# The energy cost of airplanes, trains, and buses

I’ve come to conclude that airplane travel, and busses makes a lot more sense than high-speed trains. Consider the marginal energy cost of a 90kg (200 lb) person getting on a 737-800, the most commonly flown commercial jet in US service. For this plane, the ratio of lift/drag at cruise speed is 19, suggesting an average value of 15 or so for a 1 hr trip when you include take-off and landing. The energy cost of his trip is related to the cost of jet fuel, about \$3.20/gallon, or about \$1/kg. The heat energy content of jet fuel is 44 MJ/kg or 18,800 Btu/lb. Assuming an average engine efficiency of 21%, we calculate a motive-energy cost of 1.1 x 10-7 \$/J, or 40¢/kwhr. The amount of energy per mile is just force times distance: 1 mile = 1609 m. Force is calculated from the person’s weight in (in Newtons) divided by lift/drag ratio. The energy per mile is thus 90*9.8*1609/15 = 94,600 J. Multiplying by the \$-per-J we find the marginal cost of his transport is 1¢ per mile, virtually nothing.

The Wright brothers testing their gliders in 1901 (left) and 1902 (right). The angle of the tether reflects a dramatic improvement in lift-to-drag ratio; the marginal cost per mile is inversely proportional to the lift-to-drag ratio.

The marginal cost for carrying a 200 lb person from Detroit to NY (500 miles) is 1¢/mile x 500 miles = \$5: hardly anything compared to the cost of driving. No wonder airplanes offer crazy-low, fares to fill seats on empty flights. But this is just the marginal cost. The average energy cost per passenger is higher since it includes the weight of the plane. On a reasonably full 737 flight, the passengers and luggage  weigh about 1/4 as much as the plane and its fuel. Effectively, each passenger weighs 800 lbs, suggesting a 4¢/mile energy cost, or \$20 of energy per passenger for the flight from Detroit to NY. Though the fuel rate of burn is high, about 5000 lbs/hr, the cost is low because of the high speed and the number of passengers. Stated another way, the 737 gets 80 passenger miles per gallon, a somewhat lower mpg than the 91 claimed for a full 747.

Passengers must pay more than \$20, of course because of wages, capital, interest, profit, taxes, and landing fees. Still, one can see how discount airlines could make money if they arrange a good deal with a hub airport, one that allows them low landing fees and allows them to buy fuel at near cost.

Compare this to any proposed super-fast or Mag-lev train. Over any significant distance, the plane will be cheaper, faster, and as energy-efficient. Current US passenger trains, when fairly full, boast a fuel economy of 200 passenger miles per gallon, but they are rarely full. Currently, they take some 15 hours to go Detroit to NY, in part because they go slow, and in part because they go via longer routes, visiting Toronto and Montreal in this case, with many stops along the way. With this long route, even if the train got 200 passenger mpg, the 750 mile trip would use 3.75 gallons per passenger, compared to 6.25 for the flight above. This is a savings of 2.5 gallons, or \$8, but it comes at a cost of 15 hours of a passenger’s life. Even train speeds were doubled, the trip would still take more than 7.5 hours including stops, and the energy cost would be higher. As for price, beyond the costs of wages, capital, interest, profit, taxes, and depot fees — similar to those for air-tragic – you have to add the cost of new track and track upkeep. While I’d be happy to see better train signaling to allow passenger trains to go 100 mph on current, freight-compatible lines, I can see little benefit to government-funded projects to add the parallel, dedicated track for 150+ mph trains that will still, likely be half-full.

You may now ask about cities that don’t have  good airports. Something else removing my enthusiasm for super trains is the appearance of a new generation of short take-off and landing, commercial jets, and of a new generation of comfortable buses. Some years ago, I noted that Detroit’s Coleman Young airport no longer has commercial traffic because its runway was too short, 1051m. I’m happy to report that Bombardier’s new CS100s should make small airports like this usable. A CS100 will hold 120 passengers, requires only 1463m of runway, and is quiet enough for city use. The economics are such that it’s hard to imagine Mag-lev beating this for the proposed US high-speed train routes: Dallas to Houston; LA to San José to San Francisco; or Chicago-Detroit-Toledo-Cleveland-Pittsburgh. So far US has kept out these planes because Boeing claims unfair competition, but I trust that this is just a delay. As for shorter trips, the modern busses are as fast and energy efficient as trains, and far cheaper because they share the road costs with cars and trucks.

If the US does want to spend money on transport, I’d suggest improving inner-city airports. The US could also fund development of yet-better short take off planes, perhaps made with carbon fiber, or with flexible wing structures to improve the lift-to-drag during take-offs and landings. Higher train speeds should be available with better signaling and with passenger trains that lean more into a curve, but even this does not have to be super high-tech. And for 100-200 mile intercity traffic, I suspect the best solution is to improve the highways and busses. If you want low pollution and high efficiency, how about hydrogen hybrid buses?

Robert Buxbaum, October 30, 2017. I taught engineering for 10 years at Michigan State, and my company, REB Research, makes hydrogen generators and hydrogen purifiers.

# my electric cart of the 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.

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.

# Hydrogen cars and buses are better than Tesla

Hydrogen fueled cars and buses are as clean to drive as battery vehicles and have better range and faster fueling times. Cost-wise, a hydrogen fuel tank is far cheaper and lighter than an equivalent battery and lasts far longer. Hydrogen is likely safer because the tanks do not carry their oxidant in them. And the price of hydrogen is relatively low, about that of gasoline on a per-mile basis: far lower than batteries when the cost of battery wear-out is included. Both Presidents Clinton and Bush preferred hydrogen over batteries, but the current administration favors batteries. Perhaps history will show them correct, but I think otherwise. Currently, there is not a hydrogen bus, car, or boat making runs at Disney’s Experimental Community of Tomorrow (EPCOT), nor is there an electric bus car or boat. I suspect it’s a mistake, at least convening the lack of a hydrogen vehicle.

The best hydrogen vehicles on the road have more range than the best electric vehicle, and fuel faster. The hydrogen powered, Honda Clarity debuted in 2008. It has a 270 mile range and takes 3-5 minutes to fuel with hydrogen at 350 atm, 5150 psi. By contrast, the Tesla S-sedan that debuted in 2012 claims only a 208 mile range for its standard, 60kWh configuration (the EPA claims: 190 miles) and requires three hours to charge using their fastest charger, 20 kW.

What limits the range of battery vehicles is that the stacks are very heavy and expensive. Despite using modern lithium-ion technology, Tesla’s 60 kWh battery weighs 1050 lbs including internal cooling, and adds another 250 lbs to the car for extra structural support. The Clarity fuel system weighs a lot less. The hydrogen cylinders weigh 150 lb and require a fuel cell stack (30 lb) and a smaller lithium-ion battery for start-up (90 lb). The net effect is that the Clarity weighs 3582 lbs vs 4647 lbs for the Tesla S. This extra weight of the Tesla seems to hurt its mileage by about 10%. The Tesla gets about 3.3 mi/kWh or 0.19 mile/lb of battery versus 60 miles/kg of hydrogen for the Clarity suggesting  3.6 mi/kWh at typical efficiencies.

High pressure hydrogen tanks are smaller than batteries and cheaper per unit range. The higher the pressure the smaller the tank. The current Clarity fuels with 350 atm, 5,150 psi hydrogen, and the next generation (shown below) will use higher pressure to save space. But even with 335 atm hydrogen (5000 psi) a Clarity could fuel a 270 mile range with four, 8″ diameter tanks (ID), 4′ long. I don’t know how Honda makes its hydrogen tanks, but suitable tanks might be made from 0.065″ Maranging (aged) stainless steel (UTS = 350,000 psi, density 8 g/cc), surrounded by 0.1″ of aramid fiber (UTS = 250,000 psi, density = 1.6 g/cc). With this construction, each tank would weigh 14.0 kg (30.5 lbs) empty, and hold 11,400 standard liters, 1.14 kg (2.5 lb) of hydrogen at pressure. These tanks could cost \$1500 total; the 270 mile range is 40% more Than the Tesla S at about 1/10 the cost of current Tesla S batteries The current price of a replacement Tesla battery pack is \$12,000, subsidized by DoE; without the subsidy, the likely price would be \$40,000.

Next generation Honda fuel cell vehicle prototype at the 2014 Detroit Auto Show.

Currently hydrogen is more expensive than electricity per energy value, but my company has technology to make it cheaply and more cleanly than electricity. My company, REB Research makes hydrogen generators that produce ultra pure hydrogen by steam reforming wow alcohol in a membrane reactor. A standard generator, suitable to a small fueling station outputs 9.5 kg of hydrogen per day, consuming 69 gal of methanol-water. At 80¢/gal for methanol-water, and 12¢/kWh for electricity, the output hydrogen costs \$2.50/kg. A car owner who drove 120,000 miles would spend \$5,000 on hydrogen fuel. For that distance, a Tesla owner would spend only \$4400 on electricity, but would have to spend another \$12,000 to replace the battery. Tesla batteries have a 120,000 mile life, and the range decreases with age.

For a bus or truck at EPCOT, the advantages of hydrogen grow fast. A typical bus is expected to travel much further than 120,000 miles, and is expected to operate for 18 hour shifts in stop-go operation getting perhaps 1/4 the miles/kWh of a sedan. The charge time and range advantages of hydrogen build up fast. it’s common to build a hydrogen bus with five 20 foot x 8″ tanks. Fueled at 5000 psi., such buses will have a range of 420 miles between fill-ups, and a total tank weight and cost of about 600 lbs and \$4000 respectively. By comparison, the range for an electric bus is unlikely to exceed 300 miles, and even this will require a 6000 lb., 360 kWh lithium-ion battery that takes 4.5 hours to charge assuming an 80 kW charger (200 Amps at 400 V for example). That’s excessive compared to 10-20 minutes for fueling with hydrogen.

While my hydrogen generators are not cheap: for the one above, about \$500,000 including the cost of a compressor, the cost of an 80 kW DC is similar if you include the cost to run a 200 Amp, 400 V power line. Tesla has shown there are a lot of people who value clean, futuristic transport if that comes with comfort and style. A hydrogen car can meet that handily, and can provide the extra comforts of longer range and faster refueling.

Robert E. Buxbaum, February 12, 2014 (Lincoln’s birthday). Here’s an essay on Lincoln’s Gettysburg address, on the safety of batteries, and on battery cost vs hydrogen. My company, REB Research makes hydrogen generators and purifiers; we also consult.

# Camless valves and the Fiat-500

One of my favorite automobile engine ideas is the use of camless, electronic valves. It’s an idea whose advantages have been known for 100 years or more, and it’s finally going to be used on a mainstream, commercial car — on this year’s Fiat 500s. Fiat is not going entirely camless, but the plan is to replace the cams on the air intake valves with solenoids. A normal car engine uses cams and lifters to operate the poppet valves used to control the air intake and exhaust. Replacing these cams and lifters saves some weight, and allows the Fiat-500 to operate more efficiently at low power by allowing the engine to use less combustion energy to suck vacuum. The Fiat 500 semi-camless technology is called Multiair: it’s licensed from Valeo (France), and appeared as an option on the 2010 Alfa Romeo.

How this saves mpg is as follows: at low power (idling etc.), the air intake of a normal car engine is restricted creating a fairly high vacuum. The vacuum restriction requires energy to draw and reduces the efficiency of the engine by decreasing the effective compression ratio. It’s needed to insure that the car does not produce too much NOx when idling. In a previous post, I showed that the rate of energy wasted by drawing this vacuum was the vacuum pressure times the engine volume and the rpm rate; I also mentioned some classic ways to reduce this loss (exhaust recycle and adding water).

Valeo’s/Fiat’s semi-camless design does nothing to increase the effective compression ratio at low power, but it reduces the amount of power lost to vacuum by allowing the intake air pressure to be higher, even at low power demand. A computer reduces the amount of air entering the engine by reducing the amount of time that the intake valve is open. The higher air pressure means there is less vacuum penalty, both when the valve is open even when the valve is closed. On the Alfa Romeo, the 1.4 liter Multiair engine option got 8% better gas mileage (39 mpg vs 36 mpg) and 10% more power (168 hp vs 153 hp) than the 1.4 liter cam-driven engine.

David Bowes shows off his latest camless engines at NAMES, April 2013.

Fiat used a similar technology in the 1970s with variable valve timing (VVT), but that involved heavy cams and levers, and proved to be unreliable. In the US, some fine engineers had been working on solenoids, e.g. David Bowes, pictured above with one of his solenoidal engines (he’s a sometime manufacturer for REB Research). Dave has built engines with many cycles that would be impractical without solenoids, and has done particularly nice work reducing the electric use of the solenoid.

Durability may be a problem here too, as there is no other obvious reason that Fiat has not gone completely camless, and has not put a solenoid-controlled valve on the exhaust too. One likely reason Fiat didn’t do this is that solenoidal valves tend to be unreliable at the higher temperatures found in exhaust. If so, perhaps they are unreliable on the intake too. A car operated at 1000-4000 rpm will see on the order of 100,000,000 cycles in 25,000 miles. No solenoid we’ve used has lasted that many cycles, even at low temperatures, but most customers expect their cars to go more than 25,000 miles without needing major engine service.

We use solenoidal pumps in our hydrogen generators too, but increase the operating live by operating the solenoid at only 50 cycles/minute — maximum, rather than 1000- 4000. This should allow our products to work for 10 years at least without needing major service. Performance car customers may be willing to stand for more-frequent service, but the company can’t expect ordinary customers to go back to the days where Fiat stood for “Fix It Again Tony.”

# Purifying the Hydrogen from Browns gas, HHO, etc.

Perhaps the simplest way to make hydrogen is to stick two electrodes into water and to apply electricity. The gas that is produced is mostly hydrogen, and is sometimes suitable for welding or for addition to an automobile engine to increase the mileage. Depending on the electrodes and whether salt is added to the water, the gas that is produced can be Browns gas, HHO,  town gas, or some relative of the three. We are sometimes asked if we can purify the product of this electrolysis, and my answer is typically: “maybe,” or “it depends.”

If the electrode was made of stainless steel and the water contained only KOH or baking soda, the gas that results will be mostly hydrogen and you will be able to purify it somewhat with a polymer membrane if you wish. The gas isn’t very explosive generally, since most of the oxygen that results from the electrolysis will go into rusting out the electrodes. The reaction is thus, H2O + Fe –> H2 + FeO. To see if this is what you’ve got, you can use determine the ratio of gas production with a simple version of the Hoffman apparatus made from (for example) two overturned glass jars, or by separating the electrodes with a paper towel. You can also determine the H2 to O2 ratio (if you know a bit more physics) from a measure of the amperage and the rate of gas production. The hydrogen you form with steel plates will always contain some oxygen though, as well as some nitrogen and water vapor. While a polymer membrane will remove most of the oxygen and nitrogen in this gas, it won’t remove all, and it will not generally remove any of the water. With this gas, I suspect that you would be better off just using it as it is. This is particularly so if the fraction of oxygen is more than a few percent: hydrogen with more oxygen than this becomes quite explosive.

Since this gas will contain water, you probably don’t want to store it, and you probably don’t want to purify it over a metal, either, There are two reasons for this: the water can condense out during storage, and will tend to rust whatever metal it contacts (it’s often alkaline). What’s more, the small amount of oxygen in the hydrogen is likely to react over a hydrogen storage metal to form water and heat. This may give rise to the explosion you were trying to avoid. This is clearly the quick a dirty approach to making hydrogen.

Another version of electrolysis gas, one that’s even quicker and dirtier than the above involves the use of table salt instead of KOH or baking soda. The hydrogen that results will contain chlorine as an impurity, and will be quite toxic, but it will be somewhat less explosive.The hydrogen will smell like bleach and the water you use will turn slightly greenish and quite alkaline. Both the liquid and gas are definitely bad news unless your aim was to make chlorine and alkali; this is called the chlor-alkali process for a reason. On a personal note, as a 12 year old I tried this and was confused about why I got equal volumes of gas on the cathode and anode. The reason was that I was making Cl2, and not O2: the chemistry is 2 H2O + 2 NaCl –> H2 + Cl2 + 2 NaOH. I then I used the bromide version reaction to make a nice sample of bromine liquid. That is, I used KBr instead of table salt. Bromine is brown, oily, and only sparingly soluble in water.

Another version of this electrolysis process involves the use of graphite electrodes. If you are lucky, this will give you a mix of CO and hydrogen and not H2 and O2. This mix is a called “town gas.” It’s a very good welding gas since it is not explosive. It is, however, quite toxic. If you begin to get a headache using this gas stop immediately: you’re experiencing CO poisoning. The reaction here is H2O + C –> H2 + CO. CO headaches just get worse and worse until you die. If you are not lucky here you can get HHO instead of town gas, and this is quite explosive: H2O –> H2 + 1/2 O2. The volume ratio will be a key clue as to which you are making; another clue is to put a small volume in a paper bag and light it. If the bag explodes with a terrific bang, you’ve made the wrong gas. Stop!

With all of these gases I would recommend that you add a polymer of paper membrane in the water between the electrodes. Filter paper will work fine for this as will ceramic paper; the classic membrane for this was asbestos. If you keep the two product gas streams separate as soon as they are formed, you’ll avoid most of your explosion-safety issues. Few people take this advice, I’ve found; they think there must be some simpler way. Trust me: this is the classic, safe way to make electrolysis hydrogen.

A balloon filled with pure hydrogen will not ignite. To show you, here is a 2.5 min long video where I poke a lit cigar into a mylar balloon filled with hydrogen from my membrane reactor generators. Note that this hydrogen does not even burn in the balloon because it is oxygen free. As a safety check try this with your hydrogen, but only on a much-smaller scale. Pure hydrogen will not go boom, impure hydrogen will. My advice: keep safe and healthy. You’ll feel better that way, and your heirs will be less inclined to sue me.

In case you are wondering how electrolysis hydrogen can add to the gas mileage, the simple answer is that it increases the combustion speed and the water vapor decreases the parasitic loss due to vacuum. I’ve got some more information on this here. I hope this advice helps with your car project or any other electrolysis option. In my opinion, one should use a membrane in the water to separate the components at formation in all but the smallest experiments and with the smallest amperage sources. Even these should be done only in a well-ventilated room or on a car that is parked outside of the house. Many of the great chemists of the 1800s died doing experiments like these; learn from their mistakes and stay among the living.

# How hydrogen and/or water can improve automobile mileage (mpg)

In case you’ve ever wondered why it was that performance cars got such poor milage, or why you got such bad milage in the city, the biggest single problem has to do with the vacuum drawn by the engine, some of the problem has to do with the speed of combustion, some has to do with rolling friction, and some with start/stop loss too. Only a very small fraction of the energy is lost on air friction until you reach highway speeds.

Lets consider vacuum loss first as it is likely the worst offender. A typical US car, e.g. a Chevy Malibu, has a 3.5 liter engine (a performance car has an engine that’s much larger). As you toodle down a street at 35 mph, your engine is going at about 2000 rpm, or 33 rps. Since the power required to move the car is far less than the 200 hp that the car could deliver, the air intake is throttled so that the engine is sucking a vacuum of about 75 kpa (10 psi for those using English units). To calculate the power loss this entails, multiply 33*3.5*80; this is about 8662 Watts, or 12 hp. To find the energy use per mile, divide by your average speed, 25 mph (it would be 35 mph, but you sometimes stop for lights). 8 kW/25 mph = .21 kW-hr/mile. One finds, as I’ll show that the car expends more energy sucking this vacuum than pushing the car itself. This is where the majority of the city mpg goes in a normal car, but it’s worse in a high performance car is worse since the engine is bigger. In city driving, the performance mpg will be lower than for a Malibu even if the performance car is lighter, if it has better aerodynamics (it does), and if you never stop at lights.

The two other big places were city mileage goes is overcoming rolling friction and the need to stop and go at lights, stop signs, etc. The energy used for rolling friction is the force it would take to push your car on level ground when in neutral times the distance. For a typical car, the push force is about 70 lbs or 32 kgs or 315 Nt; it’s roughly proportional to the car’s weight. At 35 mph, or 15.5 m/s, the amount of power this absorbs is calculated as the product of force and speed: 15.5*315 = 4882 W, or about 6.5 hp. The energy use is 4.9 kW/35 mph =.14 kWhr/mile. The energy loss from stop lights is similar to this, about .16 kWhr/mile, something you can tell by getting the car up to speed and seeing how far it goes before it stops. It’ll go about 2-3 blocks, a little less distance than you are likely to go without having to stop. Air resistance adds a very small amount at these speeds, about 2000 W, 2.7 hp, or .05 kWhr/mile; it’s far more relevant at 65 mph, but still isn’t that large.

If you add all this together, you find the average car uses about .56 kWhr/mile. For an average density gasoline of 5.6 lb/gal, and average energy-dense gasoline, 18,000 BTU/lb, and an average car engine efficiency of 11000 BTU/kWhr, you can now predict an average city gas mileage of 16.9 mpg, about what you find experimentally. Applying the same methods to highway traffic at 65 mph, you predict .38 kWhr/mile, or 25 mpg. Your rpms are the same on the highway as in the city, but the throttle is open so you get more power and loose less to vacuum.

Now, how do you increase a car’s mpg. If you’re a Detroit automaker you could reduce the weight of the car, or you the customer can clean the junk out of your trunk. Every 35 lbs or so increases the rolling friction by about 1%. These is another way to reduce rolling friction and that’s to get low resistance tires, or keep the tires you’ve got full of air. Still, what you’d really like to do is reduce the loss to vacuum energy, since vacuum loss is a bigger drain on mpg.

The first, simple way to reduce vacuum energy loss is to run lean: that is, to add more air than necessary for combustion. Sorry to say, that’s illegal now, but in the olden days before pollution control you could boost your mpg by adjusting your carburator to add about 10% excess of air. This reduced your passing power and the air pollution folks made it illegal (and difficult) after they noticed that it excess air increased NOx emissions. The oxygen sensor on most cars keeps you from playing with the carburator these days.

Another approach is to use a much smaller engine. The Japanese and Koreans used to do this, and they got good milage as a result. The problem here is that you now had to have a very light car or you’d get very low power and low acceleration — and no American likes that. A recent approach to make up for some of the loss of acceleration is by adding a battery and an electric motor; you’re now making a hybrid car. But the batteries add significant cost, weight and complexity to these cars, and not everyone feels this is worth it. So now on to my main topic: adding steam or hydrogen.

There is plenty of excess heat on the car manifold. A simile use of this heat is to warm some water to the point where the vapor pressure is, for example, 50 kPa. The pressure from this water adds to the power of your engine by allowing a reduction in the vacuum to 50 kPa or less. This cuts the vacuum loss at low speeds. At high speed and power the car automatically increases the air pressure and the water stops evaporating, so there is no loss of power. I’m currently testing this modification on my own automobile partly for the fun of it, and partly as a preface to my next step: using the car engine heat to run the reaction CH3OH + H2O –> CO2 + H2. I’ll talk more about our efforts adding hydrogen elsewhere, but thought you might be interested in these fundamentals.

http://www.rebresearch.com

# Hydrogen addition to an automobile engine

Today, I began a series of experiments putting hydrogen into my car engine. Hydrogen is a combustion promotor, increasing the flame speed significantly, even at low compositions, and it has a very high octane value, so it does not cause pre-ignition. I used my Chevy Malibu, shown, and generated the hydrogen using one of our (REB Research’s) methanol-reformer hydrogen generators. I used a small hydrogen generator we sell for gas chromatographic use, and put 280 ccm hydrogen into engine, as shown. This is enough to provide 1% of the energy content about during idle.

I’ve not measured mpg change yet (as a stationary experiment the mpg is 0), but was really looking for outward signs of knock or other engine problems. Adding 280 ccm of hydrogen should increase the flame speed by ~2%, which should increase the degree of high pressure combustion, and this should increase the mpg by about 3% or 4% if you don’t include the hydrogen energy. So far, I saw no ill effects: no ill sounds and no check engine lights.

Hydrogen added to a Chevy Malibu engine at REB Research

About half the hydrogen energy comes from waste heat of the engine, and half the methanol. Either way this energy is very cheap: methanol costs about \$1.20/gal, about half of what gasoline does on a per-energy basis.  Next step is to make my hydrogen generator mobile, and check the effect on mpg. I’m glad it worked OK so far. There was a reporter watching.