Norway's Sognefjord is 1,308 m deep and ~5 km wide where Highway E39 needs to cross. You can't build a pillar bridge (seafloor too deep), a suspension span needs towers ~700 m tall (taller than the Burj Khalifa minus the spire), and a bored tunnel would have to dive to ~1,400 m below sea level — uncomfortable pressures, terrible grades. Enter the submerged floating tunnel (SFT), sometimes called an Archimedes bridge: a sealed concrete-steel tube suspended 30 m beneath the surface, held in place by tethers to the seabed.

Let's see if the physics cooperates.

Sizing the tube. Two traffic lanes plus an emergency lane and service galleries means an inner diameter of about 12 m. Add a composite wall — outer steel skin, structural concrete core, inner liner — roughly 2 m thick. So outer diameter ≈ 16 m, outer cross-section π·8² ≈ 201 m², inner ≈ 113 m². The concrete annulus has area ≈ 88 m².

Weight vs. buoyancy per meter:

• Concrete shell: 88 m² × 2,500 kg/m³ = 220,000 kg/m
• Steel reinforcement + skins (~10%): ~22,000 kg/m
• Pavement, services, traffic load (avg): ~15,000 kg/m
• Total weight per meter: ~257,000 kg → 2.52 MN/m downward
• Displaced seawater: 201 m² × 1,025 kg/m³ = 206,000 kg/m → 2.02 MN/m upward

That's negatively buoyant by ~500 kN/m. Bad — we'd need pontoons on the surface, blocking ships. So engineers tune the wall: switch to lightweight aggregate concrete (~1,900 kg/m³) and thin the shell. Recalculating with 1.2 m walls of lightweight concrete gets you to ~155,000 kg/m total — and now you have ~50 kN/m net positive buoyancy. The tube wants to rise. Now we tether it.

Tethers to the abyss. Place anchor cable pairs every 200 m. Each cable pair must hold 200 m × 50 kN/m = 10 MN in steady tension, plus dynamic loads from currents, tides, and (the scary one) accidental flooding of a section. Design for ~30 MN per cable. High-strength steel rope at 1,800 MPa needs ~170 cm² cross-section — a cable about 15 cm diameter. At 1,300 m depth, each cable weighs ~200 tonnes; the cable's own weight is non-trivial but manageable.

The seabed anchors are the real problem. Soft fjord sediment can't hold 30 MN in straight uplift — you'd need suction caissons (steel cylinders ~15 m diameter driven into mud, sealed, then pumped to create negative pressure that locks them in) or rock-anchored if bedrock is shallow. Cost per anchor: roughly that of a small offshore wind turbine foundation.

The terrifying failure modes:

• Resonance. The tube is a 5 km long beam with tethers acting like springs. Tidal currents (~1 m/s in Sognefjord) shed vortices at frequencies that must not match any structural mode. Stagger tether spacing and add hydrodynamic fairings.
• Submarine collision. A 100,000-tonne tanker at 10 m/s carries 5 GJ. The tube needs a sacrificial outer cell + active vessel exclusion.
• Cable fatigue. Every wave on the surface modulates pressure. Over 100 years that's ~10⁹ load cycles. Cables need redundancy: lose any one, the rest still hold.

Total steel + concrete for 5 km: ~800,000 tonnes — comparable to two Golden Gate Bridges, but distributed underwater where it's largely supported by its own buoyancy rather than fighting gravity from a tower top.