You can think of the Farad as a Coulomb-Volt, similar to how you can think of a Watt as a Volt-Amp.
A one-farad capacitor will store one coulomb (6.241*1018) of electrons when charged to one volt.
An amp is the current that flows through a one-ohm resistor when one volt is applied, which also happens to be one coulomb per second.
So a one-farad capacitor charged to one volt will supply one amp for one second, supplying one watt of power (also for one second, AKA one joule!).
Does all that math scale? So a 30F cap at 1V will supply 30A for 1sec? What about 30F at 2V? 60A for 1sec?
How about a 30F cap at 1V for 2sec? 15A?
Am I thinking about this wrong?
It scales minus resistance losses in the array. And yes, you lose capacitance as you run them in series but supercaps have high enough energy density that you can just compensate by running more of them in parallel to create a series/parallel array.
I get too stoned every few years and go on a super capacitor deep dive, hoping that prices/efficiency have hit a āmaybe worth a shotā level. If I recall, when you quoted me above, the end result still ballparked it at like $2500 in supercaps to get around 80Wh of usable capacity (that could theoretically have an 800A discharge)
In addition to that, these would need dedicated charge/discharge controllers and over the lifespan, the current leak will start to vary between caps. This leads to uneven discharge rates which can lead to failures, so itās not simply a matter of building a supercap array and best hooking it up.
Just a side note for anyone doing the mathā¦
Unfortunately we have to take into account that we would only use a part of the small amount of energy stored in a cap.
Twenty 2.7V caps that were charged to 2.5V (50.0V total) would give us something to use in parallel with 12S li-ion pack.
Discharging the pack down to 36V (3V each for the li-ion cells) would bring the caps down to 1.8V each, leaving a lot of energy still in each cap. 
A lot of MOSFETs, a bunch of other parts, and a microprocessor (ābrainā) to run it all.
Would it have to communicate with the VESC at all? Or could it just be a current sensing circuit in parallel with the main power circuit?
No comms with the VESC is necessary but could potentially simplify some things if the signals were useful (I donāt know whatās available). This is a big and complex circuit though, needing to be exceptionally reliable, handle lots of current, and have redundancy and numerous safety features.
Also known as āNot compactā 
The only thing I could think of is if there was a way rather than to use a boat load of caps in series to match voltage - provided that the discharge is there, you could use a boost converter (complications on this concept not withstanding). This would give you much more ālifeā from the cap since youād be able to set an output voltage at the converter side and it would draw from the cap until dead.
The problem is, size, heat, and efficiency. Good Boost Converters are pretty efficient (90+%), high wattage/output converters are rather large (130x84x52mm) and generally that 10% loss is going to be heat, which means cooling is a factor that needs to be taken care of. But if the loss/efficiency are the only concerning points 10% loss over what was proposed here:
which I presume is not linear therefore its not just a simple division for state of charge. Would be much more desirable than 30, 40, 50% unutilized capacity plus a smaller cap-bank footprint.
But again, there are several other factors that come into play with this approach that likely make it less than viable.
I wonder if you could make the super capacitor bank voltage 2 times your battery voltage. And then the discharge circuitry could be a Fet controlled by high frequency PWM and some more capacitors on the output to smooth the ripple. The Fet control would be able to control the output voltage of the super capacitor bank via duty cycle. Then just a small boost converter to recharge the super caps when not being used.
This would only be to allow the super caps more depth of discharge then if they were wired in parallel with the battery. Make the MCU controlled by monitoring battery voltage sag. Iām probably overlooking something with this idea tho, Main issue i see is the high frequency output might mess with some of the electronics down wind
Its in theory a good idea if the battery is a bottleneck in terms of current draw, but a terrible one in terms of cost and space.
More fancy then practical in esk8 Iād say.
How large is āreally largeā? What about in a large eMTB enclosure? I have 25x 30F supercaps that are about 10mm x 30mm in size. Is there anything fun that can be done with those?
Charge em up and lick em 
Done. Weird, they taste like charred meat.
Twenty 30F caps in series (12S li-ion equivalent voltage) gives you a 1.5F string of caps. That gives you about 0.03 seconds of current at 20A going from 50V down to 36V.
If you had two thousand of those caps you could get about three seconds at 20A, assuming they had a low enough ESR (resistance). 
If those caps have a very low ESR, much lower than the internal resistance of the cells you are using, then they might work to absorb some voltage spikes if placed just before the ESC. You will need a balancer for them.
Once you calculate the equivalent capacitance for the number of them in series then this calculator is very handy: http://www.circuits.dk/calculator_capacitor_discharge.htm
@BenjaminF what is the voltage rating on your caps?
I run all my boards with cap banks just before the ESCsā¦ If they are rated for higher voltage than your battery pack, just put a bunch in parallel with themselves and the battery just before the ESCs, and that way there is no need for balancing or anything else fancy. Iāve noticed way less faults on fault prone ESCs connected to long battery leads when running cap banks, so thereās that. Each additional cap you add in parallel reduces overall ESR and increases ripple current capacity.
The ESR (equivalent series resistance, their āinternal resistanceā) of the caps is critical too. To absorb the voltage spikes on ESC input wires you need low resistance caps like the ones used on ESCās. Some ultracaps, particularly the higher voltage ones (often just a āpackā of lower voltage ones in series), have incredibly high ESR.
