The general problem of determining cruise fuel burn is addressed by considering the variation of the product of engine overall efficiency and airframe lift-to-drag ratio, (ηoL/D), with Mach number and lift coefficient. This quantity is the aerothermodynamic determinant of fuel burn rate. Using a small amount of real aircraft data and exploiting normalisation, it is found that near universal relationships exist between the key variables. With this major simplification, an analytic, near exact solution is derived in which the aircraft-related input data are reduced to just three parameters, namely the optimum value of (ηoL/D) and the lift coefficient and Mach number combination at which it occurs. These are quantities that are either available from open information sources or can be estimated using established analytic methods. By introducing models of the take-off and climb and the descent and landing phases, the method is extended to provide accurate trip fuel estimates.
It is shown that there is an ideal flight level (IFL) at which the fuel consumption rate is a minimum for all speeds in the normal cruise operating range. Furthermore, the IFL at the end of cruise is approximately the same for all aircraft, whilst the IFL at the beginning of cruise depends, primarily, on the distance to be flown. There is little dependence on the size of the aircraft, or its take-off mass.
In the context of the ‘fuel-based’ assessment of operational inefficiency, the method is further developed to determine the sensitivity of the trip fuel requirement to changes in the operational parameters governed by air traffic management (ATM). The result is two simple equations. These are used to estimate the current ATM fuel burden. At the global level, this is about 20% with more than half being attributable to flights of less than 1,200 km.
Finally, the method is used to estimate the fuel burn penalty associated with reducing contrail formation by simply avoiding those regions of the atmosphere that are supersaturated with respect to ice. If the aircraft is at the IFL when avoiding action is required, flying below the supersaturated region minimises the additional fuel use. Even when multiple evasive manoeuvres are needed, the additional trip fuel requirement is expected to be less than 0.5%.