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Add blueprints archive: ARACHNE-001, MARIONETTE-001, AIRFOIL-CORDAGE-SYSTEM, PERSPECTIVE

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Airfoil-Cordage Force Direction System

Classification: Aerodynamic Force Vectoring via Tether Control
Status: REFERENCE DOCUMENT
Date: 2026-01-22

1. CORE PRINCIPLE

Cordage (tethers/cables) direct wind forces by controlling airfoil orientation.

The tether is NOT just a passive connector—it's an active control linkage that:

Transmits force from airfoil to anchor
Controls airfoil angle of attack via tension
Enables collective/cyclic pitch across multiple sails

         WIND ───────────────────────────────────────────────►
                                  
                           ╔═══════════════╗
                           ║   AIRFOIL     ║
                    ┌──────╫───────────────╫──────┐
                    │      ╚═══════════════╝      │
                    │             ▲               │
                    │     LIFT    │               │
                    │             │               │
                    │      ───────┼───────        │
                    │             │ α (pitch)     │
                    │             │               │
                    │             └───────        │
                    └────────────────┬────────────┘
                                     │
                              TETHER │ (tension)
                                     │
                                     ▼
                             ┌───────────────┐
                             │    ANCHOR     │
                             │  (human/spool)│
                             └───────────────┘

2. AIRFOIL FORCE GENERATION

2.1 Lift Equation

L = ½ ρ V² S Cₗ

Where:
  L  = Lift force (N)
  ρ  = Air density (1.225 kg/m³ at sea level)
  V  = Airspeed (m/s)
  S  = Wing area (m²)
  Cₗ = Lift coefficient (function of α)

2.2 Lift Coefficient vs Angle of Attack

    Cₗ
    ↑
1.4 │                  ●──────● STALL
    │              ●
1.0 │          ●
    │      ●
0.5 │  ●
    │
  0 ├──────────────────────────────► α (angle of attack)
    0°    5°    10°   15°   20°
              ▲
              │
        LINEAR REGION
        Cₗ = 2π sin(α) ≈ 2πα

Source: src/physics/aerodynamics.py → AerodynamicsEngine.compute_lift_coefficient()

2.3 Drag Components

    TOTAL DRAG = PARASITIC + INDUCED + STALL
    
    Cd = Cd₀ + Cₗ²/(π·e·AR) + Cd_stall

         ↑       ↑              ↑
    skin    drag due      separation
    friction   to lift       drag
    + pressure             (post-stall)

Source: src/physics/aerodynamics.py → AerodynamicsEngine.compute_drag_coefficient()

3. CORDAGE FORCE TRANSMISSION

3.1 Tether as Force Vector

The tether transmits force along its length. By controlling anchor position and tension, you control the airfoil's resultant force vector.

                     AIRFOIL
                       ⛵
                      /│\
                     / │ \
           LIFT ────►  │  ◄──── SIDE FORCE
                       │
                       │ DRAG
                       ▼
                       │
                       │ TETHER
                       │ (transmits NET force)
                       │
                       │
                       ▼
                    ANCHOR
                    
                    
    ════════════════════════════════════════════
    
    FORCE RESOLUTION:
    
         ↑ LIFT (L)
         │
         │    ┌──► NET TETHER FORCE
         │   /     (what anchor feels)
         │  /
         │θ/
         │/        θ = atan(D/L)
         ●───────►
           DRAG (D)

3.2 Multi-Tether Airfoil Control

A single airfoil with multiple tethers gains attitude control:

    ┌─────────────────────────────────────┐
    │           AIRFOIL                   │
    │  ╔═════════════════════════════╗    │
    │  ║         WING SURFACE        ║    │
    │  ╚═════════════════════════════╝    │
    │     ▲              ▲              ▲  │
    │     │              │              │  │
    │  TETHER A      TETHER B      TETHER C│
    │     │              │              │  │
    └─────┼──────────────┼──────────────┼──┘
          │              │              │
          │              │              │
          ▼              ▼              ▼
       DRUM A         DRUM B         DRUM C
       └──────────────────────────────────┘
                   SPOOL BODY


    PITCH CONTROL:
    ─────────────────
    Shorten A, lengthen C → Nose UP
    Shorten C, lengthen A → Nose DOWN
    
    ROLL CONTROL:
    ─────────────────
    Differential tension → Bank left/right

4. CONSTELLATION GEOMETRY

4.1 Hubless Dervish Topology

Multiple airfoils connected by tethers with no central body.

              ⛵ NODE 0
             ╱│╲
            ╱ │ ╲
           ╱  │  ╲    ← TETHER LINKS
          ╱   │   ╲
         ╱    │    ╲
    ⛵ 5      │      ⛵ 1
      ╲      │      ╱
       ╲     ╳     ╱   ← VIRTUAL CENTROID
        ╲    │    ╱      (no physical mass)
         ╲   │   ╱
          ╲  │  ╱
           ╲ │ ╱
            ╲│╱
             ⛵ 3
            ╱ ╲
           ╱   ╲
          ╱     ╲
     ⛵ 4       ⛵ 2


    The "vehicle" IS the network.
    Center of mass is emergent.

Source: src/physics/hubless_dervish.py → Lines 1-20

4.2 Force Balance in Constellation

Each node experiences:

Aero forces (lift/drag from its airfoil)
Tether forces (tension from connected nodes)
Gravity

         LIFT ↑
              │
              │    TETHER
              │   TENSION ↗
    DRAG ◄────●─────────►
              │         ↘
              │          TETHER
              ▼           TENSION
           GRAVITY


    EQUILIBRIUM CONDITION:
    ───────────────────────
    Σ F_aero + Σ F_tether + F_gravity = 0

Source: src/physics/hubless_dervish.py → HublessDervish.step()

5. CYCLIC PITCH CONTROL

5.1 Collective vs Cyclic

    COLLECTIVE PITCH                CYCLIC PITCH
    ────────────────               ──────────────
    All airfoils same α            α varies with position
    
         ⛵ α=10°                      ⛵ α=15°
        ╱    ╲                       ╱    ╲
       ╱      ╲                     ╱      ╲
    ⛵         ⛵                 ⛵         ⛵
    α=10°     α=10°              α=5°      α=10°
       ╲      ╱                     ╲      ╱
        ╲    ╱                       ╲    ╱
         ⛵ α=10°                      ⛵ α=5°
    
    Effect: Uniform lift          Effect: NET THRUST
    (hover/climb)                 (directional movement)

5.2 Cyclic Pitch Formula

    α(θ) = α_collective + α_cyclic · sin(θ - φ_cyclic)

    Where:
      θ = Node angular position in constellation
      φ_cyclic = Phase angle (determines thrust direction)
      α_cyclic = Amplitude (determines thrust magnitude)

Source: src/physics/hubless_dervish.py → HublessDervish.get_node_pitch()

def get_node_pitch(self, node: AirfoilNode) -> float:
    # Node's angular position relative to centroid
    r = node.position - self.centroid
    angular_pos = np.arctan2(r[1], r[0]) + self.spin_phase
    
    # Cyclic variation
    cyclic = self.cyclic_amplitude * np.sin(angular_pos - self.cyclic_phase)
    
    return self.collective_pitch + cyclic

6. CORDAGE TENSION DYNAMICS

6.1 Spring-Damper Model

    NODE A ───────[SPRING]───────[DAMPER]─────── NODE B
           ←────── stretch ──────→
           ←────── velocity ─────→

    TENSION = k · Δx + c · Δv

    Where:
      k = Stiffness (50,000 N/m typical)
      Δx = Stretch beyond rest length
      c = Damping coefficient (500 Ns/m)
      Δv = Relative velocity along cable

Source: src/physics/hubless_dervish.py → TetherLink class, compute_tether_forces()

6.2 Tension-Only Constraint

    CABLES CAN PULL, NOT PUSH
    
    IF stretch < 0:
        tension = 0  (slack cable)
    ELSE:
        tension = k * stretch + damping
    
    ┌──────────────────────────────────────────────┐
    │  TAUT            │  SLACK                    │
    │                  │                           │
    │  ─────●─────●    │    ●                      │
    │  (tension > 0)   │     ╲                     │
    │                  │      ╲ (catenary sag)     │
    │                  │       ●                   │
    └──────────────────────────────────────────────┘

7. AIRFOIL NODE SPECIFICATION

7.1 Physical Properties

Property	Symbol	Value	Units	Source
Mass	m	2.0	kg	`AirfoilNode.mass`
Wing area	S	0.5	m²	`AirfoilNode.wing_area`
Aspect ratio	AR	6.0	-	`AirfoilNode.aspect_ratio`
Pitch authority	-	±15°	rad	`HublessDervish`
Roll authority	-	±30°	rad	-

7.2 Aerodynamic Surface Properties

Property	Symbol	Value	Units	Source
Span	b	1.5	m	`TABAerodynamics.tab_wing`
Chord	c	0.3	m	`TABAerodynamics.tab_wing`
Lift slope	Cₗ_α	5.7	/rad	`TABAerodynamics.tab_wing`
Max Cₗ	Cₗ_max	1.4	-	`TABAerodynamics.tab_wing`
Zero-lift drag	Cd₀	0.04	-	`TABAerodynamics.tab_wing`
Stall angle	α_stall	15°	deg	`AerodynamicsEngine`

Source: src/physics/aerodynamics.py → AeroSurface, TABAerodynamics

8. FLIGHT REGIME CLASSIFICATION

    ┌────────────────────────────────────────────────────────────┐
    │                                                            │
    │   ATTACHED     STALL       DEEP        POST                │
    │   FLOW         ONSET       STALL       STALL               │
    │                                                            │
    │   │←────────→│←────→│←──────────→│←──────────────→│       │
    │   0°        15°   18°          45°              90°        │
    │                                                            │
    │   Cₗ linear   Cₗ drops   Cₗ ≈ 2sin(α)cos(α)               │
    │   Cd low      Cd rises   Cd massive                        │
    │                                                            │
    └────────────────────────────────────────────────────────────┘

Source: src/physics/aerodynamics.py → FlightRegime enum

9. CROSS-SYSTEM INTEGRATION

9.1 MARIONETTE Sail Control

The MARIONETTE spool uses drum-based cordage to control sail pitch:

    SPOOL DRUM ─────cable────→ SAIL AIRFOIL
    
    REEL IN  = Increase α = More lift
    PAY OUT  = Decrease α = Less lift
    
    Champion brain reads tension → decides cable lengths

Cross-reference: MARIONETTE-001

9.2 ARACHNE Launch Integration

The ARACHNE launcher provides initial velocity to deploy the constellation:

    FOREARM ──elastic──→ SPOOL ──throw──→ CONSTELLATION
                                              │
                                              ▼
                                         CENTRIFUGAL
                                         DEPLOYMENT
                                              │
                                              ▼
                                         CYCLIC PITCH
                                         CONTROL

Cross-reference: ARACHNE-001

10. OPERATIONAL SECTORS

Each TAB operates in a designated wedge-shaped sector:

                    UP (+Z)
                     │
                     │ 90°
          135° ╲     │     ╱ 45°
                ╲    │    ╱
                 ╲   │   ╱
    LEFT          ╲  │  ╱          RIGHT
    (-Y) ──────────╲─┼─╱────────── (+Y)
    180°           ╲│╱             0°
                   ╱│╲
                  ╱ │ ╲
                 ╱  │  ╲
          -135°╱    │    ╲-45°
                    │
                    │ -90°
                  DOWN (-Z)
                  
                  
    SECTOR BOUNDARIES:
    ─────────────────
    UP:    45° to 135°
    DOWN: -45° to -135°
    LEFT: 135° to 225° (or -135° to -180°, 180° to 135°)
    RIGHT: -45° to 45°

Source: src/physics/cable_geometry.py → Lines 1-45, OperationalSector

11. SOURCE FILE INDEX

File	Purpose	Key Classes/Functions
`src/physics/aerodynamics.py`	Lift/drag/side-force	`AerodynamicsEngine`, `AeroSurface`
`src/physics/hubless_dervish.py`	Constellation physics	`HublessDervish`, `AirfoilNode`, `TetherLink`
`src/physics/cable_geometry.py`	Cable intersection	`CableGeometry`, `OperationalSector`
`src/physics/marionette_spool.py`	Sail spool control	`MarionetteSpool`, `CableDrum`
`src/physics/tether_dynamics.py`	Tether physics	(referenced)
`src/physics/slingshot_dynamics.py`	Launcher physics	(referenced)

12. KEY EQUATIONS SUMMARY

Aerodynamics

Lift:     L = ½ρV²SCₗ
Drag:     D = ½ρV²SCd
Cₗ:       Cₗ = 2π·sin(α) · η    (thin airfoil, η = efficiency)
Cd:       Cd = Cd₀ + Cₗ²/(π·e·AR)

Tether Mechanics

Tension:  T = k·Δx + c·Δv      (spring-damper)
Force:    F⃗ = T·n̂             (along cable direction)

Constellation Control

Pitch:    α(θ) = α_coll + α_cyc·sin(θ - φ)
Thrust:   F⃗_thrust = Σ L_asymmetric
Centroid: r⃗_c = Σ(m_i·r⃗_i) / Σm_i

Document generated from source code analysis. All equations and parameters traced to implementation.