Beyond the instrumental mode

Scientific research is undertaken nowadays primarily for its eventual material benefits (§9.1). For this reason, our discussion of the external social relations of science has focused almost exclusively on its instrumental connections through technology. But the influence of scientific knowledge and ways of thought is far wider than the contributions of R & D to industry, medicine, agriculture, war and other typical human pursuits (§12.1). In this final chapter, therefore, we consider science as a general cultural resource, with significant societal effects beyond those directly due to technical change.

This is a large and diffuse metascientific theme, which can only be treated very schematically. Science is only one amongst the many elements that go into the making of contemporary culture. These other elements – psychic, political, philosophical, humanistic, aesthetic, religious, etc. – have to be appreciated in their own right and not looked at solely through eyes that have already been ‘blinded by science’. Scientism (§3.9) is not just a philosophical doctrine; it has its sociological, political and ethical manifestations, which are equally misleading and dangerous.

Recognition

Scientists make ‘contributions’ to knowledge: what do they get in return? Nowadays most scientists are paid a salary to do research, either on a full-time basis or as a normal part of their academic duties (§10.4). From the point of view of an economist, they are simply professional employees, earning a living by their labour. A psychologist, on the other hand, might emphasize the peculiar personal gratifications of research and discovery, for which there is ample testimony in the autobiographical writings of (mostly successful) scientists. In practice, scientists (like other people) respond to a complex mixture of professional and vocational incentives, which arise from the social environment in which they live and work. Sociologically speaking, academic scientists get both their psychological and material inducements primarily through membership of the community of other scientists. Satisfactory research performance earns recognition within the scientific community, which is usually linked to more obvious rewards from society at large.

Scientific recognition takes a variety of forms, graded to the various stages of a successful career. At the very lowest level, an academic scientist scarcely exists unless his or her work has been published in a reputable scientific journal (§4.4).

In Teaching and Learning about Science and Society (Cambridge University Press, 1980), I argued at length that everybody ought to learn something about science, but that science is a large and open-ended topic, which needs to be treated in various ways at various stages of educational maturity. At school level, the most natural approach is through case studies of the place of science and technology in modern life, as we presented them, for example, in the SISCON in Schools units (published in 1983 by the Association for Science Education and Basil Blackwell). For slightly older students, a conception of science as a social institution can be built up from historical case studies, along the lines of the lectures I wrote up as The Force of Knowledge (Cambridge University Press, 1976).

The present work goes one level deeper. It is addressed to students – and other diligent readers – who want to discover, beneath the historical and contemporary particulars, a more general framework of principle. They want to understand what is being said about science by the historians, philosophers, sociologists, psychologists, economists and political scientists who have been making such notable contributions to ‘science studies’ these last few years. They need access to the scholarly literature in these various fields, both for its intrinsic interest and as a possible guide to action in scientific research, in industrial management, in political administration, and in public affairs.

Science as an instrument of policy

As we have already remarked (§9.1), to the eyes of the general public, science is simply one of the components of ‘science and technology’, which is primarily an instrument in the hands of society. This instrument can be used to do whatever society wants, over a very wide range. These wants are impossible to list in full, and have very varied sources of motivation, such as:

In the past half century, the vague Victorian belief in science as a source of ‘progress’ has been transformed into an established doctrine.

Societal demand

Even though the differences between ’science’ and ‘technology’ (§9.7) between ‘research’ and ‘development’ (§10.1) and between ‘pure science’ and ‘applied science’ (§10.7) have never been easy to define in principle, an institutional distinction between the academic and industrial modes of research was maintained in practice throughout the first half of the twentieth century. In the past few decades, however, this gap has been steadily closing. Some metascientific observers follow Jerome Ravetz in describing this process as the industrialization of science, implying that the industrial mode of research has become dominant. The evidence is, however, that a more general transformation is taking place, to a new collectivized form in which characteristics of both the academic and industrial modes are intermingled.

This transformation is often supposed to have come about solely by societal forces acting on science from the ‘outside’; as we shall see (§11.2) it is also a natural result of its own internal development. The external influences are obvious. The demand for more and more R & D to meet societal needs (§9.1) has not only had the effect of expanding industrial science on a very large scale: it has also had an immense effect on the scale and style of academic science.

Behaving as a scientist

Academic science is not formally organized as a whole. It is not governed by a bureaucratic hierarchy, like an army or an industrial firm (§5.6). It does not have a constitution, a charter, or an official book of regulations. In principle, it is simply a community of individuals, each of whom has a permanent tenure of an academic post as a teacher or researcher. To adopt traditional political metaphors, academic scientists are like free citizens of a democratic republic of learning, or like a community of farmers, each secure on his own holding.

And yet this community is not a mere collection of individuals. Although it does not have an overall organizational plan, it is structured around a number of formal institutions, such as learned societies, and informal institutions, such as invisible colleges. It is spanned by an elaborate communication system which follows standard practices in the management of publications and archives, regulates the roles of authors, editors, and referees, and has strict conventions on the style and format of papers (§4.5). The procedures by which scientists are ‘recognized’ (§5.1) are less systematic, but are just as elaborate.

The archival literature of science

The basic principle of academic science is that the results of research must be made public (§1.5). Whatever scientists think or say individually, their discoveries cannot be regarded as belonging to scientific knowledge until they have been reported to the world and put on permanent record. The fundamental social institution of science is thus its system of communication.

How can one get to know what is known to science? In its most primitive form, scientific knowledge is to be found in the primary literature of science. This is a vast collection of ‘articles’, ‘papers’, ‘research reports’ and similar documents usually in a very conventional style and format that dates back to the origins of modern science in the late seventeenth century. A primary scientific communication is an original contribution to knowledge, by a named author or authors, normally published as a paper or article, of limited length (up to 50 pages, say) in a periodical, or journal devoted to a specific scientific subject.

Cognitive change

The world's scientific archives acquire something like a million new scientific papers a year. The growth in the quantity of scientific information was, until quite recently, an accelerating process. The number of papers published annually has been increasing exponentially for the best part of 300 yean. An elementary calculation shows that this corresponds to an annual growth rate of about 5%: that is to say, the amount of new scientific information reported each year has been doubling about every 15 years, since the late seventeenth century.

The steady growth in its contents and in the scale of its operations has very important implications for the place of science in society (chapter 11). It is also one of its major internal characteristics. At this rate of growth, for example, half the information in a scientific archive must be less than 15 years old. Perhaps only a tiny fraction of this information is scientifically interesting or novel. Much of it will consist of factual data on very minor topics, recorded at higher levels of precision than previously. Nevertheless, unless the norm of originality (§6.2) is being systematically violated, scientific knowledge is changing rapidly by the sheer accumulation of new information.

The limited extent of the stream of air in a wind tunnel, whether of open or of closed working section, imposes certain restrictions on the flow past an aerofoil or other body under test, and the determination of the magnitude of this interference is of considerable importance, since it is found that certain corrections must be applied to the aerodynamic characteristics of an aerofoil tested in a wind tunnel before they are applicable to free air conditions. This interference correction is independent of and additional to any correction which may be necessary to allow for the change of scale from a model aerofoil to an actual aeroplane wing.

The theory of the interference has been developed by Prandtl in his second aerofoil paper by considering the conditions which must be satisfied at the boundary of the stream. The continental wind tunnels usually have an open working section and the condition of constant pressure must be satisfied at the boundary of the stream. British wind tunnels, on the other hand, have a closed working section of square or rectangular cross section, and the boundary condition takes the form that the component of the velocity normal to the tunnel walls must be zero. This boundary condition can be satisfied analytically by the introduction of a suitable series of images of the model, and the interference experienced by the model is the induced velocity corresponding to the vortex systems of these images.

Circulation and vorticity.

The definition of the circulation round a closed curve in two dimensions (see 4·1) as the integral of the tangential component of the velocity round the circumference of the curve can be extended at once to the more general case of motion in three dimensions by removing the restriction that the curve must lie in a single plane. Also by dividing any surface bounded by this curve into a network by a series of intersecting lines it can be shown that the circulation round the curve is equal to the sum of the circulations round the elementary areas formed by the network.

The vorticity of a fluid element in two-dimensional motion was defined (see 4·3) as twice the angular velocity of the element. This definition is retained in the more general case of three-dimensional motion but the axis of rotation of the fluid element may now point in any direction. By following the direction of the axis of rotation of successive fluid elements it is possible to construct a curved line whose direction coincides at every point of its length with the axis of rotation of the corresponding fluid element. Such a line is called a vortex line.

The vortex lines which pass through the points of the circumference of a small closed curve C will form the surface of a vortex tube, of which the curve C is a cross section.

The aim of aerofoil theory is to explain and to predict the force experienced by an aerofoil, and a satisfactory theory has been developed in recent years for the lift force in the ordinary working range below the critical angle and for that part of the drag force which is independent of the viscosity of the air. Considerable insight has also been obtained into the nature of the viscous drag and into the behaviour of an aerofoil at and above the critical angle, but the theory remains at present in an incomplete state. The problem of the airscrew is essentially a part of aerofoil theory, since the blades of an airscrew are aerofoils which describe helical paths, and a satisfactory theory of the propulsive airscrew has been developed by extending the fundamental principles of aerofoil theory.

The object of this book is to give an account of aerofoil and airscrew theory in a form suitable for students who do not possess a previous knowledge of hydrodynamics. The first five chapters give a brief introduction to those aspects of hydrodynamics which are required for the development of aerofoil theory. The following chapters deal successively with the lift of an aerofoil in two dimensional motion, with the effect of viscosity and its bearing on aerofoil theory, and with the theory of aerofoils of finite span. The last three chapters are devoted to the development of airscrew theory.

An airscrew normally consists of a number of equally spaced identical radial arms, and the section of a blade at any radial distance r has the form of an aerofoil section whose chord is set at an angle θ to the plane of rotation. The blade angle θ and the camber of the aerofoil section decrease outwards along the blade. If the airscrew moved through the air as through a solid medium, the advance per revolution would be 2πr tan θ and this quantity would define the pitch of the screw. Actually this quantity will not have the same value for all radial elements of the blade and so it is customary to define as the geometrical pitch of the airscrew the value of 2πr tan θ at a radial distance of 70 per cent. of the tip radius. An airscrew rotates in a yielding fluid and in consequence the advance per revolution is not the same as the geometrical pitch and may in fact assume any value. The value of the advance per revolution for which the thrust of the airscrew vanishes is called the experimental mean pitch, and in many respects the characteristics of an airscrew are defined by the ratio of the experimental mean pitch to the diameter.

An ordinary propulsive airscrew experiences a torque or couple resisting its rotation and gives a thrust along its axis.

The theory of the lift force given by an aerofoil in two-dimensional motion has been developed by considering the flow of a perfect fluid governed by Joukowski's hypothesis that the flow leaves the trailing edge of the aerofoil smoothly. It is necessary now to examine the fundamental basis of this theory and the extent to which the assumed motion represents the actual conditions which occur with a viscous fluid.

All real fluids possess the property of viscosity and the conception of a perfect fluid should be such that it represents the limiting condition of a fluid whose viscosity has become indefinitely small. Now it is well known that the limit of a function f(x) as x tends to zero is not necessarily equal to the value of the function when x is equal to zero, and hence, to obtain the true conception of a perfect fluid, it is not sufficient to assume simply that the coefficient of viscosity is zero. The viscosity must be retained in the equations of motion and the flow for a perfect fluid must be obtained by making the viscosity indefinitely small.

Slip on the boundary.

The first point to be considered is the motion of the fluid at the surface of a body. In a viscous fluid the relative velocity at the surface of a body is zero and the body is surrounded by a narrow boundary layer in which the velocity rises rapidly from zero to a finite value.

Great advances in the theory of aeronautics have taken place since the first edition of this book by my late husband appeared in 1926, but the more fundamental parts of the theory, which are the subject of this book, remain in large measure unchanged. Particularly important advances have been made in the theory of viscous motion and of the flow in the boundary layer. At my request Mr H. B. Squire of the Royal Aircraft Establishment, Farnborough, who was a colleague of my husband, has prepared a set of notes which appear as an Appendix to the present edition and these notes indicate where important developments have taken place and where further information on the subject matter can be found. I am most grateful to Mr Squire for his assistance and desire to tender him my sincere thanks.

In preparing this second edition the opportunity has been taken to replace the non-dimensional k coefficients by the now more generally accepted C coefficients and my son, M. B. Glauert, has undertaken the necessary revision. One or two other minor changes have been made and a bibliography of some of the more important modern books on aerodynamics has been added.