|
Size: 3528
Comment: 0
|
Size: 3975
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 29: | Line 29: |
| The arc current should repel the track and push it up to intercept the nose. | 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. |
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 |
|||||||
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 |
|||||||
Shock energy J/m |
8M |
2300 |
6300 |
1700 |
413 |
190 |
90 |
Vehicle velocity m/s WAG |
na |
na |
2000 |
3000 |
5000 |
7500 |
10640 |
Shock power Watts |
na |
na |
13MW |
5.1MW |
2.1MW |
1.4MW |
1.0MW |
Blunt Drag power 2m2 |
na |
na |
8MW |
8MW |
10MW |
17MW |
22MW |
I should compute arc voltage and current with Paschen's law --- I must estimate arc length, too |
|||||||
Arc voltage V/m WAG |
1000 |
1000 |
50 |
20 |
20 |
20 |
20 |
Arc current amp WAG |
|
|
|
|
|
|
|
Arc mass kg WAG |
|
|
|
|
|
|
|
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.