Figure 1.

Schematic explanation of the dimensionless speed. (a) The red shape is an example of a 3D reconstruction of a propeller. The dashed black line indicates the axis of rotation. (b) After n (here n = 79 to suit the illustration) rotations, the propeller has moved a certain distance due to rolling (Δx) and a certain distance due to propulsion (Δy). The propeller speed v is the speed parallel to the rotation axis. The length scale L is chosen to be the size of the propeller in the projection in which it appears largest (see methods in Supporting Information). The dimensionless speed is thus the number of body lengths moved per rotation (times 1000) and can be thought of as an effective screw pitch. (c) The net magnetic moment (yellow arrow) of the propeller is likely rotating in the same plane (indicated by the blue shape) as the external magnetic field, perpendicular to the axis of rotation. This corresponds to a precession angle of 90°. (d) The precession angle does not necessarily have to be equal to 90°. Because of the interplay between magnetic and hydrodynamic forces, other precession angles are possible as well.