Experimentation, Validation, and Uncertainty Analysis for Engineers, 4th Edition

APPENDIX B TAYLOR SERIES METHOD (TSM) FOR UNCERTAINTY PROPAGATION¹

In nearly all experiments, the measured values of different variables are combined using a data reduction equation (DRE) to form some desired result. A good example is the experimental determination of drag coefficient of a particular model configuration in a wind tunnel test. Defining drag coefficient as

(B.1)

one can envision that errors in the values of the variables on the right-hand side of Eq. (B.1) will cause errors in the experimental result C_D.

A more general representation of a data reduction equation is

(B.2)

where r is the experimental result determined from J measured variables X_i. Each of the measured variables contains systematic (bias) errors and random (precision) errors. These errors in the measured values then propagate through the data reduction equation, thereby generating the systematic and random errors in the experimental result, r. Our goal in uncertainty analysis is to determine the effects of these errors, which result in the random and systematic uncertainties in the result. In this appendix, a derivation of the equation describing uncertainty propagation is presented, comparisons with previously used equations and approaches are discussed, and, finally, the approximations leading to ...