(A) Background-subtracted micrograph showing the track of a bull sperm in a cylindrical channel (viscosity μ = 3 mPa·s shear rate ), channel boundary false-coloured with black, see Video 1 for raw data. (B) Schematic representation not drawn to scale. The conical envelope of the flagellar beat holds the sperm close to the surface (Kantsler et al., 2013). The vertical flow gradient exerts a torque that turns the sperm against the flow, but is counteracted by a torque from the chirality of the flagellar wave, resulting in a mean diagonal upstream motion. (C) Tracks of bull sperm near a flat channel surface. (D) Upstream and transverse mean velocities vs shear flow speed u20 at 20 μm from the surface for different viscosities. All velocities are normalised by the sample mean speed v0μ at . For human sperm, in order of increasing viscosity v0μ = 53.5 ± 3.0, 46.8 ± 3.7, 36.8 ± 3.3, 29.7 ± 3.9 μm/s, and for bull sperm v0μ = 70.4 ± 11.8, 45.6 ± 4.7, 32.4 ± 4.8, 29.6 ± 4.1 μm/s, where uncertainties are standard deviations of mean values from different experiments. Each data point is an average over >1000 sperms. (E) Histograms for selected points in (D).