Airfoil Geometry Manipulation Tools

Here we include the variety of methods for manipulating airfoil geometries in useful ways implemented in AirfoilTools.

Deconstruction

It is often convenient to deconstruct an airfoil into its upper and lower halves. The split_upper_lower function makes this process straightforward.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = naca4()

xl, xu, yl, yu = split_upper_lower(x, y)

plot(xl, yl; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Lower Side")
plot!(xu, yu; label="Upper Side")

FLOWFoil.AirfoilTools.split_upper_lower — Function

split_upper_lower(x, y; idx::Integer=nothing)

Split the upper and lower halves of the airfoil coordinates.

Assumes leading edge point is at first minimum x value if idx is not provided. Returns the upper and lower coordinates each with the leading edge point. Assumes airfoil is defined clockwise starting at the trailing edge.

Arguments

x::AbstractArray{Float} : Vector of x coordinates
y::AbstractArray{Float} : Vector of y coordinates

Keyword Arguments

idx::Integer : optional index at which to split the coordinates

Returns

xl::AbstractArray{Float} : Vector of lower half of x coordinates
xu::AbstractArray{Float} : Vector of upper half of x coordinates
yl::AbstractArray{Float} : Vector of lower half of y coordinates
yu::AbstractArray{Float} : Vector of upper half of y coordinates

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split_upper_lower(coordaintes; idx::Integer=nothing)

Split the upper and lower halves of the airfoil coordinates.

Arguments

coordinates::Matrix{Float} : Matrix of [x y] coordinates

Keyword Arguments

idx::Integer : optional index at which to split the coordinates

Returns

xl::AbstractArray{Float} : View of lower half of x coordinates
xu::AbstractArray{Float} : View of upper half of x coordinates
yl::AbstractArray{Float} : View of lower half of y coordinates
yu::AbstractArray{Float} : View of upper half of y coordinates

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Translation

There are various transformation functions that can also be helpful in various situations.

We can flip an airfoil.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = naca4()

plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Nominal")
plot!(flip!(copy(x)), y; label="x Flipped")

Note

Note that this function both flips and translates. It's primarily useful for flipping the x coordinates. If you want to flip the y coordinate, applying a simple negative would be best

plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Nominal")
plot!(x, flip!(copy(y)); label="y Flipped")
plot!(x, -y; label="y Negated")

Another thing we could do is translate the airfoil so that the trailing edge is at y=0.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = naca4()
y .+= 0.2

plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Nominal")

xy = [x y]
zero_y_te!(xy)
plot!(xy[:,1], xy[:,2]; label="TE zeroed")

Note

This only vertically translates the geometry, it does not rotate things to put the leading edge on the axis as well if the geometry is rotated.

FLOWFoil.AirfoilTools.zero_y_te! — Function

zero_y_te!(coordinates)

Places trailing edge on the x-axis.

Arguments

coordinates::Array{Float} : Array of [x y] coordinates to be updated in place.

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Rotation

We can also rotate airfoils about arbitrary points.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = naca4()

plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Nominal")

xy = [x y]
angle = 10.0 # degrees

# rotate by angle about default point: (0,0)
rotate_coordinates!(xy, angle)

plot!(xy[:,1], xy[:,2], label="rotated about (0,0)")

# rotate again but about the trailing edge
xy2 = [x y]
rotate_coordinates!(xy2, angle; rotation_point=[1.0,0.0])

plot!(xy2[:,1], xy2[:,2], label="rotated about (1,0)")

FLOWFoil.AirfoilTools.rotate_coordinates! — Function

rotate_coordinates!(coordinates, angle; rotation_point=[0.0; 0.0])

Rotate coordinates clockwise about rotation_point by angle in degrees.

Arguments

coordinates::Array{Float} : Array of [x y] coordinates to be updated in place.
angle::Float=0.0 : Angles, in degrees, by which to rotate the coordinates clockwise (positive angle will pitch airfoil up).

Keyword Arguments

rotation_point::AbstractArray{Float}=[0.0; 0.0] : Array of [x y] position of point about which to perform rotation.

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Normalization

It can also be convenient to normalize coordinates to have a chord length of one.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = 2.0.*naca4()

plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Nominal")

normalize_coordinates!(x, y)

plot!(x, y; label="Normalized")

Note

This function is designed to go from a nominal airfoil (length 1, leading edge and trailing edges on the axis, etc.) to something else. The operations are in the order: scale, rotate, then translate.

FLOWFoil.AirfoilTools.normalize_coordinates! — Function

normalize_coordinates!(coordinates)

Normalize airfoil to unit chord and shift leading edge to zero. Adjusts coordinates in place.

Arguments

coordinates::AbstractArray{Float} : Array of [x y] coordinates

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normalize_coordinates!(x, y)

Normalize airfoil to unit chord and shift leading edge to zero. Adjusts coordinates in place.

Arguments

x::Array{Float} : Array of x coordinates
y::Array{Float} : Array of y coordinates

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Scale, Rotate, and Translate

Sometimes, we might want do several operations together, which we can with the position_coordinates! function.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = naca4()
plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Unscaled")

xy = [x y]
position_coordinates!(
    xy; scale=0.8, angle=3.0, location=[-0.2; 0.1], rotation_point=[0.0; 0.0], flipped=true
)

plot!(xy[:, 1], xy[:, 2]; label="Re-positioned")

FLOWFoil.AirfoilTools.position_coordinates! — Function

position_coordinates!(coordinates, scale, angle, location)

Scale, Rotate, and Transform (in that order) airfoil coordinates.

Arguments

coordinates::Array{Float} : Array of [x y] coordinates to be updated in place.

Keyword Arguments

scale::Float=1.0 : Value by which to scale coordinates.
angle::Float=0.0 : Angles, in degrees, by which to rotate the coordinates clockwise (positive angle will pitch airfoil up).
location::AbstractArray{Float}=[0.0; 0.0] : Array of [x y] position of leading edge location.
rotation_point::AbstractArray{Float}=[0.0; 0.0] : Array of [x y] position of point about which to perform rotation.
flipped::Bool : flag whether to flip airfoil upside down.

Returns

x::Array{Float} : array of x-coordinates
y::Array{Float} : array of y-coordinates

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position_coordinates!(
    coordinates::Vector{AbstractArray{TF}};
    scales=[1.0],
    angles=[0.0],
    locations=[[0.0; 0.0],],
    rotation_points=[[0.0; 0.0],],
    flipped=[false],
) where {TF}

Multi-airfoil version of position_coordinates!.

If keyword arguments are give as single valued vectors, the same values are used for all coordinate sets. If keyword arguments are provided as vectors of length greater than 1, they must have the same length as the set of coordinates. For example, if scaling 3 airfoils, there will be a vector of 3 airfoil coordinate sets input and scales must either be a one element vector or a vector of length 3.

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Re-definition

Sometimes, we may want to "re-panel" an airfoil, (a good example is the PANE command in Xfoil). The repanel_airfoil method splines the provided geometry and then resamples it using cosine spacing to give a higher density of coordinates at the leading and trailing edges.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

x, y = naca4(; x = range(0.0,1.0,30))
plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="Linear Spaced", marker=true, markersize=4)

x_rp, y_rp = repanel_airfoil(x,y; N=161)

scatter!(x_rp, y_rp; label="Cosine Spaced", markersize=1.5)

Note

Note that if you simply have too few coordinates to begin with, repaneling the airfoil isn't going to smooth out an inaccurate leading edge. In such a case you should consider fitting the geometry with one of the airfoil parameterizazation methods, which will ensure a round leading edge.

FLOWFoil.AirfoilTools.repanel_airfoil — Function

repanel_airfoil(x, y; N=160)

Repanels airfoil coordinates using Akima splines with N coordinate points.

Arguments

x::AbstractArray{Float} : vector containing the x coordinates of the airfoil
y::AbstractArray{Float} : vector containing the y coordinates of the airfoil

Keyword Arguements

N::Int : Number of data points to be returned after repaneling. Will only return odd numbers, if N is even, N+1 points will be returned.

Returns

repaneled_x::AbstractArray{Float} : Repaneled, cosine spaced x corrdinates of the airfoil
repaneled_y::AbstractArray{Float} : y coordinates of the repaneled airfoil obtained using an akima spline

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repanel_airfoil(coordinates; N=160)

Repanels airfoil coordinates using Akima splines with N coordinate points.

Arguments

coordinates::Array{Float} : Array of [x y] coordinates

Keyword Arguements

N::Int=160 : Number of data points to be returned after repaneling. Will only return odd numbers, if N is even, N+1 points will be returned.

Returns

repaneled_coordinates::Array{Float} : new coordinate array.

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FLOWFoil.AirfoilTools.repanel_revolution — Function

repanel_revolution(coordinates; N=160)

Repanels body of revolution coordinates using Akima splines with N coordinate points.

Arguments

coordinates::Array{Float} : Array of [x y] coordinates

Keyword Arguements

N::Int=160 : Number of data points to be returned after repaneling. Will only return odd numbers, if N is even, N+1 points will be returned.

Returns

repaneled_coordinates::Array{Float} : new coordinate array.

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Contributing

We welcome the addition of more convenience functions for airfoil geometry manipulation.