```html Seastead Scale‑Model Calculations

Seastead – Froude‑Scale Model Calculations

Goal: Use 5‑in‑diameter cylinders for the legs and two 55‑gal plastic barrels for the “body” to build a 1:9.6 (full‑scale : model) replica. All linear dimensions are given in inches (in) and weights in pounds (lb). Conversions to feet are shown for convenience.

1. Scale Ratio

Full‑scale leg diameter = 4 ft = 48 in. Model leg diameter = 5 in.

Scale factor (full : model) = 48 in / 5 in = 9.6 : 1.

Thus the model is 1⁄9.6 ≈ 10.4 % of the full‑scale size in every linear dimension.

2. Leg Dimensions

Parameter	Full Scale	Model (scaled)
Diameter	48 in (4 ft)	5 in (by design)
Length	35 ft = 420 in	420 in ÷ 9.6 = 43.75 in (≈ 44 in)
Vertical drop (45° incline)	35 ft × sin 45° = 24.75 ft = 297 in	297 in ÷ 9.6 = 30.9 in
Horizontal offset (45° incline)	35 ft × cos 45° = 24.75 ft = 297 in	297 in ÷ 9.6 = 30.9 in
Submerged length (≈ 60 % underwater)	0.60 × 420 in = 252 in	0.60 × 43.75 in = 26.25 in

3. Body (Living‑Area) Dimensions

Full‑scale body: 60 ft × 14 ft × 8 ft → 720 in × 168 in × 96 in.

Model body using two 55‑gal barrels

Typical 55‑gal plastic drum: 22.5 in OD, 33.5 in height (empty).

Two drums end‑to‑end → model length = 2 × 33.5 in = 67 in.
Model diameter (width) = 22.5 in.

Dimension	Model (with barrels)	Full‑scale equivalent (×9.6)
Length (along the hull)	67 in (≈ 5 ft 7 in)	67 in × 9.6 = 643 in = 53.6 ft
Width / Diameter	22.5 in (≈ 1 ft 10 in)	22.5 in × 9.6 = 216 in = 18 ft
Height (if placed on side)	33.5 in (≈ 2 ft 9 in)	33.5 in × 9.6 = 322 in = 26.8 ft

Note: The barrel‑derived full‑scale length (≈ 53.6 ft) is close to the target 60 ft; the width (18 ft) is larger than the original 14 ft. This is acceptable for a first‑order model.

4. Weight Scaling (Froude相似)

When the same material is used in model and full scale, weight scales with volume (i.e. with the cube of the linear scale factor).

Scale factor S = 9.6
Volume (and weight) scale factor = S³ ≈ 9.6³ = 884.7

Legs – steel example

Item	Full‑scale weight (steel*)	Model weight (steel*)
One leg (solid cylinder)	π × (24 in)² × 420 in × 0.2836 lb/in³ ≈ 215 600 lb	215 600 lb ÷ 884.7 ≈ 244 lb
All 4 legs	≈ 862 400 lb	≈ 976 lb

*Using steel density 0.2836 lb/in³ (≈ 490 lb/ft³). In practice you will probably build the model legs from a lightweight material (e.g., PVC, foam, or wood), so the actual model weight will be far lower.

Body – typical steel hull (approx. 0.5‑in wall)

Item	Full‑scale weight (steel hull)	Model weight (plastic barrels)
Hull (sheet‑metal box)	≈ 58 500 lb (see calculation below)	Two 55‑gal drums ≈ 44 lb (empty)

How the hull weight was estimated:

External surface area of the box = 2·(60·14 + 60·8 + 14·8) = 2·(840 + 480 + 112) = 2·1 432 = 2 864 ft².
Assuming 0.5‑in (0.0417 ft) wall thickness → steel volume ≈ 2 864 ft² × 0.0417 ft = 119.4 ft³.
Weight = 119.4 ft³ × 490 lb/ft³ ≈ 58 500 lb.

Buoyancy (leg‑generated)

Full‑scale: 60 % of each leg is underwater → submerged volume per leg = 0.6 × 439.8 ft³ = 263.9 ft³. Four legs → 1 055.6 ft³ displaced. Seawater density ≈ 64 lb/ft³ → buoyant force ≈ 67 600 lb.

Model (with 5‑in‑diam., 43.75‑in‑long legs):

Submerged volume per leg = 0.6 × π·(2.5 in)²·43.75 in = 515 in³ ≈ 0.298 ft³.
Four legs → 1.19 ft³ displaced → buoyant force ≈ 1.19 ft³ × 64 lb/ft³ ≈ 76 lb.

This buoyancy is more than enough to support the model body (~44 lb), giving a stable floating platform.

5. Summary Table

Component	Full‑Scale (in / lb)	Model (in / lb)	Notes
Leg diameter	48 in (4 ft)	5 in (given)	Scale 9.6:1
Leg length	420 in (35 ft)	43.75 in (≈ 44 in)	—
Leg weight (steel)	≈ 215 600 lb each	≈ 244 lb each (if steel)	Model will likely use lightweight material
Body length	720 in (60 ft)	67 in (two barrels)	≈ 53.6 ft when scaled up
Body width/dia.	168 in (14 ft)	22.5 in (one barrel)	≈ 18 ft when scaled up
Body weight (hull)	≈ 58 500 lb (steel)	≈ 44 lb (two plastic drums)	Model uses empty drums
Buoyancy (legs)	≈ 67 600 lb	≈ 76 lb	Sufficient for model

6. How to Use These Numbers

Build the legs from 5‑in‑diameter cylinders, cut to ~44 in long. If you want the 45° angle, mount each leg so that its centreline makes a 45° angle to both the vertical and the longitudinal axis of the body.
Build the body by fastening two 55‑gal drums end‑to‑end (total length ~67 in). This represents a hull roughly 53‑ft long and 18‑ft wide at full scale.
Check buoyancy: The four legs, when 60 % submerged, produce ≈ 76 lb of lift—more than the ~44‑lb weight of the barrel body, leaving margin for extra equipment or payload.
Dynamic testing: Because Froude scaling preserves the ratio of inertial to gravitational forces, the model’s motion in water will be qualitatively similar to the full‑scale seastead (wave pattern, stability, etc.).

Caution: The calculations above assume the same material density (steel) for weight scaling. In the real model you will likely use lightweight materials, so the actual model weight will be far lower than the “scaled‑steel” numbers shown. The buoyancy estimate, however, is based on water displacement and is independent of the leg material.

Enjoy building your scale seastead! If you need further details (e.g., cable tensions, motion tests, or a CAD sketch), just let me know.

```