Solar FREAKIN' Roadways: snow melting feasibility

Snow removal test (from Solar Roadways
Press Images library).

This video ("Solar FREAKIN' Roadways!") has been circulating on Facebook in the last few days. I find the style rather annoying (the kind that piques my BS-o-meter) and the claim of being able to melt snow off the road hit a major BS alarm bell for me. But rather than poo-poo the idea, I did some back-of-the-envelope calculations on the feasibility of this claim (remember that melting ice takes a lot of energy: the equivalent to heating the same quantity of water by 83.5 degrees C).

I'm going to make the following assumptions in this calculation.

• Ambient temperature is close to freezing (ie 0C). Ie not that cold, but not warm enough to melt ice.
• These road tile PV panels are 10% efficient (taking into account losses due to covering material, dirt, and that not all the tile area is covered in PV material, loss due to battery storage, non-optimal angle ie horizontal). This I think this is a very generous assumption.
• 1m of snow fall melts to 0.1 meters of water [1]
• Heater is a simple resistive heating element (100% efficient)

So let's assume that 'h' meters of snow needs to be melted over area 'A' (obviously we're dealing with fractions of meters here!)

 (mass  = volume x density of water)

M (kg) = A . h . 1000

The latent heat of fusion of water (334kJ/kg) is the energy required to melt ice from 0C ice to 0C water. So energy requirement is:

E (Joules) = 334x10^6 . A . h

Let's express this energy in terms of sunlight time required. The solar constant (the amount of energy arriving per  unit area that would be incident on a plane perpendicular to the rays) is 1kW/m^2. So with 10% efficiency that's 100W / m^2

So sunlight time needed is t = E / 100W

t (seconds) = 334x10^4 . A . h

So for 1cm of snow, translating to 1x10^-3 m of water and expressing on a per m^2 (ie A=1)
t  = 3340 seconds. A little under one hour.

So subject to the very generous assumptions above, one hour of stored sunshine can melt 1cm of snow.

Now bear in mind that snowfall occurs during overcast periods, so we're going to have to rely on storage of this sunlight energy (presumably in electrochemical batteries, although there may be other ways, eg phase change materials). Looking at the current (2014) costs of Lithium ion rechargeable batteries, I'm seeing figures around $500 (USD) per kWh of storage [2][3][4]. So $500 in battery costs gives you about 1m of snow melting capability on a 1 meter square panel.

So the idea isn't complete bunkham. It's within the realm of physical possibility. This will only work in certain places where snowfall is relatively light and intermixed with regular spells of sunshine. Obviously in areas where the sun does not shine (canyons, forests, extreme latitudes) it just won't work. It takes just one heavy snowfall to exhaust the batteries and after that they'll be starved of sunlight until the snow melts naturally. Also remember that snow falls in winter when the sun is low in the sky and only for a few hours a day.

Addendum:

I notice the heating aspects of these tiles is briefly discussed (but without any hard numbers) on their website FAQ here [5] and general information about Solar Roadways is here [6].

Dave Jones of the EEVBlog has a rather damning analysis of the power budget for the LED lighting (let alone the heating aspect) here [7]

References:

[1] Snow-water equivalent
http://en.wikipedia.org/wiki/Snow_water_equivalent#Snow_Water_Equivalent_.28SWE.29
[2] http://www.forbes.com/sites/sarwantsingh/2014/02/27/elon-musks-500000-unit-battery-plant-myth-or-reality/
[3] http://www.mckinsey.com/insights/energy_resources_materials/battery_technology_charges_ahead
[4] http://en.wikipedia.org/wiki/Electric_vehicle_battery#Battery_cost_and_parity
[5] http://www.solarroadways.com/faq.shtml#faqHeat
[6] http://www.solarroadways.com/intro.shtml
[7] https://www.youtube.com/watch?v=obS6TUVSZds

Edits:

26 May 2014: My initial figure of $160 (USD) per kWh of battery storage (2014 prices) seems to be very much on the low side. Seeing more consensus at $500 per kWh. See references [2][3].
26 May 2014: Added links to the company website and a link to a FAQ where the heating of the tiles is discussed. Also image of snow remove test added (taken from Press Images page.
24 June 2014: Added link to Dave Jone's analysis of the project

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