Here's your complete design sheet. Key result: **your 5" cylinders against 48" (4 ft) legs gives an exact 1:9.6 scale**, which conveniently means **1 inch of model = 0.8 ft of full scale**.
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Tensegrity Seastead — 1:9.6 Froude Scale Model Design Sheet
Tensegrity Semi-Submersible Seastead — Scale Model Design Sheet
Froude-scaled model derived from 5-inch diameter leg cylinders
SCALE RATIO λ = 9.6 : 1 (1 in model = 0.8 ft full scale)
1 · Derivation of Scale Ratio
The leg diameter sets the scale:
λ = Full-scale leg dia ÷ Model leg dia = 48 in ÷ 5 in = 9.6
Quantity
Full Scale
Model
Ratio
Leg diameter
48 in (4.0 ft)
5.00 in
9.600
Leg length
420 in (35 ft)
43.75 in
9.600
Luckily convenient: 9.6 in = 0.8 ft, so every inch of model equals exactly 0.8 ft of full-scale seastead.
2 · Froude Scaling Laws (λ = 9.6)
Quantity
Multiplier (full → model)
Value
Length, distance
÷ λ
÷ 9.6
Area
÷ λ²
÷ 92.16
Volume, Weight, Displacement, Force
÷ λ³
÷ 884.736
Speed
÷ √λ
÷ 3.0984
Time, wave period
÷ √λ
÷ 3.0984
Acceleration (g-levels)
× 1
unchanged
Moments (pitch/roll)
÷ λ⁴
÷ 8,493.5
Power
÷ λ3.5
÷ 2,741
Wave height
÷ λ
÷ 9.6
KG, GM, radii of gyration
÷ λ
÷ 9.6
3 · Full-Scale Reference Geometry
Geometry assumption: "45° in front view AND 45° in side view" means each leg's lateral, longitudinal, and vertical components are all equal: 420 ÷ √3 = 242.5 in (20.2 ft) each way. Legs attach at the four deck-corner "points" of the body.
Item
Dimension (inches)
Body (L × W × H)
720 × 168 × 96
Legs (4) — diameter × length
Ø 48 × 420
Leg offset per axis (lateral / longitudinal / vertical)
242.5 each
Lateral spacing between front leg tips (= tip-to-tip cable)
485.0
Longitudinal overhang of tips beyond body ends
242.5
Overall footprint incl. legs (L × W)
1,205 × 653
Cross cables (leg tip → opposite-end underside center), 4 ea
≈ 1,022 long
Waterline location along leg (60 % submerged)
252.0 from leg top
Vertical drop, deck → waterline (freeboard)
145.5
Air gap, body bottom → water
49.5
Leg tip depth below surface
97.0
4 · MODEL Dimensions (build to these)
Item
Full Scale (in)
Model (in)
Body length
720
75.00
Body width
168
17.50
Body height
96
10.00
Leg diameter (your cylinders)
48
5.00 ✔
Leg length
420
43.75
Leg offset per axis (lat / long / vert)
242.5
25.26
Tip-to-tip cables (front pair, aft pair)
485.0
50.52
Cross cables (tip → opposite underside center)
≈1,022
≈106.4
Overall footprint (L × W)
1,205 × 653
125.5 × 68.0
Waterline mark along leg from top (60 %)
252.0
26.25
Freeboard (deck → waterline)
145.5
15.16
Air gap under body
49.5
5.16
Leg tip depth
97.0
10.10
Scribe a waterline mark 26.25 in down each leg (measured along the leg from its top). Ballast until all four marks sit exactly at the surface — that guarantees correct displacement and trim.
5 · Weights & Displacement
Buoyancy comes from the submerged 60 % of the four legs (body rides fully above water):
Build the model to a total weight of ≈ 74.5 lb (fresh water) or 76.4 lb if testing in salt water.
6 · Suggested Model Weight Budget (target 74.5 lb)
Component
Est. Weight (lb)
2 × 55-gal plastic barrels (body)
44.0
4 leg tubes (keep them LIGHT — thin-wall tube, sonotube, or foam-cored)
12.0
Frame, joints, deck skeleton
6.0
Cables, turnbuckles, hardware
4.0
Adjustable ballast (place LOW — in leg tips or under body center)
8.5
Total
74.5
Weigh your actual parts, then set ballast = 74.5 − (actual dry weight). If your 5-inch cylinders are heavy (e.g., thick PVC ≈ 2.3 lb/ft → 33 lb for four!), the budget breaks — switch to lighter tube stock.
7 · 55-Gallon Barrel "Body" — What It Represents
Typical poly drum: Ø 22.5 in × 33.5 in long each; two joined end-to-end = 67 in long × 22.5 in dia.
Barrel Dimension
Model (in)
Represents Full Scale (×9.6)
Design Intent
Total length (2 drums)
67.0
643 in = 53.6 ft
60 ft → 10.7 % short
Diameter
22.5
216 in = 18.0 ft
14 ft beam → 28.6 % wide
Enclosed volume (110 gal = 14.71 ft³)
—
13,013 ft³ equiv.
Body envelope 6,720 ft³ → 1.94×
Reserve buoyancy if fully flooded-proof
—
—
Supports ≈ 918 lb — huge safety margin
Add a 4-in spacer/fairing at each end to stretch 67 → 75 in (full 60 ft).
The 22.5-in circle is wider than the 17.5-in design beam — acceptable; it reads as a rounded hull and adds reserve stability.
Keep barrels sealed and dry: in the real design the body is fully above water, and the rigid legs must carry the load, not the barrels.
Barrel buoyancy is your crash insurance — even if a leg floods, the model cannot sink.
8 · Test Conversions (Froude)
Full Scale
Model (÷3.0984)
2 kn
0.65 kn
4 kn
1.29 kn
6 kn
1.94 kn
8 kn
2.58 kn
10 kn
3.23 kn
Wave period 6 s
1.94 s
Wave period 10 s
3.23 s
Wave height 6 ft
7.5 in
1 minute of time
19.4 s
9 · Assumptions & Notes
Leg direction: equal 242.5-in components laterally, longitudinally, and vertically (both orthographic views show 45°). If your intent was a different 3-D angle, tip spacings and cable lengths change but the scale ratio, weights, and body dimensions do not.
Legs assumed attached at the four deck corners; cables run to the underside center of the opposite body end.
Displacement assumes only the legs are submerged (body fully above water), matching the semi-submersible concept.
Froude scaling reproduces wave-making and gravity effects; structural stresses do not scale by λ³ — treat model members as representative geometry, not stress-scaled structure.
Barrel dimensions are industry-typical (22.5 × 33.5 in); verify your drums and recompute ×9.6 if they differ.
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A few key takeaways:
- **Scale = 9.6:1** — every model inch = 0.8 full-scale feet, which makes mental conversions easy on the shop floor.
- **Target model weight ≈ 74.5 lb** (fresh water). Mark each leg at **26.25 in** from the top and ballast until all four marks sit at the surface.
- **The barrels represent a 53.6 ft × 18.0 ft body** — slightly short and wide versus your 60 × 14 ft design, but with ~918 lb of reserve buoyancy they're excellent insurance during testing.
- Watch the leg tube weight: four 43.75-in lengths of thick-wall 5" PVC would eat ~33 lb of your 74.5 lb budget. Thin-wall tube, sonotube, or foam-cored cylinders keep the budget workable.