, cm)

findstall

Finds the stall angle of attack and the associated

import af_tools.findstall
[alpha_s, cl_s, cd_s] = findstall
[alpha_s, cl_s, cd_s] = findstall(Polar)
[alpha_s, cl_s, cd_s] = findstall(alpha, cl, cd)

findzerolift

Finds the zero-lift angle of attack and the associated

import af_tools.findzerolift
[alpha_zeroL, cd_zeroL] = findzerolift
[alpha_zeroL, cd_zeroL] = findzerolift(Polar)
[alpha_zeroL, cd_zeroL] = findzerolift(alpha, cl, cd)

findcllinearrange

Finds the range of angles of attack for which the

import af_tools.findcllinearrange
[alphaRange, clRange, clSlope] = findcllinearrange
[alphaRange, clRange, clSlope] = findcllinearrange(Polar)
[alphaRange, clRange, clSlope] = findcllinearrange(alpha,cl)

Licence

Copyright (c) 2022 Thomas Lambert, University of Liège.

All functions and scripts of the af_tools code are licensed under the Apache 2.0 Licence.