```html 1/10 Froude Scale Seastead Model Calculations

1/10 Froude Scale Model Calculations

Below are the calculations for your triangular seastead concept using a 1/10 linear scale Froude model.

Important assumption: For buoyancy and foam volume, I treated each leg as a simple solid shape with overall dimensions 19 ft long × 10 ft chord × 3 ft width. Since you said “in the shape of a NACA wing,” the true volume of an actual airfoil-shaped body would be less than a full rectangular block. So the buoyancy and foam numbers below are based on the bounding prism volume, unless you later provide a specific airfoil thickness/profile and whether the 3 ft width is max thickness or spanwise thickness.

1) Full Scale Dimensions

Main triangle frame

Item Feet Inches
Side length (2 sides, front-to-back) 80 ft 960 in
Back width (side-to-side) 40 ft 480 in

Each buoyancy leg

Item Feet Inches
Length 19 ft 228 in
Chord 10 ft 120 in
Width 3 ft 36 in
Submerged length at rest (50%) 9.5 ft 114 in
Above water length at rest (50%) 9.5 ft 114 in

2) 1/10 Scale Model Dimensions

For a 1:10 Froude model, every linear dimension is divided by 10.

Scale triangle frame

Item Feet Inches
Side length (2 sides) 8.0 ft 96.0 in
Back width 4.0 ft 48.0 in

Each scale leg

Item Feet Inches
Length 1.9 ft 22.8 in
Chord 1.0 ft 12.0 in
Width 0.3 ft 3.6 in
Submerged length at rest (50%) 0.95 ft 11.4 in
Above water length at rest (50%) 0.95 ft 11.4 in

3) Buoyant Volume and Target Displacement Weight

Volume per full-scale leg

Using the simple box volume:

V_leg = 19 × 10 × 3 = 570 ft³

Since each leg is 50% submerged:

Submerged volume per leg = 570 × 0.5 = 285 ft³

With 3 legs total:

Total submerged volume = 3 × 285 = 855 ft³

Caribbean seawater weight

Typical seawater density is about 64 lb/ft³. Caribbean seawater is close to this, so I used:

γ_seawater = 64 lb/ft³

Full-scale target displacement

W_full = 855 × 64 = 54,720 lb

Scale-model target displacement

Volume scales as (1/10)^3 = 1/1000, so:

W_model = 54,720 / 1000 = 54.72 lb

Item Value
Total submerged volume, full scale 855 ft³
Target displacement weight, full scale 54,720 lb
Target displacement weight, 1/10 scale model 54.72 lb
If your leg is a true streamlined NACA body rather than a full 19×10×3 solid, the actual displacement may be much lower than these values. So these weights should be treated as a first-pass estimate based on the dimensions given.

4) Foam Volume and Foam Mix Per Scale Leg

Scale leg total volume

Each full-scale leg is 570 ft³, so one 1/10 scale leg has:

V_scale_leg = 570 / 1000 = 0.57 ft³

Expanded foam weight per scale leg

Foam density given: 2 lb/ft³

W_foam_leg = 0.57 × 2 = 1.14 lb

Expanded foam volume in cups

1 ft³ = 7.48052 gallons = 119.688 cups

0.57 ft³ × 119.688 = 68.22 cups expanded foam

If the foam system is mixed 1:1 by volume and assuming final expanded volume is the stated expanded volume, then per batch:

Total mixed liquid needed ≈ final expanded volume / expansion ratio

But you did not give the liquid-to-expanded expansion ratio, only the final expanded density. So from density alone, we can calculate the final foam volume and final foam weight, but not the exact starting cups of Part A and Part B unless we know the supplier’s expansion ratio or mixed liquid density.

What we can state exactly

Item Per scale leg
Expanded foam volume required 0.57 ft³
Expanded foam volume required 68.22 cups
Expanded foam weight 1.14 lb

If your foam is mixed 1:1 by volume

Then the total starting liquid volume depends on the manufacturer expansion ratio:

Starting liquid volume (cups) = 68.22 / (expansion ratio)

Part A = Part B = 34.11 / (expansion ratio)

Examples

Expansion Ratio Total Mixed Liquid per Scale Leg Part A Part B
10× 6.82 cups 3.41 cups 3.41 cups
15× 4.55 cups 2.27 cups 2.27 cups
20× 3.41 cups 1.71 cups 1.71 cups
25× 2.73 cups 1.36 cups 1.36 cups

To get the exact cups of each part, please use the expansion ratio from your foam supplier’s datasheet.

5) Model Tow Speed for Full-Scale 5 Knots

Full-scale speed

5 knots = 5 × 1.68781 = 8.439 ft/s

Froude scaling for speed

For 1/10 scale:

V_model = V_full / √10 = 8.439 / 3.1623 = 2.668 ft/s

Item Value
Full-scale speed 5 knots = 8.439 ft/s
1/10 scale model tow speed 2.67 ft/s

6) Convert Scale Drag Reading to Full-Scale Power

Force scaling

Under Froude scaling, force scales as:

F_full = F_model × λ³

where λ = 10, so:

F_full = F_model × 1000

Power calculation

Mechanical power:

P = F × V

Using full-scale speed at 5 knots:

P_full(ft·lb/s) = (F_model × 1000) × 8.439

P_full(ft·lb/s) = F_model × 8439

Convert ft·lb/s to watts:

1 ft·lb/s = 1.35582 W

P_full(W) = F_model × 8439 × 1.35582

P_full(W) = F_model × 11,442

Resulting constant

If your sensor on the scale model reads drag in lb-force, then:

Full-scale ideal mechanical watts at 5 knots = (model drag in lb) × 11,442

So the constant is:

11,442

This gives ideal tow power / effective propulsive power, not actual electrical input power to thrusters. Real electrical input must account for propeller, motor, controller, and transmission efficiency.

If you want electrical input power

Use:

Electrical watts = (model drag in lb) × 11,442 / η

Example efficiencies:

Overall Thruster Efficiency η Multiply Sensor Reading By
0.70 16,346
0.60 19,070
0.50 22,884

If you do not yet know thruster efficiency, use 11,442 for the ideal hydrodynamic power and then divide by your estimated total propulsion efficiency later.

7) Roll Period Scaling

Under Froude scaling, time scales as the square root of length scale:

T_full = T_model × √10

T_full = T_model × 3.1623

So the multiplier is:

3.1623

8) Summary

Quantity Result
Scale ratio 1:10
Scale triangle side length 8.0 ft = 96 in
Scale triangle back width 4.0 ft = 48 in
Scale leg length 1.9 ft = 22.8 in
Scale leg chord 1.0 ft = 12.0 in
Scale leg width 0.3 ft = 3.6 in
Scale submerged leg length 0.95 ft = 11.4 in
Full-scale target displacement 54,720 lb
Scale-model target displacement 54.72 lb
Expanded foam volume per scale leg 0.57 ft³ = 68.22 cups
Expanded foam weight per scale leg 1.14 lb
Scale tow speed to simulate 5 knots full scale 2.67 ft/s
Power constant for ideal full-scale watts 11,442 × (model drag in lb)
Roll-period scaling multiplier 3.1623

9) Recommended Next Step

If you want, I can do a second-pass refined version using a more realistic estimate for the actual volume of a NACA-shaped leg instead of a full rectangular block. That would give you much better numbers for:

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