Aircraft emissions differ from other anthropogenic pollution in that they occur mainly in the upper troposphere and lower stratosphere where they can form condensation trails (contrails) and affect cirrus cloud cover. In determining the effect of aircraft on climate, it is therefore necessary to examine these processes. Previous studies have approached this problem by treating aircraft emissions on the grid scale, but this neglects the subgrid scale nature of aircraft emission plumes. We present a new model of aircraft emission plume dynamics that is intended to be used as a subgrid scale model in a large scale atmospheric simulation. The model shows good agreement with a large eddy simulation of aircraft emission plume dynamics and with an analytical solution to the dynamics of a sheared Gaussian plume. We argue that this provides a reasonable model of line-shaped contrail dynamics and give an example of how it might be applied in a global climate model.