buffalo_wings.airfoil.Naca4AirfoilParams

class buffalo_wings.airfoil.Naca4AirfoilParams(spec)[source]

Bases: OrthogonalAirfoil

Parametric NACA 4-digit airfoil built from explicit parameters.

Methods

`arc_length`(u_s, u_e)	Calculate the arc-length distance between two points on surface.
`arc_length_breakpoints`()	Return the breakpoint locations in arc-length coordinates.
`breakpoint_parameter_limits`(*, index)	Return parameter limits for one breakpoint.
`breakpoints`()	Return the locations of breakpoints or discontinuities.
`camber_curve`(*[, num_points, spacing])	Return the exact native camber curve for this orthogonal airfoil.
`camber_location`(u)	Return the camber-line location associated with `u`.
`chord`()	Return the airfoil chord length.
`curvature_from_xi`(xi, *, surface)	Return one-surface curvature values at surface-local `xi` locations.
`d2ydx2`(u)	Return the second surface derivative at curve parameter locations.
`dydx`(u)	Return the surface slope at curve parameter locations.
`from_params`(*, m, p, t[, trailing_edge, ...])	Build a parametric NACA 4-digit airfoil from explicit params.
`k`(u)	Calculate the curvature at parameter location.
`leading_edge`()	Return the leading-edge location.
`normal`(u)	Calculate the unit normal at parameter location.
`slope_from_xi`(xi, *, surface)	Return one-surface slope values at surface-local `xi` locations.
`tangent`(u)	Calculate the unit tangent at parameter location.
`thickness_value`(u)	Return the thickness offset associated with `u`.
`to_spec`()	Return the schema definition needed to recreate this airfoil.
`trailing_edge`()	Return the midpoint of the trailing-edge points.
`u_from_s`(s)	Return curve parameters that correspond to arc length.
`u_from_x`(x, *, surface)	Return curve parameters that correspond to `x`.
`u_from_xi`(xi, *, surface)	Convert one-surface `xi` coordinates to curve parameters.
`xi_from_u`(u)	Convert curve airfoil parameters to surface-local `xi` values.
`xy_from_s`(s)	Return curve coordinates at arc-length locations.
`xy_from_u`(u)	Calculate the airfoil coordinates at one parameter location.
`xy_from_xi`(xi, *, surface)	Return one-surface coordinates at surface-local `xi` locations.
`xy_s`(s)	Calculate first derivatives at arc-length location.
`xy_s_breakpoint`(*, index)	Return one-sided arc-length derivatives at one airfoil breakpoint.
`xy_ss`(s)	Calculate second derivatives at arc-length location.
`xy_ss_breakpoint`(*, index)	Return one-sided arc-length second derivatives at one breakpoint.
`xy_u`(u)	Calculate first derivatives with respect to the airfoil parameter.
`xy_u_breakpoint`(*, index)	Return one-sided first derivatives at one airfoil breakpoint.
`xy_uu`(u)	Return second derivatives of the airfoil coordinates.
`xy_uu_breakpoint`(*, index)	Return one-sided second derivatives at one airfoil breakpoint.

Attributes

`camber`	Return the concrete NACA 4-digit camber model.
`length`	Return the full airfoil surface length.
`spec`	Return the source spec for this airfoil.
`thickness`	Return the concrete parametric NACA thickness model.
`xmax_parameter`	Return the parameter of the largest x-coordinate for the airfoil.
`xmin_parameter`	Return the parameter of the smallest x-coordinate for the airfoil.

property camber: Naca4DigitCamber

Return the concrete NACA 4-digit camber model.

This property exposes the camber-line object constructed from the explicit 4-digit parameters.

property thickness: Naca45DigitThicknessParams

Return the concrete parametric NACA thickness model.

This property exposes the parametric thickness relation constructed from the explicit 4-digit parameters.

classmethod from_params(*, m, p, t, trailing_edge='standard', leading_edge_radius='standard')[source]

Build a parametric NACA 4-digit airfoil from explicit params.

Parameters:

m (buffalo_core.typing.FloatScalar) – Maximum camber as a fraction of chord.
p (buffalo_core.typing.FloatScalar) – Chordwise location of maximum camber as a fraction of chord.
t (buffalo_core.typing.FloatScalar) – Maximum thickness as a fraction of chord.
trailing_edge ({"standard", "sharp"}, default "standard") – Trailing-edge closure model for the thickness distribution.
leading_edge_radius ({"standard", "exact"}, default "standard") – Leading-edge radius treatment for the thickness distribution.

Returns:

Runtime airfoil built from the explicit parameters.

Return type:

Self

Raises:

ValueError – If the parameter set falls outside the supported NACA 4-digit range.

property spec: Naca4AirfoilSpec

Return the source spec for this airfoil.

This property returns a defensive copy of the serialized source spec.

to_spec()[source]

Return the schema definition needed to recreate this airfoil.

Returns:: Serialized source spec for this airfoil.
Return type:: Naca4AirfoilSpec

arc_length(u_s, u_e)

Calculate the arc-length distance between two points on surface.

Parameters:

u_s (buffalo_core.typing.FloatScalar) – Start point of distance calculation.
u_e (buffalo_core.typing.FloatInput) – End point of distance calculation.

Returns:

Distance from start point to end point.

Return type:

buffalo_core.typing.FloatArray

arc_length_breakpoints()

Return the breakpoint locations in arc-length coordinates.

Returns:: Arc-length coordinates measured from the minimum native parameter.
Return type:: list[FloatScalar]

Notes

These values include the two curve endpoints as boundary markers. Interior breakpoints correspond to the native-parameter interior breakpoints returned by breakpoints().

breakpoint_parameter_limits(*, index)

Return parameter limits for one breakpoint.

Notes

Endpoint breakpoints return the exact boundary parameter. Interior breakpoints return nearby one-sided parameters chosen within the neighboring breakpoint interval for the current generic breakpoint-side implementation. These limits exist to support the sampled fallback in the generic *_breakpoint methods and should not be treated as the primary source of truth when a subclass can provide exact one-sided values directly.

Return type:: tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]

breakpoints()

Return the locations of breakpoints or discontinuities.

Returns:: Sorted unique parameter values induced by camber-line joins, thickness discontinuities, and their mirrored surface partners.
Return type:: list[float]

Notes

This list always includes -1, 0, and 1. Additional interior values are induced by mapped camber breakpoints or mapped thickness discontinuities that require one-sided derivative information at the airfoil level.

camber_curve(*, num_points=81, spacing='cosine')

Return the exact native camber curve for this orthogonal airfoil.

Parameters:

num_points (int, default 81) – Unused compatibility argument accepted for API consistency with the approximate extraction path on other airfoil families.
spacing ({"uniform", "cosine"}, default "cosine") – Unused compatibility argument accepted for API consistency with the approximate extraction path on other airfoil families.

Returns:

Exact camber result exposing the native camber runtime.

Return type:

AirfoilCamberResult

camber_location(u)

Return the camber-line location associated with u.

Parameters:: u (buffalo_core.typing.FloatInput) – Signed or unsigned airfoil parameter values.
Returns:: Tuple (x, y) of camber-line coordinates evaluated at the mapped camber parameter.
Return type:: tuple[FloatArray, FloatArray]

chord()

Return the airfoil chord length.

Returns:: Distance between the leading-edge reference and trailing-edge midpoint reference.
Return type:: buffalo_core.typing.FloatScalar

curvature_from_xi(xi, *, surface)

Return one-surface curvature values at surface-local xi locations.

Parameters:

xi (buffalo_core.typing.FloatInput) – Surface-local coordinates in [0, 1] measured from the leading edge to the trailing edge.
surface ({"lower", "upper"}) – Surface to evaluate.

Returns:

Surface-oriented curvature values on the selected surface.

Return type:

buffalo_core.typing.FloatArray

d2ydx2(u)

Return the second surface derivative at curve parameter locations.

Parameters:: u (buffalo_core.typing.FloatInput) – Airfoil parameters.
Returns:: Second derivative values d^2y/dx^2 evaluated at u.
Return type:: buffalo_core.typing.FloatArray

dydx(u)

Return the surface slope at curve parameter locations.

Parameters:: u (buffalo_core.typing.FloatInput) – Airfoil parameters.
Returns:: Surface slope values dy/dx evaluated at u.
Return type:: buffalo_core.typing.FloatArray

k(u)

Calculate the curvature at parameter location.

Parameters:: u (buffalo_core.typing.FloatInput) – Parameter for desired locations.
Returns:: Curvature of surface matching the normalized shape of u.
Return type:: buffalo_core.typing.FloatArray

leading_edge()

Return the leading-edge location.

Returns:: (x, y) location of the leading-edge reference point.
Return type:: tuple[FloatScalar, FloatScalar]

property length: buffalo_core.typing.FloatScalar

Return the full airfoil surface length.

Returns:: Total airfoil surface length measured from the lower trailing edge to the upper trailing edge.
Return type:: buffalo_core.typing.FloatScalar

normal(u)

Calculate the unit normal at parameter location.

Parameters:: u (buffalo_core.typing.FloatInput) – Parameter for desired locations.
Returns:: Tuple (n_x, n_y) of float64 arrays matching the normalized shape of u.
Return type:: tuple[FloatArray, FloatArray]

slope_from_xi(xi, *, surface)

Return one-surface slope values at surface-local xi locations.

Parameters:

xi (buffalo_core.typing.FloatInput) – Surface-local coordinates in [0, 1] measured from the leading edge to the trailing edge.
surface ({"lower", "upper"}) – Surface to evaluate.

Returns:

Surface slope values dy/dx on the selected surface.

Return type:

buffalo_core.typing.FloatArray

tangent(u)

Calculate the unit tangent at parameter location.

Parameters:: u (buffalo_core.typing.FloatInput) – Parameter for desired locations.
Returns:: Tuple (t_x, t_y) of float64 arrays matching the normalized shape of u.
Return type:: tuple[FloatArray, FloatArray]

thickness_value(u)

Return the thickness offset associated with u.

Parameters:: u (buffalo_core.typing.FloatInput) – Signed or unsigned airfoil parameter values.
Returns:: Thickness magnitude evaluated at the mapped thickness parameter.
Return type:: buffalo_core.typing.FloatArray

trailing_edge()

Return the midpoint of the trailing-edge points.

Returns:: (x, y) location of the trailing-edge midpoint reference.
Return type:: tuple[FloatScalar, FloatScalar]

u_from_s(s)

Return curve parameters that correspond to arc length.

Parameters:: s (buffalo_core.typing.FloatInput) – Arc lengths measured from the lower trailing edge.
Returns:: Curve parameters corresponding to s.
Return type:: buffalo_core.typing.FloatArray
Raises:: ValueError – When arc-length provided is larger than airfoil surface length.

u_from_x(x, *, surface)

Return curve parameters that correspond to x.

Parameters:

x (buffalo_core.typing.FloatInput) – Chordwise coordinates in the normalized airfoil frame.
surface ({"lower", "upper"}) – Surface to solve on.

Returns:

Curve parameters on the requested surface.

Return type:

buffalo_core.typing.FloatArray

Raises:

ValueError – If any requested chordwise coordinate lies outside the reachable x-range of the selected surface.

u_from_xi(xi, *, surface)

Convert one-surface xi coordinates to curve parameters.

Parameters:

xi (buffalo_core.typing.FloatInput) – Surface-local coordinates in [0, 1] measured from the leading edge to the trailing edge.
surface ({"lower", "upper"}) – Surface to evaluate.

Returns:

Curve parameters matching xi on the selected surface.

Return type:

buffalo_core.typing.FloatArray

xi_from_u(u)

Convert curve airfoil parameters to surface-local xi values.

Parameters:: u (buffalo_core.typing.FloatInput) – Curve airfoil parameters in [-1, 1].
Returns:: Surface-local xi values and upper-surface membership flags.
Return type:: SurfaceMappedValues

Notes

Concrete airfoil families define this mapping because xi need not equal |u| for every airfoil parameterization.

property xmax_parameter: buffalo_core.typing.FloatScalar

Return the parameter of the largest x-coordinate for the airfoil.

This property caches the native airfoil parameter at the maximum x-location.

property xmin_parameter: buffalo_core.typing.FloatScalar

Return the parameter of the smallest x-coordinate for the airfoil.

This property caches the native airfoil parameter at the minimum x-location.

Raises:: RuntimeError – If the internal scalar root solve for the x-minimum does not converge.

xy_from_s(s)

Return curve coordinates at arc-length locations.

Parameters:: s (buffalo_core.typing.FloatInput) – Arc length location of point.
Returns:: (x, y) coordinates matching the normalized shape of s.
Return type:: tuple[FloatArray, FloatArray]

xy_from_u(u)

Calculate the airfoil coordinates at one parameter location.

Parameters:: u (buffalo_core.typing.FloatInput) – Signed surface parameter values in [-1, 1].
Returns:: Tuple (x, y) of float64 arrays matching the normalized shape of u.
Return type:: tuple[FloatArray, FloatArray]

xy_from_xi(xi, *, surface)

Return one-surface coordinates at surface-local xi locations.

Parameters:

xi (buffalo_core.typing.FloatInput) – Surface-local coordinates in [0, 1] measured from the leading edge to the trailing edge.
surface ({"lower", "upper"}) – Surface to evaluate.

Returns:

Tuple (x, y) of float64 arrays matching the normalized shape of xi.

Return type:

tuple[FloatArray, FloatArray]

xy_s(s)

Calculate first derivatives at arc-length location.

Parameters:: s (buffalo_core.typing.FloatInput) – Arc length location of point.
Returns:: (dx/ds, dy/ds) coordinates matching the normalized shape of s.
Return type:: tuple[FloatArray, FloatArray]

Notes

If s matches one of arc_length_breakpoints() exactly, this method returns the minus-side derivative limit. Subclasses should override xy_s_breakpoint() when exact one-sided breakpoint derivatives are available analytically.

xy_s_breakpoint(*, index)

Return one-sided arc-length derivatives at one airfoil breakpoint.

Notes

This method composes the exact arc-length tangent values from the exact native breakpoint derivatives returned by xy_u_breakpoint(). When the native derivative vanishes at a cusp-like breakpoint, such as the orthogonal leading edge, this method uses the one-sided native second derivative to recover the exact one-sided tangent direction.

Return type:: tuple[tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)], tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]]

xy_ss(s)

Calculate second derivatives at arc-length location.

Parameters:: s (buffalo_core.typing.FloatInput) – Arc length location of point.
Returns:: (d^2x/ds^2, d^2y/ds^2) coordinates matching the normalized shape of s.
Return type:: tuple[FloatArray, FloatArray]

Notes

If s matches one of arc_length_breakpoints() exactly, this method returns the minus-side derivative limit. Subclasses should override xy_ss_breakpoint() when exact one-sided breakpoint second derivatives are available analytically.

xy_ss_breakpoint(*, index)

Return one-sided arc-length second derivatives at one breakpoint.

Notes

This method composes the exact arc-length curvature-vector values from the exact native breakpoint derivatives returned by xy_u_breakpoint() and xy_uu_breakpoint(). When the native derivative vanishes at a cusp-like breakpoint, such as the orthogonal leading edge, the generic sampled fallback is retained because the exact arc-length second derivative depends on higher-order native data, such as one-sided xy_uuu values, that this runtime does not expose.

Return type:: tuple[tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)], tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]]

xy_u(u)

Calculate first derivatives with respect to the airfoil parameter.

Parameters:: u (buffalo_core.typing.FloatInput) – Parameter for desired locations.
Returns:: Tuple (dx/du, dy/du) of float64 arrays matching the normalized shape of u.
Return type:: tuple[FloatArray, FloatArray]

Notes

If u matches one of breakpoints() exactly, this method returns the minus-side derivative limit.

xy_u_breakpoint(*, index)

Return one-sided first derivatives at one airfoil breakpoint.

Notes

This method composes the one-sided camber and thickness values that apply on each side of the requested airfoil breakpoint. It is the exact-breakpoint contract paired with xy_u().

Return type:: tuple[tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)], tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]]

xy_uu(u)

Return second derivatives of the airfoil coordinates.

Parameters:: u (buffalo_core.typing.FloatInput) – Parameter for desired locations.
Returns:: Tuple (d^2x/du^2, d^2y/du^2) of float64 arrays matching the normalized shape of u.
Return type:: tuple[FloatArray, FloatArray]

Notes

If u matches one of breakpoints() exactly, this method returns the minus-side derivative limit.

xy_uu_breakpoint(*, index)

Return one-sided second derivatives at one airfoil breakpoint.

Notes

This method composes the one-sided camber and thickness values that apply on each side of the requested airfoil breakpoint. It is the exact-breakpoint contract paired with xy_uu().

Return type:: tuple[tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)], tuple[TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’), TypeAliasForwardRef(‘buffalo_core.typing.FloatScalar’)]]