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Optical Design & Engineering

Toward a flexible electronic flying carpet

Piezoelectrically deformed substrates provide traveling wave-induced aerodynamic propulsive forces for a flat plastic sheet.
23 May 2013, SPIE Newsroom. DOI: 10.1117/2.1201305.004838

After being intrigued by a theoretical paper with calculations describing the principles that might be applied to a flying carpet1 a few years ago, we set out to make one. Our resulting ‘flying carpet’ consists of a flat plastic sheet a few inches in size and about 1/100th of an inch thick. The sheet consists of special piezoelectric material that expands or contracts when an electrical voltage is applied to it.2 By making an appropriate layered structure, the sheet can be induced to bend, or curve itself, when voltage is applied. With multiple electrodes to apply different voltages in different sections, the sheet can be caused to bend into a snake-like shape, that is, one that bends up and down along its length, as shown in Figure 1. Finally, by varying the voltage over time, the snake-like oscillation can move forward or backward in a shape technically known as a traveling wave.

This traveling-wave shape is somewhat related to the way certain biological objects, such as manta rays or cells with flagella, propel themselves.3 Figure 1 shows a schematic diagram of a flying carpet sheet just above the ground. As the wave moves backward, it traps some air under a high peak of the wave, and pushes that section of air toward the back of the sheet as the high peak moves backward, eventually expelling it out the back end of the sheet. By Newton's laws of equal and opposite reactions, as the air is pushed backward, the sheet must be propelled forward.

Figure 1. Cross section of ‘flying carpet’ sheet just above the ground, changing its shape with time (at times t0 to t5). As the wave shape moves to the right, it pulls air with it and pushes it out to the right, resulting in a propulsive force Fp, which pushes the sheet forward to the left.2h0: Height above the ground.

To create the exact snake-like shape moving with time required to get the ‘carpet’ to propel itself was very complicated4 and required a few years of work. First, we had to build in sensors throughout the carpet to measure its shape at any given time. If the shape was not the exact one desired, the voltages driving the piezoelectric actuators, which caused the bending, were adjusted until the desired shape was obtained. Due to non-linearities and other real-world imperfections, if we wanted the sheet to move up and down 500 times per second, in the end electrical inputs with components oscillating as fast as 2500 times per second were required.

Figure 2. Propulsive force generated by a sheet as a function of the amplitude of the vertical wave. The wave frequency was 100Hz. The force was measured by attaching the carpet to a spring, and measuring how far it stretched the spring (‘lateral displacement’).2

We used two basic experimental arrangements. In one, the movement of the sheet was constrained by its ‘tethers’ (i.e., the wires from the sensors and actuators) and the height of the carpet above the ground was experimentally adjusted. In the second, we designed a ‘cart’ holding all the wires to automatically follow the carpet, so that it could move without being constrained by the wires. Figure 2 shows an example of data taken from a sheet that was propelling itself. The vertical axis shows the measured force and the horizontal axis shows the magnitude of the wave. Data is shown for conditions with the sheet at three different heights above the ground (1, 1.5, and 2mm). Forces pushing the sheet to the right (defined as positive) were observed when the wave moved to the left, and the sheet was pushed to the left (negative force) when the wave moved to the right, as expected.

One challenge involves integrating onboard electronics as thin-film transistors, power sources, and so on. Another key issue at present is friction with the ground when the carpet starts up. It needs to hit a critical velocity of ∼20 cm/s to attain ‘lift-off’ so that friction with the ground no longer matters. Right now it can propel itself only to a few centimeters per second while on the ground, and we are considering routes to improve this. Finally, looking to the future, because the device has no moving parts, such as motors, gears, or axles, it might be well suited for environments where high reliability is required, exploring the Martian surface, for example.

James Sturm
Department of Electrical Engineering
Princeton University
Princeton, NJ

James C. Sturm, the William and Edna Macaleer Professor of Engineering and Applied Science, has been a professor at Princeton since 1986. He received his BS in electrical engineering from Princeton University, and his MSEE and PhD from Stanford University.

Noah Jafferis
Wyss Institute Harvard University
Cambridge, MA

Noah T. Jafferis is currently a postdoctoral fellow. He received his BS from Yale in 2005, and his PhD in electrical engineering from Princeton University in 2012. He was home-schooled before matriculating at Yale University at the age of 16.

1. M. Argentina, J. Skotheim, L. Mahadevan, Settling and swimming of flexible fluid lubricated foils, Phys. Rev. Lett. 99, p. 224503, 2007. doi:10.1103/PhysRevLett.99.224503
2. N. T. Jafferis, H. A. Stone, J. C. Sturm, Traveling wave-induced aerodynamic propulsive forces using piezoelectrically deformed substrates, Appl. Phys. Lett. 99(11), p. 114102, 2011. doi:10.1063/1.3637635
3. A. J. Reynolds, The swimming of minute organisms, J. Fluid Mech. 23(2), p. 241-360, 1965.
4. N. T. Jafferis, J. C. Sturm, Fundamental and experimental conditions for the realization of traveling-wave induced aerodynamic propulsive forces by piezoelectrically-deformed plastic substrates, IEEE J. Microelectromech. Syst. 22, p. 495-505, 2013.