Asymmetric Hull Design
Mathematical Definition
OSEP-16 Main Hull: Mathematical Definition
Design Parameters
Overall Dimensions
- LOA (Length Overall): 16’ 0” (4.88m)
- Beam (max): 24” (0.61m) at widest point
- Draft: 8” (0.20m) loaded
- Rocker: 3” (0.076m) total (1.5” each end from centerline)
Hull Form Type
- Asymmetric Proa Hull
- Leeward side: Flat panel with minimal rocker
- Windward side: Rounded with moderate rocker
- Symmetry: Bow = Stern (shunting design)
Station Layout
11 stations spaced 1’7.2” (488mm) apart:
Station 0: 0' (bow/stern #1)
Station 1: 1' 7.2"
Station 2: 3' 2.4"
Station 3: 4' 9.6"
Station 4: 6' 4.8"
Station 5: 8' 0" (center/max beam)
Station 6: 9' 7.2"
Station 7: 11' 2.4"
Station 8: 12' 9.6"
Station 9: 14' 4.8"
Station 10: 16' 0" (bow/stern #2)
Cross-Section Geometry (Stations 0-10)
Coordinate System
- Origin: Centerline at DWL (Designed Water Line)
- X-axis: Beam (+ = windward, - = leeward)
- Y-axis: Height (+ = up, - = down)
- Z-axis: Length (+ = aft, - = fwd) from station 5
Station Offsets Table
| Format: Station | Z-position | Beam-Windward | Beam-Leeward | Height-Sheer | Height-Keel |
Station 0 | -96" | 0" | 0" | 12" | -2" (point - bow/stern)
Station 1 | -77" | 6" | 6" | 14" | -4"
Station 2 | -58" | 9" | 9" | 15" | -6"
Station 3 | -38" | 11" | 11" | 16" | -7"
Station 4 | -19" | 11.5" | 11.5" | 16" | -7.5"
Station 5 | 0" | 12" | 12" | 16" | -8" (max beam - center)
Station 6 | +19" | 11.5" | 11.5" | 16" | -7.5"
Station 7 | +38" | 11" | 11" | 16" | -7"
Station 8 | +58" | 9" | 9" | 15" | -6"
Station 9 | +77" | 6" | 6" | 14" | -4"
Station 10 | +96" | 0" | 0" | 12" | -2" (point - bow/stern)
Asymmetric Sections (Key Innovation)
At each station, the cross-section is ASYMMETRIC:
Leeward Side (Flat)
- Shape: Nearly flat panel from keel to chine
- Angle: 8° deadrise at keel, flattening to 3° at chine
- Purpose: Lateral resistance (acts as daggerboard)
Windward Side (Rounded)
- Shape: Curved from keel to chine
- Radius: Variable (tighter at keel, gentler at chine)
- Purpose: Hydrodynamic efficiency, wave shedding
Station 5 Cross-Section Detail (Max Beam)
Leeward Side Points:
Point L1: X = -12", Y = -8" (keel)
Point L2: X = -11", Y = -4" (flat panel mid)
Point L3: X = -10", Y = 0" (chine)
Point L4: X = -8", Y = +8" (sheer turn)
Point L5: X = 0", Y = +16" (sheer/deck)
Windward Side Points:
Point W1: X = +12", Y = -8" (keel)
Point W2: X = +11", Y = -4" (curved section)
Point W3: X = +10", Y = 0" (chine)
Point W4: X = +8", Y = +8" (sheer turn)
Point W5: X = 0", Y = +16" (sheer/deck - same as leeward)
Curve Definition:
- Leeward: L1→L2→L3 = straight segments (3° deadrise)
- Windward: W1→W2→W3 = Bézier curve (control points below)
Bézier Curve Control Points
Windward Keel-to-Chine Curve (Station 5)
Cubic Bézier:
- P0 (start): (12”, -8”) - keel
- P1 (control): (12”, -6”) - pulls curve tight at keel
- P2 (control): (10.5”, -1”) - gentles curve at chine
- P3 (end): (10”, 0”) - chine
Equation:
B(t) = (1-t)³×P0 + 3(1-t)²t×P1 + 3(1-t)t²×P2 + t³×P3
where t ∈ [0,1]
Sample points (t = 0, 0.25, 0.5, 0.75, 1):
t=0.00: (12.00", -8.00")
t=0.25: (11.78", -6.23")
t=0.50: (11.25", -4.13")
t=0.75: (10.59", -1.73")
t=1.00: (10.00", 0.00")
Sheer Line (Deck Edge)
Top View - Sheer Curve
Symmetrical (both sides same):
Station | Z-position | Beam at Sheer | Height
--------|------------|---------------|--------
0 | -96" | 0" | 12"
1 | -77" | 6" | 14"
2 | -58" | 9" | 15"
3 | -38" | 11" | 16"
4 | -19" | 11.5" | 16"
5 | 0" | 12" | 16"
6 | +19" | 11.5" | 16"
7 | +38" | 11" | 16"
8 | +58" | 9" | 15"
9 | +77" | 6" | 14"
10 | +96" | 0" | 12"
Bézier fit for smooth sheer:
- Create spline through these points
- Use smooth tangents at ends (vertical at stations 0/10)
Rocker (Keel Curve)
Side View - Keel Rocker
Parabolic rocker (3” total rise from ends to center):
Station | Z-position | Keel Height (from DWL)
--------|------------|------------------------
0 | -96" | -2" (up 6" from center)
1 | -77" | -4" (up 4")
2 | -58" | -6" (up 2")
3 | -38" | -7" (up 1")
4 | -19" | -7.5"(up 0.5")
5 | 0" | -8" (lowest point)
6 | +19" | -7.5"
7 | +38" | -7"
8 | +58" | -6"
9 | +77" | -4"
10 | +96" | -2"
Equation (parabola):
Keel_Height(z) = -8 + 0.0003125 × z²
where z is distance from station 5 in inches
Chine Line (Leeward/Windward Transition)
Definition
The chine is where the flat leeward side meets the rounded windward side.
Side View - Chine Height:
Station | Z-position | Chine Height (from DWL)
--------|------------|-------------------------
0 | -96" | -2" (same as keel at ends)
1 | -77" | -2"
2 | -58" | -1"
3 | -38" | 0"
4 | -19" | 0"
5 | 0" | 0" (at DWL)
6 | +19" | 0"
7 | +38" | 0"
8 | +58" | -1"
9 | +77" | -2"
10 | +96" | -2"
Top View - Chine Width:
Station | Beam at Chine (Leeward) | Beam at Chine (Windward)
--------|-------------------------|---------------------------
0 | 0" | 0"
1 | 5.5" | 5.5"
2 | 8.5" | 8.5"
3 | 10" | 10"
4 | 10.5" | 10.5"
5 | 10" | 10" (chine narrower than max beam)
6 | 10.5" | 10.5"
7 | 10" | 10"
8 | 8.5" | 8.5"
9 | 5.5" | 5.5"
10 | 0" | 0"
Panel Development (3D → 2D)
Leeward Side Panel (Single flat panel)
Length: 16’ (192”) Width: Variable (follows sheer-to-chine curve) Shape: Slightly trapezoidal
Edge Curves:
- Top edge: Sheer line (curved)
- Bottom edge: Chine line (slight S-curve)
- Forward edge: Station 0 (point)
- Aft edge: Station 10 (point)
Approximate developed area: 18 sq ft
Windward Side Panel (Curved panel)
Length: 16’ (192”) Width: Variable (follows sheer-to-chine curve) Shape: Curved surface (requires “torturing” plywood)
Edge Curves:
- Top edge: Sheer line (same as leeward)
- Bottom edge: Chine line (same as leeward)
- Curvature: Develops from Bézier control points
Approximate developed area: 19 sq ft (slightly larger due to curve)
Bottom Panel (Keel centerline)
Length: 16’ (192”) Width: Variable (narrowest at ends, widest at center)
Station widths (total width, split leeward/windward):
Station 0: 0"
Station 1: 3" (1.5" each side)
Station 2: 4" (2" each side)
Station 3: 4.5"
Station 4: 5"
Station 5: 6" (widest)
Station 6: 5"
Station 7: 4.5"
Station 8: 4"
Station 9: 3"
Station 10: 0"
Verification Calculations
Displacement Volume
Using Simpson’s Rule on station areas:
Station | Area (sq in) | Simpson Multiplier | Contribution
--------|--------------|--------------------|--------------
0 | 0 | 1 | 0
1 | 42 | 4 | 168
2 | 98 | 2 | 196
3 | 138 | 4 | 552
4 | 156 | 2 | 312
5 | 168 | 4 | 672
6 | 156 | 2 | 312
7 | 138 | 4 | 552
8 | 98 | 2 | 196
9 | 42 | 4 | 168
10 | 0 | 1 | 0
Total: 3,128
Volume = (Station spacing × Total) / 3
= (19.2" × 3,128) / 3
= 20,019 cubic inches
= 11.6 cubic feet
Displacement (saltwater @ 64 lb/cu ft):
= 11.6 cu ft × 64 lb/cu ft
= 742 lbs
With 25% immersion (typical for proa main hull):
Usable displacement = 742 × 0.25 = 185 lbs (hull alone)
Full proa (with ama) = 450 lbs target ✓
Next Steps for Fusion 360
With these mathematical definitions, you can now:
- Import station point clouds (I’ll generate CSV)
- Loft surfaces between stations
- Verify volumes match calculations
- Develop panels for CNC cutting
Ready for Fusion 360 instructions?