Wedge data sheets give the height of the centre of the first element above the contact surface, usually called H1, together with the roof angle and the distance from the wedge front to that element. Everything else follows from geometry. Element i sits higher by (i−1)·p·sin θ_w and further back by (i−1)·p·cos θ_w, so the whole array is a ladder climbing the wedge face.

The path from an element to the interface at the natural angle is h / cos θ_w, and the wedge delay the instrument needs is twice that divided by the wedge velocity. The wedge is plastic and the wave in it is always a compression wave at about 2730 m/s, whatever mode is refracted into the part – that is why wedge delay is calculated with 2730 m/s and never with a shear velocity.

The exit point, or beam index point, is not fixed the way it is on a monolithic angle probe. It moves as the active group is stepped along the array, and it moves again with steering. For a wedge angle below 45 degrees the exit point walks backwards as the group moves up the wedge, because the extra height gained is smaller than the extra set-back.

Getting the exit point right matters for plotting. An error in the index offset moves every indication along the scan axis by the same amount, which shows up as a weld that appears to be systematically off centre.

Compression wave

Worked example

First element height (H1)	10 mm
Element pitch	0.6 mm
Wedge (roof) angle	36 deg
Wedge velocity	2730 m/s
First element of the active group	1
Elements in the active group	16
Wedge front face to element 1 foot	12 mm
Centre element of the active group	8.5
Height of the group centre above the surface	12.645 mm
One-way wedge path at the natural angle	15.63 mm
Wedge delay (round trip)	11.45 µs
Exit point ahead of the element 1 foot	5.55 mm
Exit point behind the wedge front face	6.45 mm

The centre of a 16 element group starting at element 1 is element 8.5, so it sits 7.5 × 0.6 × sin 36° = 2.645 mm above element 1, i.e. 12.645 mm above the surface. The wedge path is 12.645/cos 36° = 15.630 mm, giving a round trip delay of 2 × 15.630/2730 × 1000 = 11.45 µs. The exit point is 10 × tan 36° − 4.5 × cos 72°/cos 36° = 7.265 − 1.719 = 5.55 mm ahead of the element 1 foot, i.e. 12 − 5.55 = 6.45 mm behind the wedge front.

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