This is a follow-up on my “Dollar a Gallon Gasoline” article from April 2. That article proposed power satellites as a way to solve energy, carbon, climate, water and even economic stagnation problems. The follow up is on an alternate transport system powered by microwaves rather than lasers.

Power satellites are a complicated subject. It involves economics, “rocket science,” i.e., the rocket equation, orbital mechanics, radiators, thermodynamics, microwave and laser optics, geography, geometry, radio frequency interference with communications, Skylon (rocket plane), atmospheric damage effects (from NOx), chemistry, electrochemistry, military policy, international politics, and in-space operations and assembly. It’s difficult to put enough detail in an article for it to be believable and little enough detail for it to be readable. But I will try.

The engineering has developed over the decades from 1968. It’s unusual to need an update even once a year, much less one in a few months. However, progress has recently picked up. In May, there was an article about Japanese plans for power satellites in the IEEE Spectrum by Susumu Sasaki, a senior scientist with JAXA. JAXA is Japan’s equivalent of NASA. The IEEE is the largest technical society in the world

http://spectrum.ieee.org/green-tech/solar/how-japan-plans-to-build-an-orbital-solar-farm

More recently there was a CNN article on Skylon, one of the keys to making power satellites economical.

http://www.cnn.com/2014/08/08/tech/innovation/spaceship-reinvented/index.html?hpt=hp_c3

The current schedule for Skylon is for it to fly in 2021. That means that on an ambitious schedule the first power satellite could come on line in 2023. Rapid growth could lead to displacing fossil fuels by the mid 2030s.

If you want to displace coal with cheaper power from space, the cost limit for lifting power satellite parts to GEO is around $200/kg. That depends to some extent on how many kg it takes in GEO to deliver a kW on the ground. The current consensus is 5-7 kg/kW. That’s $1000 to $1400 per kW for the transport cost. If the parts and rectenna add another $1100, the cost will be from $2100 to $2500 per kW. To get from capital cost to electric power cost you divide by 80,000, which puts the cost in the range of 2.6 to 3.2 cents per kWh. That’s far enough below coal at 4 cents to gain market share. 

 Figure 1.

At the minimum volume (10,000 flights per year) needed to build power satellites, Reaction Engines, Ltd. estimates the cost of cargo to LEO will be $120/kg. For chemical rockets, the cost multiplier is about 2.5 from LEO to GEO (because you have to lift the fuel as well as cargo). A multiplier of 2.5 ($300/kg) is excessive if the lift cost has to stay below $200/kg.

Chemical rockets are not the only choice.  Ion engines are slower but they take much less reaction mass. At an exhaust velocity (V_e) of 20 km/s, only 21% of the mass lifted from earth is required for reaction mass.

Figure 2.

This is not a new idea; see the 1992 paper by Brown and Eves.

http://www.utdallas.edu/~pxm017500/gap4s/Doc/Ref/Recten/00141357.pdf

The problem with ion engines is the high power consumption. To accelerate reaction mass of 1 kg per second to 20 km/s takes 200 MW. It’s a tradeoff between the cost of lifting reaction mass and the cost of supplying a lot of power.

 Figure 3.

Microwaves are how we propose to bring power down from power satellites; they can also send power up to power ion engine rockets from LEO to GEO. However, the same microwave optics problem (focusing and scale) affects up-transmission as well as down. This sets the minimum rectenna in space at close to a km in size and the transmitter on the ground at 10 by 14 km, possibly larger. We also have to consider the effects of blasting communication satellites with the spillover that misses the rectenna on the vehicle.

If a 1000 ton rectenna and another 1000 tons of engines and structure are around 10%, the entire vehicle will mass upwards of 20,000 tons and the payload will consist of 1001 (13 layers and 91 per layer) fifteen ton Skylon cargo modules full of power satellite parts. For a dry mass of 17,000 tons, 4500 tons of reaction mass will be needed (plus a bit more to make the trip back). If the trip time is 28 days and the vehicle is in view ten percent of the time, the ground transmitter can power the vehicle for 244000 seconds. The flow rate, 4,500,000 kg/244000 seconds is 18.4 kg/s

3.7 GW would be required to accelerate 18.4 kg/s to 20 km/s. That is ~66 tons per hour, so ~4460 tons of reaction mass would flow through the engines in ~67 hours. That is in reasonable agreement with a numerical model in Excel that gave a thrust time to GEO of 73 hours. The model gave a trip time of ~28 days, close enough to the starting assumptions.

The power level at the ground is not much different for a transmitter going up compared to that from a power satellite coming down, perhaps 8 GW input to the transmitter to power ~4 GW of VASIMR thrusters. The microwave radiation level would be around 450 W/m² at the transmitter surface. The power level will be lower if the transmitter is larger. I.e., this will not cause birds to burst into flame.

Figure 4 shows an arm putting the last layer of cargo modules on the stack.

Figure 5 shows 15,000 tons of cargo under way using VASIMR engines making the purple glow.

Artwork by Anna Nesterova 

The microwave transmitter and combustion turbines to power it will cost less than $16 B.

Written off over 5 years, the cost will be around $3.2 B/year. Using only one ion transfer vehicle and ten trips per year, the capital cost for the microwave transmitter will be $3.2 B/0.15 B kg or ~$21/kg. To that we need to add the cost of writing off the 2000 ton transfer vehicle over a number of trips and the cost of the fuel to run the turbines. If the vehicle cost in space is 3 x the lift cost, the vehicle will cost around 2 million kg x $120/kg x 3 or around $720 million. Written off in 5 years (50 trips), the cost per trip for the vehicle would be $14.4 M. The fuel cost to run the turbines per trip is around $59 M figured at 10 cents per kWh  Divided by 15 M kg payload, these two add less than five dollars per kg increasing the LEO to GEO cost to $26/kg. It will take about 3 kg of reaction mass per 15 kg delivered to GEO making the cost per 15 kG kg to GEO $120×18 for the cargo plus reaction mass plus + $26×15 for the LEO to GEO cost, ~$170/kg. We will have to watch cost carefully, but this is somewhat under $200/kg.

Laser-boosted Skylons (discussed in the previous article) are a still lower-cost approach for ground to LEO. They have a payload fraction 3 to 4 times the LOX carrying Skylon. If the cost per flight is about the same, the cost per kg to LEO using lasers would be about $40/kg plus a proportionate share of the (expensive) laser cost.

During the Strategic Defense Initiative (Star Wars) research scientists and engineers solved most of the problems with high-power lasers and tracking. This included constructing mirrors large enough to track a hydrogen heater on the wing of a Skylon from GEO. But VASIMR propulsion and microwave transmitters and receivers are at a relatively high technology readiness level (TRL) compared to big lasers and would be less risk.

Of course the combination of laser boosted Skylons and microwave propulsion (powered from GEO) would be even better, getting the cost of transport to GEO down to about $60/kg, the cost for power well under 2 cents per kWh and the cost of synthetic oil under $50/bbl.

Humans may not solve the energy and carbon problems, but it not because we lack engineering paths to do so.

Epilogue

Peter Glaser, who patented the power satellite idea in 1968, died in late May of this year.  RIP

http://www.nytimes.com/2014/06/06/us/peter-glaser-who-envisioned-space-solar-power-dies-at-90.html?_r=0