## Launching the Space Elevator

Published on September 7, 2008, by in Uncategorized.

Recent years have seen a lot of optimistic reappraisals of the requirements for space elevators – instead of multi-billion ton structures anchored to asteroids the current designs mass less than 1,000 tons and can support 20-ton elevator cars. However there are a few problems, one of which I’ll discuss here: How to power it? If you’re observant you might notice I’ve written a few thoughts on this issue before but a few modifications of my first discussion are necessary.

Firstly, a potentially high efficiency solar-thermal conversion system is doable using a Johnson Thermoelectric converter – basically a closed-cycle fuel-cell that is aiming for an 85% of Carnot Limit efficiency. But what does that mean? Carnot efficiency is basic to thermodynamics – it’s the extractable work from a cyclical thermal process. In this case a fluid is heated by concentrated sunlight, goes through the converter then through a heat-sink, then returns to the concentrator. When it comes to dumping “waste” heat in space the hotter the heat-sink, the better. I’ve seen 600 K quoted so often it’s what I’ll assume. The Johnson converter is hoped to operate at 1300 K, thus the Carnot Limit is (1300K – 600K)/1300K or 0.5385. Thus the Johnson converter can turn 45.77 % of the heat directly into electricity, and 54.23% has to be dumped by a heat-sink to space.

How much power is needed? Assuming the 20 tons usually quoted for the ribbon-crawler, then to lift-off at a sustained 56 m/s straight up needs a lifting-power of 11 MW – which means about raw 12.2 MW electrical power with 90% efficiency in the power supply and motor systems. That means 26.7 MW of solar heat needs to be collected. If we assume the solar constant, 1365 W/sq.metre, then our collector is 19,560 sq.metres. Our heat sink, which at 600 K is radiating 7350 W/sq.m from BOTH sides (assuming a flat radiator), is 985 sq.metres. The solar collector, focussing on a converter at 1300 K, means the sunlight is being concentrated by a factor of ~120 times, thus the heavier thermal converter has an area of just 165 sq.metres (assuming all collectors and radiators are close to being perfect black-bodies.)

How big is 19,560 square metres? Almost 5 acres – if it was two circular collectors they would have a diameter of 158 metres each. Big, but doable with large inflatables, which is easy to do in space. However for about 60 km or so the crawler isn’t in space, and inside the atmosphere, with ravenous winds, big solar collectors aren’t practical. So what to do?

Current designs assume high powered lasers, but the efficiency of lasers is dreadful – less than 20% of wall-socket power becomes laser beam energy. Assuming the 12.2 MW at the crawler, about 85% conversion efficiency from laser light, then the crawler’s laser light receivers are taking a beating of ~14.4 MW of laser energy, and the ground base is pumping 72 MW of electrical power into the lasers on the ground – or worse, depending on atmospheric absorption. Still the laser receivers don’t have to be really huge – if they’re dissipating the waste heat at 500 K, then twin receivers would only 20 metres in diameter each.

But what if we can get above the atmosphere before inflating the collectors? To power that climb – 60 km – we need a sufficiently energy dense power source to do the job. First question: could it be done with a petrol engine? As air thins out in a hurry it would need oxygen tanks for at least part of the trip – a big part probably. Also the power the engine would need to supply would be over 13,000 horsepower, which would be quite an impressive engine. Obviously it would be a gas turbine as that’s the only design regularly built at such power-levels – they’re frequently used to provide peak power by electrical utilities in the multi-megawatt range. At 35% efficiency thermal efficiency and 90% power conversion efficiency then the 13,000 hp of electrical power means a 42,000 hp gas-turbine… which is starting to get seriously heavy. Good-bye 20 ton crawler.

So what about EEstor ultra-capacitors? According to Wikipedia’s latest update on EEstor they’re now claiming about 2.5 MJ/kg energy density. If we assume 0.9 efficiency electrical-to-mechanical power efficiency and 0.9 from battery-to-motor then a 60 km trip at 56 m/s straight up needs 14.55 GJ of energy – some 5,820 kg of capacitors. Not bad and improved by a “booster crawler” that carries the main crawler to the desired height, then rolls back down while regeneratively braking and recouping some of the power.

So, if EEstor’s claims pan out, then the Solar-powered space-elevator might just be viable.