Kinetic and Potential Energy

By Marcus Wilson 31/01/2011

I read last week an electronics magazine article about developments in electric aircraft. Yes – for real – the aviation industry is not confined to using truck loads of fossil fuel to get from A to B. The article got off to a bad start by using the word ‘electric’ with the phrase ‘reduced greenhouse emissions’ in the same sentence (it depends on how you generate the electricity, doesn’t it?) but from then on it was very interesting.

There are lots of aircraft (mostly small ones at the moment) being designed and built to run off electricity. (Propellor driven, obviously.) Indeed, there is a team aiming to get a solar power aircraft to fly non-stop round the world. When you think about it, solar power for aircraft is a good idea – you have lots of wing area to put solar cells on, and above the cloud it’s always sunny. 

"Yes", I hear you say, "but what about at night? There’s not much sunshine then." True. But with supercapacitors becoming bigger (in terms of ability to store electric charge) and cheaper and smaller, storing the energy collected in the daytime and releasing it at night is now much more realistic.  

And there’s another energy storage method too, that is available to aircraft. That’s to gain height. Store up your energy in the day as gravitational potential energy, and then release it at night by losing altitude.  

A quick back-of-the-envelope calculation tells me that a plane at 10 km height doing about 800 km/h has about four times as much potential energy as it has kinetic. There’s a lot to give up. Indeed, one of the problems facing a descending aircraft preparing to land is that it has to dump both potential energy (drop in height) AND kinetic energy (slow down) at the same time. The only option to it is the drag force – use air-resistance to get rid of that energy. Another rough calculation for a 777 tells me that the amount of energy it has to get rid of is equivalent to burning about 700 litres of fuel  Not terribly large considering the amount of fuel that can be carried (Wikipedia says about 180 000 litres), but wasted energy nonetheless.

(Based on 32 MJ per litre as energy density of petrol – aviation fuel will be a touch different, and 250 000 kg maximum landing weight for a 777-300ER. Not that I expect Boeing to realease a solar-powered version of the 777 anytime soon. Probably the 777 isn’t a good example to pick anyway because it’s a jet not a prop, but it’s my favourite plane which is why I picked it.)