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Comparison of Generalized Approximate Cruise Range Solutions for Turbojet/Fan Aircraft
Abstract
Two different approximate solutions are proposed and compared with the numerical solution of the constant-altitude-constant-Mach-number cruise range for turbojet/fan aircraft. The approximate solutions consider both cambered wing drag polar and dependence of specific fuel consumption on Mach number. It is also proved that the classical analytical approach assuming constant specific fuel consumption and uncambered wing drag polar results in higher optimum Mach numbers and shorter ranges for constant-altitude-constant-airspeed flight of turbojet/fan transport aircraft.
... Other recent studies applying forms of the range equation include Cavcar and Cavcar [11], who compared different cruise range solutions for high-subsonic-Mach-number aircraft, and Poll [12], who used developments to the Bréguet range equation to assess the potential for aircraft total fuel-burn reduction through advances in technology, air traffic management, and fundamental changes to passenger aircraft design. ...
This paper uses measurements from flight-data recorders to develop an improved, simple model for aircraft fuel burn. The model is an adaptation of the Breguet range equation, with straightforward adjustments made for headwind, cruise flight conditions, climb performance, and descent operation. The adjustments made are based on physical reasoning combined with results from real flight operations. The analysis of flight data shows that the additional fuel burn required for takeoff and climb is constantly around 1.5% of takeoff weight. The fuel burn during descent shows greater variation and there appears to be scope for improvements through more consistent approach procedures. The new model is validated against fuel-burn data from a large number of flights and is shown to have greatly improved accuracy relative to a simple form of the Breguet range equation.
Air traffic plays a crucial role in the global economy and connectivity, directly strengthening international trade, job creation, and global connectivity. The number of flights is predicted to increase from 2024 to 2050. However, these increases in traffic numbers will also lead to a rise in fuel consumption and CO2 emission values. Therefore, optimizing the cruise altitude can significantly increase the specific range and lower CO2 emissions. Various factors, including cruise altitude, airspeed, mass, weather conditions, and air traffic management, alter the CO2 emissions of a flight. The air traffic system assigns a flight level for each aircraft based on the current air traffic situation. Aircraft can use three flight regimes for cruise operations: constant altitude and lift coefficient, constant airspeed and lift coefficient, and constant airspeed and altitude. The study aims to calculate the CO2 emission for all flight regimes using a linear regression equation. The flight regime with constant altitude and lift coefficient produces approximately 1.6% more CO2 emissions than the constant airspeed and lift coefficient. In addition, the constant altitude and airspeed flight regime also leads to approximately 4.4% more CO2 emissions than the constant airspeed and lift coefficient. Besides, the Ordinary Least Squares linear regression equation has an R2 = 0.958 for calculating total CO2 emission using the initial weight of the aircraft, initial air density, initial airspeed, initial lift coefficient at the beginning of the cruise phase, distance, aircraft type and flight regime information.
The objective of this study is to show the environmental and operating cost savings that could be achieved if long-range transport aircraft were designed for shorter ranges, and long-range flights were operated with an intermediate stop, obviously, with the drawback of longer trip duration and the increase in the number of flight cycles. The maximum take-off weight and operating empty weight, the main design variables of transport airplanes, noticeably diminish. The overall result depends on the length of the route, the extra distance due to the detour, the location of the intermediate airport and the technology level (range factor and operating empty weight fraction with respect to the maximum take-off weight). In all the routes analysed, the uneven splitting between both legs plays a secondary role. It is shown that long routes are well adapted to intermediate stop operations, particularly when the airliner serving the route has been designed for a medium range. However, intermediate stop operations produce a negative impact for medium and short city pair distances, since the reduction in aircraft weight is more than counterbalanced by the extra fuel and time required in the non-cruise phases of the flights.
Air routes are mainly determined by the interaction of geographical, political, economic, and social factors. On another side, airlines use their aircraft for a diversity of missions. Because of both factors the actual utilization of transport aircraft is well inside the payload-range envelope, which means that the design features are oversized for most flights. The objective of this paper is to evaluate the savings that could be achieved if transport aircraft were designed for shorter ranges: i.e., closer to the actual utilization pattern. In this design scenario the maximum takeoff weight and the operating empty weight would be remarkably reduced. This would lead to a reduction in aircraft price, trip fuel, maintenance cost, landing and navigation charges, and environmental impact. Direct operating cost is used as the figure of merit of the reduced-range approach.
A model for the aircraft performance including a Brayton turbojet engine cycle analysis was developed in
order to study the effect of different flight profiles on the range of a medium-sized business jet. In the classic
flight mechanics treatment of aircraft performance, maximizing range requires maximizing CL1/2/CD. This classic approach, however, assumes that thrust specific fuel consumption is a constant. Past studies which include the effect of variation in thrust specific fuel consumption typically seek to determine the optimum flight Mach number under a constant altitude - constant speed flight condition. Actual aircraft, on the other hand, may
involve fixing the engine throttle or thrust output to a set value and allowing the aircraft to speed up as the
weight decreases. This project is motivated by a desire to study what effect variations in flight conditions such
as speed, lift-to-drag ratio, throttle, or thrust settings have on aircraft performance. An increase in range of
about 2% was obtained by maximizing U(L/D)/TSFC compared to the case where CL1/2/CD is maximized.
A model for the aircraft performance including a Brayton turbofan engine cycle analysis was developed in
order to study the effect of varying the fan pressure ratio and bypass ratio on the range performance of a
medium-size business jet. In the classic flight mechanics treatment of aircraft performance, maximizing range
requires maximizing CL /CD. This classic approach, however, assumes that thrust specific fuel consumption is 1/2 a constant. Previous studies, which include the effect of variation in thrust specific fuel consumption, typically seek to determine the optimum flight Mach number under a constant altitude - constant speed flight condition. This project was motivated by a desire to study what effect variations in flight conditions such as speed, lift-to drag ratio, or thrust settings have on aircraft performance. An increase in range of approximately 2% to 8% was obtained, depending upon the bypass ratio, by maximizing U(L/D)/TSFC compared to the case where CL /CD 1/2 was maximized.
With rising fuel costs there is an initiative to conserve fuel during fight. Several methods have been proposed to calculate an optimum speed to y during cruise flight to maximize the range of a particular aircraft. This paper compares 11 of these methods using the same aircraft model and discusses how to implement these techniques in an autothrottle. Alternative implementations also include adding the algorithm to the Flight Management System to use during flight planning, or to including it in the databases to use during dispatch calculations. The results show that the speeds calculated by these methods are more fuel efficient than the usual cruise operating speed.
Since flying at the optimum speed is not always practical, this research also looked at the design of the industry autothrottle. Improvements to the industry autothrottle speed control law were implemented to see if improvements to fuel consumption could be achieved at any speed. The results show that the improvements proposed did not improve the fuel consumption during the conditions simulated.
An approximate solution of the constant altitude-constant Mach number cruise range for high subsonic speed flight of the turbojet/fan aircraft is proposed. The solution considers cambered wing drag polar of modern transport aircraft, dependence of the specific fuel consumption on Mach number, and compressibility effects on aerodynamic characteristics of the aircraft. The method aims for a quick assessment of the cruise range during conceptual or preliminary design phase. An application of the method to a known type of aircraft is also presented.
Aircraft have greatly changed over the last decades, mainly due to astonishing developments in key technological areas. The present note attempts to correlate the evolution of jet airliners with improvements in aerodynamics and propulsion. A simple model is elaborated from the range equation, taking the main magnitudes of the payload-range diagram as input data. Results show the robustness and potential of such procedures.
Approximate cruise range solutions are introduced for the constant altitude – constant high subsonic speed flight of turbojet/fan transport aircraft with cambered wing design. The variation of the specific fuel consumption with Mach number is also considered in derivation of the approximate solutions. The method aims at estimation of the cruise range of aircraft during conceptual or preliminary design phase. An application of the solutions is also presented.
An attempt is made to develop a more realistic model of the optimum cruise of a jet aircraft by considering the effect of the Mach number on the specific fuel consumption. It is assumed that the specific fuel consumption is influenced by the Mach number in accordance with a potential law, which, along with the constant altitude constraint, allows a simple analytical treatment of the range equation and related expressions. The final results are written in closed form. An application of the results to performance prediction is illustrated. 12 refs.
Analytic expressions, based on the exact performance relationships without making the approximations, are developed to predict cruising range and endurance of turboprop, turbofan, or piston-propeller aircraft at constant speed and altitude. A numerical example was presented to illustrate the accuracy of the classical Coffin-Brequet equation as well as an approximate one obtained from the exact equation by a limiting process. Also, the optimal cruising speed to achieve maximum range is determined.
A unified analytical treatment of the cruise performance of subsonic transport aircraft is derived, valid for gas turbine powerplant installations: turboprop, turbojet and turbofan powered aircraft. Different from the classical treatment the present article deals with compressibility effects on the aerodynamic characteristics. Analytical criteria are derived for optimum cruise lift coefficient and Mach number, with and without constraints on the altitude and engine rating.A simple alternative to the Bréguet range equation is presented which applies to several practical cruising flight techniques: flight at constant altitude and Mach number and stepped cruise/climb. A practical non-iterative procedure for computing mission and reserve fuel loads in the preliminary design stage is proposed.