What is the formula for tofd gate start and width?

t_LW = PCS / c + t_delay; t_BW = 2 × √(S² + T²) / c + t_delay; gate start = t_LW − pre-margin; gate end = t_BW + post-margin; gate width = gate end − gate start. Derives the digitising gate start, end and width from the predicted lateral wave and backwall arrival times plus operator margins.

What should I check before relying on the result?

Never start the gate on the lateral wave. Clipping it destroys the near-surface depth reference and any lateral-wave-based drift correction. Increase the post-backwall margin if mode-converted signals or a second backwall are to be recorded; they help confirm the setup and the far-surface condition. Verify the gate against a real A-scan on known-thickness material before scanning, and re-check after any wedge change. Wider gates mean larger files and, on some instruments, a lower maximum line rate; check the achievable scan speed after setting the gate. Verify against the governing edition: ISO 10863:2011 §8 (time base range and recording window); ASME BPVC Section V, Article 4, Mandatory Appendix III.

ToFD gate start and width — ToFD Calculator

A ToFD A-scan is only useful if the digitising window contains everything between the lateral wave and the backwall, with margin at both ends. The lateral wave arrives at PCS/c and the backwall at 2*sqrt(S^2 + T^2)/c, and both are shifted later by the delay through the two wedges. The gate is then started a little before the lateral wave and ended a little after the backwall.

Starting the gate on the lateral wave itself is a common and expensive mistake. The wave gets clipped, the reference for near-surface depth is lost, and the software can no longer use the lateral wave to correct for probe lift-off or velocity drift during the scan. Procedures typically call for something like a microsecond of clear material either side; check the governing procedure for the figure that applies to the job.

Extending the window past the first backwall is also worth doing. Mode-converted signals arriving after the backwall carry information about flaws near the far surface, and seeing a second backwall arrival confirms that the assumed thickness and velocity are right. The cost is file size and, on some instruments, a lower maximum line rate.

Set the gate from calculated times, then verify it on the actual A-scan against a known thickness before the scan starts. If the lateral wave or backwall does not fall where predicted, fix the setup rather than moving the gate to suit.

Compression wave

Worked example

Probe centre separation	70 mm
Wall thickness	25 mm
Compression velocity	5900 m/s
Total probe delay	2.5 µs
Margin before lateral wave	1 µs
Margin after backwall	1 µs
Half separation	35 mm
Lateral wave arrival	14.36 µs
Backwall arrival	17.08 µs
Lateral wave to backwall window	2.72 µs
Gate start	13.36 µs
Gate end	18.08 µs
Gate width	4.72 µs

c = 5.9 mm/us and S = 35 mm. Lateral wave = 70/5.9 + 2.5 = 11.8644 + 2.5 = 14.3644 us (14.36). Backwall = 2 x sqrt(1850)/5.9 + 2.5 = 14.5802 + 2.5 = 17.0802 us (17.08), so the window is 2.7158 us (2.72). Gate start = 14.3644 - 1.00 = 13.3644 us (13.36); gate end = 17.0802 + 1.00 = 18.0802 us (18.08); width = 18.0802 - 13.3644 = 4.7158 us, that is 4.72 us.

Use at your own risk — verify before you act

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