Rationale

6.6.2.3 When method (b) is used and a series of applied calibration torque values are applied before return to zero calibration torque, the zero-corrected indication at each applied calibration torque in the series shall be calculated by linear interpolation between the initial and final zero indications. Linear interpolation assumes the zero drift to be linear with respect to the applied calibration torque within the series and is not appropriate where the magnitude of the zero drift exceeds the zero-return error criteria of 6.7.6. The laboratory should select and document an interpolation method appropriate to the calibration. Note—Equation (X) is one example of a linear-interpolation method consistent with 6.6.2.3: Vcorr(ti) = V(ti) - [ti / tmax] · [V(0final) - V(0initial)] (X) where: V(ti) = The indicated output at the applied calibration torque ti V(0initial) = The zero-torque indication taken immediately before application of the series of calibration torques V(0final) = The zero-torque indication taken immediately after removal of the series of calibration torques ti = The applied calibration torque at the i-th step of the series, and tmax = The maximum applied calibration torque within the series Equation (X) applies to method (b) when a series of applied calibration torque values is applied before return to zero calibration torque. Only two zero indications are required to apply the equation: the initial zero before the series and the final zero after. When additional zero indications are taken mid-series, the equation is applied to each adjacent pair in turn, with the prior zero serving as the initial and the next zero serving as the final for the loaded points between them. All viable interpolation methods are linear and differ only in their weighting scheme. Equation (X) weights the correction by ti / tmax, the ratio of applied calibration torque to maximum calibration torque in the series. Alternative weighting schemes are allowed and yield different deflection values; for example, indexing by point number with weight (i - 1) / (N - 1) assigns no correction to the first point and full correction to the last, while weight i / N assigns 1/N to the first point and full correction to the last. The weighting scheme in Equation (X) indexes the correction directly to the applied calibration torque, is independent of the number and spacing of test points, reduces continuously to zero as ti approaches zero, and is dimensionally consistent with the deflection-versus-torque relationship being calibrated. The choice of weighting scheme changes the polynomial coefficients fitted to the deflection data and therefore the lower limit factor and the lower torque limit derived from it. Equation (X) is provided as an example only and is not required. Rationale Existing 6.6.2.2 permits the use of “interpolated zero torque indications” under method (b) for a series of applied calibration torque values, but does not define how the interpolation is performed. Practice across torque calibration laboratories has historically applied a linear correction proportional to the ratio of applied calibration torque to the maximum calibration torque in the series, but the absence of any worked example in the standard has produced documented inconsistencies in deflection calculation, particularly where zero drift is non-trivial relative to the lower torque limit of the verified range. The proposed insertion provides one mathematical example of how the interpolation may be performed, identifies the assumption of linear zero drift on which the example depends, and acknowledges that alternative weighting schemes are mathematically valid and produce different deflection values. The example is informative rather than prescriptive: the laboratory retains responsibility for selecting and documenting an interpolation method appropriate to the calibration. Because the calculation has only two data points (the initial and final zero indications), all viable interpolation methods are linear; polynomial, spline, and similar higher-order methods are not applicable without intermediary return-to-zero points. The viable methods differ only in their weighting scheme , that is, in how the total drift V(0final) - V(0initial) is distributed across the loaded series. The proposal, therefore, does not constrain the laboratory to a single calculation; it provides one defensible example to help those who struggle with various interpolation methods.