## onsdag 24 oktober 2018

### How Far Can a Battery Fly?

Electrical vehicles of all kinds are currently being investigated with electrical airplanes as an novel option attracting eager investors. Let us seek an answer to the key question of the possible range of such a device powered with lithium-ion batteries.

The energy density of lithium-ion battery is about 1 MegaJoule per kilogram. Equipped with weightless wings with a lift-to-drag ratio of 15 a battery of weight 1 kp = 10 N would be able to fly a distance S determined by the equation
• 10/15  x S = 10^6
that is S = 1500 km. Not so bad. But that is the theoretical maximum which will be reduced  adding weight for passengers, airplane structure and engine efficiency. How much?

Let us compare with kerosene fuel with energy density 40 MJ giving a jumbojet with again lift-to-drag of 15 a maximal range of 40 x 1500 km = 60 000 km, which we compare with the real range of about 10 000 km , thus with a reduction factor of about 6 to account for passenger+structure+engine efficiency.

The practical maximal flying distance of a battery driven airplane could then be about 250 km.  In contrast to surface travel, the energy consumption for subsonic flight is independent of speed.

With a lift-to-drag of 30 the maximal distance would be up to 500 km, which may be what is needed
to make electrical flight economical. For a more information on flight take a look at The Secret of Flight.

PS A bar-tailed godwit (Limosa lapponica) each year flies without interruption from Alaska to New Zealand, a distance of 12 000 km over a period of 11 days. Assuming an energy density of meat/fat of about 30 MJ the above calculation gives a maximal distance of 15 000 km assuming total loss of weight at arrival, which roughly fits with the observation.