Creating Carpet Plots that Address Uncertainty for Aircraft Sizing

Abstract

*† All designers are aware of the uncertainty inherent in conceptual aircraft design. Most often it is dealt with by the use of a safety factor or a design margin that is added to constraints or limits to account for variability between a predicted result and the actual result. Both safety factors and design margins can be very effective; however, they may result in an “over designed” aircraft and sometimes an “under designed” one. This may require late design changes, which are typically costly to perform. Engineers understand that a large source of uncertainty in initial aircraft sizing comes from the empty weight equations. They generally use an empirically-based equation or a set of such equations that are a function of major aircraft design parameters, like wing area, sweep, and aspect ratio and have been defined during conceptual design. It is possible to characterize the uncertainty in these equations and to use Monte Carlo simulations to combine all of the component weight uncertainties into a distribution of empty weight. Because empty weight affects the overall size and performance of the aircraft, the uncertainty in the weight equations can be propagated to the vehicle level. The end result is a “probabilistic carpet plot” that is much like a traditional carpet plot, only each design point in the sizing matrix is now represented by distributions of weight and performance values. A “minimally invasive” approach to account for uncertainties in aircraft sizing is provided here. Seemingly insignificant scatter about component weight trend lines leads to large uncertainties in the final design point.