On the relationship between non-optimum operations and fuel requirement for large civil transport aircraft, with reference to environmental impact and contrail avoidance strategy

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A simple yet physically comprehensive and accurate method for the estimation of the cruise fuel burn rate of turbofan powered transport aircraft operating in a general atmosphere was developed in part 1. The method is built on previously published work showing that suitable normalisation reduces the governing relations to a set of near-universal curves. However, to apply the method to a specific aircraft, values must be assigned to six independent parameters and the more accurate these values are the more accurate the estimates will be. Unfortunately, some of these parameters rarely appear in the public domain. Consequently, a scheme for their estimation is developed herein using basic aerodynamic theory and data correlations. In addition, the basic method is extended to provide estimates for cruise lift-to-drag ratio, engine thrust and engine overall efficiency. This step requires the introduction of two more independent parameters, increasing the total number from six to eight. An error estimate and sensitivity analysis indicates that, in the aircraft’s normal operating range and using the present results, estimates of fuel burn rate are expected to be in error by no more than 5% in the majority of cases. Initial estimates of the characteristic parameters have been generated for 53 aircraft types and engine combinations and a table is provided.

“…Cd 0 is the zero-lift, profile drag coefficient 1 , e LS is the 'low-speed' Oswald efficiency factor, AR is the wing aspect ratio, defined as…”

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Section: Introductionmentioning

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An estimation method for the fuel burn and other performance characteristics of civil transport aircraft during cruise: part 2, determining the aircraft’s characteristic parameters

Poll

Schumann²

2020

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An estimation method for the fuel burn and other performance characteristics of civil transport aircraft in the cruise. Part 1 fundamental quantities and governing relations for a general atmosphere

Poll

Schumann

2020

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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.

On the conditions for absolute minimum fuel burn for turbofan powered, civil transport aircraft and a simple model for wave drag

Poll,

Schumann

2024

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In a recent series of papers, Poll and Schumann have been developing a simple model for estimating fuel burn for turbofan powered, civil transport aircraft for a given mass, Mach number and flight level and in a specified ambient temperature profile for all phases of flight. This paper focuses upon the combination of Mach number and flight level at which an aircraft cruises with the absolute minimum fuel burn. For a given aircraft type, the information necessary to determine these conditions must be specified and this poses a challenge. An initial attempt to obtain these data has been described previously by the first author. In this paper, the optimum conditions are found using a completely different approach. Starting from first principles and using established theory, the equations governing the situation where engine overall efficiency and airframe lift-to-drag ratio both have local maxima at the same flight condition are developed. This special case is termed the “design optimum” condition and, for a specified aircraft mass and a specified atmospheric temperature versus pressure profile, it gives the lowest possible fuel burn for any aircraft and engine combination. The design optimum occurs at a particular Mach number and Reynolds number, and it is a fixed characteristic of the aircraft. The analysis reveals the significance of Reynolds number variations, wave drag, including its derivatives with respect to both lift coefficient and Mach number, and the atmospheric properties. Whilst wave drag is notoriously difficult to determine accurately, it is found that solutions to the equations are not particularly sensitive to the accuracy of this quantity. Consequently, a simple, physically realistic model can give good results. An appropriate model is developed and a complete, approximate solution is obtained. Taking the International Standard Atmosphere as the design atmosphere, results are presented for the 53 aircraft types previously considered by Poll and Schumann. Relative to the design optimum conditions, when Reynolds number is constant and wave drag is zero, compressibility alone reduces L/D by about 5%, reduces lift coefficient by about 1.5% and increases drag coefficient by about 3.5%. Reynolds number variation has little effect upon L/D, but it reduces lift coefficient and drag coefficient by a further 7% and 8% respectively. The reduction in lift coefficient has a significant impact on the optimum cruise flight level. In general, an aircraft’s operating optimum will not coincide with its design optimum, but deviations are expected to be small. Therefore, using the design optimum solution as a reference point, an improved version of the operating optimum estimation method described by Poll and Schumann in previous work is developed. This allows the estimation of the conditions for absolute minimum fuel burn for an aircraft of given mass flying thorough any atmosphere. Updated coefficients for the 53 aircraft types are given.