Bootstrapped distributions of l_v as a function of sample size. Using the S-NSB (left panels) and W-NSB (right panels) models with a nuclear bar angle α = −60°, we sample stars from fields shown with (ℓ, b) coordinates indicated in each panel. We also indicate the position of each field (white markers) in the top left panel for the S-NSB model in Fig. 6. For each field, we perform B = 1000 bootstrap iterations using sample sizes of 120 (dotted red), 500 (dashed green), and 1000 (solid blue) stars. For the S-NSB model, the mean uncertainty (using Eq. (4)) decreases from ±6.18° for 120 stars to ±2.97° for 500 stars, and ±2.01° for 1000 stars. We note that l_v varies marginally across fields, ranging from −66.4° to −62.8° (with a standard deviation of σ_ℓv ± 2.58°;). The uncertainty in l_v for the W-NSB case is 16.08°, 9.43° and 6.52° for 120, 500 and 1000 stars per field respectively. Across the fields, we find that the median l_v value ranges between −70.4° and −60.1°. This variation likely reflects both the intrinsic differences in stellar kinematics across fields and varying contamination from large-scale bar stars.