Calculations of a relatively comprehensive chemical reaction mechanism applied to individual parcels of aircraft emissions under upper tropospheric conditions show that over a typical residence time of air in the upper troposphere, each aircraft-emitted NO_x molecule produces about 2-3 molecules of O₃ per day as long as the reactive NO_y remains in the upper troposphere. In the upper tropospheric environment characterized by low ambient turbulence and appreciable vertical wind shear, aircraft plumes grow slowly during initial stages, and take several days to diffuse to a size comparable to the grid volume used by global-scale Eulerian models. by assuming aircraft emissions are immediately diluted into a larger grid cell volume, larger-scale models will overestimated the calculated O₃ production by 20 to 30%. This overestimate depends on the vertical diffusion efficiency, vertical wind shear, and NO_x concentrations in the ambient environment. This overestimate can be compensated for in larger scale models by reducing the reaction coefficient of the NO + HO₂ reaction by less than 3% under typical upper tropospheric conditions.