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Session 2526

A Multivariate Calculus Approach to Uncertainty Error Estimation in Teaching Laboratories

Laura J. Genik, Craig W. Somerton University of Portland/Michigan State University

Abstract

In the engineering profession, a key component of any experimental work and its results is the presentation of the error associated with those results. Many undergraduate engineering programs have moved away from a standard instrumentation or measurements laboratory, and have also eliminated the laboratory components of the basic physics and chemistry courses. These changes could lead to a hole in the student’s education with respect to the process of error evaluation. With this hole, the process of error estimation within the undergraduate teaching laboratory is often left to attributing everything to ’human error’. Students do have a fundamental understanding of the error within an instrument impacting the overall error of a calculation; however, they do not necessarily know how to mathematically account for the error in the resulting calculation. It is the approach of the authors to look at the impact of the tolerance error within an instrument to determine the overall effect on the final experimental value. The authors utilize a multivariate calculus approach instead of the more conventional statistical approach. The authors use this approach throughout two courses, ME 412 Heat Transfer Laboratory at Michigan State University and ME 376 Thermodynamics Laboratory at the University of Portland. It is first introduced with a specific experiment to familiarize students with the methodology, and then is expected with each experiment thereafter. Within each course the introductory experiment is different: determining the thermal efficiency of an immersion heater and estimating the specific heat of a fluid of unknown thermal properties. The details of the error estimation procedure and it’s application to each experiment is presented. It is also shown how this error estimation approach compares to the statistical approach. Finally, the relationship between uncertainty error and systematic error is discussed.

Introduction

One of the major problems in any experimental work involves the fact that nothing can be measured exactly, an interesting fact that students have difficulty quantifying. Also, we find that rarely do we seek only values for parameters that are measured directly. More often than not we are interested in parameters, such as thermal conductivity or surface emissivity, which are calculated from experimental measurements, say of temperature or length. Hence, the

Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright  2001, American Society for Engineering Education”

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Genik, L., & Somerton, C. (2001, June), A Multivariate Calculus Approach To Uncertainty Error Estimation In Teaching Laboratories Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9589