201. The static deformation of the asymmetric Japanese bow: modelling bow asymmetries with the elastica theory
- Author
-
G. Mariani and M. Matsuo
- Subjects
Physics ,Mechanical Engineering ,Geometry ,02 engineering and technology ,Deformation (meteorology) ,Condensed Matter Physics ,Elastica theory ,01 natural sciences ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,Position (vector) ,Bending stiffness ,0103 physical sciences ,Development (differential geometry) ,Total energy ,010301 acoustics ,Energy (signal processing) - Abstract
The static deformation of symmetric bow limbs has been widely studied in the last century. However, asymmetries in shape and length which correspond to a more realistic situation, have not been thoroughly investigated. Here, we report a model for asymmetric bows based on the elastica theory and solved numerically by the Runge–Kutta method. We apply the model to describe the large asymmetric deformation which occurs in the Japanese bow, currently employed in the Japanese martial art of Kyūdō. We compare the model with experimental data acquired from a modern glass-fiber bow and a traditional bamboo bow, different in shape and construction. The model provides accurate results in predicting the deformation and the total energy stored in the bows, as long as the bending stiffness of the limbs is correctly reproduced. The energy is reproduced with an error within 1% and the unbraced and drawn shapes are reproduced with an RMSE of few millimeters compared to the length of $$\sim \,2.2\,\hbox {m}$$ of the bows. We investigate the influence of the grip position on the bow strength and shape which is not possible using classic symmetric models. At the end we show the possibility to analyze the bow design and potential failures by computing the bending stress extracted from the solution of the model. This study provides a further development with respect to the existing bow models by including the effect of the limb’s asymmetries in the static performances of the bows. The model for asymmetric limbs can bring important contributions for the design of the bows, reconstruction of ancient bows as well as to study the influence of the asymmetries on the targeting performance in modern competitive archery.
- Published
- 2020