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Hybrids less important than Hummers

Assuming the same # of miles will be driven, is it better to spend $X to increase an individual vehicle's mileage from 10 to 20 miles per gallon, 20 to 30 mpg, 20 to 40, 20 to 50, 20 to 100, or 20 to 1000?

Space for you to ponder in...

10 to 20 mpg! As monty00 pointed out, the numbers we're used to using (mpg) are the reciprocals of what we actually care about saving (gallons) which makes them misleading. More useful would be gallons per 10,000 miles, say, and the numbers then convert respectively to 1000 gallons, 500, 333, 250, 200, 100, and 10 gallons.

Which makes it easy to see that the initial efficiency gain of 10 to 20 mpg saves us 500 gallons per 10,000 miles, and it is physically impossible to realize an equivalent gain. Even the extraordinary efficiency of 100 mpg would save only an additional 400 gallons. (Conversely, going from 5 to 10 mpg saved 1000 gallons, and equivalent savings per vehicle will never be realized again.)

So, for an individual, upgrading your vehicle may make sense (and the gallons per mile figure is what you want for figuring out total cost of operation), but for public policy the first priority should be getting low-mileage vehicles off the road, whether 30 year old smoking Cadillacs (not to mention their pollution) or particularly egregious SUVs. Going from decent modern efficiency to spiffy cutting edge hybrids is less important.

Of course, I was assuming the same upgrade cost per vehicle. If you can upgrade four 500 gallon vehicles to 333 gallons, or three 500 gallons to 250 gallons, for the same cost as upgrading one 1000 gallon vehicle to 500, then the former is better. OTOH, usually the later efficiency gains are more expensive than the earlier ones, so the 1000->500 upgrade is probably cheaper than the rest, for vehicles in roughly the same weight class.

The same logic can be applied to power plants. I'm used to thinking of them as X% efficient, as in converting 25% of the energy in the fuel to useful electric power. But, after we're done making all of our appliances as efficient as we can, we'll still want some fixed amount of power, and we're trying to save fuel, so again we want the reciprocal figure, how much fuel is burned to generate our power. 20% means 5 Joules fuel per 1 J power, 25% is 4/1, 33% is 3/1, 50% 2/1, 66% 1.5/1, 75% 1.33/1, 80% 1.25/1, 90% 1.1/1, and the impossible 100% is 1/1. If we look at how much energy is wasted per Joule of power generated, it's 4, 3, 2, 1 (at 50%), 0.5, 0.33, 0.25, 0.1, and 0. Once again, the low end is clearly a much higher priority for improvement than the high end; going from 20% to 25% is better than anything you can do with a 50% plant.

Cars, by the way, can be thought of as tiny distributed power plants (generating mostly mechanical work, with a bit of electricity), typically around 20-25% efficient, *I think*. Conventional 'real' electric plants are around 33%, spiffier ones clawing up to 50%, or even higher with co-generation (using the waste heat for heating and industry, though since it's not electricity I should ignore it for current purposes.) Electric cars have lots of problems at the individual level, because batteries suck, but moving the power generation from the car to a large stationary more efficient power plant obviously has a lot of potential at the global level.

Developing a gasoline fuel cell, or converting with minimal loss gasoline into something that could go into a fuel cell, and said fuel cell having efficiency upward of 50% due to being electrochemical rather than a heat engine, would completely rock. Not that I've ever heard of a gasoline fuel cell, just alcohol and hydrogen ones, with the alcohol ones risking getting clogged by the carbon. And generating hydrogen has its own large factors of loss. (Wikipedia mentioned hydrocarbon fuel cells, but doesn't say much about them. Fuel cells for solid carbon exist, but for mixed carbon/hydrogen fuels I'm not sure if anything reacts the C for power vs. using the H and trying not to be poisoned by CO. One strategy is reforming, generating hydrogen from the fuel, and there's a seven year old article about reforming gasoline for a fuel cell, with the "potential" for 40% efficiency vs. 20% for internal combustion. As far as I can tell such things basically throw away the C and its energy, but get energy out of the H really efficiently.)

(Hey, mrs_feltner, behold the power of MATH!)


( 3 comments — Leave a comment )
Jul. 8th, 2008 06:04 am (UTC)
extra credit:

If a 50mph hybrid receives a $3200 tax credit over a 25mpg car, how much of a penalty should a 10mpg H2 pay?

If you said negative $10,000 you're in line with the way our tax incentives work. By my reckoning, that's pretty much a sign error in terms of fuel conservation assessment.
Jul. 8th, 2008 06:22 am (UTC)
Geez, my post is a lot longer than I thought it'd be.

50 mpg vs. 25 mpg is 200 gallons vs 400 gallons, so $3200/200 gallons. 10 mpg is 1000 gallons, burning 600 more gallons than the 25 mpg baseline, so should be $9600. Yep, sign error!
Jul. 8th, 2008 12:30 pm (UTC)
( 3 comments — Leave a comment )


Damien Sullivan

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