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Seastead Wing/Leg Mold — Foam Volume, Buoyancy & Froude 1:6 Scaling
Seastead Wing/Leg Scale Model — Foam, Buoyancy & Froude Scaling
Mold volume & 2‑part foam mixing • Model weight • 1:6 Froude full‑scale size, displacement, drag & power
Geometry & Assumptions
The mold cross‑section is taken as a true “wing” taper: the half‑pipe (Ø 3.75 in,
R = 1.875 in) forms the rounded leading edge, and the two 16‑in plywood panels
tilt inward until their free edges meet at the trailing edge.
Mold cross‑section (18 px = 1 in). Waterline shown at ½ draft for the floating model.
Cross‑section area = semicircle + triangle:
A = πr²/2 + ½·w·√(s² − (w/2)²)
= 5.52 + 29.79 = 35.32 in²
Seawater density: 64.0 lb/ft³ (1025 kg/m³)
Foam: 2‑part polyurethane, finished density 2.0 lb/ft³,
mixed 1:1 by volume, liquid ≈1.08 g/mL (≈0.56 lb per cup)
Legs float long‑axis vertical (“long way up and down”); motion is in the
low‑Cd direction (leading edge first), so drag area = frontal area =
thickness × length
Streamlined‑strut drag coefficient baseline Cd = 0.08
(band 0.05–0.10)
V = A × L = 35.32 in² × 42 in = 1,483 in³
= 0.858 ft³ = 6.42 US gal = 24.3 LFoam mass = 0.858 ft³ × 2 lb/ft³ = 1.72 lb mixed liquid
≈ 3.0 cups total → ≈1½ cups Part A + 1½ cups Part B
Recommended batch (adds ~15% margin for bag/mold losses and density variation):
mix 1¾ cups of each part
Pour fast (cream time is short), the liquid expands ~30× to fill the mold.
If your kit’s ratio is not 1:1, target ~2.0 lb total mixed liquid by weight.
If instead you stand the plywood vertical (U‑channel, no taper):
Wall configuration
Section area
Volume
Foam @2 pcf
Cups total (1:1)
Per part w/ margin
Tapered to trailing edge (wing)
35.3 in²
1,483 in³ (0.86 ft³)
1.72 lb
3.0
1¾ cups each
Vertical walls
65.5 in²
2,752 in³ (1.59 ft³)
3.19 lb
5.7
≈3¼ cups each
2) Model Weight for 50% Submergence (3 legs, seawater)
A floating body displaces its own weight, so the correct total model weight equals
the weight of seawater displaced by the submerged halves:
The three foam shells themselves weigh only ≈5.2 lb total,
leaving ≈77 lb for frame, tensegrity cables, deck, motors, batteries and trim ballast.
Add/remove ballast until each leg floats at half draft.
Froude Scaling λ = 6 — Full‑Scale Dimensions
Feature
Model
Full scale (×6)
Leading‑edge diameter
3.75 in
22.5 in (1.875 ft)
Plywood panel width
16 in
96 in (8 ft)
Hinge‑to‑trailing‑edge depth
15.9 in
95.3 in (7.94 ft)
Overall chord (LE apex → TE)
17.8 in
106.6 in (8.88 ft)
Leg length
42 in (3.5 ft)
252 in (21 ft)
Section area (×36)
35.3 in²
1,271 in² (8.83 ft²)
Volume per leg (×216)
1,483 in³
320,400 in³ (185.4 ft³)
Corresponding model test speeds (divide by √6):
full‑scale 1 / 2 / 3 mph ↔ model 0.41 / 0.82 / 1.22 mph.
Full‑Scale Displacement (each leg half‑submerged)
Per leg: ½ × 185.4 ft³ = 92.7 ft³ × 64 lb/ft³
= 5,933 lb
3 legs: ≈17,800 lb (≈8.9 short tons of seawater displaced — this is the full‑scale
vessel’s total weight allowance at design draft.)
3) Drag Force — 3 Full‑Scale Legs, Low‑Cd Direction
F = ½ ρ v² Cd A
ρ = 1.99 slug/ft³; A = 3 × (22.5 in × 252 in) = 118.1 ft² frontal
Speed
q = ½ρv² (psf)
F @ Cd=0.05
F @ Cd=0.08 (base)
F @ Cd=0.10
1 mph (1.47 ft/s)
2.14
12.6 lbf
20.2 lbf
25.3 lbf
2 mph (2.93 ft/s)
8.56
50.5 lbf
80.9 lbf
101 lbf
3 mph (4.40 ft/s)
19.29
114 lbf
182 lbf
228 lbf
Wave‑making drag is negligible here (Froude number ≤ 0.17 even at 3 mph
on a 21‑ft hull), so viscous drag on the struts dominates. Expect real totals 20–50% higher once
tensegrity cables, cross‑bracing and deck appendages are added.
4) Power to Drive the 3 Legs
Thrust power P = F × v → Electrical input = P / η,
η ≈ 0.50 (propeller × motor × ESC)
Speed
Thrust power @ Cd=0.08
Electrical @ η=50%
Per thruster (electrical)
1 mph
40 W
≈80 W
≈27 W
2 mph
322 W
≈645 W
≈215 W
3 mph
1,088 W
≈2,175 W
≈725 W
1 mph: trivial — small kayak/thruster units on each leg suffice.
2 mph: small trolling‑motor‑class pod per leg (≈200–300 W each).
3 mph: roughly a 55–80 lb‑thrust trolling motor per leg (≈700–900 W each),
≈2.2 kW total — plan battery/solar accordingly.
Small slow‑turning propellers often achieve only η ≈ 0.4–0.55;
at η=0.4 the 3‑mph electrical load rises to ≈2.7 kW.
Practical Notes & Caveats
Wall angle dominates Q1. The 1.72 lb / 3‑cup figure assumes the panels
meet at a trailing edge. If yours sit vertical, use the 3.19 lb / ≈3¼‑cup‑per‑part row.
Weigh, don’t just measure. Cup conversions assume ≈0.56 lb/cup liquid.
A kitchen scale is more accurate: target 1.7–2.0 lb total mixed liquid for the tapered mold.
Molded density runs high. Constrained foam can cure 10–30% denser than the
free‑rise 2 pcf rating — another reason for the 15% margin.
Pour technique: mix parts separately, then combine and stir ~20–30 s, pour
immediately into the deepest end, tap/bounce the mold to bubble out, leave a small vent gap at the seam.
Scaling caveat: the model’s Reynolds number (≈2.5×10⁵ at Froude‑matched
speed) is lower than full scale (≈1.2×10⁶), so the model will read slightly higher
Cd than the full‑size legs — model drag tests are conservative.
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Quick highlights:
- **Q1:** Tapered-wing mold holds **≈1,483 in³ (0.86 ft³)** → **1.72 lb** of mixed foam ≈ **1½ cups of each part** (mix **1¾ cups each** for margin). If your plywood sit vertical instead, it's 3.19 lb / ~3¼ cups each.
- **Q2:** Half-submerging 3 legs displaces **≈82.4 lb** of seawater — that's your target model weight (foam shells are only ~5 lb of it).
- **Full scale (λ=6):** 21-ft legs, 22.5-in thick, displacing **≈17,800 lb** total; drag of **20 / 81 / 182 lbf** and electrical power of roughly **80 W / 645 W / 2.2 kW** at 1 / 2 / 3 mph (Cd = 0.08, propulsion η = 50%).
The most sensitive assumptions are the plywood wall angle (changes foam volume ~2×) and Cd — both are easy to update in the tables if your actual mold geometry differs.