弓箭手悖论
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弓箭手悖论(Archer's paradox),是指射箭时,尽管箭刚搭上弦时指向目标的侧面,看起来好像会射偏。但射出的箭还是会沿着拉满弓时箭头指示的方向前进,进而命中目标。箭射出时箭身的弯曲可以解释这一悖论。
弓箭手悖论一词最早由E.J. Rendtroff在1913年提出[1],当时理解的原因是箭被射出时箭身弯曲偏离弓(第一次被Clarence Hickman拍摄到)[2][3],并在朝目标飞行过程中不断左右来回弯曲[4]。这种动态的弯曲过程常常被错误的用来指代 “弓箭手悖论”,给那些只熟悉现代的中心撒放弓的人造成误解。因为中心撒放弓的箭身总是指向目标,在射击过程中并未真正出现这种看似矛盾的现象。
细节
[编辑]箭必须具有足够的挠度(或称刚性或 “动态挠度”),才能在瞄准时偏离弓身、但射出后回到正确的飞行路线上[5]。如果箭的挠度不正确,箭与弓接触的接触情况不确定,从而箭飞出后的受力也无法预测导致准头下降[6]。另外,如果弓箭选手选用挠度各不相同的几只箭,射出时箭身会有不同的弯曲,因此会命中不同的位置。因此,专业弓箭手不仅要根据弓尽量选用挠度在合理范围内的箭,也要注意一组箭的挠度要高度一致。[7]这些要求可以在静态挠度测试仪的帮助下实现。
弓的选择与挠度
[编辑]拉力较弱的弓需要配挠度较低的箭(挠度是箭身的刚性)[8]。拉力较弱的弓在加速箭时造成箭身的变形较小(参考欧拉挫曲),因此箭在射出前必须较容易被弯曲。相反,拉力大的弓需要挠度较大的箭,因为箭被加速时产生的弯曲效果更加显著[9]。如果箭的挠度太大(箭身较硬),箭身较难被弯曲。因此撒放后随着弦靠近弓,箭头会被迫射向目标的旁边。反之,如果箭的挠度太小(箭身较软)变形太大,加速时会射向目标的另一边。极端情况下,箭身可能在撒放之前折断,造成安全隐患。[10][11][12]
校准
[编辑]动态挠度很大程度上取决于箭杆长度,箭头重量,与静态挠度。静态挠度是静态条件下箭杆中点的刚性[13]。射箭贸易协会(ATA)(原称为射箭制造商和招商局组织(AMO))静态挠度测试方法是在26英寸(0.66米)箭杆的中点处悬挂2磅(0.91千克)的重物[14][15]。美国检测与材料协会(ASTM)F2031-05(《箭杆静态挠度(刚度)测量的标准检测方法》)为在28英寸(0.71米)箭杆的中点处悬挂1.94磅(0.88千克)的重量[16]。 (过时的)英国国家射箭协会(GNAS)系统使用1.5磅(0.68千克)的重量并将箭身两端(两支点位于箭头之后和扣弦处之前)支起。由于两支点间距离不固定, GNAS不能直接转换为ATA或ASTM,现已废弃不再使用。
挠度的主要测量单位是千分之一英寸的偏转(500的偏转等于0.500英寸)。有时也通过将26除以英寸的偏转,将此数值转换为磅。 (26除以0.500等于挠度为52磅)[17][17]
引用
[编辑]- ^ The Toxophilist’s Paradox. Forest and Stream. 1913-02-08.
- ^ Rheingans, W. R. Exterior and Interior Ballistics of Bows and Arrows - Review. Archery Review. March–April 1936: 236 ff.
- ^ Rheingans, W. R.; Nagler, F. Spine and Arrow Design. American Bowman Review. June–August 1937: 226–232.
- ^ Park, James L. Arrow behaviour in the lateral plane during and immediately following the power stroke of a recurve archery bow. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology. 2013-09-08, 227 (3): 172–183 [9 November 2012]. doi:10.1177/1754337112464844.
- ^ Park, James L. High-speed video analysis of arrow behaviour during the power stroke of a recurve archery bow. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology. June 2013, 227 (2): 128–136 [1 June 2012]. doi:10.1177/1754337112446406.
- ^ Carmichael, A. Ron. Archer's Paradox. texasarchery.org. Texas State Archery Association. 2001-06-24 [2013-02-13]. (原始内容存档于2013年10月20日).
- ^ The Archer's Paradox. Bega Valley Traditional Archers. February 2013 [2013-02-13]. (原始内容存档于2013-04-09).
- ^ Jim Hill's Spine Tester. texasarchery.org. Texas State Archery Association. [2013-02-13]. (原始内容存档于2013-10-20).
- ^ Carbon Arrow University. Hunter's Friend LLC. 2011 [2013-02-13]. (原始内容存档于2016-04-04).
- ^ Controlling Dynamic Arrow Spine (PDF). Arrow Trade Magazine. July 2006 [2013-02-13]. (原始内容 (PDF)存档于2013-10-21).
- ^ Rieckmann, Marianne; Park, James L.; Codrington, John; Cazzolato, Ben. Modelling the three-dimensional vibration of composite archery arrows under free–free boundary conditions (PDF). Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology. June 2012, 226 (2): 114–122 [3 April 2012] [2013-02-13]. doi:10.1177/1754337112442273. (原始内容 (PDF)存档于2021-03-01).
- ^ Yononindo, Daniel. Archers Paradox up to the Limit !!! Extended Version. YouTube. 2012-02-02. 事件发生在 6m15s [2017-08-03]. (原始内容存档于2016-03-10).
The breaking of the arrow at the end of the video was NOT due to a lack of knowledge on my part !!! IT WAS QUITE DELIBERATE !!!
- ^ Arrow Spine Information (PDF). yeoldedelphbowmen.com. December 2012 [2013-02-13]. (原始内容 (PDF)存档于2013-10-20).
- ^ AMO Standards (1987) (PDF). Archery Manufacturers and Merchants Organization. 1987 [2013-02-13]. (原始内容存档 (PDF)于2020-11-12).
- ^ AMO Standards (2001) (PDF). Archery Manufacturers and Merchants Organization. 2001 [2013-02-13]. (原始内容存档 (PDF)于2021-06-13).
- ^ ASTM F2031 - 05(2010) Standard Test Method for Measurement of Arrow Shaft Static Spine (Stiffness). American Society for Testing and Materials. 2010 [2013-02-13]. (原始内容存档于2021-03-01).
- ^ 17.0 17.1 Cosgrove, Gabriela. Wooden Arrows. The Traditional Bowyer's Bible. Volume Three. Guilford: The Lyons Press. 1994: 228. ISBN 1-58574-087-X.