The capacitor bank designer

Capacitors arrange the opposite way round to cells: series multiplies voltage and divides capacitance. This works out the bank and the three protections it needs.

A bank stores far less than it looks like it should

Energy is half C times V squared, which sounds generous until you convert it. A 100 farad bank at 16 volts holds under four watt-hours — less than a single 18650. Capacitors are for delivering energy quickly, never for holding much of it.

The three things that go wrong

Series stages drift apart on leakage and need balancing resistors. A charged bank stays dangerous with the power off and needs a bleeder. And charging an empty bank is electrically close to a short circuit, so it needs a pre-charge resistor or the inrush destroys the supply, the switch, or both.

Questions

Are these designs safe to build?

They are a design aid, not an engineering sign-off. Every result states the assumptions it used so you can check them, marks which figures rest on a typical value rather than a measurement, and always includes the protection the pack needs. Anything that will be charged unattended should be reviewed by somebody qualified.

Why does the pack voltage drop when I put a load on it?

Every cell has internal resistance, and current through resistance drops voltage. Series multiplies that resistance and parallel divides it, so sag is a property of the arrangement as much as the cells. Resistance also roughly doubles near freezing, which is why a cold pack sags far more than the same pack indoors.