Track Tension

The 2017 upgraded transformer-track launch loop will distribute the vehicle acceleration force between the rotor and the track, proportionally to the velocity of the vehicle. The following analysis assumes launch at the maximum cadence, and ignores longitudinal resonances in the track (which may be detrimental or beneficial, hopefully the latter with clever design).

A transformer track can be very efficient because slip will be a tiny fraction of the huge motor speed, perhaps 99% or better. For this analysis, we will assume 100% to simplify the math.

Parameters used

6000 kilograms

Vehicle mass including the launch sled

45 seconds

launch cadence

30 m/s²

launch acceleration

472 m/s

Earth rotation velocity

Likely destination apogees and loop relative launch velocities

Destination

Apogee

Vperigee

Vlaunch

m/s

m/s

422 km LEO

6800 km

7938.74

7466.36

Server Sky

12790 km

9038.17

8565.78

GEO

42164 km

10328.29

9855.91

Moon

384600 km

11001.06

10528.68

Escape

Infinity

11093.37

10620.98

Track Tension Versus Vehicle Number

Vehicle

Velocity

Trackforce

downrange

Summed

Tension

Number

m/s

Newtons

km

Newtons

kg/m

With strain relief
at 200 km

0

0

180000.00

0.00

180000

0.26

1

1350

162642.86

30.38

342643

0.50

Summed

Tension

2

2700

145285.71

121.50

487929

0.71

Newtons

kg/m

3

4050

127928.57

273.38

615857

0.90

127929

0.19

4

5400

110571.43

486.00

726429

1.06

238500

0.35

5

6750

93214.29

759.38

819643

1.19

331714

0.48

6

8100

75857.14

1093.50

895500

1.31

407571

0.59

7

9450

58500.00

1488.38

954000

1.39

466071

0.68

8

10800

41142.86

1944.00

995143

1.45

507214

0.74

The track tension and lateral relief cable could be inconveniently large, but the first 200 km is climbing from the station at 70 km to the main launch path at 100 km, and there will be strain relief cables to the surface to relieve incline forces anyway; they can relieve the track launch tension of the first three payloads as well.

This describes aspects of an advanced 400 tonne/hour-to-escape launch loop using perhaps 7 GW of powerplant.

Earlier, this system will have lower power capacity and lower launch cadence, and before that, a smaller, higher acceleration launch loop will send low cadence payloads to server sky and GEO.

In the longer term, a much larger launch loop will launch 40 tonne payloads (fully loaded 40 foot intermodal shipping containers) at lower acceleration to highly inclined orbits for the assembly of enormous interplanetary spacecraft (such as Aldrin cyclers), while others launch supplies and passengers for multiple docking intercepts; I'll let someone else calculate that.

libreoffice spreadsheet