| Research Abstract |
In this project, the unfolding pattern of regularly corrugated simple leaves such as hornbeam, beech, common alder and silver birch leaves were observed from buds to fully unfolded leaves. Based on these observations, a number of numerical models with various vein angles were considered to investigate the effect of vein angles on the unfolding manner of a corrugated leaf. By using vector analysis and transformation of coordinates, the unfolding of a corrugated leaf was simulated. The kinematic energy during unfolding of leaves was also estimated to examine the effects of vein angle, alpha, and crease interval ratio, alpha*(= alpha_2/alpha_1, alpha_1 the distance from a valley crease to a crest crease, alpha_2 the distance from a crest crease to a valley crease), on the unfolding manners.
From the simulation, the leaf with large alpha such as 75ﾟ or 85ﾟ can be folded more compactly than that with small alpha like 30ﾟ or 45ﾟ, From the geometry of leaves fully folded, therefore, large alph
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a are recommended. From the leaf are a during unfolding, however, it can be considered that the leaf with small alpha is more favorable than that with large alpha. Because, the leaf with small alpha can keep relatively large leaf area in the early stage of unfolding. In addition, the whole energy required for the fully unfolding leaves increases with the increase of alpha. This means that small alpha may be more advantageous for corrugated leaves than large alpha. Common beech, hornbeam and common alder have corrugated leaves whose most alpha are 30ﾟ- 50ﾟ. This appears to be a quite adequate choice from thinking about unfolding manner such as the geometrical properties of fully folded leaf, the leaf area during unfolding and energy consumed by full open of leaves.
The leaf of hornbeam has alpha* = 1.0 and unfolds keeping a flat shape. On the other hand, the leaves of common alder with alpha* = 1.4 unfold with V-shape. Although total kinetic energy does not change in leaves with alpha* * 1.0 and alpha* = 1.4, the folding pattern with alpha* 1.0 has a big advantage, i.e. the relatively thick veins do not overlap each other. Less
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