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Wind tunnel research at NASA Langley Research Center's 31-inch Mach 10 hypersonic facility utilized a 5-component force balance, which provided a pressurized flow-thru capability to the test article. The goal of the research was to determine the interaction effects between the free-stream flow and the exit flow from the reaction control system on the Mars Science Laboratory aeroshell during planetary entry. In the wind tunnel, the balance was exposed to aerodynamic forces and moments, steady-state and transient thermal gradients, and various internal balance cavity pressures. Historically, these effects on force measurement accuracy have not been fully characterized due to limitations in the calibration apparatus. A statistically designed experiment was developed to adequately characterize the behavior of the balance over the expected wind tunnel operating ranges (forces/moments, temperatures, and pressures). The experimental design was based on a Taylor-series expansion in the seven factors for the mathematical models. Model inversion was required to calculate the aerodynamic forces and moments as a function of the strain-gage readings. Details regarding transducer on-board compensation techniques, experimental design development, mathematical modeling, and wind tunnel data reduction are included in this paper. Nomenclature

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The current approach used to apply uncertainty intervals to balance estimated loads is based on the root mean square error from calibration. Using the root mean square error, a constant interval is applied around the estimated load and it is expected that a predetermined percentage of the check-loads applied fall within this constant uncertainty interval. However, this approach ignores additional sources of uncertainty and assumes constant uncertainty regardless of the load combination and magnitude applied to the balance. Rigorous prediction interval theory permits varying interval widths but fails to account for the additional error sources that are unrelated to the mathematical modeling. An engineered solution is proposed that combines prediction interval theory and the need to account for the additional sources of uncertainty from calibration and check loading. Results from a case study using the in-situ load system show improved probabilistic behavior in terms of uncertainty interval capture percentage when compared with the current root mean square error method.Nomenclature CG x = location of center of gravity along x bal axis from balance moment center CG y = location of center of gravity along y bal axis from balance moment center CG z = location of center of gravity along z bal axis from balance moment center d BMC = distance vector from balance moment center to load point x BMC y BMC z BMC 0 F = expanded load calibration matrix F app = applied force, lbf. F bal = applied force vector F x F y F x 0 F x = force along x bal axis, lbf. F y = force along y bal axis, lbf. F z = force along z bal axis, lbf. F 0 = expanded load vector g = gravity vector g x g y g z 0 g x = x component of the gravity vector g y = y component of the gravity vector g z = z component of the gravity vector M bal = applied aerodynamic moment vector M x M y M z 0 M x = moment about x bal axis, in-lbf. M y = moment about y bal axis, in-lbf. M z = moment about z bal axis, in-lbf. n = number of calibration points p = number of terms in calibration model rF = strain-gage bridge response, mV∕V t= value from Student's t distribution x BMC = distance from balance moment center to load point along x bal axis, in. y BMC = distance from balance moment center to load point along y bal axis, in. z BMC = distance from balance moment center to load point along z bal axis, in. α = level of significance β = regression coefficient in balance calibration model σ 2 = error variance from calibration, also known as the mean squared error