A set of simple laboratory experiments aimed to understand the physical origin of lift is presented. The experiments are realized with simple materials and the use of multimedia reference sources (movies, computer simulations,

flow visualizations) is extensively applied in order to put forward otherwise complex fluid dynamical concepts. Emphasis is put in the individuation and correction of

commonly found misconceptions or wrong principles regarding, in particular, the concept of pressure, the role of viscosity, the flow behavior around an airfoil, the

domain of applicability of fluid dynamical principles, the role of flow curvature in attaining lift and the dynamical mechanisms at the basis of flight

Gratton, L. M.

Lopez-Arias, T.

Oss, S.

Zendri, G.

English

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10636-7Colloquia: MPTL14IL NUOVO CIMENTO Vol. 33 C, N. 3 Maggio-Giugno 2010Flying with the right principles at hand: An interactive labto understand the physical origin of liftG. Zendri, L. M. Gratton, T. Lopez-Arias and S. OssLaboratorio di Comunicazione delle Scienze Fisiche, Dipartimento di FisicaUniversita` di Trento - Trento, Italy(ricevuto il 30 Novembre 2009; pubblicato online il 27 Luglio 2010)Summary. — A set of simple laboratory experiments aimed to understand thephysical origin of lift is presented. The experiments are realized with simple ma-terials and the use of multimedia reference sources (movies, computer simulations,flow visualizations) is extensively applied in order to put forward otherwise complexfluid dynamical concepts. Emphasis is put in the individuation and correction ofcommonly found misconceptions or wrong principles regarding, in particular, theconcept of pressure, the role of viscosity, the flow behavior around an airfoil, thedomain of applicability of fluid dynamical principles, the role of flow curvature inattaining lift and the dynamical mechanisms at the basis of flight.PACS 01.50.-i – Educational aids.PACS 01.50.F- – Audio and visual aids.1. – The rights and wrongs of the physical explanation of lift at an elementarylevelMore than a hundred years have passed since the first flight in the history of humanityand there is still a “debate” about what is the most correct explanation of the physicalorigin of lift. There is certainly no doubt this is not a problem for aeronautical engi-neers who everyday design and test new aircrafts using the right principles and the rightmathematical and physical tools. However, the problem of portraying a correct thoughaccessible account of this complex subject to the student (high-school or undergraduatelevel) in possess of a much lighter educational baggage, or even to the layman, is an-other story. Several misconceptions are implicitly conveyed, wrong (and experimentallyfalsified) principles are invoked and the risk of getting a confused picture of the problemremains.Lift can be easily explained using Newton’s dynamics principles, provided a correctcomprehension of fluid (in this case, air) behavior in its interaction with a solid boundaryis achieved. To generate lift we need air speed (relative to the aircraft) which is attainedthrough propulsion, wings, and downwards air’s deviation (downwash). To deviate airc© Societa` Italiana di Fisica 8990 G. ZENDRI, L. M. GRATTON, T. LOPEZ-ARIAS and S. OSSFig. 1. – Basic parts and fluid movements around an airfoil.downwards a force must be acting on it. The reaction force to the “bending” force onthe fluid, air, is precisely lift which acts on the wing and keeps the aircraft airborne(Anderson and Eberhardt 2009). Simple Newtonian reasoning.A closer look to this line of reasoning reveals that the origin of the fluid’s bendingaround the airfoil needs to be investigated. What makes the fluid in contact with thewing bend? Here arise the many misunderstandings and wrong statements of the socalled “simplified” explanations of lift in terms of the famous Bernoulli’s principle. Thisnotoriously wrong account of the origin of lift goes as follows: a) airfoils need to becurved (false) b) air flow separates at the wing’s leading edge (see fig. 1) and travelsabove and below the wing to rejoin at the trailing edge in an equal time lapse (false: thisis the so-called “equal transit time principle” which is experimentally falsified). Becauseof the previous assertions, in order to follow the equal transit time principle, air “needs”to accelerate on top of the wing to catch up with air travelling under it. As Bernoulli’sprinciple states, higher air speed means lower pressure on top of the wing, resultingin the desired upwards net force, i.e. lift. The problem is that to achieve this simpleexplanation two wrong statements are made, Bernoulli’s principle is not properly appliedand the invoked pressure, transverse to the flow, cutting through several streamlines andresponsible of the resultant lift is not the pressure which Bernoulli’s principle discuss(which is the static pressure along a streamline) and which may well not relate to thesame “constant” in the famous equation for every streamline in the flow (Prandtl 1952).To begin with, let us remind that Bernoulli’s principle applies to an inviscid (zeroviscosity) and incompressible flow. While incompressibility is a good approximationfor subsonic flow, air is not inviscid. No real fluid is. Fortunately (as it simplifiesenormously the calculations), for many applications the hypothesis of an inviscid fluidcan be applied. However, the conditions under which this simplifying hypothesis canbe done are not discussed neither in the “simplified” explanation with Bernoulli. Thetruth is that if the air were not viscous, lift could not be attained at all, since viscosityis the only mechanism (together with pressure) by which a fluid can interact with a solidboundary, sticking to it due to the so called no-slip condition. This fact, experimentallyverified, asserts that at the solid-fluid boundary the relative velocity of the fluid andthe solid surface is zero, i.e., the fluid “sticks” to the surface, slowing down the flowand generating asubstrate where the flow speed grows from zero (at the surface) to theoutside flow speed (see fig. 2). This substrate, called boundary layer, is actually verythin for the flow conditions of an aircraft (relative wind-wing speed, air density and wingdimensions) but it is enough to constrain the flow to adhere to the wing and follow itsFLYING WITH THE RIGHT PRINCIPLES AT HAND: AN INTERACTIVE LAB ETC. 91Fig. 2. – Velocity distribution v(x) along the developing boundary layer of a fluid sticking to asolid surface. Its free velocity is v0.profile, inducing the downwards air deviation which ultimately explains lift. Outside theboundary layer, where viscosity plays a fundamental role, the fluid can be consideredinviscid and there Bernoulli’s principle can be correctly applied.This represents the boundary layer hypothesis, introduced by Ludwig Prandtl in 1903(Anderson 2005) and which marked the beginning of a new era in the history of fluiddynamics and aerodynamics in particular. It is the boundary layer to force air to followthe wing profile, as it generates a favorable pressure gradient (lower pressure) in theflow direction. And this is why air accelerates. As we know from simple experience,air tends to travel from areas of higher pressure to areas of lower pressure and in doingso it accelerates, as atmospheric circulation demonstrates, for instance. The “simple”explanation of lift using Bernoulli neglects the only thing which is needed for air toaccelerate, i.e. viscosity.Emphasizing this is the main scope of this laboratory proposal. For once the role ofviscosity is properly taken into account, the simplifying approximations of non viscousflow outside the boundary layer can be done, but a proper understanding of the fluiddynamical mechanisms at the core of the lift have been correctly put forward. Now,we know that air accelerates over the top of a wing because air is slowed down by theboundary layer formation which generates a favourable pressure gradient in the flowdirection. But this is not enough. To attain lift we still need asymmetry in the flow andthis can be achieved only if the wing and the wind meet at a certain angle, the angle ofattack (AOA). This is the angle between the wind’s direction and the chord of the wing(see fig. 1), the geometrical line that connects its leading and trailing edges. A symmetricwing with no AOA will not develop lift as the flow encounters and leaves the wing inthe same direction. The AOA is necessary for it forces the air to up wash at the leadingedge and then downwash at the trailing edge (see again fig. 1), inducing flow curvature.Curving means accelerating, as we know, and since air is sticking to the surface (no-slipcondition) a centripetal force is actually acting on the air which is constrained to benddown following the wing profile. This centripetal force generates a pressure gradient (thistime acting in the transverse direction) following Euler’s equation which in its simplestform can be written as (Faber 2001) ∂P/∂r = ρv2/r, where P is pressure, r is distancefrom the center of curvature, v is the flow speed and ρ is density.Hence, when air encounters a wing with a given AOA, two things happen: air bendsand accelerates (both things because viscosity is acting between the air and the wingsurface!). Then, the transverse pressure gradient forces air downwards, generating down-wash: the reaction to the flow curvature is lift. Flow curvature implies associated forces.Can we measure them easily in the laboratory? The answer is yes. The typical levitating92 G. ZENDRI, L. M. GRATTON, T. LOPEZ-ARIAS and S. OSSFig. 3. – A levitating ball is pulled back into the air jet as shown by the scale because of thereaction force to the bending fluid (Coanda effect).ball experiment on an air jet is paradigmatic of what we have just discussed. Needless tosay this fascinating experiment is also typically bending fluid (Coanda effect) explainedusing Bernoulli’s principle (Cohen and Horvath 2003) while its simple explanation reliesin viscosity (air sticking to the ball’s surface), flow curvature (easily visualized using afew cotton threads, see fig. 3) and the corresponding force (easily measurable with aspring scale). It should be remarked, of course, that airplanes do not fly in air jets butare fully embedded by the flow, but this simple experiment is extremely useful to putforward the intimate relation between flow curvature and lifting forces. The levitatingball experiment is a simple example of Coanda effect(1), the tendency of a fluid jet toadhere to the surface (curved or not) over which it flows (Lo´pez-Arias, Gratton e Oss,2009), and it deserves a better physical treatment at an elementary level as it is used inseveral applications, from heating and cooling devices, to thrust reversal in jet enginesor boundary layer control in airfoils (Gerhab and Eastlake 1991) to name just a few.The conclusion is that in order to build a coherent and accessible account of the physicalorigin of lift, we need to put forward and demonstrate experimentally:a) The role of viscosity and the no-slip condition (Experiment 1).b) The Coanda effect as a paradigm of flow interaction with a solid surface, measuringthe force associated to the flow curvature (Experiment 2).c) The measurement of the reaction force to downwash using a simple surface or anairfoil (Experiment 3).2. – The experiments2.1. Experiment 1: The way fluids behave. Viscosity and the “no-slip” condition.– Real fluids are viscous. We can walk because of the friction between our shoes andthe floor. Similarly, airplanes can fly thanks to air’s viscosity (fluid’s internal friction).When a fluid flows over a solid surface, a thin layer of fluid (the so called boundary(1) After Henri Coanda (1886-1972), romanian aeronautical engineer who discovered this, upto then unknown effect, by serendipity during the test flight of the first jet airplane (Coanda 1)designed by Coanda himself.FLYING WITH THE RIGHT PRINCIPLES AT HAND: AN INTERACTIVE LAB ETC. 93Fig. 4. – A cylinder is rotated while partly submerged in a thin layer of a glycerine. A strip ofblack ink makes clear the no-slip condition close to the cylinder surface.layer) sticks to the surface (the so called no-slip condition). In it the relative speed ofthe surface and the fluid is zero (fig. 4). The boundary layer modifies fluid’s flow byviscous stress. Air sticks to the wings of an airplane, modifying its own trajectory andgenerating “downwash” (air is pushed downwards). An airplane could never fly in aninviscid fluid.2.2. Experiment 2: Bending fluids. The Coanda effect . – A jet of fluid (liquid orgaseous) will stick to a curved surface and follow its profile. At the origin of the fluid’sbending lays viscosity and the no-slip condition at the solid-fluid boundary. An equaland opposite reaction to the force that bends the fluid acts on the cylinder (fig. 5). Air isa fluid. Momentum exchange between air and a surface takes place through shear stressand viscosity.2.3. Experiment 3: Changing air direction: downwash and the lift force. – Under ap-propriate conditions any solid surface will divert a flux of air. The amount of diverted air(“downwash”) is directly related to the generated lifting force on the surface. Airplanesand helicopters divert air down for generating the needed lifting force to remain airborne(fig. 6). Such a force corresponds to the added contribution of the pressure field alongthe airfoil surface. Pressure gradient along an airfoil determines air’s speed in the flowdirection.A very simple set of experiments made with simple materials and the use of multimediavisual aids (Multimedia Fluid Mechanics 2008) can help to build a simple though correctunderstanding of the physical origin of lift. In the way new concepts of fluid dynamicsFig. 5. – Coanda effect of water on a solid cylinder.94 G. ZENDRI, L. M. GRATTON, T. LOPEZ-ARIAS and S. OSSFig. 6. – The double scale experiment: lower weight on the right (lift) higher weight on the left(downwash).can be introduced which may enlarge the interest of students in an otherwise complexsubject which nevertheless has an extremely wide spectra of applications in almost anybranch of science. The use of virtual flight simulation software (Try to fly 2009) can helpto increase students interest and comprehension of the practical aspects of flight at thelight of the new acquired concepts.REFERENCESAnderson D F and Eberhardt S, Understanding flight, (McGraw-Hill, 2nd Ed.).Prandtl L (1952), Essentials of Fluid Dynamics, (London and Glasgow: Blackie and SonLtd.).Anderson J D Jr. (2005), Ludwig Prandtl’s Boundary Layer, Physics Today 58 42-48.Faber T E (2001) Fluid Dynamics for Physicists (Cambridge: Cambridge Univ. Press).Cohen H and Horvath D (2003), Two Large-Scale Devices for Demonstrating a BernoulliEffect, Phys. Teach. 41 9-11.Lopez-Arias T, Gratton L M and Oss S (2009), Back of the spoon outlook of Coandaeffect, Phys. Teach. 47 508-512.Gerhab G and Eastlake G (1991), Boundary layer control on airfoils, Phys. Teach. 29150-151.Multimedia Fluid Mechanics 2008 (DVD) (Cambridge University Press).Try to fly: The history of flight simulation from the first aircraft to space exploration(2009) ISBN 9788887621846 Ed. by Museo dell’Aeronautica Gianni Caproni, Trento,Italy.

Flying with the right principles at hand: An interactive lab

to understand the physical origin of lift

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Flying with the right principles at hand: An interactive lab to understand the physical origin of lift

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