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All the numbers used in this article are Rough Order of Magnitude (ROM) numbers. Nothing nuanced here – just back of the napkin numbers. If you disagree with my assessment let me know, send me your numbers and I will publish you in the next newsletter.

On one of our programs this week we have got into the subject of cabin heating. This is a relatively high altitude cabin and the heating requirement is going to be more than your run of the mill eVTOL aircraft.

But I am sure that eVTOL UAM operators will want to run their service in Toronto or Stavanger in the middle of winter so this will still be a problem at some level.

For electrical conversion of regular fixed wing aircraft this is a more significant problem.

Turbo propeller and turbo fan engines generate the two things that are lacking for humans at altitude. Pressure and heat. Turbine engines allow you to tap into the hot air under pressure from the turbine to provide both heat and air pressure for the cabin.

The addition of turbochargers allows you to ‘harvest’ heat and pressure from piston engines. This heat and pressure is not only useful for providing a comfortable cabin environment but can also be used for intake lip and flying surface anti-ice systems.

It is important to note that these systems, called bleed air systems, do not convert the waste energy from the engine. They tap into the energy of the motive system and further reduce engine efficiency. 

Waste heat from engines is very hard to recover, as is any inefficiency as it is entropic by nature. Reconcentrating that entropic waste is difficult, heavy, expensive or impossible.

Electrical motive systems have inefficiencies and those inefficiencies are represented as waste heat. When batteries release energy they generate heat. The motor controllers and motors are not 100% efficient and that inefficiency is represented as heat. All in all between the battery and the rotating shaft of the motor you can expect to lose 10-15% of the overall energy.

If you are cruising at 350HP or around 200kw that can mean you are also generating up to 0.15 x 200 = 30kw of heat throughout the system. This is also true of UAVs. In recent talk with university students at Tuskegee University we touched on the subject that if each motor is, say, 93% efficient and pulling 1kw you have a 70W heater at each motor. These issues need to be managed and this heat, like all waste heat, has to be dissipated through vanes, circulating air systems, radiators etc.

In order to pressurize and heat the cabin at 41,000ft (high altitude cruise for a pressurized aircraft) for 8 occupants you generally need 10-12kw.

Well, if you have 30kw of waste energy that is more than enough, right? 

Well, no. That energy is in the form of entropic waste heat. If you could gather most of it and cool it using a heat exchanger you may be able to recover some of the heat for use in the cabin but it would necessitate the use of a large, over complex heat exchanging system, would not recover enough energy and would still fail to pressurize the cabin.

So you have to pull that 12kw out of the batteries. If you need 12kw of heat and pressure and your heater and your compressor are, lets say 70% efficient then you need 12 / 0.7 = 17.14kw  – let’s say 17kw from the battery.

For one hour of flight at 41,000ft the battery energy requirement to maintain the cabin environment is therefore 17 kwh.

Using the packaged battery energy density of 150wh/kg this means you need to carry around 250lb of batteries to provide the necessary cabin environment for one hour.

For eight passengers this would be 30lb of batteries per passenger per hour to cruise at 41,000ft.

On the Explorer AIrcraft program we had a series of conversations with some of the world’s leading researchers in the field of fuel cells at one of the US National Laboratories. I raised the issue of the lack of harvestable excess energy in the form of heat and pressure being a barrier to the adoption of fuel cell and battery technology in aviation and it was not something that had been examined or considered.

So not only will electric aircraft have to rely on extracting additional power from the already weight inefficient batteries, they will also have to carry the excess weight of an electric compressor and heating system for the cabin air.

While lower performance and lower altitude aircraft do not have to provide pressure to the cabin they do have to provide heat. For those operators who want to offer electric UAM in the middle of winter the heating requirement overall is roughly half of the overall bleed air energy mix. So around 5-6kw.

So the battery mass requirement for unpressurized flight will be roughly half of the number calculated above – that is 15lb of batteries per passenger per flight hour.

The Joby S4 with one pilot and 4 passengers will require 75lb of batteries per flight hour for cabin heating in cold conditions.

This amount of additional battery weight would not be a problem if you were not already fighting the unfavorable physics of battery energy density in all other aspects of design and operation.

Is this article just dumping on electric aviation from a negative point of view? Well, yes it is. Batteries have their useful applications in aviation. Powering commuter style passenger aircraft is definitely not one of them.

Sometimes lousy energy density and immature technology is just lousy energy density and immature technology.