  A typical inflatable reflector for space application consists of two thin
membranes with a parabolic shape. It is critical to understand the interaction
of the inflatable and the micrometeoroid environment to which it is exposed.
This interaction leads to a series of penetrations of the inflatable membrane
on entrance and exit of the impacting particle, creating a pathway for gas
escape. To increase the fidelity of the damage expected, we examine the
literature for descriptions of micrometeoroid fragmentation and present a
theoretical formulation for the damage caused by an impacting particle to the
entrance and exit membranes. This theory is compared to an initial set of
hyper-velocity tests for micrometeoroid-sized particles on thin film membranes.
We use the results of these tests to produce a predictive model. This model is
applied to estimate the damage rate near the 1 AU location and output
predictions for the effectiveness of a micrometeoroid shield to reduce the
damage on the lenticular and effectively optimize its lifetime. Lastly, we
apply the kinetic theory of gasses to develop expressions for the expenditure
of gas over a specified mission lifetime due to penetrations. Although this
paper examines the specific case of an inflated lenticular protected by extra
membrane layers, our predictive model can be applied for any gossamer structure
composed of polyimide membranes.
