Elevator Friction Motors
Previous versions of the launch loop west station elevator assumed a "three stage" elevator structure. A main cable loop did most of the lifting between 4 and 76 km, at 400 meters per second, while two short segments of cable loop accelerate or decelerate at two gees.
There is an easier way. First, we assume a lower west station, at 50km. Ascent speed is still 400 meters per second.
But we do not need to be so finicky about saving energy. Rather than accelerate and decelerate a loop of cable with an attached payload, we can use a "friction wheel" clamp on the main elevator cable to get up to speed. The "friction wheel" is a lightweight wheel (or wheels), a clutch, a generator, and an incandescent resistor.
At the bottom of the elevator run, the payload will be supported by a cradle with friction wheels. It will be brought up to the fast-moving elevator cable, and the unclutched wheels will be spun up, perhaps by ablative friction on the elevator cable, or perhaps by motor action. When the wheel is spinning at 400m/s, we engage the clutch and the generator until the cable is supporting the full weight of the 5 tonne cradle and payload (stationary for now). 49000 Newtons times 400 m/s is about 2 megawatts. What do we do with the heat? Waste it in a resistor! A 2 square meter incandescent tungsten band, perhaps exposed to air, inside an outwards pointing reflector. If the emissivity of the filament is 0.6 on the outward side, and 0.2 on the inward side, and there is no appreciable air cooling, it will heat up to about 2000K.
We now increase the drag to 150KN, and lift the payload and cradle with a vertical acceleration of 20m/s2, added to the gravitational acceleration of 9.8m/s2. That brings the emission up to 6MW, and the tungsten band temperature up to 2600K (incandescent lights run at 3300K). The payload accelerates upwards, with the drag power decreasing as the speed difference decreases. After 20 seconds, the payload and the elevator cable are moving at the same speed, and the drag power is zero. We engage a different clutch, and lock the wheel.
As we speed up, we would like the drag force to remain high while the drag power reduces. The drag force is proportional to generator current, while the velocity difference is proportional to generator voltage. So we would like some approximation of constant current operation. Fortunately, filament resistance increases as it gets hotter, and so the material itself does part of the regulation. The rest can be approximated with filament segments, and switches. We will want extra segments for reliability, anyway. With pendulum-and-spring activated switches, the entire regulation system could be non-electronic - positively Victorian! In actual fact, electronics will be more reliable, though probably more expensive. We will reuse the cradles many times per day, so we can spare some expense. Properly sized electronic switches will not dissipate much power, as they will only switch once or twice per ascent.
While the filaments are running near the ground, we can visually observe them from quite a distance, and monitor payload position and acceleration. The filaments will be brighter than noontime sunlight within 15 meters or so. At night, the light will be a bright as the full moon for 10km or more. Not as good as the rocket's red glare, perhaps, but still thrilling to watch!
At the upper end, we release the locked wheel, and coast vertically to a stop. We can take extra nudges of force from the elevator cable to rendezvous with the west station platform, but some other station-controlled rendezvous method (springs and bumpers? hoists?) might be lower energy and safer. The station should control the rendezvous, not the payload and cradle.
So, 20 seconds acceleration to speed at 4km altitude, a 95 second climb at 400m/s to 42 km altitude, and 40 seconds of weightless deceleration to arrive, at rest, at the west station platform at 50km altitude. Less than 3 minutes to space ... plus the decades needed to build this stuff!
Tangling
A single elevator loop helps prevent tangling. When it is running at 400m/s, Coriolis acceleration will push the upwards cable westwards at 6 cm/sec2 and the downwards cable eastwards by the same amount. That is not large, compared to the tension on the cable, but it is enough to cumulatively bow the loop apart by tens of meters (needs verification!). Payload masses will be subject to similar accelerations, and at lower altitudes, the tensions will be less, so the bowing will be "egg shaped" - wider at the bottom. That is where the wind forces are highest - how fortunate!
But starting the elevator loop will be challenging. We could take the wussy way out - run four 90 degree pulleys, widely spaced on the surface and at west station. If they were 500 meters apart, they probably would never tangle! But it might be better to use one pulley on top and on the bottom; less moment arm on the station that way, if tensions are mismatched. How to untangle two very close cables?
We can start by rotating the bottom pulley back and forth, left and right, around its vertical axis, while monitoring the top of the tangle. The lower segments will tend to swing outwards by centrifugal force, which will increase more and more the farther they can swing. Properly done (with good measurement and modelling, and adaptive turning trajectories, not willy-nilly!) this will push the separation up the pair.
These will be round cables, no sharp edges, and will tend to have quite similar wind loading. So wind forces that affects one segment will tend to affect the other. They will not be perfectly matched - there will be wind shear and rotational turbulence - but if these cables are massive enough it the effects will be relatively small. Above the tropopause, there will be relatively little wind loading, and almost no shear or turbulence.
Pulley Flanges
If there is a sudden release of tension in the cable, a "compression wave" will travel upwards, pushing the cable faster than the nominal 400m/s . That might be enough to push a loop of cable beyond the top of the upper pulley flange. The flanges will need to be much wider than might be naively expected (2 meters?), and the pulleys themselves fairly large diameter - 5 or ten meters seems right (needs verification!). The rim speed of the flanges will be high, but less than half as fast as the rim speed of some commercial power storage flywheels. The extra rotational inertia of the pulleys could cause friction against the cable, if there is an abrupt change in cable speed. All this needs further detailed analysis.