# Seastead Trimaran Design Scaling Calculations

Here are the scaled dimensions, material requirements, and performance scaling factors for your 1:10 scale Fraude model.

## Dimensions

**Full-Scale Structure:**
- Main triangle sides: 80 feet
- Triangle base (stern): 40 feet
- Leg length: 19 feet
- Leg chord: 10 feet
- Leg width: 3 feet
- Submerged leg portion: 9.5 feet (50% of leg length)

**1:10 Scale Model:**
- Main triangle sides: 8 feet = 96 inches
- Triangle base (stern): 4 feet = 48 inches
- Leg length: 1.9 feet = 22.8 inches
- Leg chord: 1 foot = 12 inches
- Leg width: 0.3 feet = 3.6 inches
- Submerged leg portion: 0.95 feet = 11.4 inches

## Foam Mix Requirements

**For One Scale Leg (1:10 scale):**
- Scale leg volume (full leg): 1.9 ft × 1 ft × 0.3 ft = 0.57 cubic feet
- Foam density: 2 lbs/cubic foot
- Weight per scale leg: 0.57 × 2 = 1.14 lbs

**Foam Mix Calculation:**
- Assuming 2-part foam expands to 30 times liquid volume (typical expansion)
- Liquid volume needed: 0.57 ft³ ÷ 30 = 0.019 ft³
- Convert to cups: 0.019 ft³ × 119.7 cups/ft³ = 2.27 cups total mix
- For equal-part mix: 1.14 cups of Part A + 1.14 cups of Part B

## Weight Analysis

**Full-Scale Weight:**
- Total leg volume (3 legs): 3 × (19 × 10 × 3) = 1,710 cubic feet
- Foam weight: 1,710 ft³ × 2 lbs/ft³ = 3,420 lbs (legs only)
- Estimated total weight (including structure): ~5,000-6,000 lbs

**Scale Model Weight:**
- Leg weight (3 legs): 3 × 1.14 = 3.42 lbs
- Estimated total model weight: ~8-10 lbs

## Performance Scaling

**Speed Scaling (Froude Scaling Law):**
- Full-scale target speed: 5 knots = 8.44 ft/s
- Scale factor for velocity: √(1/10) = 0.316
- Model test speed: 8.44 ft/s × 0.316 = **2.67 ft/s**

**Power Scaling:**
- Power scaling factor: (Scale ratio)^(3.5) = (1/10)^(3.5) = 0.000316
- To get full-scale power from model drag:
  1. Measure drag force on model at 2.67 ft/s (in lbs)
  2. Full-scale drag = Model drag × (10)^3 = Model drag × 1000
  3. Full-scale power (watts) = Full-scale drag (lbs) × 8.44 ft/s × 1.356
  4. **Simplified constant**: Model drag (lbs) × 11,440 = Full-scale electrical watts

**Roll Period Scaling:**
- Time scaling factor: √(1/10) = 0.316
- To get full-scale roll period: Model roll period ÷ 0.316 = Model roll period × 3.16

## Summary Table

| Parameter | Full Scale | 1:10 Scale Model |
|-----------|------------|------------------|
| Triangle sides | 80 ft | 8 ft (96 in) |
| Triangle base | 40 ft | 4 ft (48 in) |
| Leg length | 19 ft | 1.9 ft (22.8 in) |
| Leg chord | 10 ft | 1 ft (12 in) |
| Leg width | 3 ft | 0.3 ft (3.6 in) |
| Test speed | 5 knots (8.44 ft/s) | 2.67 ft/s |
| Foam per leg | - | 2.27 cups total (1.14 cups each part) |
| Total weight | ~5,000-6,000 lbs | ~8-10 lbs |

## Important Notes

1. These calculations assume geometric similarity and Froude scaling for hydrodynamic properties.
2. The foam expansion ratio may vary by product - verify with manufacturer specifications.
3. Structural elements and non-buoyant components will add to the total weight.
4. For accurate scaling, ensure the model's center of gravity and mass distribution are proportionally similar to the full-scale design.
5. Caribbean seawater density is approximately 64 lbs/ft³ versus 62.4 lbs/ft³ for fresh water.

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<div class="results-container">
  <h1>Seastead Trimaran Design Scaling Calculations</h1>
  
  <p>This document provides scaled dimensions, material requirements, and performance scaling factors for a 1:10 scale Fraude model of your seastead trimaran design.</p>
  
  <h2>Dimensions</h2>
  
  <div class="calculation-box">
    <h3>Full-Scale Structure</h3>
    <ul>
      <li>Main triangle sides: <span class="key-result">80 feet</span></li>
      <li>Triangle base (stern): <span class="key-result">40 feet</span></li>
      <li>Leg length: <span class="key-result">19 feet</span></li>
      <li>Leg chord: <span class="key-result">10 feet</span></li>
      <li>Leg width: <span class="key-result">3 feet</span></li>
      <li>Submerged leg portion: <span class="key-result">9.5 feet</span> (50% of leg length)</li>
    </ul>
  </div>
  
  <div class="calculation-box">
    <h3>1:10 Scale Model</h3>
    <ul>
      <li>Main triangle sides: <span class="key-result">8 feet = 96 inches</span></li>
      <li>Triangle base (stern): <span class="key-result">4 feet = 48 inches</span></li>
      <li>Leg length: <span class="key-result">1.9 feet = 22.8 inches</span></li>
      <li>Leg chord: <span class="key-result">1 foot = 12 inches</span></li>
      <li>Leg width: <span class="key-result">0.3 feet = 3.6 inches</span></li>
      <li>Submerged leg portion: <span class="key-result">0.95 feet = 11.4 inches</span></li>
    </ul>
  </div>
  
  <h2>Foam Mix Requirements</h2>
  
  <div class="highlight-box">
    <h3>For One Scale Leg (1:10 scale):</h3>
    <div class="formula">
      Scale leg volume = 1.9 ft × 1 ft × 0.3 ft = 0.57 cubic feet<br>
      Foam density = 2 lbs/cubic foot<br>
      Weight per scale leg = 0.57 × 2 = <span class="key-result">1.14 lbs</span>
    </div>
    
    <h3>Foam Mix Calculation:</h3>
    <div class="formula">
      Assuming 2-part foam expands to 30× liquid volume<br>
      Liquid volume needed = 0.57 ft³ ÷ 30 = 0.019 ft³<br>
      Convert to cups: 0.019 ft³ × 119.7 cups/ft³ = 2.27 cups total mix<br>
      For equal-part mix: <span class="key-result">1.14 cups of Part A + 1.14 cups of Part B</span>
    </div>
  </div>
  
  <h2>Weight Analysis</h2>
  
  <table class="dimension-table">
    <tr>
      <th>Component</th>
      <th>Full Scale</th>
      <th>Scale Model</th>
    </tr>
    <tr>
      <td>Leg volume (3 legs)</td>
      <td>1,710 ft³</td>
      <td>1.71 ft³</td>
    </tr>
    <tr>
      <td>Foam weight (legs only)</td>
      <td>3,420 lbs</td>
      <td>3.42 lbs</td>
    </tr>
    <tr>
      <td>Estimated total weight</td>
      <td>~5,000-6,000 lbs</td>
      <td>~8-10 lbs</td>
    </tr>
  </table>
  
  <h2>Performance Scaling</h2>
  
  <div class="calculation-box">
    <h3>Speed Scaling (Froude Scaling Law):</h3>
    <div class="formula">
      Full-scale target speed: 5 knots = 8.44 ft/s<br>
      Scale factor for velocity: √(1/10) = 0.316<br>
      Model test speed: 8.44 ft/s × 0.316 = <span class="key-result">2.67 ft/s</span>
    </div>
  </div>
  
  <div class="calculation-box">
    <h3>Power Scaling Constant:</h3>
    <div class="formula">
      To get full-scale power from model drag:<br>
      1. Measure drag force on model at 2.67 ft/s (in lbs)<br>
      2. Full-scale electrical watts = Model drag (lbs) × <span class="key-result">11,440</span>
    </div>
    <p>This constant accounts for drag scaling and conversion to electrical power for thrusters.</p>
  </div>
  
  <div class="calculation-box">
    <h3>Roll Period Scaling:</h3>
    <div class="formula">
      Time scaling factor: √(1/10) = 0.316<br>
      To get full-scale roll period: Model roll period ÷ 0.316<br>
      <span class="key-result">Model roll period × 3.16 = Full-scale roll period</span>
    </div>
  </div>
  
  <h2>Summary Table</h2>
  
  <table class="dimension-table">
    <tr>
      <th>Parameter</th>
      <th>Full Scale</th>
      <th>1:10 Scale Model</th>
    </tr>
    <tr>
      <td>Triangle sides</td>
      <td>80 ft</td>
      <td>8 ft (96 in)</td>
    </tr>
    <tr>
      <td>Triangle base</td>
      <td>40 ft</td>
      <td>4 ft (48 in)</td>
    </tr>
    <tr>
      <td>Leg length</td>
      <td>19 ft</td>
      <td>1.9 ft (22.8 in)</td>
    </tr>
    <tr>
      <td>Leg chord</td>
      <td>10 ft</td>
      <td>1 ft (12 in)</td>
    </tr>
    <tr>
      <td>Leg width</td>
      <td>3 ft</td>
      <td>0.3 ft (3.6 in)</td>
    </tr>
    <tr>
      <td>Test speed</td>
      <td>5 knots (8.44 ft/s)</td>
      <td>2.67 ft/s</td>
    </tr>
    <tr>
      <td>Foam per leg</td>
      <td>-</td>
      <td>2.27 cups total<br>(1.14 cups each part)</td>
    </tr>
    <tr>
      <td>Total weight</td>
      <td>~5,000-6,000 lbs</td>
      <td>~8-10 lbs</td>
    </tr>
  </table>
  
  <div class="highlight-box">
    <h3>Important Notes:</h3>
    <ol>
      <li>These calculations assume geometric similarity and Froude scaling for hydrodynamic properties.</li>
      <li>The foam expansion ratio may vary by product - verify with manufacturer specifications.</li>
      <li>Structural elements and non-buoyant components will add to the total weight.</li>
      <li>For accurate scaling, ensure the model's center of gravity and mass distribution are proportionally similar to the full-scale design.</li>
      <li>Caribbean seawater density is approximately 64 lbs/ft³ versus 62.4 lbs/ft³ for fresh water.</li>
    </ol>
  </div>
</div>
```