Finally got around to picking up a couple of these and did some testing. I don't have a 1D battery holder handy so I just rigged up something by taping test leads onto the supplied heavy-duty cell. Here are results for various resistor values.
R
| Vb
| Vr
| Vf
| I
| eff
| hours
| days
|
10
| 1.61
| 0.69
| 0.92
| 66
| 57%
| 121
| 5
|
22
| 1.62
| 0.78
| 0.84
| 35
| 52%
| 229
| 10
|
33
| 1.62
| 0.81
| 0.81
| 24
| 50%
| 330
| 14
|
47
| 1.62
| 0.83
| 0.79
| 18
| 49%
| 452
| 19
|
100
| 1.63
| 0.96
| 0.66
| 10
| 41%
| 824
| 34
|
R is the nominal value of the resistor
Vb is measured voltage across the +/- ends of the battery
Vr is voltage across the resistor
Vf is voltage across the LED
I is current (milliamps) calculated as I = Vb / R
eff is "efficiency" defined as power consumed by the LED divided by total power supplied by the battery
hours is a crude estimate of battery life in hours obtained by dividing the rated battery capacity by I, and days is the equivalent number of days.
Subjectively the brightness with the 10 ohm resistor is a little lower than with no resistor. The 22, 33 and 47 ohm resistors are a little dimmer still but there isn't a huge difference between them. With the 100 ohm resistor the light is quite dim. It's similar to or maybe a little dimmer than the moonlight mode on my Nitecore Tip which is supposed to be 1 lumen.
The efficiency and lifetime values shouldn't be taken literally because things will change as the battery runs down. As the voltage decreases there will be less current drawn (this relation between voltage and current is a basic characteristic of LEDs) so the actual lifetime will probably be longer. This is consistent with what lampeDépêche said about getting 45 days of life when using a 33 (or was it 39?) ohm resistor. Maybe these values are somewhat useful in a relative sense.
My ramshackle "workbench" isn't much to admire and there are lots of smart people who probably knew about this sort of thing already. But it was a fun little experiment and it inspired me to look into some of the principles about how LEDs work.