*Note – on the basis that each equation loses 50% of readers, I’ll assume only the hard-core readership remain.*

**EVs and other new energy technologies such as PV solar are disruptive. **

**But incumbent auto and oil companies, and industry analysts assume they will follow non-disruptive, simple growth curves. **

**They won’t. **

**It’s time to model disruption, and confront reality.
**

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**The Mathematics of Disruption**

Electric Vehicles (EVs*), like their gasoline predecessors, are a disruptive technology.

By 2020 or thereabouts, they are forecast to become cheaper than conventional internal combustion engines (ICE), and offer running and maintenance costs 90% lower. At this point, there could be a mass exodus from gasoline cars to electrified ones.

All disruptive technologies, in nature and economics, follow a prescribed pattern of growth. It’s commonly called the S curve due to the shape of expansion: slow incubation, sudden lift-off and break-neck growth, and a final mature plateau phase.

The examples are numerous:

S curves are based on two governing principles: rates of growth change quickly over time as demand or resources develop, but there is an upper limit to expansion as the resources get eaten up. So, disruptive populations or products start out small, explode in size, then level off as resources or demand are depleted.

The fearsome equation above – a Logistic Function – contains all these moving parts and so generates an S curve, with take-off point, dynamic rate change and upper limit; a disruptive piece of mathematics in its own right.

You would therefore expect forecasters of EV demand (or PV solar) to use S curve mathematics to try and pinpoint the time of lift-off, and the duration of the explosive, volatile phase of growth.

Not so.