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.

中文翻译：

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民用运输机巡航燃油消耗及其他性能特性估计方法[J]. 第 1 部分 一般大气的基本量和支配关系

本文是解决对简单而准确的估计巡航燃油消耗和其他重要飞机性能参数的方法的需求的系列文章之一。在这里，以前发布的涡轮风扇动力民用运输机的恒定雷诺数模型被扩展为包括雷诺数效应。如果温度随压力的变化是已知的，则该方法适用于任何大气条件下的飞行。对于给定的飞机，在给定的大气中巡航，只有一个马赫数和飞行高度对，在该对中，每单位飞行距离的燃油消耗具有绝对最小值。这两个量都取决于雷诺数，而雷诺数又取决于飞机重量和大气垂直温度分布。简单的，为最佳条件下的所有参数开发了显式表达式。这些被证明与控制方程的数值解非常一致。发现典型的运行质量和温度分布变化可以将巡航燃料燃烧率改变几个百分点。在国际标准大气中，当速度和高度偏离其最佳值时，相对于恒定雷诺数情况，燃油燃烧损失会略微降低。举例来说，该方法用于估计在现实大气中巡航的最小燃料、速度与高度轨迹。对于每架飞机，巡航燃料消耗由六个独立参数控制。都是常数。两个很简单，只涉及尺寸和重量，而四个是复杂的，必须通过理论或经验手段来确定。这些数量的估计将在第 2 部分中考虑。