Forget maglev. Imagine a 500-meter-tall concrete ballistic ramp at the edge of every major city: trains roll in at grade level, dive into a curved acceleration track, and get flung out the top on a parabolic arc to the next city. No rails between cities. No tunnels. Just physics.

The appeal: rails are expensive (~$3M/km for HSR, $50M+/km for tunnels). An arc through empty sky is free real estate.

The launch physics

To reach a city 100 km away on a parabolic trajectory (ignoring drag), the range equation gives us:

R = v² sin(2θ) / g

Optimal angle is 45°. Solving for v with R = 100,000 m and g = 9.81 m/s²:

v = √(R·g) = √(981,000) ≈ 990 m/s ≈ Mach 2.9

That's a hypersonic train. And the flight time is ~143 seconds — Chicago to Milwaukee in under three minutes. But now the problems start.

The g-force problem

To reach 990 m/s along a ramp of length L, the acceleration is a = v²/(2L). Even with a generous 5 km acceleration track:

a = (990)² / (2 × 5,000) = 98 m/s² ≈ 10 g

Passengers black out around 5 g sustained. To keep it below 3 g, the ramp needs to be 16.7 km long — longer than most airport runways and now it's not a skyscraper, it's a mountain range.

The re-entry problem

Coming down at Mach 2.9 into a "catcher" ramp is essentially a controlled crash. The kinetic energy of a 400-tonne train at 990 m/s is:

KE = ½ × 400,000 × 990² = 1.96 × 10¹¹ J ≈ 54 MWh

That's the energy of roughly 47 tonnes of TNT. Regenerative braking on the descent ramp could theoretically recover 60-70% of it (magnetic induction brakes are ~90% efficient but you lose ~30% to air drag on the arc). Net: you might recover 30 MWh per trip — enough to power ~1,000 homes for a day, or launch the next train.

The atmosphere problem (the killer)

At Mach 2.9 at sea level, aerodynamic drag on a train-shaped object (Cd ≈ 0.4, frontal area 12 m²) with air density 1.2 kg/m³:

F_drag = ½ × 1.2 × 990² × 0.4 × 12 = 2.8 MN

Stagnation temperature at the nose hits ~490°C. The train needs a titanium leading edge and the acoustic footprint on the ground is a continuous sonic boom rolling across two cities. Every launch is basically an artillery shell people are trapped inside.

The verdict

To make it survivable, cap velocity at ~150 m/s (Mach 0.44, no boom, minimal heating). But now range collapses to:

R = 150² / 9.81 ≈ 2.3 km

Congratulations, you've built the world's most expensive commuter catapult that goes from one suburb to the next.

The atmosphere is the merciless referee here: ballistic transport only pays off in a vacuum (which is why Hyperloop exists in the first place). Once you've built the vacuum tube, you may as well just... run a train in it.