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. 2018 Nov 5;8:16314. doi: 10.1038/s41598-018-34588-0

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Pictures of the leaves of the four species studied, from left to right: (a) Red Oak, (b) American Sycamore, (c) Yellow Poplar, and (d) Sugar Maple. Under each picture there is a plot of the area A and the polar moment of Inertia J along the petiole. An exponential fit done on J (in black) allows us to calculate α × L_p corresponding at the location where J is decreased by 99%. This coefficient α is then used to accurately determine the twisting length L_t = (1 − α)L_p.