Aircraft at cruise levels can cause two kinds of contrails, the well known exhaust contrails and the less well-known aerodynamic contrails. While the possible climate impact of exhaust contrails has been studied for many years, research on aerodynamic contrails began only a few years ago and nothing is known about a possible contribution of these ice clouds to climate impact. In order to make progress in this respect, we first need a climatology of their formation conditions and this is given in the present paper. <br><br> Aerodynamic contrails are defined here as line shaped ice clouds caused by aerodynamically triggered cooling over the wings of an aircraft in cruise which become visible immediately at the trailing edge of the wing or close to it. Effects at low altitudes like condensation to liquid droplets and their potential heterogeneous freezing are excluded from our definition. We study atmospheric conditions that allow formation of aerodynamic contrails. These conditions are stated and then applied to atmospheric data: first to a special case where an aerodynamic contrail was actually observed and then to a full year of global reanalysis data. We show where, when (seasonal variation), and how frequently (probability) aerodynamic contrails can form, and how this relates to actual patterns of air traffic. We study the formation of persistent aerodynamic contrails as well. Furthermore, we check whether aerodynamic and exhaust contrails can coexist in the atmosphere. We show that visible aerodynamic contrails are possible only in an altitude range between roughly 540 and 250 hPa, and that the ambient temperature is the most important parameter, not the relative humidity. Finally, we argue that currently aerodynamic contrails have a much smaller climate effect than exhaust contrails, which may however change in future with more air traffic in the tropics.