Effects of the distance bias on a perfect Archimedean spiral. For all panels, the centre of the spiral is at 4 kpc from the Sun, and the black curve is the true spiral. Left column: Mock particles sampled with a constant parallax over error of 5. Right column: Same but the parallax over error is sampled uniformly from 1 to 10. Rows correspond to different distance estimates, from top to bottom: parallax inversion; Bayesian estimate with L = 1 kpc and taking the mode of the posterior; same as above but with L = 4 kpc; Bayesian estimate with L = 1 kpc but taking the median of the posterior.