First, the best case scenario. A bike rack over the rear wheel can hold a solar panel approximately 12" wide by 18" long. The sunniest place in North America is Inyokem California in the high desert, where it is sunny 355 days a year.
7.7kWh of sunlight energy per square meter on the average day, or about the equivalent of 7.7 hours with the sun directly overhead and no clouds. That means that the solar panel on our bike would receive 1070Wh of sunshine on a normal day in Inyokern. However, solar panels do not convert all of this to electricity. In fact, the most efficient solar panels in a lab are pushing 44% efficiency (awesome graph of this!), but the best commercially available solar panels are the SunPower X-Series which boast 21.5% efficiency. If we assume that our bike panel has the same efficiency, even though SunPower doesn't make any panels this small, that brings our energy down to 230Wh. A typical electric bike traveling at 20 miles/hr, a quick biking pace but somewhat leisurely for an ebike, uses about 17Wh per km, which gives us our average range of 13.8km, or 8.6 miles. This is actually fairly good, considering this is just on electric power, and you can always pedal to extend the range.
However, this is still assuming no losses in the electrical system, using solar panels better than anything on the market, and in the sunniest place in North America. Not all of the power our solar panel generates goes into making the bicycle move. The heat given off by the motor is taken into account in the bicycle efficiency number, but some goes into heat from the rest of the electrical system. Being generous, I would say that the charger has about 96% efficiency, the balancer 99%, the batteries 98%, and the controller 95%, bringing us down to 7.6 miles.
I managed to find a solar panel which is only barely over what I estimated could fit on a bike, and by far the most efficient I could find in this size, rated for 15W. This means that once we account for the wasted sunlight falling on the aluminum frame and the lines on the panel between the solar cells, this solar panel is at 10.6% efficiency, and our range is down to 3.7 miles.
|It's not looking good for the solar panel...|
Because this person has an electric bicycle, they might want to go a little bit faster, but the problem is that air drag increases with the cube of velocity, so going 30 miles per hour they will have slightly less than half the efficiency as 20 mi/h, so at 30 miles per hour they'd be able to go almost one mile per day in Boston before they need to start pedaling.
And I haven't even gotten to the cloudy days...
As promising as a solar panel looked at the beginning, it soon became apparent why we don't see solar panels on bicycles. They might be useful for people who are off the grid, except for the fact that there is not enough space on bicycles and solar is not reliable enough to count on for getting to work every day. If one has access to the grid, the solar panels on one's bicycle only serve to reduce the already miniscule cost of charging and extend the range of the bicycle, except for the fact that the wind resistance probably costs as much energy as the panel produces. If the aim is to make money by lowering the electrical bill, it makes much more sense to install panels at the house, where they can be the larger, more efficient type as well as perhaps being angled towards the sun, or if one is truly off the grid, an array of solar panels and a battery bank would provide electricity for both the household and transportation.
The one situation where solar panels on electric vehicles do make sense is on vehicles with large, flat roofs which can have panels embedded in them. Not in electric cars, because they use on the order of 20 times more energy than electric bicycles, but on the ultralight, aerodynamic, two person vehicles such as golf carts and the vehicle I saw a solar panel on last week.