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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

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

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

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

Arc voltage V/m WAG

1000

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.

MoreLater

LightningTunnel (last edited 2020-12-02 11:50:06 by KeithLofstrom)