During the week I had 8 hours of cross country skiing with GPS tracking and 6 hours of indoor cycling with a Bluetooth speed sensor, and HR of course for all activities. Then V800 said that recharge the battery. And after charging for a couple of hours, the battery is full again (100%). It is not what Polar has promised (13h of GPS tracking) but this is OK for me. At least much better that with the old battery.
