# 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.