## 1162: "Log Scale"

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mathmannix
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### Re: 1162: "Log Scale"

Invertin wrote:It might be both

"Gases" and "Gasses" are in the rare overlap between synonyms and homophones:

Although this one doesn't seem to be divided along "Atlantic Ocean" lines, most others I can think of are (color/colour, civilize/civilise, defense/defence)
I hear velociraptor tastes like chicken.

K^2
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### Re: 1162: "Log Scale"

javahead wrote:What about this Thorium stuff? I know it's been tried for ages with little proof of success, but it keeps showing up on my FB stream as THE thing.

Thorium fuel cycle takes Th-232 to U-233 (neutron capture + beta decay twice.) U-233 gives you 200MeV of energy. That's 0.925% of mass. U-235 reaction, in contrast, gives you 211MeV, which is 0.963% of mass. So Uranium can give you slightly better energy density in theory, but in practice, U-235 fuel will not be as pure as Th-232 can be, so the later will probably win.

These are tiny differences, however. Both fuels are very similar in terms of ideal efficiency. Where you win with Thorium is that you can run reaction at higher temperatures, allowing for better efficiency of energy generation via steam turbines or whatever. There are many other advantages to Thorium as fuel, but the biggest one is the fact that we simply have more of it around, and it's pretty much the only thing we've got that has a chance of replacing fossil fuels completely without running out too soon.

NiteClerk
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### Re: 1162: "Log Scale"

Just take the number you wish to record and convert it to a fraction with one as the numerator. Take a metal bar of a known length, say one meter. Cut the bar to the exact length of the fraction. When you need to know the number, measure the bar and reverse the process.
Bob (who has a very good tape measure)

K^2
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### Re: 1162: "Log Scale"

NiteClerk wrote:Just take the number you wish to record and convert it to a fraction with one as the numerator. Take a metal bar of a known length, say one meter. Cut the bar to the exact length of the fraction. When you need to know the number, measure the bar and reverse the process.
Bob (who has a very good tape measure)

You'll start having problems before you get to 10 digits with this method. You can push this method further if your bar happens to be made of nuclear matter, but regardless of materials, at 35 digits you'll run into Plank length limitations, and at that point even modern Physics cannot help you.

NiteClerk
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### Re: 1162: "Log Scale"

K^2 wrote:
NiteClerk wrote:Just take the number you wish to record and convert it to a fraction with one as the numerator. Take a metal bar of a known length, say one meter. Cut the bar to the exact length of the fraction. When you need to know the number, measure the bar and reverse the process.
Bob (who has a very good tape measure)

You'll start having problems before you get to 10 digits with this method. You can push this method further if your bar happens to be made of nuclear matter, but regardless of materials, at 35 digits you'll run into Plank length limitations, and at that point even modern Physics cannot help you.

Okay. Forget the metal bar. I'll use a piece of String.

peewee_RotA
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### Re: 1162: "Log Scale"

NiteClerk wrote:Okay. Forget the metal bar. I'll use a piece of String.

Should work, in theory.
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rmsgrey
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### Re: 1162: "Log Scale"

eculc wrote:I always thought it was just "gases"

What's a "gase"?

San Fran Sam
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### Re: 1162: "Log Scale"

keithl wrote:Uranium is for quitters who can't find enough antimatter to power a Kardeshev Type V civilization properly.

Is that a Bob Kardeshev Type V civilization or a Steve Kardeshev Type V civilization?

enginerd22
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### Re: 1162: "Log Scale"

Crosshair wrote:I try to do the same thing when I try to point out the people why electric cars have been dead for 100 years and will still be dead in 100 years and that the time and money is better spent perusing Algae Diesel or other alternatives while continuing to develop current reserves.

If you're going to make a broad statement about the viability of a technology you should examine more than one metric. The things you have labelled liquid fuels and gasses are completely consumed, while batteries are rechargeable a large number of times. All this chart examines is the mass a car needs to carry to power itself a certain amount. Which matters and must not be prohibitive (don't use batteries to power spaceships, for instance). Other factors such as lifecycle cost of fuel, vehicle (electric engines are completely different than those based on repeated contained explosions), renewability, and pollution also matter.

Bunnahabhain
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### Re: 1162: "Log Scale"

Well, back of envelope calculations indicate you'd need a 7 meter stack of paper- given the numbers of rough measurements, I wouldn't trust my measurments beyond one significant figure, so the card would read either 2 or 3, assuming we're not in a bunker or the V.A.B....

ManaUser
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### Re: 1162: "Log Scale"

RAGBRAIvet wrote:
zukenft wrote:this comparison was bad, because the energy density in uranium is due to nuclear fission, while the others are due to chemical reaction.

You are free to compare the amount of energy that is able to be obtained by nuclear fission of fat, coal, gasoline, etc.

Surely it would be easier to work out the energy from burning uranium.

cellocgw
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### Re: 1162: "Log Scale"

squonk wrote:Instead of juryrigging the Base 10 system of counting to do a job it's not cut out for, why not just use Base Googolplex?

Then, no matter how big the stack of cards, its quantity can be written out in a single symbol.

This I really like. Now estimate the size (in decimal) of a Graham's number base googolplex
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cellocgw
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### Re: 1162: "Log Scale"

jgh wrote:
Crosshair wrote:

Gasses? What's a gass?

It's what Jumpin' Jack Flassh is, of course.
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keithl
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### Re: 1162: "Log Scale"

keithl wrote:Uranium is for quitters who can't find enough antimatter to power a Kardeshev Type V civilization properly.

philip1201 wrote:More importantly though, there simply is no significant amount of natural antimatter in the accessible universe.

That would be a mere Kardeshev Type IV civilization, access to only one measly universe containing a vacuum-thin soup of normal matter, dark matter, dark energy, etc. Importing antimatter from antimatter-dominant universe 2 - or more safely, combining dense antimatter from universe 2 with dense normal matter in universe 3, importing the radiation, then exporting the waste heat to universe 4 - is the proper way to expoit a multiverse.

BTW, we know that alternate universes exist, because they are where most politicians, journalists, and media stars get their facts about science, economics, etc.

ctdonath
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### Re: 1162: "Log Scale"

zukenft wrote:this comparison was bad, because the energy density in uranium is due to nuclear fission, while the others are due to chemical reaction.

Fine. Let's update it for nuclear fission across the board:

Sugar: 0
Coal: 0
Fat: 0
Gasoline: 0
Uranium: 76000000

peewee_RotA
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### Re: 1162: "Log Scale"

keithl wrote:BTW, we know that alternate universes exist, because they are where most politicians, journalists, and media stars get their facts about science, economics, etc.

lol
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### Re: 1162: "Log Scale"

Invertin wrote:It might be both
Not really. "Gases" is 24 times more common than "gasses", which suggests that the second spelling is rather nonstandard.

cellocgw wrote:This I really like. Now estimate the size (in decimal) of a Graham's number base googolplex
If you're standing at Graham's number, 10 and a googolplex look to be about equally tiny. Graham's number is g64, and you'd need (a lot) more than g63 digits to express it in either base-10 or base-googolplex.

Remember, a googolplex is only 10^(10^100), which is tiny compared to 10^10^10^10 = 10↑↑4, which is microscopic compared to 3↑↑↑↑3, which is g1.
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ShuRugal
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### Re: 1162: "Log Scale"

javahead wrote:What about this Thorium stuff? I know it's been tried for ages with little proof of success, but it keeps showing up on my FB stream as THE thing.

a few problems with thorium. The first of which is Thorium has no naturally fissile isotopes, it has to be mixed with 233U, 235U, or Plutonium to start a burn. Another problem is that Thorium takes fer fekking ever to get from 232Th to 233U (almost 30 days), during which time you get a crapton of 233Pa (which is a neutron absorber) building up. 233Pa eventually breeds to 235U, but until it does so, it just sits there poisoning the reaction.

The last problem is political: 233U was once (ever) used in a test nuclear device. While it underwent fission with ridiculously lower yield than anything else being used a the time, it did undergo a fission explosion, which makes it's production subject to various non-profileration and non-development treaties. Since 233U is part of the Thorium fuel cycle, this makes it politically difficult to build thorium reactors.

hlangeveld
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### Re: 1162: "Log Scale"

K^2 wrote:
javahead wrote:What about this Thorium stuff? I know it's been tried for ages with little proof of success, but it keeps showing up on my FB stream as THE thing.

Thorium fuel cycle takes Th-232 to U-233 (neutron capture + beta decay twice.) U-233 gives you 200MeV of energy. That's 0.925% of mass. U-235 reaction, in contrast, gives you 211MeV, which is 0.963% of mass. So Uranium can give you slightly better energy density in theory, but in practice, U-235 fuel will not be as pure as Th-232 can be, so the later will probably win.

These are tiny differences, however. Both fuels are very similar in terms of ideal efficiency. Where you win with Thorium is that you can run reaction at higher temperatures, allowing for better efficiency of energy generation via steam turbines or whatever. There are many other advantages to Thorium as fuel, but the biggest one is the fact that we simply have more of it around, and it's pretty much the only thing we've got that has a chance of replacing fossil fuels completely without running out too soon.

An even bigger win is that Thorium supposedly would allow for an entirely different type of nuclear reactor, like the Molten Salt Reactors.
• By using Molten Salt technology, you operate under high temperature without the need for high pressure.
• Molten Salt allows you to 'burn up' all fissile material without the need for reprocessing.
• MSRs will slow down when the heat builds up, and with a fan-operated 'freeze-plug' they will shutdown safely when power to the fan is cut.

For traditional sold fuel, hot water reactors, you require thousands of tons of Uranium, that first must be enriched (removing some of the U-238, which is now waste). The enriched fuel pellets are then combined into fuel rods, which need to be reprocessed after they've produced only a percent or so of their theoretical energy capacity. Why? The byproducts of fission include Xenon, a gas that slowly breaks down the internal structure of the pellets.

TrueNarnian
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### Re: 1162: "Log Scale"

What if the number of iterations written down is too big to fit in the room?

Coyne
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### Re: 1162: "Log Scale"

Science tip: Log scales are for pinko commie environmentalism freaks who have some kind of weird thing about saving trees.
In all fairness...

R2D221
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### Re: 1162: "Log Scale"

Why has nobody pointed out that Randall is contradicting himself?
See comic #482

EDIT: Also #485
Last edited by R2D221 on Sat Jan 19, 2013 1:28 am UTC, edited 1 time in total.

brenok
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### Re: 1162: "Log Scale"

R2D221
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### Re: 1162: "Log Scale"

If it's not a contradiction, then does that mean that Randall is just a quitter? Lame.

brenok
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### Re: 1162: "Log Scale"

I can't exactly blame someone who doesn't have a paper of the size of the observable universe...

nitePhyyre
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### Re: 1162: "Log Scale"

Crosshair wrote:I try to do the same thing when I try to point out the people why electric cars have been dead for 100 years and will still be dead in 100 years and that the time and money is better spent perusing Algae Diesel or other alternatives while continuing to develop current reserves.

Yes, but energy density actually means means very little if you actually know what you are taking about. What's important is how much of that energy can be turned into useful work. The vast majority of the energy in those big hydrocarbon bars on your graph is going to be lost as waste heat.

Really, the gasoline and diesel bars should only be at around 2-3. That is before even considering that you also have to carry around a massive cooling system and enough extra mass in the engine itself to contain the bombs that are going off 60 odd times a second. And that's pure dead weight, lowering the hydrocarbons even further.

So yeah, you're wrong and should go apologize to everyone that you only have half off the story to.

That said, I agree with the conclusion. We are better off using clean energy at central locations to suck spent carbon out of the air and turn it back into usable fuel than we are to develop better eclectic cars. The (on your graph) 1.5 that you are going to get from gas is still better that the .75 you are going to get out of a battery. Barring some magical advance in batteries however the main advantage to gas I'd the ability to go from empty charge to full in under a minute. Sure most people don't need to go from empty to full that quickly, and can charge overnight, but that one time you need to go 800 km in a day, you will actually be able to. Which is nice.

Edit: I forgot that with gas cars you are going to be wasting fuel while you are stopped at red lights and stop signs. With an eclectic car, you won't be wasting anything. And when you stop our slow down in a gas car you are bleeding off even more of your energy as heat. With electric, you are recharging you battery.
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### Re: 1162: "Log Scale"

nitePhyyre wrote:Edit: I forgot that with gas cars you are going to be wasting fuel while you are stopped at red lights and stop signs. With an eclectic car, you won't be wasting anything. And when you stop our slow down in a gas car you are bleeding off even more of your energy as heat. With electric, you are recharging you battery.

That's why you have the drive train for the car be all electric, and only use a gas generator to make power as needed. Trains have done this for decades (well, with diesel instead of gas) and I've been wondering since the first parallel hybrids came out why the hell they were bothering with that instead of just sticking a gas generator in an otherwise all-electric car.
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Kit.
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### Re: 1162: "Log Scale"

Angelastic wrote:
Crosshair wrote:I try to do the same thing when I try to point out the people why electric cars have been dead for 100 years ...snip...

I don't get what you mean when you say you try to do the same thing; sure, you're presenting it without using a log scale, but who would ever present that graph on a log scale anyway?

Ah, that's an easy question.

The people that want to show that electricity is not that bad would.

nitePhyyre wrote:The vast majority of the energy in those big hydrocarbon bars on your graph is going to be lost as waste heat.

Actually, it's not "lost" or "waste" when you have -40 outside.

cwnc
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### Re: 1162: "Log Scale"

DAE think the road to workable fusion will be advanced molecular structures pushing nuclei closer together into exclusive quantum configurations, and not smashing atoms together in ways only possible within massive stars?

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### Re: 1162: "Log Scale"

Kit. wrote:
nitePhyyre wrote:The vast majority of the energy in those big hydrocarbon bars on your graph is going to be lost as waste heat.

Actually, it's not "lost" or "waste" when you have -40 outside.

Well, I think it could still be considered lost and waste, whether it's useful or not because of low temperatures, considering that the energy is no longer being used to power your car.

Daggoth
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### Re: 1162: "Log Scale"

can you prove xkcd < g_65? if so, how?

ShuRugal
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### Re: 1162: "Log Scale"

Pfhorrest wrote:
nitePhyyre wrote:Edit: I forgot that with gas cars you are going to be wasting fuel while you are stopped at red lights and stop signs. With an eclectic car, you won't be wasting anything. And when you stop our slow down in a gas car you are bleeding off even more of your energy as heat. With electric, you are recharging you battery.

That's why you have the drive train for the car be all electric, and only use a gas generator to make power as needed. Trains have done this for decades (well, with diesel instead of gas) and I've been wondering since the first parallel hybrids came out why the hell they were bothering with that instead of just sticking a gas generator in an otherwise all-electric car.

Something i have also wondered ever since i learned how a diesel-electric train works. The short answer is that it would make the car too damn heavy. Long explanation follows:

The engine would need to be powerful enough to power the car entirely when the battery is low or unable to produced the needed power to meet momentary demand of the motor. So you can't just have a tiny engine and trickle charge the whole time, or you're underpowered on hills and whatnot. But not only does this mean you need a large engine, it also means you need -two- large motors (the generator that the engine cranks must be able to match the power demand of the drive motor under the above conditions)

So already we have the engine that would be in the vehicle anyway, plus two electric motors which are each weigh half as much (or more) as the engine. The one place we are down here is a simpler (and therefore lighter) transmission: electric motors make asstons of toque at low RPM, and don't really lose anything as they speed up, so you only need one or two main drive ratios (or a nice CV transmission, but those are expensive and can be maintenance intensive).

Next we have the battery. Three options are lead, nickle, and lithium.
Lead is the heaviest, but it also provides the greatest working current ranges (both charging and discharging) and (when properly treated) has the best longevity.
Nickle has somewhat better energy-per-mass than lead, but has limited cycle life, more so at high charge rates (as a fraction or multiple of capacity) which limits the useful recovery of regenerative braking: either you can dump all the braking energy to the batts and cut their useful cycles down a quarter, or you can friction brake at heavier braking pressures and waste some of that energy. Nickel cells also waste volume because they must be cylindrical.
Lithium has astonishing energy density, and since lithium packs may be rectangular they are almost (but not quite) as volume-efficient as lead. Lithium is also capable of some truly terrifying discharge rates. the current generation of lithium batteries in use in today's RC model industry are capable of discharge rates upwards of 60C, that the maximum safe discharge rate exceeds 60 times the Ah capacity of the battery. That is, you could discharge the entire battery in a minute or less with no adverse effects. The most significant drawback of lithium though, is that it is tempermental as all hell. Forget a woman scorned, you ain't seen fury till you've seen an over-charged lithium-polymer pack go up like a fireworks stand. In addition, the fastest safe charge rate on most lithium packs is 1C, that is a one-hour charge rate. faster than that and you risk a fire, so forget regenerative braking entirely.

but yeah, the biggest thing holding electrically-driven, IC-generated cars and trucks back is the weight all that stuff adds. On a train, the weight of the locomotive is irrelevant, when you're pulling a vehicle that is over a mile long and weighs half a million tons or more, fifty tons of electrical generators and a hundred tons of batteries make fuck all difference there. On a passenger car that weighs just over one ton, however, adding five hundred pounds of motors and batteries (plus ancillary equipment like speed controllers and safety equipment) will entirely negate any benefit that would be gained from such a system.

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### Re: 1162: "Log Scale"

ShuRugal wrote:The engine would need to be powerful enough to power the car entirely when the battery is low or unable to produced the needed power to meet momentary demand of the motor. So you can't just have a tiny engine and trickle charge the whole time, or you're underpowered on hills and whatnot. But not only does this mean you need a large engine, it also means you need -two- large motors (the generator that the engine cranks must be able to match the power demand of the drive motor under the above conditions)

Couldn't this be negated by some kind of short-term energy storage just powerful enough to get the vehicle up to speed but not drive it for long, which would be mostly recharged by the reclaimative braking and only need gas power to make up for the inevitable inefficiencies of that? (I've always liked the idea of some sort of flywheel because it seems mechanically simpler and thus more efficient to keep the energy kinetic and just transfer it from the wheels to the flywheel and back as necessary, though a battery would have the advantage of not having to be spun up at ignition before you start driving. I suppose you could have both, and have the flywheel dump its energy out to the battery when the car is turned off, and the battery spin up the flywheel when you turn it on, but then you're adding more and more components and adding weight.)

But flywheels aside, you could have a small battery just enough to get from 0 to top speed before running out, not enough to drive on long-term. Most of the energy lost braking from top speed to 0 again will go to recharging the battery thanks to reclaimative braking, but of course that's not a perfectly efficient process and there are going to be losses. So you need a small gas engine just powerful enough to make up for those losses. This keeps you from needing a battery big enough to drive long range on, or an engine powerful enough to supply the momentary power demands of the electric motor; the battery supplies the momentary power demands, and the gas engine supplies the continuous power for longer range.
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ikrase
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### Re: 1162: "Log Scale"

this comparison was bad, because the energy density in uranium is due to nuclear fission, while the others are due to chemical reaction.

This comparison is fine, because it's comparing the energy density of the fuel using whatever the normal method of using the fuel is.

Incidentally, while the hydrocarbons do contain hydrogen, hydrogen-hydrogen fusion is INCREDIBLY hard to do on the small scale compared to any kind of fusion involving deuterium, tritium, or He3.
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### Re: 1162: "Log Scale"

Daggoth wrote:can you prove xkcd < g_65?
Yes, you can, because both the g sequence and the Ackermann function can be related to strings of chained arrows. I don't feel like re-running the proof at the moment, but it's not that hard to show that A(gn,gn) is less than gn+1.
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Crosshair
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### Re: 1162: "Log Scale"

Angelastic wrote:
Crosshair wrote:I try to do the same thing when I try to point out the people why electric cars have been dead for 100 years ...snip...

I don't get what you mean when you say you try to do the same thing; sure, you're presenting it without using a log scale, but who would ever present that graph on a log scale anyway? It doesn't even go up to 11.

Edit: d'oh... it does go up to 11. So much for that joke. But still, it doesn't have anywhere near the sort of ratios that people would use logs for.

I was referring to energy densities. Sorry for the confusion.

Crosshair
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### Re: 1162: "Log Scale"

Pfhorrest wrote:Couldn't this be negated by some kind of short-term energy storage just powerful enough to get the vehicle up to speed but not drive it for long, which would be mostly recharged by the reclaimative braking and only need gas power to make up for the inevitable inefficiencies of that? (I've always liked the idea of some sort of flywheel because it seems mechanically simpler and thus more efficient to keep the energy kinetic and just transfer it from the wheels to the flywheel and back as necessary, though a battery would have the advantage of not having to be spun up at ignition before you start driving. I suppose you could have both, and have the flywheel dump its energy out to the battery when the car is turned off, and the battery spin up the flywheel when you turn it on, but then you're adding more and more components and adding weight.)

But flywheels aside, you could have a small battery just enough to get from 0 to top speed before running out, not enough to drive on long-term. Most of the energy lost braking from top speed to 0 again will go to recharging the battery thanks to reclaimative braking, but of course that's not a perfectly efficient process and there are going to be losses. So you need a small gas engine just powerful enough to make up for those losses. This keeps you from needing a battery big enough to drive long range on, or an engine powerful enough to supply the momentary power demands of the electric motor; the battery supplies the momentary power demands, and the gas engine supplies the continuous power for longer range.

All you're doing is building a rube Goldberg contraption under the misguided assumption that electric cars are green. The more you rube goldberg it, the more weight you add to the car. The more weight you add to a car, the less efficient it will be. You quickly come to the point where the gas engine, with all its inefficiencies, will curb stomp any design you come up with in terms of energy efficiency, cost effectiveness, or both. As the chart I posed shows, the energy density of Gasoline and Diesel make electric anything a dead end because even at 100% efficiency, the electric cars can't compete because the gasoline engine and its fuel is lighter than an equivalent electric motor and its batteries.

A flywheel would be a horrible idea. You would be driving a gyroscope down the freeway, the handling would be horrible. The flywheel would have to either be so heavy that you'll be using more fuel just trying to cart it around. Spinning a lighter flywheel faster wouldn't work either because then you'd need a sizable scatterguard, which would eat any weight savings.

Not to mention that an internal combustion engine uses virtually no rare earth metals to build, it's mostly iron and aluminum, which are two of the most plentiful metals on the planet. Electric cars by contrast require vast quantities of rare earth metals, which is both very expensive and damaging to the environment to mine. There are upcoming technologies, like Algae Diesel, that will allow us the benefits of high energy density liquid fuels and never have to worry about running out as long as the sun shines, though by my guess they are still several decades away, but we still have plenty fo conventional sources to last us.

If you are worried about wasting fuel in traffic then a diesel engine would do more good than a bunch of batteries. Diesel engines sip fuel at idle, unlike a gasoline engine, because it always operates at "full throttle" and the speed is controlled by how much fuel is injected.

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### Re: 1162: "Log Scale"

rcox1 wrote:So should I be driving a nuclear powered car or an electric car whose power comes from nuclear power. I can certainly imagine a business model in which the former is leased to the end user and then returned. The advantage would be that fuel and maintenance of the power plant would be covered by warranty for the time of the lease. Miles should not matter.

The discussion on electrical vs thermal cars that is now ongoing shows clearly that energy density is not the whole story. You have to consider the whole weight of the fuel plus the engine and all the systems required for correct function (heating/cooling, reinforcement to prevent leaks, explosions, etc...).

The energy density of gasoline is so good that its weight is not a concern in car design. On a moderatly loaded car, it represents less than 10% of the total weight. This is this that you propose to replace with the uranium. It would make it reach 0.0..01% of the weight but you would then have to account for the additional weight of a nuclear reactor and its cooling system.

There has been a concept car by Ford, who anticipated a miniaturization of nuclear reactors : http://en.wikipedia.org/wiki/Ford_Nucleon

But right now, even the smallest nuclear power generator designs still require a big truck : http://newenergyandfuel.com/wp-content/ ... actors.jpg

I dismissed radioisotope thermoelectric generators as I don't believe that any has a sufficient output to power a car.

gigatera
Posts: 1
Joined: Sat Jan 19, 2013 9:14 pm UTC

### Re: 1162: "Log Scale"

I miss the energy density of moving air (as in wind)

ShuRugal
Posts: 75
Joined: Wed Jan 26, 2011 5:19 am UTC

### Re: 1162: "Log Scale"

Pfhorrest wrote:
ShuRugal wrote:The engine would need to be powerful enough to power the car entirely when the battery is low or unable to produced the needed power to meet momentary demand of the motor. So you can't just have a tiny engine and trickle charge the whole time, or you're underpowered on hills and whatnot. But not only does this mean you need a large engine, it also means you need -two- large motors (the generator that the engine cranks must be able to match the power demand of the drive motor under the above conditions)

Couldn't this be negated by some kind of short-term energy storage just powerful enough to get the vehicle up to speed but not drive it for long, which would be mostly recharged by the reclaimative braking and only need gas power to make up for the inevitable inefficiencies of that? [snip]
But flywheels aside, you could have a small battery just enough to get from 0 to top speed before running out, not enough to drive on long-term. Most of the energy lost braking from top speed to 0 again will go to recharging the battery thanks to reclaimative braking, but of course that's not a perfectly efficient process and there are going to be losses. So you need a small gas engine just powerful enough to make up for those losses. This keeps you from needing a battery big enough to drive long range on, or an engine powerful enough to supply the momentary power demands of the electric motor; the battery supplies the momentary power demands, and the gas engine supplies the continuous power for longer range.

Flywheel, as you noted, is complex and heavy: now you need a -third- motor to spin up the flyweel and extract energy from it, in addition to the flywheel itself.

"more batteries" is pointless, as discussed, Lead Acid can handle high-current output/input (AGM batteries are particularly impressive in this regard) and they have excellent volumetric power density, but they are heavy as all fuck. Nickel batteries -can- be charged at insane charge rates, but it kills cycle life: i've known RC Car guys to do 5-minute charges on nickel packs, and get 5 uses out of each pack before it was junk. Lithium is capable of insane discharge, but maximum safe charge rate is 1C, so unless you plan on taking an hour each time you stop, you will only recapture an insignificant fraction of your energy.

The only other sort of technology that can be charged to and discharged from full capacity in a few seconds is a capacitor, but volumetric density on caps is absolutely atrocious. a cap large enough to get your car up a 1-minute long 20% grade would be bigger than the car.