The Icesteading Living Whitepaper (WIP)
The goal of this page is to lay out in a succinct format the technical ideas behind icesteading - seasteading, but on ice!
Icesteading means constructing new cities or countries on an artificial or natural iceberg or ice composite berg, floating on the ocean in international waters; in this whitepaper we focus on an artificial (man-made) pykrete berg.
Also we will temporarily exclude any socioeconomic and geopolitical considerations: this is a purely technical review.
Pykrete is an ice composite made from water and sawdust, first developed in WWII by a British scientist called Geoffrey Pyke - the original intent was to build a 600 meter long unsinkable aircraft carrier; addition of sawdust or other fibrous material such as straw or waste paper to ice makes it considerably stronger under tension and tougher against fracture and creep.
The reference design is a hexagonal prism with side 0.6km and height 0.3km, with lower voids filled with an inexpensive antifreeze mixture and several layers of grid-shaped voids for underground habitation and transport.
The ice is insulated on both the outside and the inner spaces by a sandwich of concrete, foam insulation and more concrete. Low thermal conductivity foundations (titanium alloys) could penetrate this insulation as foundations for larger skyscrapers.
Location
The icestead would likely be located in a part of the ocean that is warm, sunny and free from hurricanes. A large icestead could probably survive essentially any storm or hurricane, but it is useful to have other more delicate floating infrastructure around it like floating solar panels or aquaculture projects which might not survive. It will be permanently anchored to the seafloor.
Counterintuitively a warm ocean is better than a cold one, because the ice inside will be far colder than even the coldest ocean so heat loss is similar, but warm sunny areas have more energy available for cooling from solar power and OTEC power.
A politically independent icestead should also be outside of any nation’s 200nm EEZ so on the high seas. A gap exists off the west coast of Africa that’s perfect for icesteads close to Europe, there are plenty of other areas around the world that are good candidates.
Thermal analysis
Rate of heat loss for insulated ice
For structural reasons the pykrete or ice needs to be kept cold. We will consider three reference temperatures: -45°C, -70°C, and -100°C.
Ambient water temperature will vary between a maximum of about 25-30°C at the surface in the tropics to about 5-7°C 1000 meters below the surface. An average temperature of say 15-20°C for the sides and lower surface can be used.
The maximum temperature difference is therefore 120°C, the minimum is 60°C, and an intermediate case is 80°C.
The design heat flow into the ice from the outside into the ice or pykrete is 1-3W/m^2. Taking the low end of 1W/m² and 100°C = 100K, and assuming an insulation thickness of 3.5 meters, the thermal conductance should be 0.035 W/(mK). Closed cell polyurethane foam insulation has a thermal conductivity of about 0.025 W/(mK), so this heat flow is achievable in practice.
The heat leak is 1W/m² for 3.5 meter thick insulation
Closed cell polyurethane foam insulation - Engineering Toolbox
Melting time for a large iceberg
Consider a reference artificial pykrete berg with a shape as shown below: a hexagonal prism. The total volume is 0.28 cubic kilometers.
For an engineering material, uncontrolled temperature changes are not desirable. The interior can be kept at approximately constant temperature using a large reservoir of frozen antifreeze material which melts at a targeted low temperature. A candidate is calcium chloride brine or calcium chloride brine with glycerol additive; this internal reservoir of coolth is called the “Freezer Block”.
Assuming the freezer block takes up 5% of the internal volume ≈ 0.014 cubic kilometers, we can calculate the time for the entire freezer block to melt, assuming a given outside temperature.
The latent heat of fusion of such a Brine mixture is around 70-100kJ/kg and it has a density of about 1300kg/m³. We’ll take the more conservative 70kJ/kg (i.e. 91.4 kJ/L), and assume an internal temperature of -60°C and an outside temperature of 20°C. We can then calculate how long it will take to melt the freezer block with a given heat leak from the environment. We’ll estimate the internal heat leaks as being 4 extra hexagonal surfaces with side 0.6km, for a total area of 6.71km². The power-down melting time is 6 years.
The power-down melting time is 6 years
The freezer block(s) can be periodically cooled using a cooling plant. To maintain thermal equilibrium, the average power from the cooling plant must equal the average power leaking in through the insulation. This can easily be calculated: the cooling power to keep the ice solid forever is about 6.7 megawatts. This is obviously a fairly small amount of power for such a large structure, for reference the island of Manhattan is 5,500 megawatts or 93 megawatts per square kilometer.
The cooling power to keep the ice solid forever is about 6.7 megawatts
Thermal uniformity and stability
To keep the structure at close to a uniform and stable temperature, coolant pipes are needed but I believe the cooling can be passive using natural convection in a coolant fluid. A mixture of glycerol and calcium chloride brine can be created which is cheap and harmless and melts at around -70 degrees. Below that temperature it gets harder.
Structural analysis
Population capacity
From national figures, the square footage of real estate per person is around 800ft². Given an average storey height of 12 feet, this is a built volume per person of 9600ft³ or 270m³. From the 3D model, the building volume is estimated at 46 million m³, leading to a population estimate of 170,000 in this floating city. This is probably slightly too dense and more parks should be added until the population is 100,000.
The population capacity is 170,000
Strength under compression
Ice has a compressive strength that increases with decreasing temperature. It also suffers from creep deformation which decreases exponentially with decreasing temperature.
Pure water ice has a compressive strength of around 50MPa at -60°C. Source.
The self-support height for a rigid material under compression with compressive strength X is X/(ρg). This can be evaluated for ice, the answer is 5km. Loading the surface with buildings adds additional stress, but it is negligible compared to a 5km column of ice.
The self-support height for ice is 5km
Tensile strength
Adding wood fibers, rice straw fiber or some other cheap organic fiber increases the tensile strength of ice by forming pykrete. Pykrete typically has a tensile strength of 5-7MPa at a 5-15% volume fraction.
Creep deformation
Creep deformation in ice is suppressed exponentially by temperature, and it is also reduced by additives like wood pulp. More research is needed to determine the exact temperature where creep is no longer a problem, but it is somewhere between -50°C and -110°C. This stackexchange answer suggests that creep probably isn’t a problem for pure ice at -110°C and below. Pykrete likely creeps a lot less. An acceptable strain rate is 10⁻¹¹ or less.
Outer surfaces and erosion
The key to extreme longevity in the sea is a tough outer surface that will not erode in contact with saltwater. One candidate for this is geopolymer concrete.
Buoyancy and Stability
Pykrete has a density quite close to that of seawater (980kg/m³ vs 1030kg/m³ ) but the structure contains about 15-35% voids which are used for habitation and recreation. These voids mean that the average density of the pykrete berg is more like 780kg/m³, so the icestead will float with a significant amount of the structure above the waterline. This is slightly increased by the freezer blocks which are denser at 1300kg/m³, but they are only 5% of the volume.
The berg is also stable because the voids for underground habitation and underground parks are mostly in the top half, and the freezer blocks are all at the bottom. The freezer blocks are in 10 separate tanks to prevent melted thermal fluid from sloshing around.
Air and Sea Transport
Sea transport for cargo costs about $2.50 per 1000 ton-miles. Source. An oceanic icestead will likely be about 2000-5000 miles from major trade hubs, so transporting goods to it by sea will add $10 to the cost per ton, or 1¢ per kg. Much of the additional cost will not be pure transport costs but lack of economies of scale. This makes scale very important - you need to achieve something like 100,000 people to hit a critical mass.
Air transport will likely be via amphibian seaplanes like this AVIC AG600, perhaps landing in an area of sea protected by a large breakwater. Larger seaplanes can tolerate rougher seas - the AG600 can land in waves up to 2m high.
Cost of materials and construction
Pykrete
The cost of desalinating and freezing water is approximately $0.50/ton
Cheap organic fibers like rice husks or coconut bagasse can be obtained for $15-30/ton in bulk. At 10% of $20 fiber, the cost is $2/ton, for a total of $2.50/ton.
With a fill fraction of 60%, the volume needed is 0.28km³ * 0.6 = 0.168 km³.
At $2.50/ton ~ $2.50/m³ the total cost of that material is $420 million
Insulation
We also need 6.71 km² * 3.5m of insulation. Polyurethane Foam insulation costs $1500/ton in bulk and has a density of 48kg/m³, so the cost is 72kg/m³.
The total cost of the insulation is thus about $1.7bn for closed cell foam or $425M for open cell foam which has 1/4 the density. Open cell foam is likely to be adequate for most of the insulation but the parts that are adjacent to water should be closed cell as closed cell is waterproof (it will also be behind concrete). Call this $600M.
Concrete
We also need something like 20cm of basalt fiber reinforced concrete across the whole 6.71 km². Concrete costs about $100/ton, basalt fiber is $2000/ton, so 2.5% basalt fiber will cost another $50/ton on top of the concrete, so call it $150/ton total.
The concrete is $725M
Freezer Blocks
The freezer blocks need 0.28km³ * 5% = 0.014 km³, of which 70% is water and 30% is CaCl. The density of this brine is 1300kg/m³ so 18.2 megatons is needed, of which 5.5 megatons is calcium chloride. This calcium chloride will be extracted from the brine when water is purified onsite, so I will ballpark the cost at $60/ton for onsite production versus $180/ton available industrially in bulk. This is $328 million for the brine. The water component is much cheaper ($0.50/ton). They also need some concrete which we will model as 10 spheres of radius 70m. At $150/ton for concrete this adds up to $44M for the concrete shells.
Total for the freezer block is $372M
Refrigeration plant
A refrigeration plant with a 10MW cooling capacity costs around $1-$5M. For redundancy we can have four of them with two distinct designs, one of each design in four different locations. Cost estimate: $15M. This is a 10x overprovision of cooling.
Total for the refrigeration plants is $15M
Piping for internal heat transfer
We will need pipes to distribute heat around the ice to maintain uniform temperature. Something like 50 loops each 1km long are likely to be needed, with a e.g. 1.5m diameter. The best material is likely copper or a copper alloy as these metals do not become brittle, and they do have very high thermal conductivity. Assuming 1.5cm thick copper, that comes to about $170M. Wolfram Alpha Calculation. A heat transfer fluid for the pipes is also needed. At $600/ton the cost is $65M. The composition of the heat transfer fluid is unclear at this stage, but it might be something like ethanol. Wolfram Alpha Calculation.
Total for heat transfer: $225M
Air conditioning and air pumping
Ballpark this at another $35M; we can use cold ocean water from a few hundred meters down for cooling the air. We will need to pump fresh air underground.
Total for air treatment: $35M
Ordinary Utilities (water/power/sewage)
The largest is likely to be power. At 0.42kW/person, the total residential power is 70MW. Add another 10MW for cooling, 10MW for air conditioning and pumping and 10MW for other stuff and we get to 100MW. Industrial scale solar is about $1.20 per installed watt. A 3x overprovisioning will be needed to account for capacity factor, so this is about $350M. A solar thermal system can provide power overnight by storing heat. The required area is about 1.5km², so this will likely be a separate low density concrete floating island if solar power is used.
A separate smaller island with a nuclear plant could also be used. A 1/5th scale ice island would cost about 1/20th the main one and would be large enough to host a nuclear plant. At that scale concrete could also be used. $500M for a 100MW power need is reasonable. Add another $100M for the other utilities.
Total cost for electrical power and utilities: $600M
Transport/utility networks
A transport/utility network layer should be installed on the bottom surface of each inhabited layer. This is mostly just more concrete, the transport itself can be in electric vehicles like Tesla Loop One, though the vehicles would not be normal Teslas (they may be modified Teslas though). The cost here is mostly the concrete: an average of 30cm of reinforced concrete on about 1.5km², which is about $160M; add another $100M for surfacing, safety systems and other costs. Then another $50M for conduits and pipes
Total for transport and utilities: $210M
Total Cost of materials = $3.2billion
Double it to account for construction cost and you get $6.4bn. With 170,000 people the cost is $100/person/month over 30 years.
The cost is $100/person/month
Surprisingly this is definitely in the “too cheap” territory! We should probably increase the amount of green spaces/parks and decrease the population so that the icestead is more expensive per person but more pleasant/less crowded.
Scaling
These ice structures can scale up in size. The limiting factor is the strength of the ice/pykrete. Adding more fibrous material to pykrete makes it stronger and other additives can also be used such as basalt fiber which will substantially increase the tensile strength. As they become larger the optimal design gets slightly flatter as the self-support of the pykrete becomes a binding constraint. This somewhat reduces the thermal performance. But each doubling of size is roughly an order of magnitude increase in livable area, so a 4km wide icestead corresponds to about 10 million people. Larger than 4km wide, the strength of ice itself becomes a limiting factor, unless substantial progress can be made on the material itself.
Room for wilderness
Wilderness is expensive in icesteads since all useable area must be paid for. However in large icesteads it can be stacked up as a 3-dimensional forest/meadow on multiple floors with artificial skies. If each storey is 15 meters tall (50 feet) then 10-20 stories of this artificial forest can occupy a square kilometer of area with a footprint of only a city block, and that city block sized area costs about 50¢/person/month shared between 100,000 people. An artificial sky can probably be made quite cheap since it is just a powerful LED light and reflectors/refractors.
Why build underground?
large artificial icebergs are better if they are quite thick for three reasons: thermally, a more spherical shape is better, and structurally a thicker shape is stronger in flexion. Internal layers also leak heat, but since the walls of the internal chambers don’t have to touch the sea they are probably substantially cheaper to insulate (can use cheaper open cell foam and air voids) and the concrete doesn’t need to be marine-rated. Another advantage is that in a 3D city, transport is much easier because everything is closer. With electric vehicles rather than internal combustion engines air quality is a much more manageable problem.
A large icestead city is shown below with buildings ~200m tall, but without underground layers. This shows mostly wasted space inside the ice, which must be paid for.
Why not build it out of concrete?
There is absolutely a concrete version of this structure. The concrete structure will need to have significantly less material since concrete is something like 100 times more expensive than pykrete. When you have a structure with walls that are 100 times thinner, catastrophic failure becomes much more likely.
With a pykrete structure, sinking is very difficult. The walls are 50-100 meters thick and they have the ultimate waterproofing tech: they’re made out of frozen water. The entire structure is overbuilt by about a factor of 20 in terms of physical strength.
Pykrete can’t be corroded by seawater because it is water. Unlike concrete it won’t crack from moisture. It can’t burn like some metals.
Why not just use a cruise ship?
The Icon of the Seas has a Gross Tonnage of 248,000 which corresponds to an internal volume of about 782,000m³. Using the previous figure of 270m³ of real estate per person, the Icon of the Seas should be able to permanently house 2897 people. Wolfram Alpha calculation. In fact its maximum capacity is 7600 passengers and 2350 crew - cruise ships pack people in very densely. If we used that same density of people for this icestead, there would be over 500,000 people on it!
Icon of the Seas cost about $2bn to build but the maintenance over its 30 year lifespan is likely quite high as it is a thin-walled steel vessel and so must be frequently repainted, inspected, etc. Royal Caribbean estimates a $355M annual operating cost. Over 30 years this is $10.6bn, of which about 37% is expenses related to the ship such as fuel and maintenance. So the true cost of this ship may be more like $2bn + 37% * $10.6bn = $5.9bn, which is quite similar to the cost of the icestead excluding its maintenance, which will hopefully be substantially less than for a steel ship.
An icestead must also last essentially forever so it can’t really be made from steel. It is a place on the map, not a vehicle. It is also important that an icestead is unsinkable by conventional means. No conventional bomb or torpedo known to man can break a 50-meter thick ice wall. But a cruise ship like Icon of the Seas is very vulnerable - a few heavyweight torps would sink it.
Major Technical Risks
A few major technical risks that could completely kill this idea:
(1) Creep deformation of ice and ice composite materials under stress is still a big uncertainty. Lower temperature and additives may be able to eliminate creep, but lower temperature also has undesirable effects (greater heat transfer, more difficult to find cheap working fluids)
(2) Pykrete may be weaker under compression than I think it is (there’s a lot of variance in the literature)
(3) It may be too costly to build large ice/pykrete structures to a precise standard
(4) There’s still some uncertainty in how large a self-supporting pykrete chamber can be before the walls are at risk of collapse
Reflections from the Author
The reference design presented here is probably inefficient with three 60-70m layers underground and would work better with 2 thicker layers each about 120 meters high, likely reducing the insulation and concrete requirements by 20% and giving people inside more space. The layers could probably also be optimized to occupy more volume to provide more buoyancy, and also provide more space.