Doublemix: A new start

Today is January 1, 2018.

Day 1 of Doublemix.

And maybe a new start, perhaps.

If you’re here for posts on the hydrogen economy, skip to the next post (in reverse chronological order), reflections on my Mirai’s first birthday.  This one is only here because I blog too little to warrant a second blog of my own, and it doesn’t fit in with any of the other blogs I like to post and comment at.

2018, if you’ll allow me to start a paragraph with a number, factors as the product of the two primes 2 and 1009.   They are the least primes with respectively one and four digits.  Furthermore each is special in is own way.

1009 in Roman numbers is MIX.  This was the name Donald Knuth gave to the pseudocomputer he used in explaining the algorithms in his volumes The Art of Computer Programming.  Twice that is 2018, hence the name Doublemix.

1009 is not only the least prime with four digits but also the least such whose fifth power, 1045817322864049, contains all ten digits.

You’ve probably heard the story how when Hardy came to visit Ramanujan in hospital he apologized for having come in a tram with such a boring number as 1729.  “Oh no,” said Ramanujan, “it is a very interesting number.  It is the least number expressible as the sum of two cubes in two ways: 9³ + 10³ and 1³ + 12³.”   Well then, what about three cubes?  Good question.  1009 is expressible in two such ways, as 1³ + 2³ + 10³ and 4³ + 6³ + 9³, and that’s the smallest.

And when you write primes in English, 1009 is the least one containing the letter ‘a’.

1009 is a remarkable number.  Many more of its properties can be found here.

So take that, 1729.  Why, you’re not even a prime!

Let’s move on now to the smaller of the two factors of 2018.  2 has been special for millennia, as the number motivating the whole idea of counting.  If whenever you counted a collection you never got past 1, no one would have invented counting.

Russell and Whitehead’s Principia Mathematica develops its subject matter with such great care that they do not feel prepared to claim 1 + 1 = 2 until page 379.  Yet two thousand years earlier, had Roman mathematicians used concatenation to denote addition, instead of multiplication as we do today, they could have proved that II est II simply by pointing harder.  (The equal sign did not appear until the 16th century.)

And half a century before Russell and Whitehead, George Boole had shocked his contemporaries with an arithmetic in which 1 + 1 was not 2 at all.  This is what we call today Boolean algebra, the arithmetic of 0 and 1.  1 +1 could not be 2 because 2 didn’t even exist in Boole’s curious system.  In Boolean algebra counting reduces to yes (1) or no (0) as the answer to the question, “Am I holding up any fingers?”, as distinct from the higher math question, “How many fingers am I holding up?”

With such a limited repertoire, the entire gamut of possible values for 1 + 1 amounts to just 0 or 1.  And in fact Boolean algebra provides for both answers by providing two ways of interpreting the operation +, namely as inclusive and exclusive disjunction respectively.  With the former, 1 + 1 = 1, and with the latter, 1 + 1 = 0.

The former was the operation that Boole regarded as the counterpart of addition in his new arithmetic, and he wrote it as +.  So in Boole’s arithmetic 0 + 0 = 0, and 0 + 1 = 1 + 0 = 1. Boole was fine with that, as were his contemporaries.

What was new about Boole’s arithmetic was 1 + 1 = 1.   This was fine with Boole, but it took his contemporaries aback.

Boole also defined conjunction, namely as the operation xy, ordinary multiplication.  This is 1 when both x and y are 1, and 0 in all three other cases.  No one had any problem with taking multiplication to mean logical conjunction.

What about the other possibility for addition?  That’s the operation in which 1 and 1 is 0.  That operation is called exclusive OR, XOR.  Today we write it as x y to distinguish it from x + y.

Boole himself knew and wrote about XOR, but he did not regard it as a basic operation.  He explained it instead as the compound operation x + y − xy : when x and y are both 1, subtract it from the result of x + y so as to not to count twice the case when both are true.

But what is subtraction x − y in Boole’s system?  Is it another basic operation?  Boole glossed over this, but the answer he should have given if anyone was to make sense of his system is that it requires one more basic operation besides x + y and xy, namely ¬x, definable on 0 and 1 at least as 1 − x.  With only the two operations x + y and xy, there is no way to construct 0 when x and y are both 1.   With ¬x we can define x − y  as the conjunction x(¬y) which is 0 except when x = 1 and y = 0.

So that’s Boolean algebra.  It has various laws that are the same as in ordinary algebra, like x + y = y + x, commutativity of addition, xyyx, commutativity of multiplication, and x(y + z) = xy + xz, distributivity of multiplication over addition.  But it also has laws not found in ordinary algebra, like x + xx, idempotence of addition, x² = x, idempotence of multiplication, and x + yz = (xy + xz), distributivity of addition over multiplication.

While these strange new laws didn’t bother Boole they bothered his contemporaries so much that they decided Boole’s system was not an arithmetic of the numbers 0 and 1 at all but the logic of truth values T and F, true and false.  With that distinction there is no reason to expect the algebra of truth values to mimic the algebra of numbers except superficially.

And that’s the way the world viewed Boolean algebra until 1927, eighty years after its introduction, when the Russian mathematician Ivan Ivanovich Zhegalkin pointed out that Boolean algebra was equivalent to arithmetic mod 2.  While keeping xy as a basic operation, he took x y as the other basic operation.  Whereas in Boole’s system xy is a compound or derived operation definable in terms of basic operations as x + y − xy, in Zhegalkin’s system x + y is a derived operation definable in terms of basic operations as  x yxy.

In this way Zhegalkin conferred legitimacy on Boole’s original concept, that truth values can be understood as numbers, by identifying arithmetical addition with XOR instead of OR and reducing all numbers to just their parity, namely their remainder mod 2, their least significant bit or LSB when represented as binary numerals instead of decimal.

Since x ⊕ x = 0 Zhegalkin had no need for a separate constant for 0.  However there was no way to express 1 and so besides the two binary operations Zhegalkin also needed a constant to denote 1.  Once he had that constant he could then express  ¬x as x ⊕ 1.  And with just xy and ¬x we can express x + y as ¬(¬x¬y), implication xy as ¬x + y, and along similar lines all of the many other operations of Boolean algebra.

And now back to the hydrogen highway.

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My Mirai’s first birthday

My wife and I bought (ok, leased) our 2016 Toyota Mirai on May 19, 2016.  A year and nine thousand miles later is a good time to reflect on the wisdom or otherwise of this acquisition.

The first thing I have to say is that my perspective on electric vehicles (EVs) at that time was very much colored by the following simple fact about them governing my purchasing decisions.

The only pure EV (one without a gasoline “range extender”) then on the market that could be guaranteed to carry me the 95 miles between the two Stanford campuses I work at, respectively Palo Alto and Pacific Grove, would have cost me more than twice anything I’d ever previously considered worth paying for personal transport.

In 2015 I’d have leased the Hyundai Tucson FCV in a heartbeat.  Unfortunately they were only available in Southern California.

In 2016 Toyota won that EV race in Northern California with their Mirai FCV.  At $349/mo (after Toyota accommodated earlier complaints) for a 36-month lease of an EPA-rated 312-mile-range sedan with the down payment paid by the state and the fuel for the duration paid by Toyota, it was irresistible.

Had I wanted to own or lease (as opposed to rent) an EV that I could drive to visit my sister in Vancouver, my colleagues in New York, or sights in Central or South America, I’d have passed. Not only would such an EV be insanely expensive, but being well over 70 I wouldn’t dream of risking falling asleep that way en route when for air fare plus $6 for a can of beer I can do so in the friendly skies and deplane completely refreshed.

But then Toyota started selling its Mirai.

Eight months after our Mirai acquisition, replacing my 1998 Mercedes Benz gasoline E430, we had the opportunity near the start of 2017 to buy a Chevy Bolt at a dealer four miles from where I worked at Pacific Grove.  As I see it the Bolt would be a great replacement for my wife’s 1987 Mercedes Benz diesel TD300 station wagon with 296,000 miles and one airbag in the steering wheel.  She still loves it, but the Bolt’s ten airbags have a certain appeal safety-wise to both of us.  On the other hand the Bolt’s lower carbon soot and CO2 output doesn’t to her, even though she’s a liberal marine biologist while I’m just a middle-of-the-road apolitical computer scientist.  Perhaps by the time she makes up her mind the Tesla Model 3 will be a no-brainer for everyone torn between it and the Bolt!

Ok, so enough about whether BEVs are the spawn of the devil or Earth’s salvation.  May 19, 2017 is my Mirai’s first birthday and so that’s what this anniversary post is about.

I have to say that I feel like Darwin must have felt in the mid-19th century when he was set upon by those who felt he was undermining humanity’s spiritual life.  FCVs are attacked for a depressingly long laundry list of their faults.  Feel free to add any I’ve overlooked here.

  1.  Hydrogen molecules are so tiny compared to any other molecule they can escape from their tanks more easily than the molecules that power other mobile engine technologies.  This is (a) the case and (b) a very bad thing.
  2. The 21 tons of hydrogen in the Hindenburg killed 36 people in 1937.  This is more than five times as many were killed in the Valentine’s Day massacre of 1929.
  3. The US has about 170,000 gasoline stations as opposed to a mere 30 or so hydrogen stations.  Moreover almost all of the latter are concentrated in California, making hydrogen irrelevant to normal people.
  4. Even though FCV manufacturers today are charging less than Tesla is charging to buy EVs of the same range, that’s only due to subsidies.  In the long run Tesla will be able to sell their cars at a greater profit per mile of range than the FCV manufacturers, who must have slipped a decimal point somewhere in their calculations of the economic benefits of hydrogen.
  5. Hydrogen currently costs $16-$17 a kilogram, which for a typical lead-footed FCV driver amounts to some US$0.37/mile.  When car manufacturers stop subsidizing fuel costs, electricity for charging BEVs will turn out to be cheaper per mile than hydrogen for refilling FCVs.  Cheap hydrogen is an oxymoron for patently obvious physical, chemical, and economic reasons.
  6. Although politically blue states like California are committed to installing a viable hydrogen highway infrastructure over the coming years, politically red states will never pull the rug out from under Big Oil.  Since red states are the majority in the US there is no hope in any foreseeable future for a nationwide hydrogen highway.
  7. The growing number of companies and countries signing on to the hydrogen highway vision is nothing more than the “bigger fool” mechanism of the booms and busts of the last several centuries nicely summarized in the book Extraordinary Popular Delusions and the Madness of Crowds by Charles Mackay.  Expect to see this dream-of-fools collapse big time for the ridiculous hydrogen-highway concept by the middle of 2020.

Points 1-7 notwithstanding, I’ve greatly enjoyed driving my Mirai for close to 10k miles.  Time to refuel is a second a mile, two seconds on very hot days so as not to overheat the tank, which is about ten times faster than for any BEV available today.  Acceleration is 0-60 in 9 seconds which while nowhere near “ludicrous” is better than consumer sports cars of two decades ago.  Finding a fuel station has only been a concern when trying to drive to the limits of California such as into Mexico, Nevada (where I’ve driven some anyway), and Oregon (hard to reach so far but I’m working on it).

Early on I worried about range as a problem. I assumed that California put a hydrogen station at Harris Ranch as a hydrogen highway connector between Northern and Southern California because an FCV couldn’t hope to make the long trip between San Francisco and Santa Barbara even by 101, let along scenic Route 1 (Cabrillo Highway) along the winding and hilly coast.  So I was very pleasantly surprised to find I could drive between the Campbell and Santa Barbara stations via either one of 101 and Route 1 with at least 20 miles to spare.

Meanwhile Honda has started selling its Clarity FCV.  My wife and I are now comparing it with the Chevy Bolt, which has been selling like hot cakes since January (there’s a Bolt dealer four miles from our house that we’ve already taken a couple of test drives with).  The Bolt’s 164″ length makes it much easier to park than the Clarity’s 192″, but the Bolt’s range is a mere 238 miles vs. the Clarity’s 366 miles (54 miles more than my Mirai) and moreover takes nearly ten times as long to refuel as the Clarity.

On the other hand the Bolt’s hatchback form factor is better for luggage-for-two than the Clarity’s small trunk.  Morever the Bolt can go anywhere in the continent that has a charger outlet, and can charge at home (mine or any relative’s or friend’s) overnight.  This makes it a very difficult choice between the Bolt and the Clarity.

Would we buy a Tesla Model 3 instead of a Bolt?  Sure, if the price is right and it’s available any time soon.

How about a Model 3 vs. a Clarity?  That’s tougher.

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A more nuanced view of BEVs

To date I haven’t been kind to BEVs.  With the appearance three weeks ago of the Chevy Bolt on dealer floors I’ve come to realize that my objections to BEVs were based on the fact that every production model BEV was either too expensive or had too short a range.

The point of electric vehicles is that they don’t emit CO2, a growing hazard for climate today.  Some approaches to climate mitigation have been denounced by their opponents as too painful to consider, much as one would not go to a medieval dentist for fear that the cure might be more painful than the disease.

The climate counterpart of modern dentistry is painless mitigation. At least in first world countries austerity will be no more effective for global warming than diet has proved for obesity.

Painless climate mitigation is coming slowly, give it time. As an early adopter I’ve put 7000 miles since May on my Toyota Mirai.  I have found it a pure joy to drive. There are just enough hydrogen stations in California for me to be able go pretty much wherever I want within the triangle bounded by Ukiah, Reno, and upper Baja.  A fill-up takes only five minutes every EPA 312 miles (best I’ve managed is 370 miles). California has 25 hydrogen stations now, almost all commissioned within the last 18 months. In 2013 California Assembly Bill 8 authorized the California Energy Commission to build a hundred at an expenditure rate of $20M a year, so there are 75 to go. The expectation is that private investment will step in once this bootstrapping phase has created a market.

Toyota and Honda have committed to ramping up delivery to California of respectively the Mirai and the Clarity. In their price bracket and range the only BEV competitor today is the Chevy Bolt which I test drove just two days ago. The past three weeks Peninsula Chevrolet Cadillac has been selling them like hot cakes a mere two miles from where I’m typing this at my beach house. (GM picked them over their nearby Salinas counterpart because last year they sold ten times as many Volts.) My wife’s 1987 MBZ 300TD needs to find a new home (even though it should still be good for another 300,000 miles) because she’d like something with more modern safety features. Interesting options for us are the Honda Clarity FCV and the GM Bolt BEV, with respective EPA ranges of 366 and 238 miles, both leasing for around $370/mo (the Mirai is $349/mo but we already have one).

While there’s no shortage of sour grapes about these cars online, most of the complaints concern mere teething problems. I’m convinced these EVs are the cars of the future, with batteries for commuting and short trips and fuel cells for that plus longer trips, infrastructure permitting. (BEVs are ok for long trips provided you set aside time for refueling, e.g. at meal stops.) Germany and Japan are way ahead of the US with FCV infrastructure and other European countries, in particular Nordic ones. are starting to put their toe in the water.

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  1.  Green hydrogen production via low-temperature alkane cracking

    (The following distinguishes renewable and green energy.  Renewable energy does not entail consumption of fossil fuels, for example wind, solar, hydro, biofuels, etc. In contrast green energy does not entail emission of CO2, for example wind, solar, hydro, and carbon-based fuels with carbon capture and sequestration (CCS).  In particular biofuels are renewable but without CCS are not green as understood here.)

    Hydrogen can be captured as an otherwise unwanted byproduct of various industrial processes.  Even if those processes are not themselves green, using such hydrogen instead of discarding it could arguably be considered green.

    Hydrogen can also be manufactured intentionally by steam reforming of methane, with oxides of carbon (CO and CO2) as byproducts.  Typically these are emitted to the atmosphere, making this method not green.

    Another commonly considered method is electrolysis of water producing hydrogen and oxygen.  This method is thermodynamically unfavorable, particularly at room temperature but less so at higher temperatures.  When the electricity comes directly from a solar panel the resulting hydrogen is clearly green.  However the 22% efficiency of solar panels in combination with the thermodynamic inefficiency of electrolysis makes this method expensive relative to the other uses to which the electricity could be put.

    Although fossil fuels are not renewable, they are still plentiful today and are projected to remain so for many decades to come, making them of considerable interest for the foreseeable future.  Natural gas (largely methane, CH4), propane (largely C3H8), gasoline (largely iso-octane, C8H18), and other alkanes (CnH{2n+2}) are refined from fossil fuels and and their principal constituent elements are carbon and hydrogen.  Hydrogen produced by removing and sequestering the carbon is green hydrogen as understood here.  Understood as a chemical reaction, this process can be expressed as the reversible reaction CnH{2n+2} <=> nC + (n+1)H2, for example CH4 <=> C + 2H2 in the case of methane.

    A straightforward implementation of this process is thermolysis or heat cracking carried out in the absence of other chemicals, especially avoiding oxygen!   In the case of methane, at 500 C and atmospheric pressure an equilibrium is reached in which half the methane has separated into hydrogen and carbon.  By 1000 C essentially all of the CH4 has been “cracked”.

    A problem with this method of producing hydrogen is that at these high temperatures the carbon tends to form carbon nanotubes that stick to the furnace orifices, eventually clogging them.  Carbon nanotubes are notoriously strong, greatly complicating cleaning them out.  Recently teams at IASS in Germany and KIT in Sweden have bubbled methane through molten tin at temperatures of 1000 C and above, with the carbon nanotubes collecting at the surface as an easily removed scum.  While this method seems very promising technically, its economics are unlikely to become clear for several years.

    We are therefore interested in alternative approaches to removing the carbon from alkanes that does not involve molten metals.  We are currently exploring methods that avoid production of nanotubes, in particular at low temperatures and low pressures.

  2. Home hydrogen

    Currently there are no practical methods of producing hydrogen at home.  As one application of the foregoing project, we would like to make a prototype of a 34″ tall device that sits on the ground directly beside the Toyota Mirai’s fuel receptacle and pumps purified hydrogen into it.

    Since natural gas is more prevalent than either propane or gasoline in typical suburban residences, and moreover is 25% hydrogen by weight, the feedstock for this device would be natural gas.   The electricity needed for the prototype can come from the house mains initially.  A more elaborate model would have a small rechargeable battery and a fuel cell powered by the generated hydrogen; alternatively it could draw its power from the Mirai’s 12 volt DC 10A power outlet.

    The pumping pressure could be anywhere from 20 to 70 MPa.   20 MPa would suffice for a range of 90 miles, 35 MPa for 155 miles, and 70 MPa for the Mirai’s EPA-rated 312 miles.

  3. Fast US crossing in an Electric Vehicle

    The record for an electric vehicle crossing the US from Los Angeles to New York, 3011 miles, is 58 hours and 55 minutes.  This included 12 hours and 48 minutes of charging time.   A fuel cell vehicle could easily shave ten hours off the recharging time.  The obstacle is the lack of infrastructure.

    Continuous production of hydrogen from a readily obtainable alkane would permit much faster refueling at either fast-fill CNG stations, purchase of bottled propane, or refilling a gasoline tank.  The tradeoffs between these alkanes need to be explored.

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Internal combustion engine vehicles, ICEVs, are powered by burning hydrocarbons like gasoline, diesel, ethanol, compressed natural gas, propane, and mixtures thereof. They pollute by emitting byproducts of the combustion, mainly CO2 as the principal cause of long-term global warming but also with traces of much more toxic emissions that can impact the immediate neighborhood more short-term [1].

Moreover ICEVs are inefficient. This is because they exploit the thermodynamics of a heat engine that converts a temperature difference into mechanical energy. Nicolas Carnot’s theorem, which he proved in 1824, states that the efficiency of any such heat engine is at most the ratio of that difference to the higher temperature. In order to have anywhere near 100% efficiency the lower temperature would need to be near absolute zero, -273 C. This might be feasible on frigid Pluto far from the Sun’s warmth, but not on Earth, and especially not in an ICE whose lower temperature as a heat engine is that of its exhaust as it leaves the cylinder! Car engines are typically well below even the already low Carnot limit, being about 20-30% efficient.

Thermodynamics is the last place efficiency experts should be looking.


Electric vehicles, EVs, are powered more indirectly, namely by converting the chemical energy of an on-board fuel of one kind or another into electrical energy. In turn an electric motor converts this electrical energy (very efficiently with the present state of the art) into mechanical energy.

An important aspect of this chemical-to-electrical conversion is that it is slow, limited by the impracticalities of driving at over 150 mph on most roads or doing twenty consecutive 0-60 mph timing runs. It therefore does not do the sort of damage to the chemicals that faster conversion can cause. This is relevant to the first essential difference below between BEVs and FCVs.

By avoiding combustion EVs are far less polluting than ICEVs, and by avoiding thermodynamics they are also much more efficient.

All this however is merely background for the immediate question of the form the chemical energy of an EV should best take.


There are two main choices: battery chemistry and fuel cell chemistry.

Critics of FCVs like Joe Romm, Tony Seba, and the Wikipedia article on fuel cell vehicles have long lists of faults that would seem to suggest many differences from BEVs. By contrast the Wikipedia article on battery electric vehicles was unable to find a single fault with BEVs.

But some of those differences are not essential. Yes there are many more Tesla supercharger stations than hydrogen stations, but that’s more an accident of timing and deployment than an essential difference. Likewise there are many more BEVs than FCVs, but that too is timing and the ratio has been shrinking rapidly over the past 12 months.


I see only two properties of BEVs and FCVs that distinguish them in anything like an essential way. In decreasing order of obviousness:

1. Refueling a BEV entails transforming electrical energy to chemical.

2. The FCV’s independent fuel cell and tank decouples its available power from its energy capacity.

The first distinction is significant because such conversion in either direction without permanent damage is slow, as noted above in the case of conversion from chemical to electrical. Charging a battery without seriously degrading its life it can take an hour or more.

In contrast the energy in an FCV’s fuel is chemical to begin with. It can therefore be pumped into an FCV’s tank much faster than a BEV’s battery can be recharged, in minutes rather than hours (but not seconds because compressing requires energy and is also thermodynamically inefficient).

The second distinction is significant because the available power from a battery is in proportion to its energy capacity. Hence if you want a BEV with a high capacity battery for longer range, you must employ a battery capable of delivering higher power, whether you want that power or not!

The Tesla S P100D’s Mirai-beating EPA range of 315 miles [2] is achieved with a battery capable of delivering 500 kW (670 HP) [3], good for a 0-60 mph time of 2.5 seconds. Tesla makes this almost record-breaking power a feature of its long-range vehicles, as well it should.

However the price for this mind-boggling power that comes with merely respectable range is a 1200 lb battery and an MSRP of $134,000 [4].   On the one hand, among cars that quick the Tesla may well be the cheapest.  On the other, if all you want is its 315-mile range you can’t get it without paying for luxury-level performance even though you may never use it.

In contrast the Mirai achieves its EPA range of 312 miles with a 204 lb tank (including 11 lb of hydrogen). Independently it achieves its 114 kW (153 HP) of power with a 124 lb fuel cell, good for a 0-60 mph time of 9.0 seconds that would have been considered very sporty a mere two decades ago [5]. The drive train weight therefore totals 328 lbs (408 with the traction battery) vs. the Tesla’s 1200 lb battery pack. And the 2017 Mirai leases for a quite modest $349/month, likely about a quarter of what the P100D would lease for were Tesla to offer a lease option.


There is a third difference, involving efficiency, but it remains to be seen whether this is an essential one. The lithium-ion batteries typically used in BEVs have an efficiency about 1.5 times that of a fuel cell. This is easily deduced from the fact that one gasoline gallon equivalent (GGE) of electrical energy (33.7 kWh) can take a Leaf or Tesla about 1.5 times as far as one GGE of hydrogen energy (about 1 kg).

So what? Both types of EV are far more efficient than ICEVs. What does that extra 1.5 factor do for the BEV owner? Obviously it doesn’t buy more range: Tesla had to go way out on a limb to match the Mirai’s range.

Which leaves cost.

So what’s the cost of hydrogen energy vs. electrical energy?

Solar energy is currently wholesaling at about 3 cents/kWh in several parts of the world. 1 kg of hydrogen has 33.7 kWh. Hence in order to match electrical power, taking into account the 1.5 efficiency factor, hydrogen would need to wholesale at $0.03*33.7/1.5 = $0.67/kg.

Is this possible? Anaerobe Systems’ Mike Cox believes his biofuel approach can achieve $0.50/kg. The jury is out, probably for quite a while.

But this overlooks the capital cost of a 300-mile range BEV. While its electrical fuel may well be cheaper than the FCV’s hydrogen fuel, mile for mile, how many years before that savings makes up for the BEV’s insanely higher price?

5? 10? The car’s lifetime? Your lifetime?

You do the math.


Meanwhile there is a positive side to inefficiency that ICEVs get in spades during winter: vast amounts of heat. While FCVs don’t get that much heat, they get more than enough to keep both cabin and equipment toasty warm. This is why FCVs have much noisier radiator fans than BEVs.

There are two advantages of this inefficiency warmth. First, there is no need to steal power from the fuel cell’s electricity to heat the cabin. (The Mirai’s electrically heated seats are a different matter, though once the cabin has warmed up they shouldn’t be needed.) Second, just as a warm battery runs more efficiently than a cold one, so does a warm fuel cell run more efficiently.  The fuel cell’s advantage in the cold is that its inefficiency provides it with free heat that can keep it operating at peak efficiency, whereas any heat used to keep a battery warm cannot be had for free but as with heating the cabin must be stolen from the battery’s electrical power.

Winter is as cruel to BEVs as it is harmless to FCVs, which start easily and run efficiently at twenty below. Winter is also tough on ICEVs, which rely on batteries to start: the cold sucks the life out of the 12 volt battery needed to start the car, and ignition is harder in a cold cylinder.

The bottom line for efficiency then is that while the jury is out on the cost benefit of the BEV’s higher efficiency, there is no doubt that the FCV’s inefficiency is a great benefit in cold climates.


For short range EVs, batteries may be fine. However for long range EVs FCVs have two clear advantages over BEVs: faster refuelling, and an independence of range and performance that greatly reduces both weight and cost. Whether the greater efficiency of BEVs is of any value remains to be seen.



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[5] (a) Road & Track credits the Leaf with 9.4 seconds. (b) One of the eight Mirais that drove from Rocklin to Truckee for the opening ceremony on August 27 was Brad’s from Santa Rosa (didn’t catch his last name but he’s in real estate). He’d bought his Mirai just weeks earlier after learning that a BEV with the same range would cost twice as much. When I told him the Mirai’s 0-60 mph time was 9 seconds he was adamant that his Mirai was much quicker than that. I didn’t want to contradict him because that’s how the Mirai feels to me too, even if it isn’t true.

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If a Mirai ran on liquid hydrogen, how many miles per gallon would it get?

The shocking answer is 18.

But wait. The EPA says the Mirai has a fuel economy of 67 MPGe. How could being liquid make that much of a difference. Is it because it is so cold it doesn’t have much energy?

No, the difference is between MPG and MPGe. Whereas a gallon is a unit of volume, a Gasoline Gallon Equivalent, 1 GGE, is a unit of energy defined as 33.7 kWh. 1 GGE of liquid hydrogen has a volume of 3.7 gallons. So one gallon of it can only take you 67/3.7 = 18 miles.

This comes about because the density of liquid hydrogen is 0.07085 kg/L (kilograms per liter). Water is more than 14 times as dense. A gallon of liquid hydrogen therefore weighs 0.07085*3.785 = 0.268 kg and can only get you 67*0.268 = 18 miles.

But then what’s the point of liquid hydrogen if isn’t dense?

Well, the combined capacity of the Mirai’s two tanks is 122.4 liters. That volume of hydrogen at room temperature and 70 MPa pressure weighs 5 kg, a density of 5/122.4 = 0.04085 kg/L. Liquid hydrogen is therefore 0.07085/0.04085 = 1.73 times as dense as H70.

So, light as it is, liquid hydrogen requires only 58% of the volume of H70. It does this by reducing the distance between hydrogen molecules by a factor of the cube root of 1.73, namely 1.2.

So then why have these two big tanks taking up space under and behind the rear seats when liquid hydrogen can shave 42% off its volume?

Well, the trouble with liquid hydrogen is that at atmospheric pressure it must be cooled to 20 K (-253 C) to liquefy. A temperature so close to absolute zero might be ok for a huge truck but in an ordinary passenger car it would greatly increase both its complexity and cost.

If compressed, would less cooling suffice? No, compressing it to 13 atmospheres (1.3 MPa) only raises that temperature by 13 degrees.

That temperature and pressure, 33 K and 13 atmospheres, is called the critical point of hydrogen. Beyond that point there is no such thing as liquid hydrogen because there is no sharp demarcation between liquid and gas, just a compressible “supercritical” (not to be confused with political campaigns) fluid that can be shrunk by cooling, compressing, or both. (But with enough of that shrinking hydrogen solidifies, i.e. freezes.)

To save on the cost and complexity of liquid hydrogen the Mirai relies on pressure alone to save space.

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Home Hydrogen

I believe the technology for home hydrogen fueling that will win out in the end will be a 1-5 cubic foot unit operating overnight, taking as inputs natural gas and electricity, and outputting hydrogen at a rate of 1-5 kg per 10 hours depending on the size (and therefore cost) of the unit. Every 36 seconds 1-5 grams of H2 at room temperature are pumped into the car at a pressure proportional to how much is already in the tank, and 3-15 grams of dry soot (broadly construed to include carbon powder, graphite, etc.) are added to a container at the bottom. Every week your waste management company collects the accumulated 25 lbs of soot per FCV separately from your garbage and recycling.

No tanks external to the car, no emissions of any gas. Assuming no subsidies, operating costs per kg should come to whatever 100 cf of gas costs, around $1.50 today, plus $0.90 for the electricity ($2.50 if you fill up during peak hours in the afternoon).  $2.40 for 60 miles worth of H2 comes to 4 cents a mile. With gasoline at $2.40 a gallon you’d need a 60 mpg ICEV to match that, and you’d also miss out on the convenience of home refueling while getting frowns from your neighbors for continuing to emit 20 lbs of CO2 for every gallon you use.

Although no such unit is available today, progress towards it has been made at IASS and KIT.   I see no obvious technical or economic obstacle to refining their current design to meet the above specifications, perhaps based on a different approach to methane cracking.

The 5 cf unit will fit comfortably in the Mirai’s 20 cf trunk, allowing you to take it on trips. A network of 1500 overnight filling stations at motels, hotels, and campsites every 20 miles along the major interstates would permit travel throughout the country at 300 miles a day, and further when FCVs with larger tanks come on the market.  Each station would consist of one or more parking spots each with a hookup providing gas and electricity and a bin in which to deposit the night’s accumulation of 33 lbs of soot in the morning, emptied by the hotel’s waste management service.  Stations could start with a single spot booked like a hotel room.  With the current small FCV population, two cars are unlikely to want the same spot and when they do the second can just book a nearby spot.  This very simple infrastructure could be built up gradually nationwide with only a few million dollars a year total, comparable to the cost of installing just a few $2M hydrogen stations around the country. Both will happen, but the former could easily happen faster.

Eventually FCVs will incorporate the unit the same way BEVs incorporate their charger today. Since the construction and operating costs of a regular hydrogen station will be at least a hundred times that of an overnight gas-and-electric parking spot, it is reasonable to expect the nation’s infrastructure to grow at the rate of a hundred such spots for every regular station, with the latter spaced apart ten times the spacing of the spots.

PG&E currently offers special electricity rates to BEV owners charging at home, so if they did the same for home hydrogen your cost could be as low as 2 cents a mile. This could be reduced to zero with a federal carbon tax of $0.001 on gasoline, rising to $0.002 when the milestone of a million FCVs in the US is reached. A portion of this tax would be paid to the utilities to compensate them for giving you free gas and electricity for your FCV. (Maybe this is already happening for their BEV subsidies.)

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