On the Estimation of Permeabilities and Draw Resistances of Cigarette Components

Abstract The goal of this study is to investigate whether the permeability of the tipping/plugwrap system, the permeability of the cigarette paper and the draw resistances of the filter and tobacco rod can be calculated from measurements of the degree of filter ventilation and of the open and closed draw resistance. This issue is investigated for a linear and a non-linear model of the flow in unlit cigarettes. At first it is proven that there exist experimental conditions to which the cigarette can be exposed such that the problem has at least a unique solution. The problem is then solved by least-squares optimisation for a linear and a non-linear model of the air flow in unlit cigarettes with various noise levels on the output quantities. The error sensitivity of the optimisation problem is estimated by calculation of the condition number. From the simulation several facts can be concluded. Firstly, for the linear model varying the flow velocity at the mouth end of the cigarette does not provide enough information to uniquely determine the properties of the cigarette's components. Secondly, estimates of these properties from the linear model have low standard deviations but a high bias, which makes the linear model useless for the estimation task. Thirdly, estimates from the non-linear model are more reliable if the pressure at the cigarette tip is varied instead of the flow velocity at the mouth end. Fourthly, the measurements of the degree of filter ventilation and of the open and closed draw resistance need to be at least 10 to 20 times more accurate than the desired accuracy of the estimate. Several methods to improve this situation are proposed.