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Seastead Design Analysis
This document provides the analysis and calculations for the 1/6th scale model of the seastead, focusing on the ballast system and displacement of water.

Froude Scaling Rules
Froude scaling is used to ensure dynamic similarity between the model and full-scale system. The Froude number (Fr) is the dimensionless parameter that equates the gravitational forces between the model and full scale:

**Fr = V / sqrt(g * L)}**, where V> is velocity, g> is acceleration due to gravity, and L> is length.

To maintain similarity, all linear dimensions are scaled by a factor of λ.>. For Froude scaling, time is scaled by λ>^(1/2), velocities by λ>^(1/2), and accelerations remain unchanged.

Dimensions of Full-Scale Model
The scale factor λ> is 1/6, meaning the model is 1/6th the size of the full-scale system. To find the full-scale dimensions, multiply the model dimensions by 1/λ (or 6).

Main Triangle Side Length (Model): 10 feet

Main Triangle Side Length (Full Scale): **10 feet * 6 = 60 feet

Leg Diameter (Model): 5 inches

Leg Diameter (Full Scale): 5 inches * 6 = 30 inches = 2.5 feet

Leg Length (Model): 6 feet

Leg Length (Full Scale): 6 feet * 6 = 36 feet**

Ballast System
The legs are angled at 45 degrees and are partially submerged. The submerged portion is 60% of the total leg length:

Submerged Leg Length (Model): **6 feet * 0.6 = 3.6 feet

Submerged Leg Length (Full Scale): 36 feet * 0.6 = 21.6 feet**

Water Displacement Calculation
The volume of water displaced by each submerged leg can be calculated using the formula for the volume of a cylinder: **V = π * r^2 * h,>, where r> is the radius and h> is the submerged height.

Leg Radius (Model): 5 inches / 2 = 2.5 inches = 0.2083 feet

Leg Radius (Full Scale): 2.5 feet / 2 = 1.25 feet

Submerged Volume per Leg (Model): π * (0.2083)^2 * 3.6 = 1.59 cubic feet

Submerged Volume per Leg (Full Scale): π * (1.25)^2 * 21.6 = 106.36 cubic feet

Total Water Displacement (Model): 1.59 cubic feet * 3 = 4.77 cubic feet

Total Water Displacement (Full Scale): 106.36 cubic feet * 3 = 319.08 cubic feet**

Target Weight of Scale and Full-Scale Models
The target weight of the model and full-scale system is approximately equal to the weight of the displaced water (Archimedes' principle). Water density is 62.4 lb/ft³..

Model Weight (1/6th Scale): **4.77 cubic feet * 62.4 lb/ft³ = 297.3 lb

Full-Scale Weight: 319.08 cubic feet * 62.4 lb/ft³ = 19,923.6 lb**

Note: Rope weights and other structural elements are not included in this analysis. Add additional weight estimates for the actual design.

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