Vortex Lattice Method Module

Vortex Lattice Method (VLM) for finite wings.

This module provides a simple implementation of the Vortex Lattice Method for computing aerodynamic forces on finite wings.

References

Katz, J., and Plotkin, A., “Low Speed Aerodynamics”, 2nd ed., Cambridge University Press, 2001.

Bertin, J.J., and Cummings, R.M., “Aerodynamics for Engineers”, 6th ed., Pearson, 2014.

class aerodemo.vlm.WingGeometry(span, root_chord, tip_chord, sweep_angle=0.0, dihedral=0.0, twist=0.0, n_spanwise=10, n_chordwise=4)[source]

Bases: object

Parameters defining a trapezoidal wing planform.

Parameters:

span (float) – Wing span [m].
root_chord (float) – Root chord length [m].
tip_chord (float) – Tip chord length [m].
sweep_angle (float) – Quarter-chord sweep angle [degrees]. Default 0.
dihedral (float) – Dihedral angle [degrees]. Default 0.
twist (float) – Tip washout (geometric twist) [degrees]. Default 0.
n_spanwise (int) – Number of spanwise panels. Default 10.
n_chordwise (int) – Number of chordwise panels. Default 4.

span: float

root_chord: float

tip_chord: float

sweep_angle: float = 0.0

dihedral: float = 0.0

twist: float = 0.0

n_spanwise: int = 10

n_chordwise: int = 4

property aspect_ratio: float: Wing aspect ratio AR = b^2 / S.

property taper_ratio: float: Taper ratio lambda = c_tip / c_root.

property reference_area: float: Wing reference area S = b * (c_root + c_tip) / 2.

property mean_aerodynamic_chord: float

Mean aerodynamic chord (MAC).

For trapezoidal wings: MAC = (2/3) * c_root * (1 + lambda + lambda^2) / (1 + lambda)

__init__(span, root_chord, tip_chord, sweep_angle=0.0, dihedral=0.0, twist=0.0, n_spanwise=10, n_chordwise=4)

Parameters:

span (float)
root_chord (float)
tip_chord (float)
sweep_angle (float)
dihedral (float)
twist (float)
n_spanwise (int)
n_chordwise (int)

Return type:

None

class aerodemo.vlm.VortexLatticeMethod(wing)[source]

Bases: object

Vortex Lattice Method solver for finite wings.

Computes lift, induced drag, and span-load distribution for trapezoidal wings using horseshoe vortex panels.

Parameters:: wing (WingGeometry) – Wing planform geometry definition.

Examples

>>> wing = WingGeometry(span=10.0, root_chord=2.0, tip_chord=1.0)
>>> vlm = VortexLatticeMethod(wing)
>>> result = vlm.solve(alpha_deg=5.0)
>>> print(f"CL = {result['CL']:.4f}")

__init__(wing)[source]

Parameters:: wing (WingGeometry)

solve(alpha_deg)[source]

Solve the VLM for given angle of attack.

Parameters:

alpha_deg (float) – Angle of attack in degrees.

Returns:

CLfloat: Lift coefficient.
CDifloat: Induced drag coefficient.
CL_distributionndarray: Spanwise lift coefficient distribution (per unit span).
y_stationsndarray: Spanwise stations corresponding to CL_distribution.
ARfloat: Wing aspect ratio.
efloat: Oswald efficiency factor.

Return type:

dict with keys

sweep_alpha(alpha_range)[source]

Compute aerodynamic coefficients over a range of angles of attack.

Parameters:: alpha_range (array_like) – Array of angles of attack in degrees.
Return type:: dict with keys ‘alpha’, ‘CL’, ‘CDi’, ‘CL_over_CDi’.