I've come up with a way of putting all the ultracapacitors in parallel, and jumping the voltage stored in them up to 12 volts for the bike's electrical system. In this way, rather than only 100 Farad with 14 ultracaps (two parallel banks of 7 caps each in series), I'll have 10 caps in parallel, giving me 3500 Farad.
There'll be a solid state DC-DC 50 amp converter to convert the cap voltage to the bike's electrical system voltage, which will turn off automatically if system voltage is high enough (ie: when the engine is running and the generator is making power, or when the bike is off and the downstream small ultracap bank is charged to 12 volts) to prevent draining the caps when the bike is off. There'll be a small ultracapacitor bank downstream of the DC-DC converter that will act as a small battery to allow a charge to be stored to keep the DC-DC converter off when the bike is off.
Assuming all the loads of the bike (headlight, brake light, ECU, spark coil, fuel pump, O2 sensor heater, running lights and starter, etc.) take about 40 amps maximum when they're all energized, we get the following.
A 1 Farad capacitor at 1 volt stores one Coulomb of charge. A 350 Farad cap at 2.5 volts would store 875 Coulomb. So for 3500 Farad, we'd have 8750 Coulomb.
One amp represents an electron flow of one Coulomb per second.
So 8750 Coulomb / 40 Coulombs per second = 218 seconds or so... not taking into account inefficiencies, losses, etc.
Even at end of life for the ultracaps (which assumes a 20% loss of storage capacity), we'd still get 174 seconds.
That's definitely enough power to get the bike started, even in the worst of circumstances. And I'll have the hand-crank generator if I'm out in the middle of nowhere with a dead battery. It's small and light, so it adds almost nothing to the weight of the bike.
For charging the caps, my electronics guy and I are looking at doing something completely different. We're going to attempt to capture some of the energy that's being thrown away anyway from the OEM ground-shunt voltage regulator before it's shunted to ground.
We'll be using a reduced back-EMF transformer with vortex windings to recapture some of that pulsed electricity (pulsed as the voltage regulator's MOSFETs turn on and off) by putting it through the primary winding before it goes to ground.
A reduced back-EMF transformer is a new invention, it is essentially a magnetic diode, allowing two magnetic flux paths... one for the primary coil, one for the secondary coils.
In a normal transformer, putting voltage through the primary coil causes a magnetic flux that travels through the core to the secondary coil. The secondary coil, when loaded, creates a magnetic flux that opposes the primary coil's magnetic flux, reducing the primary coil's inductance, and allowing more current to flow through the primary coil. This increased current flow creates a stronger primary coil magnetic flux with overpowers the secondary coil magnetic flux, allowing more power to be extracted from the secondary coil.
In a reduced back-EMF transformer, the two fluxes are more separated. Since magnetic flux flows like electricity (in that it always seeks the path of least resistance), the secondary coil magnetic flux flows in a secondary pathway thus avoiding the primary coil's opposing magnetic flux. In this way, the primary coil doesn't get much back-EMF, so its inductance doesn't change much. This allows us to design the coil's inductance such that it'll work without affecting the performance of the voltage regulator.
The vortex coils are coils that are wound such that they concentrate the magnetic flux very strongly in the center of the coil (in fact, vortex coils can be wound such that you can create high voltage plasma in a plasma tube using an air core vortex coil that's being driven with a mere 40 volts). This will ensure the highest magnetic flux coupling between the coils and the core, and means the coils can be small and light.
The core itself will be made of Ferrotron or similar. It's a high permeability, low hysteresis, non-saturating, non-conducting core material. This will minimize losses to eddy currents, hysteresis losses and saturation inefficiencies.
Not sure if it'll all work, but that's what research is for.