Seastead Sail/Kite Analysis

This analysis evaluates the feasibility of using the 12‑ft‑diameter, 60‑ft‑long cylindrical body as a “sail” or “kite” in a 20 mph (≈8.9 m/s) Caribbean wind. The platform is equipped with four submersible mixer thrusters, each capable of delivering up to 720 lb thrust at 3.2 kW electrical power.

1. Basic Assumptions & Calculations

Fwind ≈ 0.5·ρair·V²·Cd·(D·L) ≈ 740 lb

Each thruster can produce 720 lb thrust at full power (3.2 kW). All four together can deliver up to 2,880 lb.

2. Question 1 – Can the thrusters hold any orientation?

The side force that tends to rotate the platform is the component of the wind force perpendicular to the platform’s longitudinal axis. For a given angle β between the wind direction and the platform axis, the total wind force is

F(β) = Fwind·sinβ (lb)

The side (or “over‑turning”) force that the thrusters must counteract is

Fside(β) = F(β)·sinβ = Fwind·sin²β (lb)

The forward thrust that can be used for propulsion is

Fforward(β) = F(β)·cosβ = Fwind·sinβ·cosβ (lb)

Because each thruster can deliver up to 720 lb, the platform can resist any side force up to the maximum of 740 lb (at β = 90°). The power required scales roughly linearly with the needed thrust:

Power (kW) ≈ (required side force / 720 lb) × 3.2 kW

The table below summarises the required side force and approximate thruster power for a few representative angles.

β (deg) Fside (lb) Thruster power (kW) Comment
10° ≈ 22 lb ≈ 0.10 kW Very low side load – easily held.
20° ≈ 86 lb ≈ 0.38 kW Low power – one thruster at ~12 % of full‑power.
30° ≈ 185 lb ≈ 0.82 kW Moderate – still well within one thruster.
45° ≈ 370 lb ≈ 1.64 kW Two thrusters at ~½‑power each.
90° (broadside) ≈ 740 lb ≈ 3.29 kW Just above single‑thruster capacity – use two thrusters.

Answer: Yes – the four thrusters can hold any orientation. At 20 mph wind you need at most about 3.2 kW of electrical power (two thrusters at full‑power) to keep the platform broadside to the wind; for angles ≤ 30° the required power is well below 1 kW.

3. Question 2 – How fast would it drift sideways if broadside?

When the platform is allowed to move, the wind pushes it sideways while water drag resists the motion. Using a representative underwater projected area of about 300–400 ft² (the legs + lower part of the cylinder) and a drag coefficient of ≈ 0.5 for a fairly streamlined shape, the steady drift speed Vdrift follows

Fside = 0.5·ρwater·V²·Cd·Awet → Vdrift ≈ √[2·Fside / (ρwater·Cd·Awet)]

With ρwater ≈ 2.0 slug/ft³ (seawater), Cd ≈ 0.5 and Awet ≈ 350 ft² (average of the range), we obtain

Vdrift ≈ √[2·740 lb / (2·0.5·350)] ≈ √(4.2 ft²/s²) ≈ 2.0 ft/s ≈ 1.3 mph

Because the exact underwater area is uncertain, the drift speed is roughly 1–1.5 mph. This is modest – comparable to a very slow walking pace.

Answer: In a 20 mph wind the platform would drift sideways at about 1.3 mph (≈ 1 ft/s). This drift can be completely stopped by the thrusters as shown in Question 1.

4. Question 3 – Going 20°–30° off downwind – how well does it work?

When the platform is turned a few tens of degrees away from directly down‑wind, the wind component along the platform’s axis provides useful forward thrust while the perpendicular component must still be resisted by the thrusters.

Using the formulas from Question 1:

The forward speed is limited mainly by the water‑drag of the underwater hull. At 20–30° the platform moves at roughly 1 mph using wind alone – slower than a typical sailboat but comparable to a very light‑wind dinghy. The thrusters need only a few hundred watts to keep the platform at the desired heading, leaving most of their thrust capacity available for optional assist if you want to go faster.

Answer: The concept works – you can obtain a modest forward speed (≈ 1 mph) while needing only ≈ 0.4–0.8 kW of thruster power to maintain heading. This is far less than the 3.2 kW each thruster can deliver, so there is plenty of reserve thrust for occasional bursts or for higher speeds if you choose to augment with the propellers.

5. Summary & Practical Notes

Bottom line: The cylindrical body can indeed be used as a low‑speed “sail/kite”. In a 20 mph wind you can maintain any heading with modest electrical power (well below 1 kW for typical sailing angles) and achieve a cruising speed of about 1 mph using wind alone. If you need to go faster or to maneuver actively, the four 720‑lb thrusters provide ample reserve thrust.

All numbers are order‑of‑magnitude estimates; they are intended for preliminary design exploration rather than precise performance prediction.