Dot Physics

Another electric motorcycle post. (Here is the post on the wind-recharged drag racing motorcycle) This new one is a solar powered motorcycle. The site claims that the bike can go 50 miles on a full charge (from Gas2.org). This is easily possible, but how long would it take to charge with normal solar panels? Here is an image of the bike.

i-33ddebd4f61605c2e15dd65e2f692abe-solarbike-1-1.jpg

Questions to be answered: How much energy would the bike need to go 50 miles? How much power (average) could you expect to get from the solar panels? And…how long would it take to charge this sucker. I am sure you can store enough energy in a battery to go 50 miles and even a tiny solar cell could charge this – but would it be practical?

How much energy to go 50 miles

I can cheat on this question, because I am a cheater. If I were not a cheater, I would estimate the air resistance of the bike and how many times it would need to speed up so that the total energy would look something like this:

i-b6ed1b2354f61ba2f4f725db603efaa6-e-for-50-miles.jpg

If the bike were going at a constant speed, I could calculate the air resistance force (estimating some stuff). Delta x would be 50 miles. I would probably estimate 5 times the energy needed to bring it up to 70 mph for the KE and I am not sure what I would do about the other frictional forces (and energy lost).

So, how do I cheat? If I assume a normal (average) motorcycle gets about 50 miles per gallon, then the energy needed for a bike like that would related to the energy stored in 1 gallon of gas. Wikipedia has a good list of the energy densities of various materials. It lists gasoline as 34.2 MJ/L. (this would be 129 MJ/gallon). Of course, not all of this energy goes to useful things. Let me assume that the engine is about 25% efficient. This gives the energy for 50 miles as:

i-9570a845ae106b5afb76e8ad7f017777-e-50-calc.jpg

Now you see how I cheated. I assume the electric bike is similar in shape and tires to a normal gas-powered bike such that it uses the same energy. Also, I completely guessed on the efficiency of a normal motorcycle.

How much average power from the solar cells

Just want to say something about solar cells. I have seen them called “solar batteries”. I see how this term came about – the origin comes “to strike”. This went on to apply to artillery and then to electrical batteries (but not sure how). So, in that sense, it could be just as much a battery as a chemical battery. However, the current usage of battery implies “storing stuff”. A solar cell clearly doesn’t “store” stuff (energy). Ok, enough of the rant.

There are two important issues with the solar charging. How much energy per second gets to the solar cell? And how much of that energy is converted into useful electric energy? The efficiency of solar cells is one thing that has improved in recent years, but still the best you could expect would be around 30%. Here is a chart from wikipedia showing the efficiency of different solar cell types.

How much energy will hit these cells? The average solar energy hitting the Earth is around 1000 Watts per square meter. The problem with this bike is that some of the solar cells are on the side. The angle that the light hits the cells greatly effects how much energy the cell gets. Take a look at this diagram:

i-fcb5636adf4a2175bd3b3ee8bfbcfc63-a-effective.jpg

Here, a smaller area perpendicular to the light from the sun would get just as much energy as the panel on the side of the bike. If the angle the between a normal (perpendicular) line to the surface and the light is ?, then the effective area would be:

i-6e5995408a8c6a4e52404b85abb7cb18-a-effective-formula.jpg

Now I have two things to estimate: the area of the solar panels on the bike and the average angle that the light hits. From the picture above I am going to estimate that the top is 0.3 m x 0.3 meters and the side is 0.5 m x 1.0 m. There looks like there might be a part on the back also, maybe this is another 0.3 m x 0.3 m. Note that I did not count the area on the other side (although surely there are panels there). This is because sun can not hit both sides of the bike at the same time. This gives a total (hitable) area of:

i-17ce2ea84a535b1e565131978f7a095b-area-total.jpg

The angle the sunlight hits depends on the time of day, the location, the season, the orientation of the bike. I am just going to off-the-wall estimate this at 40 degrees. Maybe you don’t agree with that, that is ok. I am going to put the calculation in a zoho spreadsheet so you can change whatever values you want.

So, the power from the solar panels would be:

i-56a5b40bc12244dab48d01f75e53e4f9-power-from-panels.jpg

And finally, how long would the bike take to recharge? Power is energy use over time. I know the power and I know how much energy I need to recharge. This would give a recharge time of 57 hours. Here is the spreadsheet with the numbers so you can change them.

Ok, clearly the bike is real. I re-watched the video and I think I completely underestimated the size of the solar panels. If I put the effective area at 2 m2, this gives a charging time of 19.5 hours. Seems more reasonable. Maybe he even has more efficient solar panels. Either way, it’s like a free ride.

Comments

  1. #1 Uncle Al
    May 19, 2009

    That would be 19.5 hrs of charging at summer high noon, at the Equator, absent clouds.

    The very first law to be legislated is that all roads must be downhill to all destinations. The second law to be legislated is that all roads must be cycloids. That way everybody gets to their destination with the same elapsed time no matter where they start. No discriminaton! Zero carbon footprint, too.

  2. #2 Thomas
    May 19, 2009

    Originally a battery had multiple guns in it, as distinguished from a single gun emplacement.

    An electric battery has multiple cells, so the electric storage in cars or in your smoke detectors are ‘batteries’ but the 1.5V ones in your MP3 player are just ‘cells’. Of course, this usage is largely obsolete and ‘battery’ is used for all of them.

    Presumably the people who talk about ‘solar batteries’ are emphasizing that you have a bunch of these things in series to get a higher voltage than you could get from a single solar ‘cell’.

  3. #3 Rick
    June 8, 2009

    The Earth receives about 1350 W/m^2s above the atmosphere. However, you get from 500 W/m^2s or lower on the Earth’s surface. For example, in England they usually use 160 W/m^2s as the Sun’s flux for photo-cells.

    However, I think your guess of the efficiency of a gasoline powered engine is too high. I would expect it would be closer to 5% efficiency.

    So you were 5 times too harsh on your electric bike when looking at the gas efficiency (to calculate total Joules) but you were 6 times too generous when getting the amount of energy under the Earth’s atmosphere at mid latitudes. Based on my guestimates, I think you are a tad generous on only a 19.5 hour recharge time.

  4. #4 Sandra Sands
    September 26, 2009

    I love motorbikes, but can’t afford to ride a big one.

  5. #5 Rico
    June 17, 2011

    well your estimation of the efficiency of the motor of a motorcycle is actually still too low … an otto motor can have about 33% efficiency and i’d say 8% losses to transmission and other stuff i’d consider a bit too high …

    whereas the efficiency your takin for the panels is way too high, 30% you only get for multi-junction cells and due to the incredibly high price of multi-junction cells i highly doubt that they used such cells plus they seem pretty flexible so it must be thin film technology which limits the efficiency more to something like 12%

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