```html Froude-Scaled Model Sizing (Tensegrity Semi-Submersible)

Scale Model Using 5-inch Diameter Cylinders (Legs)

1) Geometric scale ratio (from leg diameter)

Full-scale leg diameter = 4 ft = 48 in
Model leg diameter available = 5 in

Length scale factor (model/full): λ = L_model / L_full = 5 / 48 = 0.1041667

So the scale is: 1 : 9.6 (model : full), i.e. full/model = 9.6.

Convert model → full: multiply by 9.6
Convert full → model: divide by 9.6
Handy: 1 ft full-scale corresponds to 12/9.6 = 1.25 in in the model.

2) Froude scaling relations (for later tank testing)

Quantity	Scale law (model/full)	With λ = 1/9.6
Length	`L_m/L_f = λ`	`0.10417`
Area	`A_m/A_f = λ^2`	`0.01085`
Volume / Displacement / Mass (same density)	`V_m/V_f = λ^3`	`0.001130` (≈ 1/884.736)
Time / Period	`T_m/T_f = √λ`	`0.32275`
Velocity (to match Froude number)	`U_m/U_f = √λ`	`0.32275`

Note: Froude similarity matches gravity-wave effects. Reynolds number will not match at this scale unless you use special methods.

3) Full-scale geometry you provided

Item	Full-scale
Body (living area) length	60 ft = 720 in
Body width	14 ft = 168 in
Body height	8 ft = 96 in
Leg count	4 legs (2 front, 2 back)
Leg diameter	4 ft = 48 in
Leg length	35 ft = 420 in
Leg submergence (given)	~60% of leg length/volume underwater

4) Model dimensions (at 1:9.6)

Item	Full-scale	Model-scale (divide by 9.6)
Body length	720 in	75.00 in
Body width	168 in	17.50 in
Body height	96 in	10.00 in
Leg diameter	48 in	5.00 in (your cylinders)
Leg length	420 in	43.75 in
Leg portion underwater (60%)	0.60 × 420 in = 252 in	26.25 in

5) Displacement / buoyancy of the legs (lbs)

Assuming each leg is a right circular cylinder, and seawater density ≈ 64 lb/ft³. (For freshwater use 62.4 lb/ft³.)

5A) Full-scale leg displacement and buoyancy

Leg radius = 2 ft
Leg length = 35 ft
Full volume per leg = π r² L = π × (2 ft)² × 35 ft = 140π = 439.823 ft³
At 60% submerged: V_sub = 0.6 × 439.823 = 263.894 ft³

Quantity	Per leg	All 4 legs
Buoyancy @ 60% submerged (seawater, 64 lb/ft³)	16,889 lb	67,557 lb
Buoyancy @ 60% submerged (freshwater, 62.4 lb/ft³)	16,467 lb	65,868 lb

5B) Model-scale leg displacement and buoyancy

Model leg radius = 2.5 in = 0.208333 ft
Model leg length = 43.75 in = 3.645833 ft
Full volume per model leg = π r² L = 0.4975 ft³ (≈ 859 in³)
At 60% submerged: V_sub = 0.2985 ft³

Quantity	Per leg	All 4 legs
Buoyancy @ 60% submerged (seawater, 64 lb/ft³)	19.10 lb	76.4 lb
Buoyancy @ 60% submerged (freshwater, 62.4 lb/ft³)	18.62 lb	74.5 lb

Interpretation: if (approximately) only the legs provide buoyancy and you want them at ~60% submergence, then the total model weight (including ballast) would be on the order of ~76 lb in seawater (or ~75 lb in freshwater). If your model body/barrels also displace water, the required ballast weight will be lower.

6) Using two 55-gallon plastic barrels as the model “body”

6A) What full-scale size do they represent?

You can convert whatever your barrel dimensions actually are by multiplying by 9.6.

Typical 55-gallon drum dimensions (common, but verify yours):
Diameter ≈ 23 in, length/height ≈ 34.5 in.

If you connect two barrels end-to-end:

Model length ≈ 2 × 34.5 = 69.0 in
Model diameter ≈ 23.0 in

Full-scale represented (multiply by 9.6):

Full-scale equivalent length ≈ 69.0 × 9.6 = 662.4 in = 55.2 ft
Full-scale equivalent diameter ≈ 23.0 × 9.6 = 220.8 in = 18.4 ft

Two-barrel “body” (typical barrels)	Model	Represents at full scale (×9.6)
Length	69.0 in	662.4 in (55.2 ft)
Diameter	23.0 in	220.8 in (18.4 ft)

6B) Volume / buoyancy of the barrels (optional but useful for ballast planning)

One 55-gal barrel volume = 55 gal × 231 in³/gal = 12,705 in³ = 7.35 ft³
Two barrels: 14.70 ft³
Max buoyancy if fully submerged (seawater): 14.70 × 64 = 941 lb (model-scale)

Because barrels add a lot of buoyancy, your model may need substantial ballast (or you may need to intentionally flood/vent the barrels) to achieve the desired ~60% leg submergence.

7) What I still need (if you want cable lengths and/or a full weight/ballast plan)

Where exactly each leg attaches to the body (height and fore/aft position) in inches.
Clarify the 45° descriptions: are they 45° in plan view and 45° in side view (two projections), or something else?
Target water type (fresh vs salt) for the tests.
Whether the body is intended to be buoyant in the model or only the legs.

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