# IMM Report Number 16

#### In conjunction with Foresight Update 40

## Diamond in the Sky

*by J. Storrs Hall*

Institute for Molecular Manufacturing

Institute for Molecular Manufacturing

J. Storrs Hall, PhD |

One of the frequently recurring schemes in nanotechnology-in-space discussions is the skyhook or synchronous orbital tower. If such a structure could be built at all it would almost certainly require molecular manufacturing capability. The reason is simple: the structure would require at least ten thousand, and more likely 100 thousand, tonnes of near-atomically-perfect buckytubes or other graphite cable in a tapered form on the order of 80 thousand kilometers long! (enough to wrap around the equator twice).

The theory behind the skyhook makes clear a number of other difficulties besides merely making its material: It is essentially a satellite placed in geosynchronous earth orbit (GEO), long enough on one end to reach the ground, and on the other to balance the ground arm and keep the center of mass in GEO. Objects in such an orbit move at the same speed as the Earth’s rotation, and therefore stay poised above the same location on the ground. Among other things, you have to get it up there somehow. And the stationary skyhook is among the more sedate of the blue-sky earth-to-orbit schemes, with a respectable intellectual history and numerous references and analyses in the literature.

A more practical scheme would likely be something that was marginally possible with current technology. It is difficult to find new ideas in the area, since so many have been proposed for so long. However, here is one which I have not heard of before; this may be its first time in print.

Build a structure 100 kilometers tall and 300 kilometers long. Put a linear induction (or other electromagnetic) motor along the top. An elevator goes straight up 100 kilometers to the starting end. Then they are accelerated horizontally to orbital speed. Payloads can now be launched into orbit with an acceleration of only 10 G’s (which appropriately cushioned humans can stand for the 80 seconds required). This hybrid approach overcomes the drawbacks of both the typical orbital tower schemes (it’s less than 1% the height of a skyhook) and electrolaunch ones (air resistance at 100 km is a million times less than at sea level).

Compared to the skyhook, which is just barely possible with even the theoretical best material properties, a tower 100 km high is easy. Flawless diamond, with a compressive strength of 50 GPa, does not even need a taper at all for a 100 km tower; a 100-km column of diamond weighs 3.5 billion newtons per square meter, but can support 50 billion. Even commercially available polycrystalline synthetic diamond with advertised strengths of 5 GPa would work. Of course in practice columns would be tapered so as not to waste material; and the base of the tower would be broadened to account for transverse forces, such as the jet stream. In general the bottom 15 km (i.e. 15%) of the tower would have to be built taking weather into account.

The electromagnetic accelerator along the top might be fairly heavy. In many designs, coils have iron cores; one NASA prototype weighs 100 pounds per foot. If we allow a tonne per meter, the total weight of the accelerator is 300 thousand tonnes (4 times the QE2!). However, most the weight is (relatively cheap) iron. Note that this entire weight, if it were concentrated in one place, could be supported by a column of current, commercial diamond less than 80 centimeters on a side.

The overall structure could be openwork like a radio tower, and could have approximately 60 footprints 10 km (30 long x 2 wide) apart on the ground — if we set aside a hectare for each foot, they only occupy 0.02% of the land under the tower. The footprint foundations would each bear the weight of a small office building, no great technical challenge.

For altitudes in the 100km range, we can assume gravity is constant for estimation purposes. The energy cost of sending a 10-tonne payload to the top of the tower by elevator is about 10 GJ (2778 kWh or $138.89 worth of electricity), which amounts to 1.4 cents per kg. At an express elevator speed of 50 m/s (108 mph) it takes over half an hour to get to the top.

Then accelerate at 10G along the top of the tower for 80 seconds to orbital velocity, 8 km/sec. (The numbers include an assist from Earth rotation.) The energy required is 300 GJ ($4166 worth of electricity, again for a 10 tonne payload), i.e. 42 cents per kg. Of course, there will be inefficiencies in the conversion of electricity to kinetic energy, so real electricity costs will be higher. The power (as opposed to energy) requirements average 3750 MW for the 80 seconds. A typical suburb on the same land might draw a peak load of 750MW. The tower’s power draw increases linearly from 0 to 7500 MW during the 80 seconds of a launch. Local short-term energy storage, in a form conducive to rapid drawdown such as flywheels, will be necessary for load averaging. Energy storage (and release) requirements are constant per track length and amount to 1 MJ per meter (1 MJ is the energy in an ounce of butter). Drawing at a typical power station’s production of 1000 MW, it would take 5 minutes to recharge the tower.

The other major part of the cost of a launch is amortization of the cost of the tower. If we can launch once an hour (and at an interest rate of 8%) we must charge $0.91 per kg per billion dollars of tower cost. If the traffic is there the rate might be increased (and the cost reduced) by a factor of 10 but not 100. (NB: as payload size is increased, power costs go up per launch but not per kg; amortization costs go down per kg; and more kinds of things can be launched in one piece. The main limit is the accelerator. Chances are you could build one to handle 10 tonnes, but that’s a guess.)

Also, your payload needs to be a spacecraft capable of some 330 m/s delta-V to circularize its orbit. Orbits decay rapidly at 100 km, which is why the tower is not in much danger from space debris. The tower puts you into an elliptical orbit whose apogee is higher, and perigee lower, than you want, and you have to make a small turn once you’re up there. For freight that can be a cheap one-shot strap-on

solid rocket. For passengers the vehicle needs to be re-entry capable in case of accidents, and gets expensive.

It might be possible to design the accelerator to allow a mass/acceleration tradeoff, i.e. to launch 10 tonnes at 10 G’s or 1 tonne at 30 G’s. Freight that can withstand 20 G’s can be launched at escape velocity, and sent more or less directly to the moon; 30 G’s puts it into a transfer orbit to Venus or Mars. (Power costs go up but amortization costs could actually go down, since the payload spends less time on the accelerator!)

How much might such a tower cost? It would be maybe half a million tonnes of material in a structure 300 km long. A typical superhighway that long involves 15 million tonnes of material and costs on the order of 1 to 5 billion dollars. If the coils and electronics for the accelerator cost $1000 per meter, total for the accelerator is under half a billion. The wildcard is the cost of the diamond (and the ability to fabricate it into structural beams). Diamond is a bit expensive today! If an Apollo style (and -cost) project could do for diamond what the original one did for electronics, we could build the tower in the next decade or so. Molecular manufacturing, even of a fairly unsophisticated form, could make it economical. A mature nanotechnology would put towers within the capabilities of private enterprise, and make space travel cheap.

*References:*

- A discussion thread on orbital towers
- Skyhooks with nanotechnology
- Earth-to-orbit schemes
- Electromagnetic launch
- Electromagnetic mass driver “kit” (plans) can be had from SSI
- NASA nanotechnology applications
- NASA’s maglev launch prototype

*—Dr. J. Storrs Hall is an IMM Research Fellow. He can be reached at josh@imm.org.*