Ultrasonic thickness from time of flight

A straight-beam thickness measurement is a timing measurement. The instrument fires the probe, the compression (longitudinal) wave crosses the wall, reflects from the back surface and returns, and the instrument records the round-trip time of flight. Because the pulse travels the wall twice, the thickness is half the total distance: t = c × TOF / 2.

Steel is quoted at 5900 m/s for compression waves, which is 5.9 mm/µs. Shear velocity (3240 m/s) is never used for thickness gauging — a shear wave will not propagate through the couplant film, and entering a shear velocity into a thickness gauge produces a reading roughly 55 % of the truth.

Part of the measured time is not in the steel at all. It is spent in the delay line, the wear face, the couplant and the instrument electronics. That fixed offset is the probe zero, and it must be subtracted before the halving. On a single-element probe the zero is found by calibrating on a known step; on a dual-element probe the sound follows a V-path through the delay lines and across the wall, so the zero is not constant with thickness and a two-point calibration on the thinnest and thickest steps of the range is mandatory.

Velocity is the largest source of systematic error. Cast and austenitic materials, weld metal, and any component above ambient temperature all depart from 5900 m/s, so a reading taken with a nominal velocity is an estimate until the velocity is proved on the actual material.

t = c × (TOF − t₀) / (2 n)
n = number of back-wall echo intervals timed (1 for a single echo)
with TOF and t₀ in µs and c in mm/µs → t in mm
c (mm/µs) = c (m/s) ÷ 1000
steel compression: 5900 m/s = 5.90 mm/µs