Seastead Wing/Float/Leg Scale Model and Full Scale Calculations
1. Model Scale Foam Volume and Mix Requirements
Given:
- Leading edge: half of a 4-inch PVC pipe, inner width measured as 3.75 in (hence inner radius r = 1.875 in).
- Plywood pieces: 3.5 ft (42 in) long, 16 in tall, attached to each edge of the half‑cylinder.
- The interior cavity is a half‑cylinder (radius r) plus a rectangular block of width = inner width = 3.75 in, height = 16 in, length = 42 in.
Cross‑sectional Area (model)
r = 1.875 in = 0.15625 ft
h = 16 in = 1.3333 ft
L = 3.5 ft
Areahalf‑cylinder = (π/2) r² = 1.5708 × (0.15625)² ≈ 0.03834 ft²
Arearectangle = 2r × h = 2 × 0.15625 × 1.3333 ≈ 0.41667 ft²
Total cross‑sectional area = 0.03834 + 0.41667 ≈ 0.4550 ft²
Volume (model)
Volumemodel = Area × Length = 0.4550 ft² × 3.5 ft ≈ 1.5925 ft³
(≈ 2752 in³)
Mixing 2‑Part 2 lb/ft³ Foam
- Final foam density = 2 lb/ft³ → weight of foam per wing = 1.5925 ft³ × 2 lb/ft³ ≈ 3.185 lb.
- Assume expansion ratio ≈ 30:1 (typical for 2 lb spray foam). Then initial liquid volume = 1.5925 ft³ / 30 ≈ 0.0531 ft³.
- 1 ft³ = 119.688 US cups → initial liquid per wing ≈ 0.0531 × 119.688 ≈ 6.35 cups total.
- For a 1:1 mix ratio (by volume), each part ≈ 3.2 cups per wing.
- For three wings, triple the amounts: ≈ 9.5 cups total, or 4.8 cups of each part.
Adjust the expansion ratio and mix ratio according to the manufacturer’s specifications.
2. Model Weight for 50 % Immersion
Given:
Three wings/legs, each 50 % submerged in seawater (γseawater ≈ 64 lb/ft³).
Calculation
Submerged volume per wing = 0.5 × 1.5925 ft³ = 0.79625 ft³
Total submerged volume (3 wings) = 3 × 0.79625 = 2.3888 ft³
Buoyant force = 2.3888 ft³ × 64 lb/ft³ ≈ 152.9 lb
To float with half of each wing immersed, the total model weight should be ≈ 153 lb. This includes the foam (≈ 9.6 lb) plus any additional structure, equipment, and ballast.
3. Froude Scaling (1:6 Scale Model → Full Scale)
Full‑Scale Dimensions
| Dimension | Model | Scale Factor | Full Scale |
|---|
| Span (length along water) | 3.5 ft | ×6 | 21 ft |
| Width (inner width / chord width) | 3.75 in | ×6 | 22.5 in = 1.875 ft |
| Height (vertical) | 16 in | ×6 | 96 in = 8 ft |
| Chord length (leading edge to trailing edge) | 5.625 in | ×6 | 33.75 in = 2.8125 ft |
Full‑Scale Displaced Water (Half Immersed)
Volume of one full‑scale leg = Volumemodel × 6³ = 1.5925 ft³ × 216 ≈ 344.0 ft³
Submerged volume per leg = 0.5 × 344.0 = 172.0 ft³
Displaced water weight per leg = 172.0 ft³ × 64 lb/ft³ ≈ 11,008 lb
For three legs: total displaced weight ≈ 33,024 lb
Drag Force to Move at 1, 2, 3 MPH (Low Cd Direction)
Assumptions:
- Orientation: flow parallel to chord (leading edge forward) – lowest drag.
- Only the submerged half (4 ft of the 8 ft height) contributes to drag.
- Frontal area per submerged leg = span × (height/2) = 21 ft × 4 ft = 84 ft².
- Drag coefficient (Cd) for a streamlined shape ≈ 0.1.
- Sea water density: mass density ρ = 64 lb/ft³ ÷ 32.2 ft/s² ≈ 1.99 slugs/ft³.
Velocity Conversions
1 MPH = 1.4667 ft/s
2 MPH = 2.9333 ft/s
3 MPH = 4.4 ft/s
Dynamic Pressure (q = ½ ρ V²)
| Speed (MPH) | V (ft/s) | q (lb/ft²) |
|---|
| 1 | 1.4667 | 2.151 |
| 2 | 2.9333 | 8.604 |
| 3 | 4.4 | 19.36 |
Drag Force per Leg (Fd = q × Cd × A_sub)
Cd × A_sub = 0.1 × 84 ft² = 8.4 ft²
Fd per leg = q × 8.4
Total Drag Force (3 legs)
| Speed (MPH) | Fd per Leg (lb) | Total Fd (3 legs) (lb) |
|---|
| 1 | ≈ 18.1 | ≈ 54.2 |
| 2 | ≈ 72.3 | ≈ 216.8 |
| 3 | ≈ 162.6 | ≈ 487.8 |
These forces are the steady‑state drag; acceleration and waves are neglected.
4. Electrical Power Required
Assumptions
- Propeller efficiency (ηprop) ≈ 0.5 (50 %).
- Motor efficiency (ηmotor) ≈ 0.8 (80 %).
- Overall drive train efficiency η = ηprop × ηmotor ≈ 0.4.
Power Calculation
Powershaft (ft·lb/s) = Total Drag (lb) × V (ft/s)
Powerelectrical (W) = Powershaft / η × 1.3558 (conversion to watts)
| Speed (MPH) | Total Drag (lb) | V (ft/s) | Shaft Power (ft·lb/s) | Electrical Power (W) |
|---|
| 1 | 54.2 | 1.4667 | ≈ 79.5 | ≈ 270 |
| 2 | 216.8 | 2.9333 | ≈ 636.0 | ≈ 2155 |
| 3 | 487.8 | 4.4 | ≈ 2146.3 | ≈ 7274 |
Actual power may be higher due to inefficiencies, weather, and maneuvering reserves.
Summary
| Item | Value |
|---|
| Foam volume per wing (model) | ≈ 1.59 ft³ (≈ 2752 in³) |
| Cups of each part (1:1 mix, 30:1 expansion) per wing | ≈ 3.2 cups |
| Model weight for 50 % immersion | ≈ 153 lb (including foam + ballast) |
| Full‑scale span | 21 ft |
| Full‑scale height | 8 ft |
| Full‑scale chord | 2.81 ft |
| Full‑scale displaced water (3 legs, half immersed) | ≈ 33,000 lb |
| Drag force at 1 MPH (3 legs, low Cd) | ≈ 54 lb |
| Drag force at 2 MPH | ≈ 217 lb |
| Drag force at 3 MPH | ≈ 488 lb |
| Electrical power at 1 MPH | ≈ 270 W |
| Electrical power at 2 MPH | ≈ 2.2 kW |
| Electrical power at 3 MPH | ≈ 7.3 kW |
All numbers are approximate based on the stated assumptions. Adjust Cd, efficiency, and expansion ratio for specific designs.