The Energy Density of Batteries

In an earlier post, I discussed the concept of energy density and showed the values of energy density for a variety of fuels. The big take-away message of that post was that there is a whole lot of energy stored in a gallon of gasoline! Gasoline, diesel, etcetera are high-energy-density fuels and that is very convenient for automobile and airplane applications. You can pack the energy to travel a long way into a relatively small and light package.


How do batteries compare? Before we dive into the specifics of it, the short answer is: batteries have much, much lower energy densities than liquid fuels. That’s probably not a big surprise to a lot of folks, because, well, if they did have high energy density, our electric cars would be able to travel 300 miles between recharges, and we’re well aware that they can’t do that yet.


There are a number of subtleties to considering battery energy density. A major one is that the amount of energy a given battery can deliver varies depending on how quickly you are drawing on the battery. Generally speaking, the faster you draw on the battery, the less total energy you will get out of the battery. Batteries are normally specified using the 20-hour discharge rate, that is, a 100 amp-hour battery could be expected to deliver 5 amperes at the battery voltage for 20 hours. Another major consideration is a battery’s depth of discharge. The gas tank of a car, to use an analogy, can be filled to 100% full and driven down to 0% full, i.e. empty, with no damage to the car. A battery, on the other hand, has a maximum depth of discharge it can tolerate before suffering damage. This isn’t a concern for disposable batteries, of course, but for rechargeables it’s something to be aware of. This comes up a lot in designing electric storage for renewable energy sytems, which usually use lead-acid batteries. Systems will be designed for something like routine discharge to 50% full, with perhaps occasional discharge to 20% full.


Let’s look in more detail at some different types of batteries… and believe me, there are a lot of different types! I think I’ll just list the common battery technologies and what they’re used for, and then present a comparison table.


Alkaline batteries. These are the very common AA, AAA, D, and C cells that we use for flashlights, radio, and so on. Energy density is not bad, for a battery, but these batteries are not really rechargeable, they are one-use and get rid of them; referred to as “disposable” or “primary” batteries.


Carbon Zinc batteries. Also disposable (one-use) batteries, these are cheap but poor-performing batteries. Available in common sizes like AA, AAA, D, C, these are sometimes called dry cells. They’re advertised as “heavy duty” or “super duty” batteries. They were much more common a few decades ago, now people mostly use alkaline cells.


NiCad batteries. I think of Nickel Cadmium batteries as “my father’s rechargeable batteries.” More expensive than alkalines to purchase, but rechargeable many times. I've never had good success managing against the “memory effect” they have, and their output voltage is lower than alkalines, so I found them to be short-lived in devices. I won't buy them anymore, and instead I buy...


NiMH batteries. Nickel Metal Hydride batteries are newer-technology rechargeables. These are pretty good! Used in humble forms like AA and AAA batteries all the way up to electric and hybrid vehicles.


Lithium Ion batteries. Another rechargeable technology, these are often used for portable electronics applications—laptops, camcorders, and so on. Good energy density for a rechargeable battery.


Lead-Acid batteries. This is the type of battery you have in your car. A very well established technology, it is cheap on a per-watt-hour-delivered basis, and is rechargeable. This is generally the technology of choice for electricity storage for a solar array or other renewable energy source. The typical lead-acid battery requires some care and maintenance in its use: it contains sulfuric acid which can be spilled, it generates flammable hydrogen gas when being charged, and you need to be careful not to freeze it (and its freezing temperature changes as a function of its state of charge!). Variations of the basic technology exist to eliminate or reduce some of these drawbacks, by sealing in or immobilizing the electrolyte—these are sealed gel-cell or absorbed glass mat (AGM) batteries, and are more expensive than the garden-variety lead-acid battery. Also, lead-acid batteries are engineered to optimize certain characteristics at the expense of others—car batteries, for example, are engineered to be able to deliver a lot of current for a short time, but can only be drawn down a little bit (say 20%) before causing damage to the battery; in contrast, deep-cycle batteries for storage for a solar array are meant to be repeatedly discharged deeply (80% discharged) and recharged, but can’t provide as much current in a short time as an automotive battery.


Alright, we’ve discussed different battery types. Let’s take a look at a table comparing these battery types with each other and with gasoline as a representative of liquid fuels. The table shows the energy density on a mass and volume basis, as well as values normalized to that of gasoline, much like I did in the earlier posting on energy density. I’ve also added a column listing how much weight of batteries, or volume of batteries, you’d need to equal the energy content of 15 gallons of gasoline, about the capacity of a typical car’s gas tank. Note that the battery types listed in italics are disposable one-use battery types; the rest are rechargeable.

So, what do we learn from the table? Well, first off, all types of batteries are chumps compared to gasoline in terms of energy density. There's just no way around that. By looking at the last two columns, you can see that it would take a preposterous volume and weight of any type of battery to give you the same energy held in one 15-gallon tank of gasoline. And, in fact, batteries in electric and hybrid vehicles do spend a lot of their space and weight on battery packs, and they don't have great range (on electricity). Partly, that's something we just have to live with. But, the story isn't quite as simple as that, of course. One thing working in favor of batteries in vehicles is the system's efficiency. By that, I mean that energy drawn from the battery to power a car really does mostly go to moving the car, as these electric motors are quite efficient (80%+). In contrast, internal combustion engines only convert something like 20% or 25% of gasoline's chemical energy to motive force. (Thermodynamics...it's not just a good idea...it's the LAW!)

Looking at the individual battery types, it's pretty clear that Li-ion and NiMH are the winners in that they have the best energy densities for rechargeable batteries. Only alkaline technology gives comparable performance, and since it's a one-time use battery it's clearly unsuitable for something like an electric car.

I got a lot of the values in the table from this source: http://www.allaboutbatteries.com/Battery-Energy.html

I hope this has been interesting!

Generating electricity at the gym?

The other day a friend and I were mulling over this question: “Why doesn’t the cardio equipment at the gym capture the energy from all the people working out?” It’s something I’ve thought idly about before but figured it would be fun to do some calculations on the subject. (Yes, sometimes my idea of fun is outside the norm.)

Before I even got around to posting on the subject though, the subject surfaced again when I saw some folks generating electricity on some stationary bicycles at the Seattle Green Festival this past weekend. OK, I get it, it’s time to do the calculations!

First let me make sure I’m answering the right question. The answer to the question “COULD the cardio equipment at the gym capture the energy….?” is certainly yes. People have designed and built attachments that you can hook your bicycle up to to convert it to, in essence, a stationary exercise bike that generates electricity (like I saw this past weekend). Some of the cardio equipment I have seen in the gym doesn’t plug in to an outlet, the electrical power for the display and the controls is generated by the person exercising on the machine. (Interestingly, when I looked up this type of machine on the web, it was referred to as “self-powered;” this phrasing to me seems to marginalize the rather important role we, as the people actually exercising, are performing; but, I’m willing to let it go and move on with my life.)

So we know that electrical energy can be generated fairly simply in at least some types of common cardio equipment. Why are these “self-powered” machines built? It’s not to sell electricity back to the utility, clearly, as there is no electrical cord leading into or out of the machines. A self-powered cardio machine will save some small amount of electricity, in that you don’t have to provide any electric power to it, but I’m guessing that a self-powered bike or elliptical machine or whatever is attractive because you can get away with having an exercise room without a power outlet every four feet on the floor.

Another related question we can get out of the way right away is “Could we save the planet/stop global warming/charge our plug-in hybrids by capturing this energy?” I think the answer to that is almost certainly no. The energy we, as exercisers, spend at the gym comes from our food intake. We can’t hope to get perfect efficiency out of our food calories converted into electricity this way (or any way, really), that is, for every calorie of food we burn on the treadmill we’ll get substantially less than one calorie of electrical energy out. And it gets worse, because the food calories that we eat take energy to grow, and the higher on the food pyramid you go to get your food calories, the more energy went into growing that food. That’s a whole other subject. My point is that producing electricity in this way is not an electricity source with a free fuel supply like wind or solar. Generating electricity from exercise is partially capturing a waste stream, and that’s all to the good as that energy is normally just wasted as heat; just don’t expect it to save the planet.

To get back to our original question of “Why doesn’t the cardio equipment capture the energy?,” let’s walk through some sample calculations of how much energy you could produce on a machine.

Let’s get the units out of the way. A convenient unit of energy for our purpose will be the killowatt-hour (kWh), because it’s the unit that utility electricity is metered and sold in. Watts are used in reference to athletes’ output, too, so that will be helpful…an athlete outputting 500 watts for one hour will have generated 500 watt-hours or 0.5 kWh. The equipment I use at the gym lists my output in calories per hour…that’s energy/time, so multiplying by time will give me calories which I can convert to kWh. Whew, glad that’s over with.

When I’m chugging along on the elliptical trainer, I usually have a power output of about 900 calories/hour, which works out to about 1000 watts. So I think to myself, “hmm, not bad…that’s a lot of power!” But when I look online, I see that wattage output for athletes covers a wide range, with peak outputs on the order of 1000 watts. So, am I to believe that I’m outputting about 1000 watts during a low-intensity cardio workout when top athletes can peak at around the same value? It would be nice to believe that, but it’s clearly not the case. I think the difference is this: they are probably doing 1000 watts of work, while I am expending 1000 watts of effort, but actually doing much less than that in useful work. The athlete outputting 1000 watts is probably burning much much more than that in his/her power expenditure. One tip I had that my energy usage was consumption, and not output, came from the cardio machine itself. When I start the workout it prompts me to enter my weight, among other things. The higher the weight you put in, the more calories are apparently burned at a given workout intensity. If the machine were really measuring power, it wouldn’t care what your weight was; it would just measure the speed of the flywheel or friction disc or whatever is inside there, that would be a direct measure of the work done.

The guy riding the bike at the Seattle Green Festival said he was producing about 200 watts. I find that number pretty believable for the output I’m producing on a cardio machine as well, which would mean an efficiency of about 20% in converting my food energy into electrical work. That’s a believable number…most of the effort I’m expending is going to heating up my body and moving my muscles in ways that don’t perform useful work; and an electrical generator in a cardio machine would probably not be very efficient either, losing a fair bit of mechanical motion to generating waste heat.

Let’s say an average schmoe like me working out on cardio equipment can produce about 200 watts of electricity. Working out for an hour, then, would produce 0.2 kWh. The average retail price of electricity in the U.S. is about $0.09/kWh (found that here…http://www.ppinys.org/reports/jtf/electricprices.html). So an hour of average exercise might produce about $0.09/kWh x 0.2 kWh = about 2 cents.

How much would some cardio equipment produce in a gym over a year, then? Let’s say the gym is open from 6 AM to 10 PM and figure out the dollar value of the electricity in a best case situation: the equipment is in constant use: 16 hours/day x 365 days/year x 0.2 kWh/hour x $0.09/kWh = $105/year. Keep in mind that that’s undoubtedly high, the equipment is certainly not being used every minute the gym is open. A more realistic assumption would be less than 30% utilization, bringing it down to $30/year or less.

Well, but that still adds up, right? Yes, it would over time, but there are a few things working against implementing this kind of thing. Where are you going to put the power? The electric utility doesn’t want you just shoving electrons into the wall outlet…the utility doesn’t want your gym members electrifying the grid when there is a power outage, as this could harm repair workers. You’d need electronics that would isolate the grid from this secondary power source in the event of a utility outage. These things exist, they are used in solar installations all the time, but they cost money to buy and install. Also, you’d need an inverter to convert the generated electricity from DC to AC, and to synchronize it with the grid’s frequency. Again, these exist and are commonly used in the solar biz, but they cost money. Another option to somewhat avoid the above issues would be to use the electricity to charge batteries for local use, but that comes with its own infrastructure costs. HOWEVER, if you were off-grid in a cabin or something, a piece of generating equipment like this could be extremely useful! One way to look at it is to figure your cost of electricity at your cabin or wherever…if you’re not hooked up to the grid, your cost/kWh from a gas/propane/diesel generator is going to be far, far higher than $0.09/kWh. Having an exercise bike that you ride for an hour a day, producing 0.2 kWh, would let you run two 13 watt CFL lights for 7 hours each day. Use LED lights instead and you’ll do even better. That’ll improve your quality of life in that cabin.

Back to the case of the gym, though. What if all the cardio equipment in the room generated electricity, and was plugged up to a common inverter and disconnect? That would surely save a lot on infrastructure costs. For the sake of discussion, let’s assume you can make a generating piece of cardio equipment for the same cost as a regular one (no idea if that’s true or not), and that minimal additional wiring in the room is needed…you just take all the AC circuits offline that were originally used to power the equipment, and rewire them in a junction box somewhere to feed the inverter, which feeds into the grid. Let’s say the inverter costs a couple of thousand dollars.

Now, how big is the workout room? Well, my gym is pretty big, and I estimated the number of cardio machines in the cardio room today. There were five rows of machines, each row with about 20 machines in it, for a round 100 cardio machines. Let’s say the machines are used 30% of the time, and are used by average schmoes like me outputting 200 W of electricity while exercising. The gym is open let’s say 50 weeks a year to account for holidays and is open 16 hours a day. Our new annual output is…
100 machines x 30% usage x 16 hours/day x 350 days/year x 0.2 kWh/hour = 33,600 kWh/year;

At $0.09/kWh, that works out to $3024/year.

If your costs were only a couple of thousands of dollars for hardware, that could be a pretty reasonable return. It depends a lot on the assumption of how often the machines are used, and if there is significant additional cost associated with making the machines such that they can generate electricity.

Where does that leave us? Well, with all the assumptions I’ve had to make it’s really hard to say for sure, but I think such a scheme is possibly reasonable, though it’s fairly small potatos in the scheme of things. On the other hand, if you are looking at it from the perspective of someone who wants to have one machine to supplement their electricity in an off-grid use, or to provide some minimal back-up electricity for a light or two, an electricity-generating piece of cardio equipment could be really useful.

Something I like about this type of calculation is that it gives you a good sense of perspective. In this case, it helps me appreciate how much electricity does for us. The average U.S. home uses about 10,000 kWh of electricity each year (2001 data, see here: http://www.eia.doe.gov/emeu/reps/enduse/er01_us.html#Electricity). So, the workout room from our example above could power about three average homes. So if I rearrange the calculations a bit, I figure that it’d take 20 people exercising about 8 hours a day (outputting 200 W), every day, to power a home continuously. Think about that and realize what a remarkable worker electricity is for us!

Richard Heinberg speaking on “Peak Everything” at the Seattle Green Festival

Yesterday, I went to the Seattle Green Festival (http://www.greenfestivals.org/content/view/767/390/) to check out the various “green” vendors, and to hear a particular talk being given. I was interested in hearing Richard Heinberg give a talk on material from his new book “Peak Everything: Waking Up to the Century of Declines.”

Let me first describe my thoughts about the Festival itself. It was held in a huge venue—the Washington State Convention and Trade Center—and I was impressed to see so much space packed with such a wide variety of eco-friendly businesses. When I went, in the middle of the afternoon on Sunday, the place was packed. Previous events of this kind that I’ve gone to have been much smaller affairs, and they didn’t have the same smell of money that the Seattle Green Festival had.

Because I am mostly interested in renewable energy technologies, I immediately set out towards the end of the exhibit hall where a few renewable energy firms were set up. Before I got there, though, I paused to look briefly at some folks who had a couple of PCs running off of bicycles driving small generators, which were in turn hooked up to inverters/charge controllers and small sealed batteries (AGM or gel cell, but I didn’t look to see which). It made me pause mostly because a friend and I had been talking recently about generating electricity from say cardio equipment at the gym. I was just wondering, really, how much energy you could realistically capture. I very much suspect that the answer is “not much,” but probably enough to be useful in a power outage, or if you live in an off-grid situation. Something I plan to do a few calculations on in a future post. These things have been around for a while, of course, but it’s still fun to see. The gentleman riding one of the bikes when I walked up claimed he was putting out about 200 watts, and that the PC used about 140 watts. Presumably excess was going to top up the battery.

Breaking away from them, I did make my way to the renewable energy section, where there were two residential/small commercial-scale solar design and installation firms there. I spent a while talking to folks at those two booths. Ended up spending about ten minutes talking to a representative of Thermomax; they’re a big maker of solar thermal collectors, of the evacuated tube type. After some initial pleasantries, he proceeded to bash on flat-plate solar collectors, which is the other principal collector technology that is used for domestic solar hot water. (I’m talking about systems appropriate to the climate of Washington State, where closed-loop systems should be employed.) Sure, as a manufacturer’s rep I expect him to be biased towards his company’s technology, and he admitted he was biased; but still, I felt like I was getting some half-answers on some questions. The worst one was this—I said to him, “Look, you’re telling me that it’s not simply that evacuated tube collectors are more efficient per area, or per dollar, than flat-plate collectors, you’re telling me that flat-plate collectors simply don’t peform well at all in this climate? But there are clearly design and installation firms operating in the area that do use flat-plate collectors. How do you explain this?” His answer was basically that “they don’t know what they’re doing.” I guess that is possible, though I find it hard to credit that probably several firms in my area use flat-plate collectors and all achieve poor results because the technology simply isn’t appropriate. More details on evacuated tube vs. flat plate collectors in another post, perhaps!

The event I really went to the show to see, though, was the 4 PM talk by Richard Heinberg. He’s the author of “The Party's Over: Oil, War, and the Fate of Industrial Societies,” among other books. This was the first book of a few I’ve read covering the subject of Peak Oil, and it started me on the path of studying the subject in more depth. His new book is “Peak Everything: Waking Up to the Century of Declines,” and he’s traveling around giving this talk promoting the book.

I’m not going to talk much about Peak Oil here; at some point I will discuss it, and put a bunch of links up, but I feel like I’m already droning on at this point. The videos of Heinberg’s talk will give you a good introduction, should you decide to watch them (links below). Peak Oil in as few words as I can write it is this--we have reached or are very near to reaching the global maximum extraction rate of liquid fuels (petroleum and its replacements), and because the world's economies are completely dependent on easily transportable, energy-dense fuels, we are in for some seriously hard times ahead.

I found him to be an eloquent and interesting speaker. In me, he was essentially preaching to the choir, in that I’ve already read up on the issue a fair bit and believe it to be quite real. His talk didn’t cover a lot of new ground for me, but it was still good to hear it, and to hear the message being delivered to hopefully a few more folks who will go off and do their own research.
After the talk, he was signing copies of his new book at the book stall area of the festival, so I got the chance to talk to him briefly. I told him he’d been instrumental in alerting me to Peak Oil, and that I was trying to make modifications in my life where possible; shifting my career into renewables, building a rainwater collection system to water my raised bed garden and so on. He was quite gracious and encouraging and I really enjoyed meeting him.

I heard that there will eventually be online video of the talk he gave. In the meantime, though, I see that a very similar talk (from the same “book tour,” I gather) is up on YouTube…here are links to it if you’re interested!

Part 1 of 6: http://www.youtube.com/watch?v=ybRz91eimTg

Part 2 of 6: http://www.youtube.com/watch?v=b3_mYowxlEg&feature=related

Part 3 of 6: http://www.youtube.com/watch?v=2p6U-ZvR5Yk&feature=related

Part 4 of 6: http://www.youtube.com/watch?v=JyO0WS79Xec&feature=related

Part 5 of 6: http://www.youtube.com/watch?v=F5EcK-CdLNA&feature=related

Part 6 of 6: http://www.youtube.com/watch?v=F5EcK-CdLNA&feature=related

And here are Amazon links to the two books of his I have:

The Party’s Over…: http://www.amazon.com/Partys-Over-Fate-Industrial-Societies/dp/0865715297/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1208236262&sr=8-1

Peak Everything…: http://www.amazon.com/Peak-Everything-Century-Declines-Publishers/dp/086571598X/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1208236316&sr=1-1

Happy Motoring!

The potential of rooftop solar

I think a lot about residential solar installations, and so I thought it’d be interesting to think about how much of a difference solar rooftop installations could make in the U.S. So I’m going to go through some back-of-the-envelope calculations to see how much electricity we could generate if all of the roofs in the U.S. had solar PV (photovoltaic) modules on them.

Before I start, please keep in mind that these are pretty rough calculations. There will be a lot of assumptions made. I’m just trying to get a ballpark number.

Here is the main result I came up with...to see how I got this number, read through the paragraphs following!

Installing solar PV on all of the single-family detached homes in the U.S., using current technology, could potentially offset about 2/3 of the country's residential electricity use. That number is an estimate, and probably a bit high. The discussion following talks about the assumptions I made.

On to the calculations. First let’s calculate roughly how big the average roof is in the U.S. From this link, I learned that the average size of a home in the U.S. is 2330 square feet (http://www.infoplease.com/askeds/us-home-size.html). Now we have to figure out how much that average home area is in terms of roof space. If I assume that the average home is two stories, that would mean that two floors of 1,165 square feet (since 2,330/2 = 1,165) are covered by one roof of 1,165 square feet. But, that’s assuming that roofs are flat, and we can be pretty confident that for single-family detached homes, that’s generally not true. They’re pitched, and that actually gives us a bit more roof area. Let’s assume that the average roof has a typical roof pitch such as 6:12, meaning for every 12” of horizontal extent, the roof drops 6”. So, I can use some simple trigonometry that I won’t bore you with (having already bored myself with it), to calculate that the roof area we started with of 1,165 should be multiplied by 1.12 to get a better estimate of the roof area. Multiplying gives our new roof area of 1302 square feet.

Let’s find out how many single-family detached homes there are in the U.S. From the 2000 census, I see that there are about 70 million of them (see Table 1 on page 2 of this link: http://www.census.gov/prod/2003pubs/c2kbr-32.pdf).

If I multiply those two numbers, number of homes and roof area per home, I come up with 91,175,671,783 square feet of roof space, or, put into scientific notation, and rounding off so as not to be silly, 9.12E+10 square feet. Now, because my teachers in school told me the metric system was the wave of the future, I’ll convert that number of square feet into square meters, which gives me 8.47E+09 square meters. About 8.5 billion square meters.

But now we need to consider how much of those rooftops are exposed to the sun. Since all of the U.S. is north of the equator, to get the maximum sun exposure solar modules should ideally be pointing south. Any modules mounted on a north roof will get little or no sun. East or west facings will get some sun. For the sake of simplicity, let’s say that half of all the roofs in the U.S. have a ridge running east-west (giving you a north and a south roof face), and the other half have a ridge running north-south (giving you an east and a west roof face). So one quarter of all roof area is facing south, and gets the full benefit of sun—we’ll take that roof area at full value. One quarter of all roof area is facing north, and gets no sun/very little sun—we’ll take that roof area as being of zero value for solar, and we certainly wouldn’t go to the trouble and expense of putting solar modules on north-facing roofs. One half of all roof area is facing east or west, and gets moderate sun—we’ll take that roof area as being half-value for solar purposes. Our effective “fully useful” roof area then becomes: 8.47E+09 square meters x [(1/4 x 1) + (1/4 x 0) + (1/2 x 1/2) = 4.24E+09 square meters. A bit over 4 billion square meters.

A big assumption I made in the previous paragraph is that all of the roofs that have sun exposure are not shaded. This is clearly not true; plenty of homes have roofs that are partially or even fully shaded. In the solar business they would be described as not having a full "solar window;" a full solar window would have unshaded access between 9 AM and 3 PM, year-round. So my assumption means that the final number I come up with for potential electricity generation is going to be high. There ARE ways for some of those homes to get better solar access--pole-mounting the solar array immediately comes to mind--but not in every case, I'm sure.

Well, how much electricity could we generate if all of those roofs were covered with solar PV modules? To calculate this, we need to know how much sunlight hits a south facing, and how often it hits it. That can get complicated, because the amount of sunlight coming in at a particular location depends on the time of day, the time of year, the weather, and any shading of the modules. Fortunately, metrics have been developed that help deal with these complexities. The concept of “peak sun” tells us how much solar energy we are going to get under optimum conditions at the Earth’s surface—sun directly overhead, no cloud cover, and so on. The value of peak sun is 1000 watts/square meter. This leads to the idea of “peak sun hours,” which means how many hours of maximum sunlight you get in a day at a given location. This doesn’t mean how many hours between sunrise and sunset at a location, but rather, if we summed up all of the solar energy on a given square meter at a given location over the course of a day, how many equivalent hours of “peak sun” (1000 watts/sq. meter) would we get. So using peak sun-hours for a location, we can determine how good or how bad a site is for solar energy capture.

Peak sun hour data is tabulated at many internet sites; you can look at maps by region, or look up data for specific cities. Listings are for daily averages over the course of a month, or over the course of a year. Unfortunately, I haven’t been able to find a U.S. average number over a year…the best I have found is average number over a year for a given region, as shown in this map here: http://www.wholesalesolar.com/Information-SolarFolder/SunHoursUSMap.html. So I’m unfortunately just going to have to guess at a national average. The worst zone, Zone 6, gets about 3.5 peak sun hours/day, year round. The best zone, Zone 1, gets about 6 peak sun hours/day, year round. A lot of the country falls into Zones 3, 4, and 5, so let’s just call Zone 4’s value of 4.5 peak sun hours/day the U.S. average value.

Whew! From all this, we can estimate how much energy is falling on our roofs on an average day—it’ll be more in the sumer months, less in the winter months, but on an annual basis it’ll average out.

4.24E+09 square meters x 1000 watts/square meter x 4.5 hours/day = 1.91E+10 killowatt-hours per day. (I quietly converted watts into kilowatts). But how much of this could our solar modules capture? For this calculation, let's plan on using the "traditional" silicon PV modules, with efficiencies around 13%, rather than thin-film modules which have substantially lower efficiency (but which have the benefit of lower cost). So if we multiply the amount of incoming energy by our efficiency that should give us the amount we could hope to capture in a day.

1.91E+10 kWh/day incoming energy x 13% efficiency = 2.48E+09 kWh/day potentially captured

Over the course of a year, that could provide 2.48E+09 kWh/day x 365 days = 9.04E+11 kWh total. That’s 907,000,000,000 kWh, or 907 billion kWh annually.

How does that compare to the total amount of electricity generated in the U.S.? From the EIA (Energy Information Administration: see http://www.eia.doe.gov/cneaf/electricity/epa/epat1p1.html), I see that the total amount of electricity generated in the U.S. in 2006 (the latest year for which they list the data) was 4.06E+12 kWh, or 4 trillion kWh.

Diving the two numbers, we find out that we could replace about 22% of our total electricity generation needs using just rooftops of single-family detached homes! If we look at it just on the basis of powering residences, I calculate you could offset about 67% of total residential electricity use with just single-family detached rooftop solar! (See http://www.eia.doe.gov/cneaf/electricity/epa/epat7p2.html for a breakdown of electricity use by sector).

I realize there are other issues involved than just kWh generated per year. Rooftop PV isn't just a drop-in replacement for power plants. The electricity generated from rooftop PV is variable, and not controllable, in the sense that 1) you can't just bring it on-line or take it off-line to match electrical demand, like you can with gas-fired generation, or 2) you can't use it 24 hours a day for baseload generation, like you can with coal/nuclear. I'm just trying to be as up-front as I can with the limitations of this estimate.

But as an estimate of the order of magnitude of what could be accomplished, even with today’s technology, I find the potential of solar photovoltaics to be quite impressive!

Hope you enjoyed this!