Ultrasonic Flat-Plate Ray and Circular-Element Reference
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.
Controlled inputs
Reference results
Equations and units
First leg: s₁ = t / cos β; x₁ = t tan β
Two legs / one full skip: s₂ = 2t / cos β; x₂ = 2t tan β
Wavelength: λ = c / f
Circular-element exact near field: N₀ = (D² − λ²) / (4λ)
Large-aperture approximation: N₀ ≈ D² / (4λ) = D²f / (4c)
- β is the refracted angle in the test piece measured from the surface normal. The formulas do not calculate refraction from a wedge incident angle.
- t, s, x, D, λ and N₀ are in millimetres. c is entered in m/s and f in MHz; λ(mm) = c / [1000 f(MHz)].
- The displayed transit times include only propagation in the test piece: time(µs) = 1000 × path(mm) / c(m/s). Wedge, delay-line, couplant and instrument zero time are excluded.
- The circular-element exact equation is evaluated only for D/λ > 1. The Olympus reference prints the approximation with D/λ > 10; the worksheet reports whether that condition is met without treating it as a probe-selection verdict.
- 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.
Model exclusions
| Excluded item | Why the simple result is insufficient | Required control |
|---|---|---|
| Material velocity table | Velocity depends on wave mode, composition, structure and condition; a generic value does not calibrate distance. | Verify velocity/zero with the actual setup and an applicable reference block or known path. |
| Wedge and index-point geometry | Wedge transit, incident angle, beam index point and temperature affect the actual assembly path and angle. | Calibrate the probe/wedge assembly and verify refracted angle. |
| Curved test piece | Flat-plate trigonometry becomes inaccurate and the reflection angle changes. | Use validated curved-surface correction for the actual inside/outside geometry. |
| Beam width, focusing and coverage | A centerline ray does not describe the sound field or scan coverage. | Use the probe model, procedure and coverage verification. |
| Detection, characterization and sizing | Reflector orientation, response, attenuation, scattering, coupling, bandwidth, sensitivity and signal-to-noise are not calculated. | Use calibrated reference reflectors and the applicable detection/sizing technique. |
| Acceptance | Geometry alone contains no testing level, evaluation level or acceptance criterion. | Apply the product/code/contract procedure and its current acceptance rules. |
Evidence and standard status
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.
Official manufacturer paperGives N₀ = (D² − λ²)/(4λ), the D²f/(4v) approximation with D/λ > 10, and separate effective-near-field equations for disc or rectangular probes on wedges.
Official manufacturer PDFStates 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.
Official manufacturer tutorialThe 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.
Official ISO recordThe 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.
Official ISO recordSources accessed 16 July 2026. No closed standard clause, testing level or acceptance table is reproduced or inferred.
Interpretation questions
Is “probe angle” the value to enter?
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’s law.
Does two-leg path mean distance to a single reflector?
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.
Is the calculated N₀ valid for my angle-beam probe?
Not as an effective assembly near field. The displayed N₀ is a separate direct circular-element reference. A wedge/angle probe requires additional geometry and correction data explicitly omitted here.
Is λ/2 the minimum flaw that will be detected?
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.
Revision: 16 July 2026. Result classification: non-normative geometry/acoustics reference only.
