The Electric Schoolbus

Would it be a good idea to turn all 480,000 school buses in the United States into electric vehicles?

That question struck me recently, so I decided to check it out. If you're the type who doesn't like math or reading, let's start with the conclusion.

Conclusion

There are good reasons to consider it, but the electrification of 20 ton vehicles is not currently cost effective.

Diesel Powered Buses (current state)

Modern school buses (the big ones) have seating for 84 students, weigh 14 tons and get 7 MPG. Each burns about 10 gallons of fuel per day resulting in 823,000,000 gallons per year at a cost of about $3,200,000,000 dollars.

Route Distances

I couldn't find data that explicitly stated the average distance of school bus routes, but I found enough data to approximate. School buses drive an average of 12,000 miles per year over about 180 days school days. Some quick math says this equates to 12,000 ÷ 180 = 67 miles per day.

This is a big estimate; school buses are used for other purposes than just daily routes, so I'm likely over estimating the daily needs for the buses and underestimating peek demand. A more informed version of this plan may call for electrifying enough buses to cover a shorter daily route distance and keeping some diesel buses for long haul duty.

Range per kWh

To estimate how far an electric bus could go, I'm estimating based on electric vehicles available today. One vehicle, for instance has a 7.6 kWh battery that can move a 1.95 ton car for ~20 miles. That equates to 5.13 ton miles per kWh.

Our 14 ton bus will consume 2.73 kWh per mile.

That 7.6 kWh battery that moves our plug-in hybrid 20 miles won't even move our bus 3 miles.

Batteries are Heavy

One problem with a plug-in hybrid is that it needs a big battery. Batteries are heavy, so we end up needing more battery to provide the power to move our battery. It's a terrestrial version of the Rocket Problem.

What does that mean for us?

After some math, our 14 ton bus with 2 tons of people will require 8,000 pounds (4 tons) of lithium ion batteries.

This isn't looking good.

Target EV Range

We can't have our target range be the 67 mile average route. Climate control and hard braking will reduce the achievable range. Let's give a 50% buffer and set a target of a 100 mile range.

To meet that range, we'll need 404 kWh of lithium ion batteries.

Batteries are Big

404 kWh of batteries are going to take up a lot of space. It's entirely possible our electric school bus will be so full of batteries that students won't fit. That much power would be the same as 29 Tesla Powerwalls; 202,230 cubic inches of lithium ion.

Busses are Big, Too

Fortunately busses are big, too. Our 40 foot bus is 8 feet wide, giving us about 46,080 square inches of floor. If we were to lay our batteries across the floor, they'll raise it by 4.4 inches.

Not bad! That is entirely workable.

Batteries are Expensive

Good news! Our bus can easily hold 4 tons of batteries and still have space for students. Unfortunately, batteries are expensive.

Let's be a little optimistic here. Some reports forecast lithium ion batteries costing $100 per kWh by 2020. We'll use that estimate.

Buying 404 kWh of batteries will cost us $40,400. That's a lot, but not as bad as I thought.

Electricity isn't Free

We may have 404 kWh of power for 100 miles of range, but we won't use that much power everyday. Hopefully be closer to just 67 miles daily; consuming 270 kWh.

Although there is a lot of variability, the national average cost of electricity is $0.12 per kWh. That means we're spending $32 a day on electricity for our bus.

Uh Oh

If you're keeping track you'll notice that our bus burned 10 gallons of diesel a day. At current prices of $2.40 per gallon, we'd be spending $24 a day for diesel as opposed to $32 for electricity.

So it turns out we'll never break even with prices as they are.

What Would Need to Change?

There are a lot of variables that could change. Electricity Price, bus weight, battery weight, battery power density, gas prices, cost of capital, and the list goes on.

Turns out our biggest problem is the cost of the batteries. However, those won't change enough any time soon to solve our problems.

We could do a few things to drive down the cost of electricity, but that would be even more cash intensive than our batteries (but with a better payoff).

The best option is actually increasing the price of diesel.

At $3.39 per gallon, the cost of diesel would equal the cost of electricity. That makes it feel attractive, but the savings won't pay for those batteries.

How High Would Diesel Prices Need to Go, To Make the Electric Bus the Economic Choice?

I'll spare you the math here (in part because I decided to do this as a 15 year plan where we replaced 1/15th of our busses per year, continued to pay for gas for the rest, and adjusted the results to be in net present value).

The answer is $6.51 per gallon of diesel. At that price, EV busses become economically viable.

So, this was a pretty bad idea…

From the sole perspective of minimizing money spent on busses, you're right. However, there are numerous reasons the idea holds merit beyond the savings.

  • If we wanted to convince more companies to get into the battery game, it would create demand.
  • The large orders could also help industrial battery manufacturing reach scales that could reduce battery prices for other scenarios.
  • Or, we could turn the whole thing into an R&D fest by offering the contract to provide the batteries to anyone who can design a solution that has the same energy storage but at half the weight ($20,000,000,000 would provide a goodly amount of motivation and instant scale in manufacturing).
  • Exposing kids to fewer noxious gases may also have some value
  • And quite a few more if you exercise a little imagination

If the Economics Are That Bad, Why Are There Electric Cars?

The economics of the bus don't apply to cars.

Remember how busses are big and need to drive far? Those are problems. Adding all the batteries to move the bus 100 miles makes the bus a lot heavier, meaning our batteries need batteries. At the end of that cycle, 25% of the bus's weight is batteries.

Remember those plug-in Ford C-Maxes? They can comfortably go 20 miles on electricity with a 7.6 kWh battery. The car weighs almost 2,000 pounds and that volume of battery probably weighs about 100 pounds (extrapolating from other batteries). That's a mere 5% of the weight.

Plug-in hybrids make a great deal of sense as long as their typical use is short distances for personal transportation. Those conditions can leverage a small battery and allow zero burning of gasoline. And, because we're not using 25% of our energy to move batteries, a car's break even with gasoline is in the middle to upper $2 a gallon range.

Of course, all this talk of "breaking even" assumes that saving money is the only reason to do the right thing and use fewer resources.

MATH!

Variable Calculation Value
Battery Weight Budget = 4.00 (Ton)
Weight of Occupied Bus (16.70) + (4.00) (Ton) = 20.70 (Ton)
Average Daily Miles (66.67) (Mile) = 66.67 (Miles)
Ton Miles per kWh (5.13) ((Ton) × (Mile)) ÷ (kWh) = 5.13 ((Ton) × (Mile)) ÷ (kWh)
Target Range (100) (Mile) = 100.00 (Mile)
Extra Range 100.00) − (66.67) (Mile) = 33.33 (Mile)
kWh Needed for Target Range ((20.70) × (100.00)) ÷ (5.13) ((Ton) × (Mile)) × ((kWh) ÷ ((Ton) x (Mile))) = 403.42 (kWh)
kWh per Battery (14.00) (kWh) ÷ (Battery) = 14.00 (kWh) ÷ (Battery)
Batteries for Target Range (403.42) ÷ (14.00) (kWh) ÷ ((kWh) ÷ (Battery)) = 28.82 (Battery)
Cost of Battery (100.00) × (14.00) (Dollar) ÷ (Battery) = 1,400.00 (Dollar) ÷ (Battery)
Cost of Batteries per Bus (1,400.00) × (28.82) (Battery) × ((Dollar) ÷ (Battery)) ÷ (Bus) = 40,342.36 (Dollar) ÷ (Bus)
Volume per Battery (29.00) × (44.00) × (5.50) (Inch) × (Inch) × (Inch) ÷ (Battery) = 7,018.00 (Inch3) ÷ (Battery)
Battery Volume for Range (7,018.00) × (28.82) (Battery) × ((Inch3) ÷ (Battery)) = 202,230.48 (Inch3)
Bus Square Inches of Floor (480.00) × (96.00) (Inch2) = 46,080.00 (Inch2)
Additional Floor Height (202,230.48) ÷ (46,080.00) (Inch3) ÷ (Inch2) = 4.39 (Inch)
Cost of Electricity (0.12) (Dollars) ÷ (kWh) = 0.12 (Dollar) ÷ (kWh)
Cost per Mile for Electricity = 0.48 5,809.30
Power Used per Day per Bus ((20.70) × (66.67)) ÷ (5.13) ((Ton) × (Mile)) × ((kWh) ÷ ((Ton) x (Mile))) = 268.95 (kWh) ÷ ((Day) × (Bus))
Power Used per Year per Bus (268.95) × (180.00) ((Day) ÷ (Year)) × ((kWh) ÷ ((Day) × (Bus))) = 48,410.83 (kWh) ÷ ((Year) × (Bus))
Daily Electricity Cost per Bus (0.12) × (268.95) (kWh) × (((Dollar) ÷ (kWh)) ÷ (Day)) ÷ (Bus) = 32.27 (Dollar) ÷ ((Day) × (Bus))
Yearly Electricity Cost per Bus (32.27) × (180.00) (((Dollar) ÷ (Day)) × ((Day) ÷ (Year))) ÷ (Bus) = 5,809.30 (Dollar) ÷ ((Year) × (Bus))
Bus MPG (7.00) (Mile) ÷ (Gallon) = 7.00 (Mile) ÷ (Gallon)
Cost per Gallon (Dollars) ÷ (Gallon) = 2.40 (Dollars) ÷ (Gallon)
Cost per Mile for Diesel (2.40) ÷ (7.00) ((Dollars) ÷ (Gallon)) ÷ ((Mile) ÷ (Gallon)) = 0.34 (Dollars) ÷ (Mile)
Gallons per Day per Bus (66.67) ÷ (7.00) (Mile) ÷ ((Mile) ÷ (Gallon)) ÷ ((Day) × (Bus)) = 9.52 (Gallon) ÷ ((Day) × (Bus))
Cost per Day per Bus (9.52) × (2.40) (Gallon) × (Dollars) ÷ (Gallon) ÷ ((Day) × (Bus)) = 22.86 (Dollars) ÷ ((Day) × (Bus))
Yearly Cost per Bus (22.86) × (180.00) ((Day) ÷ (Year)) × (Dollar) ÷ ((Day) × (Bus)) = 4,114.29 (Dollars) ÷ ((Year) × (Bus))
Break Even Percent Increase in Diesel (22.86) ÷ (32.27) ((Dollar) ÷ ((Day) × (Bus))) ÷ ((Dollar) ÷ ((Day) × (Bus)) = 0.71
Break even Diesel Price (2.40) ÷ (0.71) (Dollars) ÷ (Gallon) = 3.39 (Dollars) ÷ (Gallon)
Break even Daily Diesel Cost ((66.67) ÷ (7.00)) × (3.39) ((Mile) ÷ (Day)) ÷ ((Mile) ÷ (Gallon)) × ((Dollar) ÷ (Gallon)) = 32.27 (Dollars) ÷ (Day)

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