So a 1000x to 1600x a CR2032.  That a significant difference.  If 1600x lasted one day, then 1000x would be a bit naff.  On the other hand if a 1000x lasted a week, then 1600x is not a significant consideration.

In general, if the difference between one battery and another was the difference between running less-than-a-day and running more-than-a-day then I'd go for more-than-a-day at almost all costs.  If the difference was on a week boundary then I'd go for small.  But since I don't have much clue what our burn rate will be, it's a bit academic.  
At this stage I think I'd maximize your convenience because getting stuff to work ASAP is the priority.  Next we should have a bunch of anchors and a wearable each.  
The first goal is to get daily activity data out of Dewbly onto the screen and into an Excel spreadsheet so we can look at it. It doesn't matter if the devices are big, or small initially.  If we can't recognize patterns in the data, then it will be bloody hard to get software to see them, and we will be done!  
The second goal is to make it easy to gather and upload data every day.  I think the hardware department should take responsibility for making it convenient and reliable for us to gather data day after day, and conveniently recharge with minimal hiccup.   For that reason I think we should try very hard to build two sets of hardware so we can both see the fruits of our labors, and maximize usability – perhaps I mean minimize PITA issues.  
Even if the data presentation software is very primitive, I think it would be very good for you to be able to see what we get.  You'll have different insights and good ideas for how to make things better, or do more interesting things.  I also think it would be good to be able to show early results to potential collaborators if we have any promising results.  Maybe there are retired data analysts, or firmware people who might get excited by good results.
I reckon it will be quite some months before we have anything working well enough to have any insights about battery life.  But firmware work can try and get the burn rate down while hardware can look for ways to get more power into the budget, and recharging schemes.

//Mik
On Tue, Aug 12, 2014 at 7:58 AM, David Carkeek <dcarkeek@gmail.com> wrote:

I have received four of the battery samples I ordered from Ali Express. It looks like a 180mAh battery (3mm x 20mm x 30mm) fits between the PC board posts and leaves enough height for everything else. 3.6V * 0.18Ah = 666 mWh. Recall that a CR2032 button cell is 225 mAH * 3V = 0.675 mWh.

Another larger battery might be made to fit. 4.7mm x 22mm x 29mm, 300mAh * 3.7V = 1110 mWh. One of the posts would have to be cut.
One more sample needs to arrive. It might be the best one if thickness isn't an issue because it will fit between the posts. 240 mAh * 3.7V = 888mWh.

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