Tensegrity Seastead Scale Model Calculator

This calculator uses Froude scaling to determine the appropriate scale ratio for your tensegrity seastead model. Froude scaling preserves dynamic similarity between a model and its full-scale counterpart for systems where gravity and inertia are dominant forces (like floating structures).

The key principle: Froude number (Fr) = V / √(gL) must be equal for both model and full-scale structure.

Scale Ratio: 1:14.4

How the Scale Ratio Was Calculated

You have 5-inch diameter cylinders for the model legs. The full-scale legs are 4 feet in diameter.

Calculation: 4 feet = 48 inches. Model leg diameter = 5 inches.

Scale ratio (linear) = 48 inches / 5 inches = 9.6

But for Froude scaling, the time scale is √(scale ratio). Since we want dynamic similarity, we use the linear scale ratio directly for dimensions.

However, with Froude scaling, weight/mass scales with the cube of the linear scale: Weight_model = Weight_full / (scale ratio)³

Note: In marine engineering, Froude scaling typically uses length ratio (λ). For your convenience, I've calculated both the geometric scale and the Froude scaling relationships.

Dimension Comparison

Full-Scale Seastead

Body Length: 60 ft = 720 inches
Body Width: 14 ft = 168 inches
Body Height: 8 ft = 96 inches
Leg Diameter: 4 ft = 48 inches
Leg Length: 35 ft = 420 inches
Leg Angle: 45° in both directions
Waterline: ~60% of legs submerged

Scale Model (1:9.6 scale)

Body Length: 75.0 inches (6.25 ft)
Body Width: 17.5 inches
Body Height: 10.0 inches
Leg Diameter: 5.0 inches
Leg Length: 43.75 inches (3.65 ft)
Leg Angle: 45° (same as full-scale)
Waterline: ~60% of legs submerged

Using 55-Gallon Barrels for the Model Body

Two standard 55-gallon plastic barrels connected end-to-end:

Typical 55-gallon barrel dimensions: ~34.5 inches tall, ~23 inches diameter
Two barrels end-to-end: Length ≈ 69 inches, Diameter ≈ 23 inches
Your model body should be: Length = 75 inches, Width = 17.5 inches, Height = 10 inches

The barrels are slightly shorter (69" vs 75") and wider (23" vs 17.5") than ideal, but could work with some modifications.

You could cut the barrels down to reduce diameter and extend length with connectors to better match the model dimensions.

Weight Scaling

With Froude scaling, weights scale with the cube of the linear scale:

Weight scale factor = (1/9.6)³ = 1/885 ≈ 0.00113

This means the model weight should be about 0.113% of the full-scale weight.

To determine model weight, you need to estimate the full-scale weight:

Body volume: 60ft × 14ft × 8ft = 6,720 ft³
Assuming 30% of volume is structure: 2,016 ft³
Assuming steel construction (490 lb/ft³): ~987,840 lbs
Plus equipment, supplies, etc.: Estimated total ~1,200,000 lbs

Model weight should be approximately: 1,200,000 lbs × 0.00113 = 1,356 lbs

This is a rough estimate. Actual weight will depend on materials and construction. For a functional floating model, you'll need to adjust ballast to achieve the proper 60% leg submersion.

Front View

Two legs extending at 45° angles to the sides, forming an isosceles triangle with the connecting cable underwater.

        Body (above water)
        ------------------
               /   \
              /     \
             /       \
            /         \
          Leg        Leg
          (45°)      (45°)

Side View

Legs also angled at 45° downward and away from the body when viewed from the side.

        Body
        -------
          \   \
           \   \
            \   \
             \   \
              \   Cable to center
               \   underside
                \
                 Leg (45° down/forward)

Key Relationships for Froude Scaling

Parameter	Scaling Law	Scale Factor (1:9.6)
Length	λ	1/9.6
Area	λ²	1/92.2
Volume, Weight, Mass	λ³	1/885
Time	√λ	1/3.1
Velocity	√λ	1/3.1
Acceleration	1	1 (gravity same)
Force	λ³	1/885