“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)

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.