James Benford works out the details around economic rules for scaling power beaming space sails

Arxiv – Starship Sails Propelled by Cost-Optimized Directed Energy by James Benford (25 pages) (H/T – Centauri Dreams)

Microwave propelled sails are a new class of spacecraft using photon acceleration. It is the only method of interstellar flight that has no physics issues. Laboratory demonstrations of basic features of beam-driven propulsion, flight, stability (‘beam-riding’), and induced spin, have been completed in the last decade, primarily in the microwave. It offers much lower cost probes after a substantial investment in the launcher. Engineering issues are being addressed by other applications: fusion (microwave, millimeter and laser sources) and astronomy (large aperture antennas). There are many candidate sail materials: carbon nanotubes and microtrusses, graphene, beryllium, etc. For acceleration of a sail, what is the cost-optimum high power system? Here the cost is used to constrain design parameters to estimate system power, aperture and elements of capital and operating cost. From general relations for cost-optimal transmitter aperture and power, system cost scales with kinetic energy and inversely with sail diameter and frequency. So optimal sails will be larger, lower in mass and driven by higher frequency beams. Estimated costs include economies of scale. We present several starship point concepts. Systems based on microwave, millimeter wave and laser technologies are of equal cost at today’s costs. The frequency advantage of lasers is cancelled by the high cost of both the laser and the radiating optic.

Carbon sail lifting off of rectangular waveguide under 10 kW microwave power at 2 gees (four frames, first at top) in vacuum chamber [5]. Sail heats up, lifts off, and in the bottom frame the sail has flown away.

The cost is largely not the spacecraft, but the reusable launcher or ‘beamer’ (a system comprised of beam source and antenna(s) to radiate it). I derive general relations for cost-optimal transmitter aperture and beam power, then estimate both capital coat and operating cost of costtransmitters using current cost parameters ($/W, $/m2). Costs for large-scale manufacture of transmitters and antennas are well documented. (However, costs for space manufacture not known.) Below we account for economies of scale, which will be important, and characterize specific missions. In particular,

• Interstellar probes for exploration of the Oort Cloud, characterization of the nearby interstellar medium, and its interaction with the Heliosphere.

• Starships, either as primary propulsion of the mothership or as a means of decelerating probes from the mothership for Exoplanet exploration as the mothership flies on.

Melting Points limit how much energy can be used for accelertion

Materials with low melt temperatures (Al, Be, Nb, etc.) cannot be used for fast beam-driven missions. For example, aluminum has a limiting acceleration of 0.36 m/s2, which is <4% of a gee. The invention of strong and light carbon mesh materials has made laboratory sail flight possible because carbon has no liquid phase, and sublimes instead of melting. Carbon can operate at very high temperature, up to 3000 C (and graphene paper up to 4000 C), and limiting acceleration is in the range of 10-100 m/s2, sufficient to launch in vacuum (to avoid burning) in earth-bound laboratories. Experiments with carbon-carbon microtruss material driven by microwave and laser beams have observed flight of ultralight sails of at several gee acceleration [5]. In the microwave experiments, propulsion was from a 10 kW, 7 GHz beam onto sails of mass density 5g/m2 in 10-6 Torr vacuum. At microwave power densities of ~kW/cm2, accelerations of several gravities were observed. Sails so accelerated reached temperatures ~2000 K from microwave absorption, and remained intact. (Much lower power densities and accelerations are needed in the missions we’ll analyze. We had to hit it powerfully because we needed >1 gee to lift off.)

Tradeoffs in mission design

While microwave transmitters have the advantage that they have been under development much longer than lasers and are currently much more efficient and inexpensive to build, they have the disadvantage of requiring much larger apertures for the same focusing distance. This is a significant disadvantage in missions that require long acceleration times with correspondingly high velocities. However, it can be compensated for with higher acceleration. The ability to operate carbon sails at high temperature enables much higher acceleration, producing large velocities in short distances, thus reducing aperture size. Very low-mass probes could be launched from Earth-based microwave transmitters with maximum acceleration achieved over a
few hours using apertures only a few hundred meters across.

A number of such missions have been quantified. These missions are for high velocity mapping of the outer solar system, Jupiter, Kuiper Belt, Plutinos, Pluto and the Heliopause, and the interstellar medium. Meyer and co-workers [9] described an attractive interplanetary mission: rapid delivery of critical payloads within the solar system. For example, such emergencies as crucial equipment failures and disease outbreaks, can make fast delivery of small mass payloads to, say, Mars colonies, urgent. They describe missions with 175 km/sec speeds driven by lasers or microwaves at fast boost for a few hours of acceleration, coast at high speed, decelerate for a few hours into Mars orbit (by aerocapture or a decelerating Beamer) — transit time 10 days. The Bedford’s’ Mars Fast Track then extended this to missions with 5 gee acceleration near Earth. Using a ground station, acceleration occurs for a couple of hours for a 100 kg payload. Jordin Kare quantified a Jupiter mission with beamed energy

Interstellar Probes are solar/interstellar boundary missions out to ~1000 AU. The penultimate is the interstellar precursor mission. For this mission class, operating at high acceleration the sail size can be reduced to less than 100 meters and accelerating power ~100 MW focused on the sail. At 1GW, sail size extends to 200 m and super-light probes reach velocities of 250 km/s for very fast missions. In a NIAC study, McNutt and co-workers have described such missions driven by rocket and gravity assists. Beaming power could make for shorter mission durations. Here transit time is a serious factor driving mission cost.

Starships Truly the biggest and grandest mission. This concept requires very large transmitter antenna/lens and receiver (sail) optics (e.g., 1,000-km diameters for missions to 40 ly. A Space Solar Power station radiates a microwave beam to a perforated sail made of carbon nanotubes with lattice scale less than the microwave wavelength. The scale of the first concept was enormous, but Geoff Landis found ways to reduce it dramatically. Frisbee has sketched systems much smaller than those described by Forward in peak power (~10 GW), size (~1km sail, ~1000 km antenna array aperture). Presumably, cost is also lowered, but has not been quantified. We describe here an economic approach to further reduction in power, size and cost.

Learning curves for four learning curve f’s: 95%, 90%, 85%. 80%. Power beaming technologies data fit the 85% curve.

Microwave propelled sails have no physics issues and offer much lower cost probes. But its large -scale antenna and powerful radiator mean the questions to face are engineering and cost. Relations have been derived here for quantifying this question, including economies of scale (‘learning curve’). The usefulness of the beamed power/sail method awaits further quantification by:
• Analyzing past concepts (Forward, Landis, Frisbee, Matloff) to see if they are offoptimal, so can be improved.
• Quantifying an alternate use of sails-deceleration of sail probes from a fusion-powered starship as it approaches stellar systems.