Impact and Estimation of Balance Coordinate System Rotations and Translations in Wind-Tunnel Testing

Abstract

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

Comparative Analysis of Two Cryogenic Force Balance Calibration Systems

“…An optimization routine was implemented to find possible rotations and translations of the balance coordinate system. 6 This method finds a rotation matrix and coordinate translation that minimizes the load discrepancies shown in Figure 3. Estimated offsets that partially correlate the two calibration matrices are shown in Table 2.…”