“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Sunday, July 14, 2019

Eviation Alice

Image Credit: Eviation
As I've mentioned in quite a few previous posts, I'm a pilot by avocation and a dedicated follower of all things aviation. My YouTube feed recently decided that I'd be interested in the Eviation Alice, an all-electric airplane currently being developed by Eviation Aircraft, an Israeli company.

On my first time through the video, I was quite skeptical. The performance claims seemed to be outside of the range of current or near future technology (see below). 

Image Credit: Eviation
As is well-known, the specific energy (energy/mass) of chemical batteries is far below that of aviation fuel and so my first thought was that a 900 kWh battery pack would make the airplane far too heavy to carry any significant payload. However, Eviation claims to have achieved a specific energy "surpassing the 400 Wh/kg mark." This is quite an achievement if true. Such a battery pack would weigh (using 400 Wh/kg and ignoring "surpassed") 2,250 kg., or 4,960 pounds.

On the other hand, Eviation also states that the battery is 65% of the airplanes weight. Let's work back. They state it's a 9+2 airplane, i.e., 9 passengers, 2 pilots. There is no fuel. A standard FAA adult weighs 170 pounds, we'll add a few for (ahem) girth growth and baggage, call it 185 pounds. 11*185 = 2,035 pounds or 923 kg. The maximum gross weight is shown as 6,350 kg. We subtract the payload and get 5,427 kg in airframe and power plant weight. Eviation states that the batteries comprise 65% of the aircraft's weight, yielding (an approximation, of course) an implied battery weight of 3,528 kg.
Image Credit: Eviation

In any case, current lithium ion technology achieves specific energies on the order of 250 wH/kg, but aluminum-air batteries can achieve much higher specific energies. Eviation states on their site (from which the graphic at right is copied) that they have a proprietary aluminum-air system in addition to (?) their lithium ion batteries. However, naive as I am, I don't see how this is feasible, given the fact that in an aluminum-air battery, the aluminum anode is consumed in the oxidation half-reaction. The electrode can be reprocessed, but this is hardly the same as plugging into a charging system! Until I know more about the proprietary system, my skepticism is intact.

But lets suppose that Eviation has conquered this issue and can achieve 400 wH/kg in a practical system. As mentioned, they state that the airplane is a 9+2 configuration (9 passengers and two pilots). The usual tradeoff of fuel for payload with which I deal (and which is a consideration for all fossil fuel powered aircraft) is not a factor here. But we have (at least, depending on which of Eviation's numbers we use) 2,250 kg of batteries and 923 kg of passengers and miscellaneous for a total of at least 3,173 kg and probably more. From the maximum gross weight, this leaves 6,350-3,173 = 3,177 kg for the airframe and power plant.

The YouTube video states that the current prototype uses three Siemens 260 kW electric motors. The best information I can find gives a weight of 50 kg for these motors, so the total is 150 kg. We're down to 3,027 kg for the rest of the aircraft - avionics, fuselage, wings, empannage, propellors, interior furnishings, and miscellaneous. And recall that this is the absolute maximum possible weight in that it assumes the absolute minimum battery weight. With more conservative (not to say plausible!) assumptions for battery specific energy something like 1,830 kg would be the maximum. It's stated that the aircraft is all composite, I'll say it had better be!

All in all, given the contradictory and confusing information on the web site and the weight considerations outlined above, I find it very hard to be anything but skeptical, though I wouldn't go so far (at this point) as to call it a fraud. According to the YouTube video, Cape Air made a double digit "launch order" (airline industry terminology for the first purchaser of a new model). With  such an order and with Honeywell (fly by wire controlls), Bendix (avionics), Siemens (motors), Hartzell (propellors) and others signed on to supply components, there seems to be at least some level of confidence. And Eviation is expecting type certification in 24 to 30 months for the unpressurized version. But I wouldn't book a seat just yet.

What about aerodynamic calculations? None of the key parameters are given to calculate from first principles, so I'll use comparisons to known aircraft. Proceeding in this manner, 260 kW is 349 horsepower (call it 350) so the total power available is 1,050 horsepower and the cruise airspeed is listed as 240 knots. The Pilatus PC-12 uses a Pratt and Whitney PT6A-67P gas turbine engine flat rated to 1,200 horsepower and cruises at 280 knots. The maximum takeoff weight of the PC-12 is 4,740 kg. So, on its face, it would appear that the Alice has sufficient power to produce the listed speed.

How about range? Here we have the statement that the range of the Alice is 650 miles (statute I assume). Again, using the Pilatus PC-12 as a measuring stick, that airplane has a normal range of 1,646 statute miles. It has a fuel capacity of 403 gallons and, if we assume 40% efficiency of the gas turbine engine and use 131 megajoules/gallon, the engine delivers 2.111*10^10 joules or 5,866 kilowatt hours to the propellor to go 1,646 miles. The Alice has a battery capacity of 920 "usable kilowatt hours" (yes, different than 900 used above, but the statements from Eviation are widely variable depending on which interview or site I look at). Then, if we take (920 kWH/5,866 kWH)*1,646 mi., we can estimate that the Alice should have a range of 258 miles. It's implausible that the Alice has an aerodynamic efficiency of over twice that of the PC-12 so, again, I'm very skeptical.

Eviation states that the Alice on display at the recent Paris Air Show is a flying prototype and they are only awaiting FAA approval to begin flight tests. They state that they expect to fly later this year. Given the lack of consistency of their claims and the rough estimates above, I'll await the results. But, despite the apparent confidence of the very reputable OEM suppliers listed above, I'm putting this in my "I'll believe it when I see it" file.

Saturday, June 22, 2019

Energy Vault: A mashup of two of my interests

Image Credit: Energy Vault
My occupation is as an executive in a firm that provides materials testing, inspection, consulting, and engineering in the construction space. We deal with all aspects of the built environment with the exception of single family housing. As such, concrete is a fundamental area of my firm's expertise. And, as is clear, energy in all its aspects is a personal interest, not to say obsession, of mine. Finally, as I've elaborated in multiple posts, to bring renewable energy to the level of being able to provide base load power, I contend that relatively inexpensive energy storage will be needed.

Energy comes, basically, in two forms: kinetic; and potential. And while storage via kinetic energy is possible (think flywheels and thermal storage), most forms of storage utilize potential energy. Batteries utilize chemical potential energy, compressed air energy storage utilizes mechanical energy, etc. And finally, gravitational potential energy is utilized in various systems. In fact, most grid scale storage currently in place uses pumped hydro storage.

But any system of raising a mass against the force of gravity has the potential (get it?) to be used for storage. And a Swiss firm called Energy Vault has constructed a prototype of a storage solution using concrete lifted by tower cranes. It's clear that the technology for producing concrete is not new, and tower cranes are ubiquitous in the developed world. The innovation claimed by Energy Vault lies in the software to efficiently determine crane movements to optimize storage of excess energy and to deliver energy when needed.

In a previous set of posts (the last one is here), I estimated that a 3 MW nameplate capacity wind turbine combined with 40 MWh of storage could reliably provide 725 kW of base load power. What would 40 MWh of storage look like with the Energy Vault system? Energy Vault's web site states that an operational plant would have the capacity to store "between 10 and 35 MWh" of electrical energy and be able to deliver that energy at a rate of from 2 to 5 MW. Based on this claim, perhaps two such plants would be sufficient to provide storage for our hypothetical 735 kW plant and would be able to deliver the energy at the needed rate.

So as not to subject my readers to endless calculations, suffice it to say that the energy stored by lifting a mass against gravity is simply the product of the mass of the object lifted, the height to which it is lifted, and the local gravitational acceleration constant. Let's say we'll settle for two storage plants, each with a capacity of 20 MWh. For calculating purposes, we need to convert 20 MWh to the 7.2*10^10 J (joules, the SI unit of energy). 

We have two "knobs" that we can control to determine how much energy is stored in a storage system of the nature of that of Energy Vault. We can control the height to which our masses are lifted and we can control the amount of mass. And (net of losses), energy stored by lifting a mass against gravity is E=mgh, where E is the energy, m is the mass, g is the acceleration of gravity, and h is height. However, for the purposes of the physical logistics of our plant, we're really concerned about the volume of concrete so we'll use m=ρ*v where ρ is density and v is volume. This yields E=ρvgh. To isolate the knobs we can control, a little algebra yields E/(ρg)=vh. Concrete is typically quoted as having a density of 2,400 kg/m^3, g is 9.8m/s^2 and we need 7.2*10^10 J. Plugging these in, we see that we need v*h=7.2*10^10/(9.8*2,300)=3.06*10^6. This is the required product of height in meters times volume in meters^3.

In order to determine the feasibility we need to understand what an actual installation might look like, and Energy Vault helpfully includes an animated video of a hypothetical production facility.

While there's not a lot of information on the Energy Vault site with respect to tower height, plant radius, etc., Quartz has a writeup on the system that states that a tower would be on the order of 120 meters tall and the diameter of the installation would be around 100 meters. For our 40 MWh system, we need two of these.

It's also stated that each concrete block weighs about 35 metric tons (35,000 kg) and so the volume of each block would be 35,000/2,400 = 14.6m^3. Judging from the video, the concrete height is about 100 meters, and clearly it's not possible to have each block raised from the ground to 100 meters and lowered back to the ground, the blocks have to be stacked. I'd assume that it would be possible to have the average of the lift and drop to be 50 meters.

Does all of this make sense in comparison to the numbers from the earlier paragraph? We need height times volume to be 3.06*10^6 m^4. This means that we need about 3.06*10^6/50 = 61,200 m^3 of concrete. The video shows the beginning configuration to be basically a cylinder of concrete about 100 meters tall and a radius of, I estimate, 13 meters. This yields a volume of about 53,000m^3. This is not too bad, given the accuracy of estimates for height, radius, etc.

Now, in the U.S., we typically measure concrete volume in cubic yards, where a cubic meter is 1.308 cubic yards, so we're talking about a little over 80,000 yd^3 of concrete. Right now, a cubic yard of generic concrete costs around $80/yd^3 so the concrete cost alone (not counting concrete for the foundation) would be on the order of $6.4MM. However, Energy Vault claims to have developed the capability to use discarded materials as aggregate. Further, the concrete really needs very little compressive strength and so the cement requirement could be very low. Let's generously cut the $6.4MM by two thirds and call it $2.13MM. So we see that the concrete cost might be on the order of $2.13MM/20MWh = $156,500/MWh or $156.50/kWh. This is similar to the current cost of a lithium ion battery storage but doesn't include the cranes, the foundation, the construction, the control system, or the power electronics. To be fair, Li ion storage costs also are higher than strictly the battery costs.

Among the advantages of the Energy Vault solution are: negligible degradation of capacity over time; no use of rare elements; no toxic chemicals; no danger of thermal runaway. Is this the answer for turning our 3MW wind turbine into a reliable 725kW base load energy system? Well... as in so many things, it boils down to economics. I'll cover that in a future post at some yet to be determined future time.

Sunday, June 03, 2018

Requiem for LightSail Energy

Image Credit: LightSail Energy
I've published multiple posts concerning LightSail Energy and its Chief Science Officer, Danielle Fong. I was enthusiastic about the the Lightsail Energy compressed air energy storage technology concept, wherein a water mist was to have been used during compression in order to produce a quasi isothermal compression process and consequently reducing thermal losses. And I wasn't alone in my enthusiasm, such notables as Vinod Khosla, Bill Gates, Peter Thiel, Total, and others invested somewhere in the vicinity of $80MM in LightSail.

But, despite the confidence of these very bright investors and the large amount of capital invested, LightSail Energy is, according to co-founder Stephen Crane, in a state of "hibernation." I follow Ms Fong on Twitter and, off and on, have corresponded with her. I haven't read anything from her with respect to the fate and apparent demise of LightSail, but the tenor of her Tweets is that she's moved on.

This saddens me because, the potential of near-term success of hydrogen fusion as an energy source notwithstanding, I am firmly convinced of the urgency of weaning ourselves from near-total reliance on fossil fuels for energy and saving those resources for applications for which substitution is extremely difficult such as transportation fuels (airlines, transoceanic shipping for example). Electricity is the low-hanging fruit here, albeit a pretty high low-hanging fruit! We have wind, solar, hydro, geothermal, and other ways to harvest energy that don't directly involve the burning of fossil fuels and all of them result in the generation of electricity.

But the most bountiful categories are solar and wind (hydro, while certainly a large contributor, has mostly been "built out," i.e., the best sources have already been exploited) and those are intermittent sources. In order for them to provide so-called "base load" power, a method of eliminating this intermittency must be employed. This can be accomplished in part by wide geographic dispersion, but the holy grail would be the ability to store energy when the wind blows and the sun shines.

Currently, nearly all new storage installations involve large lithium ion battery installations. But Li ion batteries, while good and continuing to improve, have downsides. They degrade over time, they require assiduous management both to preserve lifespan and to prevent issues of thermal runaway. And, in comparison to large scale pumped hydro storage (PHS) and compressed air energy storage (CAES), the energy capacity of Li ion battery installations is not as large (see chart below, note the log-log scale).

Image credit: unknown

Image credit: LightSail Energy
In the chart, you'll find the "Large CAES" installations in the upper right hand corner. However, the two installations plotted use underground caverns as their containment vessel and need natural gas heating in order to function. LightSail was developing modular units of much smaller size using above-ground storage in tanks. And, in what now seems to have been a last-ditch effort to continue, LightSail began an attempt to market the tanks they'd developed and, apparently, delivered at least one.

Unfortunately, the LightSail web site is gone and with it, I'm afraid, is the investors' money and the hopes and dreams of Danielle Fong.

Saturday, April 28, 2018

My airline fuel use

Undoubtedly to the disdain of those who seek to minimize energy use and, in particular, energy use that involves travel via the burning of fossil fuels, I do a significant amount of airline travel. And, beginning in August of 2017, I added fuel burn (by asking the flight crew, who is invariably happy to entertain my questions), distance traveled, and number of passengers on each flight to my log. I calculate such things as passenger miles per gallon, joules of fossil fuel energy used per passenger, and a variety of other pieces of data.

For the “big numbers,” I’ve flown 27,068 miles on 25 “legs.” Over these miles, I’ve been responsible for 383 gallons of jet A being burned, for a mileage of 70.7 m.p.g. As my patient readers likely would infer, despite my having exchanged my Lexus CT 200h in which I achieved over 50 m.p.g. for a Jeep Grand Cherokee SRT that achieves about 16.5 m.p.g., I still obsessively log my driving fuel burn. In the time that I’ve traveled the 27,000 miles in airliners, I’ve driven 12,573 miles and burned 758 gallons of gasoline for a mileage of 16.46 m.p.g. I very rarely have a passenger in my car. I'd estimate that, of the 12,573 miles, I've had a single passenger for something like 750 miles which results in a passenger mileage of 17.6 m.p.g. Miles driven with more than one passenger were negligible. Had I traveled those same miles in the CT 200h, I'd have burned about 241 gallons of fuel.

What can I make of this? 68.3% of my miles traveled have been in airliners (ignoring when I've been in the road vehicles of friends and associates) but only 33.6% of the volume of fossil fuels burned have been in those airliners. Again, had I still been driving the Lexus CT 200h, the figures would be 68.3% (of course) and 61.4%.

The fact of the matter is that modern airliners are amazingly efficient. If I drove my Jeep with three passengers, I'd still not exceed the fuel economy of the airliner, though the same four people in the Lexus would far exceed that fuel economy. But I'm not aware of anyone who carries a full car load of people any for any significant fraction of their driving.

The most common engines on my flights are the CFM56-7B series (the dash 7B24 variant was the culprit on Southwest flight 1380 that suffered a fan blade rupture resulting in the death of a passenger). The dash 7B24 variant produces a maximum thrust of 24,200 lbf (pounds force) and the dash 7B26 produces 26,300 lbf, though these thrust levels are only used during takeoff and early climb. A typical number in cruise is more like 5,800 lbf. Giving that a little thought, it's pretty startling that a force of 11,600 pounds is all that's needed to push a vehicle with a weight on the order of 150,000 pounds through the air at 530 m.p.h.

There's no doubt that my travels, both now in the Jeep and multiple times per year in the "big silver bird" are contributing more than my fair share of carbon emissions. If I use very rough figures, the 39,641 miles that I've traveled since August of 2017 annualize to the emission of something like 15 tons (Imperial short tons that is) per year of carbon dioxide attributable to my travel with about 36% of those emissions due to airline travel.

Wednesday, December 27, 2017

Charging the Tesla class 8 semi

This is my third post regarding the Tesla class 8 truck. The first covered the range claim and the consequent weight ramifications. The second covered the cost. And, of course, the numbers were my estimates only. In this post I'll consider the charging situation.

The "poster" claim is that charging stations will enable the 500 maximum mile range truck to charge sufficiently for a 400 mile range in 30 minutes. In my first Tesla truck post I estimated that the battery pack capacity to enable a range of 500 miles would need to be about 1,145 kWh (kilowatt hours) so 400 miles would need about 915 kWh. To deliver this energy in 30 minutes requires power to be delivered at 1,830 kilowatts, that is, 1.83 mW (megawatts). And battery charging isn't 100% efficient, so we'll say 90%. Now we need to deliver energy at a rate of just over 2 megawatts!

The current inventory of Tesla Superchargers for the Models X, S, and 3 deliver energy at a rate of up to 140 kW, about 8% of the required power for a "Megacharger" for the 30 minute/400 mile charge for a Tesla semi. Now, Elon Musk has hinted on Twitter of much higher charging rates, hinting that the megacharger's rate will be far in excess of 350 kW.

Elsewhere, rates on the order of 1.6mW are discussed in the main article here, and the comments are interesting as well. There is discussion of the solar charging aspect, even to the extent of putting solar panels on the roofs of the trailers to be hauled by the semi, something that I may take up in a subsequent post.

There are several concerns with respect to delivering energy at the rate of 2 mW. First, what will such a charge actually cost?Second, how will such power be delivered given that multiple trucks will be charging simultaneously? Third, will a battery pack hold up under such charging rates, presumably applied on a daily basis?

While the first question might seem like a no-brainer advantage for the Tesla, we'll take a look anyway. It's true that, at about 2 kWh/mile and a typical industrial rate of $0.0692/kWh, the implied rate of about $0.14/mile for energy looks very favorable in comparison to 1/7 of a gallon of diesel at $2.93/gallon yielding $0.42/mile. But the infrastructure for delivering diesel fuel to trucks is long since built out and the capital costs fully recovered. The Tesla megachargers are merely hypothesized, not built out and paid for. Unfortunately, I have no idea what Elon Musk has in mind with respect to what he'll build, where he'll build it, and how he'll recover its costs. He does say, in his introductory video, that there are "guaranteed low electricity rates for Tesla." But, one way or another, the infrastructure will have to be paid for. Call it a wild card.

What about question number two? Musk has mentioned solar power for the megacharger stations, but that doesn't necessarily imply a solar roof over a few acres at every truck stop. It could just as easily mean offsetting grid supplied electricity at truck stops with solar electricity offsets at favorable locations. Musk makes somewhat contradictory statements when he discusses recharging at destinations while trucks unload and/or at the truck's base while loading. Whether he's discussing a megacharger at such locations (so that the truck owner would own or lease the charger) or whether he's discussing standard charging isn't clear.

He also discusses being able to take the trucks "anywhere in the world," implying that charging facilities will be ubiquitous. Again, whether all of these facilities would be megachargers isn't made clear. Another possibility would be having a premium charge for the megacharger. Again, details aren't available. Thus, I have insufficient information to speculate in detail.

But I do have to look at one aspect. Here, we find that something like two million tractor trailers are registered in the US. I'll just speculate (really, guess, though I hate guessing) that something like 1.5 million are actively earning money for their owners by hauling freight. I'll also use the estimation that each such truck drives about 45,000 miles per year.

Now, if Tesla were to replace 10% of the semi truck fleet, their trucks would travel 45,000 * 150,000 or 6.75 billion miles/year. At 2 kWh/mile, they'd use 13.5 billion kWh or 13.5 gWh (gigawatt hours)/year of electrical energy. As an aside, this rate represents an average power of a bit over 1.5 mW, though the rate will obviously vary hugely. Nevertheless, this hardly seems like a large strain on the US electrical grid. Discovery Network's Science Channel is currently replaying all of the Mythbusters episodes from the original crew's 14 seasons so I'll echo their nomenclature and call it "PLAUSIBLE."

Both for the reason that this post is already plenty long and the reason that I'm still doing some reading on the effects of consistent extremely high charge rates on Li ion batteries, I'll defer to a subsequent post on that topic and end this post here.

Sunday, December 17, 2017

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).

Monday, December 11, 2017

The Tesla class 8 truck

Image Credit: unknown
Well, it's been a long time since my last post and I promise to be more.... Oh, hell, never mind. Anyway, to those who know me, it will come as no surprise that I am an admirer (possibly bordering on a fan boy) of Elon Musk. I know that Musk has received a fair amount of criticism, some of it quite biting and not all of it without justification. Musk has been accused of rent seeking, excessive hyperbole, and squandering of investors' funds among other things. His biography is available in plenty of places and I won't go into it here. Rather, I'd like to evaluate the viability of his newly revealed Tesla class 8 truck.

At a very high level, a Class 8 truck is meant to transport as heavy a load as possible as far as possible at as low cost as possible. On US highways the maximum gross vehicle weight for a Class 8 truck is 80,000 lbs. (36,280 kg). A typical diesel powered class 8 tractor will have a weight of 17,000 pounds (7,711 kg) and the empty trailer "tare weight" might be 15,000 pounds (6,803 kg). Thus, a diesel semi-tractor trailer may be able to haul 48,000 pounds (21,772 kg).

There are many significant considerations with respect to the viability of the Tesla Truck:
  • Cost (both initial purchase and lifetime, including maintenance)
  • Range
  • Time to recharge
  • The effect of the weight of the battery on the load that can be transported
And, of course, there is interplay between these items. For example, to achieve longer range, larger battery packs are needed. This will add significant cost and charging time and, due to the added weight of the larger pack, will reduce the payload that can be carried.

Image Credit: Tesla
In order to evaluate the practicality of the Tesla Truck, I'll start with the energy required per highway mile at 65 m.p.h. on a smooth and level highway in good condition and in good weather. We'll assume that the semi tractor trailer is loaded to its maximum weight of 80,000 pounds. As I've detailed in other posts, for such unaccelerated motion, the sum of the external forces acting on the vehicle must be zero. The forces resisting the forward motion are aerodynamic drag and tire rolling resistance. The sum of these is the total that the electric motor must provide to the pavement through the drive train and the tires.

Starting with the drag, to a reasonable degree of accuracy, the drag force is ~D=1/2\,C_{D}\,A\rho\,{v}^{2}~ where D is the drag, CD is the vehicle's drag coefficient, A is the frontal area presented to the relative wind, ~\rho\,~ is the density of air, and ~v~ is the vehicle's speed. From a youtube video presentation, Musk states that the drag coefficient is 0.36, which is very low for such a vehicle. I haven't found the frontal area of the vehicle, but various sources seem to indicate that a reasonable estimate is about 10.75 m2. We'll use 1.2 kg/m2 for air density and convert 65 m.p.h. to 29.06 m/s. Plugging, this yields a drag force of 1,961 Nt (440.8 pounds).

For rolling resistance, we'll look at four driven wheels, two steering wheels, and four free rolling tires on the tractor and eight free rolling tires on the trailer. I'll give Tesla the benefit of the lowest rolling resistance tires that I've been able to find. Then, to first order, rolling resistance is dependent only on the coefficient of rolling resistance of the tires and the normal force (weight) on those tires.

While the actual rolling resistance will depend on how much weight is on which tires (because the rolling resistance will vary) and I won't know how much weight can be in the trailer until I've determined battery weight. I'll assume tires with "state of the art" low coefficient of rolling resistance (Crr of an average of 0.0056. And I'll assume that each of the tires carries an equal load so that the rolling resistance, R, is determined by ~R=C_{rr}w~, where ~C_{rr}~ is the coefficient of rolling resistance and w is the vehicle weight. Converting 80,000 pounds to 355,858 Nt and plugging and chugging, we find that the approximate rolling resistance is 1,993 Nt.

Thus, the approximate force that the motor must apply to the pavement through the drive train and tires is 3,954 Nt. And, since force times distance is work (and energy), the motor must do 3,954 joules of work (that is, supply 3.954 joules of energy) to move the truck one meter at 65 m.p.h. And, since there are 1609.3 meters in a mile, the motor must do 6.36317*106 joules of work. The battery system must supply enough energy to do this work, and must supply more, given that the motor/drive train combination is not 100% efficient. If we assume 85% overall efficiency, the battery system must supply 7.486*106 joules/mile. This is 2.079 kilowatt hours. Note that Tesla says "less than 2 kWh/mile." I'm sticking with my number but it shows that my estimates can't be too far off.

In order to travel 500 miles on a level road in good conditions with no starts and stops at 65 m.p.h., Tesla will need a battery system that can supply 2.079*500 or 1,039 kilowatt hours, or 1.039 megawatt hours. If we use a number of 140 watt hours/kilogram for specific energy of a Li ion battery, such a battery pack would weigh 7,421 kg, or 16,360 pounds.

This is as ideal as it can possibly be. The truck will climb hills and, though some of the potential energy paid for in kilowatt hours can be recovered coming downhill and even energy normally wasted by braking as the truck rolls downhill will be partially recovered by a regenerative system. Nevertheless, there will be waste associated with climbing and descending. Similar considerations apply to stops and starts for traffic, stoplights, stop signs, meals, etc.

Therefore, we need a "fudge factor" for the various starts and stops, accelerations, etc. While I've seen numbers such as 90% bandied about for how much of the kinetic and potential energy in the Tesla truck can be recaptured by regenerative braking, my experience in the Lexus CT 200h makes that number seem very high. I've calculated that, in my CT 200h, about 39% of the potential energy from a hill descent went into the batteries. But I'll be generous and speculate that Tesla is much more efficient at 75%.

Suppose that the truck does the equivalent of stopping 100 times in 500 miles. An 80,000 pound vehicle travelling at 65 m.p.h. has a kinetic energy of 1.537*10^7 joules. Losing 25% of this number 100 times wastes 3.830*10^8 joules, or 106.4 kWh. Adding this to the 1,039 kWh we find that the battery pack must supply 1,145 kWh or 1.145 mWh. This will require a battery pack weighing 8179 kg or 18,031 pounds. Call it 18,000.

We now need to determine how much the battery pack weight will reduce the payload that can be hauled. To compare apples to apples, we'll figure that a very fuel efficient diesel powered semi tractor gets about 7 m.p.g. and thus will use about 71 gallons of diesel fuel weighing about 490 pounds (numbers for the weight of a gallon of diesel fuel are all over the place, but I think this represents a good average). The engine and transmission might weigh something like 3,500 pounds. The total of the materials not needed in the Tesla truck (diesel fuel, engine, transmission) is about 4,000 pounds. Thus, the available payload for the Tesla is some 14,000 pounds less than that of the diesel powered semi. And this understates the issue since we've removed the internal combustion engine and transmission, but the electric motors weigh something!

A typical heavy hauling semi tractor trailer can legally haul somewhere around 44,000 to 48,000 pounds of payload, so the 14,000 pound reduction represents a 29% to 32% reduction in payload. I imagine that many loads are not at the maximum allowable to have the total vehicle weight not exceed 80,000 but, as best I can find, most intermediate and long haul loads do exceed the approximately 30,000 pounds available in the Tesla truck.

As far as weight is concerned, the Tesla truck with a sufficiently sized battery to achieve a 500 mile range is at a significant disadvantage. I'm sure there are applications where this disadvantage would not be relevant, but the average over the road trucker would be severely disadvantaged. For the 500 mile range version, I believe that significant advances in battery technology will be necessary.

Next time: cost.