Four-Tower Module

Four towers stand at the corners. Plastic film on a fine cable net is strung between their outer faces. A slab of ice heavy enough to balance the air pressure roofs the courtyard, and steel ties between the towers hold the walls in.

Click to look (Esc releases) · WASD move · Shift run · Space jump · V fly · Scroll fly fast · 1–9 views · R see-through roof · F full screen

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walking

Load sheet

first-order statics

Courtyard–

Air–

Tower floors–

Ice roof

Ice this thick passes blue-green light and strips most of the red, so the garden needs grow lights. The slab has to stay below 0 °C over a 20 °C courtyard: it needs insulation underneath and a cover film on top to stop it sublimating.

Sky funnels

Spreading force across the module

–pushing the two halves apart

Colour these members in the 3D view

Design

Make one wall ice (the side the tower-gap view faces)

Modules

Diagonal ties across modules with kinked corners

Members

Hold-down

How these numbers are worked out

Cut the module through the middle. The air pushes the halves apart with p × the cross-section area. Everything crossing the cut pulls back: the hoop cables in the two walls (T = p·R at mid-height) and the straight ties. The ties take whatever is left. The ice slab could carry some tension too, but ice is brittle, so it is left out.

Ice roof: thickness = p / (ρg) with ρ = 917 kg/m³. The slab rests on sliding bearings on the tower tops and covers the whole footprint, so its weight balances the pressure over the courtyard and the tower roofs alike.

Lost pressure: the slab spans between the towers it already sits on. Its peak bending is taken as 1.5 × a one-way span across the gap (it is held only at the towers), checked against 1 MPa for cold ice with a safety factor of 1.5. Post-tension squeezes the ice by the chosen amount each way. If the ice still cracks, the tendons are checked as reinforcement in the cracked slab.

Wrapped walls: each film wall spans from one tower's outermost corner to the next and rises straight from the ground, with the ice slab extended over its bulge. With no curvature up the wall, the hoops carry everything; they are gathered into belt tendons that run unbroken round the corners (frictionless saddles), so each wall's hoop tension is the same. Ties are worked out from a cut each way through the module. With an ice wall, the towers beside it are anchored into its ends, so the belts' pull offsets the air's push on it; on the circle through the four outer corners the two cancel and only the ice side needs ties.

More modules: each new one joins a module already built along a whole side, sharing its two towers, and its walls clamp to the existing corners. Along a straight run the new wall clamps to the same outer corner as the old one; where two modules make an inside corner, both walls end on the tower corner facing out, so the older wall is re-clamped there. Each module's walls bow onto the circle through the corners they clamped to when it was built, and the belts are clamped wherever walls from two modules meet, so their tension steps from one module to the next. A wall pulls on each clamp with p·H·(e along the chord + half the chord outward), e being the distance from its arc's centre to the chord. Ties along every side between two towers, the ice wall's anchors and buttress, and the tower footings balance these pulls. Of all the sets of forces that do, the sheet takes the one with the least strain energy in ties of equal size (the elastic answer), treating the buttress and footings as far softer.

Ice wall: a 4 m upright slab backed by a continuous ice buttress, a wedge reaching out to its toe. Per metre of wall, the air's push acts at mid-height; tipping is checked about the toe and sliding on friction (μ = 0.5), both against a safety factor of 1.5, with the roof edge over the wall counted as weight. The ties on that side still hold the towers against the courtyard pressure; each side's ties carry their own half of the cut.

Creep: in service the air carries the ice, so its only lasting stress is the post-tension. Glen's flow law (Cuffey & Paterson 2010) gives the creep rate under that biaxial squeeze. The tendons are re-tensioned when they have lost 10% of their stretch.

The towers are pressurised too. They weigh 1.2 t per m² of floor per storey (g = 3.71 m/s²); the ice over their roofs balances their uplift, so they need no anchors.

Cable steel is sized at 1 GPa working stress. The film spans between net cables with pillows that sag 10% of the mesh and is sized at 50 MPa.

Sky funnels: each mirror stands on a mast north of its funnel, since the sun keeps to the southern sky here. It tracks the sun and sends the light 25° off vertical into the cowl, so it catches its area × the cosine of the angle it meets the sun at. Direct sun is 590 W/m² above the air, dimmed by dust of optical depth 0.5 along the slant path. Light is counted at 95 lm and 2.0 µmol/s of plant light per watt, and a sol gives about 7 hours' worth at the rate the sun in the view gives. The tube loses 3% at each bounce. Each tube leaves a hole in the slab; the window at its throat takes the air's push over the hole and passes it into the ice round the sleeve, a shear of a few kPa.

Not modelled: tower bending between tie levels, thermal and seismic loads, the floor, the sliding seal between the slab and the towers, mirrors shading each other.