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Here's my first draft at a formula for working out a BEV's ability to travel a given distance successfully.

Basically we need four facts to work out the chances of success (Ps) in completing a trip.

These are:

Probability of a failed charge point (Pf)

Range of vehicle (r)

Total Distance (d)

Number of points enroute*

* I have assumed equidistant spacing.

Ready for this ?

Ps = (1 - Pf / [r/(d/n)]) ^ [d/r]

Plugging some numbers in to test:

250 mile journey in a 300 mile range car = 100% (obviously)

250 mile journey in a 60 mile range car, 5 points, 5% chance of a point being down = 80%

250 mile journey in a 100 mile range car, 5 points, 5% chance of a point being down = 95%

250 mile journey in a 200 mile range car, 5 points, 5% chance of a point being down = 99.8%

So clearly battery range has a big impact on actually reaching your destination (not just time or convenience) all things being equal.

What if we double the number of points?

250 mile journey in a 60 mile range car, 10 points, 5% chance of a point being down = 90%

250 mile journey in a 100 mile range car, 10 points, 5% chance of a point being down = 98%

What if we double the reliability?

250 mile journey in a 60 mile range car, 5 points, 2% chance of a point being down = 92%

250 mile journey in a 100 mile range car, 5 points, 2% chance of a point being down = 98%

This formula by the way could equally be applied to PHEVs or ICE's but of course range, number of points (i.e. petrol stations) and reliability are all MUCH better so it would be pointless

I calculated the 550 mile Aviemore trip at 77% guessing at 10 chargers along the way, and for giggles a Model S if stopping at Superchargers only on the same trip, a 95% chance of making it. (Though I suspect Supercharger up-times are much higher, but not guaranteed as the unfortunate incident at the Hyatt proves)

I have this in an Excel spreadsheet, if anyone wants to scrutinise.. but not sure how to upload it here though as xlsx files aren't allowed..

There maybe errors in my transposition to a formula rather than Excel, and anyone with some better software for formatting it is welcome to post an image (For example I have used [ to represent floor rather than the more modern symbol for example)

Enjoy