# How Good Can Battery-Electric Planes Get?

I recently watched a video on electrifying planes from DarkAero, an extremely great YouTube channel from a bunch of alarmingly young-looking guys running a company that's trying to make a very cool plane optimised for speed and range. In the video they walk through the maths of working out how converting their plane to be battery-electric would affect its range, and show that it would take a pretty huge hit. But there's a company called Otto that's also developing a plane, and they're making even more ambitious claims about its range, so I've decided to run the numbers on that and see how it fares from electrification.

The Otto Celera 500L is a bizarre-looking prototype plane that's designed to carry up to six passengers for long distances (8,300km) at high speeds (740km/h) while having operating costs that are roughly a third of that of comparable planes. There's a lot of online scepticism about whether it will actually be able to meet these goals, but I'm assuming it can so I can use it as a sort of best-case for airframe efficiency, and asking the question: what sort of performance would it have if we replaced its diesel/piston engine drivetrain with a battery-electric drivetrain? This should hopefully give us some idea of the best-case for practical battery-electric airplanes made using currently available technology.

We can work out the mass of fuel the Celera 500L carries from with *range × fuel consumption × fuel density*, which works out to *8300km × 7.8L/100km × 0.85kg/L = 550kg*. It's powered by a RED A03, which has a dry mass of 363kg. So ripping out the engine and fuel tanks would give us 913kg to spare for an electric drivetrain.

So let's start with the easy part of that drivetrain: the motor. H3X is developing a motor, the HPDM-250, that they claim will produce 200kW (268hp) while weighing only 16kg. Since the 500L's engine produces 340kW (456hp) we can exceed its power by connecting two HPDM-250s to a driveshaft for a mass penalty of only ~32kg, with the added redundancy bonus of having two engines.

Now for the not-so-easy part. We have 881kg left for batteries. CATL, the biggest li-ion battery manufacturer in the world, recently announced they're going to start mass production of a 500Wh/kg battery. Given Tesla's current best battery cells have an energy density of 296Wh/kg, this is a pretty big deal. If we filled our remaining mass budget with these batteries that would give us 440,500Wh, or 1,585MJ of energy onboard. So how far would that get us?

Diesel fuel has an energy density of 45.6MJ/kg, diesel engine efficiency can vary quite a bit, but 45% seems like a reasonable figure for our purposes. Using these numbers, and our fuel mass of 550kg we can work out the enregy use at the prop shaft as *0.45 × 45.6MJ/kg × 550kg = 11,286MJ*. If we assume, pretty generously, that there are no losses in the electric drivetrain then our electric Celera can deliver only *1,585MJ / 11,286MJ = 14%* as much energy to the prop as the real Celera. Which, in the best case (since a large, constant fraction of energy is used climbing to crusing altitude), probably translates to just 14% of the range, or 1,162km rather than 8,300km.

For context 8,300km is about the distance from Torronto to Rio de Janeiro, or Sarajevo to Bangkok. While 1,160km is slightly less than the distance from Torronto to Atlanta, or London to Florence. I still think this would be a very cool plane. It would presumably go just as fast, be significantly quieter, and have a fraction of the running cost. Hopefully I'll look up and see one one day!