Launch Loop Rotor Heating During Launch

NOTE: This page is obsolete.

Transformer track launch loops will not heat the rotor significantly, less than a percent of launch energy, because of low slip operation and momentum coupling and heat dissipation in the transformer track instead. This page will get reworked sooner or later.

The vehicle is accelerated by magnetic drag on the rotor. This adds kinetic energy to the vehicle, but subtracts more kinetic energy from the rotor. The difference is turned into heat, which is carried away by the rotor moving ahead of the vehicle. The heating is proportional to the force on the vehicle. A 5000 kg vehicle accelerating at 30 meters per second will heat the rotor by 85C (or 85K). Since the rotor does not make physical contact, the heat is removed by black body radiation. Since this is proportional to the 4th power of the temperature, the rotor on an active launch loop will be very hot. This limits the maximum launch rate - the rotor must stay below its Curie temperature (1000K ?).

The rotor slows down, more when the vehicle is moving faster and the relative velocities are smaller. Since the mass flow rate (on average) must be constant, this will be compensated (in the long term) by rotor stretching. The rotor's thermal expansion may help.

Waste Heat Disposal

The infrared "top" of the atmosphere is well below the top of the launch and return tracks, which constitute the vast majority of the heat radiating surface of the launch loop. The waste heat from a launch to 9km/s is perhaps twice that of the kinetic energy put in the vehicle. If the rotor (and surrounding structure) radiates infrared heat isotropically, about half the waste heat will be absorbed in the atmosphere below, and half will be radiated into space.

However, a wide reflector underneath (which could be quite lightweight) could reflect most of the downwards infrared radiation into deep space. This would both lower the background temperature seen by the rotor, and avoid adding to the Earth's heat budget.

Assume that we can reflect 80% of the emitted rotor heat into deep space. Also, assume we are powering the loop with space solar energy, and can turn space microwaves (or light) into rotor power with 75% efficiency. Assume half of our payloads eventually reenter, with 40% of the heat going to space and 60% heating the atmosphere. The energy loss would be:

So, if we launch 100 billion tons per year (about 60 times 2010 global cargo tonnage, and about 20 times global concrete production rates) to 9km/s, the vehicle kinetic energy will be 4E21 joules per year, or 130 Terawatts. The microwave energy input will be 4 times that, about 510 Terawatts. The earth heating will be 170 Terawatts, compared to the solar input of 120,000 Terawatts. Assuming the existing black body temperature of the Earth is 250K, the launch related heating of the planet will be about 0.1C, mostly ground losses from the rectennas. 100 billion tons per year is enough to launch more than the excess CO2 projected for 2100 into space in about 25 years. 0.1C is a tiny fraction of the expected heating that CO2 would produce, the equivalent of descending 15 meters in the atmosphere.

Simulations

These are a few simulations of the heating of the launch loop rotor for the first hour after the beginning of launch operations, under different conditions. At 12 frames per second, the animated graphs should repeat every 60 seconds, simulating one hour of operation.

The rotor is simulated as 5600 1km long elements in a 14km/sec moving frame of reference. The viewing window (2000 km launch path, and 200 km of the inclines to each side) is rotated around this frame, as are the payloads. There is some numerical noise, probably resulting from inadequate assignment of heat impulses to rotor elements. But this can be used to get some estimate of the heating of the rotor under various conditions. Modify the #defines in the source - the code should be rewritten with an input file instead.

5 ton payloads to 10800 m/s at 30 m/s²

This drawing is a snapshot from the animation below. The first three payloads began acceleration at t=0 sec, t=45sec, and t=90sec. They are indicated by the three bars at the bottom, the longest at the bottom being the first payload. It has been accelerating for 95 seconds at the time of this snapshot; it is moving at 30x95 or 2850 meters per second, and is currently 153 kilometers from west station at X=0. In front of it stretches a heatwave, which has moved 95x14km or 1130 km. Here is a table for the three payloads:

Notice that the heatwave overlap of 2 and 3, between 37.500 km to 70.000 km, has not reached the heatwave overlap of 1 and 3, which runs from 135.375 km to 910.000 km, leaving what looks like a negative-going spike in the plot. The overlaps will create positive spikes, the gaps between overlaps create negative spikes, and the resulting temperature graph can be quite complicated.

5 ton payloads to 10800 m/s at 30 m/s², burst of 30, 45 seconds apart

Here is the source, Here is the gnuplot command file, and you will need gnuplot , libgd, and apngasm. This animated plot shows the temperature profile for a burst of 30 payloads over 22 minutes, followed by a cooldown. The rotor sheds heat by black body radiation, which is proportional to the rotor temperature (in Kelvins, absolute) to the fourth power, minus the 4th power of the sheath temperature.

The sheath and track can have much larger radiating areas (perhaps with heat dissipating and micrometeoroid-deflecting wings to the side), so if it is as hot as 500K (223C) it will only reduce cooling rates at 900K by 10%.

5 ton payloads to 10800 m/s, 30 m/s², burst launch 15 payloads 24 seconds apart

- Burst payloads to the moon, perhaps to slingshot into lower orbits.

Here is the source, Here is the command file,, and you will need gnuplot and apngasm.

1.6 ton payloads to 8600 m/s, 20 m/s², continuous, 10 seconds apart

- Smaller payloads into m288. 8640 payloads, 13,800 tons per day.

Here is the source, Here is the command file,, and you will need gnuplot and apngasm.