Second-Leg Flaw Depth (Angle-Beam Ultrasonics)

The indication turned up at 80 mm of sound path, on a 25 mm plate, with a 60° probe. Feeding that into the first-leg formula yields 40 mm of depth, deeper than the plate is thick, and that absurdity is what gives the mistake away. Past the half skip the beam is travelling back up, and depth starts shrinking as sound path grows. Knowing whether the reflector sits at the root, mid-bead or near the cap changes the acceptance criterion and the repair plan, so the right formula matters.

On the first leg d = S × cos(θ) holds, up to the half-skip path, which equals t ÷ cos(θ). Past that point the arithmetic folds over: d = 2 × t − S × cos(θ). With the defaults, 2 × 25 − 80 × 0.5 gives 10.00 mm of depth. The two formulas agree exactly at the boundary: at S = 25 ÷ 0.5 = 50 mm the first gives 25 mm and this one gives 25 mm too, which is the back wall. At the other end, S = 100 mm returns 0 mm, meaning the beam has come back to the scanning surface.

The arithmetic assumes a flat, parallel back wall, a single specular reflection and the true refracted angle of the assembly, measured on a calibration block rather than read off the wedge. At the back wall part of the shear wave converts to a faster longitudinal wave, throwing up spurious indications that the instrument places at the wrong path — a weak, misplaced signal on the second leg is often exactly that. A third leg, with projection beyond two thicknesses, needs d = S × cos(θ) − 2 × t and gets rejected here. Where access allows, favour the first leg: less divergence, less attenuation.