The three balance force components are a function of the applied load and the orientation of the balance in three-dimensional space. To generate a desired combination of the three forces, the balance is manipulated to a prescribed orientation using the non-metric positioning system and precisely measured on the metric end using the accelerometer system. This accelerometer system provides the components of the gravitational vector projected onto the three axes of the balance coordinate system. Combining the measured gravitational components on the balance axes and the known dead-weight enables the determination of the three force components.

The three balance moment components are a function of the three force vectors and the position of the point of load application in three-dimensional space relative to the balance moment center (BMC). The BMC is a defined location in the balance coordinate system that serves as a reference point in which the moment components are described. The point of load application is set using the multiple-degree-of-freedom load-positioning system. This system utilizes a novel system of bearings and knife-edge rocker guides to maintain the load orientation, regardless of the angular orientation of the balance, which makes the point of load application independent of the angular orientation of the balance. Stated another way, when the balance is manipulated in three-dimensional space, the point of load application remains constant.

The SVS performs rapid and accurate setting of the independent variables. Even though this load application system would greatly enhance the execution of the current OFAT design, it is particularly well suited to meet the requirements for the execution of a formal experimental design. The use of a single calibration load reduces the set-up time for the randomized multi-axis load combinations prescribed by a formal experimental design.

The purpose of using an MDOE approach is to efficiently achieve the primary objective of the calibration experiment; namely, the determination of an accurate mathematical model to estimate the aerodynamic loads from measured balance responses. Theoretical and experimental results have shown that MDOE makes it possible to perform a given calibration with an order of magnitude fewer data points than current methods.

The three fundamental MDOE quality-assurance principles are randomization, blocking, and replication. Randomization of data-point ordering ensures that a given balance load combination is just as likely to be applied early in the calibration as it is near the end. If some systematic variation (e.g., instrumentation drift, temperature effects, or operator fatigue) causes earlier measurements to be biased differently from later measurements, then randomization converts such unseen systematic errors to an additional component of simple random error.

Blocking entails organizing an experiment into relatively short blocks of time within which the randomization of point ordering ensures stable sample averages and statistical independence of measurements. While randomization defends against systematic within-block variations, substantial between-block systematic variations are also possible. Blocking makes it possible, during the subsequent analysis of the data, to remove this between-block component of the unexplained variance.

Averaging of genuine replicates causes random errors to cancel. These errors can include what would otherwise be undetectable systematic variations that are converted to random errors by randomizing the loading schedule. Replication also facilitates unbiased estimates of pure error, the component of error attributable to ordinary chance variations in the data. Estimates of pure error enable an objective assessment of the quality of fit of the mathematical model.

Integration of the single-vector hardware system with MDOE techniques has enabled an order of magnitude reduction in wind-tunnel balance calibration time and cost, while simultaneously increasing the quality of the information obtained from the calibration experiment. The SVS provides the basis for further advancement in force measurement technology in the areas of higher-order mathematical models, implementation of statistical process control, and an expansion of the calibration mathematical model to include temperature as an independent variable.

*This work was done by P. A. Parker and R. DeLoach of Langley Research Center.*

*This invention is in the process of being exclusively licensed. Inquiries concerning technical aspects of the invention may be directed to the inventor, Pete Parker, at (757) 864-4709. Inquiries concerning the licensing and commercialization of the invention may be directed to Barry Gibbens of the NASA LaRC Technology Commercialization Program Office at (757) 864-7141. LAR-16020.*