## Fig. 4

Analysis of the empirical uncertainty for short-term repeat observations of *v*sin*i* using order-sorting filter HR15N. Plot **a) **shows the variation of *E*_{vsini} × (*S*/*N*)( [ *v*sin*i* ] /*C*)^{2}/ (1 + ( [ *v*sin*i* ] /*C*)^{2})^{5/4} with S/N . The horizontal line indicates the value of parameter *β* in Eq. (3) fitted to the full dataset. Blue crosses show the estimated values *β* as a function of S/N corrected for the measured variation of *β* with *T*_{eff} (see Sect. 4.4 and Table 3). Plot **b) **shows the variation of *E*_{vsini} × *S*/*N* with *v*sin*i*. The solid line show the relationship predicted using the theoretical value of *C* and the value of *β* from plot **a)**. In plots **a) **and **b) **the *y*-axis shows an estimate of the standard deviation based on the MAD divided by 0.82 (for *ν* = 2, see Sect. 3.3). Plot **c) **shows the cumulative probability distribution (CDF) of the normalised uncertainty in *v*sin*i* for short-term repeats. The red solid line shows results for measured data, the dashed line shows the cumulative distribution of a Gaussian with unit dispersion, and the diamond symbols show the cumulative distribution function for a Student’s t-distribution with *ν* = 2.