Tag Archives: cars

Hydrogen powered trucks and busses

With all the attention to electric cars, I figure that we’re either at the dawn of electric propulsion vehicles or of electric propulsion vehicle hype. Elon Musk’s Tesla motor car company stock is now valued at $59 B, more than GM or Ford despite the company having massive losses and few cars. The valuation, I suspect, has to do with the future and autonomous vehicles. There are many who expect self-driving vehicles will rule the road, but the form is uncertain. In this space, i suspect that hydrogen-battery hybrids make more sense than batteries alone, and that the first large-impact uses will be trucks and busses — vehicles that go long distance on highways.

Factory floor, hydrogen fueling station for plug-power forklifts. Plug FCs reached their 10 millionth refueling this January.

Factory floor, hydrogen fueling station for fuel cell forklifts. This company’s fuel cells have had over 10 million refuelings so far.

Currently there are only two bands of autonomous vehicles available in the US, the Cadillac CT6, a gasoline powered car, and the Tesla. Neither work well except on highways because the number of highway problems are fewer than the number of city problems and only the CT6 allows you to take your hands off the wheel — see review here. To me, being able to take your hand off the wheel is the only real point of autonomous control, and if one can only do this only on the highway, that’s acceptable. Highway driving gets quite tiring after the first hundred miles or so, and any relief is welcome.

Tesla’s battery cars allow for some auto-driving on the highway, but you can’t take your hand off the wheel or the car stops. That battery cars compete at all for highway driving, I suspect, is only possible because the US government highly subsidizes the battery cost. Musk then hides the true cost among the corporate losses. Without this, hydrogen – fuel cell vehicles would be cheaper, I suspect, while providing better range, see my calculation here. Adding to the advantage of hydrogen over batteries, the charge time for hydrogen is much faster. Slow charge times are a real drawback for highway vehicles traveling any significant distances. While hydrogen fuel isn’t cheap — it’s becoming cheaper and is now about double the price of gasoline on a per mile basis. The advantage over gasoline is it provides pollution-free, electric propulsion, and this is well suited to driverless vehicles. Both gasoline and battery vehicles can have odd acceleration issues, e.g. when the gasoline gets wet, or the battery gets run down. And it’s not like there are no hydrogen fueling stations. Hydrogen, fuel-cell power has become a major competitor for fork-lifts, and has recently had its ten million refueling in that application. The same fueling stations that serve the larger fork-lift users could serve the self-driving truck and bus market.

For round the town use, hydrogen vehicles could still use batteries, and the combined vehicle can have very impressive performance. A Dutch company has begun to sell kits to convert Tesla model S autos to combined battery + hydrogen. With these kits, they boast a 620 mile (1000 km) range instead of the normal 240 miles. See the product here.  On the horizon, in the self-driving fuel cell market, Hyundai has debuted the “Nexo” with a range of 370 miles. Showing off the self-driving capability, Nexos were used to carry spectators between venues at the Pyongyang olympics. Japanese competitors, the Toyota Mirai (312 miles) and the Honda Clarity Fuel Cell (366 miles) can be expected to provide similar capabilities.

Cadillac CT6 with supercruise. An antonymous vehicle that you can buy today that allows you to take your hand off the wheel.

Cadillac CT6 with supercruise. An antonymous vehicle that you can buy today that allows you to take your hand off the wheel.

The reason I believe in hydrogen Trucks and Busses more than cars is the difficulty of refueling, Southern California has installed some 36 public hydrogen refueling stations at last count, but that’s too few for most personal car use. Other states have even fewer spots where you can drive up and get hydrogen; Michigan has only two. This does not matter for a commercial truck or bus because they go between fixed depots and these can be fitted with hydrogen dispensers as found for forklifts. It’s possible trucks can even use the same dispensers as the forklifts. If one needs a little extra range one can add a “hydrogen Jerry can” to provide an extra kg of H2 to provide 20-30 miles of emergency range. I do not see electric vehicles working as well because the charge times are so slow, the range so modest, and the electric power needs so large. To charge a 100 kWhr battery in an hour, the charge station would have to have an electric feed of 100 kW, about as much as a typical mall. With 100A, 240 V, the most you can normally get, expect a 4 1/2 hour charge.

The real benefit for hydrogen trucks and busses is autonomy. Being able to run the route without major input from a driver. So why not gasoline, as with the Cadillac? My answer is simplicity. If you want driverless simplicity, you want electric or hydrogen. And only hydrogen provides the long-range, fast fueling to make the product worthwhile.

Robert Buxbaum March 12, 2018. My company, REB Research provides hydrogen purifiers and hydrogen generators.

Keeping your car batteries alive.

Lithium-battery cost and performance has improved so much that no one uses Ni-Cad or metal hydride batteries any more. These are the choice for tools, phones, and computers, while lead acid batteries are used for car starting and emergency lights. I thought I’d write about the care and trade-offs of these two remaining options.

As things currently stand, you can buy a 12 V, lead-acid car battery with 40 Amp-h capacity for about $95. This suggests a cost of about $200/ kWh. The price rises to $400/kWh if you only discharge half way (good practice). This is cheaper than the per-power cost of lithium batteries, about $500/ kWh or $1000/ kWh if you only discharge half-way (good practice), but people pick lithium because (1) it’s lighter, and (2) it’s generally longer lasting. Lithium generally lasts about 2000 half-discharge cycles vs 500 for lead-acid.

On the basis of cost per cycle, lead acid batteries would have been replaced completely except that they are more tolerant of cold and heat, and they easily output the 400-800 Amps needed to start a car. Lithium batteries have problems at these currents, especially when it’s hot or cold. Lithium batteries deteriorate fast in the heat too (over 40°C, 105°F), and you can not charge a lithium car battery at more than 3-4 Amps at temperatures below about 0°C, 32°F. At higher currents, a coat of lithium metal forms on the anode. This lithium can react with water: 2Li + H2O –> Li2O + H2, or it can form dendrites that puncture the cell separators leading to fire and explosion. If you charge a lead acid battery too fast some hydrogen can form, but that’s much less of a problem. If you are worried about hydrogen, we sell hydrogen getters and catalysts that remove it. Here’s a description of the mechanisms.

The best thing you can do to keep a lead-acid battery alive is to keep it near-fully charged. This can be done by taking long drives, by idling the car (warming it up), or by use of an external trickle charger. I recommend a trickle charger in the winter because it’s non-polluting. A lead-acid battery that’s kept at near full charge will give you enough charge for 3000 to 5000 starts. If you let the battery completely discharge, you get only 50 or so deep cycles or 1000 starts. But beware: full discharge can creep up on you. A new car battery will hold 40 Ampere-hours of current, or 65,000 Ampere-seconds if you half discharge. Starting the car will take 5 seconds of 600 Amps, using 3000 Amp-s or about 5% of the battery’s juice. The battery will recharge as you drive, but not that fast. You’ll have to drive for at least 500 seconds (8 minutes) to recharge from the energy used in starting. But in the winter it is common that your drive will be shorter, and that a lot of your alternator power will be sent to the defrosters, lights, and seat heaters. As a result, your lead-acid battery will not totally charge, even on a 10 minute drive. With every week of short trips, the battery will drain a little, and sooner or later, you’ll find your battery is dead. Beware and recharge, ideally before 50% discharge

A little chemistry will help explain why full discharging is bad for battery life (for a different version see Wikipedia). For the first half discharge of a lead-acid battery, the reaction Is:

Pb + 2PbO2 + 2H2SO4  –> PbSO4 + Pb2O2SO4 + 2H2O.

This reaction involves 2 electrons and has a -∆G° of >394 kJ, suggesting a reversible voltage more than 2.04 V per cell with voltage decreasing as H2SO4 is used up. Any discharge forms PbSO4 on the positive plate (the lead anode) and converts lead oxide on the cathode (the negative plate) to Pb2O2SO4. Discharging to more than 50% involves this reaction converting the Pb2O2SO4 on the cathode to PbSO4.

Pb + Pb2O2SO4 + 2H2SO4  –> 2PbSO4 + 2H2O.

This also involves two electrons, but -∆G < 394 kJ, and voltage is less than 2.04 V. Not only is the voltage less, the maximum current is less. As it happens Pb2O2SO4 is amorphous, adherent, and conductive, while PbSO4 is crystalline, not that adherent, and not-so conductive. Operating at more than 50% results in less voltage, increased internal resistance, decreased H2SO4 concentrations, and lead sulfate flaking off the electrode. Even letting a battery sit at low voltage contributes to PbSO4 flaking off. If the weather is cold enough, the low concentration H2SO4 freezes and the battery case cracks. My advice: Get out your battery charger and top up your battery. Don’t worry about overcharging; your battery charger will sense when the charge is complete. A lead-acid battery operated at near full charge, between 67 and 100% will provide 1500 cycles, about as many as lithium. 

Trickle charging my wife's car. Good for battery life. At 6 Amps, expect this to take 3-6 hours.

Trickle charging my wife’s car: good for battery life. At 6 Amps, expect a full charge to take 6 hours or more. You might want to recharge the battery in your emergency lights too. 

Lithium batteries are the choice for tools and electric vehicles, but the chemistry is different. For longest life with lithium batteries, they should not be charged fully. If you change fully they deteriorate and self-discharge, especially when warm (100°F, 40°C). If you operate at 20°C between 75% and 25% charge, a lithium-ion battery will last 2000 cycles; at 100% to 0%, expect only 200 cycles or so.

Tesla cars use lithium batteries of a special type, lithium cobalt. Such batteries have been known to explode, but and Tesla adds sophisticated electronics and cooling systems to prevent this. The Chevy Volt and Bolt use lithium batteries too, but they are less energy-dense. In either case, assuming $1000/kWh and a 2000 cycle life, the battery cost of an EV is about 50¢/kWh-cycle. Add to this the cost of electricity, 15¢/kWh including the over-potential needed to charge, and I find a total cost of operation of 65¢/kWh. EVs get about 3 miles per kWh, suggesting an energy cost of about 22¢/mile. By comparison, a 23 mpg car that uses gasoline at $2.80 / gal, the energy cost is 12¢/mile, about half that of the EVs. For now, I stick to gasoline for normal driving, and for long trips, suggest buses, trains, and flying.

Robert Buxbaum, January 4, 2018.

The hydrogen jerrycan

Here’s a simple invention, one I’ve worked on off-and-on for years, but never quite built. I plan to work on it more this summer, and may finally build a prototype: it’s a hydrogen Jerry can. The need to me is terrifically obvious, but the product does not exist yet.

To get a view of the need, imagine that it’s 5-10 years in the future and you own a hydrogen, fuel cell car. You’ve run out of gas on a road somewhere, per haps a mile or two from the nearest filling station, perhaps more. You make a call to the AAA road-side service and they show up with enough hydrogen to get you to the next filling station. Tell me, how much hydrogen did they bring? 1 kg, 2 kg, 5 kg? What did the container look like? Is there one like it in your garage?

The original, German "Jerry" can. It was designed at the beginning of WWII to help the Germans to overrun Europe.

The original, German “Jerry” can. It was designed at the beginning of WWII to help the Germans to overrun Europe. I imagine the hydrogen version will be red and roughly these dimensions, though not quite this shape.

I figure that, in 5-10 years these hydrogen containers will be so common that everyone with a fuel cell car will have one, somewhere. I’m pretty confident too that hydrogen cars are coming soon. Hydrogen is not a total replacement for gasoline, but hydrogen energy provides big advantages in combination with batteries. It really adds to automotive range at minimal cost. Perhaps, of course this is wishful thinking as my company makes hydrogen generators. Still it seems worthwhile to design this important component of the hydrogen economy.

I have a mental picture of what the hydrogen delivery container might look like based on the “Jerry can” that the Germans (Jerrys) developed to hold gasoline –part of their planning for WWII. The story of our reverse engineering of it is worth reading. While the original can was green for camouflage, modern versions are red to indicate flammable, and I imagine the hydrogen Jerry will be red too. It must be reasonably cheap, but not too cheap, as safety will be a key issue. A can that costs $100 or so does not seem excessive. I imagine the hydrogen Jerry can will be roughly rectangular like the original so it doesn’t roll about in the trunk of a car, and so you can stack a few in your garage, or carry them conveniently. Some folks will want to carry an extra supply if they go on a long camping trip. As high-pressure tanks are cylindrical, I imagine the hydrogen-jerry to be composed of two cylinders, 6 1/2″ in diameter about. To make the rectangular shape, I imagine the cylinders attached like the double pack of a scuba diver. To match the dimensions of the original, the cylinders will be 14″ to 20″ tall.

I imagine that the hydrogen Jerry can will have at least two spouts. One spout so it can be filled from a standard hydrogen dispenser, and one so it can be used to fill your car. I suspect there may be an over-pressure relief port as well, for safety. The can can’t be too heavy, no more than 33 lbs, 15 kg when full so one person can handle it. To keep the cost and weight down, I imagine the product will be made of marangeing steel wrapped in kevlar or carbon fiber. A 20 kg container made of these materials will hold 1.5 to 2 kg of hydrogen, the equivalent of 2 gallons of gasoline.

I imagine that the can will have at least one handle, likely two. The original can had three handles, but this seems excessive to me. The connection tube between two short cylinders could be designed to serve as one of the handles. For safety, the Jerrycan should have a secure over-seal on both of the fill-ports, ideally with a safety pin latch minimize trouble in a crash. All the parts, including the over- seal and pin, should be attached to the can so that they are not easily lost. Do you agree? What else, if anything, do you imagine?

Robert Buxbaum, February 26, 2017. My company, REB Research, makes hydrogen generators and purifiers.

Of grails: holy, monetary, and hip

The holy grail is pictured as either a cup or a plate that Jesus used at the Last supper. It either held the wine or the bread upon which he said: this wine is my blood and this bread (or cake*) is my body. The British have a legend, or made-up story, that this cup or plate made it to England somehow, and because of divine grace was revealed to king Arthur. The story is important because it underlies the idea of divine grace favoring the English crown  — that God favors England, and English royalty over other nations and the common folk.

A George III coin, engrailed for decoration and to keep people from carving off silver.

A George III coin, engrailed for decoration and to keep people from carving off silver.

What makes this item holy is that, by oral tradition, but not the gospels, Jesus’s blood was saved into the same plate or cup that he’d used at the last supper, but what about this plate or cup makes it a grail.

As it turns out, there are many unholy grails on runs into. The edges of many US coins are engrailed. That is, they are decorated with cut lines at the edges. They are there for decoration, and to make it unlikely that someone would cut off a piece. I suppose these coins are monetary grails, though I’ve never seen them described literally that way. They are engrailed, and one can presume that the holy cup or plate was engrailed the same way. Perhaps as decoration like on the coins, or perhaps for some aspect of use.

The grille on the front of a Ford is not only for decoration; it allows air to flow through. Some plates, and most broilers have grilles like this to that allow crumbs or gravy to drop through.

The front grille (or grill) on a Ford. It allows air to flow through. Broilers and some plates have through-slots like this; did The Grail?

The front end of most cars include a grille, or grill, an area cut all the way through to allow air to flow to the engine. Some plates and most barbecues are made this way to allow crumbs or blood from the barbecue to flow through. If this is flow through grill were the holy grail, it might have held Jesus’s bread, but not his wine or his blood.

And finally we come to an entirely modern type of grail, or grill, the one on the mouth of some rappers. The point is not entirely decorative, but to make one think more highly of the rapper. Clearly, a person with teeth like this, is a person to be respected. Clearly successful, the idea is make you think of the fellow as chosen by God to be a leader. There is a certain magic in wearing a grille.

Wholly Grilled, not the holly grail.

Wholly Grilled, but not the holly grail.

Robert Buxbaum, July 8, 2016. One of my Grad School chums, Al Rossi, tells me that, in the original Greek version of the gospels, Jesus says ‘this cake is my body.’  The normal version, ‘this bread’ comes from the Latin translation of St. Jerome. He also tells me there is no comment about this being Passover. As for how Jesus could celebrate passover with bread or cake and not matzoh, he claims it’s an example of having one’s cake and eating it too, as it were.

Alcohol and gasoline don’t mix in the cold

One of the worst ideas to come out of the Iowa caucuses, I thought, was Ted Cruz claiming he’d allow farmers to blend as much alcohol into their gasoline as they liked. While this may have sounded good in Iowa, and while it’s consistent with his non-regulation theme, it’s horribly bad engineering.

At low temperatures ethanol and gasoline are no longer quite miscible

Ethanol and gasoline are that miscible at temperatures below freezing, 0°C. The tendency is greater if the ethanol is wet or the gasoline contains benzenes

We add alcohol to gasoline, not to save money, mostly, but so that farmers will produce excess so we’ll have secure food for wartime or famine — or so I understand it. But the government only allows 10% alcohol in the blend because alcohol and gasoline don’t mix well when it’s cold. You may notice, even with the 10% mixture we use, that your car starts poorly on the coldest winter days. The engine turns over and almost catches, but dies. A major reason is that the alcohol separates from the rest of the gasoline. The concentrated alcohol layer screws up combustion because alcohol doesn’t burn all that well. With Cruz’s higher alcohol allowance, you’d get separation more often, at temperatures as high as 13°C (55°F) for a 65 mol percent mix, see chart at right. Things get worse yet if the gasoline gets wet, or contains benzene. Gasoline blending is complex stuff: something the average joe should not do.

Solubility of dry alcohol (ethanol) in gasoline. The solubility is worse at low temperature and if the gasoline is wet or aromatic.

Solubility of alcohol (ethanol) in gasoline; an extrapolation based on the data above.

To estimate the separation temperature of our normal, 10% alcohol-gasoline mix, I extended the data from the chart above using linear regression. From thermodynamics, I extrapolated ln-concentration vs 1/T, and found that a 10% by volume mix (5% mol fraction alcohol) will separate at about -40°F. Chances are, you won’t see that temperature this winter (and if you you do, try to find a gas mix that has no alcohol. Another thought, add hydrogen or other combustible gas to get the engine going.

Robert E. Buxbaum, February 10, 2016. Two more thoughts: 1) Thermodynamics is a beautiful subject to learn, and (2) Avoid people who stick to foolish consistency. Too much regulation is bad, as is too little: it’s a common pattern: The difference between a cure and a poison is often just the dose.

The french engineering

There is something wonderful about French Engineering. It is good, but different from US or German engineering. The French don’t seem to copy others, and very few others seem to copy them. Nonetheless French engineering managed to build an atom bomb, is a core of the Airbus consortium, and both builds and runs the fastest passenger trains on earth, the TGF, record speed 357 mph on the line between Paris and Luxembourg.

JULY 14, 2015 Students of the Ecole Polytechnique (the most prestigious engineering school in France march in the Paris Bastille Day military parade. commemorating the storming of the Bastille in 1789.  (Photo by Thierry Chesnot/Getty Images).

JULY 14, 2015 Female engineering students of the Ecole Polytechnique, march in the Paris Bastille Day military parade. (Photo by Thierry Chesnot/Getty Images).

France was almost the only country to sell Israel weapons for the first 20 years of its existence, and as odd as the weapons they sold were, they worked. The Mirage jet was noted for short-range and maneuverability; in 1967, they handily defeated Egypt and Syria’s much larger force of Russian Migs. More recently, Argentina used French Exocet missiles to sink 3 British warships in the Argentine war, and last week, Turkey used a french missile to down a Su24, the new main Russian fighter-bomber. not bad for a country whose main engineering school marches in Napoleonic garb.

The classic of French Engineering, of course is the Eiffel Tower. It is generally unappreciated that this is not the only Eiffel structure designed this way. Eiffel designed railroad bridges, aqueducts. Here’s an Eiffel railroad bridge.

Eiffel railroad bridge, still in use

Eiffel railroad bridge, still in use. American, German, or British bridges of the era look nothing like this.

To get a sense of the engineering artistry of the Eifflel tower, consider that when the tower was built, in 1871, self-financed by Eiffel, it was more than twice as tall as the next-tallest building on earth. ff one weighed the air in a cylinder the height of the tower with a circle about its base, the air would weigh more than the steel of the tower. But here are some other random observations, while first level of the tower houses a restaurant, a normal American space-use choice,the second level housed, when the tower opened the print shop and offices of the International Herald Tribune; not a normal tenant. And, on the third level, near the very top, you will find Mr Eiffel’s apartment. The builder lived there; he owned the place. It’s still there today, but now there are now only mannequins in residence. It’s weird, but genius, like so much that is French engineering.

Eiffel's apartment atop the tower, now occupied by mannequins of Eiffel and Edison, a one-time guest.

Eiffel’s apartment atop the tower, now occupied by mannequins of Eiffel and Edison, a one-time guest.

Returning to the French airplane, The french were the first to make mono-planes. But having succeeded there, they made a decent-enough plane-like automobile, the 1932 Helicon car. It’s a three-man car with a propeller out front and rear-wheel steering. At first, you’d think this is a slow, unmanageable, deathtrap, like Buckminster Fuller’s Dymaxion,.  But you’d be wrong, the Helicon (apparently) is both speedy and safe it moves at 100 mph or more once it gets going, still passed French safety standards in 2000, and gets taken out for (semi-normal) jaunts. Don’t stand in front of the propeller (there’s a bicycle version too).

1932 Helicon; seats 3, rear staring, propeller-driven. Normal-ish. Photo by Yalon.

1932 Helicon car; 100 mph, seats 3, propeller-driven. Photo by Yalon.

The Helicon never quite took off, as it were, but an odd design motorcycle did quite well, at least in France, the Solex, front wheel motorcycle.Unlike US motorcycles, it’s just a bicycle with an engine above the front wheels. The engine runs “backwards” and drives the front wheel via a friction-cam. The only clutch action involves engaging the cam. Simple, elegant, and unlikely to be duplicated elsewhere.

A French Solex motorcycles, and an e-Solex. The e-Solex uses a battery.

A Solex motorcycle and an e-Solex, the battery-powered version. A Citroen and a Peugeot sport are in the background. Popular in France.

The reason I’m writing about French Engineering is perhaps because of the recent attacks. Or perhaps because of aesthetic. It’s important to have an engineering aesthetic — an idea you’re after — and to have pride in one’s craft too. The French stand out in how much they have of both. Some months ago I wrote about a more American engineering aesthetic, It’s a good article, but interestingly, I now note that some main examples I used were semi-French: the gunpowder factory of E. I. Dupont, the main productions facility of a Frenchman’s company in the US.

Robert Buxbaum, December 13, 2015. Some months ago, I wrote about a favorite car engine, finally being used on the Fiat 500 and Alfa Romeo. Fast, energy-efficient, light, maneuverable, and (I suspect) unreliable; the engine embodies a particularly Italian engineering aesthetic.

my electric cart of the future

Buxbaum and Sperka cart of future

Buxbaum and Sperka show off the (shopping) cart of future, Oak Park parade July 4, 2015.

A Roman chariot did quite well with only 1 horse-power, while the average US car requires 100 horses. Part of the problem is that our cars weigh more than a chariot and go faster, 80 mph vs of 25 mph. But most city applications don’t need all that weight nor all of that speed. 20-25 mph is fine for round-town errands, and should be particularly suited to use by young drivers and seniors.

To show what can be done with a light vehicle that only has to go 20 mph, I made this modified shopping cart, and fitted it with a small, 1 hp motor. I call it the cart-of the future and paraded around with it at our last 4th of July parade. It’s high off the ground for safety, reasonably wide for stability, and has the shopping cart cage and seat-belts for safety. There is also speed control. We went pretty slow in the parade, but here’s a link to a video of the cart zipping down the street at 17.5 mph.

In the 2 months since this picture was taken, I’ve modified the cart to have a chain drive and a rear-wheel differential — helpful for turning. My next modification, if I get to it, will be to switch to hydrogen power via a fuel cell. One of the main products we make is hydrogen generators, and I’m hoping to use the cart to advertise the advantages of hydrogen power.

Robert E. Buxbaum, August 28, 2015. I’m the one in the beige suit.

The mass of a car and its mpg.

Back when I was an assistant professor at Michigan State University, MSU, they had a mileage olympics between the various engineering schools. Michigan State’s car got over 800 mpg, and lost soundly. By contrast, my current car, a Saab 9,2 gets about 30 miles per gallon on the highway, about average for US cars, and 22 to 23 mpg in the city in the summer. That’s about 1/40th the gas mileage of the Michigan State car, or about 2/3 the mileage of the 1978 VW rabbit I drove as a young professor, or the same as a Model A Ford. Why so low? My basic answer: the current car weighs a lot more.

As a first step to analyzing the energy drain of my car, or MSU’s, the energy content of gasoline is about 123 MJ/gallon. Thus, if my engine was 27% efficient (reasonably likely) and I got 22.5 mpg (36 km/gallon) driving around town, that would mean I was using about .922 MJ/km of gasoline energy. Now all I need to know is where is this energy going (the MSU car got double this efficiency, but went 40 times further).

The first energy sink I considered was rolling drag. To measure this without the fancy equipment we had at MSU, I put my car in neutral on a flat surface at 22 mph and measured how long it took for the speed to drop to 19.5 mph. From this time, 14.5 sec, and the speed drop, I calculated that the car had a rolling drag of 1.4% of its weight (if you had college physics you should be able to repeat this calculation). Since I and the car weigh about 1700 kg, or 3790 lb, the drag is 53 lb or 233 Nt (the MSU car had far less, perhaps 8 lb). For any friction, the loss per km is F•x, or 233 kJ/km for my vehicle in the summer, independent of speed. This is significant, but clearly there are other energy sinks involved. In winter, the rolling drag is about 50% higher: the effect of gooey grease, I guess.

The next energy sink is air resistance. This is calculated by multiplying the frontal area of the car by the density of air, times 1/2 the speed squared (the kinetic energy imparted to the air). There is also a form factor, measured on a wind tunnel. For my car this factor was 0.28, similar to the MSU car. That is, for both cars, the equivalent of only 28% of the air in front of the car is accelerated to the car’s speed. Based on this and the density of air in the summer, I calculate that, at 20 mph, air drag was about 5.3 lbs for my car. At 40 mph it’s 21 lbs (95 Nt), and it’s 65 lbs (295 Nt) at 70 mph. Given that my city driving is mostly at <40 mph, I expect that only 95 kJ/km is used to fight air friction in the city. That is, less than 10% of my gas energy in the city or about 30% on the highway. (The MSU car had less because of a smaller front area, and because it drove at about 25 mph)

The next energy sink was the energy used to speed up from a stop — or, if you like, the energy lost to the brakes when I slow down. This energy is proportional to the mass of the car, and to velocity squared or kinetic energy. It’s also inversely proportional to the distance between stops. For a 1700 kg car+ driver who travels at 38 mph on city streets (17 m/s) and stops, or slows every 500m, I calculate that the start-stop energy per km is 2 (1/2 m v2 ) = 1700•(17)2  = 491 kJ/km. This is more than the other two losses combined and would seem to explain the majority cause of my low gas mileage in the city.

The sum of the above losses is 0.819 MJ/km, and I’m willing to accept that the rest of the energy loss (100 kJ/km or so) is due to engine idling (the efficiency is zero then); to air conditioning and headlights; and to times when I have a passenger or lots of stuff in the car. It all adds up. When I go for long drives on the highway, this start-stop loss is no longer relevant. Though the air drag is greater, the net result is a mileage improvement. Brief rides on the highway, by contrast, hardly help my mileage. Though I slow down less often, maybe every 2 km, I go faster, so the energy loss per km is the same.

I find that the two major drags on my gas mileage are proportional to the weight of the car, and that is currently half-again the weight of my VW rabbit (only 1900 lbs, 900 kg). The MSU car was far lighter still, about 200 lbs with the driver, and it never stopped till the gas ran out. My suggestion, if you want the best gas milage, buy one light cars on the road. The Mitsubishi Mirage, for example, weighs 1000 kg, gets 35 mpg in the city.

A very aerodynamic, very big car. It's beautiful art, but likely gets lousy mileage -- especially in the city.

A very aerodynamic, very big car. It’s beautiful art, but likely gets lousy mileage — especially in the city.

Short of buying a lighter car, you have few good options to improve gas mileage. One thought is to use better grease or oil; synthetic oil, like Mobil 1 helps, I’m told (I’ve not checked it). Alternately, some months ago, I tried adding hydrogen and water to the engine. This helps too (5% -10%), likely by improving ignition and reducing idling vacuum loss. Another option is fancy valving, as on the Fiat 500. If you’re willing to buy a new car, and not just a new engine, a good option is a hybrid or battery car with regenerative breaking to recover the energy normally lost to the breaks. Alternately, a car powered with hydrogen fuel cells, — an option with advantages over batteries, or with a gasoline-powered fuel cell

Robert E. Buxbaum; July 29, 2015 I make hydrogen generators and purifiers. Here’s a link to my company site. Here’s something I wrote about Peter Cooper, an industrialist who made the first practical steam locomotive, the Tom Thumb: the key innovation here: making it lighter by using a forced air, fire-tube boiler.

Statistics of death and taxes — death on tax day

Strange as it seems, Americans tend to die in road accidents on tax-day. This deadly day is April 15 most years, but on some years April 15th falls out on a weekend and the fatal tax day shifts to April 16 or 17. Whatever weekday it is, about 8% more people die on the road on tax day than on the same weekday a week earlier or a week later; data courtesy of the US highway safety bureau and two statisticians, Redelmeier and Yarnell, 2014.

Forest plot of individuals in fatal road crashes over 30 years. X-axis shows relative increase in risk on tax days compared to control days expressed as odds ratio. Y-axis denotes subgroup (results for full cohort in final row). Column data are counts of individuals in crashes. Analytic results expressed with 95% confidence intervals setting control days as referent. Results show increased risk on tax day for full cohort, similar increase for 25 of 27 subgroups, and all confidence intervals overlapping main analysis. Recall that odds ratios are reliable estimates of relative risk when event rates are low from an individual driver’s perspective.

Forest plot of individuals in fatal road crashes for the 30 years to 2008  on US highways (Redelmeier and Yarnell, 2014). X-axis shows relative increase in risk on tax days compared to control days expressed as odds ratio. Y-axis denotes subgroup (results for full cohort in final row). Column data are counts of individuals in crashes (there are twice as many control days as tax days). Analytic results are 95% confidence intervals based on control days as referent. Dividing the experimental subjects into groups is a key trick of experimental design.

To confirm that the relation isn’t a fluke, the result of well-timed ice storms or football games, the traffic death data was down into subgroups by time, age, region etc– see figure. Each groups showed more deaths than on the average of the day a week before and after.

The cause appears unrelated to paying the tax bill, as such. The increase is near equal for men and women; with alcohol and without, and for those over 18 and under (presumably those under 18 don’t pay taxes). The death increase isn’t concentrated at midnight either, as might be expected if the cause were people rushing to the post office. The consistency through all groups suggests this is not a quirk of non-normal data, nor a fluke but a direct result of  tax-day itself.Redelmeier and Yarnell suggest that stress — the stress of thinking of taxes — is the cause.

Though stress seems a plausible explanation, I’d like to see if other stress-related deaths are more common on tax day — heart attack or stroke. I have not done this, I’m sorry to say, and neither have they. General US death data is not tabulated day by day. I’ve done a quick study of Canadian tax-day deaths though (unpublished) and I’ve found that, for Canadians, Canadian tax day is even more deadly than US tax day is for Americans. Perhaps heart attack and stroke data is available day by day in Canada (?).

Robert Buxbaum, December 12, 2014. I write about all sorts of stuff. Here’s my suggested, low stress income tax structure, and a way to reduce/ eliminate income taxes: tariffs– they worked till the Civil war. Here’s my thought on why old people have more fatal car accidents per mile driven.

Seniors are not bad drivers.

Seniors cause accidents, but need to get places too

Seniors are often made fun of for confusion and speeding, but it’s not clear they speed, and it is clear they need to get places. Would reduced speed limits help them arrive alive?

Seniors have more accidents per-mile traveled than middle age drivers. As shown on the chart below, older Canadians, 75+, get into seven times more fatal accidents per mile than 35 to 55 year olds. At first glance, this would suggest they are bad drivers who should be kept from the road, or at least made to drive slower. But I’m not so sure they are bad drivers, and am pretty certain that lower speed limits should not be generally imposed. I suspect that a lot of the problem comes from the a per-mile basis comparison with folks who drive long distances on the same superhighways instead of longer, leisurely drives on country roads. I suspect that, on a per-hour basis, the seniors would look a lot safer, and on a per highway-mile basis they might look identical to younger drivers.

Canadian Vehicle Survey, 2001, Statistics Canada, includes drivers of light duty vehicles.

Deaths per billion km. Canadian Vehicle Survey, 2001, Statistics Canada, includes light duty vehicles.

Another source of misunderstanding, I find, is that comparisons tend to overlook how very low the accident rates are. The fatal accent rate for 75+ year old drivers sounds high when you report it as 20 deaths per billion km. But that’s 50,000,000 km between fatalities, or roughly one fatality for each 1300 drives around the earth. In absolute terms it’s nothing to worry about. Old folks driving provides far fewer deaths per km than 12-29 year olds walking, and fewer deaths per km than for 16-19 year olds driving.

When starting to research this essay, I thought I’d find that the high death rates were the result of bad reaction times for the elderly. I half expected to find that reduced speed limits for them helped. I’ve not found any data directly related to reduced speeds, but now think that lowered speed limits would not help them any more than anyone else. I note that seniors drive for pleasure more than younger folks and do a lot more short errand drives too — to the stores, for example. These are places where accidents are more common. By contrast, 40 to 70 year olds drive more miles on roads that are relatively safe.

Don't walk, especially if you're old.

Don’t walk, especially if you’re old. Netherlands data, 2001-2005 fatalities per billion km.

The Netherlands data above suggest that any proposed solution should not involve getting seniors out of their cars. Not only do seniors find walking difficult, statistics suggest walking is 8 to 10 times more dangerous than driving, and bicycling is little better. A far better solution, I suspect, is reduced speeds for everyone on rural roads. If you’re zipping along a one-lane road at the posted 40, 55, or 60 mph and someone backs out of a driveway, you’re toast. The high posted speeds on these roads pose a particular danger to bicyclists and motorcyclists of all ages – and these are folks who I suspect drive a lot on the rural roads. I suspect that a 5 mph reduction would do quite a lot.

For automobiles on super-highways, it may be worthwhile to increase the speed limits. As things are now, the accident fatality rates are near zero, and the main problem may be the time wasted behind the wheel – driving from place to place. I suspect that an automobile speed limit raise to 80 mph would make sense on most US and Canadian superhighways; it’s already higher on the Autobahn in Germany.

Robert Buxbaum, November 24, 2014. Expect an essay about death on tax-day, coming soon. I’ve also written about marijuana, and about ADHD.