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.

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