{"id":100272,"date":"2026-02-15T20:31:18","date_gmt":"2026-02-15T20:31:18","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100272"},"modified":"2026-07-16T00:05:07","modified_gmt":"2026-07-16T00:05:07","slug":"ultrasound-velocity-materials","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/th\/calculators\/ultrasound-velocity-materials\/","title":{"rendered":"Ultrasonic Flat-Plate Ray &#038; Circular-Element Reference"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Ultrasonic Flat-Plate Ray and Circular-Element Reference Worksheet\",\"description\":\"A controlled ultrasonic reference for flat-plate leg and skip geometry, wavelength and an explicitly separate unfocused circular-element near-field calculation. It is not an inspection procedure, flaw-detection limit or acceptance decision.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/ultrasound-velocity-materials\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"browserRequirements\":\"JavaScript enabled\",\"isAccessibleForFree\":true,\"dateModified\":\"2026-07-16\",\"inLanguage\":\"en\",\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"featureList\":[\"Flat parallel-plate first-leg and full-skip ray geometry\",\"Calibrated wave-mode wavelength\",\"Circular-element exact and approximate near-field reference\",\"Strict decimal-point and decimal-comma validation\",\"Explicit calibration and model-boundary confirmations\"]}\n<\/script>\n<script 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10px;border-radius:7px;background:var(--warnbg);color:#693805;font-size:13px;font-weight:800;text-transform:uppercase}.utg-metrics{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:12px;margin:18px 0}.utg-metric{padding:15px;border:1px solid var(--line);border-radius:10px;background:var(--soft)}.utg-metric-label{display:block;color:var(--muted);font-size:13px}.utg-metric-value{display:block;margin-top:4px;font:700 18px\/1.35 ui-monospace,SFMono-Regular,Consolas,monospace;overflow-wrap:anywhere}.utg-section-label{margin:20px 0 8px;padding-bottom:6px;border-bottom:2px solid var(--line);font-size:17px;font-weight:800}.utg-formula{padding:13px 15px;border:1px solid #cbd5e2;border-radius:9px;background:#f7f9fc;font:600 15px\/1.75 ui-monospace,SFMono-Regular,Consolas,monospace;overflow-x:auto}.utg-list{padding-left:22px}.utg-list li{margin:7px 0}.utg-table-wrap{overflow-x:auto;margin-top:12px}.utg-table{width:100%;border-collapse:collapse;min-width:660px}.utg-table th,.utg-table td{padding:10px 11px;border:1px solid var(--line);text-align:left;vertical-align:top}.utg-table th{background:#edf3f8}.utg-source{padding:13px 0;border-top:1px solid var(--line)}.utg-source:first-of-type{border-top:0}.utg-tag{display:inline-block;margin-right:7px;padding:2px 7px;border-radius:4px;background:#e8eef5;color:#31475f;font-size:12px;font-weight:700}.utg-small{font-size:13px;color:var(--muted)}details.utg-card summary{cursor:pointer;font-weight:800;font-size:20px}details.utg-card[open] summary{margin-bottom:14px}\n@media(max-width:760px){#utg-tool{padding:12px}.utg-hero,.utg-card{padding:18px}.utg-grid,.utg-metrics{grid-template-columns:1fr}.utg-wide{grid-column:auto}.utg-btn{width:100%}}@media print{#utg-tool{max-width:none}.utg-actions{display:none}.utg-card,.utg-hero{box-shadow:none;break-inside:avoid}}\n<\/style>\n<main id=\"utg-tool\">\n  <header class=\"utg-hero\">\n    <span class=\"utg-kicker\">Controlled ultrasonic reference<\/span>\n    <h1>Ultrasonic Flat-Plate Ray and Circular-Element Reference<\/h1>\n    <p class=\"utg-lead\">Calculate ideal first-leg and full-skip ray geometry in a flat parallel plate, wavelength for a user-supplied calibrated wave velocity, and a separate circular-element near-field reference.<\/p>\n    <div class=\"utg-badges\"><span class=\"utg-badge\">Refracted angle from surface normal<\/span><span class=\"utg-badge\">User-supplied calibrated velocity<\/span><span class=\"utg-badge\">No material presets<\/span><span class=\"utg-badge\">No detection or acceptance verdict<\/span><\/div>\n  <\/header>\n\n  <div class=\"utg-alert utg-danger\"><strong>This worksheet is not an ultrasonic testing procedure, coverage plan, calibration, discontinuity-sizing method or acceptance decision.<\/strong> It does not select a probe, wedge, wave mode, frequency, angle, scan plan, sensitivity, reference reflector or acceptance criterion. A qualified procedure and instrument\/probe calibration remain mandatory.<\/div>\n\n  <section class=\"utg-card\" aria-labelledby=\"utg-input-title\">\n    <h2 id=\"utg-input-title\">Controlled inputs<\/h2>\n    <form id=\"utg-form\" novalidate>\n      <div class=\"utg-grid\">\n        <div class=\"utg-field utg-wide\"><label for=\"utg-source\">Procedure \/ calibration source record<\/label><textarea id=\"utg-source\" maxlength=\"260\" placeholder=\"Written procedure revision, probe\/wedge identification, calibration block and velocity\/angle verification record\"><\/textarea><span class=\"utg-hint\">Required. The worksheet supplies no material velocity or nominal probe setup.<\/span><\/div>\n        <div class=\"utg-field\"><label for=\"utg-mode\">Calibrated wave mode<\/label><select id=\"utg-mode\"><option value=\"\">Select the verified mode<\/option><option value=\"longitudinal\">Longitudinal<\/option><option value=\"shear\">Shear \/ transverse<\/option><\/select><span class=\"utg-hint\">The selected mode must match the entered velocity and refracted angle.<\/span><\/div>\n        <div class=\"utg-field\"><label for=\"utg-thickness\">Flat-plate thickness t (mm)<\/label><input id=\"utg-thickness\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 25\"><\/div>\n        <div class=\"utg-field\"><label for=\"utg-angle\">Refracted angle \u03b2 in test piece (\u00b0)<\/label><input id=\"utg-angle\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 60\"><span class=\"utg-hint\">Measured from the surface normal; 0 \u2264 \u03b2 &lt; 90\u00b0. This is not the wedge incident angle.<\/span><\/div>\n        <div class=\"utg-field\"><label for=\"utg-velocity\">Calibrated wave velocity c (m\/s)<\/label><input id=\"utg-velocity\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 3255\"><span class=\"utg-hint\">Use the verified velocity for the selected material, wave mode and test condition.<\/span><\/div>\n        <div class=\"utg-field\"><label for=\"utg-frequency\">Verified center frequency f (MHz)<\/label><input id=\"utg-frequency\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 4\"><span class=\"utg-hint\">Use a documented effective\/nominal value appropriate to the reference purpose.<\/span><\/div>\n        <div class=\"utg-field\"><label for=\"utg-diameter\">Active circular-element diameter D (mm)<\/label><input id=\"utg-diameter\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 20\"><span class=\"utg-hint\">For the separate ideal near-field reference only; not case diameter or wedge footprint.<\/span><\/div>\n      <\/div>\n      <div class=\"utg-checks\" role=\"group\" aria-label=\"Required confirmations\">\n        <label class=\"utg-check\"><input id=\"utg-confirm-calibration\" type=\"checkbox\"><span>I confirm that c and \u03b2 are verified values for the selected wave mode in the actual test piece or applicable calibration, not generic material-table values.<\/span><\/label>\n        <label class=\"utg-check\"><input id=\"utg-confirm-plate\" type=\"checkbox\"><span>I confirm that the ray calculation is intentionally limited to a flat plate with parallel surfaces and specular centerline reflection; curvature, wedge path, index-point offset and beam width are outside it.<\/span><\/label>\n        <label class=\"utg-check\"><input id=\"utg-confirm-near\" type=\"checkbox\"><span>For the near-field result only, I confirm that D represents a flat circular, unfocused, monolithic active element radiating directly into a homogeneous medium. I will not apply it as the effective near field of an angle-beam wedge, delay line, focused probe or array.<\/span><\/label>\n      <\/div>\n      <div class=\"utg-actions\"><button class=\"utg-btn\" type=\"submit\">Calculate references<\/button><button class=\"utg-btn utg-btn-secondary\" id=\"utg-clear\" type=\"button\">Clear<\/button><\/div>\n      <div id=\"utg-errors\" role=\"alert\" aria-live=\"assertive\"><\/div>\n    <\/form>\n  <\/section>\n\n  <section class=\"utg-card\" id=\"utg-results\" aria-labelledby=\"utg-results-title\" aria-live=\"polite\" hidden>\n    <div class=\"utg-result-head\"><div><h2 id=\"utg-results-title\">Reference results<\/h2><p id=\"utg-result-source\" class=\"utg-small\"><\/p><\/div><span class=\"utg-classification\">Geometry \/ acoustics only<\/span><\/div>\n    <div class=\"utg-section-label\">Flat parallel-plate ray<\/div>\n    <div class=\"utg-metrics\">\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">First-leg sound path to back wall<\/span><span class=\"utg-metric-value\" id=\"utg-out-leg-path\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">First-leg surface projection<\/span><span class=\"utg-metric-value\" id=\"utg-out-leg-projection\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Two-leg reflected sound path<\/span><span class=\"utg-metric-value\" id=\"utg-out-full-path\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">One full-skip surface distance<\/span><span class=\"utg-metric-value\" id=\"utg-out-full-skip\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">First-leg transit time in test piece<\/span><span class=\"utg-metric-value\" id=\"utg-out-leg-time\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Two-leg transit time in test piece<\/span><span class=\"utg-metric-value\" id=\"utg-out-full-time\"><\/span><\/div>\n    <\/div>\n    <div class=\"utg-section-label\">Wave and separate circular-element reference<\/div>\n    <div class=\"utg-metrics\">\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Wavelength \u03bb for entered mode<\/span><span class=\"utg-metric-value\" id=\"utg-out-wavelength\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">D\/\u03bb aperture ratio<\/span><span class=\"utg-metric-value\" id=\"utg-out-ratio\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Exact circular-element N\u2080<\/span><span class=\"utg-metric-value\" id=\"utg-out-near-exact\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Large-aperture approximation D\u00b2\/(4\u03bb)<\/span><span class=\"utg-metric-value\" id=\"utg-out-near-approx\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Approximation relative difference<\/span><span class=\"utg-metric-value\" id=\"utg-out-near-error\"><\/span><\/div>\n      <div class=\"utg-metric\"><span class=\"utg-metric-label\">Handbook approximation condition<\/span><span class=\"utg-metric-value\" id=\"utg-out-condition\"><\/span><\/div>\n    <\/div>\n    <div class=\"utg-alert\"><strong>Required interpretation:<\/strong> These are geometric and acoustic reference values only. No displayed length is a guaranteed coverage limit or a detectable\/sizable discontinuity dimension. Use the applicable written procedure, calibrated instrument\/probe assembly, reference reflectors and acceptance criteria.<\/div>\n  <\/section>\n\n  <section class=\"utg-card\" aria-labelledby=\"utg-method-title\">\n    <h2 id=\"utg-method-title\">Equations and units<\/h2>\n    <p class=\"utg-formula\">First leg: s\u2081 = t \/ cos \u03b2; x\u2081 = t tan \u03b2<br>Two legs \/ one full skip: s\u2082 = 2t \/ cos \u03b2; x\u2082 = 2t tan \u03b2<br>Wavelength: \u03bb = c \/ f<br>Circular-element exact near field: N\u2080 = (D\u00b2 \u2212 \u03bb\u00b2) \/ (4\u03bb)<br>Large-aperture approximation: N\u2080 \u2248 D\u00b2 \/ (4\u03bb) = D\u00b2f \/ (4c)<\/p>\n    <ul class=\"utg-list\">\n      <li>\u03b2 is the refracted angle in the test piece measured from the surface normal. The formulas do not calculate refraction from a wedge incident angle.<\/li>\n      <li>t, s, x, D, \u03bb and N\u2080 are in millimetres. c is entered in m\/s and f in MHz; \u03bb(mm) = c \/ [1000 f(MHz)].<\/li>\n      <li>The displayed transit times include only propagation in the test piece: time(\u00b5s) = 1000 \u00d7 path(mm) \/ c(m\/s). Wedge, delay-line, couplant and instrument zero time are excluded.<\/li>\n      <li>The circular-element exact equation is evaluated only for D\/\u03bb &gt; 1. The Olympus reference prints the approximation with D\/\u03bb &gt; 10; the worksheet reports whether that condition is met without treating it as a probe-selection verdict.<\/li>\n      <li>For an angle-beam wedge or rectangular probe, effective near field also depends on incident\/refracted angles, element length, wedge path, velocities and a correction factor. This worksheet deliberately does not guess those inputs.<\/li>\n    <\/ul>\n  <\/section>\n\n  <section class=\"utg-card\" aria-labelledby=\"utg-exclusions-title\">\n    <h2 id=\"utg-exclusions-title\">Model exclusions<\/h2>\n    <div class=\"utg-table-wrap\"><table class=\"utg-table\"><thead><tr><th>Excluded item<\/th><th>Why the simple result is insufficient<\/th><th>Required control<\/th><\/tr><\/thead><tbody>\n      <tr><td>Material velocity table<\/td><td>Velocity depends on wave mode, composition, structure and condition; a generic value does not calibrate distance.<\/td><td>Verify velocity\/zero with the actual setup and an applicable reference block or known path.<\/td><\/tr>\n      <tr><td>Wedge and index-point geometry<\/td><td>Wedge transit, incident angle, beam index point and temperature affect the actual assembly path and angle.<\/td><td>Calibrate the probe\/wedge assembly and verify refracted angle.<\/td><\/tr>\n      <tr><td>Curved test piece<\/td><td>Flat-plate trigonometry becomes inaccurate and the reflection angle changes.<\/td><td>Use validated curved-surface correction for the actual inside\/outside geometry.<\/td><\/tr>\n      <tr><td>Beam width, focusing and coverage<\/td><td>A centerline ray does not describe the sound field or scan coverage.<\/td><td>Use the probe model, procedure and coverage verification.<\/td><\/tr>\n      <tr><td>Detection, characterization and sizing<\/td><td>Reflector orientation, response, attenuation, scattering, coupling, bandwidth, sensitivity and signal-to-noise are not calculated.<\/td><td>Use calibrated reference reflectors and the applicable detection\/sizing technique.<\/td><\/tr>\n      <tr><td>Acceptance<\/td><td>Geometry alone contains no testing level, evaluation level or acceptance criterion.<\/td><td>Apply the product\/code\/contract procedure and its current acceptance rules.<\/td><\/tr>\n    <\/tbody><\/table><\/div>\n  <\/section>\n\n  <details class=\"utg-card\" open><summary>Evidence and standard status<\/summary>\n    <div class=\"utg-source\"><span class=\"utg-tag\">RAY GEOMETRY<\/span><strong>Evident, Theory and Use of Curved Surface Correction in EPOCH Series Flaw Detectors.<\/strong><p>Explains that default angle-beam position calculations assume a flat test piece and use calibrated velocity, refracted angle, thickness and beam index point; curvature requires different relationships.<\/p><a href=\"https:\/\/ims.evidentscientific.com\/en\/learn\/white-papers\/theory-and-use-csc\" rel=\"noopener\" target=\"_blank\">Official manufacturer paper<\/a><\/div>\n    <div class=\"utg-source\"><span class=\"utg-tag\">NEAR FIELD<\/span><strong>Olympus, Phased Array Testing: Basic Theory for Industrial Applications, 3rd ed., 2014, Appendix A, report p. 82 (PDF p. 88).<\/strong><p>Gives N\u2080 = (D\u00b2 \u2212 \u03bb\u00b2)\/(4\u03bb), the D\u00b2f\/(4v) approximation with D\/\u03bb &gt; 10, and separate effective-near-field equations for disc or rectangular probes on wedges.<\/p><a href=\"https:\/\/adobeassets.evidentscientific.com\/content\/dam\/downloads\/276826961\/Olympus-Phased_Array_Testing_C_en.pdf\" rel=\"noopener\" target=\"_blank\">Official manufacturer PDF<\/a><\/div>\n    <div class=\"utg-source\"><span class=\"utg-tag\">CALIBRATION<\/span><strong>Evident Ultrasonic Flaw Detection Tutorial, Calibration Concepts.<\/strong><p>States that velocity\/zero calibration is required when a new test material or transducer is used and that reference calibration is specific to the test procedure.<\/p><a href=\"https:\/\/ims.evidentscientific.com\/en\/learn\/ndt-tutorials\/flaw-detection\/calibration-concepts\" rel=\"noopener\" target=\"_blank\">Official manufacturer tutorial<\/a><\/div>\n    <div class=\"utg-source\"><span class=\"utg-tag\">GENERAL STANDARD<\/span><strong>ISO 16810:2024, Edition 2.<\/strong><p>The official ISO card states that application-specific conditions belong to product standards, specifications, codes, contracts or written procedures, and that ISO 16810 does not specify scan extent\/plans or acceptance criteria.<\/p><a href=\"https:\/\/www.iso.org\/standard\/86362.html\" rel=\"noopener\" target=\"_blank\">Official ISO record<\/a><\/div>\n    <div class=\"utg-source\"><span class=\"utg-tag\">WELD SCOPE<\/span><strong>ISO 17640:2018, Edition 4, stage 90.92 (to be revised).<\/strong><p>The official card limits its main scope to specified manual UT of fusion-welded metallic joints and states the material\/temperature\/testing-level conditions. This worksheet does not claim to implement that procedure.<\/p><a href=\"https:\/\/www.iso.org\/standard\/75737.html\" rel=\"noopener\" target=\"_blank\">Official ISO record<\/a><\/div>\n    <p class=\"utg-small\">Sources accessed 16 July 2026. No closed standard clause, testing level or acceptance table is reproduced or inferred.<\/p>\n  <\/details>\n\n  <details class=\"utg-card\"><summary>Interpretation questions<\/summary>\n    <h3>Is \u201cprobe angle\u201d the value to enter?<\/h3><p>Enter the verified refracted angle in the test piece, measured from the surface normal. A wedge incident angle is not interchangeable with it; refraction depends on the velocities and Snell&#8217;s law.<\/p>\n    <h3>Does two-leg path mean distance to a single reflector?<\/h3><p>No. It is the ideal centerline path from the entry surface to the opposite parallel wall and back to the entry surface after one specular reflection. A reflector can occur anywhere on a leg and must be located from calibrated sound path and leg information.<\/p>\n    <h3>Is the calculated N\u2080 valid for my angle-beam probe?<\/h3><p>Not as an effective assembly near field. The displayed N\u2080 is a separate direct circular-element reference. A wedge\/angle probe requires additional geometry and correction data explicitly omitted here.<\/p>\n    <h3>Is \u03bb\/2 the minimum flaw that will be detected?<\/h3><p>This worksheet makes no such claim. Detection and sizing depend on the complete sound field, reflector type and orientation, attenuation\/scattering, coupling, bandwidth, sensitivity, signal-to-noise, calibration and the applicable procedure.<\/p>\n  <\/details>\n\n  <p class=\"utg-small\">Revision: 16 July 2026. Result classification: non-normative geometry\/acoustics reference only.<\/p>\n<\/main>\n<script>\n(function(){\n  'use strict';\n  const byId=function(id){return document.getElementById(id);};\n  const form=byId('utg-form'),errors=byId('utg-errors'),results=byId('utg-results');\n  function decimalToken(raw,label){\n    const s=String(raw).trim();\n    if(!s||s.length>40||!\/^\\+?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))throw new Error(label+' must be one complete nonnegative decimal number.');\n    const value=Number(s.replace(',','.'));if(!Number.isFinite(value))throw new Error(label+' must be finite.');return value;\n  }\n  function parsePositive(raw,label){const value=decimalToken(raw,label);if(value<=0||value>1000000)throw new Error(label+' is outside the supported positive numerical range.');return value;}\n  function parseAngle(raw){const value=decimalToken(raw,'Refracted angle');if(value<0||value>=90)throw new Error('Refracted angle must satisfy 0 \u2264 \u03b2 < 90 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