The optimal distribution of the reinforcing fibers for stiffening hollow cylindrical composites is explored using the linear elasticity theory. The spatial distribution of the vascular bundles in wild bamboo, a nature-designed functionally graded material, is the basis for the design. Our results suggest that wild bamboos maximize their flexural rigidity by optimally regulating the radial gradation of their vascular bundle distribution. This fact provides us with a plant-mimetic design principle that enables the realization of high-stiffness and lightweight cylindrical composites.

Bamboo has a distinctive structure wherein a long cavity inside a cylindrical woody section is divided into many chambers by stiff diaphragms. The diaphragms are inserted at nodes and thought to serve as ring stiffeners for bamboo culms against the external load; if this is the case, the separation between adjacent nodes should be configured optimally in order to enhance the mechanical stability of the culms. Here, we reveal the hitherto unknown blueprint of the optimal node spacings used in the growth of wild bamboo. Measurement data analysis together with theoretical formulations suggest that wild bamboos effectively control their node spacings as well as other geometric parameters in accord with the lightweight and high-strength design concept.

I investigated the relationships between stem surface area outside bark and other stem dimensions for Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) trees. The stem dimensions used here were the basal area and the product of diameter at breast height (dbh) and total tree height. The regression equation of the stem surface area s against basal area g was s = 184.216 g for the cedar trees and s = 156.878 g for the cypress trees. The slope of the equation was significantly different between the two species. For the same dbh, the cedar trees tended to have a higher total tree height than the cypress trees. The cedar trees also had a larger surface area of relative stem form than the cypress trees. These results indicated that the difference in the slope was produced by the differences in both the stem slenderness and tapering between the two species. On the other hand, the regression equation between the stem surface area and the product of dbh and total tree height dh was s = 1.937 dh for the cedar trees and s = 1.921 dh for the cypress trees, whereas no significant difference in the slope was found. The obtained slopes for the cedar and cypress trees seemed to be in accord with that for other coniferous species reported in earlier studies, suggesting that the variation in the slope among coniferous species would be small. The estimation from the basal area would provide a simpler means for estimating the stem surface area and would be useful in obtaining an approximation of the surface area. By contrast, the estimation from the product of dbh and total tree height would provide a more accurate and precise estimate as well as a wider applicable range, i.e., a parameter for physiological growth models. In conclusion, it could not be judged which regression equation examined in the present study was superior to the other, and thus it was important to select an appropriate equation depending both on the purpose and on the time and labor available.

Recently, an inexpensive digital camera that can equip with a fish-eye converter lens, FC-E8, has been available from Nikon. The converter has more than 180° view angle and lens distortion. The objectives of the present study were to develop a procedure for calibrating the view angle and lens distortion of the fish-eye converter, and to examine the effect of the calibration on light environment estimates. Based on unpublished data provided by the Electric Image Technical Center of Nikon, a 12-order poly-nomial expression for the calibration was derived. The expression enabled us to calibrate the view angle and lens distortion for all selectable resolution digital images. Using a Nikon Coolpix 990 digital camera with the fish-eye converter, 105 hemispherical photographs were taken in 15 stands, and then the canopy cover and weighted openness were measured as the light environment estimates. The calibrated estimates were significantly higher than uncalibrated ones, but the differences were comparatively small, with the average differences being 0.658% for canopy cover and 0.344% for weighted openness. A strongly positive correlation between calibrated and uncalibrated estimates was observed. Both slope and intercept of the regression lines of the calibrated estimate against the uncalibrated one were significantly different between canopy cover and weighted openness, suggesting that the calibration effect would be different among light environment estimates. In conclusion, we should pay attention to the view angle and lens distortion of the fish-eye converter in estimating light environments using the Coolpix digital camera.