Classes and Immutability

This document describes the consistent pattern of immutability and lazy caching across the following core data and geometry classes in the Ptera Software codebase:

• UnsteadyProblem

• Movement

• AirplaneMovement

• WingMovement

• WingCrossSectionMovement

• OperatingPointMovement

• SteadyProblem

• OperatingPoint

• Airplane

• Wing

• WingCrossSection

• Airfoil

• Panel

• RingVortex

• HorseshoeVortex

• LineVortex

Design Principles

Class Attribute Categories

Most attribute falls into one of these categories:

Category	Pattern
Immutable	Read-only property (no setter), set once in __init__
Derived (Immutable)	Manual lazy caching (check None, compute, cache, return)
Set Once	Property with setter that raises AttributeError if already set
Mutable	Property with setter, or plain attribute
Derived (Set Once)	Manual lazy caching, depends on set once attributes

Key Decisions

1. No cache invalidation for immutable/set once attributes: Since these are only set once, we don’t need invalidation logic in setters.

2. Enforce set once semantics at runtime: Set once properties raise AttributeError if assigned a second time. This catches bugs early where code incorrectly attempts to modify values that should be immutable after initial assignment.

3. Use manual lazy caching for all derived properties: This approach:

   • Works consistently for properties derived from both immutable and set once attributes

   • Is compatible with __slots__ (no dependency on __dict__)

   • Simplifies __deepcopy__ (cache variables can be copied directly)

   • Maintains the existing pattern already used throughout the codebase

4. Solver mutable attributes remain mutable: Properties that the solver needs to set keep their setters.

5. __slots__ on every class: All classes in the package define __slots__, which eliminates per-instance __dict__ overhead and prevents accidental dynamic attribute assignment. This catches typos like self.num_panles = 5 at runtime with an AttributeError instead of silently creating a new attribute.

NumPy Array Mutability

Even with read-only properties, numpy arrays can still be mutated in place via the getter (e.g., panel.Frpp_G_Cg[0] = 999.0). To prevent this, all numpy arrays that should be immutable are set to read-only using arr.flags.writeable = False:

1. Immutable arrays: Set in __init__ immediately after assignment

2. Set once arrays: Set in the setter after assignment

3. Derived cached arrays: Set in the lazy property after computation (since numpy operations like subtraction create new writable arrays regardless of input writability)

4. Deepcopy: Use .copy() then set flags.writeable = False on the copy

Deepcopy Cache Handling

When implementing __deepcopy__, handle cached derived properties based on their source:

1. Derived from Immutable -> Preserve: Copy the cached values (they remain valid since the source immutable attributes are also copied). For numpy arrays, use .copy() then set flags.writeable = False.

2. Derived from Set Once -> Reset to None: These depend on values that will be set fresh by the solver or meshing, so reset them.

Serialization Attribute Handling

The _serialization module uses the same object.__new__() + object.__setattr__() pattern as the __deepcopy__ methods but with a simpler strategy: the logical state of each object is preserved exactly as it was at save time, including all cached values on primary slots. For these primary attributes, no values are reset to None during deserialization.

Some redundant or alias slots (for example, solver alias slots and Movement._airplanes / Movement._operating_points) are treated specially: they are serialized as null and then deterministically rebuilt from their canonical sources during deserialization. This preserves object graph identity and avoids duplicating equivalent objects while still yielding the same effective state as the original instance.

This works because:

1. Deserialized objects are fully formed snapshots. There is no subsequent __init__, solver run, or meshing step that would populate set once attributes, so there is no conflict with set once guards.

2. Cached derived values remain valid because the immutable and set once attributes they depend on are also restored with their original values, and any alias slots are rebuilt to match.

3. NumPy array writeable flags are preserved through serialization, maintaining the same mutability guarantees as the original objects.

When adding or renaming __slots__ on any class, both __deepcopy__ and _serialization are affected. The serialization module discovers attributes generically via __slots__, so new slots are automatically serialized (subject to the intentional omission of redundant/alias slots described above). However, adding or removing slots requires incrementing _FORMAT_VERSION in _serialization.py to ensure old files are not loaded with incompatible code.

List Collection Immutability

Store collections as tuples internally to prevent external mutation via .append(), .pop(), etc.

---

UnsteadyProblem Class (problems.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
movement	Movement	Movement definition
only_final_results	bool	Results flag
num_steps	int	Copied from Movement
delta_time	float	Copied from Movement
first_averaging_step	int	Computed during init
first_results_step	int	Computed during init
max_wake_rows	int | None	Copied from Movement
steady_problems	tuple[SteadyProblem, ...]	Generated during init

Mutable (populated by solver)

Attribute	Type	Notes
finalForces_W	list[np.ndarray]	Final forces
finalForceCoefficients_W	list[np.ndarray]	Final force coefficients
finalMoments_W_CgP1	list[np.ndarray]	Final moments
finalMomentCoefficients_W_CgP1	list[np.ndarray]	Final moment coefficients
finalMeanForces_W	list[np.ndarray]	Cycle averaged forces
finalMeanForceCoefficients_W	list[np.ndarray]	Cycle averaged coefficients
finalMeanMoments_W_CgP1	list[np.ndarray]	Cycle averaged moments
finalMeanMomentCoefficients_W_CgP1	list[np.ndarray]	Cycle averaged moment coefficients
finalRmsForces_W	list[np.ndarray]	RMS forces
finalRmsForceCoefficients_W	list[np.ndarray]	RMS force coefficients
finalRmsMoments_W_CgP1	list[np.ndarray]	RMS moments
finalRmsMomentCoefficients_W_CgP1	list[np.ndarray]	RMS moment coefficients

Note: The solver result lists must remain mutable as they are populated after initialization by the solver. These are initialized as empty lists and appended to during the solve.

Movement Class (movements/movement.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
airplane_movements	tuple[AirplaneMovement, ...]	Tuple prevents mutation
operating_point_movement	OperatingPointMovement	Operating point changes
delta_time	float	Time step
num_cycles	int | None	Number of cycles
num_chords	int | None	Number of chord lengths
num_steps	int	Total time steps
max_wake_rows	int | None	Max wake rows per Wing
max_wake_chords	int | None	Max wake in chord lengths
max_wake_cycles	int | None	Max wake in motion cycles
airplanes	tuple[tuple[Airplane, ...], ...]	Generated Airplanes
operating_points	tuple[OperatingPoint, ...]	Generated OperatingPoints

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
lcm_period	airplane_movements, operating_point_movement	Cached
max_period	airplane_movements, operating_point_movement	Cached
min_period	airplane_movements, operating_point_movement	Cached
static	max_period	Cached

Note on airplanes and operating_points: These are generated during __init__ by calling the child movements’ generate_* methods. Are stored as nested tuples to prevent modification after generation.

AirplaneMovement Class (movements/airplane_movement.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
base_airplane	Airplane	Base geometry
wing_movements	tuple[WingMovement, ...]	Tuple prevents mutation
ampCg_GP1_CgP1	np.ndarray	CG position amplitudes
periodCg_GP1_CgP1	np.ndarray	CG position periods
spacingCg_GP1_CgP1	tuple	CG position spacing
phaseCg_GP1_CgP1	np.ndarray	CG position phases

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
all_periods	Own periods + child all_periods	Tuple of unique non zero periods (cached)
max_period	Own periods + child max_period	Scalar float, longest period (cached)

WingMovement Class (movements/wing_movement.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
base_wing	Wing	Base geometry
wing_cross_section_movements	tuple[WingCrossSectionMovement, ...]	Tuple prevents mutation
ampLer_Gs_Cgs	np.ndarray	Position amplitudes
periodLer_Gs_Cgs	np.ndarray	Position periods
spacingLer_Gs_Cgs	tuple	Position spacing
phaseLer_Gs_Cgs	np.ndarray	Position phases
ampAngles_Gs_to_Wn_ixyz	np.ndarray	Angle amplitudes
periodAngles_Gs_to_Wn_ixyz	np.ndarray	Angle periods
spacingAngles_Gs_to_Wn_ixyz	tuple	Angle spacing
phaseAngles_Gs_to_Wn_ixyz	np.ndarray	Angle phases
rotationPointOffset_Gs_Ler	np.ndarray	Rotation point offset

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
all_periods	Own periods + child all_periods	Tuple of unique non zero periods (cached)
max_period	Own periods + child max_period	Scalar float, longest period (cached)

WingCrossSectionMovement Class (movements/wing_cross_section_movement.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
base_wing_cross_section	WingCrossSection	Base geometry
ampLp_Wcsp_Lpp	np.ndarray	Position amplitudes
periodLp_Wcsp_Lpp	np.ndarray	Position periods
spacingLp_Wcsp_Lpp	tuple	Position spacing
phaseLp_Wcsp_Lpp	np.ndarray	Position phases
ampAngles_Wcsp_to_Wcs_ixyz	np.ndarray	Angle amplitudes
periodAngles_Wcsp_to_Wcs_ixyz	np.ndarray	Angle periods
spacingAngles_Wcsp_to_Wcs_ixyz	tuple	Angle spacing
phaseAngles_Wcsp_to_Wcs_ixyz	np.ndarray	Angle phases

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
all_periods	Period arrays	Tuple of unique non zero periods (cached)
max_period	Period arrays	Scalar float, longest period (cached)

OperatingPointMovement Class (movements/operating_point_movement.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
base_operating_point	OperatingPoint	Base operating conditions
ampVCg__E	float	Amplitude
periodVCg__E	float	Period
spacingVCg__E	str | Callable	Spacing function
phaseVCg__E	float	Phase offset

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
max_period	periodVCg__E	Cached

SteadyProblem Class (problems.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
airplanes	tuple[Airplane, ...]	Tuple prevents external mutation
operating_point	OperatingPoint	Operating conditions

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
reynolds_numbers	airplanes, operating_point	Tuple of Re for each Airplane (cached)

OperatingPoint Class (operating_point.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
rho	float	Fluid density
vCg__E	float	CG speed
alpha	float	Angle of attack
beta	float	Sideslip angle
angles_E_to_BP1_izyx	np.ndarray	Earth-to-body orientation
CgP1_E_Eo	np.ndarray	CG position in Earth axes
surfaceNormal_E	np.ndarray | None	Image surface normal
surfacePoint_E_Eo	np.ndarray | None	Image surface point
externalFX_W	float	External force
nu	float	Kinematic viscosity

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
qInf__E	rho, vCg__E	Dynamic pressure (cached)
T_pas_GP1_CgP1_to_BP1_CgP1	(constant)	Geometry-to-body matrix (cached)
T_pas_BP1_CgP1_to_GP1_CgP1	T_pas_GP1_CgP1_to_BP1_CgP1	Inverse of above (cached)
T_pas_BP1_CgP1_to_W_CgP1	alpha, beta	Body-to-wind matrix (cached)
T_pas_W_CgP1_to_BP1_CgP1	T_pas_BP1_CgP1_to_W_CgP1	Inverse of above (cached)
T_pas_GP1_CgP1_to_W_CgP1	T_pas_GP1_CgP1_to_BP1_CgP1, T_pas_BP1_CgP1_to_W_CgP1	Geometry-to-wind matrix (cached)
T_pas_W_CgP1_to_GP1_CgP1	T_pas_GP1_CgP1_to_W_CgP1	Inverse of above (cached)
T_pas_E_CgP1_to_BP1_CgP1	angles_E_to_BP1_izyx	Earth-to-body matrix (cached)
T_pas_BP1_CgP1_to_E_CgP1	T_pas_E_CgP1_to_BP1_CgP1	Inverse of above (cached)
T_pas_E_CgP1_to_GP1_CgP1	T_pas_E_CgP1_to_BP1_CgP1, T_pas_BP1_CgP1_to_GP1_CgP1	Earth-to-geometry matrix (cached)
T_pas_GP1_CgP1_to_E_CgP1	T_pas_E_CgP1_to_GP1_CgP1	Inverse of above (cached)
surfaceNormal_GP1	surfaceNormal_E, T_pas_E_CgP1_to_GP1_CgP1	Surface normal in GP1 (cached)
surfacePoint_GP1_CgP1	surfacePoint_E_Eo, CgP1_E_Eo, T_pas_E_CgP1_to_GP1_CgP1	Surface point in GP1 (cached)
surfaceReflect_T_act_GP1_CgP1	surfacePoint_GP1_CgP1, surfaceNormal_GP1	Active reflection matrix (cached)
vInfHat_GP1__E	T_pas_W_CgP1_to_GP1_CgP1	Freestream direction (cached)
vInf_GP1__E	vInfHat_GP1__E, vCg__E	Freestream velocity (cached)

Note on caching: While vInfHat_GP1__E and vInf_GP1__E are simple computations once the transformation matrix is cached, they are cached for consistency with the overall pattern and because they are called repeatedly during solver operations. The same is true for qInf__E.

Note on T_pas_GP1_CgP1_to_BP1_CgP1: This matrix is a constant (180-degree rotation about y) and does not depend on any __init__ parameters. It is still lazily cached for consistency with the overall pattern and to avoid recomputing it on every access.

Note on transformation decomposition: The geometry-to-wind transformation (T_pas_GP1_CgP1_to_W_CgP1) is composed from T_pas_GP1_CgP1_to_BP1_CgP1 and T_pas_BP1_CgP1_to_W_CgP1 via compose_T_pas. Similarly, T_pas_E_CgP1_to_GP1_CgP1 is composed from T_pas_E_CgP1_to_BP1_CgP1 and T_pas_BP1_CgP1_to_GP1_CgP1. Decomposing through body axes enables the Earth transformation chain to reuse the geometry-to-body and body-to-geometry matrices without duplication.

Airplane Class (geometry/airplane.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
wings	tuple[Wing, ...]	Processed for symmetry during init (tuple prevents mutation)
name	str	Airplane identifier
Cg_GP1_CgP1	np.ndarray	CG position in formation coordinates
weight	float	Aircraft weight in Newtons
s_ref	float	Reference wetted area
c_ref	float	Reference chord length
b_ref	float	Reference span

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
num_panels	wings	Sum of wing panel counts
T_pas_G_Cg_to_GP1_CgP1	Cg_GP1_CgP1	Transformation matrix

Mutable (set by solver)

Attribute	Type	Notes
forces_W	np.ndarray | None	Forces in wind axes
forceCoefficients_W	np.ndarray | None	Force coefficients
moments_W_CgP1	np.ndarray | None	Moments in wind axes
momentCoefficients_W_CgP1	np.ndarray | None	Moment coefficients

---

Wing Class (geometry/wing.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
wing_cross_sections	tuple[WingCrossSection, ...]	Wing cross sections (tuple prevents mutation)
name	str	Wing identifier
Ler_Gs_Cgs	np.ndarray	Leading edge root position
angles_Gs_to_Wn_ixyz	np.ndarray	Rotation angles
num_chordwise_panels	int	Chordwise panel count
chordwise_spacing	str	“cosine” or “uniform”

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
T_pas_G_Cg_to_Wn_Ler	Immutable attrs	Transformation matrix
T_pas_Wn_Ler_to_G_Cg	Above	Inverse transformation
WnX_G, WnY_G, WnZ_G	Above	Basis vectors
children_T_pas_*	Cross sections	Child transformations

Set Once (set by generate_mesh, never modified after)

Attribute	Type	Set By	Notes
symmetry_type	int | None	generate_mesh	1, 2, 3, or 4
num_spanwise_panels	int | None	generate_mesh	Total spanwise count
num_panels	int | None	generate_mesh	Total panel count
panels	np.ndarray | None	generate_mesh	Panel matrix

Derived from Set Once (use manual lazy caching)

Property	Depends On	Notes
projected_area	panels	Projected area
wetted_area	panels	Wetted area
average_panel_aspect_ratio	panels	Average aspect ratio
span	Wing cross sections, symmetry_type	Wing span
standard_mean_chord	projected_area, span	Standard mean chord
mean_aerodynamic_chord	projected_area, symmetry_type	MAC

Note on caching: Most derived properties iterate over panels or wing cross sections. For large meshes, caching projected_area, wetted_area, and span provides meaningful performance gains if they’re accessed multiple times. Since their source attributes are immutable or set once, these are cached after first computation without invalidation logic.

Mutable (modified by process_wing_symmetry for type 5 symmetry)

Attribute	Type	Notes
symmetric	bool	Modified to False for type 5
mirror_only	bool	Modified to False for type 5
symmetryNormal_G	np.ndarray | None	Modified to None for type 5
symmetryPoint_G_Cg	np.ndarray | None	Modified to None for type 5

Note: These are modified by Airplane.process_wing_symmetry() when type 5 symmetry is detected. The original Wing becomes a type 1 wing and a new reflected Wing is created with type 3 symmetry.

Mutable (modified during simulation for wake)

Attribute	Type	Notes
wake_ring_vortices	np.ndarray | None	Wake vortex array, grows
gridWrvp_GP1_CgP1	np.ndarray | None	Wake vortex positions, grows

WingCrossSection Class (geometry/wing_cross_section.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
airfoil	Airfoil	Wing cross section airfoil
num_spanwise_panels	int | None	Spanwise panel count
chord	float	Chord length
Lp_Wcsp_Lpp	np.ndarray	Position in parent axes
angles_Wcsp_to_Wcs_ixyz	np.ndarray	Rotation angles
control_surface_hinge_point	float	Hinge location (0-1)
control_surface_deflection	float	Deflection in degrees
spanwise_spacing	str | None	“cosine” or “uniform”

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
T_pas_Wcsp_Lpp_to_Wcs_Lp	Lp_Wcsp_Lpp, angles_...	Transformation matrix
T_pas_Wcs_Lp_to_Wcsp_Lpp	Above	Inverse transformation

Set Once (set by parent Wing)

Attribute	Type	Set By	Notes
validated	bool	Wing.__init__	Validation flag
symmetry_type	int | None	Wing.generate_mesh	Inherited symmetry type

Mutable (modified by process_wing_symmetry)

Attribute	Type	Notes
control_surface_symmetry_type	str | None	Set to None for type 5 symmetry

Note: Modified at when type 5 symmetry is split into two wings.

Airfoil Class (geometry/airfoil.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
name	str	Airfoil identifier
outline_A_lp	np.ndarray	Outline coordinates
resample	bool	Resampling flag
n_points_per_side	int	Points per side for resampling
mcl_A_lp	np.ndarray	Mean camber line coordinates

Note: The add_control_surface method creates and returns a new Airfoil instance rather than modifying the existing one. This is the correct immutable pattern.

Panel Class (_panel.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
Frpp_G_Cg	np.ndarray	Front right corner (geometry axes)
Flpp_G_Cg	np.ndarray	Front left corner (geometry axes)
Blpp_G_Cg	np.ndarray	Back left corner (geometry axes)
Brpp_G_Cg	np.ndarray	Back right corner (geometry axes)
is_leading_edge	bool	Edge flag
is_trailing_edge	bool	Edge flag

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
rightLeg_G	Frpp_G_Cg, Brpp_G_Cg	Right leg vector
frontLeg_G	Flpp_G_Cg, Frpp_G_Cg	Front leg vector
leftLeg_G	Blpp_G_Cg, Flpp_G_Cg	Left leg vector
backLeg_G	Brpp_G_Cg, Blpp_G_Cg	Back leg vector
Frbvp_G_Cg	Brpp_G_Cg, rightLeg_G	Front right bound vortex point
Flbvp_G_Cg	Flpp_G_Cg, leftLeg_G	Front left bound vortex point
Cpp_G_Cg	Multiple corners	Collocation point
unitNormal_G	All corners	Unit normal vector
area	All corners	Panel area
aspect_ratio	All legs	Aspect ratio

Set Once (set after construction by meshing or Problem)

Attribute	Type	Set By	Notes
is_right_edge	bool | None	Meshing	Edge flag
is_left_edge	bool | None	Meshing	Edge flag
local_chordwise_position	int | None	Meshing	Grid position
local_spanwise_position	int | None	Meshing	Grid position
Frpp_GP1_CgP1	np.ndarray | None	Problem	Front right (formation axes)
Flpp_GP1_CgP1	np.ndarray | None	Problem	Front left (formation axes)
Blpp_GP1_CgP1	np.ndarray | None	Problem	Back left (formation axes)
Brpp_GP1_CgP1	np.ndarray | None	Problem	Back right (formation axes)

Derived from Set Once (use manual lazy caching)

Property	Depends On	Notes
rightLeg_GP1	Frpp_GP1_CgP1, Brpp_GP1_CgP1	Right leg (formation axes)
frontLeg_GP1	Flpp_GP1_CgP1, Frpp_GP1_CgP1	Front leg (formation axes)
leftLeg_GP1	Blpp_GP1_CgP1, Flpp_GP1_CgP1	Left leg (formation axes)
backLeg_GP1	Brpp_GP1_CgP1, Blpp_GP1_CgP1	Back leg (formation axes)
Frbvp_GP1_CgP1	Brpp_GP1_CgP1, rightLeg_GP1	Front right BVP (formation)
Flbvp_GP1_CgP1	Flpp_GP1_CgP1, leftLeg_GP1	Front left BVP (formation)
Cpp_GP1_CgP1	Multiple GP1 corners	Collocation point (formation)
unitNormal_GP1	All GP1 corners	Unit normal (formation)

Mutable (set by solver)

Attribute	Type	Notes
ring_vortex	RingVortex | None	Attached vortex
horseshoe_vortex	HorseshoeVortex | None	Attached vortex
forces_GP1	np.ndarray | None	Computed forces
moments_GP1_CgP1	np.ndarray | None	Computed moments
forces_W	np.ndarray | None	Forces in wind axes
moments_W_CgP1	np.ndarray | None	Moments in wind axes

---

RingVortex Class (_vortices/ring_vortex.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
Frrvp_GP1_CgP1	np.ndarray	Front right corner
Flrvp_GP1_CgP1	np.ndarray	Front left corner
Blrvp_GP1_CgP1	np.ndarray	Back left corner
Brrvp_GP1_CgP1	np.ndarray	Back right corner

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
Crvp_GP1_CgP1	All corners	Centroid position
area	All corners	Vortex area

Mutable (solver sets these)

Attribute	Type	Notes
strength	float	Vortex strength (solver finds this)
age	float	Age in simulation time (incremented for wake)

Derived (special: child objects)

Property	Depends On	Notes
front_leg	Frrvp_GP1_CgP1, Flrvp_GP1_CgP1, strength	Child LineVortex
left_leg	Flrvp_GP1_CgP1, Blrvp_GP1_CgP1, strength	Child LineVortex
back_leg	Blrvp_GP1_CgP1, Brrvp_GP1_CgP1, strength	Child LineVortex
right_leg	Brrvp_GP1_CgP1, Frrvp_GP1_CgP1, strength	Child LineVortex

Note on legs: The leg LineVortex objects depend on both geometry (immutable) and strength (mutable). Since strength is set by the solver AFTER the vortex is created, we propagate strength updates to existing legs. Since legs are accessed repeatedly during induced velocity calculations, option 2 (keeping the current propagation) is more efficient.

---

HorseshoeVortex Class (_vortices/horseshoe_vortex.py)

Attribute Classification

Immutable (set in __init__, never modified)

Attribute	Type	Notes
Frhvp_GP1_CgP1	np.ndarray	Front right point
Flhvp_GP1_CgP1	np.ndarray	Front left point
leftLegVector_GP1	np.ndarray	Direction of left leg (normalized)
left_right_leg_lengths	float	Length of semi-infinite legs

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
Brhvp_GP1_CgP1	Frhvp_GP1_CgP1, leftLegVector_GP1, left_right_leg_lengths	Back right point
Blhvp_GP1_CgP1	Flhvp_GP1_CgP1, leftLegVector_GP1, left_right_leg_lengths	Back left point

Mutable (solver sets these)

Attribute	Type	Notes
strength	float	Vortex strength

Derived (child objects)

Property	Depends On	Notes
right_leg	Brhvp_GP1_CgP1, Frhvp_GP1_CgP1, strength	Child LineVortex
finite_leg	Frhvp_GP1_CgP1, Flhvp_GP1_CgP1, strength	Child LineVortex
left_leg	Flhvp_GP1_CgP1, Blhvp_GP1_CgP1, strength	Child LineVortex

---

LineVortex Class (_vortices/_line_vortex.py)

Attribute Classification

Since LineVortex is an internal class whose endpoints ARE updated by parent vortex classes when their corners change, we need to consider whether this mutation actually happens.

Immutable (set in __init__)

Attribute	Type	Notes
Slvp_GP1_CgP1	np.ndarray	Start point
Elvp_GP1_CgP1	np.ndarray	End point

Derived from Immutable (use manual lazy caching)

Property	Depends On	Notes
vector_GP1	Elvp_GP1_CgP1, Slvp_GP1_CgP1	Line vector
Clvp_GP1_CgP1	Slvp_GP1_CgP1, vector_GP1	Center point

Mutable

Attribute	Type	Notes
strength	float	Updated by parent vortex

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Solver Classes (Not Covered Above)

The three solver classes (SteadyHorseshoeVortexLatticeMethodSolver, SteadyRingVortexLatticeMethodSolver, and UnsteadyRingVortexLatticeMethodSolver) are intentionally omitted from the immutability and lazy caching patterns described in this document. Unlike the data and geometry classes above, the solver classes are algorithmic classes whose attributes are internal mutable working state in a procedural computation pipeline. They are not shared data that external code accesses or modifies, so immutable properties, set once enforcement, and lazy caching would add significant boilerplate with no meaningful safety benefit. The solver classes do still use __slots__, like all other classes in the package, to protect against dynamic attribute assignment typos.