My foray into electric vehicles

Over the course of the 16 years that I've maintained this blog (sporadically at best in recent years), there have been a wide variety of cars that I've driven. Some have been very stingy with respect to fuel consumption (my Lexus CT200H is the best example) to fuel hogs (I just ended the lease on a Jeep Trackhawk). My early blogging was almost exclusively related to fuel consumption, both personally and generally. As the years have gone by, my topic space expanded well beyond vehicle fuel consumption and into energy in general and even into politics.

But, for this post, it's back to basics. I turned in the Trackhawk that I'd leased and purchased a battery electric vehicle, the Genesis GV60. The performance model I purchased features all-wheel drive, with 160kW (215 horsepower) to the front wheels and the same to the rear wheels for a total of 320 kW. It delivers 350 Nm (258 ft lbs) of torque to the front wheels and the same to the rear for a total of 700 Nm. Its 77.4 kWh battery pack makes it a heavy car for its size, with a curb weight of 4,890 pounds but in "sport' mode with the "boost" on, it will go from 0 to 60 mph in about 3.8 seconds, very similar to the 710 horsepower Trackhawk I turned in.

With a full charge, it's good for about 250 miles but, unlike an internal combustion engine, there's no fuel economy vs. speed curve with a peak. There's no "engine map." The vehicle "fuel economy," as far as I've been able to determine, is strictly a function of tire rolling resistance and aerodynamic drag. Thus, freeway travel at, say, 75 m.p.h. is far less efficient than lower speeds in city driving.

I'm not getting what I expected, my most recent charge was 67.5404 kWh to drive 181 miles, or 2.68 miles/kWh. I expected something more on the order of 3.5 miles/kWh but the bulk of my driving has been on the freeway at around 80 m.p.h. Still though, I'm paying something like $0.17/kWh at the moment, so I'm spending around 6.34 cents per mile.

In comparing that to an internal combustion engine, it's probably unfair to compare it to my Trackhawk, which is a 710 horsepower beast in which I averaged something like 14.5 m.p.g. and which required 91 octane fuel. But if I consider a vehicle averaging 30 m.p.g. and 87 octane fuel with California 87 octane fuel around $4.49/gallon at the moment, the owner of that vehicle is spending 14.97 cents per mile, over twice what I'm paying. Further, I can utilize a perquisite to get free charges for three years!

I will say that I encounter the "range anxiety" often described for purchasers of battery EVs, and I approach trips that are outside of my commute with more forethought than previously, given that there's not a charging station on every corner. For example, I have a relative that lives in Ramona, CA. The round trip from my home to hers is about 202 miles. To make that trip with no concerns, I need to be close to fully charged and, without locating a charging station, I'd need to avoid side trips. And, as recommended, I generally limit my charging to 80% of full capacity. This limits me to 200 miles at best!

The car is heavy, the battery pack consists of 384 Lithium Ion Polymer cells with a nominal capacity of 77.4 kWh and a usable capacity of 74.0 kWh. As mentioned above, the curb weight of the car is 4,890 pounds. 

In an unusual move, parent Hyundai Motor Group opted to use an electronic architecture for the E-GMP platform that can operate at either 400 or 800 volts (but see below). That allows for “ultra-speed charging” when the latest, 350 kilowatt charger is plugged in — the battery pack going from 10 to 80% of capacity in 18 minutes.

In any case, I'm over 11,000 miles in the GV60 as I type this. When asked if I'm happy with the purchase, my answer is that I would not purchase this particular EV again. There are several reasons, but most are related to ergonomics and systems engineering, not the actual EV platform. However, even with respect to that, my suggestion would be to wait. Range seemingly goes up with each passing month, and many game-changing energy density developments are being touted. There will likely be no retrofit for current EVs!

And now Ford, GM, and Rivian are adopting (and adapting) their EVs to use the Tesla Superchargers, which pretty much assures that the Superchargers will become the national standard. My GV60 would need an adapter, and Hyundai is considering it.

All that said, I believe that the GV60 provides good value for its price and it's pretty clear that EVs are the coming thing. But I'll look elsewhere for my next EV a few years from now.

Inserted because it's a fantastic cover of a Dylan song and it's from Hendrix' album "Electric Ladyland."

The Fisker Ocean

I've published previously on the seeming futility of solar panels on the roofs of vehicles. But Fisker has announced the "Ocean" in various configurations. It's an SUV style vehicle with the "Fisker Ocean Extreme" boasting solar panels for the full length of the passenger cabin. The claim is that solar charging will produce 1,500 miles worth of charge, or even up to 2,000 miles. Let's investigate!

First, how much energy is needed to travel 1,500 miles in the Fisker? Unlike internal combustion engine powered vehicles, there's no curve with a peak in terms of energy mileage as a function of speed. For the IC vehicle going very slowly uses a lot of the energy from burning fuel to keep the engine turning over, and going very fast has a high drag penalty. The sweet spot differs for various models but might be in the range of 50 m.p.h.

For a battery electric vehicle, there's no such function. The faster you go, the worse your energy economy since it's only a matter of overcoming drag. So, in earlier data collection of my own driving, my overall block speed was on the order of 30 m.p.h. with a blend of city driving, freeway driving, and freeway driving in traffic. I'll use that number, but convert it to 13.41 meters/second.

We'll go to the naive drag equation, ~D=1/2 \rho C_dAv^2~ where D is drag force, ~\rho~ is air density (I'm using sea level, at altitude density would be lower and insolation would be slightly higher), ~C_d~ is the vehicle's drag coefficient, ~A~ is flat plate area, and ~v~ is speed. All are in SI base units. I can't find a drag coefficient spec for the Ocean, I'll go with 0.3. The vehicle's height is 1.631 meters, its width is 1.995 meters. Sea level atmospheric density is about ~1.225 kg/m^s~. Multiplying, we get ~D=0.595 (kg/m) v^2 Nt.~

The other drag factor is rolling resistance. This is, to first order, linearly dependent only on the vehicle's weight (NOT mass!). The curb weight is 2,250 kg force or 22,065 Nt. Add, say, 250 kg of people and luggage for a traveling weight of 2,500 kg force or 24,516 Nt. We'll use 0.014 as the coefficient of rolling resistance, resulting in a rolling resistance of 343 Nt. The result is a total drag of ~D=0.595 (kg/m) v^2+343 Nt~.

Next, power (work/time) is force times speed, so, at 13.41 meters/second, we need ~((0.595*13.41^2)+343)*13.41~ or 6,034 Watts or 8.09 horsepower. This is surprisingly small but, to first order, I'm confident that it's close. Call it 7 kW for our purposes.

Then, we'll assume the electric motor operates at 95% efficiency and that the drivetrain is 85% efficient, so we need 6,352 watts from whatever energy source we're utilizing. Now, 1,500 miles at 30 m.p.h. will take 50 hours or 180,000 seconds. And power times time is energy so the Ocean's solar panel will need to deliver 6,352 watts * 180,000 seconds, 1.14*10^9 joules, or 317 kWh. OK, can the panel on the Ocean's roof deliver 317 kWh in a year?

I'll estimate that the dimensions of the panel are 1.5 meters X 3 meters, or 4.5 m^2. In my Southern California area, the average solar insolation is about 5 kWh/(day*meter^2). This has to be reduced because the panel on the Ocean sits horizontally rather than following the sun. We'll use 50%, so if the Ocean sits outside in the sun all day, we might average 11.25 kWh delivered to the panels. Next, we'll estimate that the panels are 18% efficient, so about 739 kWh ~(11.25*0.18*365)~ are delivered to either the motor or the battery pack over the course of a year. And here, we're assuming that either the car is in motion and the panels are delivering energy to the motor or that there is capacity in the battery pack to accept the energy.

Now, speeds above 30 m.p.h. will hurt more than those below will help due to the dependence of drag on the square of speed (refer to plot at right). And this doesn't account for use of accessories, losses due to climbing hills (not all the gravitational potential energy is regained on the downhill), and stopping and starting (even regenerative braking doesn't recapture all of the kinetic energy). It doesn't include being blocked by buildings and trees, and many other factors. And Minnesota, New York, and other Northern states don't receive the insolation of Southern California. That said, I can't say that the claim is irresponsibly exaggerated so, using the Mythbusters' scale, I'll call it plausible.

How "Real" is the Covid-19 Pandemic?

Yes, it's been a long time. No excuses. But, here we go. No one will dispute that the arrival of Covid-19 has disrupted almost every facet of life in every corner of the world. And yet, just as in almost every aspect of life in the United States these days, Covid-19 has become a political battlefield. As would be expected, the right considers that mask mandates, vaccine mandates, quarantines, lockdowns, and other measures imposed by various governments at all levels are an infringement on freedom, and useless at best and counterproductive at worst. And the left characterizes the right as conspiratorial, intransigent, destructive to society and more. They consider that the measures railed against by the right are common sense, effective measures and that compliance with such measures is necessary for the greater societal good, albeit with serious negative collateral damage.

I'm not an epidemiologist, virologist, statistician, doctor of any type, or public health expert (whatever that may mean). But it seemed to me that it should be possible to, at least, determine if a real thing has happened. In trying to understand the data that's available, one can find numbers for cases, infections, death rates, deaths attributed to Covid-19, positivity rate and many others. However, the one number in which I have at least some confidence is the simple number of deaths. Death certificates are a binary data point - someone died or did not.

I use the Human Mortality Database, a database that is updated weekly and has all cause deaths for 38 countries, separated into age groups. One can download the current data in spreadsheet form. The U.S. data goes back to 2015 and is sourced from the CDC. I started downloading this data most weeks over the last couple of years. In the beginning, I only wanted to see if there was a noticeable increase in overall ("all-cause") deaths. Below is a chart of this data from the beginning of the database through the first week of 2022 (the data is a few weeks behind as reports are gathered). Note that it is NOT zero scaled.

The abscissa is the number of weeks since the beginning of data (2015) through week one of 2022. The ordinate is the total number of deaths for each week in the United States. You'll note some interesting points. Among them is the very clear annual periodicity. Also, midway in the chart, you can see the evidence of the very bad flu season in the winter of 2017 - 2018. Finally, the very high numbers at the right end of the chart begin, when one would expect the numbers to begin falling in accordance with the periodicity in the spring of 2020, to climb in fairly spectacular fashion.

The next chart shows each year as its own set of points, though I didn't include all years as the chart is already busy enough. I included 2017 through 2022. Again, the ordinate is not zero scaled.

It's easy to see that there the data is very consistent by year for 2017, 2018, and 2019 (though the 2017 - 2018 flu season is clearly visible). The various "waves" (initial wave in the spring of 2020, the summer wave of that year, the Delta variant wave, and the Omicron variant wave) are also clearly visible.

That led me to think that it would be easy to estimate what people refer to as "excess deaths" attributable to the pandemic. Now, as an aside, I recognize that many excess deaths were not directly due to Covid-19 infections. There have been deaths due to people not getting diagnosis or treatment for heart disease, cancer, kidney disease, etc. due to lockdowns or lack of hospital facilities. There have been suicides and drug overdoses due to depression and idle time. There have been deaths that are likely attributable to vaccinations. I haven't checked, but I wouldn't be surprised to find that automobile fatalities rose due to much less traffic on freeways and consequent higher speeds leading to more severe accidents. Nevertheless, it's clear that the pandemic has greatly increased the number of deaths beyond what would have previously been expected.

I took an extremely naive approach. It's clear that, even if nothing else changes, there will be more deaths as population increases. So, for each week, I took the mid-year population for each of the years of 2017, 2018, and 2019 and multiplied the deaths for that week and year by the ratio between that number and the equivalent number in 2020, 2021, and 2022. I then subtracted the mean of the adjusted deaths for the week in 2017, 2018, and 2019 from the 2020, 2021, and 2022 deaths for that week number. I estimated the result to be the number of excess deaths in that week for that year. I then totalled the numbers for each year, resulting in the following:

Year	Excess deaths
2020	504,562
2021	571,400
2022	8,946

Based on this, admittedly rather superficial, analysis, it's reasonable to estimate that on the order of 1,085,000 people have died beyond what would have been expected prior to the pandemic. This number compares quite well with other estimates I've seen of Covid-19 deaths.

I'll make another post with some breakdowns by age but, suffice it to say for now, that the numbers are very heavily skewed toward the highest age groups. So, in terms of lost years of life, the numbers above overstate the situation. Nevertheless, even as recently as the first week of this year, we're still significantly above the adjusted mean of more normal years. If we think that the very old and infirm were already not far from their demise and thus, the pandemic, in a sense, culled the herd, we'd expect a time to come post-pandemic when the total deaths drop noticeably below the adjusted mean for more normal years. I see no sign of that at this time.

The Celera 500L

Image credit: Otto Aviation

As anyone who's spent any time reading my publications knows, I'm a pilot and have been involved (non-commercially) in aviation for over 40 years. As such, I keep track of developments in the field. Thus, I was fascinated by the news of the Celera 500L by Otto Aviation. The performance claims made for the airplane are spectacular, to say the least.

Otto claims that the aircraft has a range of 4,500 miles (statue rather than nautical as far as I can tell) at a speed of 460 m.p.h. (again, statute m.p.h., not knots, as far as I can tell). It's stated that the Celera 500L does so while burning "8 times lower fuel consumption" and "5-7 times reduction in operating cost." For those who don't follow general aviation (that is, all aviation other than air carriers and military), the claimed speed is well above the speeds of high end turboprop business aircraft and not far below those of business jets. For example, the King Air B360ER turboprop achieves 349 m.p.h. in high-speed cruise, the Cessna Latitude business jet has a maximum speed of 512 m.p.h. But the range of the King Air is 3,092 miles and that of the Longitude is 3,105 miles. Otto claims that the Celera 500L achieves 18 - 25 miles per gallon fuel economy. What might be considered a comparable small jet, the Embraer Phenom 300E will get, perhaps, 5 miles per gallon. 

Otto states that the Celera 500L achieves these spectacular specifications due to a design for laminar flow over both the wings and the fuselage. Laminar flow is a fluid flow state wherein there is minimal mixing between layers and the flow is "smooth" rather than turbulent. It is a flow regime that minimizes drag, and all (well, most) aircraft designers seek to maximize laminar flow. It is a well-known phenomenon and no aeronautical engineer looks at Celera's web site or the many web sites and YouTube channels featuring the Celera 500L and slaps him or herself on the forehead and says "laminar flow, why didn't I think of that?"

Image credit: RED Aircraft

 The engine for the Celera 500L is the "RED A03" by RED Aircraft, GmbH. This is a compression ignition (i.e., diesel) engine. The engine is stated to be a V12 configuration with each six cylinder side operating independently. It's also stated to be all-aluminum in construction. Per RED's website, the engine is approved by both the FAA and EASA (the European Union Aviation Safety Agency). While diesel engines are typically very efficient due to the high compression ratio required for combustion of the fuel-air mixture, they are also typically heavy as a consequence of the strength required due to that high compression ratio. I'm not aware of any other all-aluminum compression engines.

As can be seen in the photo above, the aircraft is a "pusher" configuration, the propeller is behind the aircraft and pushes the airplane rather than the standard configuration wherein the propeller(s) pulls the airplane. This configuration has the advantage of letting the wings "see" a flow undisturbed by prop wash. Of course, the propeller is composed of airfoils as well, and they now see air disturbed by the wings and the fuselage, though not nearly so much as the propeller causes, especially given the laminar flow claim. It's also the case that the propeller is more subject to damage from ice shed from the wings in icing conditions and, at the altitudes stated in Otto Aviation's material, icing is certainly possible.

With all of that said, what is the likelihood that Otto Aviation can live up to their claims for the Celera 500L? It's difficult to do a thorough analysis given that nearly 100% of the numbers given consist only of those claims. The only hard data I could find is the takeoff power of the engine. They do claim that drag has been reduced by approximately 59% in comparison to similar sized aircraft. What can we infer from this?

With thanks to "Simplex11" at aviation stack exchange for the approach, we'll use the "59% lower drag" claim along with figures for my airplane, a Cessa 441. My airplane cruises at about 345 m.p.h., using 450 horsepower per side in cruise, or a total of 900 horsepower. The Celera 500L cruises at 460 m.p.h. and a drag of 0.41 ("59% less") times that of a typical aircraft.

We then have that ~D1=\frac{1}{2}C_{D1}\rho S_{D1}V_{D1}^{2}~ and ~D2=\frac{1}{2}C_{D2}\rho S_{D2}V_{D2}^{2}~, where ~D1~ is the total drag on the Celera 500L and D2 is the total drag on the C441. The Cs, Ss, and Vs are the drag coefficients, reference areas, and velocities of the Celera 500L and the C441 respectively, and ~\rho~ is air density. We can then combine these to get ~\frac{D1}{D2}=0.41(\frac{V1}{V2})^{2}~. Then, we know that power is speed times force, so we have ~P1=D1V1~ and ~P2=D1V2~ and so ~\frac{P1}{P2}=0.41(\frac{V1}{V2})^{3}~. Plugging in numbers, we can calculate that the Celera 500L needs something like 875 horsepower* to achieve the claimed speed. These numbers are, of course, approximate, but note that the maximum continuous power of the RED A03 is 460. And, as a reminder, this assumes that the "59% reduction in drag" is true.

What about fuel economy? Otto claims "18 - 25 m.p.g." (again, as above, I assume statute miles). The fuel economy can be calculated from the speed, power, and energy density of Jet-A fuel. Should the hordes demand that I show my work, I'll show the calculations but, having already produced an equation dense post, I'll just give results. And, as above, these are approximations based on sparse information. If the power requirement calculated above is correct, the Celera 500L would achieve something like 11.5 m.p.g. If, on the other hand, the speed of 460 m.p.h. can be achieved with the 460 maximum continuous power of the RED A03 engine then a figure of about 21.8 m.p.g. could be achieved. But, as I indicate above, it does not seem plausible to travel at 460 m.p.h. with less than 875 horsepower. And, yet again, all of this is contingent on the Celera 500L achieving the claimed 59% drag reduction. Time will likely tell.

Further questions are raised by Otto's claim that "The Celera 500L has a glide ratio of 22:1 (typical GA aircraft of similar size have a glide ratio of < 9:1)." While I can't question the 22:1, the "<9:1" claim is absolutely false. My airplane has a glide ratio of 14.8:1. Many business aircraft do better. Possibly such airplanes as the Cessna 172 Skyhawk (a four seat, fixed gear airplane with wing struts) may have glide ratios in the range mentioned by Otto, but no light jets or turboprops do. When falsehoods are stated as facts on web sites, I have to question all of the information to be found there.

And finally, in the immortal words of Carl Sagan, "extraordinary claims require extraordinary evidence." Otto Aviation's claims for the performance specifications of the Celera 500L are, without a doubt, extraordinary and I've seen no evidence, let alone extraordinary evidence.

Otto Aviation has completed their A round of financing. They anticipate B round financing in 2021 and 2022, during which they plan to begin FAA certification. In 2023 to 2025, their web site calls for C round financing and the beginning of manufacturing and first commercial deliveries. Based on my strong skepticism, I'm not a participant in Otto's financing!

*It should be noted that Simplex11's calculations are slightly different and yield a larger power requirement for the Celera 500L.

More on Eviation Alice

Image credit: Jasper Juinen/Bloomberg

I published a post on the "Alice," a fully electrically powered airplane being designed and built by the Israeli Company "Eviation." The Alice is being promoted as a "9+2" airplane, that is, two pilots flying nine passengers. It is claimed that the airplane will have a range of 650 miles at a speed of 260 knots. Cape Air had made a "double digit" (actual quantity not stated that I can find) order (the "launch order") for the Alice. I expressed considerable skepticism, particularly with respect to the battery pack and to the claimed range.

Image credit: Eviation

The latest news is that two more airlines have placed orders for the Alice, bringing the total ordered to over 150. So three airlines have made substantial orders and several well-known OEM vendors (Honeywell, Bendix, Siemens, Hartzell) are providing equipment for the airplane. Is my skepticism unwarranted?

In my previous post, because the parameters needed for a direct calculation were not given anywhere that I could find, I got my estimate for the range by comparing the energy stated for the battery pack in the Alice to the energy in the Jet A fuel in a Pilatus PC-12. The number I came up with was 258 miles, far short of the claimed 650 and likely a deal breaker for the orders. Can I derail a multi-million dollar endeavor by back of the envelope calculations on an obscure blog?

There are two factors contributing to my vagueness on the range calculations: actual energy available in the battery pack; and the drag force on the airplane in flight. A rudimentary dimensional analysis show that the range is directly proportional to energy available and inversely proportional to drag, that is, ~R\propto\frac{E}{F_{d}}~, where R is range, E is total energy available, and F_d is the drag force. This, of course, makes intuitive sense but, at the moment, I don't know the proportionality constant.

Eviation claims a capacity of 900 kWh in the battery pack, though it's not at all clear how this can be accomplished. Eviation states that they use Li-Ion chemistry and also make a claim for a proprietary aluminum-air chemistry. I don't see how the aluminum-air chemistry can be feasible in an airplane, but who knows? Per the Wikipedia page for the Alice, the aluminum-air battery will be used on a later evolution of the Alice.

But, for Li-Ion chemistry, the current state of the art is about 260 watt hours/kilogram. At this energy density, 900 kWh would require 3,460 kg, or a bit under 7,630 pounds. At a maximum takeoff weight of 6,350 kg, this leaves 2,890 kg or 6,371 pounds for airframe, power plants, passengers, pilots, and baggage. Again, I don't have any data on the weights of the airframe and power plants. And, in my effort to be generous, the 260 watt hours/kilogram doesn't include the pack.

As to drag, I found a site that stated that the "L/D" (lift to drag) ratio of the Alice to be 24. This is likely to be the maximum L/d. Now, in cruise flight, lift is equal to weight. We'll assume a full load, giving a weight of 6,350 kg or 62,230 Nt. With a L/D ratio of at a maximum of 24, drag would be at least 2,593 Nt. Clearly, this is generous to Alice but we'll use it. Now, drag=thrust in straight and level flight, so we're looking at a thrust delivered by the propeller of 2,593 Nt. And P=F*V where P is power, F is force (thrust) and V is speed. So we have P=2,593 Nt * 134 m/s (260 knots converted to meters/second) = 346,817 watts or 347 kilowatts required in cruise.

Now, a constant speed propeller may be about 90% efficient, so the electric motors must deliver 347/.9 = 385 kilowatts. We have 900 kilowatt hours available so that's 900 kWh/385 kW = 2.34 hours. IFR (instrument flight rules) flight requires a minimum 45 minute (0.75 hour) reserve (we'll hold it to the minimum though I doubt a procedures manual for an air carrier operator would do so, and my policy is to never fly into my last hour of fuel) so we now have 1.59 hours or an hour and 35 minutes of battery capacity for cruise. Note: the specifications page for the Alice has been updated since my earlier post and gives some numbers that aren't too far off of mine, but I'm sticking with mine because they're derived from Eviation's performance claims.

I'm ignoring climb and this is generous because more power is used in climb (though that may not be the case for an electric airplane) and is at a slower speed (in all airplanes). So we can cruise at 260 knots for an hour and 35 minutes for a range estimate of 413 nautical miles or 475 statute miles. And, given the minimal reserve and ignoring climbing at low speed, this is generous.

I will agree that my rough calculations result in a range estimate higher than that I got using the Pilatus comparison, but it's significantly less than the 650 miles claimed by Eviation (I can't determine whether this is nautical or statute miles).

And this might be practical for a flight from, say, John Wayne Airport in Orange County to Las Vegas McCarran International, a distance of 226 (statute) miles, or Kennedy to Dulles, a distance of 228 (statute) miles. You wouldn't want to fly it to Reagan Airport because flight to

or from Reagan requires an air marshall and now you've lost 11% of your paying passenger capacity. There are many such city pairs. At right are 300 statute mile radius circles centered on New York City, Chicago, Houston, and Los Angeles. Such city pairs  as NYC - Philadelphia, Chicago - Detroit, Houston - Dallas, and Los Angeles - Las Vegas seem to be feasible.

And the economics seem favorable. 900 kWh of electricity probably would cost something on the order of $100, and a crew of two might be $100/hour. Maintenance on electric motors is much less demanding than on turbine or piston internal combustion engines.

So, taking everything into consideration, and if the data that's been provided so far is accurate, I think there may be a role for such an airplane.

Am I safe to break in?

I saw a commercial for the Google Home Speaker in which the spokesperson was touting the speaker's ability to scare off burglars by playing the sound of a barking dog. I realize there are multiple systems out there to achieve this but that's not my point. I started thinking about this in terms of Bayesian inference. If I'm a burglar and, during an attempted intrusion, I hear the sound of a vicious dog, what's the likelihood that there's actually a dog ready to attack?


This is analogous to the archetypal example of Bayesian inference wherein the likelihood of actual breast cancer is evaluated in light of a positive mammogram ("test"). The "test" in this case would be listening for the sound of a barking dog prior to breaking into a home. A true positive would be hearing a barking dog when there is such a dog (analogous to a positive mammogram and actual breast cancer). A false positive would be hearing a barking dog when none exists, i.e., when the Home Speaker sounds a dog alarm but there is no dog.

In order to come up with an estimate of my safety when breaking in should I hear a barking dog, I need to have an estimate for:

• The fraction of homes have appropriate (i.e., big and scary) dogs (analogous to how many women have breast cancer).
• The fraction of homes have a barking dog sound generator (analogous to a false positive).
• The fraction of the time that, if there is a big, scary dog in the house, it will bark and I will hear it (analogous to a true positive).

I'll estimate that 40% (0.4 fraction) of homes have a dog, and 30% of those are of a size that would deter me. I'll estimate that 2% (0.02 fraction) of homes have a dog sound generator. I'll estimate that 90% (0.9 fraction) that I case a home with an appropriate dog, that dog will bark and I will hear it.

In the table below, I've shown that 12% of homes have a big (barking) dog, and 88% do not. When I hear a big, scary dog, I'm in the "Test pos" row. The 0.108 entry is the 0.12 fraction of homes with a big, scary dog * the 0.9 fraction that the dog will bark and I will hear it. The 0.0176 entry is the 0.88 fraction of homes with no big, scary dog * the 0.02 fraction of homes with a barking dog sound generator.

	Actual big dog	No actual big dog
	0.12	0.88
Test pos (heard barking big dog)	0.108	0.0176
Test neg (didn't hear barking big dog)	0.012	0.8624

Now, the probability of a true positive (I hear a big, scary dog and there's actually one in the house) is the number of true positives divided by the total number of positives, or 0.108/(0.108+0.0176)=0.8599 or about 86%. Of course, this number will vary, depending on the actual values for the needed parameters but I think that this is in the ballpark.

Moral of the story: If I'm intending to burgle a house and I hear a big, scary dog, I'd best move on.

Solar energy is GREAT but...

Image credit: 4Patriots, LLC

As is pretty clear from previous posts (and despite my current vehicle, airplane, and travel itinerary), I'm a very big fan of renewable energy. And thus, also a fan of solar power. But sometimes solar isn't appropriate for a particular application. To the left is a collage from 4Patriots, LLC, let's see if this device is in the "inappropriate" category.

This is a charger for such electronics as cell phones, tablets, etc. Is this an appropriate application? Lithium ion battery in the device is specified on the advertising web site as storing 8,000 mAh (milliamp hours) or 8 amp hours. The solar array is specified as delivering 1.5 watts.

Let's first see if the 1.5 watts is reasonable. To do so, we'll need to estimate the size. Using the measuring tool in Tracker Video Analysis and Modeling Tool, I estimate that there is an area of about 0.0068 m^2 of solar cells. This is actually generous as I've used to whole area of the face of the charger with the cells. And, during bright sunlight at my location if I hold the device facing the sun I can count on about 350 w/m^2 over the course of a day of actual insolation. Let's give the solar cells an estimated efficiency of 18% (again, generous) and figure the charging can take place at the rate of 350*.18*0.0068=0.42 watts. Well, if we use a full 1000 watts/m^2, we get 1.22 watts. I'd say that the 1.5 specification is an exaggeration at best.

Well, let's go with the 1.2 as a compromise between the 1.5 watts claimed and the 0.42 watts by my best estimate. And let's think about an iPhone 8, standard model. Such a phone has a battery capacity of 1.821 amp hours at 3.7 volts. This means it will deliver 1.821 amps at 3.7 volts for 1 hour, or 3,600 seconds. Since volts * amps is watts, we have 6.7377 watts. Since joules of energy are the same as watt seconds, we can use 3,600 seconds * 6.7377 watts to determine that the iPhone 8 battery stores 24,256 joules. Charging at 1.2 watts, or 1.22 joules/second, we find that it will take 24,256 joules/1.2 watts = 20,213 seconds or 5.6 hours to go from complete discharge to full charge.

Of course, if you're in the middle of nowhere with no other way to charge your phone and you're completely discharged, you won't need to wait for 100% charge to use your phone. Below is a graph of time needed as a percentage of charge from complete discharge. You can click on it to enlarge. Keep in mind that this is specific to the iPhone 8, other phones with different (and typically larger) batteries will be different. The new Samsung Galaxy Note 10+, for example, will carry a 4,300 mAh battery pack, well over twice as large as that in the iPhone 8, and the Apple iPhone XS Max sports a 3,174 mAh battery pack. And, of course, charging is a non-linear process so don't use this as a "to the minute" guide. It's more of a very best case scenario.

Still, this is actually a lot better than I'd anticipated when I started. It would take about an hour to go from complete discharge to 20%, certainly enough to make a few calls or send some texts. Of course it assumes perfect efficiency in the charger circuit but the efficiency is likely to be fairly high. Even if we use the low end estimate for the area of the solar array, the device will still give usable energy in a not too extreme amount of time, though if we use the more conservative estimates for insolation and charging on a state of the art, top of the line phone, we'd be looking at something more like 7 hours to go from complete discharge to 20%. Nevertheless, unlike the two previously published posts I linked above, this seems to be a good use of a small solar panel.