Your transistor is wrong. You need an NPN with the Emitter tied to ground, the collector to the LED string and a series resistor to your 13.8 V source.
i thought i fixed it, and redesigned in the first post just as you described..
ok, after a bit of studying last night, i come up with this to calculate transistor base
2n2222 hfe = 100 - 300. (im gonna use 200 in respect to the currents listed on datasheet)
(5v-.7v) / (.3/200) = 2866.66666 (2.8k)
so, ive taken arduino voltage, subtract transistor voltage drop, and divide current by hfe value. is that correct?
As for the leds, they are 3watt rgbs, but each die is rated at 350ma, hence why i said 1 watt leds.
i will be running 2 series strings of these rgb's, so that will require 6 pins from arduino, , and 6 transistors.
i realize the best method of driving them is CC, but ill need 6 drivers here..
i also understand the voltage curve vs current flow. All thats on the datasheet. I also agree that not every led has same performance, even from the same bin type.
i just used ohms law of r= i/v
blue = (13.8-13.2)/.3 = 2 ohm
green (same as blue)
red = (13.8-8.4)/ .3 =18 ohm
edit:
I2 x R = watts
blue = (.3x.3) x 2 = 18mw (1/4w resistor)
red= (.3x.3) x 18 = 1.62w (2watt resistor)
so, in a led perfect world, am i close??