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.

中文翻译：

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不对称日本弓的静态变形：用弹性理论模拟弓不对称

对称弓肢的静态变形在上个世纪得到了广泛的研究。然而，对应于更现实情况的形状和长度的不对称尚未得到彻底研究。在这里，我们报告了一个基于弹性理论的非对称弓形模型，并通过 Runge-Kutta 方法进行了数值求解。我们应用该模型来描述日本弓中发生的大的不对称变形，目前日本弓道武术中采用了这种变形。我们将该模型与从形状和结构不同的现代玻璃纤维弓和传统竹弓获得的实验数据进行比较。只要正确再现四肢的弯曲刚度，该模型就可以提供准确的结果来预测变形和存储在弓中的总能量。与弓的 $$\sim \,2.2\,\hbox {m}$$ 的长度相比，能量以 1% 以内的误差再现并且未支撑和绘制的形状以几毫米的 RMSE 再现。我们研究了握把位置对弓强度和形状的影响，这是使用经典对称模型无法实现的。最后，我们展示了通过计算从模型解中提取的弯曲应力来分析弓设计和潜在故障的可能性。该研究通过将肢体不对称性对弓的静态性能的影响包括在内，为现有弓模型提供了进一步的发展。非对称肢体的模型可以为弓的设计带来重要的贡献，