Unless you came up with some circuit magic.. you are still just using a linear solution... but what i think you did.. was fine-tune the set-points so that the 15-turn pot eliminates the wasted portion of the dial so it 'gets right to business'.. i would like to see the circuit though to see what you came up with!
®S sells a 10k audio taper pot with a switch.
You are 100% correct that most non-linar pots are actually two linear segments bent in the middle.. the do an ok job and that's the exact type i have.. usually called 'audio taper'.. far easier to fabricate than an actual log taper.. especially if using a stereo model!
The key to it working at least mostly smoothly is that the 'low end' of the scale will get you some precision.. i.e. you need to have control where the resistance is the highest.. the other end.. you need to change the resistance quickly to see any difference .. so on a linear scale what you will see depending on how you wire it.. is this..
A) very little change on the bright side.. and when it starts to dim.. it goes to off almost immediately.. it's very easy to dial in a precise level for the high.. impossible for the low.
B) very slow changes on the dim side.. and when it starts to get bright.. gets to high very quickly.. very hard to adjust say between 800 and 900 mA.. very easy for 100-200.. obviously this is the way to have it set up.
if you have a linear pot.. that is 'trimmed' properly.. you will be able to smoothly dial anywhere in between.. no 'tricky side'... however.. what you will see.. is that you have to dial most of the dialing to get from high to medium.. and much less dialing from medium to off.. because of the way apparent brightness is a log relation to mA.. you want to have a pot so that dialing from 0 to 10 on a dial.. if you are at 5.. the output will be still only like 15% not 50%.. it makes the linear dial change to an exponential change in output so that the 'brightness' follows a linear path.
On a related topic.. here's my latest creation.. a low-volt cutout for the buckpuck.. 'take two'..
Of interest in this picture:
on the bottom right of the pot.. two white 30ga wires.. they go to a 6.65K resistor in parallel with the 10k pot.. the value was determined by first using a 100k pot, and dialing the pot to max.. and dialing down the 100k pot 'til i can start to see dimming and backing off slightly.. this trims the 'high end' of the pot to match the particular circuit.
follow the blue wire from the wiper on the pot.. it goes to a tiny white resistor that is soldered to the control pin on the buck puck.. this resistor is a 470ohm resistor.. also determined initially by using a trimpot (ala your 15 turn model).. 2k.. and adjusted for in my case.. 130-150mA.. (i need an extra 30-50mA for my fan).. this would normally be a little lower resistance.. the buck puck can stay stable as low as 50mA maybe less.. i think i use 40-50mA for low on megasonic.. but the influence of the fan.. it wont run stable lower than about 150 (could also be from my accident that killed the 5V reference pin on the buck puck).
On the far left.. soldered by the Vin pin to the switch 'out'.. you can clearly see the hole in the heat-sink of the replacement 5V regulator.. that i use to run the low-volt cutout.. which is that tiny tiny circuitboard on top of the buckpuck.
The other blue wire that goes to the control pin.. (behind the flagg-soldered resistor).. is the output from the LVC circuit.. it goes 'high' and applies 5V to the control pin when Vbat goes low.. if it's attached on the other side of the resistor.. rather than go 'off' it goes to 'low' when bat is dead.. nicer for bike-riding!
I would actually have a second resistor.. maybe 200-300ohm so i could have a manual low of 100mA but when vBat goes low.. it will go to 40-50mA.. this will be just enough light to come to a stop should the bat die while riding.
The beauty of this type of setup.. is that when vLow is hit.. the light shuts off and the bat. will recover.. if you had the light on high-beam.. you can go to 'low' and get an hour more light if you have a big bat pack (mine on megasonic is 60WH).. i get 5 days or something on low beam!
did you mention what if anything you are using to protect your batteries from over discharge in your circuit?
-awr