PAUT wedge geometry and refracted angle range

A phased array wedge fixes the incident angle at the interface. The natural angle is the one obtained with no steering, from Snell's law sin θ_refracted = c_material · sin θ_incident / c_wedge. With Rexolite or Perspex at 2730 m/s and steel shear at 3240 m/s, a 36 degree wedge gives about 44 degrees of shear in steel - which is why nominally 45 to 60 degree wedges have roof angles in the mid thirties.

Electronic steering adds or subtracts from the incident angle inside the wedge, and Snell's law then magnifies it. Because the sine relationship is non-linear, a symmetric electronic sweep produces an asymmetric refracted sweep: the upper angles stretch out far more than the lower angles compress. That is why sectorial scans lose sensitivity fast at the top of the sweep.

Two critical angles bound the useful range. Below the first critical angle, asin(c_wedge / c_L) - about 27.6 degrees for Rexolite on steel - a compression wave is refracted as well as the shear wave, and the two produce confusing paired indications. Above asin(c_wedge / c_S), about 57.4 degrees of incidence, the shear wave is totally internally reflected and only a surface wave remains.

Practical wedges therefore sit between roughly 28 and 55 degrees of incidence. If the required refracted range cannot be reached from one wedge angle, the answer is a second wedge, not more steering: steering beyond the element directivity limit costs more sensitivity than it buys coverage.

sin θ_r = c · sin θ_i / c_wedge
θ_natural = asin(c · sin θ_wedge / c_wedge)
θ_crit1 = asin(c_wedge / c_L)
θ_crit_shear = asin(c_wedge / c)