estimate of the contrail optical properties. According to the model, the plume opacity falls off rapidly as the plume expands. To be clearly visible in daylight, the opacity through the width of the contrail should exceed 0.1. Note that, while the opacity along the axis of the trail decreases rapidly with time — approximately as A~' for several hours (where A is the cross-sectional area), the opacity perpendicular to the axis decreases more slowly during this time — approximately as A h After several hours, the opacity of the contrail begins to decrease at a faster rate because the ice particles at some altitudes are evaporating spontaneously (i.e., the axial optical depth falls off faster than A-1; see Fig. 5). Our calculations indicate that an HLLV launch trail could be visible for as long as 12 h and cover an area of several hundred square kilometers, if the horizontal mesospheric eddy diffusion coefficient is 10" cm2/sec. The actual horizontal extent of the cloud would be enhanced by the slant of the launch trajectory and the inevitable stretching and twisting of the contrail induced by strong wind shears, which are common at mesospheric altitudes. If the rate of lateral dispersion of the rocket plume is faster than assumed, the lifetime of the visible contrail would be reduced accordingly. Thus, with an effective horizontal diffusion coefficient of 109 cm2/sec, the contrail could dissipate within one hour after launch. These results confirm previous estimates of HLLV cloud persistence (3). If the air layers near the mesopause are unusually stable at the time of launch, a subvisible rocket cloud could persist for a day or more before the water vapor satura-
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