Dollar a Gallon Gasoline

Gail Tverberg recently posted an article here.  She makes a strong case that, if we are to avoid economic disaster, a sustainable source of energy must not only be abundant; it must be cheap.  I pinned her down at a conference late last year and she bracketed oil at $30-50 per bbl for a vibrant economy.

Some years ago, the first time gasoline went over $4 per gallon, I set a similar goal of synthetic gasoline (or other transport fuels) for a dollar a gallon, close enough to Gail’s numbers.  Electric power at 1-2 cents per kWh will make transport fuel out of CO2 from the air and hydrogen from water at that price.  At this energy cost, the synthetic fuel is about 1/3 capital investment and 2/3 energy.  There is about 40 kWh of energy in a gallon of gasoline, so this is reasonable.  (Physics and chemistry worked out here: http://htyp.org/Dollar_a_gallon_gasoline)

So how do you get 1-2 cent per kWh?  Nuclear will not do it; neither will wind nor ground solar.  Projections for the best of them are several times too much for making dollar a gallon gasoline.  Hydropower will get into this cost range, but there is not enough of it.

Space-based solar power (or powersats), are one possible exception.  (There may be others.)  Located in geosynchronous orbit (GEO) they are out of the Earth’s shadow 99% of the time.  The solar collectors (PV or thermal) get about 5 times the illumination of the driest deserts.  The percentage of time with illumination is over ten times that of cloudy Germany or Japan.  There is a 50% loss getting the energy down by microwaves.  That still gives a 2.5 times advantage over the best and 5 times or more for typical places where humans want energy.  Powersats don’t need storage.  In most cases, the power can come down to receiving antennas (rectennas) located near large loads.  That reduces the cost of earth-side transmission to well under 1 cent per kWh.  (The cost is ~1 cent per kWh per 1000 km.)

Over time, we will build far more powersats than needed for peak demand.  Excess energy above current load will go into making hydrogen.  Combined with carbon, the hydrogen makes synthetic transport fuels via Fisher/Tropsch synthesis.

The problem with this idea is the cost of lifting parts for powersats to geosynchronous orbit.  That’s been the problem ever since Dr. Peter Glaser patented them in 1968.  The transport cost is so high that one study arrived at a figure of $145,000 per kW.  Powersats are low maintenance and no-fuel-cost energy sources.  The method for converting capital cost in dollars to power cost in cents for such sources is to divide by 80,000.  Electricity from a powersat costing $145k/kW would break even at $1.81 per kWh.  That is about 100 times too expensive to solve the problems.

Design to Cost

Design to cost is a management strategy with supporting methodologies.  The point of design to cost is to achieve an affordable product.  It does so by treating target cost as a design parameter during the development of a product.  If you have not met the target price, then you keep working on the design until you do, or management gives up on the product.

A design that does not meet the cost metric is worse than useless; it will bankrupt the company or country that tries it.  The Germans are to some extent in this situation with expensive renewable energy.

Two cents per kWh implies at most a capital expenditure of $1600/kW or $1.6 B/GW.  (For comparison, nuclear costs ~$5 B/GW even in China.)  Major cost items for power satellites are the rectenna, the power satellite parts (and labor) and the transport to GEO.

That is, rectenna plus power satellite parts and labor plus transport cost to GEO must be less than $1600/kW.

The rectennas should cost around $200/kW.  This assumes near zero cost for the land, perhaps trading air rights over farmland for electricity.  If $200/kW is close to the actual rectenna cost, it is 1/8th of the total target cost.  Thus, the total cost is not sensitive to even major variation in the rectenna cost.  At the scale needed, $900/kW is a reasonable figure for the parts and labor.  That’s the case even including the microwave generators and transmitting antenna.  It includes a factor of two for the loss in the microwave transmission link.

To stay inside the cost target requires no more than $500/kW for transport to GEO.  At a specific mass of 5 kg/kW, the transport cost has to come in at $100/kg or less.  This is a hundred-fold reduction from current prices for sending communication satellites to GEO.  That sounds like a lot of reduction, but based on the physics, it is well above the lower limit of around a dollar a kg.  It takes less than a dollar of energy to raise a kg to GEO.  The design-to-cost target for power satellites is to get the transport cost to GEO down to $100/kg.

That’s not the only design to cost solution.  Taking the rectenna and the power satellite parts and labor as fixed, the product of kg/kW and $/kg to GEO needs to come in at $500 or less.  Solaren has proposed as much as 85 times as much power from a kg of power satellite.  As an electrical engineer, I am skeptical that such low masses are possible.  The other end of the range is John Mankin’s recent design at 10 kg/kW.  That requires a difficult (but not impossible) transport cost of $50/kg.  The original work by Boeing in the 1970s proposed 10 kg/kW.  Phil Chapman (Solar High) has a thermal design at 8 kg/kW.

So what does it take to reduce the cost of lifting parts to space?

There are several reasons rockets are so expensive.  First, we build and fly rockets in small numbers.  That raises the cost just as you expect to pay a lot more for automobiles built in limited numbers.  For cars this is around a factor of ten, i.e., a hand built $250,000 car would cost about $25,000 if it came off a production line.  Just making and flying thousands or tens of thousands of identical rockets would reduce the cost per flight by a factor of 10-20.

Unfortunately, that’s not enough.  We need another reduction factor of at least five.  To explain how takes “rocket science” at the level taught in high school.  You also need a bit of understanding of the tradeoffs between reusability and payload.

The rocket equation sets the fuel fraction of a rocket.  If exponentials in equations scare you, perhaps they should.  They are the essence of compound interest and eat into the performance of rockets like a payday loan shark eats into income.  The formula for the propellant fraction of a rocket is:

 

The Space Shuttle Main Engine (SSME) is about the limit of performance practical for chemical fuels.  They have an exhaust velocity (V_e) above the atmosphere of about 4.5 km/s.  It takes somewhat over 9 km/s to get into orbit.  At a V_e of 4.5 km/s, the equation reduces to 1 – 1/e² where  e is 2.71828183 . . . , squared is ~7.39, and 1/7.39 ~.135.  The fuel fraction of a single stage to orbit (SSTO) using the best engines is 86.5% and everything else 13.5%.

The engineering consensus is that a reusable vehicle will need about 15% of takeoff mass in structure.  If the fraction available is 13.5%, we get a negative payload.  It is no wonder that SSTO rockets, especially reusable ones, don’t exist.

The situation is much better if the average exhaust velocity is twice that high.  By the formula, 1/e is ~.368, making payload plus structure 36.8%.  Even with 16.8% rocket structure, the payload fraction is 20%.

It’s possible to get exhaust velocity in this range.  The NERVA engines (nuclear reactors heating hydrogen) did it in the 1960s.  Unfortunately, NERVA type rockets are not suitable for the hard step of getting into orbit.  Engineering might overcome the weight problem for nuclear reactors.  Overcoming political opposition to flying nuclear reactors would be much harder.

The Skylon rocket plane does better than the equivalent of an exhaust velocity of 9 km/s.  This counts only the hydrogen consumed, not the air.

Skylon, was developed over the last 20 years by a UK company, Reaction Engines, Ltd.  They now have serious funding from the UK government and other sources.  They worked on a small scale for many years and finally produced a precooler.  It is the hardest part of the Synergetic Air-Breathing Rocket Engine that powers the Skylon to orbit.

Figure 1 Slylon taking off

The precooler has 26 km of fine tubing in it, so fine it looks like fabric.  Ram air at high Mach numbers is too hot to compress.  The precooler drops the temperature from as high as 1000 deg C to -140 deg C in a fraction of a second.  The low temperature makes the air easy to compress.  The engines use the heat extracted from the incoming air and the cold from hydrogen flowing to the engines to power a helium turbine.  The output of the turbine runs a compressor for the cooled air.  This method gets more energy out of the liquid hydrogen than just burning it (50 kWh/kg).  The helium turbine recovers much of the 20 kWh it takes to liquefy hydrogen.

At ~26 km, and about 1/4 of the velocity to orbit, a Skylon runs out of air.  After that, on 150 tons of internal liquid oxygen it does no better than a SSME.  Still, the high exhaust velocity up to 26 km allows an estimated payload of 15 tons out of ~300 tons at takeoff (5%).  A  Skylon that used air until it ran out and then switched to laser heated hydrogen would have a payload of 20%.  This would be better by a factor of four than the already remarkable payload of a SSTO Skylon.

Lasers will heat hydrogen into the 7-8 km/s range (or higher).  It takes a high power level, a few GW, to heat the hydrogen reaction mass.  Spread over 500,000 tons per year and 5 years, the cost for the laser lift is under $20/kg of payload.

Figure 2 Laser variation of Skylon nearing LEO on hydrogen heated by lasers

Running it only half time would double the laser part of the lift cost.  If you are trying to launch vehicles using lasers, the only way that makes sense is to run the lasers as close to 24/7 as possible

Figure 3 Laser propulsion station, disk is a rectenna powering the lasers.  Large surface is 3 GW of waste heat radiators.

Figure 4 Detail of lasers, optics, radiator tubes, flash drums and steam recovery compressors.  Shapes between radiator tubes are reflectors.

The smallest production of power satellites that makes economic sense is about 100 GW/year.  At 5 kg/kW, that’s 500,000 tons per year or 57 tons per hour, 60 tph if run 95% of the time.  The longest launch time is around 20 minutes.  Any longer or slower acceleration and the vehicles do not go into orbit.

Thus, the problem is to get a few GW of lasers into GEO where they can energize launching three 30-ton payloads per hour.  Smaller lasers then push the payload out to GEO at a high enough exhaust velocity that 2/3rd of the vehicle mass gets to GEO.  Rather than return empty, we scrap the second stage at GEO for part of the material needed to build power satellites.  This way the entire dry mass of the second stage becomes payload.

If we already had a power satellite in GEO, we would hook lasers to it and use it to power the transport of parts for hundreds more powersats.

Unfortunately we don’t.  We need to bootstrap the Skylon into a full-scale laser transport system.

The current scheme is to use 5-6 conventional Skylons to lift the parts needed for a 3 GW laser and a 3 GW radiator to LEO.  This will take around a thousand flights in a bit over a year.  At first, we power the propulsion laser from the ground since a 6 GW rectenna weighs a lot less than a power satellite of the same output.

Using power from the ground and electric thrusters, we fly the laser propulsion station [LPS] from LEO to GEO.  This takes a month or two.  Then the LPS powers a half million ton per year stream of cargo.  After the installation of such industrial base as needed, a small power satellite replaces the rectenna on the LPS.  Then we turn off the ground station and rebuild it as a rectenna.

On one LPS (and 150 Skylons), power satellite production ramps up to 100 GW per year.  With the transport system in place, it is much less expensive to add more lasers.  When there are 20 laser propulsion stations, the production rate for power satellite would be about two TW per year of new, low-cost power.

It takes less than a decade at that rate to displace fossil fuels of all kinds with clean, low- cost, electric power from space and low-cost synthetic fuel.

It looks like there is a way to engineer our way out of the energy, carbon, climate and economic problems.  At least that’s what the work to date indicates.

More details including the transfers orbits are here:

http://nextbigfuture.com/2013/09/propulsion-lasers-for-large-scale.html or at http://htyp.org/dtc

There is also a rapidly changing technical draft document on the design of the laser propulsion station shown in the illustrations.  It is available on request from hkeithhenson@gmail.com

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