Flyback Launch Magnet Sleds
At the end of the acceleration run and a coasting run (for launch angle adjustment), the vehicle is released and the sled decelerates. Assuming some allowance for drag, an escape-velocity launch is about 10.7 km/s. Assuming a 5 tonne vehicle and a 2 tonne launch sled accelerating at 30 m/s², the sled can produce 210 kN of thrust. Assume it can produce the same deceleration thrust after release that is -105 m/s².
The old method to recycle the sled was to slow it to a stop at east station, perhaps 550 km of slowdown run. Then it would be lowered to the surface, loaded on a cargo aircraft on a floating runway, and flown back to the logistics base at below west station. This is time consuming and expensive; the cycle rate for a sled might be twice a day, and the cost of a sled might approach $300K. That is a lot of expensive capital expense, for both sleds and aircraft.
An alternative method is to merely slow the sled to LEO orbit velocity, use wing lift to deflect it upwards a few meters per second, and launch it for a reentry a few thousand kilometers west of west station, where it drags and reenters. The heat of reentry may demagnetize the NdFeB magnets, so a re-magnetizing step during sled refurbishment (in addition to heatshield and parachute replacement) may be required before re-use.
Assume a 2500 km long launch loop. Assume launch-to-escape with an Earth-relative release velocity of 10.64 km/s.
After vehicle release at 2187 km track distance (including 300 km of launch-point-adjusting coasting distance), the sled decelerates at -105 m/s² from 10.64 km/s to 7.87 km/s, using 244 km of track. At 2431 km distance from west station (69 km from east station), the sled releases from the loop and aerodynamically accelerates vertically to add 12.1 m/s of radial (upwards) velocity. This puts the sled into a 78 km X 130 km altitude orbit. The orbit "reenters" at 80 km altitude 4540 seconds later, 5110 km west of the sled launch point - except that the earth has rotated eastward 2140 kilometers in that time, and will rotate more during sled entry.
The sled will enter inverted, lift down, at 7.87 km/s tangential (horizontal) velocity. The sled (with vestigal wings, or as a lifting body) is assumed to have a drag of 25 m/s² and a lift-to-drag ratio of 0.4. As it slows to 7.38 km/s, it will roll to rotate the lift vector sideways, and continue to roll clockwise or counterclockwise to shape the entry azimuth, altitude, and descent rate, resembling Apollo and MSL roll-maneuvering entry.
The sled flies 2290 km eastward, slowing to sub-mach velocities, and descends to perhaps 10 km altitude (28,000 feet), where it releases a pair of drogue chutes. At this place and time, an aircraft catches the chutes and reels in the sled, much like the mid-air captures used to snag reentering film canisters from the Corona spy satellites in the 1960s. The plane (one of many) flies to the floating airstrip below west station, where its cargo of launch sleds are removed. The plane is serviced, refueled, and returns to the capture area to catch more incoming sleds.
A fleet of (presumably robotic) planes may capture as many as 2000 sleds per day, which were used to launch perhaps 10,000 metric tonnes to orbit per day for a minimum scale launch loop.
An illustration goes here someday.
Crude libreoffice spreadsheet with some hypothetical numbers.
On The Other Hand ...
This uses up a LOT of energy; for 700,000 7.38 km/s entries at 2 tonnes each, that is 3.8e16 joules per year, or 1.2 GW average. Using $50/MHr electricity, more than half a billion dollars worth. A 2 day supply of 4000 sleds at $300,000 each is $1.2B, probably cheaper than the power plant.
The sled entry will probably create NOX emissions, and the heat shields and parachutes must be replaced every trip. Some sleds will not be recovered. Perhaps this option should be reserved for special high mass launches above escape velocity, which "run out of runway" on a normal-length loop.
In any case, it is MUCH faster and lower energy to use the westbound segment of the loop, at altitude, to return the sled at high speed to west station for another vehicle launch. If the testing, refurbishment, and heat-shield fitting was quick, this could cycle a sled faster than once per hour.