Minimizing the cost of a project is no small matter because, as Jim Benford points out in the paper we’ve been examining over the past several days, cost determines how we decide on competing claims for resources. In the case of a beamed sail mission and its infrastructure, the cost is largely the reusable launcher or ‘beamer,’ which is the beam source and the antennae needed to radiate the beam. Benford is able to derive general relations for cost-optimal transmitter aperture and beam power, from which he can estimate capital cost and operating cost using today’s parameters. He can then study the economics of high-volume manufacturing.
How to get from today’s economics to tomorrow’s? This is where the concept of the ‘learning curve’ comes into play — it is the decrease in unit cost of hardware with increased production. A 90 percent learning curve means that the cost of a second item is 90 percent the cost of the first, while the fourth is 90 percent the cost of the second, and as Benford explains, the 2Nth item is 90 percent of the cost of the Nth item. Usefully, the author notes that the learning curve in power-beaming technologies is well documented. Antennae and microwave sources have an 85 percent learning curve based on large-scale production of antennae, magnetrons, klystrons, etc.
Image: Jim Benford, whose focus on beam-powered propulsion led to the first laboratory demonstrations of microwave-driven carbon sails and showed their ‘beam-riding’ stability under power.
Yesterday we saw these principles applied to an interstellar precursor mission, a 1-kilometer sail moving at 63 kilometers per second, and found that a capital cost of $144 billion could be reduced to $21.6 billion as we factor in economies of scale. But consider how intractable a true starship moving at 10 percent of the speed of light is even when all factors are cost-optimized. Here’s we’re pushing up against serious problems, not the least of which is the high acceleration demanded, about 50 g’s at an acceleration distance of roughly 1 AU. As we’ve seen with beamed sail concepts, acceleration is strongly temperature-limited. As Benford writes:
Not even carbon can survive the heating due to absorption at this acceleration. Sail reflectivity would have to be close to perfect to allow such acceleration. How to change this concept, via the assumed parameters, to bring down the acceleration is left as an exercise for the reader. Cost is in the T$ range, even with economies of scale, and is larger than any past human project.
Some (but not all) of Benford’s observations based on applying cost-optimized scaling to beamed sails:
- Given that the highest costs are found in the antenna and power source elements, it’s important to note that both are proportional to velocity, transmitter diameter and frequency. Costs can therefore be reduced through larger sails, lower mass sails, and higher frequencies.
- Reducing the cost of power will be more important than reducing the cost of antennae.
- Halving the transit time by doubling the speed will cost 2.5 times as much.
Charting a way forward for directed energy propulsion involves building on what we already have by working through a sequence of applications. To make power beaming economic, we need to move power from places where it is cheap to places where it is scarce:
Previous work has shown that it is often more economical to transmit power than to move the equipment to produce power locally. Modern power systems are complex, but if power for space can be located where it is easily accessible and adjacent to where the required skilled people are located, i.e., on Earth, then it becomes more practical.
We use microwave and millimeter-wave antennae in astronomy already, and gyrotron sources at high frequencies are being developed for fusion. Benford thinks that orbital debris mapping could be an early objective, as could recharging of satellite batteries in LEO and, eventually, GEO. He also notes microwave thermal thruster concepts that could provide economical launches of supply modules to low-Earth orbit. Given the economic realities, it is clear that technology development must demonstrate commercial applicability, incremental commercial growth in these areas leading to a space-based infrastructure.
Beamed propulsion offers one path to precursor and eventual interstellar missions. What Benford has been tackling in this paper are the questions of engineering and cost that take economies of scale into consideration. But he also notes that we need to apply this kind of cost analysis not only to past interstellar mission designs, many of which could presumably be improved by working out cost issues, but also to that other possible application of sails — as a method for decelerating a probe when it approaches a destination stellar system. In the broadest sense, determining what is feasible not only in physics but also in economics makes our interstellar thinking more focused and provides needed tools for assessing new concepts.
The paper is J. Benford, “Starship Sails Propelled by Cost-Optimized Directed Energy.” The paper is now available on the arXiv site.
Comments on this entry are closed.
…clear that technology development must demonstrate commercial applicability, incremental commercial growth in these areas leading to a space-based infrastructure.
Absolutely. This path of technology development is the only sensible way to go to prevent “one off” technology solutions for projects with no real economic benefits to the taxpayer. While I would be cautious that beamed power development for propulsion might be a solution in search of a problem, the technology path outlined looks promising and I would like to see it fleshed out. One historical note. O’Neill tried this approach for his space colonies idea, that they would be the solution for building SPSs for the earth. Had SPSs been economic then, it still would not have made economic sense to build his space colonies. The good news is that Benford’s technology path puts power beaming as the central component, so there is a potential economic driver even if the propulsion use is not viable (or of no interest) and we do not build beamed sails. (We might well build other beamed propulsion spacecraft, or even aircraft).
What if the power required would be collected at synchronous orbit of the Sun? That may reduce the power generation costs significantly (assuming that we will find the way how to accumulate massive amounts of energy).
Power can come very easy if each transmitter of the array has its own local solar energy source. This could be a flat array on Earth, or a 3-d array orbiting in formation, either in solar orbit or in sun-synchronous Earth orbit. The elements would be mass-produced commodities (e.g. stripped down cell phones with a solar panel), and zero additional infrastructure would be necessary. In space, the array could be scaled up to arbitrary size, for arbitrarily well-focused and powered beams.
Some careful balancing of collector area, transmitter power and spacing, and wavelength is required to deal with the thinned-array curse.
I don’t know if the Paul’s title of this article was intentional or not. Still, I take as a compliment to the memory of a great man, Robert Forward.
“One historical note. O’Neill tried this approach for his space colonies idea, that they would be the solution for building SPSs for the earth. Had SPSs been economic then, it still would not have made economic sense to build his space colonies.”
I had a strong interest in O’Neill and his concepts in the mid 80’s so I joined the L5 Society. At the time I did feel that the SPS concept, valid in its own right, was used as a justification to build the Colonies and the main reason was never economics but the non tangible emotional reasons one has for moving off planet. So I agree that to build Space Colonies or an Interstellar Starship involves far more than basic economics.
Tom Baty writes:
Right you are, Tom! I held the man in great esteem.
O’Neils main practical contribution was to build the first working model of a masslauncher . His basic idea of launching moonmaterial in ” sandbags” is still the only practical solution to building any serious industrial project in space . Researching the moon for relevant rawmaterials would be a good first step , but at the present level of funding for un-cool moon business , it could take a hundred years to find out whats upthere and where.
I wonder how the economics would change if the authors included the ideas from the NASA report ‘Advanced Automation for Space Missions’ edited by Robert A. Freitas, Jr? Basically, this 1980 study discussed the concept of self replicating systems and how such systems can bring down the cost of large space systems.
Mass producing components for an armada of space based solar powersats might be the answer to one of the problems mention in the directed energy paper,the capital costs of such a system.
SBSP capital costs would be paid for by the sale of electrical power, directed energy missions would be just another additional customer.
The challenge would be to optimize the spacecraft to use a space based powersat as its directed energy suppler.