A kinematic analysis of the previously neglected effect of velocity inhomogeneity on the topology of the heliospheric current sheet in a radially flowing solar wind shows how the originally smooth current sheet becomes ''ruffled.'' In the highly idealized case of a totally uniform, radial, steady solar wind, the shape of the current sheet is independent of distance from the sun. However, the real solar wind is inhomogeneous; the velocity varies from point to point along the current sheet, causing a distortion in the current sheet of progressively greater amplitude with increasing distance from the sun. This is true even for purely radial flow. Significant and observable distortion is produced by relatively small gradients in velocity; thus to predict or understand the shape of the heliospheric current sheet it is essential to know the solar wind in which the current sheet is embedded. We give examples of mild velocity gradient which demonstrate the principles, the magnitude, and the character of the effect; deformation of the actual heliospheric current sheet in the highly variable solar wind is expected to be of far greater amplitude and complexity than in the simplified, tutorial examples. We also derive a new expression for the inclination of the current sheet as a function of velocity inhomogeneity and distance from the sun that is easily applied to the interpretation of solar wind data.