Lower West Incline

Most of the acceleration track of the launch loop should be at 80 kilometers altitude, to avoid most atmospheric drag. However, near the start of acceleration, the vehicle is moving relatively slowly, and can tolerate higher air density. This is an opportunity to lower west station, permitting a shorter west incline, shorter stabilization cables, and a heavier incline. This detail is not essential to the launch loop, but it will save money and improve operations considerably.

The velocity along the track is V^2 ~ = ~ 2 a L . The drag is proportional to density and velocity squared, so for constant drag, the density can increase inversely proportional to track distance L+0 . The scale height H_S varies between 50km and 80km geometric altitude, but averages 7200 meters. So the height is H ~ = ~ H_0 + H_S \ln { L / L0 } , until we get so close to the west station and the west incline that the angle becomes limited.

The slope of the track is d H / d L ~ = ~ H_S / L . The curvature of the track is d^2 H / d L^2 ~ = ~ - H_S / L^2

Given a total track length of 2000 km, height versus track length might vary as:

That last entry is problematic - the incline starts at 20 degrees, and curves downwards, so the angle at west station is quite a bit less than 20 degrees. So the curve of the launch track must stop increasing somewhere above 50 km altitude. This is a "flat earth" calculation. The earth's curvature is -1 / R_E , or 1.57E-4 km^-1, so significant extra weight and cable tension is needed to curve the track and rotor as it approaches west station. Lets stop dropping the track quite so steeply at about 200 kilometers out, and

WORK IN PROGRESS, MORE LATER