Fuel sensitivity analyses for jet and piston-propeller airplanes

Two mathematical relationships have been derived to estimate the impact on fuel consumption during cruise - one for jet airplanes and one for piston-propeller airplanes -arising from design changes that alter the airplane's weight (W), lift-to-drag ratio (L/D) and Specific Fuel Consumption (SFC). Using cruise fuel burn as the figure of merit, the expressions may be used to rapidly assess proposed airplane design changes (or modifications) where simultaneous changes to these three fundamental design parameters occur. Two case studies are presented. The first considers the incorporation of an active drag reduction system, such as Hybrid Laminar Flow Control (HLFC), which reduces the skin friction drag, but increases the airplane's weight, and - as such systems require power -increases the power off-take from the engines, leading to an SFC penalty. Using a commercial jet airplane as a reference vehicle, the results of the numerical expression are compared to those obtained using a computer program, which is capable of accurately determining the cruise fuel. The underlying assumption of linear independence of the three parameters is explored - the results indicate that the parameters are only weakly linked, the nature of which depends on the airplane's performance characteristics. The second case study concerns a proposed design change to piston-propeller airplane, where the incorporation of a retractable landing gear reduces drag, but a weight penalty is incurred. A target for the weight change is rapidly computed for the associated drag change.