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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

Discrepancies between the model and balance coordinate systems lead to biases in the aerodynamic measurements during wind-tunnel testing. The reference coordinate system relative to the calibration coordinate system at which the forces and moments are resolved is crucial to the overall accuracy of force measurements. This paper discuses sources of discrepancies and estimates of coordinate system rotation and translation due to machining and assembly differences. A methodology for numerically estimating the coordinate system biases will be discussed and developed. Two case studies are presented using this methodology to estimate the model alignment. Examples span from angle measurement system shifts on the calibration system to discrepancies in actual wind-tunnel data. The results from these case-studies will help aerodynamic researchers and force balance engineers to better the understand and identify potential differences in calibration systems due to coordinate system rotation and translation. Nomenclature β Regression Coefficients F Force Vector, lbs. M Moment Vector, in-lbs. φ Roll Angle, Deg. ψ Yaw Angle, Deg. θ Pitch Angle, Deg. a Skew-Symmetric Matrix T Rotation Transformation Matrix y FMS Voltages