# 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.

# Future airplane catapults may not be electric

President Trump got into Hot Water with the Navy this week for his suggestion that they should go “back to god-damn steam” for their airplane catapults as a cure for cost over-runs and delays with the Navy’s aircraft carriers. The Navy had chosen to go to a more modern catapult called EMALS (electromagnetic, aircraft launch system) based on a traveling coil and electromagnetic pulses. This EMAL system has cost \$5 Billion in cost over-runs, has added 3 years to the program, and still doesn’t work well. In response to the president’s suggestion (explosion), the Navy did what the rest of Washington has done: blame Trump’s ignorance, e.g. here, in the Navy Times. Still, for what it’s worth, I think Trump’s idea has merit, especially if I can modify it a bit to suggest high pressure air (pneumatics) instead of high pressure steam.

Tests of the navy EMALS, notice that some launches go further than others; the problem is electronics, supposedly.

If you want to launch a 50,000 lb jet fighter at 5 g acceleration, you need to apply 250,000 lbs of force uniformly throughout the launch. For pneumatics, all that takes is 250 psi steam or air, and a 1000 square inch piston, about 3 feet in diameter. This is a very modest pressure and a quite modest size piston. A 50,000 lb object accelerated this way, will reach launch speed (130 mph) in 1.2 seconds. It’s very hard to get such fast or uniform acceleration with an electromagnetic coil since the motion of the coil always produces a back voltage. The electromagnetic pulses can be adjusted to counter this, but it’s not all that easy, as the Navy tests show. You have to know the speed and position of the airplane precisely to get it right, and have to adjust the firing of the pushing coils accordingly. There is no guarantee of smooth acceleration like you get with a piston, and the EMALS control circuit will always be vulnerable to electromagnetic and cyber attack. As things stand, the control system is thought to be the problem.

A piston is invulnerable to EM and cyber attack since, if worse comes to worse, the valves can be operated manually, as was done with steam-catapults throughout WWII. And pistons are very robust — far more robust than solenoid coils — because they are far less complex. As much force as you put on the plane, has to be put on the coil or piston. Thus, for 5 g acceleration, the coil or piston has to experience 250,000 lbs of horizontal force. That’s 3 million Newtons for those who like SI units (here’s a joke about SI units). A solid piston will have no problem withstanding 250,000 lbs for years. Piston steamships from the 50s are still in operation. Coils are far more delicate, and the life-span is likely to be short, at least for current designs.

The reason I suggest compressed air, pneumatics, instead of steam is that air is not as hot and corrosive as steam. Also an air compressor can be located close to the flight deck, connected to the power center by electric wires. Steam requires long runs of steam pipes, a more difficult proposition. As a possible design, one could use a multi-stage, inter-cooled air compressor connected to a ballast tank, perhaps 5 feet in diameter x 100 feet long to guarantee uniform pressure. The ballast tank would provide the uniform pressure while allowing the use of a relatively small compressor, drawing less power than the EMALS. Those who’ve had freshman physics will be able to show that 5 g acceleration will get the plane to 130 mph in only 125 feet of runway. This is far less runway than the EMALS requires. For lighter planes or greater efficiency, one could shut off the input air before 120 feet and allow the remainder of the air to expand for 200 feet of the piston.

The same pistons could be used for capturing an airplane. It could start at 250 psi, dead-ended to the cylinder top. The captured airplane would push air back into the ballast tank, or the valve could be closed allowing pressure to build. Operated that way, the cylinder could stop the plane in 60 feet. You can’t do that with an EMAL. I should also mention that the efficiency of the piston catapult can be near 100%, but the efficiency of the EMALS will be near zero at the beginning of acceleration. Low efficiency at low speed is a problem found in all electromagnetic actuators: lots of electromagnetic power is needed to get things moving, but the output work,  ∫F dx, is near zero at low velocity. With EM, efficiency is high at only at one speed determined by the size of the moving coil; with pistons it’s high at all speeds. I suggest the Navy keep their EMALS, but only as a secondary system, perhaps used to launch drones until they get sea experience and demonstrate a real advantage over pneumatics.

Robert Buxbaum, May 19, 2017. The USS Princeton was the fanciest ship in the US fleet, with super high-tech cannons. When they mis-fired, it killed most of the cabinet of President Tyler. Slow and steady wins the arms race.

# 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.

# 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.