A flat wedge on a pipe touches along one line and lifts away either side. The gap at the edge of the contact face is R − √(R² − (L/2)²), closely approximated by L²/(8R). On a concave surface – inside a pipe or a vessel – the wedge touches at its two ends instead and the gap in the middle is the same size.

A gap fills with couplant, and couplant is not wedge plastic. It changes the incident angle at the interface, adds an uncontrolled delay, and above all it drains sensitivity: the transmission through a thick, variable couplant layer is poor and unstable. European weld inspection standards call for the probe shoe to be adapted to the surface once the gap exceeds about 0.5 mm, and that is a reasonable working trigger whatever the governing code.

Contouring is machining the contact face to the component radius. Because the fit degrades slowly, one contoured wedge serves a band of diameters; the usual guidance is from about 0.9 to 1.5 times the radius the wedge was cut to. Outside that band, cut another wedge.

Contouring also moves the exit point and changes the wedge path, so the setup has to be recalibrated on a curved calibration block of the same radius. A wedge contoured after calibration is an uncalibrated wedge.

Worked example

Component diameter at the scan surface	168.3 mm
Wedge contact length across the curvature	30 mm
Surface	convex
Radius the wedge is contoured to	84.15 mm
Component radius	84.15 mm
Gap between a flat wedge and the surface	1.348 mm
Gap by the L²/(8R) approximation	1.337 mm
Smallest radius the contoured wedge suits	75.735 mm
Largest radius the contoured wedge suits	126.225 mm

A 168.3 mm pipe has a radius of 84.15 mm. A 30 mm wedge footprint spans a half chord of 15 mm, so the gap is 84.15 − √(84.15² − 15²) = 84.15 − 82.802 = 1.348 mm, against the L²/(8R) estimate of 900/673.2 = 1.337 mm. That is well over the 0.5 mm adaptation trigger, so the wedge must be contoured; a wedge cut to 84.15 mm then serves radii from 75.735 to 126.225 mm.