*Tesla appears to have hit on a recipe that will permit them to lease a battery that will completely exhausted in 5 years. This is potentially game-changing because it means payback comes quickly.*

This week Tesla announced the details on their semi truck. Some key metrics below:

- 500 mile range (800 km) @ 60 MPH (96 kph)
- 7 hours of driving time
- 400 miles of range in 30 minutes of charging
- $0.07/kWh network energy costs
- < 2 kWh per mile, which is 1250 Wh/km

This post will look into the economics in more detail, and also determine if the application of the cells used in the Semi is *that *different from that of the Model S today. If you can't wait to the end, the economics look promising, and taking the cell tech straight from the Model S/3 would probably work just fine. In fact, the Semi is probably more gentle on the cells than the Model S.

## Cost per Mile

Most interesting this week was Tesla's graph on cost-per-mile, which is $1.26/mile.

Tesla is assuming a $0.07/kWh cost for energy, and they will presumably deliver on these numbers via a combination of strong utility agreements (eg. charge megacharger batteries during off-peak) married with some local generation and storage. But the energy costs, as we'll see, are a fairly small part of the overall per-mile cost (roughly 11% of the $1.26/mile figure). There's no reason to doubt Tesla's claim here.

## Battery Lifetime

With 500 miles of range, and 2 kWh/mile, we can deduce the battery capacity is about 1 MWh. This is larger than many had been thinking prior to this announcement. But there's a good reason for this.

The lifetime of lithium batteries is related to the depth of discharge, among other things. With reasonable charge and discharge rates, the typical specs from cell manufacturers usually suggests that at very high depths of discharge (nearly 100%) you will get about 500 cycles over the life of the cell. That means that if your battery capacity is 1 watt-hours, then you have 500 watt-hours of total energy delivered over the life of the cell. Assume that you only discharge to 50%, though. How many watt-hours of energy will be delivered over a lifetime? You might think you'd get get twice as many half cycles, which would deliver the same 500 watts hours of the life of the cell. But in fact, something magical happens: The total energy delivered can grow nearly 3X, meaning the cost per delivered kWh is now 1/3. That is, the 1 watt-hour cell can deliver as much as 1500 watt-hours of energy over its life *if you take care of the cell and follow some very simple rules.*

Musk made an important point during his presentation: 80% of trucking routes are 250 miles (400 km) or fewer. This starts to give us insight into where Tesla might be headed with this: Start with a 1 MWh pack, which could deliver a max range of 500 miles (800 km) at 2 kWh/mile. Derate that so that you'd seldom consume more than 70-80% of the total charge (70 to 80% Depth of Discharge). That gives you 1200 to 1500 full cycle equivalents, and a total range of 625,000 miles (1M km) over the lifetime of the pack.

## Diesel and Electric Economics

In a diesel truck, fuel costs are about 40% of the total operating costs per mile, and repairs and maintenance are about 10%. This means that half of the $1.51/mile figure goes towards fixed items such as driver salary, tires and insurance. This breakdown is in the table below.

Since Tesla claimed they can hit $1.26/mile and the fixed costs are $0.76/mile, we can subtract out repair cost and arrive at the battery depreciation costs. Let's assume that since electrics are simpler than ICE (fewer moving parts), that the repair costs is only half as much. And Tesla said the cost to travel a mile at speed would be $0.14. This gives us $0.18/km left over for battery depreciation costs.

In the table below, we break down the battery costs, and arrive at a "operating cost per km". This figure doesn't include the electricity cost. This is simply the battery cost divided by the total number of miles delivered. And once we have the operating cost, we can derive the pack cost.

This suggests that Tesla will initially be leasing (selling?) the pack out for about $187/kW to hit the published per-mile figure they claimed. No matter how you slice it, the pack is expensive.

Remember, too, that Tesla stated their pack cost on Model 3 was "below $190/KWH". In fact, in 2014, Elon Musk noted in an investor call "I would be disappointed if it took us 10 years to get to a $100/kWh pack." With production slated to begin in 2019, some penciling around the quote above (assuming 8% YoY) suggests a pack price around $150/kWh for 2020. Yes, the pack *is* expensive. Probably $150,000 to $200,000. But remember, it's an asset that generates revenue. Your monthly pack lease bill should be less than your monthly fuel bill. It's that simple.

If a typical truck is logging 130K miles per year ($180,000 annual operating cost/$1.38 per mile = 130K miles = 208 km), then this means a pack has a 5 year life time. Keep that figure in mind, it's important later.

## Battery Kindness

### Model S P85D

We'll look at this in more detail in a future post, but it's important to note just how gentle Tesla is being to these cells.

The Model S can hit about 300 miles of range from its 85 kWh battery at a constant 60 MPH speed. This is 5 hours of driving, and suggests 17 kWh consumed per hour and thus 17 kW is required from the battery to move the car. This is a 0.2C rate discharge. Most driving is probably occurring around this rate, and this rate is very comfortable for 18650-type cells to deal with.

Supercharging in the Model S delivers 50% charge in 20 minutes. On a P85, this means around 45 kWh delivered in 20 minutes (ignoring losses), which means the battery was hit with 135 kW for 20 minutes. This is about a 1.6C charge rate. In order to charge at this rate, the battery needs to be nearly flat. As the battery state-of-charge increases, the charging must be tapered down.

The Model S P85 pack can experience two different types of discharge extremes. The first is a short-term discharge experienced during hard acceleration. With a peak power of 310 kW, this is a 3.6C draw from the pack. At this level of draw, the cells temps will quickly rise. Worse, the temp rise is happening deep in the cell before any thermal solution can help. For this reason, this mode of operation can only happen when the cells are at a reasonable temperature to start AND for a few seconds at a time.

The second discharge extreme is sustained during high speed driving. Tesla's graph shows the Model S P85 with a range of 200 mile at 80 mph (about 0.4C discharge). Other reports on the internet indicate a P90 on the track thermally limiting at about 100 MPH. Eyeballing from the Tesla graph, the range at that speed would drop to perhaps 150 miles, which is about 0.6C. It's not clear if the thermal limit is due to the pack or the motor or both. In a perfectly designed system, both power train and battery would limit at about the same point. Regardless, we'll go with that figure.

### Semi

The numbers for the Semi appear to be much kinder to the pack, primarily because the pack is so large. If the Semi indeed has 2 kWh/mile energy usage at 60 MPH, then this means the semi is consuming 120 kW to move at 60 MPH. This is a discharge rate of 0.12C. This is quite a bit lower than the P85. But that's good, because it makes the battery happier, and happy batteries live longer.

To deliver 400 miles of range in 30 minutes of charging means 400 * 2 kWh = 800 kWh delivered in 30 minutes. This is 1.6 MW for 30 minutes, or about a 1.6C charge rate. This is the same as the P85 at the Supercharger.

But how about hills? We saw above it takes 120 KW to move the loaded Semi at 60 MPH. What does a 7 degree hill mean? High-school physics says the power adder required would be:

P = m * g * sin(theta) * v

Where P is the added power required (assuming 100% efficiency), m is the mass (kg), theta is the hill angle in radians, and v is the velocity in m/s. At 80,000 pounds and 60 MPH, 7 degree hill would be a doubling of flat-ground cruise power. This doubles the cell draw to 0.24C, which is still very comfortable. It will indeed cut your range. But if the backside of the hill is properly handled, the impact might not be so bad.

A bit more study and speculation is needed for the acceleration rates. But we'll take a swing at that later.

## New cell tech?

Tesla has a decade of 18650 learning under their belt. No doubt, they are probably running thousands of driving profiles on individual cells 24x7 to learn just what the chemistry likes and doesn't like and what it will and won't tolerate. They don't need a full pack to learn this. They can run a scaled down profile on a single 18650 cell, taking into account hard acceleration, cruising, regen, fast and slow charging--all of the parameters you might ever want to understand. Their engineers can then make statements along the lines of "With a sample size of 20 cells and confidence of 98%, Supercharging at 1.7C every 5 standard charges reduces cell cycle life by just 1%." In other words, this is a numbers game. And to win the game, you need to know the rules better than your competitor.

So, is Tesla using some brand new cell technology for the Semi? Some in the last few days have suggested that. But it seems that they could meet the top-level requirements easily with the current cells used in the Model S (or Model 3). And this is key, because if you are Tesla, you'd like to bet everything on a single core chemistry (perhaps with a few tweaks) if you could.

P85 | Semi | |
---|---|---|

Average Draw at 60 MPH | 0.2C | 0.12C |

Supercharge Rate | 1.7C | 1.6C |

Hard accel (2 sec) | 3.6C | ??? |

Sustained High Speed | ~0.6C | ??? |

From the above, we can see that some new, exotic technology isn't needed from a charge/discharge rate perspective. What would be nice, obviously, is a longer cycle life. If you can get 10% more cycle life from the cells, then you reduce your costs by 10%.

Much has been written about cities and governments mandating the end of ICE. At the end of the day, ICE is dead REGARDLESS of what cities and governments decide to do. Purely because we've seen per-mile costs destroyed by electric in passenger cars like the Model 3, and now, per-mile costs destroyed by electric in Semis. It's the economics. And it's irrefutable.

# Summary

Tesla appears to have hit on a recipe where they can generate an OK return on a very expensive asset from the beginning. Roughly, in 2020, it seems reasonable that Tesla could be looking at a $150/KWH pack cost, and 5 year lease on a pack could generate $187/KWH. So, out of the gates that would be a 4.4% return beginning in 2020. Meh. OK.

But when you take into account the fact that gas prices over the next decade will probably remain where they are today or go up (meaning Tesla doesn't have to drop their per mile price and might be even able to raise it), and when you also factor in Tesla's claim they can readily hit $100/KWH pack price in 2024, this suggests than a 5 year lease on a pack would start generating 13.7% annual returns. Wowza.