We have not seen an EEStor ultracap car on the road yet, but AFS Trinity Power has a prototype plug-in hybrid on the road for the auto show that mixes batteries, ultracapacitors and a gas engine, creating a hybrid hybrid. Matthew Wald of the New York Times explains why with a tasteful analogy:
"The problem in a hybrid is not only how much energy the batteries hold, a quality called energy density, but how fast they can deliver it, called power density. The difference between energy density and power density is like the difference between a wine jug and a peanut butter jar — the containers may have the same capacity, but the size of their openings differ greatly."
The AFS Trinity Vue undergoing modification for the installation of its new drivetrain. Brad Husick
Wald notes that under acceleration the batteries have huge momentary discharge rates, so a lot of them are needed to spread the load. They are the wine bottles- you can only get so much out of them in a given time. With batteries, they can heat up and even catch fire.
That is where the ultracapacitors come in: "To cover the gap between the batteries’ ability to supply energy and the demand of the hybrid’s electric motor, the experimental Vue uses ultracapacitors, which are the electrical equivalent of the peanut butter jar....the ultracapacitors can be filled from the lithium-ion batteries and then emptied quickly into the motor that drives the wheels as the driver demands."
And in case you are feeling analogy deprived he adds another: "In use, the capacitors function much like the water tank on a toilet. That reservoir lets the toilet get by with a small supply pipe, yet still delivers a large volume at once for flushing."
Result: a car that can go forty miles on electricity only (farther than the great majority of trips Americans take in a day) before the gas engine kicks in. More in the ::New York Times
more at AFS Trinity
See John's explanation of Hybrid Proplusion Vehicles Using Ultracapacitors