Bobbin probe sizing for tube ID

Probe selection for tube examination is a compromise between coupling and clearance, and fill factor is how it is expressed. Fill factor is the square of the diameter ratio, eta = (d_probe / D_id)^2, so the probe diameter that achieves a required fill factor is d_probe = D_id x sqrt(eta). Working the relationship in this direction is what a technician actually needs: the tube dimensions are given, and the question is which probe out of the kit to fit.

Too small a probe loses signal to the annular gap and, worse, loses noise margin. Wobble becomes a larger fraction of the clearance, small OD-initiated indications sink into the noise, and the phase readings that carry depth information get noisier along with everything else. Too large a probe gives excellent coupling right up to the moment it jams in a dent, an ovalised span, a deposit or a U-bend - and retrieving a stuck probe from an in-service heat exchanger costs far more than the few percent of amplitude that a smaller probe would have given away.

Common practice settles at 85 to 90 % fill for bobbin probes in straight tubing, and lower - often 75 to 80 % - for U-bend and severely fouled tubes where passage matters more than sensitivity. Note that fill factor changes far more slowly than diameter: over the whole 85 to 90 % band the probe diameter only moves about 3 %, so a kit with a sensible diameter increment covers a wide range of tube sizes.

Whatever probe is selected, sensitivity has to be proved and not assumed: the calibration standard is examined with that same probe, at the same frequencies, and the response from the calibration reflectors is what sets the gain. A probe change mid-job is a re-calibration, not an adjustment.

D_id = OD - 2 x wall
d_probe = D_id x sqrt(fill factor)
radial clearance = (D_id - d_probe) / 2
check: fill factor = (d_probe / D_id)^2