Seastead Fraude Model Calculations

This page provides the dimensions and calculations for a 1/10th scale Fraude model of the trimaran seastead design, including foam mix quantities, target weights, speed, power constant, and roll period multiplier.

1. Scale Model Dimensions (1/10th Scale)

Full-scale dimensions are scaled down by a factor of 1/10. All lengths are provided in both feet and inches.

Component	Full-Scale Dimension (ft)	Model Dimension (ft)	Model Dimension (in)
Leg Length	19	1.9	22.8
Leg Chord	10	1.0	12
Leg Width (Thickness)	3	0.3	3.6
Triangle Frame Sides (front to back)	80	8.0	96
Triangle Frame Back (side to side)	40	4.0	48

Note: The leg dimensions are based on a NACA wing shape with an assumed cross-sectional area factor of 0.68 (area = 0.68 × chord × thickness). The triangle frame is above water and may not affect hydrodynamic testing directly.

2. Foam Mix for One Scale Leg

Each leg is made from a 2-part foam mix with an expanded density of 2 lbs/ft³. The same mold is used three times for the three legs.

Volume of one scale leg (expanded foam): 0.3876 ft³

Expanded foam volume in cups: 0.3876 ft³ × 119.688 cups/ft³ ≈ 46.4 cups total.

Since the foam expands, the amount of mix needed depends on the expansion ratio. Assuming a typical expansion ratio of 20 for two-part polyurethane foam:

Mixed volume before expansion: 46.4 cups / 20 = 2.32 cups total.
For a 1:1 mix by volume, each part: 2.32 / 2 = 1.16 cups.

Note: The expansion ratio is assumed. If your foam has a different expansion ratio, adjust accordingly. If the foam mix is measured by weight, consult the manufacturer's specifications.

3. Target Weights in Caribbean Sea Water

The target weight is calculated so that the seastead floats with each leg 50% submerged. Seawater density is taken as 64 lbs/ft³.

Scale	Total Submerged Volume (ft³)	Target Weight (lbs)
Full Scale	581.4	37,209.6
Scale Model (1/10th)	0.5814	37.21

Note: The weights include the buoyancy from the submerged parts of the legs only. The frame weight is included in the total weight through equilibrium.

4. Speed for Scale Model Simulating 5 Knots

For Froude scaling, the model speed is scaled by the square root of the scale factor.

Full-scale speed: 5 knots = 8.4389 ft/s

Scale factor: 1/10, so √(1/10) = 0.316227766

Model speed: 8.4389 ft/s × 0.316227766 ≈ 2.67 ft/s

Thus, aim for 2.67 ft/s when pulling the scale model.

5. Constant for Power Conversion

To convert the force measured on the scale model (in lbs) to electrical watts needed for full-scale thrusters at 5 knots, use the following constant:

Assuming 100% thruster efficiency, the useful power is given by:

P_full (watts) = 11442 × F_model (lbs)

Where:

F_model is the force reading from the sensor on the scale model in pounds-force (lbs).
P_full is the power in watts required to overcome drag at full scale.

Note: This constant accounts for Froude scaling and unit conversions. If thruster efficiency η is known, divide the result by η to get electrical watts. For example, if η = 0.7, then electrical watts = (11442 × F_model) / 0.7.

6. Roll Period Multiplier

For Froude scaling, time periods scale with the square root of the scale factor.

If T_model is the natural roll period measured on the scale model (in seconds), then the full-scale roll period T_full is:

T_full = T_model × √10 ≈ T_model × 3.162

Thus, multiply the model roll period by approximately 3.162 to get the full-scale roll period.

Summary

Scale model leg dimensions: 22.8 in long, 12 in chord, 3.6 in width.
Foam mix per leg: ~1.16 cups of each part (assuming 1:1 mix and expansion ratio 20).
Target weights: 37,209.6 lbs (full scale), 37.21 lbs (model).
Model speed: 2.67 ft/s for 5 knots simulation.
Power constant: 11442 watts per lb of model force.
Roll period multiplier: 3.162.

Disclaimer: These calculations are based on assumptions such as airfoil shape factor and foam expansion ratio. Verify with actual measurements and manufacturer data for accuracy.