Lightning Tunnel
An artificial lightning-like discharge collinear with the nose of the launch sled can drastically reduce heating and drag with a surprisingly low amount of power in the electric arc.
The main launchloop acceleration track is at 80 km equatorial altitude, with sled velocities ranging from 7.5 km/s to 11 km/s tangential to the Earth's surface. According US Standard Atmosphere 1976, the atmosphere at 80 km is cold and about 15 ppm pressure and density. While the real atmosphere is turbulent, frisky, and varies with time of day and weather conditions, for the following simplified analysis we will use these conditions:
altitude, km |
0 |
40 |
50 |
60 |
70 |
75 |
80 |
density kg/m³ |
1.2250e+0 |
3.9957e-3 |
1.0269e-3 |
3.0968e-4 |
8.2829e-5 |
3.9921e-5 |
1.8458e-5 |
pressure Pa |
10132.5 |
287.14 |
79.779 |
21.958 |
5.2209 |
2.3881 |
1.0524 |
temperature K |
288.150 |
250.350 |
270.650 |
247.021 |
219.585 |
208.399 |
198.639 |
Number dens. n/m³ |
2.5470e25 |
8.3077e22 |
2.1351e22 |
6.4387e21 |
1.7222e21 |
8.3003e20 |
3.8378e20 |
particle speed m/s |
458.94 |
427.78 |
444.79 |
434.93 |
400.64 |
390.30 |
381.05 |
Collision freq. Hz |
6.9189e+9 |
2.1036e+7 |
5.6210e+6 |
1.6195e+6 |
4.0839e+5 |
1.9175e+5 |
8.6559e+4 |
mean free path m |
6.6332e-8 |
2.0336e-5 |
7.9130e-5 |
2.6239e-4 |
9.8102e-4 |
2.0354e-3 |
4.4022e-3 |
sound speed m/s |
340.39 |
317.19 |
329.80 |
315.07 |
297.06 |
289.40 |
282.54 |
Kinematic viscosity m²/s |
1.46073-5 |
4.0066e-3 |
1.6591e-2 |
5.1141e-2 |
1.7357e-1 |
3.4465e-1 |
7.2557e-1 |
Breakdown voltage proportional to density (or pressure? TBD), 3MV/m at ground level |
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Blunt Drag power 2m² |
na |
na |
8 MW |
8 MW |
10 MW |
17 MW |
22 MW |
Breakdown V/m |
3M |
9800 |
2500 |
760 |
200 |
100 |
45 |
Shock energy per meter to accelerate 2 meter radius cylinder of air to mach 3 |
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Shock energy J/m |
8M |
23K |
6300 |
1700 |
413 |
190 |
90 |
Vehicle velocity m/s WAG |
na |
na |
2000 |
3000 |
5000 |
7500 |
10640 |
Shock power Watts |
na |
na |
13 MW |
5.1 MW |
2.1 MW |
1.4 MW |
1.0 MW |
Acceleration 30 m/s², 7000 kg vehicle plus sled, hence acceleration power is velocity times 210KN |
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Acceleration power Watts |
na |
na |
420 MW |
630 MW |
1050 MW |
1600 MW |
2200 MW |
I should compute arc voltage and current with Paschen's law --- I must estimate arc length, too |
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Arc voltage V/m WAG |
1000 |
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Arc current amp WAG |
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Arc mass kg WAG |
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I can probably guesstimate the arc voltage from upper atmosphere sprites, though the power density for a lightning tunnel will be much higher.
Lorentz force should push the arc current away from the counter current in the track in order to intercept the nose. This will of course be a function of speed, which is a fixed function of distance along the track. The basic geometry can be baked into the track and the windings, diodes, connections, etc, with some second-order tweaks to accomodate atmospheric variation.