# 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.

# I make weapons too, but they don’t work

My company, REB Research, makes items with mostly peaceful uses: hydrogen purifiers and hydrogen generators — used to make silicon chips and to power fuel cells. Still, several of our products have advanced military uses, and these happen to be our most profitable items. The most problematic of these is the core for a hydrogen-powered airplane designed to stay up forever. An airplane like this could be used for peace, e.g. as a cheap, permanent cell tower, or for finding shipwrecks in the middle of the ocean. But it could also be used for spying on US citizens. Ideally I’d like to see my stuff used for desirable ends, but know it’s not always that way.

See what I mean? No matter how many times I pull the trigger the damned thing just won’t fire! Gahan Wilson;

I’d be less bothered if I had more faith that my government will only spy on bad guys, but I don’t. Our politicians seem focused on staying in office, and most presidents of the 20th century have kept enemies lists of those who they’d like to get back at — politics isn’t pretty. I’d be more picky if I could figure out how to sell more stuff, but so far I have not. I thus need the work. I take a sort-of comfort, however, in the fact that the advanced nature of the technology means that my customers keep having troubles getting things to work. My parts work, but the plane has yet to fly as intended. Perhaps, by the time they do get it flying, spying may have changed enough that my stuff will be used only for beneficial service to mankind, or as a stepping stone to more general use. Hydrogen as a fuel makes a lot of sense, especially for airplanes.

Robert E. Buxbaum, June 15, 2015. Here’s a description of my membrane reactors, and a description of my latest fuel cell reformer idea. There are basically two types of engineer; those who make weapons and those who make targets. I make the case here that you want to make targets. Some weapons have only one short day in the sun, e.g. the Gatling gun.

# Statistics Joke

A classic statistics joke concerns a person who’s afraid to fly; he goes to a statistician who explains that planes are very, very safe, especially if you fly a respectable airline in good weather. In that case, virtually the only problem you’ll have is the possibility of a bomb on board. The fellow thinks it over and decides that flying is still too risky, so the statistician suggests he plant a bomb on the airplane, but rig it to not go off. The statistician explains: while it’s very rare to have a bomb onboard an airplane, it’s really unheard of to have two bombs on the same plane.

It’s funny because …. the statistician left out the fact that an independent variable (number of bombs) has to be truly independent. If it is independent, the likelihood is found using a poisson distribution, a non-normal distribution where the greatest likelihood is zero bombs, and there are no possibilities for a negative bomb. Poisson distributions are rarely taught in schools for some reason.

By Dr. Robert E. Buxbaum, Mar 25, 2013. If you’ve got a problem like this (particularly involving chemical engineering) you could come to my company, REB Research.

# Why the Boeing Dreamliner’s batteries burst into flames

Boeing’s Dreamliner is currently grounded due to two of their Li-Ion batteries having burst into flames, one in flight, and another on the ground. Two accidents of the same type in a small fleet is no little matter as an airplane fire can be deadly on the ground or at 50,000 feet.

The fires are particularly bad on the Dreamliner because these lithium batteries control virtually everything that goes on aboard the plane. Even without a fire, when they go out so does virtually every control and sensor. So why did they burn and what has Boeing done to take care of it? The simple reason for the fires is that management chose to use Li-Cobalt oxide batteries, the same Li-battery design that every laptop computer maker had already rejected ten years earlier when laptops using them started busting into flames. This is the battery design that caused Dell and HP to recall every computer with it. Boeing decided that they should use a massive version to control everything on their flagship airplane because it has the highest energy density see graphic below. They figured that operational management would insure safety even without the need to install any cooling or sufficient shielding.

All lithium batteries have a negative electrode (anode) that is mostly lithium. The usual chemistry is lithium metal in a graphite matrix. Lithium metal is light and readily gives off electrons; the graphite makes is somewhat less reactive. The positive electrode (cathode) is typically an oxide of some sort, and here there are options. Most current cell-phone and laptop batteries use some version of manganese nickel oxide as the anode. Lithium atoms in the anode give off electrons, become lithium ions and then travel across to the oxide making a mixed ion oxide that absorbs the electron. The process provides about 4 volts of energy differential per electron transferred. With cobalt oxide, the cathode reaction is more or less CoO2 + Li+ e– —> LiCoO2. Sorry to say this chemistry is very unstable; the oxide itself is unstable, more unstable than MnNi or iron oxide, especially when it is fully charged, and especially when it is warm (40 degrees or warmer) 2CoO2 –> Co2O+1/2O2. Boeing’s safety idea was to control the charge rate in a way that overheating was not supposed to occur.

Despite the controls, it didn’t work for the two Boeing batteries that burst into flames. Perhaps it would have helped to add cooling to reduce the temperature — that’s what’s done in lap-tops and plug-in automobiles — but even with cooling the batteries might have self-destructed due to local heating effects. These batteries were massive, and there is plenty of room for one spot to get hotter than the rest; this seems to have happened in both fires, either as a cause or result. Once the cobalt oxide gets hot and oxygen is released a lithium-oxygen fire can spread to the whole battery, even if the majority is held at a low temperature. If local heating were the cause, no amount of external cooling would have helped.

Something that would have helped was a polymer interlayer separator to keep the unstable cobalt oxide from fueling the fire; there was none. Another option is to use a more-stable cathode like iron phosphate or lithium manganese nickel. As shown in the graphic above, these stable oxides do not have the high power density of Li-cobalt oxide. When the unstable cobalt oxide decomposed there was oxygen, lithium, and heat in one space and none of the fire extinguishers on the planes could put out the fires.

The solution that Boeing has proposed and that Washington is reviewing is to leave the batteries unchanged, but to shield them in a massive titanium shield with the vapors formed on burning vented outside the airplane. The claim is that this shield will protect the passengers from the fire, if not from the loss of electricity. This does not appear to be the best solution. Airbus had planned to use the same batteries on their newest planes, but has now gone retro and plans to use Ni-Cad batteries. I don’t think that’s the best solution either. Better options, I think, are nickel metal hydride or the very stable Lithium Iron Phosphate batteries that Segway uses. Better yet would be to use fuel cells, an option that appears to be better than even the best batteries. Fuel cells are what the navy uses on submarines and what NASA uses in space. They are both more energy dense and safer than batteries. As a disclaimer, REB Research makes hydrogen generators and purifiers that are used with fuel-cell power.

More on the chemistry of Boeing’s batteries and their problems can be found on Wikipedia. You can also read an interview with the head of Tesla motors regarding his suggestions and offer of help.

# Big new hydrogen purifier ships

We shipped out our largest hydrogen purifier to date on Thursday, one designed for use in hydrogen-powered airplanes. I’m pretty happy; lots of throughput, light weight, low pressure drop, quite durable. We had a pizza party Friday to celebrate(if we didn’t invite you, sorry). I’m already working on design improvements (lessons learned) in case we get another order, or another, similar customer. I think we could do even better in our next version.