Airfoil Class¶

All functionality is wrapped in the Airfoil class. The Airfoil class can create geometries, create a database using Xfoil, export and import databases, curve fit a database, import and export curve fits, and calculate section properties. For an example of using the Airfoil class to generate and export a database, see the examples/ directory.

The following member functions are available:

class airfoil_db.Airfoil(name, airfoil_input, **kwargs)¶

A class defining an airfoil. If the airfoil geometry is defined using outline points, then when this class is initialized, a solver will be automatically run to determine the camber line and thickness distribution of the airfoil. The parameters “camber_relaxation”, “le_loc”, and “camber_termination_tol” then have bearing on this solver.

When using the member methods get_CL, get_CD, get_Cm, get_CLa, get_CLM, get_CLRe, and get_aL0, the default parameters are dependent upon the type of airfoil.

For all airfoil types except ‘functional’, ‘alpha’, ‘trailing_flap_deflection’, and ‘trailing_flap_fraction’ default to 0.0.

For ‘functional’ airfoils, the defaults are specified by the user.

For ‘linear’ airfoils, ‘Mach’ and ‘Rey’ have no effect on computations.

For ‘database’ airfoils, ‘Mach’ and ‘Rey’ default to the average value in the database, if the database is dependent on that variable. Otherwise, they default to the value specified as constant when the database was generated.

For ‘poly_fit’ airfoils, ‘Mach’ and ‘Rey’ default to the values given in the fit file. If export_polynomial_fits() is used, these values are the same as those for the ‘database’ type.

Parameters:

name (str) – Name of the airfoil.
airfoil_input (dict or str) – Dictionary or path to JSON object describing the airfoil.
verbose (bool, optional) – Whether to display information on the progress of parameterizing the geometry for an airfoil defined by a set of outline points. Defaults to False.
camber_relaxation (float, optional) – A value between 0.0 and 1.0 that defines how much of the update at each iteration of the camber line solver should be accepted. Helpful for some poorly behaved cases. Defaults to 1.0 (full update).
le_loc (list, optional) – Gives the location of the leading edge relative to the given points for an airfoil defined by a set of outline points. If this is given, the camber line will be forced to intersect this point. THIS POINT SHOULD LIE ON THE AIRFOIL OUTLINE. If not given, the camber line solver will try to iteratively find the leading edge (the point where the camber line intersects the front of the profile).
camber_termination_tol (float, optional) – The tolerance below which the maximum approximate error in the camber line estimate must fall in order for the camber line solver to terminate. Defaults to 1e-10.
max_iterations (int, optional) – Maximum number of iterations for the camber line solver. Defaults to 100.

check_against_NACA(naca_des)¶

Checks the error in the camber and thickness against that predicted by the NACA equations. This is recommended as a check for the user if unusual geometries are being imported. Checks against the open trailing edge formulation of the NACA equations.

Parameters:	naca_des (str) – NACA designation of the airfoil to compare against as a string. May only be 4-digit series.

export_database(**kwargs)¶

Exports the database generated by generate_database().

Parameters:	filename (str) – File to export the database to.

export_linear_model(**kwargs)¶

Exports the linear coefficients used to predict the behavior of the airfoil.

Parameters:	filename (str) – JSON file to export the model data to.

export_polynomial_fits(**kwargs)¶

Save the polynomial fit to a JSON object.

Parameters:	filename (str) – JSON object to write polynomial fit data to. write_limits (bool, optional) – Whether to limit the polynomial fits based on the original range of data. Defaults to True.

generate_database(**kwargs)¶

Makes calls to Xfoil to calculate CL, CD, and Cm as a function of each given degree of freedom.

Parameters:

degrees_of_freedom (dict) –
A dict specifying which degrees of freedom the database should perturb. Allowable degrees of freedom are “alpha”, “Rey”, “Mach”, “trailing_flap_deflection”, and “trailing_flap_fraction”.

Each key should be one of these degrees of freedom. To specify a range for the degree of freedom, a dictionary with the following keys should be given:

”range” : list

The lower and upper limits for this DOF.

”steps” : int

The number of points in the range to interrogate.

”index” : int

Index of the column for this degree of freedom in the database.

”log_step” : bool, optional

Whether the steps in this dof should be spaced linearly (False) or logarithmically (True). Defaults to False.

If instead of perturbing a variable, you want the database to be evaluated at a constant value of that variable, a float should be given instead of a dictionary. That variable will then not be considered a degree of freedom of the database and will not appear in the database.

An example is shown below:

dofs = {

“alpha” : {

“range” : [math.radians(-15.0), math.radians(15.0)], “steps” : 21, “index” : 1

}, “Rey” : 2900000.0, “trailing_flap_deflection” : {

”range” : [math.radians(-20.0), math.radians(20.0)], “steps” : 1, “index” : 0

}, “trailing_flap_fraction” : 0.25

}

The above input will run the airfoil through angles of attack from -15 to 15 degrees at a Reynolds number of 2900000.0 and through flap deflections from -20 to 20 degrees with a chord fraction of 25%.

If a float, the degree of freedom is assumed to be constant at that value.

If not specified, each degree of freedom defaults to the following:

”alpha” : 0.0
”Rey” : 1000000.0

”Mach” : 0.0

”trailing_flap_deflection” : 0.0

”trailing_flap_fraction” : 0.0

Please note that all angular degreees of freedom are in radians, rather than degrees.

Currently, the number of steps in Reynolds number multiplied by the number of steps in Mach number may not exceed 12. This is due to internal limitations in Xfoil. However, due to the weak dependence of airfoil properties on Reynolds number, we do not expect this to be a great hinderance.
N (int, optional) – Number of panel nodes for Xfoil to use. Defaults to 200.
max_iter (int, optional) – Maximum iterations for Xfoil. Defaults to 100.
x_trip (float or list, optional) – x location, non-dimensionalized by the chord length, of the boundary layer trip position. This is specified for the top and bottom of the airfoil. If a float, the value is the same for the top and the bottom. If a list, the first list element is the top trip location and the second list element is the bottom trip location. Defaults to 1.0 for both.
N_crit (float or list, optional) – Critical amplification exponent for the boundary layer in Xfoil. If a float, the value is the same for the top and the bottom. If a list, the first list element is for the top and the second list element is for the bottom. Defaults to 9.0 for both.
update_type (bool, optional) – Whether to update the airfoil to use the newly computed database for calculations. Defaults to True.
show_xfoil_output (bool, optional) – Display whatever Xfoil prints out. Defaults to False.
show_xfoil_plots (bool, optional) – Display Xfoil plots. Defaults to True.
resize_xfoil_window (float, optional) – resizes the xfoil window to screen size fraction. Xfoil defaults to 0.8 window/screen size. This variable defaults to None. Has no effect if show_xfoil_plots is False.
CD_type (str, optional) – Which drag coefficient to read in. May be ‘total’, ‘friction’, or ‘pressure’. Defaults to ‘total’.
verbose (bool, optional) – Defaults to True

generate_linear_model(**kwargs)¶

Creates a linearized model of the airfoil coefficients in alpha. Pulls from the database or poly_fit information to generate this model. Cannot be used on a type “linear” airfoil.

linear_limits : list, optional: Limits in alpha for which the behavior of the airfoil can be considered linear. If not given, the user will be prompted to graphically select this region. Given in degrees.
update_type : bool, optional: Whether to change the type of the airfoil to “linear” once the model is determined. Defaults to True.
plot_model : bool, optional: Whether to display a polar of the linear region determined. Defaults to False.
Rey : float, optional: Reynolds number at which to evaluate the model.
Mach : float, optional: Mach number at which to evaluate the model.

generate_polynomial_fit(**kwargs)¶

Generates a set of multivariable polynomials using least-squares regression to approximate the database. Note: This airfoil must have a database already for fits to be created.

Parameters:

CL_degrees (dict or str, optional) –
If dict, order of fit polynomial for the coefficient of lift for each degree of freedom, formatted as

{

“<DOF1_NAME>” : <ORDER>, “<DOF2_NAME>” : <ORDER>, …

}

Orders must be integers. Defaults to 1 for any not specified.

Can also be specified as “auto”. In this case, the fit degrees will be determined automatically using the method described in Morelli, “Global Nonlinear Aerodynamic Modeling Using Multivariate Orthogonal Functions,” Journal of Aircraft, 1995. The algorithm tried to minimize the RMS error between the data and the prediction while also minimizing the degree of the fit. This will automatically determine the fit order for each degree of freedom.
CD_degrees (dict, optional) – Same as CL_degrees.
Cm_degrees (dict, optional) – Same as CL_degrees.
CL_kwargs (dict, optional) –
keyword arguments sent to the CL polynomial fit function

When CL_degrees is specified as “auto” then CL_kwargs can be

”max_order” : int, optional

gives the max order of polynomial for any one of the independent varialbes to try. Defaults to 6.

”tol” : float, optional

Gives the cut-off value for any polynomial coefficient to not be included in the final results. If a coefficient has an absolute value below tol, it won’t be included. Defaults to 1e-12.

”sigma” : float, optional

value used to determine the trade off between how good of a fit to perform and how many terms to keep. Defaults to None, which causes the function to calculate sigma automatically using the mean squared of the difference of the independent variable values with respect to the mean independent variable value of the dataset

”sigma_multiplier” : float, optional

term multiplied onto sigma to change it’s value. Allows using a multiple of the automatically determined sigma value. Defaults to 1.

Otherwise CL_kwargs could be

”interaction” : boolean, optional

value with default set to True. This variable determines whether or not interaction terms are included in the fit function. If set to True, interaction terms up the max order for each independent variable are included, i.e. if Nvec = [3,2] then the highest interaction term included is x_1^3*x_2^2. Specific interaction terms can be omitted using the constraints input

”sym” : list, optional

Defaults to an empty list. If used, the length should be V and each element should contain a boolean, True or False. The ith element determines if the ith independent variable is symmetric either even or odd, which is determined by the order given in Nvec. This will also remove the cooresponding interaction terms if they are enabled.

”sym_same” : list, optional

Defaults as an empty list. If used, the entries in the list should be tuples with two integers. The integers represent the independent variables that the “same” symmetry condition will be applied. The “same” symmetry ensures all interaction terms with exponents of the two independent variables that are either odd-odd or even-even to be forced to zero

”sym_diff” : = list, optional

Defaults as an empty list. Similar to “sym_same” except it enforces the “diff” symmetry condition which ensures all interaction terms with exponents of the two independent variables that are either odd-even or even-odd to be forced to zero

”zeroConstraints” : list, optional

Defaults as an empty list. Entries in the list contain integer tuples of length V. The integer values represent the powers of the independent variables whose coefficient will be forced to 0 before the best fit calculations are performed, allowing the user to omit specific interaction terms or regular polynomial terms

”constraints” : list, optional

Defaults to an empty list. Entries in the list contain tuples of length 2. The first entry is a list of integers that represent the powers of the independent variables whose coefficient will then be forced to be equal to the second entry in the tuple, which should be a float.

”percent” : boolean, optional

Default set to False. When set to True the least squares is performed on the percent error squared. This option should not be used if y contains any zero or near zero values, as this might cause a divide by zero error.

”weighting” : function, optional

Defaults to None. If given, weighting should be a function that takes as arguments x, y, and p where x and y are the independent and dependent variables defined above and p is the index representing a certain data point. weighting should return a ‘weighting factor’ that determines how important that datapoint is. Returning a ‘1’ weights the datapoint normally.
CD_kwargs (dict, optional) – Same as CL_kwargs
Cm_kwargs (dict, optional) – Same as CL_kwargs
update_type (bool, optional) – Whether to update the airfoil to use the newly computed polynomial fits for calculations. Defaults to True.
verbose (bool, optional) –

get_CD(**kwargs)¶

Returns the coefficient of drag. note: all parameters can be given as numpy arrays, in which case a numpy array of the coefficient will be returned. to do this, all parameter arrays must have only one dimension and must have the same length.

Parameters:	alpha (float, optional) – Angle of attack in radians. Defaults to 0.0. Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0.
Returns:	Drag coefficient
Return type:	float or ndarray

get_CL(**kwargs)¶

Returns the coefficient of lift. Note: all parameters can be given as numpy arrays, in which case a numpy array of the coefficient will be returned. To do this, all parameter arrays must have only one dimension and must have the same length.

Parameters:	alpha (float, optional) – Angle of attack in radians. Defaults to 0.0. Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0.
Returns:	Lift coefficient
Return type:	float or ndarray

get_CLM(**kwargs)¶

Returns the lift slope with respect to Mach number using a forward-difference approximation. Simply returns 0 for a type ‘linear’ airfoil.

Parameters:	alpha (float, optional) – Angle of attack in radians. Defaults to 0.0. Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0. dx (float) – Step size for finite-difference equation. Defaults to 0.05.
Returns:	Lift slope with respect to Mach number
Return type:	float or ndarray

get_CLRe(**kwargs)¶

Returns the lift slope with respect to Reynolds number using a central-difference approximation. Simply returns 0 for a type ‘linear’ airfoil.

Parameters:	alpha (float, optional) – Angle of attack in radians. Defaults to 0.0. Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0. dx (float) – Step size for finite-difference equation. Defaults to 1000.
Returns:	Lift slope with respect to Reynolds number
Return type:	float or ndarray

get_CLa(**kwargs)¶

Returns the lift slope using a central-difference approximation.

Parameters:	alpha (float, optional) – Angle of attack in radians. Defaults to 0.0. Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0. dx (float, optional) – Step size for finite-difference equation. Defaults to 0.001 radians.
Returns:	Lift slope
Return type:	float or ndarray

get_Cm(**kwargs)¶

Returns the moment coefficient. note: all parameters can be given as numpy arrays, in which case a numpy array of the coefficient will be returned. to do this, all parameter arrays must have only one dimension and must have the same length.

Parameters:	alpha (float, optional) – Angle of attack in radians. Defaults to 0.0. Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_moment_deriv (float or ndarray, optional) – Change in section moment with respect to trailing flap deflection. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0.
Returns:	Moment coefficient
Return type:	float or ndarray

get_aL0(**kwargs)¶

Returns the zero-lift angle of attack, taking flap deflection into account.

Parameters:	Rey (float, optional) – Reynolds number. Mach (float, optional) – Mach number. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians. Defaults to 0. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord length. Defaults to 0.
Returns:	Zero-lift angle of attack
Return type:	float

get_camber(x)¶

Returns the y coordinate(s) of the camber line at the specified x location(s).

Parameters:	x (float or ndarray) – x location(s) at which to get the thickness.
Returns:	Camber line y coordinate(s) as a percentage of the chord.
Return type:	float or ndarray

get_max_camber()¶: Returns the maximum camber of the airfoil, divided by the chord length.

get_max_thickness()¶: Returns the maximum thickness of the airfoil, divided by the chord length.

get_outline_points(**kwargs)¶

Returns an array of outline points showing the geometry of the airfoil.

Parameters:	N (int, optional) – The number of outline points to return. This function will not always return exactly this many but never more. Defaults to 200. cluster (bool, optional) – Whether to cluster points about the leading and trailing edges. Defaults to True. trailing_flap_deflection (float, optional) – Trailing flap deflection in radians (positive down). Defaults to zero. trailing_flap_fraction (float, optional) – Trailing flap fraction of the chord. Defaults to zero. export (str, optional) – If specified, the outline points will be saved to a file. Defaults to no file. top_first (bool, optional) – The order of the coordinates when exported. Defaults to going from the trailing edge along the top and the around to the bottom. close_te (bool, optional) – Whether the top and bottom trailing edge points should be forced to be equal. Defaults to False plot (bool, optional) – Whether a plot of the outline points should be displayed once computed. Defaults to False. original_points (bool, optional) – Whether this should simply return the original inputted points. If set to True, all other kwargs relating to the geometry will be ignored. Defaults to False.
Returns:	Outline points in airfoil coordinates.
Return type:	ndarray

get_thickness(x)¶

Returns the thickness normal to the camber line at the specified x location(s).

Parameters:	x (float or ndarray) – x location(s) at which to get the thickness.
Returns:	Thickness as a percentage of the chord.
Return type:	float or ndarray

import_database(**kwargs)¶

Imports the specified database. Please note that if you have generated your own database not using AirfoilDatabase, angle of attack should be stored in radians, rather than degrees.

Parameters:	filename (str) – File to import the database from update_type (bool, optional) – Whether to update the airfoil to use the newly imported database for calculations. Defaults to True.

import_polynomial_fits(**kwargs)¶

Read in polynomial fit data from a JSON object.

Parameters:	filename (str) – JSON object to read polynomial fit data from. update_type (bool, optional) – Whether to update the airfoil to use the newly imported polynomial fits for calculations. Defaults to True.

read_pacc_file(filename, CD_type='total')¶

Reads in and formats an Xfoil polar accumulation file.

Parameters:

filename (str) – File to read in.
CD_type (str, optional) – Which drag coefficient to read in. May be ‘total’, ‘friction’, or ‘pressure’. Defaults to ‘total’.

Returns:

alpha (list) – List of angles of attack from the accumulation polar.
CL (list) – Coefficient of lift at each alpha.
CD (list) – Coefficient of drag at each alpha.
Cm (list) – Moment coefficient at each alpha.
Re (float) – Reynolds number for the polar.
M (float) – Mach number for the polar.

run_xfoil(**kwargs)¶

Calls Xfoil and extracts the aerodynamic coefficients at the given state.

Parameters:

alpha (float or list of float) – Angle(s) of attack to calculate the coefficients at in radians. Defaults to 0.0.
Rey (float or list of float) – Reynolds number(s) to calculate the coefficients at. Defaults to 1000000.
Mach (float or list of float) – Mach number(s) to calculate the coefficients at. Defaults to 0.0.
trailing_flap_deflection (float or list of float) – Flap deflection(s) to calculate the coefficients at in radians. Defaults to 0.0.
trailing_flap_fraction (float or list of float) – Flap fraction(s) to calculate the coefficients at in radians. Defaults to 0.0.
N (int, optional) – Number of panels for Xfoil to use. Defaults to 200.
max_iter (int, optional) – Maximum iterations for Xfoil. Defaults to 100.
x_trip (float or list, optional) – x location, non-dimensionalized by the chord length, of the boundary layer trip position. This is specified for the top and bottom of the airfoil. If a float, the value is the same for the top and the bottom. If a list, the first list element is the top trip location and the second list element is the bottom trip location. Defaults to 1.0 for both.
xycm (list, optional) – x-y coordinates, non-dimensionalized by the chord length, of the reference point for determining the moment coefficient. Defaults to the quater-chord.
N_crit (float or list, optional) – Critical amplification exponent for the boundary layer in Xfoil. If a float, the value is the same for the top and the bottom. If a list, the first list element is for the top and the second list element is for the bottom. Defaults to 9.0 for both.
show_xfoil_output (bool, optional) – Display whatever Xfoil outputs from the command line interface. Defaults to False.
show_xfoil_plots (bool, optional) – Display Xfoil plots. Defaults to True.
resize_xfoil_window (float, optional) – resizes the xfoil window to screen size fraction. Xfoil defaults to 0.8 window/screen size. This variable defaults to None. Has no effect if show_xfoil_plots is False.
CD_type (str, optional) – Which drag coefficient to read in. May be ‘total’, ‘friction’, or ‘pressure’. Defaults to ‘total’.
verbose (bool, optional) –

Returns:

CL (ndarray) – Coefficient of lift. First dimension will match the length of alpha, second will match Rey, etc.
CD (ndarray) – Coefficient of drag. Dimensions same as CL.
Cm (ndarray) – Moment coefficient. Dimensions same as CL.

set_err_state(**kwargs)¶

Sets the error state for the airfoil. Each may be specified as ‘raise’ or ‘ignore’.

Parameters:	poly_fit_bounds (str, optional) – How to handle PolyFitBoundsError. Defaults to ‘raise’.

set_type(database_type)¶

Determines how the aerodynamic coefficients will be calculated.

Parameters:	database_type (str) – “linear”, “functional”, “database”, or “poly_fit”. Airfoil will automatically check if it has the necessary to perform the given type of computation and throw a warning if it does not.

set_verbosity(verbosity)¶: Sets the verbosity of the airfoil.

Airfoil Class¶

Airfoil Database

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