Just tested my circuit. I'm impressed and somewhat dissapointed at the same time. What's impressive is that the circuit passes significant current down to 1.75V input. Of course, that means that it won't automagically reduce current when the input drops below 3V (protecting rechargable cells), but it does mean that you could run a very low Vf R-O down till the batteries reach the Vf, or you could run a R-O at a lower current (resulting in a lower Vf) with the same results.
With no regulator (direct drive), these are the reasonable power options:
2 alkalines: Current drops immediately, starting at about 1A, dropping steadily over the life of the batteries (maybe 1-1.5 hrs for AA, 3-4Hrs for C, 10Hrs for D cells). If 200mA is the cutoff current for replacing batteries, then that happens at about 1.05V/cell. Start out at ~130 lumens, decreasing steadily (this is compared to the 190 lumen "spec").
2 NiMH cells: Current starts out at 800-900mA, hanging out at 700mA for the majority of battery life. Current is nearly 0 at 2V, so batteries are safe from deep discharge/reversal. 2000mA AA cells should get 2.5 hrs or so of life, 4000mAh C cells, over 5 hours, and 11Ah D cells, 14+ hours. So 80-90 lumens for the majority of battery life.
2 Lithium AAs:
Will perform almost identically to the NiMH cells (!). Current might be a bit higher. Will also last for something like 2.5 hrs (but probably will be brighter).
1 Lithium 123A:
Pretty much identical to the Lithium AAs. Current will be around 800mA for the majority of battery life. Should get about 1.5hrs of battery life.
With this linear regulator, you have the following power options:
3 alkalines: regulator keeps output at 1.4A until batteries drop to ~3V. Alkalines will be "dead" at 0.8V/cell, so at 2.4V. Current will still be around 650mA at that point. Initially, the huge current draw from the cells will cause the terminal voltage to drop to about 4.1V, efficiency will be around 70% (not too bad - though about 1.6W is going up in the regulator), increasing as the battery voltage drops (which will happen rapidly). AA alkalines will be killed off in about 1/2 hour (maybe a little more). D alkalines will last probably 4 hours.
3 nimh: regulator keeps output at 1.4A until batteries drop to ~3V (which is essentially dead for NiMH cells). You'll have to be careful to not deep discharge the cells. Some NiMH cell makers say 0.8V is the cutoff, but you'll still be drawing 600mA at that point...
Initial cell voltage will probably be 3.8V under that load (76% efficiency, 1.2W in the regulator), but, will drop to 3.6-3.5V for the majority of battery life - meaning efficiency is around 80% (0.8W in the regulator). 2000mAh AA cells should last ~1.2hrs; 5Ah C cells, ~3 hours; and 11Ah D cells, ~7.5 hrs.
3 lithium AAs: Will have the flat output of the NiMH cells, but will be a bit more wasteful with the regualtor (even worse than the alkaline cells initially). Should run for 2 hours.
Li-Ion rechargables (123A, etc) - should be similar to the NiMH cells - protection circuit will prevent overdischarging.
With 3 alkaline cells, a buck converter (if one can handle 1.4A with reasonable efficiency) would be best. You might get 45 minutes or a little more from AA cells in that case. 3 Lithium cells with a buck converter would easily get you 3 hours.
The boost converter presents an interesting challenge. To drive a R-O at 1.4A (~4W total) from 2 NiMH cells with a boost converter, at 85% efficiency, you'd need a converter that could handle 2A switch currents. Can any of the boost converters we know about do that?