Aerodynamic forces acting on an airfoil

Alex SullivanPhysics Department, The College of Wooster, Wooster, Ohio, 44691, USA

May 6, 2010

Abstract

Wind tunnel testing was conducted on NACA 3314, NACA 8321, NACA 1209, NACA6217, NACA 0014, and NACA 5417 airfoils. The lift and drag forces acting on each of theairfoils were successfully measured with an airflow velocity of 14.4 m/s, and an angle ofattack for the airfoils of 20◦ relative to airflow. The experimentation allowed a comparisonof flight characteristics between the airfoils, in which each generated an expected rangeof lift and drag forces. The exception was the NACA 6217 airfoil that produced more liftthan expected. A correct theory of lift was identified and visually confirmed as well.

1 Introduction

An airfoil is defined as the cross section of abody that is placed in an airstream in orderto produce a useful aerodynamic force in themost efficient manner possible [1]. The crosssections of wings, propeller blades, windmillblades, compressor and turbine blades in ajet engine, and hydrofoils are example air-foils. This experiment will focus on airfoilsas the aircraft wings. The basic geometry ofan airfoil is shown in Figure 1. The most im-portant features of airfoil geometry are thechord, camber, and thickness. The straightline connecting the leading and trailing edgesis the chord line, the distance measured be-tween the trailing and leading edge along thechord line is the chord of an airfoil. The line

of points that are halfway between the upperand lower surfaces is the mean camber lineas measured perpendicularly from the chordline. The thickness of an airfoil is the dis-tance from the upper and lower surfaces asmeasured perpendicularly to the chord line,and varies in distance along the chord line.Camber is the maximum distance that occursbetween the mean camber line and the chordline. Maximum camber and thickness, as wellas where they occur along the chord line, areimportant design components for airfoils, andare used in the classification of airfoils.

Lift is defined as the component of aero-dynamic force perpendicular to the relativeairflow. There are multiple incorrect theoriesconcerning the generation lift. The theory

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Figure 1: Diagram of airfoil’s geometry. [2]

most commonly found in text books and pi-lot training manuals utilizes Bernoulli’s prin-ciple which states that for a liquid or gas,areas with high relative velocity create lowerpressure systems, and areas with low relativevelocity create high pressure systems. Thetheory states that airfoils are shaped so thatthe upper surface is longer than the lower sur-face; therefore, when air molecules are sepa-rated by the leading edge of the airfoil, theyhave a greater distance to travel as they crossthe upper surface than along the lower sur-face. Thus, in order for the air molecules tomeet at the trailing edge at the same time,the molecules traveling along the upper sur-face must be traveling faster than the airmolecules along the bottom surface. Sincethe airflow on the upper surface is faster,Bernoulli’s principle states that a lower pres-sure system is created. The difference be-tween the low pressure above the airfoil andthe higher pressure below causes lift to occur.However, there are no principles of fluid dy-namics stating that two free moving air par-ticles must meet at a single point beyond an

Figure 2: Airflow about an airfoil accordingto the flow turning theory. [2]

obstacle once separated by the obstacle.The correct theory of lift generation is

known as the flow turning theory. It statesthat the airfoil bends the direction of the air-flow around it as the airflow passes over theupper surface, and creates a vertical velocityof airflow past the trailing edge. The effectof the airflow bending is due to the viscosityof a fluid and the Coanda effect [3]. As theairfoil bends the airflow near the upper sur-face, it pulls on the air above it and causesan acceleration of that air down to the airfoil.The pulling of the air causes a low pressuresystem to form over the airfoil creating a netforce that is lift. Figure 2 demonstrates air-flow about an airfoil generating lift by theflow turning theory.

The other aerodynamic force that affectsan airfoil in a wind tunnel is perpendicular tothe lifting force, called drag. The airfoil expe-riences a drag force that opposes the relativemotion of the airfoil and has direction paral-lel to the airflow [4]. Skin friction drag is thefriction that occurs between the air moleculesand the surface of the airfoil. Form drag isdependent on the overall shape of the air-

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foil, and pertains to the pressure distributionabout the airfoil’s surface. As with the liftingforce, the airfoil changes the local momentumof the air around it, affecting the velocity andpressure. The resulting pressure distributionproduces a force that acts on the airfoil.

2 Theory

The equations for calculating lift and dragare very similar. The lift that an airfoil gen-erates depends on the density of the air, thevelocity of the airflow, the viscosity and com-pressibility of the air, the surface area of theairfoil, the shape of the airfoil, and the angleof the airfoil’s angle of attack. However, de-pendence on the airfoil’s shape, the angle ofattack, air viscosity and compressibility arevery complex. Thus, they are characterizedby a single variable in the lift equation, calledthe lift coefficient. Due to the complexitiesof the lift coefficient, it is generally found viaexperimentation in a wind tunnel where theremaining variables can be controlled. There-fore, the lift equation is given by

L =1

2ρV 2SCL (1)

where L is the lifting force, ρ is the density ofair, V is the relative velocity of the airflow,S is the area of the airfoil as viewed froman overhead perspective, and CL is the liftcoefficient.

As with lift, the drag of an airfoil dependson the density of the air, the velocity of theairflow, the viscosity and compressibility ofthe air, the surface area of the airfoil, the

shape of the airfoil, and the angle of attack.The complexities associated with drag andthe airfoil’s shape, angle of attack, the air’sviscosity, and air’s compressibility are simpli-fied in the drag equation by use of the dragcoefficient. The drag coefficient is generallyfound through testing in a wind tunnel, wherethe drag can be measured, and the drag co-efficient is calculated by rearranging the dragequation

D =1

2ρV 2ACD. (2)

In the drag equation, D is the drag force, ρis the density of the air, V is the velocity ofthe air, A is a reference area, and CD is thedrag coefficient.

3 Procedure

The donated wind tunnel used in this ex-periment was constructed out of cardboard,epoxy, and masking tape. The walls of thewind tunnel where the lid met the rest of thetunnel were lined with strips of soft foam,which acted to insulate the airflow in thetunnel from outside turbulence. The airflowvelocity at the test section was found to be14.4 m/s using a Dwyer Transparent pressuregauge.

Shown in Figure 3 are six different air-foils used in the experiment. Each airfoilwas unique in camber and thickness so as toinduce various lift and drag characteristics.The airfoils have similar chords, but it wasdifficult to produce precise sizes, the mate-rials available were not ideal for airfoil con-struction. The material used as the base for

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Figure 3: Airfoils used in the experiment. Onthe top from right to left are NACA 3314,NACA 8321, NACA 1209. On the bottomfrom right to left are NACA 6217, NACA0014, NACA 5417.

the airfoil construction was a dense packingfoam. An outline of the profile for each air-foil was transferred to the foam, and was cutusing a band saw. This yielded the generalform for each airfoil, but the surfaces wererough and uneven. Thus, the surfaces of eachairfoil were sanded as smooth as could beperceived by the human eye while maintaingthe original shape. A layer of transparentpacking tape was then attached to the en-tire surface area to prevent airflow from pierc-ing the airfoils. The six airfoils were NACA3314, NACA 8321, NACA 1209, NACA 6217,NACA 0014, NACA 5417.

The wind tunnel allowed limited access tothe test section, thus an apparatus was con-structed around the existing condition of thetest section to measure the lift and drag act-ing on the airfoil. On the floor of the test sec-tion were two small rectangular holes spaced0.09 m apart, orientated perpendicular to theairflow. A Mettler Toledo PD3002-5 digitalscale was placed beneath these holes in thehollow area under the test section. A woodenapparatus was constructed such that an air-foil could be held in then test section witha freedom of movement that allowed lift and

Figure 4: Setup of the experiment to measurelift and drag.

drag to be measured, and its base was fixedto the scale. In order to measure the dragforce, a Pasco Scientific CI-6537 Force sensorwas positioned a distance from the intake ofthe wind tunnel at a height equal to that ofthe support apparatus. A string was fixedto the to the support apparatus, while theopposite end of the string was suspended bya hook on the force sensor. When measur-ing force, the force sensor output a voltage.Using the DataStudio program, the outputvoltage was converted to a force with unitsin Newtons. The force of the string pullingon the hook of the force sensor was measuredwith and without an induced airflow, and thedifference was found to be the net drag force.Figure 4 shows the basic setup of the experi-ment to measure lift and drag force acting onan airfoil. Two data runs were conducted foreach of the six airfoils at an angle of attackof 20◦ where measurements were taken withand without an induced airflow.

4 Data and analysis

The difference between the measurementstaken when the airflow was induced, andwhen it was at rest yielded the actual lift

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Figure 5: Graph of the lift force measuredfor each airfoil. The markers indicate the av-erage force of the two data runs while thevalues each error bar extends to correlate tothe measurements taken for each of the twodata runs.

force of each airfoil. This was done for thedrag force as well, but the force of drag ofthe support system was subtracted from thetotal, yielding the actual drag force for eachof the the two data runs. The measured liftand drag forces of each airfoil are shown inFigure 5 and Figure 6 respectively.

Most of the airfoils performed as expectedwith the induced airflow given the low veloc-ity relative to normal flight conditions. TheNACA 3314 airfoil, with a deep camber andhigh thickness, is generally used for larger air-craft, such as transports or bombers. It ismeant to generate a lot of lift at low speeds,which it was successful in doing. The NACA8321 airfoil was expected to generate high liftat low speeds due to its deep camber and thincross section. It was successful, producingmore lift than any of the other airfoils. The

Figure 6: Graph of the drag force measuredfor each airfoil. The markers indicate the av-erage force of the two data runs while thevalues each error bar extends to correlate tothe measurements taken for each of the twodata runs.

NACA 1208 airfoil is intended to be used athigher speeds on race planes, as well as mili-tary fighters or interceptors. Therefore, it isnot surprising that it was not able to generatea lot of lift in a wind tunnel of low velocity.The NACA 6217 airfoil was expected to gen-erate more drag than lift due to a deep cam-ber and high thickness. However, it defied ex-pectations producing a greater lift force thandrag force. The NACA 0014 airfoil was sym-metric in shape, and is not typically used inaircraft design. It produced medium lift anddrag. The NACA 5417 airfoil was intendedto generate less drag than lift due to the cam-ber being located closer to the trailing edge.It produced the least amount of drag of allthe airfoils. All references to high or low liftand drag of each airfoil are considered relativeto the rest of the airfoils tested, because the

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same flight conditions were applied for each.

5 Conclusion

This experiment demonstrated the aerody-namic forces of lift and drag that act on anairfoil. These forces occurred when a airflowwas introduced to the area around variousairfoils. This was done under controlled con-ditions through the use of a wind tunnel. As aresult, the drag and lift characteristics for air-foils of varying geometries were successfullymeasured and compared.

The variation in measurements for each air-foil may have occurred, because errors in thedesign of the experiment. Typically, airfoilsintended for wind tunnel experimentation areconstructed by computer controlled machin-ery to ensure smooth and even surfaces. Asthe airfoil’s in this experiment were formedby hand, it was difficult to produce even ge-ometries. This led to an uneven fitting of thepacking tape to the airfoils’ surfaces, whichbecame more deformed by the airflow dueto the lower pressure created. Another er-ror occurred via the string attaching the forcegauge to the support system in the test sec-tion. When the airflow was introduced to thesystem, the string oscillated slightly. The ob-struction of the string was not enough to dis-rupt the airflow at the airfoil, but it did affectthe airfoil and the support system, causingdifficulty in taking accurate measurements.

Future work could use a wind tunnel de-signed specifically for airfoil testing so that abetter measurement system could be devised,and the angle of attack and airflow velocity

could be varied. A proper means for con-struction of airfoils would be useful as well.

6 Acknowledgements

I would like to thank Dr. Jacobs for procur-ing the wind tunnel as well as his help andideas at the beginning of the experiment, Dr.Lehman for her help with problems that aroselater, and Manon Grugel-Watson for provid-ing important materials to the experiment.The wind tunnel used in this experimentwas generously donated by Dick Lewellen ofLewellen Design, Wooster, Ohio.

References

[1] E. Abrahams and D. Cladwell, McGraw-Hill Encyclopedia of Science and Tech-nology, 6th Ed. (McGraw Hill, NewYork, NY, 2005).

[2] WWW Document, (http ://www.imaph.tu −bs.de/lehre/99/irro/static/airfoil.gif),accessed April 2010.

[3] D. Anderson and S. Eber-hardt, “How Airplanes Fly: APhysical Description of Lift”,The Aviation History Online Museum,(http://www.aviation-history.com/theory/index-theory.html),accessed April 2010.

[4] K. Cummings and P. Laws, Understand-ing Physics, (Wiley, 2004)

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