Airfoil Geometry Schema

This document defines the user-facing schema for airfoil geometry definitions. Field definitions and validation rules are normative. Examples are illustrative.

1. Top-Level Structure

Required Keys

schema_version (int): schema version; current version is 1
airfoils (object): named airfoil definitions.

Example Skeleton

schema_version: 1

airfoils: {}

2. Common Conventions

Unless otherwise noted, airfoil geometry is defined in a local nondimensional section frame:

chordwise coordinate: x
thickness/camber coordinate: y
leading edge at x = 0
trailing edge at x = 1
angular quantities are specified in degrees unless otherwise noted

Positive y corresponds to the upper surface side of the airfoil. Unless otherwise specified, airfoil definitions are normalized to unit chord. Unless otherwise specified by a particular airfoil type, all coordinates are interpreted in this normalized local frame.

3. `airfoils`

airfoils is a mapping from unique airfoil names to airfoil definitions.

Example:

airfoils:
  root: {type: naca4, designation: "2412"}
  tip:  {type: dat, path: "airfoils/tip.dat"}

Keys must be unique and are case-sensitive.

4. Airfoil Definition Types

Airfoils may be defined using analytic parameterizations or point-based representations.

Analytic representations define the airfoil geometry through a parameterized model. Point-based representations define the airfoil geometry through discrete coordinates on the surface.

This schema supports standard NACA designations, externally stored coordinate files, inline coordinate definitions, and parameterized coefficient-based representations.

As of 2026-03-25, AirfoilFactory.from_spec(...) constructs runtime airfoils for naca4, naca4_modified, naca5, and naca5_modified. Other families documented in this schema are planned schema targets, but they are not yet constructable through the current runtime factory and are tracked as roadmap work rather than migration-completion work.

4.0 Construction Status

The current migration-complete construction surface is:

naca4
naca4_modified
naca5
naca5_modified

The following schema families are planned but not yet constructable through AirfoilFactory.from_spec(...):

dat
points
cst
parsec
naca4bt
naca4r
naca4f
naca16
naca6
naca6a
naca7
naca8

4.1 NACA Airfoils

These airfoils are all based on the canonical NACA airfoil specifications.

4.1.a NACA 4-digit

NACA 4-digit airfoils may be specified in either of two ways.

Code

airfoils:
  naca2412:
    type: naca4
    designation: "2412"

Explicit Parameters

airfoils:
  naca2412_explicit:
    type: naca4
    params:
      m: 0.02
      p: 0.4
      t: 0.12
      trailing_edge: sharp
      leading_edge_radius: exact

Fields

type: "naca4"
Exactly one of:
- designation: 4-digit NACA designation string
- params: explicit parameter definition

If params is present, it contains:

m: maximum camber as a fraction of chord
p: location of maximum camber as a fraction of chord
t: maximum thickness as a fraction of chord
trailing_edge: "standard" or "sharp"; default "standard"
leading_edge_radius: "standard" or "exact"; default "standard"

Designation Syntax

The designation must use the form ####.
The first digit represents 100 times the maximum camber.
The second digit represents 10 times the location of maximum camber.
The last two digits combine to represent 100 times the maximum thickness.
For example, a 2312 means:
- maximum thickness 0.12c
- maximum camber is 0.02c
- location of maximum camber is at 0.30c

Validation Rules

Exactly one of designation and params must be present.
If designation is present:
- must match ^[0-9]{4}$
If params is present:
- 0 <= m < 0.1
- 0 <= p <= 0.9
- 0 <= t <= 0.4
- if m == 0, require p == 0
- if m > 0, require p > 0
- trailing_edge must be one of standard|sharp
- leading_edge_radius must be one of standard|exact

Notes

t = 0 is permitted to support idealized zero-thickness analyses.
Airfoil definitions are normalized to unit chord.
When designation is used, the airfoil is interpreted as the classical NACA 4-digit designation.
When params is used, the airfoil remains within the NACA 4-digit family but allows higher-precision specification of the defining parameters and explicit control over trailing-edge closure and leading-edge radius treatment.
In the runtime API, AirfoilFactory.from_spec(...) maps designation-based NACA 4-digit specs to buffalo_wings.airfoil.Naca4AirfoilClassic.
In the runtime API, AirfoilFactory.from_spec(...) maps explicit-parameter NACA 4-digit specs to buffalo_wings.airfoil.Naca4AirfoilParams.

4.1.b NACA Modified 4-digit

Modified NACA 4-digit airfoils may be specified in either of two ways.

Designation

airfoils:
  naca2412_46:
    type: naca4_modified
    designation: "2412-46"

Explicit Parameters

airfoils:
  naca2412_46_explicit:
    type: naca4_modified
    params:
      m: 0.02
      p: 0.4
      t: 0.12
      leading_edge_index: 4.0
      max_thickness_location: 0.6
      trailing_edge: sharp

Fields

type: "naca4_modified"
Exactly one of:
- designation: modified NACA 4-digit designation string
- params: explicit parameter definition

If params is present, it contains:

m: maximum camber as a fraction of chord
p: location of maximum camber as a fraction of chord
t: maximum thickness as a fraction of chord
leading_edge_index: modified-thickness leading-edge radius index
max_thickness_location: location of maximum thickness as a fraction of chord
trailing_edge: "standard" or "sharp"; default "standard"

Designation Syntax

The designation must use the form ####-##.
The first four digits are the standard NACA 4-digit designation.
The first digit after the dash is the leading-edge radius index.
The second digit after the dash is 10 times the chordwise location of maximum thickness.
For example, 2412-46 means:
- NACA 4-digit camber line 2412
- leading-edge radius index 4
- maximum thickness at 0.6c

Validation Rules

Exactly one of designation and params must be present.
If designation is present:
- must match ^[0-9]{4}-[1-9][1-9]$
If params is present:
- 0 <= m < 0.1
- 0 <= p <= 0.9
- 0 <= t <= 0.4
- 1 <= leading_edge_index < 10
- 0.1 <= max_thickness_location < 1.0
- if m == 0, require p == 0
- if m > 0, require p > 0
- trailing_edge must be one of standard|sharp

Notes

The modified NACA 4-digit family reuses the standard NACA 4-digit camber definition.
The modified designation selects the modified thickness law through the dash suffix.
In the runtime API, AirfoilFactory.from_spec(...) maps designation-based modified NACA 4-digit specs to buffalo_wings.airfoil.Naca4ModifiedAirfoilClassic.
In the runtime API, AirfoilFactory.from_spec(...) maps explicit-parameter modified NACA 4-digit specs to buffalo_wings.airfoil.Naca4ModifiedAirfoilParams.

4.1.c NACA 4-digit B/T

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.d NACA 4-digit R

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.e NACA 4-digit F

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.f NACA 5-digit

NACA 5-digit airfoils may be specified in either of two ways.

Designation

airfoils:
  naca23015:
    type: naca5
    designation: "23015"

Explicit Parameters

airfoils:
  naca23015_explicit:
    type: naca5
    params:
      ideal_lift_coefficient: 0.3
      max_camber_location: 0.15
      reflexed: false
      t: 0.15
      trailing_edge: sharp
      leading_edge_radius: exact

Fields

type: "naca5"
Exactly one of:
- designation: 5-digit NACA designation string
- params: explicit parameter definition

If params is present, it contains:

ideal_lift_coefficient: theoretical lift coefficient
max_camber_location: location of maximum camber as a fraction of chord
reflexed: whether the camber line has a reflexed trailing edge
t: maximum thickness as a fraction of chord
trailing_edge: "standard" or "sharp"; default "standard"
leading_edge_radius: "standard" or "exact"; default "standard"

Designation Syntax

The designation must use the form #####.
The first digit represents 10 times two thirds of the ideal lift coefficient.
The second digit represents 10 times twice the location of maximum camber.
The third digit selects the camber-line family:
- 0: standard camber
- 1: reflexed camber
The last two digits combine to represent 100 times the maximum thickness.
For example, 23015 means:
- ideal lift coefficient 0.3
- maximum camber location 0.15c
- standard non-reflexed camber
- maximum thickness 0.15c

Validation Rules

Exactly one of designation and params must be present.
If designation is present:
- must match ^[0-9]{5}$
- the third digit must be 0 or 1
If params is present:
- 0.15 <= ideal_lift_coefficient < 0.6
- 0.05 <= max_camber_location < 0.3
- 0 <= t <= 0.4
- trailing_edge must be one of standard|sharp
- leading_edge_radius must be one of standard|exact

Notes

designation represents the traditional encoded NACA 5-digit form.
params is more general than designation.
The params form may describe airfoils that do not correspond to a historical published NACA 5-digit designation.
The designation digits are encoded indices, not the physical values stored in params.
For the first digit, digit = 10 * (2 / 3) * ideal_lift_coefficient. Equivalently, ideal_lift_coefficient = 0.15 * first_digit.
For the second digit, digit = 10 * 2 * max_camber_location. Equivalently, max_camber_location = 0.05 * second_digit.
For example, 23015 maps to:
- ideal_lift_coefficient = 0.3
- max_camber_location = 0.15
- reflexed = false
- t = 0.15
The reflex behavior selects which camber implementation is used.
The explicit-parameter thickness path exposes the same trailing-edge and leading-edge-radius controls as the NACA 4-digit params schema.
In the runtime API, AirfoilFactory.from_spec(...) maps designation-based NACA 5-digit specs to buffalo_wings.airfoil.Naca5AirfoilClassic.
In the runtime API, AirfoilFactory.from_spec(...) maps explicit-parameter NACA 5-digit specs to buffalo_wings.airfoil.Naca5AirfoilParams.

4.1.g NACA Modified 5-digit

Modified NACA 5-digit airfoils may be specified in either of two ways.

Designation

airfoils:
  naca23015_46:
    type: naca5_modified
    designation: "23015-46"

Explicit Parameters

airfoils:
  naca23015_46_explicit:
    type: naca5_modified
    params:
      ideal_lift_coefficient: 0.3
      max_camber_location: 0.15
      reflexed: false
      t: 0.15
      leading_edge_index: 4.0
      max_thickness_location: 0.6
      trailing_edge: sharp

Fields

type: "naca5_modified"
Exactly one of:
- designation: modified NACA 5-digit designation string
- params: explicit parameter definition

If params is present, it contains:

ideal_lift_coefficient: theoretical lift coefficient
max_camber_location: location of maximum camber as a fraction of chord
reflexed: whether the camber line has a reflexed trailing edge
t: maximum thickness as a fraction of chord
leading_edge_index: modified-thickness leading-edge radius index
max_thickness_location: location of maximum thickness as a fraction of chord
trailing_edge: "standard" or "sharp"; default "standard"

Designation Syntax

The designation must use the form #####-##.
The first five digits are the standard NACA 5-digit designation.
The first digit after the dash is the modified-thickness leading-edge radius index.
The second digit after the dash is 10 times the chordwise location of maximum thickness.
For example, 23015-46 means:
- ideal lift coefficient 0.3
- maximum camber location 0.15c
- standard non-reflexed 5-digit camber
- maximum thickness 0.15c
- leading-edge radius index 4
- maximum thickness at 0.6c

Validation Rules

Exactly one of designation and params must be present.
If designation is present:
- must match ^[0-9]{5}-[1-9][1-9]$
- the third digit of the 5-digit designation must be 0 or 1
If params is present:
- 0.15 <= ideal_lift_coefficient < 0.6
- 0.05 <= max_camber_location < 0.3
- 0 <= t <= 0.4
- 1 <= leading_edge_index < 10
- 0.1 <= max_thickness_location < 1.0
- trailing_edge must be one of standard|sharp

Notes

The modified NACA 5-digit family reuses the NACA 5-digit camber definition.
The camber implementation is selected by reflex behavior:
- designation third digit 0 or params.reflexed = false: standard 5-digit camber
- designation third digit 1 or params.reflexed = true: reflexed 5-digit camber
The designation digits are encoded indices, not the physical values stored in params.
For the first digit of the 5-digit designation: digit = 10 * (2 / 3) * ideal_lift_coefficient. Equivalently, ideal_lift_coefficient = 0.15 * first_digit.
For the second digit of the 5-digit designation: digit = 10 * 2 * max_camber_location. Equivalently, max_camber_location = 0.05 * second_digit.
designation represents the traditional encoded modified NACA 5-digit form.
params is more general than designation.
The params form may describe airfoils that do not correspond to a historical published modified NACA 5-digit designation.
In the runtime API, AirfoilFactory.from_spec(...) maps designation-based modified NACA 5-digit specs to buffalo_wings.airfoil.Naca5ModifiedAirfoilClassic.
In the runtime API, AirfoilFactory.from_spec(...) maps explicit-parameter modified NACA 5-digit specs to buffalo_wings.airfoil.Naca5ModifiedAirfoilParams.

4.1.h NACA 16-Series

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.i NACA 6-Series

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.j NACA 6A-Series

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.k NACA 7-Series

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.1.l NACA 8-Series

TODO: Define supported designation syntax, explicit parameter form, and validation rules. This family is planned, but it is not yet constructable through AirfoilFactory.from_spec(...).

4.2 Coordinate Files

TODO: Expand on this. There are different types of file formats that need to be read.

airfoils:
  myfoil: {type: dat, path: "airfoils/myfoil.dat"}

Notes

Coordinate files define the airfoil through discrete surface points rather than an analytic parameterization.
Imported coordinates are interpreted in the local airfoil frame unless otherwise specified by the file format.
Unless otherwise specified, imported airfoils are normalized internally to unit chord.
File parsing rules, supported formats, and normalization behavior should be defined explicitly once this section is expanded.
Coordinate-file airfoils are planned, but they are not yet constructable through AirfoilFactory.from_spec(...).

4.3 Point Coordinates

Coordinate-defined airfoils may be specified directly in the YAML file.

4.3.a Surface curve format

airfoils:
  flat_plate:
    type: points
    format: surface_curve
    orientation: clockwise
    leading_edge: 3
    normalize: false
    points:
      - [1.0,  0.0]
      - [0.7, -0.02]
      - [0.3, -0.03]
      - [0.0,  0.0]
      - [0.3,  0.03]
      - [0.7,  0.02]
      - [1.0,  0.0]

This format specifies a single ordered list of points that traces the airfoil surface starting and ending at the trailing edge.

4.3.b Upper/Lower surface format

airfoils:
  example_foil:
    type: points
    format: upper_lower
    normalize: false
    upper:
      - [0.0, 0.0]
      - [0.3, 0.06]
      - [0.7, 0.03]
      - [1.0, 0.0]
    lower:
      - [0.0, 0.0]
      - [0.3, -0.02]
      - [0.7, -0.01]
      - [1.0, 0.0]

This format specifies the upper and lower surfaces separately.

Fields

type: "points"
format: "surface_curve" or "upper_lower"
normalize: optional boolean; default true

If format: "surface_curve":

orientation: "clockwise" or "counterclockwise"
leading_edge: 0-based index of the point that represents the leading edge
points: ordered list of [x, y] coordinate pairs

If format: "upper_lower":

upper: ordered list of [x, y] coordinate pairs
lower: ordered list of [x, y] coordinate pairs

Supported Format Values

"surface_curve": points proceed around the airfoil surface starting and ending at the trailing edge
"upper_lower": points are given as separate upper and lower surfaces, each starting from the leading edge and going to the trailing edge

Validation Rules

If format: "surface_curve":
- points required
  - must contain at least 3 points
  - each point must be a numeric pair [x, y]
- orientation required
- leading_edge is required and must be a valid index into the points list
- upper and lower not allowed
If format: "upper_lower":
- upper and lower required
  - each must contain at least 2 points
  - each point must be a numeric pair [x, y]
  - the first point of both lists (the leading edge) must be coincident
  - the last point of each list defines the trailing-edge point for that surface
    - these may be coincident for a sharp trailing edge
- points, orientation, and leading_edge not allowed
If normalize: true, the geometry is normalized to unit chord internally
If normalize: false, the input must already define a valid nonzero chord extent

Notes

Point-based airfoils define the geometry directly through discrete coordinates on the surface.
Airfoil definitions are normalized to unit chord when normalize: true.
In surface_curve format, the trailing-edge point must be represented for both surfaces, even if the two points are coincident.
In upper_lower format, the upper and lower surfaces are specified independently and must share the same leading-edge point.
The leading_edge index is required in surface_curve format to avoid ambiguity in point sets with multiple candidate leading-edge points or nonuniform sampling.
Point-defined airfoils are planned, but they are not yet constructable through AirfoilFactory.from_spec(...).

4.4 CST coefficients

TODO: Expand on this. Look at Chris’s code and CodeEli.

airfoils:
  cst_foil:
    type: cst
    upper: {n1: 0.5, n2: 1.0, a: [ ... ]}
    lower: {n1: 0.5, n2: 1.0, a: [ ... ]}

Notes

CST defines the airfoil geometry through separate coefficient sets for the upper and lower surfaces.
The class function exponents and coefficient arrays determine the surface shape in the normalized local airfoil frame.
Airfoil definitions are normalized to unit chord.
The exact coefficient conventions, required fields, and validation rules should be defined explicitly once this section is expanded.
CST airfoils are planned, but they are not yet constructable through AirfoilFactory.from_spec(...).

4.5 PARSEC Coefficients

This uses a 12-parameter PARSEC specification with independently specified upper and lower leading-edge radii.

airfoils:
  parsec_foil:
    type: parsec
    leading_edge_radius:
      upper: 0.005
      lower: 0.005
    trailing_edge:
      thickness: 0.0025
      location: -0.006
      direction_angle: 7.0
      wedge_angle: 10.0
    upper_surface_max:
      location: [0.41, 0.11]
      curvature: -0.9
    lower_surface_min:
      location: [0.20, -0.023]
      curvature: 0.05

Fields

type: "parsec"
leading_edge_radius.upper: upper-surface leading-edge radius
leading_edge_radius.lower: lower-surface leading-edge radius
trailing_edge.thickness: trailing-edge thickness
trailing_edge.location: vertical coordinate of the midpoint between the upper and lower trailing-edge endpoints
trailing_edge.direction_angle: angle of the bisector of the upper and lower trailing-edge surface directions
trailing_edge.wedge_angle: included angle between the upper and lower surface directions at the trailing edge
upper_surface_max.location: [x, y] location of the upper-surface maximum
upper_surface_max.curvature: curvature of the upper surface at the upper-surface maximum
lower_surface_min.location: [x, y] location of the lower-surface minimum
lower_surface_min.curvature: curvature of the lower surface at the lower-surface minimum

Validation Rules

leading_edge_radius must contain both upper and lower
leading_edge_radius.upper > 0
leading_edge_radius.lower > 0
trailing_edge.thickness >= 0
upper_surface_max.location must be a numeric 2-tuple [x, y]
lower_surface_min.location must be a numeric 2-tuple [x, y]
0 < upper_surface_max.location[0] < 1
0 < lower_surface_min.location[0] < 1
upper_surface_max.location[1] > 0
lower_surface_min.location[1] < 0

Notes

All length quantities are nondimensionalized by the chord.
Angular quantities are specified in degrees.
Airfoil definitions are normalized to unit chord.
This representation defines the airfoil through geometric constraints rather than directly through surface points.
Upper and lower leading-edge radii are specified independently.
PARSEC airfoils are planned, but they are not yet constructable through AirfoilFactory.from_spec(...).

5. Normalization

Normalization defines how coordinate-based airfoil definitions are transformed into the canonical local airfoil frame used by this schema.

This section applies to imported coordinate files and inline point-coordinate airfoils when normalization is enabled. Analytic airfoil definitions, such as NACA, CST, and PARSEC, are already defined in the normalized local frame unless otherwise specified.

5.1 Canonical Normalized Frame

A normalized airfoil is represented in the local airfoil frame with the following properties:

leading-edge reference at [0.0, 0.0]
trailing-edge reference at [1.0, 0.0]
chord line aligned with the positive x axis
positive y directed toward the upper surface side of the airfoil
chord length equal to 1

5.2 Reference Definitions

Normalization is based on a leading-edge reference and a trailing-edge reference.

The leading-edge reference is the geometric leading-edge point used to define the start of the chord line.
The trailing-edge reference is the point used to define the end of the chord line.

For airfoils with distinct upper and lower trailing-edge endpoints, the trailing-edge reference is the midpoint of those two endpoints.

This definition avoids ambiguity for blunt trailing edges, where the upper and lower trailing-edge points may not coincide.

5.3 Reference Extraction by Representation

Coordinate Files

For file-based coordinate definitions, the leading-edge and trailing-edge references are determined from the parsed file format and the file topology.

For formats that explicitly separate upper and lower surfaces, the leading-edge reference is the shared leading-edge endpoint of the two surfaces.
For formats that represent the airfoil as a single surface curve, the trailing-edge reference is determined from the first and last surface points, and the leading-edge reference is determined from the format-specific interpretation of the curve or from explicitly supplied metadata if required by the format.

Point Coordinates

For type: "points" airfoils:

If format: "surface_curve":
- the first and last points define the two trailing-edge endpoints
- the trailing-edge reference is the midpoint of those two endpoints
- the leading_edge index identifies the leading-edge reference point
If format: "upper_lower":
- the first point of both upper and lower defines the shared leading-edge reference
- the last points of upper and lower define the upper and lower trailing-edge endpoints
- the trailing-edge reference is the midpoint of the two trailing-edge endpoints

5.4 Normalization Transform

When normalization is enabled, the following transform is applied:

Translate the airfoil so that the leading-edge reference is at the origin.
Rotate the airfoil so that the line from the leading-edge reference to the trailing-edge reference lies on the positive x axis.
Scale the airfoil so that the distance from the leading-edge reference to the trailing-edge reference is 1.

After normalization, the leading-edge reference is at [0.0, 0.0] and the trailing-edge reference is at [1.0, 0.0].

5.5 Orientation

If the input geometry is oriented such that the upper surface lies at negative y after normalization, the implementation must either:

reject the geometry as invalid, or
apply a reflection about the x axis if such behavior is explicitly supported by the implementation

Recommended behavior: reject the geometry unless automatic reflection is explicitly documented.

5.6 Validation Rules

normalization requires a valid leading-edge reference
normalization requires a valid trailing-edge reference
the distance between the leading-edge reference and trailing-edge reference must be greater than zero
for airfoils with separate upper and lower trailing-edge endpoints, both endpoints must be valid before the trailing-edge midpoint is computed
if normalization is disabled for a coordinate-based airfoil, the geometry is preserved as provided, but it must still define a valid nonzero chord extent

5.7 Notes

Normalization must not define the leading edge purely as the point with minimum x, because valid airfoil definitions may contain points with x < 0 relative to the normalized leading-edge reference.
Normalization must not define the trailing edge purely as the point with maximum x, because blunt trailing edges may have distinct upper and lower endpoints.
For blunt trailing edges, the trailing-edge midpoint is the canonical chord endpoint used for normalization.
This normalization procedure is intended to make coordinate-defined airfoils consistent with analytic airfoil definitions in this schema.

Airfoil Geometry Schema

1. Top-Level Structure

Required Keys

Example Skeleton

2. Common Conventions

3. airfoils

4. Airfoil Definition Types

4.0 Construction Status

4.1 NACA Airfoils

4.1.a NACA 4-digit

Code

Explicit Parameters

Fields

Designation Syntax

Validation Rules

Notes

4.1.b NACA Modified 4-digit

Designation

Explicit Parameters

Fields

Designation Syntax

Validation Rules

Notes

4.1.c NACA 4-digit B/T

4.1.d NACA 4-digit R

4.1.e NACA 4-digit F

4.1.f NACA 5-digit

Designation

Explicit Parameters

Fields

Designation Syntax

Validation Rules

Notes

4.1.g NACA Modified 5-digit

Designation

Explicit Parameters

Fields

Designation Syntax

Validation Rules

Notes

4.1.h NACA 16-Series

4.1.i NACA 6-Series

4.1.j NACA 6A-Series

4.1.k NACA 7-Series

4.1.l NACA 8-Series

4.2 Coordinate Files

Notes

4.3 Point Coordinates

4.3.a Surface curve format

4.3.b Upper/Lower surface format

Fields

Supported Format Values

Validation Rules

Notes

4.4 CST coefficients

Notes

4.5 PARSEC Coefficients

Fields

Validation Rules

Notes

5. Normalization

5.1 Canonical Normalized Frame

5.2 Reference Definitions

5.3 Reference Extraction by Representation

Coordinate Files

Point Coordinates

5.4 Normalization Transform

5.5 Orientation

5.6 Validation Rules

5.7 Notes

3. `airfoils`