Analysis of alternative propulsion methods for the 44-ft Equilateral Triangle Seastead (Trimaran Foil Configuration).
Configuration: 3 Legs × 2 Thrusters/Leg (Port/Starboard) = 6 Thrusters Total.
Minimum for Control: 1 Thruster Port + 1 Thruster Starboard (on any legs).
Failure Modes:
Power Redundancy: Triple independent battery/inverter/thruster groups (one per leg) is excellent architecture. Single point of failure only at the high-level control bus.
Two parachute sea anchors (drogues) deployed alternately. Seastead winches pull on Anchor A. Dinghy (or separate winch) deploys Anchor B ahead. Switch pull to B, retrieve A. Continuous cycle.
Assumptions: 2000 W continuous mechanical power at winch (after motor/gearbox losses). 10m (32.8 ft) diameter parachute anchors. Calm water, no wind/current assist. Seastead Drag Coefficient Cd ≈ 0.8 (foil legs + superstructure).
Power P = F * v → Thrust F = P / v.
Equilibrium: Thrust = Drag.
Drag D = 0.5 * ρ * v² * Cd * A.
Combining: P / v = 0.5 * ρ * v² * Cd * A → v³ = 2P / (ρ * Cd * A).
A 10m diameter parachute anchor (e.g., Para-Tech, Fiorentino) has a drag coefficient Cd_anchor ≈ 1.2 - 1.4.
Area A_anchor = π * (5)² = 78.5 m².
Force generated by anchor at speed v_water (speed of water relative to anchor): F_anchor = 0.5 * ρ * v_water² * Cd_a * A_a.
Critical Constraint: The anchor must not slip through water faster than the seastead advances, or the "kedging" gains no ground. The anchor velocity relative to seabed (earth) is v_anchor_earth = v_seastead - v_slip.
For kedging to work efficiently, v_slip << v_seastead. This requires F_anchor >> F_seastead_drag at operating speed.
| Parameter | Symbol | Value |
|---|---|---|
| Power Input | P | 2000 W |
| Water Density | ρ | 1025 kg/m³ |
| Seastead Drag Coeff | Cd_s | 0.8 (Est) |
| Seastead Ref Area | A_s | 3.06 m² (Submerged Legs Frontal) + Windage? *See Note* |
| Anchor Diameter | D_a | 10 m |
| Anchor Area | A_a | 78.5 m² |
| Anchor Cd | Cd_a | 1.3 |
Cd * A ≈ 0.04 * 3.06 ≈ 0.12 m² (foil drag at low Re).Cd * A ≈ 0.12 m² (very efficient!).v = (2 * 2000 / (1025 * 0.8 * 3.06))^(1/3) → v ≈ (1.6)^(1/3) ≈ 1.17 m/s ≈ 2.27 knots
Anchor Slip Check: At 1.17 m/s, Seastead Drag = 2000/1.17 = 1709 N.
Anchor Drag at 1.17 m/s slip = 0.5 * 1025 * 1.17² * 1.3 * 78.5 ≈ 65,000 N.
Result: Anchor holds extremely well (38x margin). Slip velocity v_slip = sqrt(1709 / (0.5*1025*1.3*78.5)) ≈ 0.19 m/s.
Speed over ground = 1.17 - 0.19 = 0.98 m/s (1.9 knots). Highly Efficient.
Wind Drag = 0.5 * 1.225 * (5.14)² * 1.2 * 24.8 ≈ 4,700 N.
Required Thrust = 4,700 N. Power = 4,700 * v.
v = 2000 / 4700 ≈ 0.43 m/s (0.83 knots).
Anchor Slip at 0.43 m/s: Anchor Drag = 0.5 * 1025 * 0.43² * 1.3 * 78.5 ≈ 9,700 N. Slip v_slip = 0.43 * sqrt(4700/9700) ≈ 0.30 m/s.
Speed over ground = 0.43 - 0.30 = 0.13 m/s (0.25 knots). Very Slow.
| Model (Typical) | Diameter | Weight | Rated Displacement | Approx Cost (USD) |
|---|---|---|---|---|
| Para-Tech Sea Anchor | 28-34 ft | 25-35 lbs (11-16 kg) | 30,000 - 50,000 lbs | $1,800 - $2,500 |
| Fiorentino Para-Anchor | 34 ft (10.3m) | ~30 lbs | 40,000+ lbs | $2,200 - $3,000 |
| Jimmy Green / Plastimo | 10m | ~20 kg | ~25,000 kg | €1,500 - €2,200 |
Rode Requirements: 300-500 ft of 1/2" to 5/8" Nylon/Dyneema per anchor. Weight: ~50-100 lbs each. Winch: 2000W electric capstan ~$3,000-$5,000 each (need 2 for continuous cycle).
Standard kedging: Deploy anchor from dinghy, winch seastead to anchor. Repeat.
No anchor slip (ideally). v = (2P / (ρ * Cd * A))^(1/3).
Using Hydrodynamic Drag only (Calm): ~2.27 knots (1.17 m/s).
Using Aerodynamic Drag (10 kt wind): ~0.83 knots (0.43 m/s).
Seastead Drag at Speed v: D = 0.5 * ρ * v² * Cd * A.
Equilibrium: Thrust = Drag.
v = sqrt( 2 * Thrust / (ρ * Cd * A) )
| Condition | Drag Area (Cd*A) | Thrust (N) | Speed (m/s) | Speed (kts) |
|---|---|---|---|---|
| Calm Water (Hydro Only) | 0.12 m² (Foils only) | 3036 (3 Motors) | 7.1 m/s | 13.8 kts |
| Calm Water (Hydro Only) | 0.12 m² | 1012 (1 Motor) | 4.1 m/s | 8.0 kts |
| 10 kt Wind on Beam | ~30 m² (Aero Dominates) | 3036 | 0.41 m/s | 0.8 kts |
| 20 kt Wind on Beam | ~30 m² | 3036 | 0.29 m/s | 0.56 kts |
3 Motors × ~3000W peak = 9000W. Seastead Leg Inverter (5-10kW) can handle this. Voltage drop over 100ft cable (10 AWG or 8 AWG) manageable at 48V/96V.
Apparent Wind Speed v_a ≈ 3-5x True Wind v_t for efficient crosswind flight.
Lift L = 0.5 * ρ * v_a² * Cl * A. Thrust (Forward Drive) F_x = L * sin(θ) - D * cos(θ).
Typical Traction Kite (LEI or Foil): L/D ≈ 4 - 6. Max Cl ≈ 1.0 - 1.2.
Power Zone Force Coefficient C_f ≈ 1.0 - 1.5 (Force / (0.5 ρ v_t² A)).
Dynamic Pressure q = 0.5 * 1.225 * 10.7² ≈ 70 Pa.
Static Downwind (Parking, Figure-8 minimal): C_f ≈ 0.8 - 1.0.
F = 1.0 * 70 * 22.3 ≈ 1,560 N (350 lbf).
Crosswind (Figure-8, Optimized): C_f ≈ 2.5 - 4.0 (Apparent wind amplification).
F = 3.0 * 70 * 22.3 ≈ 4,680 N (1,050 lbf).
Drag Eq: v = sqrt( 2F / (ρ_water * Cd * A) ).
Hydro Drag Area (Foils): Cd*A ≈ 0.12 m².
Aero Drag Area (Superstructure): Cd*A ≈ 1.2 * 24.8 ≈ 30 m² (at 20 mph relative).
| Sailing Angle | Kite Force | Opposing Drag | Net Force | Est. Speed (Water) | VMG Downwind |
|---|---|---|---|---|---|
| 1) Direct Downwind | 1,560 N (Static) | Aero: ~1,400 N (at 2kt) Hydro: ~50 N |
~110 N | ~1.0 m/s (1.9 kts) | 1.9 kts |
| 2) 30° off Downwind (Broad Reach) | 4,680 N (Crosswind) Forward Comp: 4,680 * cos(30°) = 4,050 N |
Aero: Sideforce large (Leeway) Hydro: Sideforce large |
~3,500 N (Forward) | ~3.4 m/s (6.6 kts) | 6.6 * cos(30°) = 5.7 kts |
The seastead has no daggerboard, no keel, no rudder. It is a "slippery" trimaran foil platform.
At 30° off wind, Kite Side Force = 4,680 * sin(30°) = 2,340 N.
Hydrodynamic Side Force (3 Foils @ 10.75ft draft, 1ft thick, 45° leeway angle?):
Foils are NACA 0035 (symmetric). They generate lift at angle of attack.
To balance 2,340 N side force, the hull must develop leeway angle β.
Foil Lift Curve Slope Cl_α ≈ 2π/rad ≈ 0.11/deg.
3 Foils Area (submerged) = 3 * (10.75 * 1.02) = 32.9 ft² = 3.06 m².
F_side = 0.5 * 1025 * v² * Cl_α * β * A.
At v=3.4 m/s: 2340 = 0.5 * 1025 * 11.56 * 0.11 * β * 3.06 → β ≈ 1.1 radians ≈ 63°.
Result: The seastead will slide sideways at ~60° leeway. It will move mostly downwind, not at 30°.
Effective VMG Downwind: Similar to Direct Downwind case (~2 kts), but with massive drift.
Target Force needed at 0.89 m/s:
Aero Drag (20 mph wind, seastead moving 1.7 kts downwind → Apparent Wind ~18.3 mph = 8.2 m/s):
D_aero = 0.5 * 1.225 * 8.2² * 1.2 * 24.8 ≈ 1,220 N.
Hydro Drag: D_hydro = 0.5 * 1025 * 0.89² * 0.12 ≈ 49 N.
Total Drag ≈ 1,270 N.
Static Kite Force per kite (1.11 m², Cf=1.0, q=70 Pa) = 78 N.
Required Kites = 1270 / 78 ≈ 17 Kites.
With 20 Kites: Force = 1,560 N. Speed ≈ 1.9 kts (as calc above).
Friend's seastead (identical) tows disabled unit.
Towing Vessel Thrust: 6 Thrusters. Assume 50% power reserve for towing = 3000W usable per side? Total 6000W.
Drag of 2 Hulls: 2x Hydro + 2x Aero.
Calm Water: v = (2 * 6000 / (1025 * 0.8 * 6.12))^(1/3) = (2.4)^(1/3) ≈ 1.34 m/s = 2.6 kts.
10 kt Wind: Drag doubles (Aero). Power 6000W. v = 6000 / (2 * 4700) ≈ 0.64 m/s = 1.24 kts.
Towline: Need 200ft+ of 1" Nylon/Dyneema. Bridle on both bows.
Concept: Seastead B (aft) feeds DC power to Seastead A (forward) via heavy cable. Seastead A runs all 12 thrusters.
Power Available: 2 × Solar Arrays + 2 × Battery Banks. Assume 10 kW continuous per unit = 20 kW total.
Thrusters: 12 × RIM. Efficiency ~60%. Mechanical Power ~12 kW.
Calm Water (2 Hulls): v = (2 * 12000 / (1025 * 0.8 * 6.12))^(1/3) = (4.8)^(1/3) ≈ 1.69 m/s = 3.3 kts.
10 kt Wind: v = 12000 / (2 * 4700) ≈ 1.28 m/s = 2.5 kts.
20 kt Wind: Aero Drag ~18,800 N (2 hulls). v = 12000 / 18800 ≈ 0.64 m/s = 1.24 kts.
Only 1 Thruster working (e.g., Port Forward Leg). No steering authority (Yaw).
Strategy: Set fixed Thruster ON. Use Wind Drag on Superstructure as "Sail" to balance Yaw moment. Seastead settles at equilibrium Yaw Angle ψ. Resultant velocity vector = Drift.
Forces:
T (Fixed direction, e.g., Port Side, Forward).D_h (Opposes velocity vector V).D_a (Opposes Apparent Wind W_a).Moments about CG (Center of Triangle):
M_T = T * L_arm. (Arm ≈ 22 ft / 6.7 m to CG).M_A = D_a * H_cp. (Center of Pressure Height ≈ 3.5 ft / 1.07m above WL? Wall is 7ft high, CP ~ mid height). Lever arm horizontal depends on Yaw angle.M_H = D_h * D_cp. (Center of Lateral Resistance - CLR). For 3 foils, CLR is near geometric center of submerged foil area. Deep (10ft draft). Lever arm small.Seastead rotates until M_T + M_A(ψ) + M_H(ψ) = 0.
Since Hydro CLR is deep and central, M_H is small (short lever arm to CG).
Aero CP is high (above water). Large lever arm.
Result: The wind acts as the "rudder". The seastead will align so that Aero Force creates a moment balancing the Thruster moment.
M_T = 1012 * 6.7 = 6,780 Nm (Yaw to Starboard).
Need Aero Moment to Port (Nose to Port).
Wind from Beam (Starboard side) pushes nose to Port.
Equilibrium Yaw Angle ψ where Wind is on Starboard Bow/Beam.
At 10 kt Wind (5.14 m/s), Aero Force ~4,700 N (Side). CP Height ~1m above WL. Moment Arm ~1m (horizontal offset at angle).
M_A ≈ 4,700 * 1.0 = 4,700 Nm. Close to Thruster Moment.
Equilibrium found near Beam Wind (ψ ≈ 90° to True Wind).
Thruster pushes Forward (Body X). Wind pushes Sideways (Body Y).
Velocity Vector = Vector Sum.
If Body Yaw = 90° to Wind (Wind on Beam).
Thruster → Forward (Body X). Wind → Sideways (Body Y).
Track over ground = Diagonal (Forward + Downwind).
Speed Forward Component: v_f = sqrt(2T / (ρ Cd A)) ≈ sqrt(2024 / (1025*0.8*3.06)) ≈ 0.9 m/s (1.7 kts).
Speed Drift Component: v_d determined by Wind Drag = Hydro Side Drag.
Hydro Side Drag Area (3 Foils @ 90°): Cd * A ≈ 1.2 * 32.9 ft² ≈ 3.7 m².
v_d = sqrt(2 * 4700 / (1025 * 1.2 * 3.7)) ≈ 1.4 m/s (2.7 kts) Downwind.
Net Track: 1.7 kts "Forward" (relative to body) + 2.7 kts Downwind.
If "Forward" is pointed 45° away from destination, you make progress.
| Method | Calm Speed | 10kt Wind Speed | 20kt Wind Speed | Complexity | Reliability | Key Limitation |
|---|---|---|---|---|---|---|
| Primary (6 Thrusters) | 4-6 kts | 3-4 kts | 2-3 kts | Low | High | Battery/Prop Failure |
| Degraded Primary (2-4 Thr) | 1.5-4 kts | 1-3 kts | 0.5-2 kts | Low | Med | Yaw Authority (Same side loss) |
| Dinghy Tow (3 Motor) | 2-3 kts | 0.8 kts | 0.5 kts | Med | High | Dinghy Traction/Steering |
| Bottom Kedging | 2.2 kts | 0.8 kts | N/A (Depth) | High | Med | Shallow Only / Labor |
| Sea Anchor Kedging | 1.9 kts | 0.25 kts | <0.1 kts | High | Med | Wind Kills Efficiency |
| Kites (20 stack) | 0 kts (No Wind) | 1.9 kts (DW) | 3.5 kts (DW) | Very High | Low | No Steering / Leeway / Tangles |
| Dual Tow | 2.6 kts | 1.2 kts | 0.8 kts | Low | High | Requires Buddy |
| Dual Power Share | 3.3 kts | 2.5 kts | 1.2 kts | Very High | Med | Heavy Cable / Sync SW |
| Single Thruster "Sail" | 0 (Spin) | 1.7 kts + Drift | 2.5 kts + Drift | None | Low | No Steering / Wind Dependent |