CO2 and the Nissan Leaf

Image Credit: Biomass Technology Group

In an earlier post I gave a few of the details of the Lexus CT 200h I've been driving for a few weeks now. Then, in my immediate predecessor post I discussed the fact that a much larger portion than I'd have thought of the electricity supplied by Anaheim Public Utilities, my electrical provider, comes from the burning of coal. Finally, in a much earlier post, I discussed the Nissan Leaf. The question to be addressed here: given my driver profile, which of the two vehicles would have the smaller carbon footprint with Anaheim Public Utilities supplying my electricity?


Starting with the CT 200h, let's calculate the CO2 emissions per mile (for my driving style). I'm averaging 51.16 m.p.g., and from this EPA site I find that running a gallon of gasoline through the internal combustion engine in a car (see the site for the assumptions which seem very reasonable) results in the emission of 8.8 kilograms of CO2. So dividing 8.8/51.16 yields 0.172 kilograms (172 grams) of CO2 emitted per mile.


I'm not sure of the accuracy, this site says a Prius, at 51 m.p.g. city and 48 m.p.g. highway, emits 127 grams/mile. I achieve mileage this good, so I should have a similar number. On the other hand, here at Grist we read that the Prius emits 238 grams per mile. These are large discrepancies. Since the EPA site lists its assumptions and since these seem reasonable, and since the number calculated from them is intermediate between the other two, that's what I'm using.


The Leaf would have gotten most of its energy from my home and thus, as best I can determine, 65% from the burning of coal, 20% from the burning of natural gas, and 15% from renewable sources (hydroelectric, geothermal, wind, and biomass in that order - I'm assuming no emissions from these). Here we find that the Leaf uses 34 kilowatt hours per 100 miles or 0.34 kilowatt hours/mile.


I'd need to supply this electricity, and I'll assume that the charging system is 85% efficient and that the transmission from the power plant is 80% efficient. That means that the output of the sources of my electricity need to supply 0.34/(.8*.85) or 0.50 kilowatt hours to propel my hypothetical Nissan Leaf for a mile. 65% of this half a kilowatt hour, or 0.325 kilowatt hours would be supplied by burning coal. From the same site I used in the previous post, I find that a typical 500 megawatt coal power plant will emit 3.7*10^6 (short) tons of CO2 to produce 3.5*10^9 kilowatt hours. Thus, the production of a kilowatt hour entails the emission of 1.06*10^(-3) tons of CO2. This is 0.962 kilograms, so the burning of coal to charge the Leaf will result in 962*0.325 or 313 grams emitted per mile.


For the 20% of my electrical energy supplied by natural gas,  this site shows (after some calculations, from the details of which I will spare my patient readers) that the 0.2*0.5=0.1 kilowatt hours that will derive from that source will produce 59.6 grams of CO2.


Thus, driving a mile in the Leaf will entail the emission of 313+60 or 373 grams of CO2. This is higher even than the high Grist site estimate for a gasoline powered Prius and over twice the estimate I derived for my CT 200h from the EPA site. I'd, without a doubt, spend less money on electricity in the Leaf at $0.14 per kilowatt hour vs. $3.899 (today) per gallon of gasoline in the CT 200h but my CO2 footprint would be over twice as high. And this is in the allegedly green state of California.


Finally, I'm now driving about 21,000 miles per year, thereby emitting 3.6 tonnes or 4.0 short tons (US tons of 2000 pounds) of carbon dioxide.

The Nissan Leaf

I've posted a couple of times on supplying the necessary electrical energy to replace our passenger automobile fleet with electric vehicles, and I also discussed the Chevy Volt. An all-electric vehicle appears ready to enter the fray in late 2010 - the Nissan Leaf. While Nissan seems to be playing it close to the vest (the vehicle's weight and price as well as many other specifications are not given), between Nissan's site and Autoblog's site some conclusions can be reached.

Let's look at the combined aerodynamic and rolling resistance efficiency of the vehicle. The Leaf is claimed to deliver about 100 miles on a full charge, the lithium ion battery pack capacity is stated to be 24 kilowatt-hours or about 86.4 megajoules. The electric motor is less than 100% efficient in its use of the energy in its source. Based on this page and the 80 kilowatt (or 107 horsepower) motor in the Leaf I'll use 92% (the table shows the minimum as 91.7%). Also, the Leaf site discusses "0% to 100% charge" so I'm going to assume that the vehicle uses all 24 kilowatt-hours of energy in the battery pack to go 100 miles. Thus, the Leaf uses .92*24=22.1 kilowatt hours or 79.6 megajoules to go 100 miles.

How does this compare to "miles per gallon?" The 79.6 megajoules is the energy in about .66 gallons of gasoline, but the internal combustion engine is quite inefficient so I'll use 22%. Then we'd be considering a car that goes 100 miles on (0.66/0.22) or about 3 gallons. Thus, we're looking at a car whose efficiency in terms of aerodynamics and rolling resistance is about that of a gasoline burning car getting 33 m.p.g. Seems quite reasonable, though certainly not awe inspiring.

How about cost? I drive about 62 miles per day year around, so I'd use about 62/100 of a full charge, or about 14.9 kilowatt-hours from the battery pack. Let's assume the charging system is 85% efficient, so I need (14.9/.85) or 17.5 kilowatt-hours of electricity. This would probably be at a marginal rate of $0.17/kilowatt-hour since I'd invariably be over my baseline rate with the City of Anaheim. So I'd spend 17.5*0.17 or  $3.01 per day on energy to drive. This is, of course, $3.01/62 or $0.049/mile. Right now in my Land Rover LR3 HSE I'm spending about $0.14/mile on gasoline. The Leaf would provide considerable savings, amounting, in the course of a year, to about $2,060. Certainly, that's nothing at which to sneeze (grammatical pedant that I am).

As to performance, the Leaf boasts a torque (from a dead stop) of  280 Newton-meters (208 pound-feet) and a top speed of over 140 km/h (87 mph). It will accept a full charge from a compatible 220 volt system in about 8 hours, about twice that from a 110 volt circuit. At a suitable quick charge station, it will take an 80% charge in under half an hour and a boost good for about 35 miles in about 10 minutes. Such suitable stations are, at the moment, mostly a distant dream however.

What about creature comforts? It appears to be quite comfortable, modern, and light. It will have room for at least four adults, MP3 connections via USB, a proprietary system built into the satellite navigation system to indicate charging facilities within range, systems to allow one to receive emails from the car on their smart phone and to control certain functions (heating, cooling, etc.) remotely via that smart phone. All things considered, I'm going to look very closely at the vehicle when it becomes available.

Addendum: How much might I reduce my costs if I built a solar charging system to charge the vehicle's battery pack during my working hours? I went here to find the insolation available, using average insolation, the month of March, and a horizontal flat plate to see this map:

Conservatively, 4.5 kilowatt-hours/meter^2/day are available on average. If I'm fortunate, maybe I can create a collector of 2 meter^2. If I'm even more fortunate and technology smiles, perhaps I can find cells with 18% efficiency and provide circuitry to charge the vehicle. Thus, I'd get 2*4.5 kilowatt-hours*0.18 or about 1.6 kilowatt-hours. This would be enough to bring the vehicle from, say, 65% charged to 71.7% or to go a little less than an extra seven miles.  To bring it from fully discharged to fully charged would take a little under 15 days. I can do perhaps a little under twice as well in June but still, seemingly not worth the trouble and expense.

Convert my CT200h to plug-in?

My Lexus CT200h is EPA rated to get 42 miles per gallon combined. In it, over the 2 1/2 years I've had it, my total net has been 51.0 miles per gallon. The CT200h has a hybrid power train with a 1.4 kWh (kilowatt hour) NiMH (nickel metal hydride) battery. This battery is good for a mile or so at very low speed in so-called "EV mode." Plug-in hybrid electric vehicles (PHEVs) will have much larger batteries, enabling them to travel further and faster in EV mode. For example, the Prius PHEV is estimated to be able to travel 11 miles and at a maximum EV mode speed of 62 m.p.h. It achieves this with a 4.4 kWh battery pack. And the Chevy Volt now sports a 16.5 kWh battery pack that is estimated to provide an EV mode range of 38 miles.

I wondered if it would be possible to install a larger battery back and charging capability to my CT200h to convert it into a PHEV. As it happens, the answer is yes. And a huge variety of installations are possible, all the way from 2 kWh to 15 kWh capacity. Note that the Nissan Leaf, a pure electric vehicle (EV), sports a 24 kWh battery pack and a claimed range of 75 miles.

Should I install any conversion and, if so, which one? This can be looked at from an economic viewpoint and from a CO₂ emission viewpoint. I'll look at both. As a baseline, my most common drive is the daily commute from my home in Anaheim Hills to my office in Long Beach. This round trip is about 62.5 miles and I do it, on average, four times each week. I'd be able to charge the vehicle at work, though I'd have to park at our laboratory facility about two blocks from our corporate offices. Such a strategy would enable me to utilize a battery pack with a 35 mile range to, on a typical day, never have to use the internal combustion engine.

What would this look like? The 7 kWh pack theoretically provides this 35 mile range, and I'd assume it would do so by discharging no more than 90%, but let's be conservative and assume that I'd need 14 kWh of charging per day. Assuming the charge system is 85% efficient, I'd draw about 16.5 kWh from the grid. At $0.16/kWh, this would cost about $2.64. I'll round down to $2.50 because I don't really quite go 70 miles on my daily commute.

Currently, with my 51 m.p.g. average, I use about 1.22 gallons of fuel in my commute. At a current price of $3.699/gallon, this costs about $4.50 per day. Thus, the conversion would save me something like $1.86 per day and, for 200 trips per year, I'd save $372/year. It's not completely clear from Plug In Supply's pricing page but it looks like I'd pay $9,875 for the 7 kWh system fully installed. Clearly, from a purely financial point of view, this makes no sense.

As to CO₂ emissions, this is a bit more problematic to compute. I'd be getting half of my electrical energy from our house, where the City of Anaheim provides our electricity, and the other half in Long Beach, where Southern California Edison is the provider. And, assuming that some combination of coal, nuclear, and natural gas provides almost all of the electricity, I won't figure in emissions resulting from extraction and transportation of these fuels. This is reasonable, I'm not figuring the emissions resulting from extracting, refining, and transporting the gasoline I burn.

The calculation for the CO₂ emissions from burning 1.22 gallons of fuel can't be exact as I don't know how much ethanol is in the fuel, and the mix of the various hydrocarbon chain lengths. I'm going to assume that the gasoline consists of n-heptane, C₇H₁₆ at that its density is 6 pounds per gallon. The chemical reaction would be C₇H₁₆ + 11O₂ → 7CO₂ + 8H₂O. A mole of heptane has a mass of 100.2 grams. This mole results in 7 moles of carbon dioxide, each with a mass of 44 grams for a total of 308 grams.

Now, I'll be a bit general and figure that I use 1/51=0.0196 gallons of gasoline per mile. This gasoline weighs 0.118 pounds or 53.4 grams. This produces (308/100.2)*53.4 or 164 grams of CO₂ per mile (this is the typical metric for vehicular carbon dioxide emissions) for a total on my commute of 62.5*164=10,250 grams or 10.25 kg of CO₂.

That was the easy part. The electrical emissions are much more problematic because I've not been able to determine the mix of sources for Long Beach electricity. I'll just speculate. In any case, I need to determine the emissions related to 7 kWh from the City of Anaheim and 7 kWh from Southern California Edison in Long Beach.

I'm not able to find the appropriate mix of generating facilities to use to calculate for Long Beach, so I'll back into it from information from California State University Long Beach on this page, where it's stated that the renewable generation of 656,000 kWh avoided the emission of 471 metric tons of carbon dioxide. CSULB is only a couple of miles from our office, so this will have to suffice. So the generation of 7 kWh would involve the emission of 8.25*(471,000,000/656000) or 5,923 grams of CO₂.

From Anaheim, I'll use the figures from my previous post on the Nissan Leaf. Using those numbers (and sparing my readers the gory details) I can figure that those 8.25 kWh involve the emission of 9,051 grams of CO₂. The total emissions are thus 9,051+5,923 or 14,974 grams of carbon dioxide. Call it 15 kg. This is half again as much as my CT200h emits burning gasoline and the main culprit, as was the case for the Nissan Leaf I looked at, is that the City of Anaheim derives a surprising amount of its electricity from the burning of coal. And this information comes straight off of our bi-monthly bill!

So, when all is said and done, it makes no economic sense, and certainly no sense with respect to CO₂ emissions, to undertake such a conversion. That's comforting because I don't have a spare $10K to throw at such a project!

And all of this probably overestimates the gains. The careful reader may have noticed that the Chevy Volt uses a 16.5 kWh pack to go 38 miles or 0.43 kWh/mile. The Nissan Leaf uses a 24 kWh pack to go 75 miles, or 0.32 kWh/mile. The Plug-In Supply site, where I got these figures, claims 35 miles on 7.33 kWh or 0.29 kWh/mile. It's true that these figures represent a Prius rather than a CT200h but I'm skeptical that the Prius is that much more efficient in terms of aerodynamics and rolling resistance than a Chevy Volt or a Nissan Leaf.

MPGe?

The Nissan Leaf is rated by the EPA to achieve a so-called "MPGe" (miles per gallon gasoline equivalent) of 129 city, 102 highway, and 115 combined (note that the EPA sticker to the left is for an earlier year of the Leaf, I couldn't find a 2014 version). What is this "MPGe" of which they speak? While the linked Wikipedia article gives a thorough explanation, I want to briefly cover a couple of aspects.

First, the EPA makes the assumption that a gallon of gasoline is equivalent to 33.7 kWh (kilowatt hours) of electrical energy. In a straight comparison of chemical potential energy to electrical potential energy, this is accurate to within the variability of the myriad blends of gasoline available. The energy content of various fuels is listed here (though not in units I prefer).

I pay $0.16/kWh, so the 33.7 kWh would cost me $5.39, whereas a gallon of gasoline (I bought 8.6 of them yesterday) would cost me $3.639. On the other hand, that gallon will take me a trifle more than 50 miles whereas the 33.7 kWh will (by the EPA's reckoning) take a Nissan Leaf 115 miles. And my driving habits enable me to better the EPA rating of 42 m.p.g. for my car by about 21% so I might be able to drive the leaf 140 miles. Thus, I spend about 7.1 cents per mile for energy in my CT200h versus the 3.8 cents/mile I might spend in a Leaf.

What gives? The fact is that the battery to electric motor to driving wheels efficiency of the power train in the Leaf is going to be close to 90%, while the fuel to heat to mechanical motion to wheels in the internal combustion engine will be well under 30% on a good day. Over 70% is exhausted to the environment as waste heat.

It must be kept in mind that, neither in the EPA sticker ratings nor in my calculations for my car, is the energy used in getting the battery or tank filled included. That is, the energy to generate and transmit the electricity and the energy to extract crude, refine it to gasoline, and deliver it to the gas station is not included. It counts only what's in the vehicle. Supposedly, the CAFE ratings DO utilize the so-called "well-to-wheel" efficiency. There's a very nice comparison (albeit written by Tesla employees but still very credible) of the well-to-wheel efficiencies of a few examples of internal combustion engine vehicles, hybrids (non-plug in) and the Tesla battery electric vehicle here. The Tesla is about twice as efficient as a Prius on that basis. And DAMN those Tesla Model S roadsters look good!

A quick note on the eGallon

Screen shot of my results from DOE eGallon site

In a previous post I mentioned the eGallon concept from a Department of Energy (DOE) web site. It purports to tell a visitor how much he or she would pay to drive as far in an electric vehicle as a gallon of gas takes them in an "average vehicle." It breaks down only as far as by state (or U.S. average). So, for example, if I use California, it tells me that a gallon of regular gasoline costs $3.99 and that my eGallon costs $1.53.

But my average mileage over the life of my vehicle is 50.86 m.p.g. At my most recent fill up I paid $4.059/gallon. I'll use the Nissan Leaf for a comparison, the vehicles are broadly similar in important ways. Each has a C_d (drag coefficient) of 0.29 and, while the frontal area of the CT200h is a bit larger, the Leaf weighs more. The Leaf is rated by the EPA to consume 29 kWh/100 miles for the 2013 model year.

So, on a gallon of fuel, I go 50.86 miles. The Leaf would need (50.86/100)*29 kWh = 14.75 kWh to go that distance. If I assume that the charging system is 85% efficient, I'd pay for 14.75/.85=17.35 kWh. On my most recent electric bill I paid $0.1611/kWh for electricity above the "basic lifeline" rate, so these 17.35 kWh would cost me $2.80 and that's the price of my eGallon. Quite a difference between that number and $1.53, the "true" number is 83% higher whereas the number for my gasoline cost is not far away from what I actually pay. The computed eGallon price would be even further from ReGallon cost ("Rob's eGallon") if DOE had used the 2013 model year numbers for the Leaf in lieu of previous years' 34kWh/100 miles. If I use the 2013 model year number for the Leaf and the EPA combined estimate (42 m.p.g.) for the Lexus CT200h that I drive, an eGallon would cost $2.31, only 51% higher than the site's number.

You can read about their methodology here. The confounding factors are the actual cost of electricity and the fuel economy utilized for the ICE (internal combustion engine) vehicle. For reference, the plot below (you can click it to enlarge and be able to read the numbers) shows an AeGallon ("actual eGallon") for a range of actual fuel economies from 12 m.p.g. (the driver currently in a vehicle getting less than that is not a likely candidate for an EV) to 70 m.p.g. (a hypermiler in a Prius). For this plot, I'll use the same electricity consumption as the DOE site uses, i.e., 35 kWh/100 miles, a blended rate from 5 top selling EVs. Electricity prices on the plot range from $0.09 to $0.20 per kWh. You can calculate your number yourself, it's as simple as 0.4118*(m.p.g.)*(electricity cost per kWh). You'll note that, for combinations of high mileage vehicles and expensive electricity, the eGallon may be more expensive than a gGallon (i.e., a gallon of gasoline).

On the plot, the "front" axis is m.p.g. for the vehicle being replaced with an EV, the rearward extending axis is the price of a kilowatt hour of electricity, and the vertical axis is the price of an eGallon in dollars. You can see that, for low mileage vehicles being replaced, the eGallon is quite inexpensive, regardless of electricity costs. But as replaced vehicle fuel economy climbs, the eGallon becomes much more expensive. The DOE site simply uses a single fleet average fuel economy (28.2 m.p.g.) and does not correct for the 85% charging efficiency I estimated.

Leasing the sun

There may be many such firms but I've been hearing radio commercials for a company called "Solar City." The business model is to provide rooftop photovoltaic systems at little or no initial cost. Solar City maintains ownership of the system and leases it to the home or business owner. The claim is that the total cost to the owner (lease payment plus paying for the much smaller amount of electricity used) is less than the electric bill prior to installing the system. They have a javascript application in which you install such information as your typical electric bill, your zip code (then followed by actually pointing to your house on a map), your roof slope and direction, and your electricity provider. It then returns a 15 year projection of savings, with a graphical representation of lease payments, electric bills, and the electric bills that would have been paid. There's an estimated rate of increase built in. The result of my initial inquiry looks like this:

Note that, at the outset, I can save $4.00/month. Not a lot. But I used my current electric energy usage. What if I significantly increase my usage by the purchase of a Nissan Leaf? In my post on the subject I estimated that I'd need to utilize about 17.5 kilowatt hours per day to charge the Leaf. Now, of course, I'd be charging it during the daytime rather than at night so the system would need to be sized for my use other than the Leaf plus the 17.5 kilowatt hours per day, a total I'd estimate at about 66 kilowatt hours per day. Though the javascript application doesn't allow one to play with such fine points as what can be run during the day and during the night and the system doesn't allow for storage, adding the Leaf makes a difference:

Ah, $7/month, now we're getting somewhere. Of course, the Leaf is also busily saving me money. Further, it's better to have $7/month than not to have it and I could save a few bucks more by replacing my wife's car with a Leaf. Or not.

Now, in principle, I've eliminated a large portion of my carbon footprint (moreso if I can coerce persuade my wife as well). If I could really do so, and if the solar system replaced 90% of of my household electricity and all of the energy use of mine and my wife's cars, using the information used in preparing this post and this post I can estimate that as much as 25% of my family's carbon footprint could be eliminated. This is well under the 95% that would appear to be required, but it's better than replacing incandescent bulbs with compact florescent bulbs. After appropriate due diligence, I may do so.

The Chevy Volt - is it for me?

I've already posted about the Chevy Volt and the mileage claims made for it. But the time is coming to replace the Land Rover LR3 HSE that I've been driving since 2006. The Land Rover is owned by my Company and, in the current economic environment, there's little excuse for being provided with such a vehicle. I've mentioned my partner and the BMW X5 he drove, also owned by our Company. He's purchased a Toyota Prius (NOT company owned).

So, I'm wondering what to drive. The choices really seem to be the Nissan Leaf, the Volt, and the Prius. I'm leaning against the Leaf because it's range is about 100 miles on a charge and, though my commute is about 62.5 miles round trip, I sometimes need to go to meetings from the office or go to places other than the office from home and there's no infrastructure to charge the Leaf "on the road."

The Prius is all well and good but, well.... my partner got one. So, what about the Volt? It has much to recommend it for my application - though it's only estimated to get 40 miles on a full charge prior to using the internal combustion engine (ICE) to supply energy to the electric motor and my one-way trip to work is about 30 miles, I can charge it at the office and use the ICE only in the circumstances described in the previous paragraph. So, decision made, right?

Not so fast. This vehicle has an MSRP of $41,000 for the base model. A tax credit (not sure how the money is actually collected) of "up to" $7,500 is available bringing the price after the credit down to $33,500. This is a high price for what is really a four passenger commuter car. So how does the energy situation compare to my current vehicle and to others I might consider?

In order to estimate potential savings some assumptions will need to be made regarding how often and for how far the ICE in the Volt would be used. So, I'll figure that I'll do my normal commute four days per week and that I'll plug the Volt in at the office (actually, down the street at the laboratory) during each of those days so that the ICE isn't used. On the fifth day, I'll assume I go to the office and then leave for a meeting 35 miles away, that is, 70 miles out and back from the office, and then another 32.5 back to the house. I'll also need to use the fact that the Volt is specified at 50 m.p.g. when the ICE is running the electric motor. I can, no doubt, do better than that but I'll use it.

Using these figures, I estimate that I spend $61.91 per week or $3,219.34 annually on gas in the Land Rover, and that I'd spend $22.94 per week or $1,193.04 annually for gas in the Prius, and $17.44 per week or $907.00 annually on gas plus electricity for the Volt.

Now, the Land Rover is paid for but not by me (except indirectly). The Company will get a minor cash infusion by selling it. I'd estimate that the Prius will cost about $7,000 less than the Volt after all is said and done (that is, purchase price out the door). The $286/year isn't going to make up that difference, so the rational thing to do is to buy a Prius, assuming that a pure ICE vehicle is ruled out. More to follow.

How are we doing on EV adoption?

In November, 2009, I published a post that used the logistic function along with a couple of guesses (one by Nissan CEO Carlos Ghosn, one by me) and assuming that, in the next few decades, essentially all light duty vehicles on the road would be electric, to estimate the additional electrical load needed annually. I speculated (estimated is WAY too strong) that at the peak, sometime around 2039, we'd add 12,000,000 electric vehicles to the fleet requiring 6.6 gigawatts of generating capacity (assuming no smart grid utilization of the vehicles as storage, or other load leveling techniques).

Now, almost four years later, I thought it would be interesting to take a look at how the adoption of EVs ( combining PHEVs or plug-in hybrid electric vehicles such as the Chevy Volt and AEVs or all-electric vehicles such as the Nissan Leaf) is progressing in comparison to the very rudimentary model.

I used Ghosn's response to President Obama's call for one million EVs on the road by 2015, i.e., that that number would be "easily surpassed." I assumed two million in 2015 and 230 million in 2050 and used those points as input to the logistic function. I used Wolfram Alpha to plot the data (if you click the link, the assumptions will be built into the input and you can change them to suit). Of course, the plot starts in 2015 and EVs and PHEVs started to be on the road in 2010 and it's now 2013. But nothing stops me from plugging negative numbers into the plot range to go from 2010 to 2015 (or numerically evaluating the function). Doing so predicts (here I assume January 1, 2010 is -5.0 years, January 1, 2015 is 0 years, and here, about 7/12 of the way through 2013, we're at -1.42 years) just over 1.5 million EVs and PHEVs on the road.

What is the actual number? The best data I've found is at the Electric Drive Transportation Association's site. They've compiled it here and the pertinent graph is to the left (click to enbiggen). The astute reader will note that the actual number is about 112,000, less than 10% of my speculative number. With a year and a half to reach 2015, and two and a half to reach the end of 2015, Ghosn's prediction is looking precarious. Let's speculate some more.

What if I plug actual data into a logistic curve (the curve form EDTA certainly doesn't preclude such a model)? I'll use 112,000 in 2013.5 and 230 million for the ultimate number and see what growth rate yields 6,669 (from the graph using GraphClick) in June of 2011. The rate turns out to be 141% annual growth (initially). I doubt that this growth can be sustained indefinitely as early adopters complete adoption and the curve flattens. Such a rate would result in a 230 million EV fleet in around 2022. It's unimaginable that this could take place. Still, if the growth rate continues, we'll have two million EVs on the road sometime in mid 2015.

A tonne of coal

It's been a hot few weeks in Southern California and, unfortunately, I like it chilly. Thus, my air conditioning system has been quite busy lately. I received my utility bill yesterday and, though I knew it would be high, it exceeded my expectations. Anaheim Public Utilities bills on a bi-monthly basis and my current bill represents 62 days of consumption. The total electrical usage was an eye-popping 4,473 kilowatt hours. This is an average rate of a bit over 3 kilowatts continuously. Ouch!

Along with our bill, we receive a "power content label" that tells us the energy resources used to supply our electricity and the percentage (estimated for 2010 and I used these estimates for the information to follow) of electricity supplied by each.


Let's take a look at coal: I entered the query "how much coal is burned to produce a kilowatt hour of electricity?" into Google and followed a link to this site. It could be that I should look at a variety of sources but, for my purpose in this post, this is close enough. There I found that a ton (a short ton) of coal, burned in a modern generating facility, will yield 2,460 kilowatt hours of electricity. I will assume that its transmission to my house is 80% efficient, so that ton will yield 1,968 kilowatt hours at my service entrance (where the meter is). This converts to 2.169 kilowatt hours/kilogram of coal burned.


Looking at the Power Content Label, 65% of my 4473 kilowatt hours, or 2,907 kilowatt hours were supplied by burning coal. Yes, I understand that, for these particular 62 days that might not be the right percentage, but it's the best number I can find. In any event, these 2,907 kilowatt hours required the burning of 1,340 kilograms, or 1.34 metric tons ("tonnes" - note that this is 1.48 "short tons" or 2,954 pounds) of coal. This is 21.6 kilograms/day of coal being burned to keep me cool, pump my pool water, light my house, entertain me, etc. Looking here, I see that a reasonable approximation (not knowing the nature of the coal being burned) of the density of the coal is 1000 kg/m^3 so, during the 62 days, about 1.3 m^3 of coal was burned to supply me with 65% of my electricity needs.


Frankly, I was surprised by the high percentage of coal estimated to be used by Anaheim Public Utilities to supply electricity. We have two large nuclear generating facilities in Southern California as well as a huge plant west of Phoenix, AZ. Further, Hoover Dam is about 300 miles away.


Before I purchased the Lexus CT 200h, I'd contemplated, among other vehicles, the Nissan Leaf. While that vehicle would definitely have reduced my driving costs per mile, I'm now suspecting that it wouldn't have reduced my vehicular carbon footprint. That estimate will be the subject of my next post.

Tesla class 8 truck, part 2

Image credit: Matchmakerlogistics.com

In my previous post I estimated the weight penalty imposed by the need for a battery pack that will enable the Tesla Truck to have a range of 500 miles. Next, I'll take a look at the pricing situation.

As most know, battery packs of the size to supply energy to road vehicles are very expensive. In fact, in the opinion of many, the U.S. Government subsidy is the only reason the BEVs (battery electric vehicles) have sold as well as they have, especially in the relatively lower price classes such as those occupied by such cars as the Chevrolet Bolt, the Nissan Leaf, and the Honda Clarity EV.

It's not easy to get a handle on the price of a battery pack, but synthesizing various sources, it seems likely that battery packs from the Gigafactory will cost Tesla something like $150/kWh in the 2020 time frame. That would put the cost of the estimated (by me) 1,145 kWh pack for the claimed 500 mile range at $171,750. We see here though that

The electric semi trucks will run between $150,000 and $180,000, depending on range, with a fancy "Founders Series" of semis coming in at $200,000.

It's not an easy thing to figure what the cost of a semi truck cab, wheels, etc. (i.e., the entire semi minus the engine and transmission) is but I've tried to get a handle on it by looking at some pricing of so-called "glider kits." Here, I found that a rolling glider could cost from $75,000 to $97,000. Assuming something like a 20% markup, the cost to produce the glider would be $60,000 to $77,600. Using the lower number, Tesla might spend $60,000 on the body, frame rails, axles, etc.

Next, my understanding is that the Tesla truck will utilize four 192 kW permanent magnet electric motors (the same as the Tesla Model 3 motor). I've found it to be EXTREMELY difficult to get an accurate estimate for the cost of such a motor, here we find a source to purchase Tesla 3 drive units  (Tesla motor, inverter, gear box, dash display and control unit, throttle pedal, and two axles) for $11,900. I'll estimate that the markup is 50% and so the cost of the unit is $7,933. I'll further estimate that the parts needed for all four motors (since we won't need four throttle pedals, etc.) represent 2/3 of the cost, so three of the units cost 3*(2/3)*$7,933 or $15,866. Add the full $7,933 for the fourth unit to get a total cost of $23,799 for the entire set. Call it $24,000.

So we have an estimated cost to Tesla of $171,750+$60,000+$24,000=$255,750. And there's no question that I've left a few things out. And, assuming that Tesla would like to make a profit of, say, 20%, the price out the door would be $306,900. That's over 70% higher than the cited price of the 500 mile range truck. Where may I have gone wrong? Conversely, if Tesla is selling a 500 mile range truck at $180,000 and is making some incremental profit on the sale then their cost would be, at most, $150,000 using the same 20%. And this doesn't include the subsidy that Tesla is offering for charging (I'll take up charging in a subsequent post).

It's unlikely that the cost of materials (aluminum, steel, plastic, carbon fiber, etc.) will decrease sufficiently to reduce Tesla's cost by something like 40%. My conclusion is that they are banking on some combination of manufacturing efficiencies, economies of scale, and improvements in the actual battery chemistry to reduce the cost per kilowatt hour of their battery packs.

In order reduce the cost of a truck by some $100,000 (turning now to very round numbers) by reducing the cost of a battery, the cost would need to come down to somewhere in the $63/kWh. Below we see a graph of costs projected out to 2030. And, while the cost has come down considerably and is projected to continue to do so, I've not found a credible projection that hits anything close to $63/kWh even out 13 years, let alone three years. WebPlotDigitizer quickly shows that the projection is for $170/kWh in 2020 and $75/kWh in 2030. Note that my calculation above used $150/kWh! 

The bottom line is that I see no way that a 500 mile range class 8 semi powered by batteries can be sold for $180,000. It's true that Elon Musk and Tesla have accomplished amazing things and have made skeptics eat their words, but it's also true that Musk has a habit of over promising on time frames and production numbers. A fair number of significant companies with lots of money to spend on research and lots of analysts to evaluate capital expenditures have placed their bets that Tesla will succeed in delivering as promised. It won't be long until we know!

Note: This is the unedited version of this song. While I don't condone and, in fact, I unequivocally and vehemently condemn any sort of homophobia, I consider that the unedited version is geared toward criticizing rather than supporting such a toxic attitude. Additionally, I loathe censorship in all its forms (and yes, I realize that the government was not responsible for the edited version).

Regenerative braking in the Lexus CT 200h

I've been driving my Lexus CT 200h for about two years and about 39,000 miles. In that time, I've learned a lot about driving techniques to minimize specific fuel consumption (g.p.m., gallons per mile). I've also given some thought to what it is about a hybrid that makes it more fuel efficient. One of those items is regenerative braking, where some of the kinetic energy in the moving vehicle is used to charge the battery rather than to heat the brake rotors. This is done by having the energy of the moving vehicle turn the electric motor backwards, thus making it a generator and thereby charging the battery. Of course, friction brakes are also used.

I've wondered just how much of the braking energy goes into the battery and have been hard pressed to find data for this. However, the CT 200h has a display option for "Consumption" (see photo at left). It's difficult to see (click to enlarge) but there are small boxes in the vertical bars that indicate mileage by the minute. Each complete box, according to the legend, represents 50 watt hours of energy (180,000 joules). At the top of a hill, I applied sufficient braking to keep my speed at approximately 35 m.p.h. At the bottom of the hill, a stoplight brought me to a stop.

I can calculate the energy difference from 35 m.p.h. at the top of the hill to 35 m.p.h. at the bottom of the hill by using Google Earth to find the elevation change. I determined it to be 103 meters. Because my speed didn't change, neither did my kinetic energy, therefore the reduction in my potential energy went to some combination of heating my brake rotors and charging my battery.

My best estimate of the mass of the vehicle with the 1/4 tank of gasoline and myself and my baggage is 1,600 kg. Therefore, the potential energy lost in the descent is ~E=mgh=1600kg*9.8\frac m{s^2}*103 m=1.62*10^6joules~. The display shows "E" boxes and fractions of "E" boxes and my best estimate, assuming that 3.5 "E" boxes are shown is that ~3.5*50Wh=175Wh~ or ~630,000joules~ were sent to the battery. I don't think it could be lower than ~585,000joules~ or higher than ~675,000 joules~.

Assuming that I'm interpreting the cryptic display correctly (and that Ed Davies doesn't haul me up short!), about ~630000/1620000=38.9\%~ of the potential energy went to charge the battery. The rest was dissipated as thermal energy in the disc brake rotors and, ultimately to the atmosphere. The battery pack in the CT 200h is a 1.3 kWh Ni metal hydride battery. The 630,000 joules equal 0.175 kWh or 13.5% of a full charge for the battery. Per the owners' manual, I'm able to drive in "EV mode" (battery only) for two miles, but I'd best accelerate slowly even by my standards, and not exceed about 20 m.p.h.

As an aside, this is the energy in about 18 cm^3 of gasoline. Figure I'd have to burn about four times that, or 72 cm^3 to charge the battery with the engine at 25% efficiency. And, of course, the regenerative braking isn't effective when the battery is fully charged, isn't used (much) in hard stops, etc. Still, it does increase overall fuel efficiency.

Finally all of these figures have large "error bars," the regenerated energy on the display, the elevations from Google Earth, the mass of the vehicle, and the ability to stay at precisely 35 m.p.h. (although really, all I need is to be going at the same speed when I stop logging as when I start so that the kinetic energy is unchanged). Still, it's enough for me to have a good idea of what the regenerative braking can give me.

Update: Based on a comment by Gabriel Grosskopf, I measured the distance over which I descended. It was 1,530 meters, thus the slope is 3.86 degrees (0.0673 rad). The typical instrument landing system glideslope is 3 degrees though a few, such as VNY - Van Nuys - at 3.9 degrees, are steeper. Assuming that I drove the 1530 meters at 35 m.p.h. or 15.6 m/s, it took me 98 seconds to put 630,000 joules into the battery. This is a charging rate of 6,440 watts or 6.4 kW. As mentioned in a previous post, when I put fuel in my gasoline tank, I'm adding energy at a minimum rate of 11 mW, about 1,700 times as fast. To be fair, we'll divide that by four since IC engines are much less efficient than electric motors. So we're adding useful energy at 2.75 Mw or 430 times as fast. Coincidentally, the Nissan Leaf touts a 6.6 kW charger to charge its 24 kWh battery.

Energy - what can be done?

I want to spend a few posts looking into what can be done. Unlike many of the excellent blogs to which I try to direct attention in my "blog roll," I'm not going to analyze what resources are available, what technological breakthroughs may be on the horizon, etc. I'm going to look at the amount of energy we (in the United States) can save using currently available technology and by changing currently ingrained habits. I'll first look at ground transportation, then shipping, then air transportation, then savings in the built environment. This last will include insulating, windows, lighting, motors (in industrial facilities), and HVAC (heating, ventilating, and air conditioning).

As I wander through this, please bear in mind that I'm assuming evolutionary progress in technology, not revolutionary breakthroughs (fusion, methane clathrates, etc.). In fact, in this series of posts I won't be addressing harvesting and generation at all. In other words, these benchmarks can be achieved in the near to intermediate future without dramatic scientific or societal changes (albeit using my personal definition of what would not constitute a dramatic societal change - yours may be very different).

For transportation, one of the main sources of information will be the "RITA" (Research and Innovative Technology Administration - Bureau of Transportation Statistics) site. Chapter 4 of the linked site is entitled "Transportation, Energy, and the Envionment" and it contains a cornucopia of statistics on the use of transportation fuels in the U.S. I'll start here.

For personal, non-commercial transportation (including work commutes), there are several strategies:

1. Carpooling
2. Telecommuting
3. Using more public transportation (arguably and conditionally  - see here for example)
4. Driving more efficient vehicles
5. Driving more slowly

Let's start with commuting to work. Of the listed possibilities, telecommuting offers, basically, a one for one reduction in energy expenditure. If I work from home for a day, that's 62 miles not driven and 1.2 gallons of fuel not burned. Carpooling may come close or even do better. If two people who drive, say, 25 m.p.g. vehicles carpool, the total fuel burn is halved. However, suppose I carpool with someone whose vehicle gets 25 m.p.g. (and who lives next door to me or a close approximation thereof). When each of us drives, 3.7 gallons are burned. If I drive, 1.2 gallons are burned, reducing the fuel burn by 2.5 gallons or about 68%. However, when he or she drives, 2.5 gallons are burned and the reduction is only 1.2 gallons or a bit more than 32%. That's still pretty significant.

Here we find statistics on annual commuting miles, the most recent my google-fu could uncover. The document is based on data derived from the National Household Travel Survey. According to the survey, in 2009 we (in the U.S.) commuted to work for a total distance of ~6.235*10^{11}~ (623.5 billion) miles. And according to this table, the average light vehicle fleet fuel economy that year was 22.4 m.p.g. Thus, we can estimate that we burned ~2.783*10^{10}~ (27.83 billion) gallons of gasoline and diesel fuel in this endeavor. Based on the economy in 2009, I'd expect that figures determined from that year would be conservative with respect to potential fuel savings in absolute terms, but that the percentages would be representative.

For telecommuting, let's hypothesize that 5% of the workforce could move from commuting to telecommuting and could do so for 25% of their workdays (one day per week for three weeks, two days on the fourth). That would be an annual reduction of 1.25% in the commuter miles driven and a reduction of ~3.479*10^{8}~ (347.9 million) gallons of fuel. Since a barrel of oil produces about 19 gallons of gasoline, the resulting savings would be ~1.831*10^{7}~ (18.31 million) barrels - about one days worth at current U.S. rate of consumption. Clearly, this isn't THE answer!

As to carpooling, I'd be surprised if we could coax 20% of the single occupant vehicle commuters into carpools or vanpools. On the other hand, coaxing six people into a vanpool will save something like 75% of the fuel that would otherwise be burned. I'll compromise and estimate using the following assumptions: 20% of the workforce can be incentivized, cajoled, coerced, etc. into carpooling with one other commuter; each drives a vehicle with the average fuel economy of 22.4 m.p.g.; they carpool 60% of the time because, for one reason or another, schedules won't allow it two of the five typical weekly workdays. This would mean that we'd take 10% of the commuting work force out of their own vehicles 60% of the time, thus reducing commuting miles by 6% and saving (using the numbers from the previous paragraph) ~1.670*10^{9}~ (1.67 billion) gallons of fuel distilled from ~8.790*10^{7}~ (87.9 million) barrels of oil annually.

Succeeding in accomplishing both of these (difficult but not impossible, in my opinion) measures would yield an annual savings of ~1.062*10^{8}~ (106.2 million) barrels. Here we find that, in 2009, the U.S. consumed 18.69 million barrels of oil per day, so had we accomplished the steps above that year, we'd have saved sufficient oil for 5 days and 16 hours. Let's call it 1.6%.

Okay, neither of these will get us to the promised land. Let's skip strategy 3 for the time being since the ambiguities surrounding this deserve a post all their own. Strategy 4 holds significant promise. My Lexus CT200h, driven as I drive it, achieves better than 51 m.p.g. Its EPA estimate is 42 m.p.g. combined city and highway. There are several vehicles with EPA estimates in excess of 40 m.p.g., and a few in excess of 50. At their present market penetration, I won't include the Nissan Leaf, Chevy Volt, Honda Fit, Coda, etc.

Let's assume that, in a period of a very few years, we can raise (again, through incentives as mentioned above) the average commuter m.p.g. from 22.4 m.p.g. to 35 m.p.g. In such a case, the ~2.783*10^{10}~ gallons of fuel burned would annually would be reduced to ~1.781*10^{10}~ gallons, saving ~1.002*10^{10}~ (call it 10 billion) gallons of fuel, that would otherwise have come from ~5.271*10^{8}~ (527.1 million) barrels of oil. That's enough oil for 28 days and 5 hours at the daily consumption rate from 2009. Let's call it 7.7%.

Finally, what about driving more slowly (and other non-extreme fuel efficient driving methods)? I do about 21% better than the EPA estimate, but let's assume that traffic laws, incentives, etc. can cause the average commuter to exceed EPA estimates by 10%. Calculating as above, I determine that, annually, we'd save ~2.526*10^{9 }~ (2.526 billion) gallons that came from ~1.329*10^{8}~ (132.9 million) barrels of oil. This represents about 1.9% of our consumption.

We can't simply sum these numbers since that would double count some undetermined amount of people who, for example, carpooled, got more efficient vehicles, and drove more efficiently. Cars that aren't on the road due to carpooling can't be driven more efficiently!

So let's arbitrarily take 25% off of the total. We can thus conclude (very roughly indeed) that these (relatively) painless steps could save us something like 590 million barrels of oil per year. This amounts to a bit under 9% of our annual consumption. This is really not so bad, considering that it's only one component of the efficiency possibilities at our disposal.

Update: The 590 million barrels of oil saved by not burning 11.2 billion gallons of gasoline and kerosene would result in NOT emitting about 210 billion pounds or 105 million tons of carbon dioxide.