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Optimum Range and Endurance of a Piston Propeller Aircraft with Cambered Wing
Abstract
An exact solution of the maximum range, and a highly accurate approximate solution of the maximum endurance, are proposed for cruising flight of the piston-powered aircraft installed with a constant-speed propeller and cambered wing. It is proven that the constant-altitude/constant-speed cruise range can be independently optimized, even for the aircraft with cambered wing, without substitution of the optimum speed of other flight regimes.
... Our model of the propulsive system is realistic and goes further than just taking a constant specific fuel consumption and propeller efficiency, as in previous studies (e.g., Cavcar and Cavcar [23]). For the engine, we considered potential dependencies of the power P on velocity through the maximum power delivered by the engine and of the fuel flow rate φ on velocity and power. ...
The problem of maximizing the range of a propeller-driven aircraft in a level flight cruise is analyzed within the framework of optimal control. The specific fuel consumption and propeller efficiency of its propulsive system are characterized by functions of the velocity and engine power (full model), in contrast to previous works, where they were considered to be constant. To conduct the study, a notional Piper Cherokee PA-28 is selected as representative of light aircraft, defining both the airplane and mission features. Two simplified models are also derived: the Von Mises model, with constant specific fuel consumption and propeller efficiency, and the Parget and Ardema model, defined by constant specific fuel consumption and propeller efficiency depending on the velocity. The problem is solved numerically by means of a direct transcription method. Since the optimal problems of the Von Mises and Parget and Ardema models are singular, it is necessary to incorporate a regularization term. Such a numerical algorithm is validated against the analytical solution given by the Breguet formulation. In this context, the velocity and mass (state variables), the power throttle (control), and the best range are determined. The full model provides a maximum range of 1492 km. The differences between the Von Mises and Parget and Ardema models are about 24 km and 1 km, respectively. A non-optimal steady cruise is also analyzed, providing a significant reduction in the flight time, with a decrease of about 2% of the range. The evolution of the state variables and control in the steady cruise, however, separates from the full model. On the other hand, the Parget and Ardema model almost reproduces the full model results, leading to a clear image of the physics involved: the best range comes from maximizing the product of the propeller and aerodynamic efficiencies with respect to the velocity, which determines the optimal arc.
... As a result, the battery life of electric UAVs is short [2]. Electric UAVs keep their mass unchanged during the entire mission period, which is different from oil engines, and the discharge voltage of the batteries constantly declines [3]. The discharge time of a battery is related to various factors, including discharge rate, power, and voltage [4]. ...
The lack of endurance is an important reason restricting further development of unmanned aerial vehicles (UAVs). Accurately estimating the state of charge (SOC) of the Li-Po battery can maximize the battery energy utilization and improve the endurance of UAVs. In this paper, the main current methods for estimating the SOC of vehicles were explored and discussed to unveil their advantages and disadvantages. In addition, the extended Kalman filter algorithm based on an equivalent circuit model was used to estimate SOC of power-type Li-Po batteries at different temperatures. The result showed that the closed-loop control method can effectively improve the battery life of small-sized electric UAVs.
Askeri ve sivil alanda çok büyük bir öneme sahip olan hava taşımacılığının en önemli unsurlarından biri uçak performansıdır. Uçuş fazlarının her biri için uçuş performansının artırılmasını sağlamak için birçok çalışma yapılmaktadır. Uçuş performansını etkileyen birçok unsur bulunmaktadır. Bu çalışmada uçak performansına etki eden faktörler araştırılarak belirlenmiş, daha sonra belirlenen bu faktörlerin uçak performansını ne derecede etkilediği uzman kişilerin görüşleri doğrultusunda, Aşamalı Ağırlık Değerlendirme Oran Analizi (SWARA Stepwise Weight Assessment Ratio Analysis) kullanılarak faktörlerin önem dereceleri değerlendirilmiştir. Yapılan değerlendirme sonucunda uçak performans parametrelerinin ağırlıklandırılmasında en yüksek önem derecesine sahip ilk üç kriter sırası ile Ağırlık, yapım malzemesi ve sıcaklık olarak belirlenmiştir.
Traditionally, the airplane and aero-engineAero-engine are two separate units and are not closely related. In electric aircraftAircraft, since multiple small engines can be equipped on one airplane, the integral design of aero-enginesAero-engine with the aero-vehicle becomes feasible together with its obvious advantages. The integrated design of an airplane with multiple engines requires three key elements: 1) multiple and flexible small and lightweight aero-engine with a compact structure that is easy to operate in multiple orientations; 2) powerful and long lasting aviation electric power such as using 3D HK SC for vertical takeoff and kerosene LTG for long navigation ranges; and 3) rotatable wings allowing free-scale engine orientation, including strategies and methodologies.
The existing aircraft configuration cannot satisfy the requirements for the longitudinal stability and flight performance of a static and stable fixed-wing aircraft. This is especially true for a flying wing aircraft, whose flight performance deteriorates in maintaining its static stability. Hence, we propose a new aerodynamic configuration that uses the propeller thrust to trim longitudinally the flying wing of an unmanned aerial vehicle (UAV). In the configuration, the positive cambered airfoil is used to replace the conventional reflex cambered airfoil so as to raise the lift to drag ratio and lift of the UAV, which is longitudinally trimmed by wash-out and propeller thrust. We use the commercial software CMARC and empirical formulate to calculate the aerodynamic force of the UAV and analyse its stability. During its stall, the calculation results are in good agreement with the wind tunnel experimental results. We also study the matching between the propeller of the UAV and its motor and establish the mathematical model to calculate the efficiency of its power system and merge it into the overall design by taking into account the difference in power at different mission stages. We use the genetic algorithm to optimize the overall parameters of the flying wing UAV trimmed and not trimmed with propeller thrust. The optimization results, given in Table 1 and Fig. 9, show preliminarily that: (1) the amounts of wash-out and sweepback of the UAV longitudinally trimmed with propeller thrust are reduced and its coefficient of maximum lift available and wing loading increase, thereby reducing the wing area; this leads to a larger aspect ratio when the wingspan is kept constant; (2) because of few elevon deflections and reduced wash-out, the lift to drag ratio increases during cruise and loitering. Finally, we study the effects of overall parameters on the performance of the UAV trimmed with propeller thrust.
For small electric-powered unmanned aerial vehicles (EPUAV), endurance performance largely depends on propulsion system. To improve EPUAV endurance, the electric-powered propulsion system was designed optimally. Meanwhile EPUAV endurance formula was presented. Based on vortex theory, a small screw propeller was designed optimally using genetic algorithm. A series of predicted motors were tested by dynamometer in order to match the optimized screw propeller effectively. The influences of discharged rating and voltage drop for lithium-ion battery were considered. Then a math model of battery discharge time was deduced while the battery output power was kept as constant. According to the optimal propulsion system and battery model, the EPUAV endurance formula was presented for cambered wing. Flight tests of a flying wing EPUAV indicate that optimized propulsion system operates more effectively after an optimal design. There exists approximately 12% error between flight tests and theoretical estimation. Within permissible error, good agreements have been obtained.
The increasing demand for intelligence and surveillance missions has led to the novel use of aircraft (especially unmanned aerial vehicles). Rather than flying long distances or loitering, a fleet of aircraft will maintain a permanent presence at a remote location. Two questions arise: at what distance can this presence be maintained, and at what aerodynamic efficiency shall the aircraft fly during the transits? The Breguet equations for range and endurance provide a preliminary formula for the "range for continuous coverage ", in which the aerodynamic coefficients for both transit phases appear. The optimization of these coefficients provides remarkable results: for a given propulsion type and number of aircraft, the lift coefficient for the optimal range for continuous coverage is always a constant multiple of the lift coefficient for the best range (e.g., the best continuous coverage CL for two jet aircraft is 1/root 3 of the best range C-L).
More accurate analytical solutions of the maximum rate of climb and maximum climb angle are proposed for the climbing flight of the piston-propeller airplane. For the solutions, it is assumed that the propeller efficiency is a function of the airspeed and the airplane has cambered wing drag polar. The solutions are compared with the performance calculated through traditional assumptions of a constant propeller efficiency and a symmetrical wing drag polar. Moreover, the quartic equation to find the best climb angle speed is solved exactly. The comparison proved that the solutions with traditional assumptions result in a higher service ceiling, a shorter climb time, and a shorter climb distance. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
For static stable fixed wing aircraft, there are contradictory requirements from the flight performance and the longitudinal stability. This is true especially for flying wing aircraft. The flight performance is deteriorated in order to maintain the static stability of the aircraft. To solve this problem, a new aerodynamics configuration which involves the propeller thrust to balance the pitching moment was proposed. The optimal design of the flying wing hand-launched mini-UAV is discussed as the example. The performances and dimensions of three configurations, namely the one with reflex airfoils, the one with cambered airfoil and the one involving the propeller thrust to balance the pitching moment, are compared. For the configuration with propeller thrust involved to trim the aircraft, two approaches are adopted. One is shifting the propeller thrust line well below the center of gravity. The other is using vectored thrust obtained by tilting the propeller disk. The aerodynamics coefficients are computed by CMARC, which is based on panel method. Frictional drag is evaluated by boundary layer analysis and empirical formulation correction. The maximum lift coefficient is obtained by strip theory and is corrected by wind tunnel tests. The wind tunnel experiments were performed to validate the optimal design. Good agreements between the computation results and the experimental data were obtained. The electric propulsion system including propeller and motor is designed optimally. The propeller is designed as the maximum cruise efficiency through vortex theory and several motors are tested in order to match propeller well. Then the propulsion system efficiency is involved into the conceptual design at different phases of mission. The genetic algorithm is implemented to optimize the performance of the UAV and the sensitivity analysis is performed. From the analysis, it is found that with the help of propeller thrust, the amount of wash-out and sweepback can be reduced and the maximum lift coefficient can be increased. As a result, the wing loading can be increased and hence the wing area can be reduced. This leads to larger aspect ratio if the wingspan is kept as a constant. Combined with few elevon deflections and reduced wash-out, the lift to drag ratio is improved during cruise and loitering. Hence the endurance of the aircraft can be extended.
In this paper we address the endurance optimization problem for an electric powered fixed wing aircraft. An endurance equation in terms of aircraft aerodynamics and electric power plant characteristics is obtained. The endurance equation is optimized as a nonlinear problem and handled using optimization constrained techniques. This gives an optimal basic aircraft sizing with maximum endurance.
A sound choice of the general arrangement of a new aircraft design should be based on a proper investigation into and interpretation of the transport function and a translation of the most pertinent requirements into a suitable positioning of the major parts in relation to each other. The result of this synthetic exercise is of decisive importance to the success of the aircraft to be built. However, no clear-cut design procedure can be followed and the task of devising the configuration is therefore a highly challenging one to the resourceful designer.
Considerations, arguments and some background information are presented here in order to provide the reader with a reasonably complete picture of the possibilities. The differences between a high wing and a low wing layout, and the location of the engines either on the wing or fuselage or elsewhere, are discussed on the basis of various cases from actual practice. Examples of unconventional layouts and many references to relevant literature are given to stimulate further study and may possibly generate ideas for new conceptions.
The study of possible configurations should result in one or more sketches of feasible layouts. They serve as a basis for more detailed design efforts, to be discussed in later chapters, and they can therefore be regarded as a first design phase.
There are many perspectives of any subject each providing a different view, and thus an insight. The subject of Flight Mechanics can also be viewed in many ways. Earlier the various topics in Flight Mechanics were considered by the author from the probability, statistics, and random process viewpoint. In the present paper the various parameters, variables, and the approaches utilised in the subject are viewed from optimality (or nearly so) point of view. Such a generalisation helps to systematize Flight Mechanics in one more way among many that are possible. It is not realised as to how fortuitous one is to have evolved these optimal parameters, variables, and approaches to deal with the topics in the subject. The above should provide a pleasant overview and an improved understanding of the subject in particular for fresh students.
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.
A Study of Airplane Ranges and Useful Loads
- J G Coffin
Coffin, J. G., " A Study of Airplane Ranges and Useful Loads, " Rept. 69,