As of today, October 15th, 2015, commercially available ultracaps have obtained an energy density of 10.1 wh/kg. A standard lead-acid battery, such as the one you almost certainly use to start your car, offers an energy density of 40 wh/kg.
This means that within about four times the weight (and probably the volume) of said battery, you could use ultracaps (and the appropriate control electronics), you could completely — and permanently, as the ultracaps have multi-million charge/discharge cycle capability — replace your vehicle’s starter / power battery. This capability is considerably further along the development and commercial availability road for ultracaps; the last time I really paid close attention, ultracap energy density was down in the 2.5 wh/kg range, and so it would have taken sixteen times the weight (and volume!) of them to do the same job. That’s a lot tougher to justify.
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