The Jevons Paradox

Increasing energy efficiency won’t save us.

The Jevons Paradox (W. Stanley Jevons, 1862)[note] Jevons Paradox, [2019-10-07].[/note] notes that increases in efficiency with which a resource is used tend to increase the rate of consumption of that resource, due to increasing demand. Jevons was considering British coal consumption in the 19th century, but in our own time, commercial aviation provides one of the starkest examples of the paradox.

The achievements of the early pioneers of powered flight – the Wrights, Alberto Santos-Dumont, Louis Bleriot etc. – were truly remarkable. Whether their work counts as physics or engineering is debatable. The Wrights in particular were great pragmatists, much more interested in measuring than theorising. In fact, the field of fluid dynamics didn’t really catch up until late in World War I, when Ludwig Prandtl developed, on purely theoretical grounds, a far superior airfoil to those used on aircraft up to that point.

However, it is doubtful that any of the pioneers could have envisaged that aircraft would be used to drop nuclear weapons (although Orville Wright lived long enough to see that happen) and that by the early 21st century, places like Barcelona and Venice would be drowning in a sea of selfie-sticks, and aviation would have be a major influence on the Earth’s climate.

The proximate reasons for the extraordinary rise in air transport since civil aviation got started after World War I are as follows:

  • speeds have risen
  • ranges have risen
  • costs have fallen
  • comfort levels have improved
  • safety has improved enormously

In the 1920s, biplane airliners could barely cover 500 km and were constrained by drag of struts and bracing wires to fly at speeds under 200 km/h. Aircraft cabins were extremely noisy and low cruising altitudes meant flying through the thick of weather. Since 1960, the speeds of jetliners have only been constrained, by steeply rising drag near the speed of sound, to a maximum of around 900 km/h. Attainable ranges are approaching half the circumference of the Earth, which is the approximate theoretical maximum for air-bound vehicles using oil-derived fuels with typical energy densities. Cruising altitudes are now mostly above all weather-related turbulence. In all, comfort levels have generally improved, although cabin sound pressure levels still hover around 92 dB, at least according to my own observations.

Over the past century, engine efficiencies have improved enormously, largely because materials have been developed that can operate at much higher pressures and temperatures. Engine efficiency is determined by the ratios of pressures and temperatures, between where the fuel is burned and the air in which the aircraft is flying. This is another reason to fly high, where the air is cold and thin. Since the start of the jet age, specific fuel consumption – fuel flow rate divided by engine thrust – has dropped by a factor of two[note] Vaclav Smil, Energy Transitions – Global and National Perpectives, Praeger (2016).[/note]. In addition to falling fuel costs, the operation of the entire airline system has been streamlined, often to the detriment of working conditions and personal service for passengers. The result has been the almost constant cost, in numbers of dollars, of an airline ticket since the 1930s, while inflation has eaten away at the value of those dollars. A round-trip ticket from New York to Western Europe in 1939 cost about $\$$700 (US); it was about the same when I first did it in the mid-1970s; now (2019) it would about $\$$1000, but today’s dollars are worth only 1/20 of the 1939 value.

Fig.1. Typical distribution of disposable income in many countries. The shapes tend to look the same, even if the numbers differ.

Now consider the distribution of disposable income (Fig.1). In 1939 only people at the high end tail of this distribution would have been buying air tickets. As the prices came down, the fraction of the populus able to afford the fare moved up the curve that is steeply rising toward the left. It is easy to see that halving the fuel consumption per seat-km, and thus cost, for a particular route would make the trip accessible to a much more than twice the previous number of people. Putting in some toy numbers for illustration, if it took a disposable household income of $\$$40K in order to consider taking the family on a trans-ocean vacation, then according Fig.1, 2% of households could afford it. However if the price dropped so that a household would only need a disposable income of $\$$20K to consider such a trip, then 28% of households could afford it. Thus, the fuel use per passenger would drop by a factor of two, but there will be 14 times as many passengers making the journey. Doubling efficiency causes fuel use to rise by a factor of seven (in this illustrative model). That is how the Jevons’ Paradox works.

Fig.2. Curtiss HS-2, c.1920. National Aeronautical Collection, Ottawa (author photo).


Fig.3. Boeing 767 landing at Vancouver Airport (author photo).



Created (CEW) 2019-10-07