Yes, but Meraki's Solar mesh repeater ($799) is 100% solar powered. It
combines the latest lithium iron phosphate batteries with a powerful
200 mW outdoor Wi-Fi radio. It requires a solar panel (20 or 40 watts)
— which is sold separately. I bought a 20 watt panel for $135. Add
another 20 watt panel ($270 total) with an Optima deep cycle 12V, 55
ah battery ($200) and a charge controller ($200) and it seems
feasible.

Winter overcast may not reach the necessary 13.5 volt charging
requirements. That's where wiring two 12v panels in series might work.
That creates 24 volts which, combined with a maximum power point
tracker (MPPT), adjustes charging rates depending on the battery's
level, to allow charging closer to its maximum capacity. In effect a
DC to DC converter. So even if the 24V panel only generates 15 v on a
cloudy day, it would be enough to deliver the standard 13.5 volt
charging requirement.

So for a 10 watt Meraki repeater, that would be:
1. Meraki Outdoor Repeater (or equivalent) - $200
2. Two, 20 watt solar panels @$150 each  - $300
3. Morningstar MPPT Charge controler with meter - $200
4. Optima 12V, 55 ah battery - $200
---------------------------------------------------------
Total - $900

http://meraki.com/products_services/hardware/solar/
http://www.dailywireless.org/2008/11/19/meraki-wall-warts-and-solar-power/
http://www.amazon.com/Black-Frame-Mono-crystalline-Battery-Charger/dp/B000VM9H8I/ref=pd_rhf_p_t_4
http://en.wikipedia.org/wiki/Charge_controller
http://www.morningstarcorp.com/en/pro-star
http://www.solarhome.org/morningstarprostarchargecontroller15a1224vdc.aspx
http://www.infinigi.com/unisolar-us64-64-watt-solar-module-12v-p-41.html?ref=100

I'm still not sure if that MPPT charge controller would be the
solution for grey winter days. I've heard conflicting opinions from
Solar professionals.

I also read that thin film has an advantage on cloudy days.

Perhaps a two radio system (WiMAX/WiFi) could be built using two 64
watt Unisolar panels ($350 each) and two 12V deep cycle batteries
($200 each). That would add about $1000, or a total around $2000.

WiMAX microcell access points utilize four, deep cycle batteries for backup.

- Sam

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