# Incline Shape and Velocity

If west station is below main 80 km track altitude, it is more protected from space debris and the elevators are shorter and faster. However, a vehicle launched at a full 30 m/s² acceleration from a lower altitude will soon encounter a velocity/drag limit, creating hypersonic heat from nose and sled drag. So, assuming a somewhat inclined track above the station, gentling out to a horizontal track at 80km at full speed, what is the best shape for the first (say) 500 km of track?

### West Upward Deflector

Norway's 287m deep Eiksund Tunnel was the world's deepest undersea tunnel in 2008. Norway's 392m deep Rogfast Tunnel is scheduled for completion in 2025.

These run much deeper than the air spaces of caissons of floating oil drilling platforms. Deep sea submersables range much deeper still, but those pressure hulls are very thick spheres, not long tubes.

Presume a limit of 500 meters depth. With a 5 km curvature, that is a 26° beginning incline, and for a 10 km curvature, an 18° beginning incline.

### Pre-station West Incline

This should be as steep as possible, limited by the maximum incline slope leaving the western upward deflector, the ocean depth at the bottom of the curve, and the length of the bolt-to-rotor assembly stage just above the upward deflector. The steeper the west incline, the more deflection force available to support West Station, the west deflection cables, and the west elevator cables.

### Post-station West Incline

If west station is at 40 km altitude, and the incline above west station is 5° (WAG), tangent 0.087 or 11 km horizontal per 1 km vertical, a circular curve up to 80 km altitude would have a radius of 10500 km and a track length of 460 km. Drag heating is the air density times the velocity cubed, so for a drag limit comparable to a 10 km/s exit drag at 80 km, ...