2025MNRAS.544.2665P

The orientation-based unification model proposes that radio-loud quasars and radio galaxies are the same objects observed at different angles. A key prediction of this model is that the quasars are seen at smaller angles to the line of sight and so should be more affected by projection, and hence apparently physically smaller, than corresponding radio galaxies, but this has not always been found in earlier studies. We argue that the interpretation of observations requires a less simplistic model for the effects of projection, which takes into account radio sources' finite width and their intrinsic axial ratio distribution. Using this cylindrical configuration as a basis for the simulation of radio galaxies and quasars, we simulate the distribution of the linear size ratio of quasars to radio galaxies for different sample sizes and critical angles. Our simulations predict the ratio of observed lengths in the presence of a distribution of intrinsic physical sizes and axial ratios that we derive from observation. We conclude that to test the unified scheme, samples should be completely optically identified, sizes should be measurable for all targets, and the sample size should be greater than ${\sim} 800$ sources. Such large samples with uniform optical identification and accurate size measurements have not been available in previous work, but should become available from wide-area sky surveys in the near future.