# Could Earth's electric grid be used to power rocket launches via cable?

If our regular huge power plants on the ground could be used to power part of a rocket launch, launch mass would be smaller since fuel would not have to be carried on board. I wonder what are the main weaknesses and problems with this? How could it be done, if at all?

One limit of electric ion engines seems to be that it requires quite a huge electric power plant to match the effect generated by the explosion in a chemical rocket engine. But with a reusable first stage ion electric engine which is physically connected to the electric grid on the ground, I imagine that one could turn up the power until the cable glows and electric effect is not the limit anymore.

Another limit might be how large an ion engine can be in terms of gas mass flow per second, or how many small ones that can be bunched together. Maybe lifting the cable is a problem, even if it is put on the ground/sea surface under the planned launch trajectory, because one would have to reach a substantial fraction of the escape speed in order for this to be worthwhile.

Are there other electric rocket engine types which would work better than ion engines when very high electric effect is available?

• For a booster stage the thrust to weight ratio needs to be greater than 1. In other words if the spacecraft weighs more than the thrust, it's not going to get off the ground. While ion engines have great ISP, they have very weak thrust. Oct 31, 2014 at 13:47
• One data point you need is the weight of the cable. See britned.com/About%20Us/Construction: 44 kg/m for a 1 GW DC undersea cable. A cable for a rockets can be lighter (less insulation) but needs two conductors instead of one. Ballpark 50 tons/km would not be a bad start. Oct 31, 2014 at 14:09
• @Hobbes Ouch, that's heavy! But maybe it could be made lighter? Undersea cables don't have that incentive. It's after all not as far away as the tether materials needed by a space elevator. Your link is informative: "We used over 30 special cable laying vessels and a range of support vessels..." to lay 250 km undersea cable. Floating it on the surface might or might not be easier. Oct 31, 2014 at 14:21
• The main cause of cable weight is the conductor. Copper is heavy, and there's no way to reduce the weight while still carrying the same current. Oct 31, 2014 at 16:00
• @Hobbes Don't hollow cables conduct more per unit of mass? That the electrons tend towards the surfaces of conductors. But even if conduction maps directly to mass of metal, what's the problem if one can simply turn up the power? Surely, a cable can carry enough current to lift itself from Earth gravity. Nov 1, 2014 at 4:54

1) Nobody has built an ion engine that can lift from Earth. Your system might work to take off from a place like Phobos but nothing bigger. (And it wouldn't work very well even there.)

2) The strongest wires out there will take you no farther than the stratosphere before they snap under their own weight. If you the strongest cables we can build to support the wires we can get into space--but getting up there is easy compared to building up the speed to get into orbit.

• Re 1), "lifters" could be considered such a thing: en.wikipedia.org/wiki/Ionocraft but your points are still completely correct. Oct 31, 2014 at 22:27
• @pericynthion I would not call such craft ion engines. They're based on electric charge, not upon expelling ions. Nov 1, 2014 at 0:47
• +1. Thank you for highlighting often neglected points. T/W (thrust to weight) ratio of ion engines. And tensile strength and density of tethers. A massive electric cable throughout an elevator adds to stress but contributes little tensile strength. A climber's power source is often neglected when painting rosey pictures of elevators. Nov 1, 2014 at 15:08

Laser propulsion may be a better option if unlimited power and imaginary technology were available.

That is, a land based, ground powered laser is aimed at the base of the rocket, and the heat from the laser provides the energy to heat the propellant that is exhausted to generate thrust.

Of course this has not been demonstrated to any serious level but there are small projects considering it.

There are issues in building powerful enough lasers, that can aim accurately enough over the time duration of a rocket flight. Upper stages will of course still be needed, since the first stage MIGHT stay in line of sight long enough to work, but the upper stages will be out of sight pretty quickly.

• Maybe cable electric power is the best option during the slower vertical part of a rocket launch? While laser/microwave propulsion from Earth stations have, I think, mostly been proposed for long term and very long term travel. Imaginary technology is NOT assumed here. Just the question if a concentration of today's power grid, with a cable, would enable rocket launches. Oct 31, 2014 at 14:56
• Note geoffc suggested lasers as a way to impart thermal energy. Once again, ion engines do not have the thrust to weight ratio to climb out of a steep gravity well. Nov 1, 2014 at 15:21

Recently, I am also looking into this approach. It seems that carbon nanotube (CNT) fibers might be a promising option in the near future of 'rocket-launch-via-cable', due to its excellent conductivity and high strength.

--------- Here are some ideas and calculations ----------

Consider the electric cable made of Carbon Nanotube Fibers with diameter $$1mm$$ and length $$600km$$, targeting a space launch to International Space Station (orbit $$408 km$$, velocity $$7.7066 km/s$$). https://en.wikipedia.org/wiki/International_Space_Station

The weight of the cable will be $$π (0.5 mm)^2 (600 km) (2100 kg/m^3) = 989.6 kg$$, where $$2100 kg/m^3$$ is the density of Graphite.

Winding the cable and put it on the rocket, with one end connecting to the ground of electricity supply and drop (release) the cable gradually from the rocket during launching so that the relative speed of the cable is zero to the ground during releasing.

Now, the calculation for the necessary power.

Suppose the total weight of the rocket is $$10,000kg$$, with orbit speed $$7.7066 km/s$$ and acceleration of $$3 g$$, the power needed to accelerate the rocket during launching is $$10,000kg \times 4 g \times 7.7066 km/s = 3.018 GW$$.

This is necessarily the maximum power as when the rocket reaches high altitude, its weight will decrease (gradually) and acceleration is much smaller than 3g.

Let's see whether the carbon nanotube can afford this power. Consider using Alternating Electricity with voltage $$1000kV$$, which is already possible in reality. https://en.wikipedia.org/wiki/Electric_power_transmission#Advantage_of_high-voltage_power_transmission

We need the cable to hold electric current of $$3.018 GW / 1000kV = 3018A$$.

The ampacity of a single CNT is $$10^9 A/cm^2$$, which corresponds to maximum $$2,500,000A$$ for our cable (1mm diameter), sufficient enough. While in practice, the tested CNT fiber only gives $$10^5 A/cm^2$$, but with CNT-Copper composite, it can be $$10^7 A/cm^2$$. (Data from "High Ampacity Carbon Nanotube Materials" https://pdfs.semanticscholar.org/4831/a85d7d32e170ab0eb3639da68aa5ed2de03c.pdf)

Moreover, the cable diameter can be designed so that the closer to the ground, the larger diameter. Then at around $$30km$$ altitude, we could insert a device (drop from rocket) on the wire to transform the voltage to $$10MV$$ or even bigger for the remaining cable. High voltage for high altitude could be an option in terms of air breakdown field ($$3 MV/m$$).

# Here are some possible problem.

i) The heat on the wire might be a problem. The conductive resistance of nanotube is 1.0×10−8 Ωm, which is 0.04 Ωm in our cable (0.5 mm diameter). Then the heat on 1 meter wire in one second is (3018A)^2*0.04Ω = 364 KJ, without considering the 'capacitive reactance'. My calculation might not be accurate.

ii) The cable in the air might be broken (possibly by wind). As the cable only has diameter 1mm, it does not seem to be strong, even a strong wind might break it. The released cable in the air will drop over time (might not be the main problem due to air resistance and thin cable), which implies we have to drop more cable than the real altitude. $$600km$$ of cable length for orbit $$400km$$ launch is just an estimation, while it depends on a lot factors of how long the cable should be. Also, we need an extra device to retrieve the cable after launching, maybe we can use some battery-powered motor to collect the cable.

iii) Dropping speed of cable from rocket (relative to rocket) is too high, $$7.7066 km/s$$. Maybe some tricks of winding the cable in a smarter way will reduce the dropping speed and flywheel tech could be applied.

iv) Electric motor to power the rocket. Finally, the biggest challenge I think is how to build a light-weight powerful Motor to power the rocket with the electricity from the cable, especially in high altitude where air density is low. This might be solved by considering a two stage rocket launching while the cable approach is only intended for the first stage, and apply hydrogen fuel for second stage. Another way might be compress the air during launching, and using electricity to accelerate the compressed air to high speed in high altitude. Also, the oxygen could be collected from air if two stage rocket is adopted. Some more discussion might be of interest.

v) The cloud at $$10km$$ might be a problem. In humid air, $$1000KV$$ voltage will (might) break down. An extra device above the cloud to transfer the voltage may be an option. From ground to cloud, apply $$100kV$$ voltage but with larger current, hence thicker cable.

# --- update ----

Ohm heat is corrected, and now it is $$364KWm$$, which is not possible for 0.5mm diameter cable. The solution might be raising the voltage from $$1000KV$$ to $$20MV$$ and hence decreasing the current from $$3018A$$ to $$150.9A$$, hence the new heat will be $$910Wm$$.

vi) It is a challenge to transfer energy with only one single wire. https://en.wikipedia.org/wiki/Single-wire_transmission_line From Tesla's invention, the principle behind is that the rocket could act as a capacitor, while it is not possible when the rocket reaches high altitude. Also, the capacitor of the cable in the air may affect that principle.

• what are you going to use to convert your 20MV ac to dc? and if you worried about 1 MV arcing, 20MV is going to be substantially worse.
– user20636
Jul 28, 2019 at 0:17
• This is interesting and I like your approach, but your 3 GW estimate is unrealistically low for rocket propulsion which is based on adding linear momentum. If the rocket were accelerating along a track and you were powering an electric motor, your calculation of $dE/dt = m v a$ seems correct. But you need to accelerate a reaction mass to propell the rocket, and starting with electricity you'll need to invent/describe a way to do that, which is much more complicated than using an electric motor on a track.
– uhoh
Jul 28, 2019 at 0:18
• You could use electricity to boil water and use steam for example, as discussed in Are LiPo batteries more suitable for 1st stage electric power than Li-ion batteries?'s discussion of Does ARCAspace's Water & Electric Powered Rocket Make Sense? but you'll find that it is going to need a lot more power than you estimate here. You could also put an electrically-powered railgun in the rocket and accelerate projectiles at mach-10 (shooting down your own launch pad) but...
– uhoh
Jul 28, 2019 at 0:28
• Since you are active in mathematics, there's astronaut Don Pettit's The Tyranny of the Tsiolkovsky rocket equation
– uhoh
Jul 28, 2019 at 0:28
• You need 2 conductors, + and ground. So you can't use bare CNT wires, you need insulation. At 20 MV, that insulation has to be substantial, far thicker than the 1 mm of your CNT wire. This table has insulation thickness of 14 mm at 35 kV: anixter.com/en_us/resources/literature/wire-wisdom/… Jul 28, 2019 at 7:54