Date of Award

Winter 2015

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Aerospace Engineering

Committee Director

Drew Landman

Committee Member

Colin P. Britcher

Committee Member

Sean Commo

Committee Member

Gene Hou


Currently, there is a lack of the use of mathematically rigorous methods to evaluate the performance of multivariate force measurement systems. The specific problem addressed in the research stems from the practical issues faced by test engineers when wind tunnel models with internal strain gage balances are readied for test. Check loads are applied and the question that needs to be answered is whether or not the balance is reading within acceptable limits. These systems tend to be difficult to characterize uncertainty, primarily due to their multivariate nature, but also due to the desire for an estimate on the explanatory variable of the system, instead of the response. This estimation of the explanatory variable is inherent to the calibration problem. For systems that are modeled using non-linear terms, no closed form solution will exist for the explanatory variable. This research details the development of a prediction interval which includes the measurement error in the calibration and check systems. The 20,000 lb. manual stand for calibrating balances used in the National Transonic Facility (NTF) is employed by NASA Langley Research Center and the case study for the work. The uncertainty estimates were developed using the propagation of error method on derived physics equations for the system. The uncertainty estimates were integrated into the developed prediction interval, which demonstrated a capture rate of 96% for a trial set of check loads using a 95% level of condence. Comparisons are made to prediction interval capture rates for the Single Vector System using a common set of check loads on an NTF balance.