Tensegrity Semi-Submersible Seastead
Froude Scale Model Design Specification
Scale Ratio Determined by Available 5-inch Diameter Leg Stock
1. Scale Ratio Determination
The primary scaling constraint is the leg diameter. We have 5-inch OD cylinders for the model legs. The prototype legs are 4 ft (48 in) diameter.
Scale Ratio (λ) = Prototype Dimension / Model Dimension
λ = 48 in / 5 in = 9.6
| Parameter | Symbol | Value | Units |
|---|
| Prototype Leg Diameter | Dp | 48 | inches |
| Model Leg Diameter (Stock) | Dm | 5 | inches |
| Scale Ratio (Linear) | λ | 9.6 | :-1 (Model:Proto) |
| Scale Factor (Model → Prototype) | | 9.6 | x |
| Scale Factor (Prototype → Model) | | 0.10417 | x (1/9.6) |
Froude Scaling Law: For dynamic similarity (wave interaction, stability, motions), Froude Number (Fr = V/√gL) must be constant.
This dictates:
• Linear Dimensions scale as λ (1:9.6)
• Areas scale as λ² (1:92.16)
• Volumes / Mass / Weight / Displacement scale as λ³ (1:884.736)
• Time (Periods) scales as √λ (1:3.098)
• Velocity scales as √λ (1:3.098)
2. Prototype (Full Scale) Dimensions & Geometry
Body (Living Area)
| Dimension | Feet | Inches |
|---|
| Length (Longitudinal) | 60 | 720 |
| Width (Beam) | 14 | 168 |
| Height | 8 | 96 |
Legs & Geometry (4 Legs Total: 2 Forward, 2 Aft)
Legs splay at 45° in both Front View (Transverse) and Side View (Longitudinal/Vertical). This implies a 3D angle where Direction Cosines are equal.
| Parameter | Value (ft) | Value (in) | Derivation / Notes |
|---|
| Leg Length (Pin-to-Pin) | 35 | 420 | Given |
| Leg Diameter | 4 | 48 | Given |
| Angle from Vertical | 45° | - | "Down and away at 45°" |
| Angle from Centerline (Plan View) | 45° | - | "Towards side at 45°" |
| Vertical Drop (Body Bottom to Leg Tip) | 24.75 | 297 | 35 × sin(45°) = 35/√2 |
| Horizontal Projection Length | 24.75 | 297 | 35 × cos(45°) = 35/√2 |
| Transverse Spread per Side (Y-offset) | 17.5 | 210 | Horiz Proj × sin(45°) = 35/2 |
| Longitudinal Reach (X-offset) | 17.5 | 210 | Horiz Proj × cos(45°) = 35/2 |
| Front Leg Tips Beam (Total Width) | 35 | 420 | 2 × 17.5 ft |
| Leg Tip Longitudinal Station (from Body Center) | ±17.5 | ±210 | Forward (+), Aft (-) |
| Submerged Length (60%) | 21 | 252 | 0.60 × 35 ft |
| Submerged Vertical Depth | 14.85 | 178.2 | 21 × sin(45°) |
| Waterline above Leg Tips | 14.85 | 178.2 | - |
| Body Bottom Above Waterline | 9.9 | 118.8 | 24.75 - 14.85 |
Cable Geometry (Tensegrity)
| Cable | Length (ft) | Length (in) | Description |
|---|
| Front Triangle (Base) | 35.0 | 420 | Distance between Front Leg Tips |
| Aft Triangle (Base) | 35.0 | 420 | Distance between Aft Leg Tips |
| Body-to-Tip Cables (x4) | 35.0 | 420 | √(17.5²+17.5²+24.75²) = 35 ft (Perfect Tetrahedral Symmetry) |
3. Model Dimensions (Scale 1:9.6)
All linear dimensions divided by 9.6. Angles remain identical.
Model Body Target Dimensions
| Dimension | Prototype (in) | Model Target (in) | Model Target (ft) |
|---|
| Length | 720 | 75.00 | 6.25 |
| Width (Beam) | 168 | 17.50 | 1.46 |
| Height | 96 | 10.00 | 0.83 |
Model Legs & Geometry
| Parameter | Prototype (in) | Model Target (in) | Notes |
|---|
| Leg Diameter (Stock) | 48 | 5.00 | Fixed by available material |
| Leg Length | 420 | 43.75 | ~43 3/4" |
| Vertical Drop (Body Bottom to Tip) | 297 | 30.94 | ~30 15/16" |
| Horizontal Projection | 297 | 30.94 | - |
| Transverse Spread per Side (Y) | 210 | 21.88 | ~21 7/8" |
| Longitudinal Reach (X) | 210 | 21.88 | ~21 7/8" |
| Front Tips Beam (Total) | 420 | 43.75 | - |
| Submerged Length (60%) | 252 | 26.25 | ~26 1/4" |
| Submerged Vertical Depth | 178.2 | 18.56 | - |
| Body Bottom above Waterline | 118.8 | 12.38 | - |
Model Cable Lengths
| Cable | Prototype (in) | Model Target (in) |
|---|
| Front Triangle Base | 420 | 43.75 |
| Aft Triangle Base | 420 | 43.75 |
| Body-to-Tip Cables (x4) | 420 | 43.75 |
4. Weight & Displacement Analysis (Froude Scaling: λ³ = 884.736)
Prototype displacement is derived from submerged leg volume (Body is above water static). Salt Water Density = 64 lbs/ft³.
Prototype Hydrostatics
| Parameter | Calculation | Value |
|---|
| Leg Radius | 2 ft | - |
| Submerged Length per Leg | 21 ft | - |
| Submerged Vol per Leg | π × 2² × 21 | 263.89 ft³ |
| Total Submerged Volume (4 Legs) | 4 × 263.89 | 1,055.58 ft³ |
| Prototype Displacement (Weight) | Vol × 64 lbs/ft³ | 67,557 lbs |
| Prototype Displacement (Long Tons) | / 2240 | 30.16 LT |
Model Target Hydrostatics
| Parameter | Calculation | Value |
|---|
| Scale Factor (Volume/Mass) | λ³ = 9.6³ | 884.736 |
| Target Model Displaced Volume | 1,055.58 / 884.736 | 1.193 ft³ |
| Target Model Displaced Volume | 1.193 × 1728 | 2,062 in³ |
| Target Model Weight (Fresh Water Test) | 1.193 ft³ × 62.4 lbs/ft³ | 74.4 lbs |
| Target Model Weight (Salt Water Test) | 1.193 ft³ × 64 lbs/ft³ | 76.4 lbs |
Model Leg Buoyancy Check (Actual vs Target)
Model Legs: 5" OD (Assumed 4.5" ID / 0.25" wall). Submerged Length = 26.25 in.
| Parameter | Value |
|---|
| Model Leg OD | 5.00 in |
| Model Leg ID (Est. Sch 40) | 4.50 in |
| Submerged Length | 26.25 in |
| Displaced Vol / Leg (OD) | π(2.5²)(26.25) = 514.7 in³ |
| Internal Vol / Leg (Flooded) | π(2.25²)(26.25) = 416.8 in³ |
| Net Buoyancy / Leg (Sealed) | 514.7 - 416.8 = 97.9 in³ (3.5 lbs) |
| Total Net Buoyancy (4 Legs Sealed) | 391.6 in³ (14.1 lbs) |
| Target Required Buoyancy (Model Weight) | ~2,062 in³ (74-76 lbs) |
CRITICAL DESIGN GAP: The 4 sealed legs provide only ~14 lbs of buoyancy (19% of required 76 lbs).
The Model Body MUST provide the remaining ~62 lbs of buoyancy (approx 1,670 in³ / 0.97 ft³ volume).
The legs alone are far too slender at this scale to support the Froude-scaled weight.
5. Barrel Body Analysis: 2x 55-Gallon Drums
Standard 55-gal Plastic Drum: ~22.5" OD × 33.5" Height (approx). Two connected end-to-end.
Model Dimensions (Barrel Assembly)
| Parameter | Value (inches) | Value (feet) |
|---|
| Body Length (2 Drums) | ~67.0 | 5.58 |
| Body Diameter | ~23.5 | 1.96 |
| Total Volume (External) | ~2 × 7,300 = 14,600 in³ | 8.45 ft³ (110 Gal) |
Comparison: Barrel Body vs. Froude Target Body
| Dimension | Froude Target | Barrel Actual | Difference |
|---|
| Length | 75.0 in | 67.0 in | -10.7% (Short) |
| Width / Beam | 17.5 in | 23.5 in | +34% (Wider) |
| Height | 10.0 in | 23.5 in | +135% (Taller) |
Buoyancy Check: Barrel Body
Target Model Displacement: 76.4 lbs (Salt Water).
- Barrel Assembly Max Buoyancy (Fully Submerged): 110 gal × 8.55 lbs/gal = 940 lbs.
- Required Draft for 76.4 lbs: 76.4 / (π × (23.5/2)² / 144 × 64) ≈ 0.85 inches draft.
- Legs submerged 26.25" provide ~14 lbs buoyancy.
- Body needs to provide ~62 lbs buoyancy.
- Body Draft required: 62 / (Cross Section Area × 64/1728) ≈ 0.7 inches.
RESULT: The barrel body has vastly excessive reserve buoyancy. It will float extremely high (less than 1 inch draft) unless heavily ballasted.
You MUST add ~60-70 lbs of ballast weight low in the barrels (or keel) to achieve the correct Froude-scaled displacement and vertical center of gravity (VCG).
What Full-Scale Dimensions Does This Barrel Model Represent?
If we accept the Barrel Body (67" L × 23.5" Dia) as the "Model", the implied Full Scale Prototype dimensions are:
| Full Scale Dimension | Calculation (Model × 9.6) | Result |
|---|
| Body Length | 67.0 in × 9.6 | 643 in = 53.6 ft |
| Body Beam (Width) | 23.5 in × 9.6 | 226 in = 18.8 ft |
| Body Height | 23.5 in × 9.6 | 226 in = 18.8 ft |
| Leg Diameter (Fixed by stock) | 5 in × 9.6 | 48 in = 4.0 ft (Matches Design) |
| Leg Length | 43.75 in × 9.6 | 420 in = 35 ft (Matches Design) |
Geometric Distortion Warning: Using the barrels creates a prototype that is wider (18.8 vs 14 ft) and much taller (18.8 vs 8 ft) than your 60×14×8 design.
The length (53.6 ft) is close to 60 ft.
This model tests the Leg Geometry, Tensegrity Statics, and Leg Hydrodynamics accurately (Froude scaled),
but NOT the Body Hydrodynamics (wave slamming, deck wetness, windage) due to the distorted body shape.
6. Summary & Construction Checklist
Model Bill of Materials (Target Specs)
| Item | Spec | Qty | Notes |
|---|
| Legs | 5" OD × 43.75" Long (Sealed, Watertight) | 4 | Schedule 40 PVC or Aluminum tube. Seal ends. |
| Body | 2 × 55-gal Drums (Connected) | 1 | Clean, sealed. Mount legs to drum structure. |
| Ballast Weight | ~65-70 lbs Total (Lead/Steel/Concrete) | 1 Lot | CRITICAL. Place LOW in drums (bottom 6") to lower VCG. |
| Front Triangle Cable | 43.75" Long (Adjustable) | 1 | Dyneema/Spectra or Steel Cable. Turnbuckles recommended. |
| Aft Triangle Cable | 43.75" Long (Adjustable) | 1 | Dyneema/Spectra or Steel Cable. Turnbuckles recommended. |
| Body-to-Tip Cables | 43.75" Long (Adjustable) | 4 | Connect Leg Tips to Center Bottom of Body Assembly. |
| Leg Attachment Fittings | Universal Joints / Ball Joints | 4 | Must allow 45° cone of motion. Body attach: Center Bottom. |
Key Assembly Geometry Checks
- Leg Angles: Verify 45° from vertical and 45° from centerline in plan view. Tip-to-Tip beam = 43.75". Tip Longitudinal offset from Body Center = 21.88".
- Waterline: Mark 26.25" up from leg tips. Body bottom should be 12.38" above this line (43.75" - 26.25" - 12.38" check: Vertical drop is 30.94". 30.94 - 26.25/√2? No. Vertical drop = 30.94. Submerged vertical = 18.56. Body bottom above WL = 12.38. Correct.)
- Cable Lengths: All 6 cables (2 Triangles + 4 Body-Tips) = 43.75 inches pin-to-pin.
- Tensegrity Pre-tension: Cables must be tight enough to hold triangles against body weight (76 lbs model weight) pushing legs outward. Est. tension per cable ≈ Weight / (4 × sin(45°)) ≈ 76 / 2.828 ≈ 27 lbs per cable minimum static tension.
Generated for Seastead Tensegrity Model Design | Froude Scale 1:9.6 | Units: Inches / Pounds
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