What is the formula for second?

vertical travel y = SP × cos θ; leg number n = floor(y / T) + 1; m = y mod 2T; depth d = m when m ≤ T (odd legs, descending); depth d = 2T − m when m > T (even legs, climbing); leg 2: d = 2T − SP cos θ leg 3: d = SP cos θ − 2T leg 4: d = 4T − SP cos θ; surface distance SD = SP × sin θ. Folds an angle-beam sound path back through the wall to give the true depth and leg number for reflectors beyond half skip.

What should I check before relying on the result?

Report the leg with the depth — the same sound path means a different depth in each leg. Second-leg response from a corner-trap reflector such as a root bead is normally weaker and broader than the first-leg response; sensitivity must be set for the leg actually used. The fold assumes parallel surfaces. On a taper or a nozzle the far surface is not at a constant T and the leg geometry must be drawn out. Verify against the governing edition: General engineering trigonometry; leg identification per ISO 17640 / AWS D1.1 clause 6.

Second, third and fourth leg depth

Past half skip the shear beam has reflected from the far surface and the simple d = SP cos θ relationship no longer gives depth. What the geometry actually tracks is the total vertical travel y = SP cos θ: the beam descends one wall thickness per leg, bounces, climbs one wall thickness, bounces, and so on. Depth is that vertical travel folded into the wall.

In the second leg the beam is climbing, so an indication is as far below the scanning surface as the remaining travel to the top: d = 2T − SP cos θ. In the third leg it is descending again from the top surface, d = SP cos θ − 2T, and in the fourth leg climbing once more, d = 4T − SP cos θ. The general rule is to take y modulo 2T and reflect anything greater than T back off the far wall.

Leg number matters for interpretation as much as for depth. A root indication seen in the second leg arrives at the far surface at a different incidence than in the first, corner-trap response from a root bead is far stronger in the first leg, and each extra bounce adds attenuation and mode-converted noise. Where a procedure permits second-leg examination it normally also demands that the leg be identified on the report, because the same sound path can mean two very different depths.

The surface distance keeps growing with sound path regardless of leg — SD = SP sin θ — so plotting surface distance against folded depth is what produces the familiar zig-zag beam path across a weld cross-section.

Shear wave

Worked example

Wall thickness	25 mm
Refracted shear angle	60 deg
Sound path from instrument	70 mm
Index point to probe front	0 mm
Total vertical travel	35 mm
Leg number	2
True depth below scanning surface	15 mm
Surface distance from index point	60.62 mm
Extra sound path to the next surface	20 mm

70 mm sound path at 60° is 70 × cos 60° = 35.00 mm of vertical travel. That is more than the 25 mm wall, so the beam has already reflected and is in leg 2: depth = 2 × 25 − 35 = 15.00 mm below the scanning surface. Surface distance = 70 × sin 60° = 60.62 mm, and the beam still has (35 − 25) / cos 60° = 20.00 mm of sound path before it breaks the top surface.

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