```html Seastead Sail Analysis: Cylindrical Hull Wind Propulsion

Seastead Sail Analysis

Cylindrical Hull (12'×60') Using Wind Drag with Thruster Control

Design Summary:

Hull: 60 ft long × 12 ft diameter corrugated culvert, 8 ft above water (4 ft draft)
Displacement: ~36,000 lbs
Legs: Four 4 ft diameter columns, 45° angle, creating 50'×74' base rectangle
Propulsion: Four 2.5m propeller submersible thrusters (720 lbs thrust each @ 3.2 kW)
Total Thruster Capacity: 2,880 lbs thrust / 12.8 kW
Environment: 20 MPH (17.4 knots) Caribbean wind

Important Note on Propeller Sizing: A 2.5 meter (8.2 ft) diameter propeller cannot physically fit inside a 4 ft diameter leg. This analysis assumes the thrusters are mounted externally on the leg bottoms or the leg diameter is larger than specified. The thrust and power calculations remain valid for the performance analysis.

1. Thruster Capacity for Orientation Control

When the cylindrical hull is oriented at an angle to the wind, it experiences both a forward thrust component (along the cylinder's axis) and a side force (perpendicular to the axis). The thrusters must counteract the side force to maintain the desired heading.

Wind Force Calculations

Air density (ρ): 0.00238 slugs/ft³
Wind speed (V): 29.3 ft/s (20 MPH)
Drag coefficient (Cd): 1.3 (corrugated cylinder, turbulent flow)
Projected area: 60 ft × 12 ft = 720 ft²

F_wind = ½ × ρ × V² × Cd × Area × sin(θ)
Where θ = angle between cylinder axis and wind direction

Angle to Wind (θ)	Total Wind Force	Side Force (Thruster Load)	% of Max Thruster Capacity	Est. Power Needed*
20°	328 lbs	112 lbs	3.9%	~0.5 kW total
30°	479 lbs	240 lbs	8.3%	~1.1 kW total
45°	677 lbs	479 lbs	16.6%	~2.1 kW total
90° (Broadside)	958 lbs	958 lbs	33.3%	~4.3 kW total

*Assuming linear thrust-to-power relationship at low speeds. Actual may vary.

Answer: Yes, the thrusters can easily hold any orientation up to 90° (broadside). Even at 45° (optimal for forward thrust), they use only ~17% of available power to maintain heading, leaving 83% reserve for propulsion or station-keeping.

Yaw Control (Rotation) Authority

The 50'×74' leg base provides excellent leverage. With differential thrust (front thrusters vs. rear thrusters):

Yaw moment arm: ~74 ft
Maximum differential torque: (2 × 720 lbs) × 74 ft = 106,560 ft-lbs
Typical wind-induced yaw moment: ~15,000 ft-lbs

The system has 7× safety margin for maintaining orientation even in gusty conditions.

2. Broadside Drift Speed (90° to Wind)

If the thrusters are turned off or unable to hold orientation, the vessel will drift sideways. The equilibrium speed occurs when aerodynamic drag equals hydrodynamic drag.

Drag Components

Component	Submerged Projected Area	Drag Coefficient
Hull (60'×12' cylinder, 4' draft)	~678 ft² (circular segment)	1.0
Four Legs (4'×12' submerged each)	192 ft²	1.0
Total	870 ft²	—

F_wind = 958 lbs (from above)

F_water = ½ × ρ_water × V² × Cd × Area
958 = ½ × 1.99 × V² × 1.0 × 870
958 = 866 × V²
V = √(958/866) = 1.05 ft/s

Answer: Broadside drift speed in 20 MPH wind would be approximately 0.7 knots (0.8 MPH). This is slow due to the large submerged cross-section acting as a sea anchor.

3. Sailing 20-30° Off the Wind (Drag-Based Sailing)

By orienting the cylinder at an angle to the wind, the drag force decomposes into:

A forward component (along desired track)
A side component (countered by thrusters)

This is "drag sailing"—you cannot sail upwind, but you can control your drift angle downwind.

Force Balance at 30° Off Wind

Cylinder oriented at 30° to wind direction
Wind force component along track: 415 lbs
Side force (thruster counter): 240 lbs
Hydrodynamic drag (forward motion): 69 ft² frontal area × Cd 0.8

F_forward = 415 lbs
F_drag = ½ × 1.99 × V² × 0.8 × 69 = 54.9 × V²
415 = 54.9 × V²
V = √7.56 = 2.75 ft/s (1.9 knots or 2.2 MPH)

Performance Summary by Angle

Course Relative to Wind	Hull Angle (θ)	Wind Thrust	Thruster Side Load	Speed (Wind Only)	+ Thruster Assist*
Downwind (0°)	0° (end-on)	Minimal (~50 lbs)	0 lbs	<0.5 MPH	~5 MPH max
20° Off	20°	308 lbs	112 lbs	1.8 MPH	~5.2 MPH
30° Off	30°	415 lbs	240 lbs	2.2 MPH	~5.3 MPH
45° Off (Optimal)	45°	479 lbs	479 lbs	2.3 MPH	~5.4 MPH

*Assuming thrusters provide remaining thrust after holding angle. Max speed ~4.9-5.5 MPH depending on drag.

Answer: Sailing 20-30° off the wind works moderately well. At 30°, the wind alone provides ~2.2 MPH speed using only ~1 kW to maintain heading. This is significantly faster than the 0.8 MPH broadside drift and saves considerable battery power compared to pure electric drive (which requires ~10-12 kW to achieve 2.2 MPH against wind resistance).

Optimal Strategy

Recommendation: Sail at 45° to the wind rather than 20-30°. This provides:

Maximum wind thrust (479 lbs)
Best speed (~2.3 MPH) for zero forward electrical power
Reasonable power consumption (~2 kW) for holding the angle

To reach a destination downwind, use "tacking" downwind: alternate between 45° left and 45° right of downwind (making a sawtooth pattern) to achieve better net VMG (velocity made good) than going straight downwind, while using minimal electricity.

Technical Assumptions

Wind: Steady 20 MPH at 10m height (no gusts)
Water: Salt water, ρ = 64 lbs/ft³
Drag coefficients: Cylinder perpendicular Cd=1.2-1.3, streamlined motion Cd=0.8
Hull draft: Exactly 4 feet (50% of displacement check recommended)
Legs: Cylindrical 4 ft diameter, 12 ft submerged
Thruster efficiency: Linear with power at low speeds

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