“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Tuesday, July 30, 2013

A quick note on the eGallon

Screen shot of my results from DOE eGallon site
In a previous post I mentioned the eGallon concept from a Department of Energy (DOE) web site. It purports to tell a visitor how much he or she would pay to drive as far in an electric vehicle as a gallon of gas takes them in an "average vehicle." It breaks down only as far as by state (or U.S. average). So, for example, if I use California, it tells me that a gallon of regular gasoline costs $3.99 and that my eGallon costs $1.53.

But my average mileage over the life of my vehicle is 50.86 m.p.g. At my most recent fill up I paid $4.059/gallon. I'll use the Nissan Leaf for a comparison, the vehicles are broadly similar in important ways. Each has a Cd (drag coefficient) of 0.29 and, while the frontal area of the CT200h is a bit larger, the Leaf weighs more. The Leaf is rated by the EPA to consume 29 kWh/100 miles for the 2013 model year.

So, on a gallon of fuel, I go 50.86 miles. The Leaf would need (50.86/100)*29 kWh = 14.75 kWh to go that distance. If I assume that the charging system is 85% efficient, I'd pay for 14.75/.85=17.35 kWh. On my most recent electric bill I paid $0.1611/kWh for electricity above the "basic lifeline" rate, so these 17.35 kWh would cost me $2.80 and that's the price of my eGallon. Quite a difference between that number and $1.53, the "true" number is 83% higher whereas the number for my gasoline cost is not far away from what I actually pay. The computed eGallon price would be even further from ReGallon cost ("Rob's eGallon") if DOE had used the 2013 model year numbers for the Leaf in lieu of previous years' 34kWh/100 miles. If I use the 2013 model year number for the Leaf and the EPA combined estimate (42 m.p.g.) for the Lexus CT200h that I drive, an eGallon would cost $2.31, only 51% higher than the site's number.

You can read about their methodology here. The confounding factors are the actual cost of electricity and the fuel economy utilized for the ICE (internal combustion engine) vehicle. For reference, the plot below (you can click it to enlarge and be able to read the numbers) shows an AeGallon ("actual eGallon") for a range of actual fuel economies from 12 m.p.g. (the driver currently in a vehicle getting less than that is not a likely candidate for an EV) to 70 m.p.g. (a hypermiler in a Prius). For this plot, I'll use the same electricity consumption as the DOE site uses, i.e., 35 kWh/100 miles, a blended rate from 5 top selling EVs. Electricity prices on the plot range from $0.09 to $0.20 per kWh. You can calculate your number yourself, it's as simple as 0.4118*(m.p.g.)*(electricity cost per kWh). You'll note that, for combinations of high mileage vehicles and expensive electricity, the eGallon may be more expensive than a gGallon (i.e., a gallon of gasoline).

On the plot, the "front" axis is m.p.g. for the vehicle being replaced with an EV, the rearward extending axis is the price of a kilowatt hour of electricity, and the vertical axis is the price of an eGallon in dollars. You can see that, for low mileage vehicles being replaced, the eGallon is quite inexpensive, regardless of electricity costs. But as replaced vehicle fuel economy climbs, the eGallon becomes much more expensive. The DOE site simply uses a single fleet average fuel economy (28.2 m.p.g.) and does not correct for the 85% charging efficiency I estimated.

Monday, July 29, 2013

Commentary: Is Peak Oil Dead?

Commentary: Is Peak Oil Dead?: A little rain on the parade of the new era of easy oil availability and "American Energy Independence" from an oilfield veteran.

'via Blog this'

Sunday, July 28, 2013

How are we doing on EV adoption?

In November, 2009, I published a post that used the logistic function along with a couple of guesses (one by Nissan CEO Carlos Ghosn, one by me) and assuming that, in the next few decades, essentially all light duty vehicles on the road would be electric, to estimate the additional electrical load needed annually. I speculated (estimated is WAY too strong) that at the peak, sometime around 2039, we'd add 12,000,000 electric vehicles to the fleet requiring 6.6 gigawatts of generating capacity (assuming no smart grid utilization of the vehicles as storage, or other load leveling techniques).

Now, almost four years later, I thought it would be interesting to take a look at how the adoption of EVs ( combining PHEVs or plug-in hybrid electric vehicles such as the Chevy Volt and AEVs or all-electric vehicles such as the Nissan Leaf) is progressing in comparison to the very rudimentary model.

I used Ghosn's response to President Obama's call for one million EVs on the road by 2015, i.e., that that number would be "easily surpassed." I assumed two million in 2015 and 230 million in 2050 and used those points as input to the logistic function. I used Wolfram Alpha to plot the data (if you click the link, the assumptions will be built into the input and you can change them to suit). Of course, the plot starts in 2015 and EVs and PHEVs started to be on the road in 2010 and it's now 2013. But nothing stops me from plugging negative numbers into the plot range to go from 2010 to 2015 (or numerically evaluating the function). Doing so predicts (here I assume January 1, 2010 is -5.0 years, January 1, 2015 is 0 years, and here, about 7/12 of the way through 2013, we're at -1.42 years) just over 1.5 million EVs and PHEVs on the road.

What is the actual number? The best data I've found is at the Electric Drive Transportation Association's site. They've compiled it here and the pertinent graph is to the left (click to enbiggen). The astute reader will note that the actual number is about 112,000, less than 10% of my speculative number. With a year and a half to reach 2015, and two and a half to reach the end of 2015, Ghosn's prediction is looking precarious. Let's speculate some more.

What if I plug actual data into a logistic curve (the curve form EDTA certainly doesn't preclude such a model)? I'll use 112,000 in 2013.5 and 230 million for the ultimate number and see what growth rate yields 6,669 (from the graph using GraphClick) in June of 2011. The rate turns out to be 141% annual growth (initially). I doubt that this growth can be sustained indefinitely as early adopters complete adoption and the curve flattens. Such a rate would result in a 230 million EV fleet in around 2022. It's unimaginable that this could take place. Still, if the growth rate continues, we'll have two million EVs on the road sometime in mid 2015.

Sunday, July 21, 2013


My firm is what would, in general, be viewed as one of the larger closely held, locally based construction inspection, materials testing, and geotechnical engineering firms in California. Barriers to entry for, at least, several material segments of our business are very minimal, though to provide the full spectrum of services that we offer they are significantly greater. Unfortunately for us, the "meat and potatoes" of our service line can be served (with arguable effectiveness but very low price) by those who select to provide only those services with the aforementioned low barriers.

Thus, we're constantly looking for areas where the investment we've made in people and equipment of very high capability can provide value that will be recognized by a client base willing to pay for these. In this effort, we've engaged in significant research and development, led by Dr. Boris Stein. Much of this R&D work has been related to various sustainability issues regarding concrete and its use in the built environment.

 Concrete is a construction material composed of cement (typically portland cement and thus referred to as "portland cement concrete"), coarse and fine aggregates, water, and, possibly, various admixtures to customize the concrete's properties in various ways.

The manufacture of portland cement involves (at a very simplistic level) charging a kiln with limestone (calcium carbonate, Ca CO3) and various other constituents (chiefly clay as a source of alumino-silicate), and heating the charge to around 1450°C. This results in the emission of CO2 as CaCO3 is changed to CaO in the so-called "clinker." This process is called "calcining." This clinker is then ground to an extremely fine powder in a grinding mill, and a small amount of gypsum (CaSO4) is added.

The heat may be supplied, in some instances, by the burning of manufactured materials (discarded tires, for example) but is usually accomplished by the burning of fossil fuels. Thus, the production of portland cement is a twofold emitter - the combustion product of the fuel used to heat the kiln and the "cooked off" CO2 from the calcium carbonate. Though estimates vary, for each tonne of cement produced, approximately 750 kg of CO2 is emitted. It's estimated that somewhere around 5% of the CO2 emissions worldwide are a result of the manufacture of cement (I've seen estimates as high as 7%).

Thus, finding substitutes for portland cement in concrete is an active pursuit in the academic and industrial arenas. Some of these pursuits involve replacement of calcium carbonate with a different raw material that either is a non-carbonate, requires much lower temperatures for processing, or both.
Electrotatic precipitator for collecting fly ash

Another approach is partial replacement of portland cement in a concrete mix with various industrial byproducts, "supplementary cementitious materials" or "SCMs." Chief among these are fly ash (a product of coal combustion) and ground granulated blast furnace slag ("GGBFS" or just "slag," a product of the refining of iron and of steel making). It's also possible to use "natural pozzolans" literally mined (typically from Southern California desert locations for use here).

As much as 50% or even 70% of the portland cement in concrete can be replaced with these SCMs, and the resulting concrete mixes can, with suitable attention to proportions and admixtures, result in concrete with much lower carbon footprint and characteristics as good as, or even better than, mixes utilizing only portland cement.

Books can be (and have been) written on the various methodologies of designing mixes with desired properties and I'm not going to go into that here. But let me (as is typical) use some back of the envelope calculations to see what kind of CO2 emission reductions are possible.

In 2011, 3.6 billion tonnes of cement were produced worldwide and this resulted in the emission of over 2 billion tonnes (metric ton, 1,000 kilograms - about 10% larger than a U.S. "short ton" of 2,000 pounds) of CO2. Certainly, some of that cement went into mixes already utilizing SCMs but the fraction worldwide, would be fairly small. Typical U.S. mixes at this time might utilize 15% to 25% fly ash, and many mixes don't use any. If we assume that 10% fly ash might be typical for a worldwide average and that we could ultimately get to mixes with 70% SCMs (entirely possible from a technical point of view). If so, we could reduce the 3.6 billion tonnes to 1.2 billion tonnes (to the great despair of the cement manufacturers who would fight this tooth and nail) and save the emission of something like 1.8 billion tonnes of CO2 annually.

Ah, but what about the availability of the SCMs?  We certainly don't want to burn more coal or refine more iron for the purpose of providing the concrete industry with SCMs. In 2010, 777.1 Mtonnes (megatonnes - a million tonnes or a billion kilograms) of CCPs (coal combustion products, most of which is fly ash) were produced and 415.5 Mtonnes were utilized. While much of the utilized fly ash went into concrete, there are many other uses competing for it. Let's say that, by more effective harvesting and economically incentivizing use in concrete, we could use 500 Mtonnes/year.  We're currently using about 190 Mtonnes in concrete, so we could possibly increase our use by 310 Mtonnes.

As for GGBFS, the latest year for which I could find data was 2005, in which the world produced 110 Mtonne of slag, of which 60 Mtonne went to slag cement. Suppose that we could use 100 Mtonne (assuming both an increase in production and an increase in utilization), a 40 Mtonne increase.

Totaling, and assuming that appropriate mix designs enabled all of the 310 Mtonnes of fly ash and 40 Mtonnes of slag to be used, we could replace something like 350 Mtonnes of portland cement. Thus, rather than the 2.4 billion tonnes feasible with technological implementation of mix designs, supply constrains us to the replacement of 0.31 billion tonnes and the elimination of something like 230 Mtonnes of CO2, on the order of 0.7% of worldwide emissions.

Sadly, SCMs won't save the world, but we are certainly heavily engaged in pursuing them. They have benefits in the final concrete product, they reduce the industrial waste stream and, to a limited extent, can reduce industrial CO2 emissions.

Wednesday, July 17, 2013

Regenerative braking in the Lexus CT 200h

I've been driving my Lexus CT 200h for about two years and about 39,000 miles. In that time, I've learned a lot about driving techniques to minimize specific fuel consumption (g.p.m., gallons per mile). I've also given some thought to what it is about a hybrid that makes it more fuel efficient. One of those items is regenerative braking, where some of the kinetic energy in the moving vehicle is used to charge the battery rather than to heat the brake rotors. This is done by having the energy of the moving vehicle turn the electric motor backwards, thus making it a generator and thereby charging the battery. Of course, friction brakes are also used.

I've wondered just how much of the braking energy goes into the battery and have been hard pressed to find data for this. However, the CT 200h has a display option for "Consumption" (see photo at left). It's difficult to see (click to enlarge) but there are small boxes in the vertical bars that indicate mileage by the minute. Each complete box, according to the legend, represents 50 watt hours of energy (180,000 joules). At the top of a hill, I applied sufficient braking to keep my speed at approximately 35 m.p.h. At the bottom of the hill, a stoplight brought me to a stop.

I can calculate the energy difference from 35 m.p.h. at the top of the hill to 35 m.p.h. at the bottom of the hill by using Google Earth to find the elevation change. I determined it to be 103 meters. Because my speed didn't change, neither did my kinetic energy, therefore the reduction in my potential energy went to some combination of heating my brake rotors and charging my battery.

My best estimate of the mass of the vehicle with the 1/4 tank of gasoline and myself and my baggage is 1,600 kg. Therefore, the potential energy lost in the descent is ~E=mgh=1600kg*9.8\frac m{s^2}*103 m=1.62*10^6joules~. The display shows "E" boxes and fractions of "E" boxes and my best estimate, assuming that 3.5 "E" boxes are shown is that ~3.5*50Wh=175Wh~ or ~630,000joules~ were sent to the battery. I don't think it could be lower than ~585,000joules~ or higher than ~675,000 joules~.

Assuming that I'm interpreting the cryptic display correctly (and that Ed Davies doesn't haul me up short!), about ~630000/1620000=38.9\%~ of the potential energy went to charge the battery. The rest was dissipated as thermal energy in the disc brake rotors and, ultimately to the atmosphere. The battery pack in the CT 200h is a 1.3 kWh Ni metal hydride battery. The 630,000 joules equal 0.175 kWh or 13.5% of a full charge for the battery. Per the owners' manual, I'm able to drive in "EV mode" (battery only) for two miles, but I'd best accelerate slowly even by my standards, and not exceed about 20 m.p.h.

As an aside, this is the energy in about 18 cm^3 of gasoline. Figure I'd have to burn about four times that, or 72 cm^3 to charge the battery with the engine at 25% efficiency. And, of course, the regenerative braking isn't effective when the battery is fully charged, isn't used (much) in hard stops, etc. Still, it does increase overall fuel efficiency.

Finally all of these figures have large "error bars," the regenerated energy on the display, the elevations from Google Earth, the mass of the vehicle, and the ability to stay at precisely 35 m.p.h. (although really, all I need is to be going at the same speed when I stop logging as when I start so that the kinetic energy is unchanged). Still, it's enough for me to have a good idea of what the regenerative braking can give me.

Update: Based on a comment by Gabriel Grosskopf, I measured the distance over which I descended. It was 1,530 meters, thus the slope is 3.86 degrees (0.0673 rad). The typical instrument landing system glideslope is 3 degrees though a few, such as VNY - Van Nuys - at 3.9 degrees, are steeper. Assuming that I drove the 1530 meters at 35 m.p.h. or 15.6 m/s, it took me 98 seconds to put 630,000 joules into the battery. This is a charging rate of 6,440 watts or 6.4 kW. As mentioned in a previous post, when I put fuel in my gasoline tank, I'm adding energy at a minimum rate of 11 mW, about 1,700 times as fast. To be fair, we'll divide that by four since IC engines are much less efficient than electric motors. So we're adding useful energy at 2.75 Mw or 430 times as fast. Coincidentally, the Nissan Leaf touts a 6.6 kW charger to charge its 24 kWh battery.

Tuesday, July 16, 2013

Senators Grill Refiners Over High Prices Amid Oil Boom - Bloomberg

Senators Grill Refiners Over High Prices Amid Oil Boom - Bloomberg:

'via Blog this'

My dismay with our elected representatives comes again to the fore. In the linked article above, we find Ron Wyden, Democratic Senator from Oregon and Chair of the Senate Energy and Natural Resources Committee saying "Our people want to know why the flood of new domestic crude oil isn't lowering prices at the pump. There is no question that the lower oil costs are not getting through to Americans' wallets."

To the left is a plot of oil prices (WTI) over the last five years. I'm having a very difficult time spotting Wyden's "lower oil costs." There are so many supply and demand issues that play into not only the price of crude oil (which is a world wide market and cannot be affected in any reasonable way by the Senate) but on the price of finished products from oil such as gasoline. These sorts of speeches constitute pure political pandering. But he's a politician so I guess it's to be expected (a la the scorpion in the fable of the scorpion and the frog)

Do I enjoy paying $4.099/gallon for my gasoline? No, but I'm averaging 51 m.p.g. so it doesn't hurt me as badly as many others and, were I King, I'd increase gasoline taxes by $0.25/quarter for the next three years. Many who read this will be relieved that I'm not King.

Saturday, July 13, 2013

Windation and the Turbo Windmill 5000

I've composed several posts regarding building integrated wind energy. Pictured at left is the Turbo Windmill 5000 by Windation. It's designed for rooftop installation and is represented to be "permit ready." It's dimensions are 9' X 9' X 10' and it weighs 2,200 pounds. This is claimed by Windation founder and CEO Mark Sheikhrezai to be "less than half" of the weight of an HVAC system. What particular HVAC system is the subject of this comparison is not stated.

The "5000" is the nameplate capacity of the turbine in watts, whose cut in wind speed is 2.7 m/s and whose most effective operating range is stated to be 4.5 to 9 m/s (for the SI unit impaired reader, these are 6, 10, and 20 m.p.h. respectively). It's a vertical axis wind turbine (VAWT) and thus is agnostic with respect to wind direction. The turbine itself is fully enclosed, thus eliminating the possibility of bird and bat kills.

In an interview at the CleanTechies blog, Sheikhrezai claims that the Turbo Windmill 5000 utilizes a proprietary vacuum system that "captures and funnels turbulent wind in a smooth, counterclockwise stream" and that thereby "a vortex is created beneath the internal turbine enabling a vacuum effect, pulling more wind into the frame and amplifying input loads." Sadly, he then states that "energy available in the wind is proportional to the cube of its speed." This is false, power is proportional to the cube of speed, energy is proportional to the square of speed. We'll forgive Sheikhrezai this transgression. Sheikhrezai states that the Turbo Windmill 5000 can produce 10,000 kWh per year with an average wind speed of 7.2 m/s (a bit over 16 m.p.h.).

OK, let's dive into a "back of the envelope" plausibility calculation. Using the photo above and assuming that the 9' dimensions are horizontal, the 10' dimension is height and that the only wind entrance is the "yellow" portion, I can use Tracker to scale the wind accessible dimension as 7.25' X 3.43' or 2.31 m^2. First, what's the total power in wind of cross sectional area of 2.31 m^2 travelling at 7.2 m/s? We have a volume, ~V~, of 7.2 meters X 2.31 meters passing any given point in one second. The air's density, ~\rho~, (assuming sea level - most favorable for the calculation) is 1.225 kg/m^3. We use ~E=1/2\,m{v}^{2}~ and ~m=\rho\,V~ for ~E=1/2\,\rho\,V{v}^{2}~ or 52,800 528 joules each second or a power of 0.528 kilowatts. This certainly doesn't indicate that the power claims are implausible. Windation claims to capture about 10% of the available power (assuming that the 5 kW nameplate capacity is for 7.2 m/s wind speed - if it's for a higher speed, they're claiming still less efficiency).

Update: Thanks to Ed Davies for causing me to take a look and realize that I'd been off by a couple of orders of magnitude (using 122.5 instead of 1.225 kg/m^3 for sea level mass density of the atmosphere). How embarrassing! So, what to make of the claim of 5 kilowatts? Working backwards, what would this imply for a wind speed? Betz' law provides the theoretical limit of turbine efficiency (the maximum fraction of the energy available in wind that can be captured) at about 59%. The best efficiency I've seen for a turbine is about 70% of the Betz limit or, in round numbers, 42% of the power in the intercepted wind. This is achieved by horizontal axis turbines (typically much more efficient than VAWTs) of enormous size at ideal wind speeds. But let's generously assume that the proprietary vacuum effect enables Windation to capture and utilize 45% of the wind's power. So, 0.45*(available wind power)=5000 watts and available wind power is 5000/.45 = 11,100 watts. Working backwards and solving the equation above for speed and plugging in 11,100 watts, we find a wind speed of 19.9 m/s or just under 45 m.p.h. And the generous assumptions are beyond unlikely to be met in a real installation.

With respect to the claim of 10,000 kWh/year at average wind speed of 7.2 m/s, it's hard to say. "Average" doesn't work well here. Say we had an hour of wind at 7 m/s and an hour at 7.4 m/s. Then say we had 4.2 m/s and 10.2 m/s. Because of the proportionality of power to speed cubed, the two hour span with the more extreme speeds would generate about half again as much energy yet both have, in a sense, the same "average" wind speed. That said, if the Turbo Windmill 5000 generates 5000 watts for a year (365.25*24 or 8,766 hours) it would result in 43,830 kWh so it doesn't seem like an excessive claim (IF, of course, it can generate 5kW). No cutoff speed is given. Much deeper information on wind speed distribution is here.

Update (see above): 10,000 kWh/year is a continuous power of (10,000 kWh/year)/(8,766 hours/year) or 1,140 watts. Proceeding as above, with the generous assumptions there, we're talking about a steady wind of 9.3 m/s or 21 m.p.h. Now, admittedly, a variable wind that has periods of very high speeds may improve on this but, on the other hand, my efficiency assumptions are extremely generous and highly unlikely to be realistic.

Finally, I have to point out that 10,000 kWh would cost me about $1,200 from the City of Anaheim Public Utilities. The price for a Turbo Windmill 5000 given at the web site (where, sadly, I found the sentence "the machine can generate 5 kilowatts of power per year") is $45,000. It's implied but not stated that this includes installation. The claim is that "With the available incentives and rebates, it is estimated that the initial expenditure of $45,000 can be recovered in five to seven years." Payback period is a poor indicator of the desirability of an investment when considering periods beyond two years, but even with that, we must be talking about a LOT of rebates and incentives.


Energy claim:                                                                                                   Economics claim: 

Update: An excellent overview of building integrated wind is here.

Update 2: While looking for further information to attempt to better understand Windation's claims, I noted that the article linked above was published in 2010. I'm not sure why it wound up in my inbox recently, but I decided to see if the firm is still a "going concern." The last update on their web site is from November of 2012 and I find no record of bankruptcy proceedings. However, their corporate address is 1007 Florence Ln., Apt 1, Menlo Park CA. Here's a Google Streetview screen shot of their corporate HQ:

Windation has claimed that they'd install a unit at the Palo Alto Medical Foundation in the first quarter of 2010. I located architect's renderings of the installation and then found the facility as constructed in (where else?) Google Streetview, and the Turbo Windmill 5000 was not installed as of the photo date of March, 2011.

Doing a lot more reading about "building integrated" and "urban" wind, the field seems to be full of dodgy claims and outright scams. I don't know which category, if either, Windation falls into but a lot more information on these topics can be found at Paul Gipe's site. The pertinent information is here.

Update 3: In my further digging, I located a video of an actual unit (well, possibly an actual unit, one can't really tell as it's sitting on some sort of pavement area and the intake is covered). But something does, in fact, exist. The video was uploaded on November 5, 2011 and Windation left a response to a viewer comment "a year ago." The video is FAR from professionally produced. It's embedded below for your viewing pleasure.

I have to say that this is very disturbing in that false claims, vaporware and dubious business practices provide ammunition for those who would claim that renewable energy is a chimera and that increased business as usual is our only option. It further muddies the water with respect to what constitutes sound investment opportunities in the so-called "green space." Finally (yes, finally), it's a shame that the "green press" uncritically embraces such products and schemes without doing the necessary evaluation.

Saturday, July 06, 2013

Solar sells - anything

I was watching something on the Discovery Channel (which used to be about 70% watchable and 30% "I'll pass" and is now about 90% unwatchable) when I saw an ad for the "Bell & Howell Solar Charger." While "Bell & Howell" apparently still exists as going concern, they also license their trademark "to makers of various electronic consumer products." The Solar Charger is the product of one such maker. Should you have chosen to click on the link, you'll have had the opportunity to see the charger allegedly in action "instantly" charging iPhones, iPads, a handheld GPS, and all manner of  devices. Besides the sun, the charger is also capable of charging from a computer USB port, but the advertising touts a scantily clad woman at the beach, apparently using the sun to charge her iPad.

Let's take a look. The specifications are scant at best and hard to find. I've been able to determine that the battery is a 410 mAH (milliamp hour) Li ion battery. I'm going to assume that this is at 5 volts (the required charging voltage for an i-Device). I'd really like to have specifications for its capacity in watt hours. But, assuming as stated, it's 2.05 watt hours. Now, an iPhone battery has a capacity of 5.4 watt hours, so a full charge, neglecting efficiency, on the solar charger would charge a dead iPhone to about 38% of capacity. An iPad has a 42.5 watt hour battery and thus the charger will provide just under 5% of a full charge. Mine shuts down at that percentage. The "instantly" claim isn't supported by current battery technology in the devices, so the devices must simply operate off of the charger (to the extent that it works at all).

But what about the sun? The Amazon page for the charger lists its dimensions as 5" L X 1.5" W. Using the free and terrific Tracker Video Analysis software (which works just fine on jpegs) I determined that the "high efficiency solar cell" is about 1.46" X 0.85". This is ~8.00*10^{-4}{m}^{2}~. I'll also assume the cell to be 20% efficient. I'll use ~350\,{\frac {w}{{m}^{2}}}~ as a good average for available insolation in my area. That yields a charging rate of about ~8*10^{-4}*350*0.2 = 0.056~ watts and a time to charge to capacity of ~2.05/0.056=36.6~ hours. Others at various review sites cite (sites cite? I like it) two days, which doesn't seem unreasonable. On the web site video, they show the unit being charged under a table lamp. Umm... good luck with that.

I actually have several solar chargers for my various devices, all of them are quite bulky as you'd expect. Solar power density is just not that high. It's amazing that a profit can be made by slapping a trivially small solar panel on what is otherwise an extremely poor quality auxiliary charger for your portable device. And, don't forget, for an extra $10 you can get it with a three bulb LED flashlight. Finally, they'll send a second charger free (just pay separate processing and handling). My rating for this product: