This is a quick introduction to the baseline spar buoy seastead design. A spar buoy is a long beam that is ballasted to reside vertically in the water. Interesting living structure is placed on the top end of the beam. This structure on top is typically extended out from the beam via a construction technique called a cantilever to increase the amount of living area and sunlight collection area.

Why Use A Spar Buoy?

The reason for the spar buoy design is to minimize interaction with waves. The less cross sectional area at wave level, the less wave coupling there will be. An example of this is the waves that sweep under a pier that rests on timber pilings without much fuss. This is in stark contrast to a solid pier where the waves will smash into the side and generate spectacular splashes. Minimizing interaction with waves has two overall benefits. First, there is less overall wear and tear on the structure. Second, the platform is more stable and comfortable for humans to live on. There is a trade-off when selecting the spar diameter. For spar where humans are expected to live in the spar, a larger diameter provides more floor space for each level in the spar. For example, a spar diameter of 6 meters results in a floor area of 28.27m² (=304.34ft².) However, larger spar diameters are more expensive to construct and deploy. Thus, this is a tension between providing as much usable living area within the spar and containing overall costs.

Basic Spar Design (no ballast)

For the baseline design, the spar buoy is made out of concrete. The over volume Vo is:

V_o = πR²H

where R is the spar radius and H is the spar height. The baseline spar is manufactured out of concrete with a wall thickness of T. The overall concrete volume V_c is:

V_c = V_o - π(R-T)²(H-2T)

which is computed by subtracting a the interior volume from the exterior volume. The interior volume is a cylinder of diameter 2(R-T) and height (H-2T). It should be noted that it is anticipated that the concrete will be reinforced with something -- rebar, carbon fibers, fiberglass to make it stronger that regular concrete. The mass of the concrete cylinder is:

M_c = V_cD_c

where D_c is the density of concrete (2.400gm/cm³). The maximum amount of water that the cylinder can displace is

M_w = V_aD_w

where M_w is the density of water (1.000gm/cm³ for fresh water and .025gm/cm³ for salt water.) As long as M_w > M_c, the cylinder will float, otherwise it will sink (M_w < M_c). If the two masses are exactly equal, the cylinder is at neutral buoyancy (M_w = M_c). The center of mass for such a cylinder is in the exact center. The center of buoyancy is at the center of the displaced water.

Ballasted Spar Buoy

In order to get the cylinder to stick straight up, it is necessary to ballast one end of the cylinder on the inside with a relatively dense material. Our baseline ballast is scrap steel with a density of 7.85gm/cm³. As long as the center of mass of the cylinder plus ballast is below the center of buoyancy, the spar will tend towards the vertical position. The further the center of mass is under the center of buoyancy, the more difficult it is to tip the spar. The ballast is a cylinder of steel of diameter 2(R-T) and height H_b. This results in ballast volume V_b of:

V_b = π(R-T)²H_b

that has a total mass of M_b of:

M_b = V_b D_b

where D_b is the density of steel at 7.85gm/cm³. A cut-away version of a ballasted spar buoy is shown floating vertically in blue water with a the steel ballast shown in red:

(Please click on image for a larger version.) The total mass of the ballasted cylinder M_t is:

M_t = M_c + M_b

by Archimedes principle, M_t water will be displaced by the spar. The amount of spar below the water line is F:

F = M_t/M_w

The center of buoyancy is at the center of the displaced water:

H_b = F H / 2

where H_b is the distance from the bottom of the cylinder to the center of buoyancy. Computing the center of mass for the ballasted cylinder is a bit harder. Working through the math does not yield a very pretty or useful equation. Instead of grinding away at the math, a more intuitive approach is taken. The concrete has a density of 2.40gm/cm³. When under water, the water density is subtracted to get a relative density of 1.4gm/cm³. The steel ballast has a density of 8.85gm/cm³ with a relative density under water of 7.85gm/cm³. Thus the relative contribution of the steel ballast to the concrete is 7.85/1.4 = 5.6. Thus, the steel ballast takes up 1/5.6 as much volume as the equivalent amount of concrete ballast. In economic terms, it is not until the steel costs more than 5.6 times per volume than concrete that it is useful to substitute concrete for ballast over steel.

Safty Hull

After the ballasted spar, the next aspect of the spar buoy design is the safety hull. The purpose of the safety hull is two fold.

• First, it provides insurance against sinking if the spar buoy springs a leak. In this case, the any people living in the spar evacuate out of the spar while the entire structure comes to rest on the water surface resting on the safety hull. The safety hull has enough buoyancy to keep the whole seastead floating.
• Second, the safety hull provides a substantial volume of living/work area for the seastead. While its primary purpose is for a safety backup, it also provides for storage, work shops, etc.

A cut-away version of a ballasted spar buoy with safety hull is shown floating vertically in blue water with the safety hull in green:

(Please click on image for a larger version.) Additional struts from the bottom of the safety hull to the side of spar can be added for additional strength. These struts are not shown in the picture. In order to minimize the weight of the safety hull, it is desirable to build it out of materials that are as light as possible. Traditional materials such as wood and aluminum are possible. If necessary, the safety hull could be built out of steel. However, there are interesting alternatives that can be explored. For example, a sandwich of styrofoam with thin sheets of metal or wood on either side is light, strong, and resistant to damage. To further improve the safety hull, it needs to be partitioned into a few rooms so that if one of the rooms becomes damaged, the other rooms remain water tight and retain buoyancy. While the first priority of the safety hull is to provide buoyancy in the event of a spar buoyancy failure, the vast majority of the time, the safety hull will be used as work and storage space. While large bay windows are out of the question for the safety hull, small sealed windows near the top edge are permissible to let the light in. In addition, there needs to be an air ventilation strategy for getting fresh air into the safety hull.

Additional Living Structure

The surface on top of the safety hull is basically the "land" that has been constructed via the seastead. More conventional and visually interesting structures can be placed here. Each kilogram of mass added on here, requires a corresponding kilogram of mass down in the steel ballast and an associated increase of buoyancy in both the spar and safety hull. Thus, the living structure on top of the safety hull will tend to be light. The picture below shows the living structure as a purple octagonal structure sitting on top of the safety hull:

(Please click on image for a larger version.) Each seastead will probably customize the living structure for the desired tastes and needs of the owner, so no further elaboration is presented here. The top of the living structure will probably be populated with food gardens and solar energy collection. Some of the solar panels, may be leveraged out even further to grab as much solar energy as possible. Any wind turbines may stick down from the safety hull since, they are actually insensitive to light conditions. Of course, down pointing wind turbines make take some damage if the main spar springs a leak.

Buoyancy Control

In general, the spar buoy will remain pretty much up right. However, if the inhabitants of the seastead stack more mass on one side than the other, there will be small tilt to the floor. In addition, as more mass is loaded onto the seastead it will float lower in the ocean. The ability to adjust overall buoyancy will allow the the seastead to control both its tilt and overall elevation above the water. For an internally ballasted spar, the current proposal for buoyancy control is to have some side buoyancy tanks attached to the bottom of the spar.

(Please click on image for a larger version.) The picture above has four open ended buoyancy control tanks that can be differentially inflated to compensate for floor tilt. In addition, all four tanks can have air pumped in to compensate for additional mass and vice versa. A pretty standard air compressor is used to pressurize the buoyancy tanks. The compressor is located up on the top of the spar with pressurized lines running down to each of the four buoyancy tanks. If the only valve is at the top, a pressurization line failure will cause the buoyancy tank to fill with water. Thus, there is a desire to have a safety value right at the base of the tank. This safety valve is normally closed and will only open when an electrical current opens it. Indeed, it may be prudent to have to safety valves in series.

Station Keeping

In a community of seasteads, it is important that the seasteads not bump into one another. For the baseline seastead, it is assumed that bridges connecting the seasteads will be not be viable. Instead, for the baseline seastead, it will be kept relatively motionless to one another via station keeping propellers. There will be four propellers located on the four sides of the spar. It is important that the seastead be able to move without requiring any rotation. The reason for the non-rotation requirement is because the top of the seastead may be covered with solar panels that have limited sun steering ability. With 4 propellers mounted 90 degrees apart, the seastead can independently move in X (i.e. East/West) and Y (i.e. North/South). In addition, if a twisting motion is required, the propellers can be spun differentially to accomplish that task. The overall goal is to have station keeping run off the solar panels and battery storage so that no fossil fuel needs to be imported for this task.

Summary

That pretty much wraps up the initial baseline seastead design. It is expected that there will be a multitude of alternative designs generated and compared for ease of construction, cost, safety, etc. For example, the next variation of this design uses external ballast. Another design uses an open truss instead of closed spar. All of these designs need to be proposed and analyzed.