I used a Bright Eyes bicycle light advertised @1,200 lumens and it's 4,400 mAh Li-Ion 2S-2P 8.4V battery pack. The Li-Ion cells were unmarked. I believe that the actual output is about 350 lumens. The light uses a buck converter rated for 5VDC to 20 VDC input and the driver is constant current.
These 18650 Li-Ion cells were allegedly rated 2,200 mAh. The Bright Eyes light kit package was sealed until opened about 2 weeks before this test. The battery pack was used about 6 times with approximately 4 hours total use.
If the battery pack was outside for more than 30 minutes @20°F, there was less than 12 minutes run time on high before the battery pack shutdown.
Test #1
The Bright Eyes battery pack was fully charged.
The battery pack temperature was 80°F
I placed the fully charged battery pack in a 4.9°F freezer with Bright Eyes light outside of the freezer.
I turned the Bright Eyes light on high.
The battery voltage steadily declined until low voltage shutdown occurred @5.80 VDC @0 hours, 22 minutes.
I allowed the battery pack to warm to 80°F.
I turned the Bright Eyes light on high.
The battery voltage steadily declined until low voltage shutdown occurred @6.14 VDC @0 hours, 56 minutes.
The no load voltage was 7.58 VDC.
The total run time cold and warm was 1 hour, 18 minutes.
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Test #2
I disassembled a dead aftermarket battery pack from a Mac Laptop computer. Four of the six cells were still good and had some charge left in them. The battery pack was at least 4 years old. The 2,600 mAh 18650 cells were marked: ASO FK1K031EG 814793 SZN with a sea foam green sleeve.
I removed the battery protection circuit from the Bright Eyes battery pack and wired it to these recovered batteries in a 2S2P configuration.
The battery pack was fully charged.
The battery pack temperature was 80°F
I placed the fully charged battery pack in a 4.9°F freezer with the Bright Eyes light outside of the freezer.
I turned the Bright Eyes light on high.
The battery voltage steadily declined until it reached 6.10 VDC @1 hour, 23 minutes.
The battery voltage then began to rise until it peaked at 6.43 VDC @1 hour, 56 Minutes.
The battery voltage steadily declined until low voltage shutdown occurred @6.01 VDC @2 hours, 58 minutes.
The no load voltage was 6.83 VDC.
I removed the battery pack from the freezer and I measured the battery case temperature @41°F.
Total run time 2 hour, 58 minutes.
I did not perform an additional test after the batteries were warmed back to 80 degrees.
I believe that the battery voltage rise was occurring because the internal resistance of the battery was rising significantly and causing heat to dissipate inside the battery, which allowed the battery to output voltage longer.
These tests were performed with generic Li-Ion batteries. There are some Li-Ion cells that are formulated to operate at low temperatures.
Nitecore makes low temp rated Li-Ion cells:
http://flashlight.nitecore.com/product/nl1829lthp
http://flashlight.nitecore.com/product/nl1829ltp
Whether or not these cells are actually formulated for low temperatures or not is a good question. They may just be a regular low internal resistance high current cell that works better at low temperatures that the standard high capacity cell because of the lower internal resistance
Scott Novak