Here is a complete, self-contained HTML file with an interactive calculator. It models the thruster physics using affinity laws (scaling the manufacturer's max-power curve down to your target power settings) and balances that against a physics-based drag model for your 3-column geometry. You can save this as `seastead_speed.html` and open it in any browser. Adjust the **Drag Coefficient (CdA)** slider to match your real-world observations. ```html Seastead Speed Calculator

Seastead Backup Propulsion Analysis

Equilibrium speed estimation for 2x Shinmaywa SM-VRTN (2.5m) thrusters on a 3-column platform. Drag modeled as "Tiny Oil Platform" (inclined cylinders + cables).

Drag Model Configuration

Total Hydrodynamic Drag Area (CdA) Projected Area × Cd. Default 10 m² ≈ 3× Columns (45°) + Cables. Increase for marine growth / platform superstructure.

Displacement (Weight) Lbs. Used to validate submerged volume vs column geometry.

Seawater Density1025 kg/m³

Column Draft (45°)13 ft (3.96 m)

Column Width (Dia)4 ft (1.22 m)

Thruster Power Settings

Per Thruster (2 Total). Manufacturer Max Curve: 3200N @ 3.2kW Bollard.

Setting 1 (Max)

Setting 2 (Cruise)

Setting 3 (Economy)

Equilibrium Speed Results

Power Setting (per thruster)	Total Shaft Power	Bollard Pull (Est.)	Top Speed	Thrust @ Top Speed	Drag @ Top Speed	Range @ 20kWh Bat

Physics Model Assumptions (Edit sliders above to test sensitivity):

Thruster Scaling: Uses Propeller Affinity Laws. Thrust ∝ Power²ᐟ³, Speed ∝ Power¹ᐟ³. The manufacturer's 4-point curve (0–1.5 mph) is treated as the "Max RPM" curve. Lower power settings are geometrically scaled versions of this curve.
Drag Model: Quadratic Drag Fd = 0.5 × ρ × CdA × V². No wave-making resistance (hull speed irrelevant for columns). CdA defaults to 10 m² (3× Columns @ 45°: 3.4m² proj each × Cd 0.7 ≈ 7.1 + 2× Cables ≈ 1.8 + Margin).
Columns: 3× Cylinders, 4ft Dia, 13ft length @ 45°. Projected Area/Col = D×L×sin(45) = 3.4 m². Axial Cd ≈ 0.7 (Normal Cd 1.0 × sin²45).
Cables: 2× 50mm Dia, ~15m length. Cd 1.2.
Equilibrium: Solved numerically: 2 × Thrust₁(V) = Drag(V).
Range: Assumes 20 kWh usable battery bank. Time = Energy / Total Power. Distance = Speed × Time.

⚠ Reality Check: If your actual speed is significantly lower than predicted, your CdA is higher (marine growth, deck drag, current). Increase the CdA slider until the model matches reality. If higher, your columns may be cleaner or you have favorable current.

``` ### How to use this: 1. **Save as HTML**: Copy the block above, save as `seastead_speed.html`. 2. **Open in Browser**: Double-click the file. 3. **Interpret the Chart**: * **Red Dashed Line**: Your Platform Drag (Quadratic curve). Steeper = more drag. * **Solid Lines (Green/Blue/Orange)**: Total Thrust from 2 thrusters at each power setting. * **Dots**: Equilibrium Points (Where Thrust = Drag). This is your top speed. 4. **Tune the "CdA" Slider (Top Left)**: * Default is **10.0 m²** (Calculated: 3 Columns @ 45° + 2 Cables). * If your real-world testing shows **lower speeds**, drag is higher -> **Increase CdA**. * If speeds are **higher**, decrease CdA. 5. **Adjust Power Sliders (Top Right)**: Match your actual inverter/motor controller limits. ### The Physics Inside (So you trust it / can explain it): 1. **Thruster Scaling (Affinity Laws)**: * The manufacturer gave you the "Max RPM" curve (3.2kW). * Physics dictates: `Thrust ∝ RPM²`, `Power ∝ RPM³`, `Speed ∝ RPM`. * Therefore: `Thrust ∝ Power^(2/3)` and `Max Speed ∝ Power^(1/3)`. * The code geometrically scales the *entaneous manufacturer curve* down for 2.2kW and 1.2kW. This is standard propeller theory. 2. **Drag Model (CdA = 10 m² Default)**: * **Columns**: 3 × (4ft × 13ft × sin45°) = 110 ft² projected area. Axial Cd ≈ 0.7 (Normal Cd 1.0 × sin²45). **CdA ≈ 7.1 m²**. * **Cables**: 2 × (2in × 50ft) ≈ 16 ft². Cd 1.2. **CdA ≈ 1.8 m²**. * **Total**: **~8.9 m²**. Rounded to **10 m²** for marine growth / platform shadow / safety margin. 3. **Equilibrium Solver**: Numerical bisection finding where `2 × Thrust(V) = 0.5 × ρ × CdA × V²`. ### Expected Output (Default Settings): | Setting | Power (Total) | Est. Speed | Range (20kWh) | | :--- | :--- | :--- | :--- | | **Max (3.2 kW)** | 6.4 kW | **~1.35 mph** | ~4.2 km (2.6 mi) | | **Cruise (2.2 kW)** | 4.4 kW | **~1.20 mph** | ~5.5 km (3.4 mi) | | **Economy (1.2 kW)** | 2.4 kW | **~0.98 mph** | ~8.2 km (5.1 mi) | *Note: Range assumes 100% battery-to-prop efficiency. Real world ~80-85%.*