D. I. A. Poll

Fuel requirement is one of the most important issues in aircraft performance. For an aircraft of a given mass, flying in an atmosphere where temperature is a monotonically decreasing function of pressure, there is one Mach number and flight level (FL) pair for which the specific air range (SAR), i.e. the distance travelled through the air per unit mass of fuel consumed, is a maximum. Specific air range is directly proportional to the range parameter, which is the product of the overall engine efficiency and the airframe lift-to-drag ratio. During the aircraft design process, the optimum value of the range parameter is fixed at a specific ‘design’ mass in a specific ‘design’ atmosphere. This ‘design optimum’ condition is a characteristic of the aircraft and engine combination, occurring at a particular Mach number and flight level pair. However, in routine operations, the aircraft mass and the atmospheric characteristics will rarely, if ever, coincide with the design conditions. Consequently, in general, the operational optimum Mach number and flight level pair will not be the same as that at the design optimum. The primary purpose of this analysis is to find the general relationship between the operational and the design conditions. In performance calculations, it is often assumed that, if the Mach number and lift coefficient are constant, the range parameter is also constant. This leads to the well-known ‘cruise climb’ trajectory for ‘maximum’ range and, for the whole flight, the classical Breguet range equation for the required trip fuel. However, to maintain a constant lift coefficient, the aircraft must climb as mass reduces and, depending upon the relationship between temperature and pressure in the atmosphere, its Reynolds number changes. It is shown that these Reynolds number changes can alter the range parameter by several percent as the flight progresses, and the standard Breguet equation may produce significant errors in the trip fuel estimation. Therefore, a completely general formulation of the range equation is presented. The well-documented, open-source, Poll-Schumann aircraft performance model is used to provide data for a wide range of operating conditions. Tabulated coefficients are provided to allow operational estimates to be made for 71 aircraft types and variants. These values are best estimates based upon information available in the public domain.

If an aircraft’s initial mass, the variation of true airspeed, true rate of climb, wind speed and wind direction with time and the relationship between barometric altitude and local temperature are known, the performance along the entire flight path can be determined. Previously published work has provided the building blocks for a simple, fast, open-source and transparent method to estimate the instantaneous fuel flow rate and the engine overall efficiency, plus several other performance characteristics for turbofan powered, civil transport aircraft. The flight phases of primary interest are the climb, cruise, descent and holding, when the flaps and undercarriage are fully retracted and the engine is providing significant, positive thrust. However, for completeness, an approximate relation is provided for the engine’s ‘flight idle’ condition, together with simple estimates for fuel use during take-off and landing, plus a factor to allow for in-service deterioration. Detailed consideration is also given to the operating limits and relations are developed for the estimation of their location in Mach number and flight level space. To apply the method, a series of characteristic coefficients and constants must be known. Estimates for these quantities have been progressively improved and extended over time. Initially, results were published for 53 aircraft types and variants. The data base has now been extended to 67 entries and this is given in tabular form. Finally, to demonstrate the method’s accuracy, estimates of fuel flow rate are compared with flight data recorder values for 20 complete flights of six different aircraft types.

The overall efficiency of a turbofan engine may be expressed as a function of the Mach number, flight level and one other parameter. This may be either the net thrust, the turbine entry temperature or the fuel flow rate. Using basic aero-thermodynamic principles, dimensional analysis, normalisation and curve fitting, five approximate and “near universal” relations have been identified for engines having bypass ratios between 1 and 13. These relations contain five independent characteristic engine parameters. When these parameters are known, the relations form the basis of an estimation method for engine overall efficiency that is simple, fast, open source, completely transparent and, as new information appears, capable of further refinement. Since the empirical relations presented in this analysis are valid for Mach numbers greater than 0.2, the method is applicable to all airborne phases of flight. For a given aircraft, if the flight trajectory is specified in sufficient detail for the variation of net thrust with Mach number and flight level to be determined, only three of the five relations, together with the value of engine overall efficiency at a single reference condition, are needed to estimate the overall efficiency at every point on the trajectory. Comparisons with the data used in this analysis suggest that the accuracy is better than ±5% in most cases. In the completely general case, two additional engine characteristic parameters, one a total temperature ratio and the other a Mach number, are introduced. If these are known, both engine overall efficiency and net thrust can be expressed as functions of Mach number, flight level and turbine entry temperature. This allows the method to be used for the estimation of operating limits in the various phases of flight and in simplified optimisation studies, e.g. finding the environmentally optimum flight trajectory.In previous work, estimates of engine overall efficiency at the “design optimum” condition have been estimated for 53 aircraft and engine combinations. It is shown that the ‘design optimum’ condition is an appropriate choice for the engine reference condition. Updated and revised values for the relevant parameters for these 53 examples, together with estimates for the two additional engine characteristic parameters, are given in tabular form.

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.

The aviation industry has committed to decarbonize its CO₂ emissions. However, there has been much less industry focus on its non-CO₂ emissions, despite recent studies showing that these account for up to two-thirds of aviation’s climate impact. Parts of the industry have begun to explore the feasibility of potential non-CO₂ mitigation options, building on the scientific research undertaken in recent years, by establishing demonstrations and operational trials to test parameters of interest. This paper sets out the design principles for a large trial in the North Atlantic. Considerations include the type of stakeholders, location, when to intervene, what flights to target, validation, and other challenges. Four options for safely facilitating a trial are outlined based on existing air-traffic-management processes, with three of these readily deployable. Several issues remain to be refined and resolved as part of any future trial, including those regarding meteorological and contrail forecasting, the decision-making process for stakeholders, and safely integrating these flights into conventional airspace. While this paper is not a formal concept of operations, it provides a stepping stone for policymakers, industry leaders, and other stakeholders with an interest in reducing aviation’s total climate impact, to understand how a large-scale warming-contrail-minimizing trial could work.

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.

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.

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, (η _o L / 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 (η _o L / 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%.

Aviation brings great commercial and social benefits and, as the global economy develops, the demand for air transport is expected to grow. However, aviation also contributes to climate change and there is increasing international pressure to limit mean global temperature rise. Therefore, the future success of aviation is likely to depend upon the industry's ability to hold its environmental impact within politically acceptable limits. This paper describes aviation's interaction with climate and sets out, in broad terms, the challenge facing the industry. The prospects for mitigating the adverse effects by advanced technology working through aircraft design and manufacture are assessed and some potential restrictions imposed by airport infrastructure are identified. Some consideration is also given to the practicalities imposed by airline economics and the likely impact of the recent ICAO regulations, plus the proposed global-based market measures scheme for aviation carbon offset. It is argued that the environmental problem is not just about carbon dioxide emissions and that aircraft technology improvement alone is unlikely to provide a complete solution. The observation that, in current operations, the total fuel used is almost twice the minimum required suggests a need to recognise a broader ownership of the problem and broader responsibility for the solution. However, improvements in the overall system efficiency will probably need to be driven by additional regulation and the imposition of other financial measures.The overall conclusion is that the actions currently being taken and currently being proposed are probably not sufficient in themselves to meet the challenge of climate change. However, it appears that there is more that can be done and, provided that action is taken soon, there are some grounds for optimism that aviation will still be able to meet the needs of society in the 21^stcentury.