{"id":394,"date":"2023-12-11T19:48:50","date_gmt":"2023-12-11T19:48:50","guid":{"rendered":"https:\/\/artchery.org\/wordpress\/?page_id=394"},"modified":"2024-09-28T19:12:13","modified_gmt":"2024-09-28T19:12:13","slug":"shape-of-the-yumi","status":"publish","type":"page","link":"https:\/\/artchery.org\/wordpress\/index.php\/shape-of-the-yumi\/","title":{"rendered":"Shape of the Yumi"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"394\" class=\"elementor elementor-394\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fec373d e-flex e-con-boxed e-con e-parent\" data-id=\"fec373d\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ff381b7 elementor-widget elementor-widget-heading\" data-id=\"ff381b7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.18.0 - 08-12-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Designing the Urazori Shape of a Yumi<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9ee2bda e-flex e-con-boxed e-con e-parent\" data-id=\"9ee2bda\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-115d9b3 elementor-widget elementor-widget-text-editor\" data-id=\"115d9b3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.18.0 - 08-12-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><strong>Here, we address the pragmatic question:\u00a0 What Urazori (reverse curve) shapes result in a chosen braced shape?\u00a0 Anticipating the actual construction of yumi, we require a quantitative answer.\u00a0 Traditional yumishi laminate an initially extreme Urazori shape, and the final Urazori shape is adjusted by heat aided bending.\u00a0 We anticipate using modern materials.\u00a0\u00a0 In particular, there may be carbon laminations between the bamboo back and belly laminations and the core.\u00a0\u00a0 Such a construction does not have the malleability of a traditional take-yumi, made of all natural materials. \u00a0 The correct Urazori shape has to be achieved at the outset.\u00a0 Little adjustment is possible.\u00a0\u00a0 The phrasing of the initial question suggests that there may be more than one Urazori shape corresponding to the correct braced shape.\u00a0 This is true and we will come to that.\u00a0 We begin with a simplified review of how forces applied to the ends of an elastic beam bend it.\u00a0 Of course we have in mind the yumi as the beam, and the\u00a0 string tensions due to the tsuru are the forces.<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5d7ab47 elementor-widget elementor-widget-text-editor\" data-id=\"5d7ab47\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Figure 1 compares the braced shape with the unbraced Urazori (reverse curve) shape of a Don Symanski yumi.\u00a0 We&#8217;ve seen this yumi before while investigating the aesthetics of yumi shape.\u00a0 (Figures 5 and 6 of the page <a href=\"ttps:\/\/artchery.org\/wordpress\/index.php\/aesthetics-geometry-and-the-yumi\/\">&#8220;Geometry, Aesthetics and the Yumi.&#8221;<\/a>)<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-af6e4f2 elementor-widget elementor-widget-image\" data-id=\"af6e4f2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.18.0 - 08-12-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"664\" height=\"242\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/Braced_urazori.jpg\" class=\"attachment-large size-large wp-image-1297\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/Braced_urazori.jpg 664w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/Braced_urazori-300x109.jpg 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 1:  Braced and unbraced shapes.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aa7703d elementor-widget elementor-widget-heading\" data-id=\"aa7703d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Curvature and bending<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-473c19c e-flex e-con-boxed e-con e-parent\" data-id=\"473c19c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9d3251d elementor-widget elementor-widget-text-editor\" data-id=\"9d3251d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The physics of bending in a plane singles out the geometric property called &#8220;curvature.&#8221;\u00a0 Figure 2 shows a section of a smooth plane curve.\u00a0 We assign a definite direction or &#8220;orientation&#8221; of the curve as indicated by the arrows in Fig. 2.\u00a0 At any point p along the curve, there is a circle which most closely &#8220;kisses&#8221; it.\u00a0 Imagine the curve as a trail, and you are walking along it and looking in the direction indicated by its orientation.\u00a0 If at point p, you see the portion of circle near you to your left, the curvature at p is defined to be the reciprocal of the circle&#8217;s radius r,<\/p><p>\u03ba = 1\/r.<\/p><p>If the nearby portion of circle is to your right, like at point q, the curvature is the negative of the reciprocal,<\/p><p>\u03ba = -1\/r.<\/p><p>Look at the curve in Fig. 2 from above.\u00a0 At the point p where the curvature is positive, the curve looks concave.\u00a0\u00a0 At the point q where the curvature is negative, it looks convex.\u00a0 In describing yumi shapes, we&#8217;ll refer to visualizations like the top panel of Fig. 1:\u00a0 The tsuru is horizontal and the yumi is &#8220;above&#8221; it.\u00a0 Then yumi segments with negative curvature are concave when seen from the above (or the back) and segments with positive curvature are convex.\u00a0<\/p><p>Having defined curvature of an elastic beam in a plane, we define &#8220;bending&#8221; at a material point along the beam as the change in curvature induced by forces acting on it.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fc57057 elementor-widget elementor-widget-image\" data-id=\"fc57057\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"768\" height=\"345\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/curva-768x345.jpg\" class=\"attachment-medium_large size-medium_large wp-image-1330\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/curva-768x345.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/curva-300x135.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/curva.jpg 771w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 2:  The definition of curvature.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5048393 e-flex e-con-boxed e-con e-parent\" data-id=\"5048393\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4a1796e elementor-widget elementor-widget-heading\" data-id=\"4a1796e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Bending and the torque identity<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9109013 elementor-widget elementor-widget-text-editor\" data-id=\"9109013\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Bending is quantified by the &#8220;torque identity.&#8221;\u00a0 In Fig. 3, the elastic beam is represented by the brown curve, oriented from left to right.\u00a0 You can think of it as a portion of yumi limb below the grip.\u00a0 The tsuru extends from the tip (0, 0) along the x axis to the right, exerting a horizontal tension force F.\u00a0\u00a0 What is the change\u00a0\u00a0 \u0394 \u03ba of curvature at a material point (x, y) along the beam?\u00a0 Intuitively, a force applied at the end (0, 0) is more effective at bending if it is perpendicular to the displacement from (0, 0) to (x, y).\u00a0 In Fig. 3, this displacement is represented by an arrow, and l denotes its length.\u00a0 F&#8217; denotes the component of the force perpendicular to this displacement.\u00a0 The change of curvature at the material point (x, y) along the limb is directly proportional to F&#8217;:\u00a0 We have the &#8220;torque identity,&#8221;<\/p><p>\u03bc \u0394 \u03ba = &#8211; l F&#8217;.<\/p><p>The positive number \u03bc is called the &#8220;bending stiffness&#8221; of the beam at the material point (x, y). \u00a0 The right hand side -lF&#8217; is called the &#8220;torque exerted by the horizontal force F on the beam at (x, y).&#8221;\u00a0 Geometrically, the product lF&#8217; is the area of the pink parallelogram in Fig. 3.\u00a0\u00a0 This area is also given by Fy, so we have the alternative form of the torque identity,<\/p><p>\u03bc \u0394 \u03ba = -yF.<\/p><p>This form of the torque identity informs the relationship between braced and Urazori shapes.\u00a0<\/p><p>This simple description of the torque identity idealizes the yumi as an elastic material curve with no thickness.\u00a0 Practical design calculations are improved by acknowledging the actual thickness of a physical yumi.\u00a0 In a simple model, we imagine that the mass and elasticity of the yumi are concentrated along a center line between the back and belly. The tips of this center line curve lie above the ends of the tsuru by half of the limb thickness.\u00a0\u00a0 The elevation profile is taken relative to the tsuru.\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ce508da e-flex e-con-boxed e-con e-parent\" data-id=\"ce508da\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2c3fbe1 elementor-widget elementor-widget-image\" data-id=\"2c3fbe1\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"296\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/tor_ID.jpg\" class=\"attachment-large size-large wp-image-1347\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/tor_ID.jpg 739w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/tor_ID-300x120.jpg 300w\" sizes=\"(max-width: 739px) 100vw, 739px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 3:  Geometry of the torque identity.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cebf09d elementor-widget elementor-widget-heading\" data-id=\"cebf09d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Unbraced Urazori shape determined from the braced shape<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f823c6f elementor-widget elementor-widget-text-editor\" data-id=\"f823c6f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>For a given braced yumi, the string tension F has some definite value.\u00a0 The elevation y and stiffness \u03bc are definite functions of length along the yumi, called &#8220;elevation and stiffness profiles.&#8221;\u00a0 Given the tsuru tension and elevation and stiffness profiles, the torque identity determines the curvature changes \u0394 \u03ba along along the length of the yumi when we brace it.\u00a0 If the braced shape is prescribed, then so is the braced curvature \u03ba <sub>B<\/sub>. We may now calculate the Urazori curvature profile from<\/p><p>\u03ba<sub>U<\/sub> = \u03ba<sub>B<\/sub> &#8211; \u0394 \u03ba.<\/p><p>Finally, we determine the Urazori shape from its curvature profile.\u00a0 We now proceed with the operational details.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cfee1ed elementor-widget elementor-widget-heading\" data-id=\"cfee1ed\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">Spline approximations of yumi shapes <\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f2a6262 elementor-widget elementor-widget-text-editor\" data-id=\"f2a6262\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>In the article <a href=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/09\/Urazori.pdf\">&#8220;Geometry, Aesthetics and the Yumi,&#8221;<\/a> we characterized the five curves of a yumi by their lengths and depths.\u00a0\u00a0 In the top panel of Fig. 4, the hollow dots represent curve endpoints which are also inflection points where the curvature vanishes.\u00a0 The depth of a curve is the perpendicular distance of the curve&#8217;s midpoint from the chord line connecting its endpoints.\u00a0 In Fig. 4, we&#8217;ve drawn the chord of the second curve from the top, and indicted its depth h.\u00a0 Recall that the depth is positive for curves which are convex when seen from the back, and negative if concave.\u00a0 Given the length and depth of any curve, we approximate the shape between its endpoints by a mathematically simple curve, generally called a &#8220;spline.&#8221;\u00a0 The splines we use are very close to half periods of a sine wave, so we call them &#8220;trigonometric splines.&#8221;\u00a0 The &#8220;spline approximation&#8221; to the yumi shape is obtained by joining the splines end to end in the correct order. \u00a0 In the bottom panel of Fig. 4, the green curve is the spline approximation based on the measured curve lengths and depths of the Yonsun yumi in Fig. 4.\u00a0 The spline of any given curve is symmetric about its midpoint.\u00a0 The second curve of the actual yumi is not symmetric about its midpoint, with its right side bulging above the spline curve.\u00a0 As we shall see, there is some weakness there.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e58bae1 e-flex e-con-boxed e-con e-parent\" data-id=\"e58bae1\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-61529be elementor-widget elementor-widget-image\" data-id=\"61529be\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"267\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/curve_splines-1024x267.jpg\" class=\"attachment-large size-large wp-image-1511\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/curve_splines-1024x267.jpg 1024w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/curve_splines-300x78.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/curve_splines-768x200.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/curve_splines.jpg 1028w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 4:  Top panel: The hollow dots are endpoints of the five curves of the Don Symanski Yonsun yumi in Fig. 1.  We visualize the depth h of the second curve as the elevation of its midpoint above its chord line.  Bottom panel: Spline approximation to the shape of the yumi.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9e6b9d9 e-flex e-con-boxed e-con e-parent\" data-id=\"9e6b9d9\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-61c70cd elementor-widget elementor-widget-heading\" data-id=\"61c70cd\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">The stiffness profile<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-78c5407 e-flex e-con-boxed e-con e-parent\" data-id=\"78c5407\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c1748e1 elementor-widget elementor-widget-text-editor\" data-id=\"c1748e1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Intuitively, the stiffness of a yumi is the greatest at the grip and decreases as we move towards either tip.\u00a0 What do stiffness profiles of actual yumi look like?\u00a0 We get an idea by estimating the\u00a0 stiffness profile of the Don Symanski yumi depicted in Fig. 1. \u00a0\u00a0 The estimated stiffness profile is deduced from suitable measurements and the torque identity:\u00a0 We measure the tsuru tension of the braced yumi.\u00a0 By comparing\u00a0 shapes of the braced and unbraced yumi,\u00a0\u00a0 we deduce the curvature change profile induced by bracing.\u00a0 Knowing the tsuru tension F, the elevation profile y of the braced yumi and the curvature change profile \u0394 \u03ba induced by bracing, we estimate the stiffness profile by &#8220;solving&#8221; the torque identity for the stiffness profile \u03bc.\u00a0 Details are spelled out in the article <a href=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/09\/Urazori.pdf\">&#8220;Shape of the Yumi&#8221;<\/a> linked to this page.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9f4880e e-flex e-con-boxed e-con e-parent\" data-id=\"9f4880e\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f0719a3 elementor-widget elementor-widget-text-editor\" data-id=\"f0719a3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The horizontal axis of the graph in Fig. 5 is length s along the yumi measured from the upper tsuru nock in centimeters.\u00a0 The vertical axis is the stiffness \u03bc in kilograms meters squared (kg m<sup>2<\/sup>).\u00a0 The physical units kg m<sup>2<\/sup> of stiffness is informed by the torque identity.\u00a0 In the right hand side, the tsuru tension F is measured in kilograms, and the braced elevation y in meters, so the right hand side has physical units of kilograms times meters.\u00a0 In the left hand side, curvature and hence the change \u0394 \u03ba in curvature is measured in inverse meters.\u00a0 The balance of physical units in the torque identity indicates that the physical units of stiffness are kilograms times meters squared.\u00a0 The discrete data points are obtained by measurements of braced elevation y and curvature change \u0394 \u03ba induced by bracing at distinct material points along the yumi.\u00a0 The diamonds correspond to belly or back nodes, the circles to midpoints between adjacent back and belly nodes.\u00a0 You would expect the stiffness at nodes to be a bit higher than between nodes, and the data is mostly consistent with this.\u00a0 Recall that the right side of the second curve from the top appears to be weak, because it bulges above the spline approximation in Fig. 4.\u00a0 We can see the weak section in the fifth data point of Fig. 5 above the grip.<\/p><p>Underlying the scatter in the data, we see\u00a0\u00a0 decreases in stiffness away from the grip which is roughly proportional to distance from the grip.\u00a0 The stiffness near the tips is roughly half of the stiffness at the grip.\u00a0 In our design of the Urazori shape, we assume this simple structure of the stiffness profile.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9ef4ae8 elementor-widget elementor-widget-image\" data-id=\"9ef4ae8\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"828\" height=\"661\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/stiff_profile.jpg\" class=\"attachment-large size-large wp-image-1433\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/stiff_profile.jpg 828w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/stiff_profile-300x239.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/stiff_profile-768x613.jpg 768w\" sizes=\"(max-width: 828px) 100vw, 828px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 5:  Measured stiffness profile of the Don Symanski yumi.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3c73015 e-flex e-con-boxed e-con e-parent\" data-id=\"3c73015\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-172638e elementor-widget elementor-widget-heading\" data-id=\"172638e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">A test case<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-98bb94b elementor-widget elementor-widget-text-editor\" data-id=\"98bb94b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>We have a spline approximation to the braced shape of the Don Symanski Yonsun, which yields collateral approximations to the braced elevation and curvature profiles.\u00a0 We adopt the piecewise linear approximation to the stiffness profile, as in the graph of Fig. 5.\u00a0 The braced tsuru tension is measured, F = 32.05 kg.\u00a0 This is all the information we need to calculate an approximation to the unbraced curvature profile from the torque identity.\u00a0 From the unbraced curvature profile, we finally compute the predicted Urazori shape.\u00a0\u00a0 In Fig. 6, we&#8217;ve reproduced the bottom photograph of the actual Urazori shape from Fig. 1.\u00a0\u00a0 The super-positioned green curve is the predicted Urazori shape from the torque identity calculation.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49b442c elementor-widget elementor-widget-image\" data-id=\"49b442c\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1017\" height=\"172\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Yonsun_test.jpg\" class=\"attachment-large size-large wp-image-1539\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Yonsun_test.jpg 1017w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Yonsun_test-300x51.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Yonsun_test-768x130.jpg 768w\" sizes=\"(max-width: 1017px) 100vw, 1017px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 6:    The green curve is the computed Urazori shape super-positioned over the photograph of the actual Urazori shape of the Don Symanski Yonsun.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-06f8ed7 elementor-widget elementor-widget-heading\" data-id=\"06f8ed7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">The multiplicity of Urazori shapes<\/h5>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0ca7b71 elementor-widget elementor-widget-text-editor\" data-id=\"0ca7b71\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The blue curve in the top panel of Fig. 7 is the spline approximation to the shape of the braced Don Symanski Yonsun.\u00a0 The magenta curves are computed Urazori shapes corresponding to a sequence tsuru tensions between 24 kg and 44 kg.\u00a0\u00a0 We highlight the Urazori shape whose brace tension is very near the measured value, 30.05 kg.\u00a0 We define the Urazori depth as the greatest perpendicular displacement of the Urazori shape curve from the chord line between its tips.\u00a0 The second panel of Fig. 7 plots the Urazori depth versus the brace tension.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ff5e703 e-flex e-con-boxed e-con e-parent\" data-id=\"ff5e703\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-419f8af elementor-widget elementor-widget-image\" data-id=\"419f8af\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"942\" height=\"663\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/urazori_seq.jpg\" class=\"attachment-large size-large wp-image-1552\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/urazori_seq.jpg 942w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/urazori_seq-300x211.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/urazori_seq-768x541.jpg 768w\" sizes=\"(max-width: 942px) 100vw, 942px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 7:  Top panel:  Urazori shapes (magenta curves) corresponding to the braced shape of the Don Symanski Yonsun (blue curve).   Bottom panel:   The Urazori depth increases with the tsuru tension.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-87bf2cd elementor-widget elementor-widget-heading\" data-id=\"87bf2cd\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">A proposal for the yumishi<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b4405ea elementor-widget elementor-widget-text-editor\" data-id=\"b4405ea\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>In Fig. 8, the blue curve is the original &#8220;mirror symmetry&#8221; shape, which is nearly tangent to the tsuru at the lower tip.\u00a0 The green curve is a &#8220;broken mirror symmetry&#8221; shape which opens up the angle between the yumi shape and the tsuru at the lower tip.\u00a0\u00a0 The magenta curve is the &#8220;broken mirror symmetry&#8221; Urazori shape whose depth is 15 cm.\u00a0 The layup of this shape in the shop is described in the page <a href=\"https:\/\/artchery.org\/wordpress\/index.php\/yumi-making-re-examined\/\">&#8220;Yumi Making Re-examined.&#8221;<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-dc6b824 e-flex e-con-boxed e-con e-parent\" data-id=\"dc6b824\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-05e918f elementor-widget elementor-widget-image\" data-id=\"05e918f\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"863\" height=\"168\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/design.jpg\" class=\"attachment-large size-large wp-image-1553\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/design.jpg 863w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/design-300x58.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/design-768x150.jpg 768w\" sizes=\"(max-width: 863px) 100vw, 863px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 8:  Blue curve - \"mirror symmetry \" shape.  Green curve - \"broken mirror symmetry\" shape.   Magenta curve -  \"broken mirror symmetry\" Urazori shape.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-92325d1 e-flex e-con-boxed e-con e-parent\" data-id=\"92325d1\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-851fb34 elementor-widget elementor-widget-image\" data-id=\"851fb34\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"32\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/watakuri.jpg\" class=\"attachment-large size-large wp-image-80\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/watakuri.jpg 547w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/watakuri-300x18.jpg 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Designing the Urazori Shape of a Yumi Here, we address the pragmatic question:\u00a0 What Urazori (reverse curve) shapes result in a chosen braced shape?\u00a0 Anticipating the actual construction of yumi, we require a quantitative answer.\u00a0 Traditional yumishi laminate an initially extreme Urazori shape, and the final Urazori shape is adjusted by heat aided bending.\u00a0 We &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/artchery.org\/wordpress\/index.php\/shape-of-the-yumi\/\"> <span class=\"screen-reader-text\">Shape of the Yumi<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"","ast-site-content-layout":"full-width-container","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-394","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages\/394","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/comments?post=394"}],"version-history":[{"count":309,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages\/394\/revisions"}],"predecessor-version":[{"id":2686,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages\/394\/revisions\/2686"}],"wp:attachment":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/media?parent=394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}