This paper is one of a series addressing the need for simple, yet accurate, methods for the estimation of cruise fuel burn and other important aircraft performance parameters. Here, a previously published, constant Reynolds number model for turbofan-powered, civil transport aircraft is extended to include Reynolds number effects. Provided the variation of temperature with pressure is known, the method is applicable to flight in any atmospheric conditions. For a given aircraft, cruising in a given atmosphere, there is a single Mach number and Flight Level pair, at which the fuel burn per unit distance travelled through the air has an absolute minimum value. Both these quantities depend upon the Reynolds number, which, in turn, depends upon the aircraft weight and the atmospheric vertical temperature profile. Simple, explicit expressions are developed for all parameters at the optimum condition. These are shown to be in close agreement with numerical solutions of the governing equations. It is found that typical operational mass and temperature profile variations can change cruise fuel burn rate by several percent. In the International Standard Atmosphere, when the speed and altitude deviate from their optimum values, the fuel burn penalty is reduced slightly relative to the constant Reynolds number case. By way of example, the method is used to estimate the minimum fuel, speed-versus-height trajectory for cruise in a realistic atmosphere.
For each aircraft, cruise fuel burn is found to be governed by six independent parameters. All are constants. Two are simple, involving only size and weight, whereas four are complex and must be determined by either theoretical, or empirical, means. The estimation of these quantities will be considered in Part 2.