Overview

In this chapter we introduce the concepts of distance flown by an aircraft with and without stop for refuelling (§ 12.1). We discuss a number of cruise programs at subsonic and supersonic speeds and some optimal problems in long-range cruise, with or without constraints. First we present the analysis of the instantaneous cruise parameters (§ 12.2), including the specific range. We then provide numerical solutions of the specific range for real aircraft (§ 12.3). For the sake of generality, we also present the range equation, which is solved in closed form (§ 12.4), and deal with the separate problems of jet aircraft at subsonic speed (§ 12.5) and propeller aircraft (§ 12.6).We show a number of more advanced studies in cruise altitude selection (§ 12.7), cruise performance deterioration (§ 12.8), cost index and economic Mach number (§ 12.9) and various other effects, such as the effects of high-altitude winds and centre of gravity position (§ 12.10). We deal briefly with supersonic aircraft (§ 12.11).

KEY CONCEPTS: Point Performance, Specific Air Range, Cruise Altitude Selection, Range Equation, Long-Range Mach, Maximum-Range Mach, Cost Index, Economic Mach Number, Effects of Winds, Centre of Gravity Effects, Supersonic Cruise.

Introduction

For most commercial aircraft the fuel consumed during the cruising phase of the flight makes up the bulk of the fuel carried and is a key factor in the productivity and direct operating costs of an aircraft. Since the early 1970s, with the price of fuel soaring, both the airlines and the military have been concerned with energy-efficient operations. For this reason, several cruise conditions have been studied.

Overview

The aircraft weight influences the performance of the airplane more than any other parameter. Weight has been of concern from the earliest days of aeronautics (§ 3.1). Therefore, we devote this chapter to the weight analysis and the relative aspects, such as operational and design weights (§ 3.2); weight management issues (§ 3.3); operational limits (§ 3.4); centre of gravity envelopes (§ 3.5); loading and certification issues, operational moments and corresponding errors (§ 3.6); the use of the wing tanks (§ 3.7); and, finally, mass properties, including determination of the CG and the moments of inertias of the empty airplane (§ 3.8).

KEY CONCEPTS: Aircraft Size, Design Weights, Operational Weights, Mass Distribution, Centre of Gravity Envelopes, Moments of Inertia, Fuel Tanks.

A Question of Size

By the start of the First World War, in the United Kingdom it was believed that the limiting weight of the airplane could not exceed 2,000 lb (∼800 kg). Aircraft engineers of that time ignored that in 1913–1914 the great Igor Sikorsky designed, built and flew a four-engine aircraft known as Ily'a Murometz, or S-27, whose loaded weight was 5,400 kg. The total installed power was about 400 hp (∼300 kW). The aircraft could carry as many as 16 passengers in its uncomfortable quarters.

Prior to this project, it was widely believed that a multi-engine aircraft would not be capable of flying. The main concern centred around the question of how to control the aircraft in the event of one engine failure – a likely occurrence in those days.

Overview

In this chapter, we present first-order methods, based on the principle of components, to determine the aerodynamic properties of the aircraft. One is tempted to develop methods of high accuracy, based on the physics. These methods are inevitably complex and computer intensive. The requirement for methods of general value inevitably limits the accuracy on any single aircraft. Aerodynamic data of real airplanes are closely guarded. We show how these low-order methods, with a compromise between physics and empiricism, yield results of acceptable accuracy.

We deal with aerodynamic lift in § 4.1. The wide subject of aerodynamic drag (§ 4.2) is split into several sub-sections that present practical methods. The analysis of the aerodynamic drag has a number of separate items, including a transonic model for wing sections (§ 4.3) to be used in the propeller model (Chapter 6), transonic and supersonic drag of wing-body combinations and bodies of revolution (§ 4.4), and buffet boundaries (§ 4.5). We present a short discussion on the aerodynamic derivatives in § 4.6. We expand the aerodynamic analysis to the estimation of the drag of a float-plane in § 4.7. We finish this chapter with a simple analysis of the vortex wakes and the aircraft separation distance (§ 4.8).

KEY CONCEPTS: Aircraft Lift, Aircraft Drag, Transonic Drag Rise, Supersonic Drag, Bodies of Revolution, Buffet Boundaries, Aerodynamic Derivatives, Float-Planes.

Aircraft Lift

The determination of the lift characteristics of the wing ultimately depends on the amount of information that is available. Often only the plan form shape is known.

Commercial aviation has matured rapidly since the introduction of gas-turbine engine technology. The investments required to develop new aircraft have increased exponentially. These investments include capital, human resources across a wide spectrum of competences, infrastructure and time. In this framework, the importance of operational aircraft performance is crucial because the existing technology is locked into a large fleet that is due to operate for several decades into the future. Airplane evolution is therefore inevitable and is proved in several case studies, both in the commercial and in the military world. The issues raised in this book will continue to dominate the debate; we expect considerable changes in the future, from the ATC, to aero-engine technology, to aircraft design, operations and demand management.

Each chapter has illustrated major issues in aircraft flight performance; conclusions have been drawn in each separate instance. To conclude, we wish to mention some key aspects of wider interest.

ROLE OF COMPREHENSIVE ANALYSIS IN AIRCRAFT PERFORMANCE. Performance is what sells an airplane; the ability to predict and verify performance parameters is key to the whole aircraft industry. We have emphasised the fact that the field of comprehensive analysis is not well developed (unlike rotorcraft engineering); the amount of reference data is relatively modest, as reported in the flight manual and in some type certificate documents. However, these data are often insufficient for an accurate engineering analysis. In this book we have attempted tomake advancements in this area and have proposed several numerical methods, validation strategies and sensitivity analyses that can improve the prediction of aircraft performance.

Commercial aviation has grown to become the backbone of the modern transport system. Demand for commercial air travel has grown exponentially since the 1960s. The expansion of the aviation services is set to increase further. Even in the worst moments of recession, air transport has only suffered a blip in its expansion. Our global economy has become so dependent on air transport that any inconvenience caused by weather and external factors can cause mayhem. To understand the size of commercial aviation, reflect upon the fact that by the year 2000, there had been 35.14 million commercial departures worldwide, for a total of 18.14 million flight hours. In some countries, air transport accounts for one quarter of all transported goods by value. It is estimated that there are about 50,000 airports and airfields around the world and 18,000 commercial airplanes flying every day. A number of large airports are being constructed in some rapidly expanding regions. Modern airports are the size of a city: London Heathrow covers about 12 km2; this is an area large enough to park about 1,800 Airbus A380s nose-to-tail. The support required by the aircraft is extraordinary and involves engineering, logistics, integrated transport systems, security systems, energy and people. However, at the heart of everything is the aircraft itself, interpreted as a flight system: this is the subject of our book. There will be only a superficial mention of various externalities, including air traffic control, queueing models, stack patterns, logistics, supply chains, and so on.

This book is a derivative of an earlier textbook on flight performance. This new work reflects my increased wisdom on the subject and represents an almost complete departure from closed-form solutions that are traditionally taught in under-graduate and post-graduate programs. Over the past several years, I have benefited from the experience of teaching a flight performance course to senior engineers from industry, government departments and academia. In the process, I learned a few new things that now find a place somewhere in the book.

There is an increase in numerical methods in all fields of engineering; nevertheless, flight performance has remarkably resisted change. Some closed-form solutions have been retained for those engineers who need a quick answer. The modern airplane is a complex engineering machine governed by systems, software and avionics. Primitive methods are still widely used, which are then applied to aircraft design and produce results of dubious accuracy that cannot be assessed. Worryingly, these methods are used inmost “conceptual design” and “multi-disciplinary optimisation” methods. Now assume, more realistically, that you have been hired to provide flight prediction tools to an airline operator or a manufacturer of engines or airframes, a national or international aviation authority, an air traffic control organisation. Why should they trust your performance software? What is the risk of under-predicting the mission fuel for an intercontinental flight?

As we worried about conceptual design, the world has moved on. There is increased emphasis on airplane evolution and upgrading, which is now reflected in my thinking. At the same time, the environmental performance of the aircraft has become very prominent.

Computational Aeroacoustics (CAA) is a relatively young research area. It began in earnest fewer than twenty years ago. During this time, CAA algorithms have developed rapidly. These methods soon found applications in many areas of aeroacoustics.

The objective of CAA is not simply to develop computational methods, but also to use these methods to solve real practical aeroacoustics problems. It is also a goal of CAA to perform numerical simulation of aeroacoustic phenomena. By analyzing the simulation data, an investigator can determine noise generation mechanisms and sound propagation processes. Hence, CAA offers a way to obtain a better understanding of the physics of a problem.

Computational Aeroacoustics is not the same as Computational Fluid Dynamics (CFD). In fact, CAA faces a different set of computational challenges, because aeroacoustics problems are intrinsically different from standard aerodynamics and fluid mechanics problems. By definition, aeroacoustics problems are time dependent, whereas aerodynamics and fluid mechanics problems are, in general, time independent or involve only low-frequency unsteadiness.

Computationally, there are two general ways to treat problems with complex geometry. One way is to use unstructured grids. The other is to use overset grids. Overset grids are formed by overlapping structured grids. In this chapter, the basic idea of overset grids methodology and its implementation are discussed.

Basic Concept of Overset Grids

To illustrate the basic idea of overset grids, consider the problem of computing the scattering of acoustic waves by a solid cylinder in two dimensions. In the space around the cylinder, the coordinates of choice for computing the solution is the cylindrical polar coordinates centered at the axis of the cylinder. This coordinate system provides a set of body-fitted coordinates and, hence, a body-fitted mesh when discretized around the cylinder. One significant advantage of using a body-fitted grid is the relative ease in enforcing the no-through-flow wall boundary condition using the ghost point method or other methods. Away from the cylinder, acoustic waves propagate with no preferred direction. The natural coordinate system to use is the Cartesian coordinates. Therefore, to take into account the advantages stated, one may use a polar mesh around the cylinder and a Cartesian mesh away from the cylinder with an overlapping mesh region. The overlapping mesh region is for data transfer from one set of grids to the other and vice versa.

Many aeroacoustics problems involve multiple length and time scales. This should not be difficult to understand. For, in addition to the intrinsic sizes and scales of the noise sources, the acoustic wavelength is an inherent length scale of the problem. In many instances, the length scale of the noise source differs greatly from the acoustic wavelength. This leads to a large disparity in length scales as in classical multiscales problems. For example, in supersonic jet noise, Mach wave radiation is generated by the instability waves of the jet flow. The instability waves are supported by the thin shear layer of the jet. In the region near the nozzle exit, the averaged shear layer thickness is about 0.1D, where D is the jet diameter. The acoustic wavelength, on the other hand, is two or more jet diameters long. Thus, there is an order of magnitude difference between those characteristic lengths. In sound scattering problems, the length scale of the surface geometry of the scatterers may be much smaller than the acoustic wavelength. This occurs very often in edge scattering and diffraction problems. A concrete example is the radiation of fan noise from a jet engine inlet. The acoustic wavelength could be much longer than the radius of the lip of the engine inlet. To obtain an accurate numerical solution of the inlet diffraction problem, a fine mesh is needed around the lip region. Oftentimes, an aeroacoustics problem becomes a multiscales problem because of the change in the physics governing the different parts of the computational domain. An example is the shedding of vortices at the edge of a resonator or a sharp edge of a solid body induced by high-intensity incident sound waves. Away from the solid surface, the fluid is nearly inviscid, but close to the wall, the viscosity effect dominates. The oscillatory motion of the incident sound waves induces a very thin Stokes layer on the solid surface. The Stokes layer rolls up at the corner of a solid surface to form vortices that shed periodically. To simulate the vortex shedding process, therefore, it is necessary to use very fine mesh close to the solid surface and around the corner to resolve the Stokes layer. But away from the solid surface, a coarse mesh with 7 mesh points per acoustic wavelength is all that is needed to capture the sound waves accurately using the 7-point stencil dispersion-relation-preserving (DRP) scheme.