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Seastead Cylinder Sail Analysis - 20 MPH Wind
Analysis: Using 60ft x 12ft Cylinder as Wind Sail/Kite (20 MPH Caribbean Wind)
Key Assumptions & Model
- Cylinder: 12 ft (3.66 m) dia., 60 ft (18.29 m) long, 8 ft above water → 4 ft (1.22 m) draft.
- Wind: 20 MPH = 8.94 m/s, ρ_air = 1.225 kg/m³, C_d_air ≈ 1.2 (rough cylinder).
- Max wind force (broadside): ~3,940 N (885 lbf) downwind.
- Water drag (perp. to axis): k_perp ≈ 12,580 N/(m/s)², based on A_water = 22.3 m² (draft × L), ρ_water=1,025 kg/m³, C_d_water≈1.1.
- Model: Drag force on cylinder is perpendicular to its axis. Steady-state speed is perp. to axis where wind drag = water drag. Thrusters hold orientation (negligible net lateral thrust or torque counter). Parallel-axis drag neglected (small).
- Thrusters: 4 × 720 lbf (3,200 N) @ 3.2 kW each → total 12,800 N @ 12.8 kW. Efficient at low power.
- Apparent wind ≈ true wind (slow speeds ~1 mph).
1. Thruster Capability to Hold Orientation
Yes, easily able to hold any desired orientation.
- Max wind force ~3,940 N (lateral or torque).
- Thrusters: 12,800 N total capacity → >3× overkill.
- Power needed: Very low (<0.5 kW total estimated). Uniform cylinder experiences minimal yaw torque (center of pressure at midpoint). Thrusters on 4 corner legs counter minor torques/asymmetries/waves efficiently at partial power.
- Holding broadside (ψ=90°): ~0 kW (symmetric). Angled: ~0.1-0.4 kW depending on yaw ψ.
2. Sideways Drift Speed if Broadside to Wind
Broadside (cylinder axis ⊥ wind, ψ=90°): Wind force pushes perpendicular to axis.
| Condition | Wind Force (N / lbf) | Drift Speed |
|---|
| Broadside Drift (ψ=90°) |
3,940 N / 885 lbf |
0.56 m/s = 1.25 MPH |
Moves directly downwind at speed where water drag balances. (No thrusters needed for steady drift.)
3. Performance at 20° or 30° Off Downwind
Strategy: Hold cylinder axis perpendicular to desired track. Wind hits at yaw ψ = 90° - δ (δ=off-angle). Speed = √(F_perp / k_perp), F_perp = F_max × sin²ψ.
Pure downwind (δ=0°): ψ=90°, max speed 1.25 MPH.
| Off Downwind Angle (δ) | Cylinder Yaw to Wind (ψ) | Wind Force Perp. (N / % of max) | Track Speed | Thruster Power |
|---|
| 0° (Pure Downwind) |
90° |
3,940 N (100%) |
0.56 m/s = 1.25 MPH |
~0 kW |
| 20° Off |
70° |
3,480 N (88%) |
0.53 m/s = 1.18 MPH |
<0.3 kW |
| 30° Off |
60° |
2,955 N (75%) |
0.49 m/s = 1.09 MPH |
<0.4 kW |
Summary Benefits
- Faster than props alone: 1.09-1.25 MPH vs. your 0.5-1 MPH electric (solar-limited).
- Less electricity: Thrusters at idle/low power (0-0.4 kW) vs. full propulsion (several kW).
- Works well: 20-30° off downwind viable at ~90% max speed. Steady track perp. to cylinder axis.
- Tradeoff: Larger δ → lower speed (less projected area).
Sensitivity & Caveats
- Higher wind → higher speeds (∝ √wind speed).
- Legs add ~10-20% drag/buoyancy (conservative; increases k → slightly lower speeds).
- Apparent wind reduction at speed: Minor (-5% effect).
- Torque/waves: Thrusters handle easily; test in sim.
- Mass/draft: Assumed fixed; adjust if buoyancy changes.
Generated via physics-based estimation. For engineering, use CFD/FEA (e.g., OpenFOAM) + prototype tests.
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## Key Calculations (for reference, not in HTML)
- F_max = 0.5 * 1.225 * 8.94² * 3.66 * 18.29 * 1.2 ≈ 3,940 N
- k_perp = 0.5 * 1025 * 1.1 * 1.22 * 18.29 ≈ 12,580 N/(m/s)²
- V_broad = √(3940/12580) ≈ 0.56 m/s
- For δ=20°, ψ=70°, sinψ=0.9397, sin²ψ=0.883, F_perp=3940*0.883=3,480 N, V=√(3480/12580)=0.527 m/s