Formulas and the two legs
T is plate thickness; θ is the refracted angle from the normal inside the test material. SP is the accumulated one-way sound path from the beam entry point to the reflector. Lengths use one consistent unit. The V-path follows both legs to the next top-surface intersection; it is not the round-trip echo distance back to the probe.
- Half skip (surface distance) = T × tan θ.
- Full skip (surface distance) = 2T × tan θ.
- Half-skip sound path = T / cos θ.
- Full-skip sound path (V-path) = 2T / cos θ.
- Surface distance for a reading = SP × sin θ.
- Leg 1 depth = SP × cos θ, for 0 ≤ SP ≤ T / cos θ.
- Leg 2 depth = 2T − SP × cos θ, for T / cos θ < SP ≤ 2T / cos θ.
These are right-triangle derivations using the equal-angle reflection geometry described in Evident's An Introduction to Ultrasonic Flaw Detection. For leg 2, the beam has already crossed the thickness T; its upward travel is SP × cos θ − T. Subtract that upward travel from T to get 2T − SP × cos θ.
Print a skip sheet
Press Print skip sheet under the diagram to get one page for your plate and angle: half and full skip, both sound paths, and the depth, sound path and surface distance at each quarter of the thickness on leg 1 and leg 2. It has lines for the part or weld, the probe and wedge, who checked it and the date, plus a link that reopens the same numbers. Save it as a PDF from the print dialog, keep it beside the flaw detector or work it on paper for UT Level II.
Worked example: 25 mm plate at 60°
Half skip = 25 × tan 60° = 43.3013 mm; full skip = 86.6025 mm. One leg is 25 / cos 60° = 50 mm; the V-path is 100 mm.
A 75 mm sound-path reading lies on leg 2 because 50 < 75 ≤ 100. Its surface distance is 75 × sin 60° = 64.9519 mm. Its depth is 2 × 25 − 75 × cos 60° = 12.5 mm below the top surface. Applying the leg 1 formula here would incorrectly place the reflector below the backwall.
Second example: 20 mm plate at 45°
Half skip = 20 × tan 45° = 20 mm; full skip = 40 mm. One leg is 20 / cos 45° = 28.2843 mm; the V-path is 56.5685 mm. A 40 mm sound-path reading lies on leg 2. Its surface distance is 40 × sin 45° = 28.2843 mm and its depth is 2 × 20 − 40 × cos 45° = 11.7157 mm. These numbers are invented for practice. The same formulas are on the UT and MT formula sheet.
Snell's law and critical angles
For an incident longitudinal wave in the wedge and a refracted shear wave in the plate, sin α / cW = sin θ / cS. Rearranging gives θ = arcsin[(cS / cW) × sin α]. Here α is the incident angle from normal, cW is wedge longitudinal velocity, cS is material shear velocity, and cL is material longitudinal velocity. The calculator substitutes your numbers above.
At a critical angle the relevant refracted ray reaches 90°. Setting its sine to 1 gives αc1 = arcsin(cW / cL) for the first (longitudinal) critical angle and αc2 = arcsin(cW / cS) for the second (shear) critical angle. A ratio greater than 1 means that critical angle does not exist for the entered velocities. At or beyond the second critical angle, this tool suppresses the through-thickness shear-path results.
Source: Evident, Ultrasonic Flaw Detection Tutorial: 2.5 Wave Front Dynamics. This is a ray model; it does not calculate beam spread, transmission amplitudes or surface-wave paths.
Assumptions and use limits
Use a flat, parallel-sided plate with a uniform, isotropic velocity and a calibrated angle and beam index point. This tool supports only the first two legs. Curved surfaces, anisotropy and mode conversion at reflections need a different model. Reference velocities are starting values, not a calibration: confirm the material, temperature and actual wedge velocity against your procedure.
Skip-distance calculator FAQ
How do I find half skip and full skip?
Half skip is plate thickness times tan θ, and full skip is twice that. For a 25 mm plate at 60°, half skip is 25 × tan 60° = 43.3013 mm and full skip is 86.6025 mm. Use one unit for every length.
Is the V-path the same as the echo distance back to the probe?
No. The V-path follows both legs to the next top-surface intersection, 2T / cos θ. In the 25 mm, 60° example one leg is 50 mm and the V-path is 100 mm. It is not the round-trip echo distance.
How do I tell whether a sound-path reading is on leg 1 or leg 2?
Compare the reading with one leg, T / cos θ. In the 25 mm, 60° example one leg is 50 mm, so a 75 mm reading lies on leg 2 because 50 < 75 ≤ 100. Its depth is 2 × 25 − 75 × cos 60° = 12.5 mm. The leg 1 formula would wrongly put that reflector below the backwall.
Why are the through-thickness results missing at a large angle?
At or beyond the second critical angle the calculator suppresses the through-thickness shear-path results. The second critical angle is arcsin(cW / cS), and it does not exist if that ratio is greater than 1. Check the wedge and material velocities you entered.