Where's the straight forward equation for simple LED resistors?

It is a simple equation, just applied in a way you're not used to.

V=IR. Voltage = Current * Resistance.

So what's the voltage? It's not the battery voltage. In fact, it's not a constant number at all. The voltage you use here is whatever's left after the voltage drop across the LED. So what's the voltage drop? That's why it's not a constant: The voltage drop depends on the current that's flowing through the LED. If you read the datasheet for the particular LED you're using, you'll find a graph of current vs. voltage. In this datasheet (

http://www.cree.com/led-components/media/documents/XLampXPE.pdf), it's on pages 16 and 17 for the various colors.

So, you pick a current and voltage from that graph, subtract the LED's voltage drop from your battery voltage (7.2v for 2 Li-Ions, 6v for AAAs), and plug those values into V=IR, and there you go, you have the resistance you need.

And what's with buckpucks? Do I still need a resistor if the saber has a buckpuck?

Most power sources we deal with every day are what's known as

*constant voltage* power sources. Whether they're supplying a lot of power or a little, the voltage is the same: Whether the AAA batteries are driving your saber for 2 hours, or your TV remote for 6 months, they're still 1.5v each.

What a buckpuck does is it creates a

*constant current* power source. Regardless of how many volts it needs, it will always supply the same amount of amps. In the case of the ones that UltraSabers uses, 1000 milliamps. If you think about that graph of voltage vs. current, you can think about the buckpuck as constantly measuring the current, and adjusting the voltage so that the current is 1000 milliamps.

A resistor and a buckpuck accomplish the same job: Regulate the amount of current flowing into the LED. You don't need both.