Fig. 1: Structure of PZT, a crystal commonly used for piezoelectric applications (Source: Wikimedia Commons) 
Alternative energy will become increasingly important as fossil fuel supplies inevitably run out or environmental damage sparks consumer awareness. The search for a viable energy alternative will continue until these alternatives can address the dynamic demands of the electrical grid and storage limitations. Piezoelectric devices, used for harvesting the vibrational energy of roads and walkways due to traffic, can produce electrical energy that is predictable (based on traffic patterns), and locally storable.
Piezoelectric devices generate electrical energy by means of a piezoelectric crystal. The crystal, placed about 5 centimeters below the surface of the asphalt, slightly deforms when vehicles travel across the road, thereby producing electrical current. These devices have been implemented by the East Japan Railway Company (under pedestrian subway station gates) and by Innowattech (under roads in Israel). Innowattech has advertised that these devices, if planted along a onekilometer stretch of road, could provide an average of 400 kW of power, enough to power 162 WesternU.S. homes. [1,2] These data suggest that piezoelectric energy harvesting is a competitive, clean alternative energy source. In response to these findings, in 2011 California state assemblyman Mike Gatto proposed Assembly Bill 306 to develop this technology for Californian roads. [3,4] However, it is unclear whether the data truly reflect the physical limitations of piezoelectric energy harvesting.
The generating capacity of piezoelectric devices can be crudely overapproximated by assuming that the vibrations in the road are caused by traffic alone, and that each "vibration event" from one vehicle is independent of another (i.e. the vibrations are sufficiently dampened before the next vehicle passes). Under these assumptions, the total energy harvested by piezoelectric devices along a onekilometer stretch is at most the number of cars that pass multiplied by the vibrational energy that one car transfers to the road. This vibrational energy can be overapproximated by the energy that each car consumes and puts to mechanical work across this stretch. In other words, the energy a car loses to vibrations in asphalt must be less than the energy a car puts to mechanical work over the onekilometer stretch. This value can be computed by multiplying the energy consumed from gasoline by thermal efficiency.
Expended Energy  =  (Gasoline Used) × (Energy Density of Gasoline) × (Thermal Efficiency) 
=  1 km × 0.621 mi/km ×
2.8 kg/gal × 4.43 ×10^{7} J/kg
× 0.4 20 mi/gal 

=  1.54 MJ 
This overestimation provides an appropriate upper bound to the amount of energy absorbed by piezoelectric devices from one car moving across a one kilometer strip (i.e. no more than 1.5 MJ). Of course, some of this "mechanical" (i.e. nonthermal) energy is lost as various forms of friction and used for other processes inside the vehicle (such as air conditioning), and not nearly all of the vibrational energy will be absorbed by the devices in the road. If the devices are embedded on a busy street, then such a street will generate at most this amount of energy multiplied by the number of cars moving across the street. If such a street or highway sees an average of 600 vehicles per hour (as assumed by Innowattech), then the energy provided by these devices on a onekilometer stretch could power at most 105 WesternU.S. homes (with a total of 257 kW). [1,2] If the calculation were repeated for only 18wheelers (with about 5 mpg), the maximum amount of homes a onekilometer strip could power would increase to 421 homes (with 1 MW).
However, a more reasonable approximation can be made by using the fact that approximately 5% of the energy consumed by the car is lost as rolling friction, although rolling friction accounts for both internal friction in the wheels and friction due to the asphalt. [5] By replacing thermal efficiency in the above equation with 5%, the amount of energy released into the ground for one 20 mpg car would decrease to 0.19 MJ. This onekilometer strip could then power at most 13 homes (32 kW) for the 20 mpg car, or 52 homes (128 kW) for an 18wheeler. For this calculation, there is still a major assumption that all the vibrational energy of the road is captured by piezoelectric devices.
It is not clear whether the numbers currently used to quantify generating capacity are misguided or simply misreported, but under the optimistic assumptions stated above, piezoelectric devices over a onekilometer strip of road will generate power for only about 15 homes. Unless the road carries only 5 mpg vehicles (or many more than 600 vehicles per hour), it is unlikely that anywhere near 400 kW of power can be generated from one kilometer.
With the price of gasoline hovering around $4 a gallon for the past year, the cost of driving a 20 mpg car across one kilometer is about $0.124. And by recent retail prices of residential electricity on the West Coast, the 0.19 MJ generated by one car costs about $0.0064, or about one twentieth the cost of the gasoline burned across this onekilometer strip. [6] At this rate, the road will generate a revenue of $33,565 per year.
As an approximate, the price of a piezoelectric device can be estimated by its most expensive element, namely the piezoelectric component. This component, according to Innowattech's patent, is comprised of about 50% leadzirconate titanate (PZT) ceramic and is about 14×14×2 cm^{3} in dimension. [7] Given that piezoelectric sheets of the same material currently cost $165 in bulk from Piezo Systems (for 100 sheets of 10.64 cm^{3} each), the cost per cm^{3} of this material is about $0.155. Since the devices are embedded 30 cm apart from each other and in two rows per lane, a kilometer of a twoway street will contain 13,333 devices, each device costing $30.39, adding to a total of $405,253. Even without considering the manufacturing or installation costs, it would take about 12 years to earn back this amount from the device revenue.
Generating capacity and profitability are two important factors to consider in choosing this energy alternative. There is currently a significant cap on the generating capacity. Net profits will only be seen after at least 12 years, as an underestimate. There are also many more "costs," besides the financial costs of manufacturing and installation, to take into account, such as the environmental impact of manufacturing the PZT ceramics used in Innowattech's devices. While piezoelectric devices are gaining popularity, they are less capable than previously claimed because of physical limitations.
© Rex Garland. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] K. Diamond, "Climate Change, Sustainable Development, and Ecosystems Committee Newsletter," American Bar Association, July 2009.
[2] "Annual Energy Review 2011," U.S. Energy Information Administration, DOE/EIA0384(2011), September 2012.
[3] "Assembly Bill No. 306," California Legislature, 9 Feb 11.
[4] "Legislative Index and Table of Sections Affected," California Legislature, 30 Nov 12.
[5] A. Bandivadekar et al., "On The Road In 2035: Reducing Transportation's Petroleum Consumption And GHG Emissions," Massachusetts institute of Technology, LFEE 200805 RP, July 2008.
[6] "Electric Power Monthly with Data for August 2012," U.S. Energy Information Administration, October 2012.
[7] H. Abramovich et al., "Power Harvesting From Railway; Apparatus, System and Method," U.S. Patent 7812508, 12 Oct 10.