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Experimental drag polar of the F-16 Falcon using wind

tunnel tests

D. Boucher

Ecole de l’Air, Salon-de-Provence, F-133001

and

H. Guillot

Ecole de l’Air, Salon-de-Provence, F-133002

The aerodynamics of the General Dynamics F-16 Falcon has been studied using

experimental and theoretical methods. Subsonic wind tunnel tests on a 1/48 model of the F-

16 were used to determine the lift and drag on the aircraft at several Mach numbers. The

main objective was to determine the drag polar of the model in several low speed airstream

velocities at a Mach number under 0.2 and then extrapolate the results to a higher Mach

number. This experiment has been conducted with Aerolab wind tunnel of the San Jose State

University Aerodynamics Department. The result of the experiments met the theoretical

results of lift and drag on an F-16 fuselage. The performance of the F-16 is finally discussed

using the results on the model.

I. Introduction

he F-16 is a multi-role jet fighter aircraft developed by General Dynamics since 1976 with about 5000

aircrafts already produced. It was designed exclusively for the use of the United States Air Force. Today, F-

16s are in operation in 21 nations around the world.

The purpose of this work is to obtain a drag polar (drag vs. lift curve) of the F-16 Falcon. The aerodynamics of

the aircraft were studied using experimental and theoretical methods by the use of a 1/48 scaled model of the F-

16 tested in the Aerolab Wind tunnel of the San Jose State University. The data collected are the normal and the

axial forces of the model on the earth axis at several speeds under 140 mph. This allows to obtain lift and drag

coefficients which are necessary to build the drag polar. However, we will not be able to obtain this polar for the

cruise phase of the F-16 Falcon at around Mach 0.8 – 577 mph. Thus, the problem is the relevancy of the

extrapolation of the drag polar at higher speed values than those achievable in the wind tunnel.

The drag polar of the F-16 model will be determined for several speeds and angles of attack. The speed of the

free stream velocity in the wind tunnel can be chosen very precisely by changing the fan power. In order to be

more accurate, a total of five measurements are taken in every configuration to get an average value. Although

the F-16 has already been much studied, few datas have been published for confidential reasons. Also, the

method used is interesting because it easily gave us available results.

The introduction of this paper gives a presentation of the context of our project as well as a description of the

experiments achieved. The second part explains the theory which can give results about the lift and drag of the F-

16. The third part describes precisely the experiments accomplished. The fourth and final part concludes with the

results we obtained and compares it with published data.

II. Theory

The goal of this experiment is to study the drag polar of the F-16 Falcon. Our objectives are as follows:

• Determine the axial and normal forces at 50, 75 and 100 miles per hour with an angle of attack varying

from -20 to +20 degrees.

• Determine the lift and drag forces

• Compute the lift and drag coefficients

• Draw the drag polar curve

A. Hypothesis

1 Third-year cadet, « Commandant Fayolle » Entry, dewi.boucher@gmail.com

2 Third-year cadet, « Commandant Fayolle » Entry, henri.guillot@hotmail.fr

T

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• We will study the aircraft in a steady flow which means that for each parameter

• We will consider that the fluid is perfect which implicates that the fluid is inviscid, the heat flux by

conduction is zero and transformations in the fluid are reversible.

• We will assume small .

• We will consider that the fluid is incompressible.

• The rotational speed is zero.

• The Kutta-Joukowski condition is respected which dictates at the leading edge and the tailing

edge of the wing.

• The flow speed is subsonic.

B. Lift and drag

The equation of an outline of a wing P is . The equation of the extrados is and the

equation of the intrados is . We will name c the length of the chord. The chord is the segment between

the leading edge and the trailing edge. The span where we calculate the strength of the aerodynamics forces is

named L.

Because of the perfect fluid hypothesis,

where 1)

By integration, we have the forces applied on the part of wing in the body axis:

Center of pressure is the average location of the pressure. Pressure varies around the surface of an object.

Aerodynamic force acts through the center of pressure.

Considering the non-dimensional parameters and .

We can define the law slope of the outline of the wing

In this way, we define our two coefficients:

The lift and drag coefficients computed in the aero axis are then obtained with the following relations :

Assuming small , this leads to and because of the comparison of the

strength between CA and CN.

Finally we have:

Now, we can say that and where S=cL.

In the same way, we can find the way to calculate the pitching moment in the body axis, i.e. perpendicular to

the symmetry plan (x;y) and around a given point Mo(xo;yo). If , we can find the

pitching moment coefficient .

.

Finally,

=

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C. Principles and corrections

According to our hypothesis, we can apply the potential flow theory. Indeed, the forces derived from a

potential and the rotational speed is zero at first time. Thus, considering an uniform flow and all our hypothesis,

we are allowed to use the linearized method which divides the study of the wing into three parts :

• Flat plate at incidence

• Skeleton profile

• Symmetrical thick profile

This method gives the following results:

where

,where

We can complete our study by taking into account the compressibility aspect of the problem. We have to use

Euler results within the similitude rules of Prandtl-Glauert. Indeed, those similitude rules allow to take into

account the compressibility aspect of the problem as we work in a subsonic flow.

Thus we have:

, where

If we have an infinite wing, the pressure distribution is the same everywhere which becomes false with a finite

wing. Indeed, the pressure distribution is modified due to the continuity of the pressure on the tip of the wing.

This gradient of pressure creates a transversal flow that need to be taken into account. For that, we use some

tables which give the correction factors for non-elliptic lift distribution.

Fig 3 – Presentation of a wing

We can define the creation of an induced drag written :

where

The finite wing corrections depend on the aspect ratio and taper ratio because the lift coefficient will be affected

by the perpendicular stream velocity to the quarter cord. The experiments showed that if AR then

Diederich found an equation making the link with the previous corrections.

where

Actual F-16 S= 27.88 m2 V(mph) Mach

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AR=3.20 50 0.065 3,029

75 0.097 3,027

40° 100 0.130 3,023

0° 125 0.162 3,018

b = 10 m 140 0.182 3,015

613.8 0.800 2.757

The non-linearity of the function versus is due to the small AR. As a fighter aircraft, the F-16 has a very

low AR ( around 3.2 ) compared to airliners ( around 12). We must take into account this fact by introducing the

coefficient as the non-linear lift factor and as the non-linear moment factor.

Thus, we have:

Fig 4 – Various of and for various planform shapes and aspect ratio

According to this table, =0.5, and for the F-16

D. Estimation of the Wing-body lift

We cannot just add the lift coefficient of the wing to the lift coefficient of the body separately without taking

into account interference effects between both components of the plane which produce more lift. We can

approximate the linear lift curve slope of the wing-body with this relation:

=F

The is the wing-body lift curve slope and is referenced to the total wing planform area .

Fig 5 – Description of wing planform parameters

The factor F can be divided into the interference due to the body and the interference due to the wing so

as to obtain:

There is an exact method to find and but requires the exact outline of the F-16’s wing and body. The

NACA 64A204 data corresponding to the actual airfoil of the F-16 has not been published yet and that’s why

this method will not be developed in this research project. We will use an approximate result because the

following graphic does not give the exact wing-body interference factor for the F-16 but for some planes which

can seem to be an F-16. We will interpolate these two curves to be as close as possible as the actual F-16 design.

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Fig 6 – Lift and side-force ratios for several wing-body combinations

For the F-16, =0,4 so F=0,9 according to this graphic. Thus, we can draw the lift coefficient versus the angle

of attack for the different velocity stream.

E. Wing Body drag

As for the lift, the combination of the wing and the body creates some interference for the drag. According to

Leland M. Nicolai, the results indicate that the effect of the interaction between all the components is

which can be neglected. Thus, we will assume that wing-body drag coefficient is equal to wing

because the drag due to the lift is primarily due to the wings.

Thus, considering that the drag of an aircraft is divided like this:

Where is the zero lift drag coefficient due to miscellaneous protuberances and is the drag coefficient

due to lift

The is calculated like with:

There is a parabolic behavior of the function

versus . The term is the inviscid drag due to

lift. It is the result of the vortices trailing of a finite

wing. The term is the viscious drag due to lift

from the flow separation and increased skin. is

the lift coefficient for the minimum drag coefficient

(for a cambered airfoils, ) . So,

we will use the previous study of the versus to

find .

We will use some experimental data for , using

the following chart.

Fig 8 – The minimum drag coefficient for plane wings 3

percent thick and having different types and planform

This equation is only true below the “ break” denoted . Above , the drag coefficient ceases to be

parabolic with that’s why we will not go through this high .We can calculate using the wing efficiency

e. This wing efficiency depends on the correction of the finite wing, taper ratio and sweep.

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where

According to the next table, the factor of Weissinger is equaled to 0.99. So, after computation, the wing

efficiency is equal at 0,8316.

This leads to 0.119615

The K’’ depends on the leading edge radius and taper ratio and can be find with the following table.

We know that the leading edge radius of the F-16 is 0.5 inches (1.27 cm). Furthermore, the average wing’s chord

of the F-16 falcon is 2.8 m. So, according to this

graph, we can determinate that k’’=0.034

Fig 9 – Viscous drag due to lift factor, K’’

Fig 10 – Weissinger wing planform efficiency factor

Now, we will find the for the fuselage and then the for the wings assuming that the F-16 has a delta

wing to facilitate the computation.

The zero lift drag coefficient of the wings is primarily due to skin friction at subsonic speeds and can be

calculated with :

Where L denotes the airfoil thickness

location parameter and the maximum

thickness ratio of the airfoil, L=1.2 for

located at x 0.3c and L=2.0 for

located at x 0.3c. As said above, the

airfoil of the F-16 is NACA 64A204. This

means that this airfoil has a maximum

thickness of 4% of the chord. So, L equals

1.2.

We know that for supersonics aircraft, a

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typical wing is around 6% or 9%. 3

is the wetted area of the wing (2 )

R is the lifting surface correlation factor

obtained from the following table and

leading to R=1,0.

is the turbulent flat plate skin friction

coefficient. The velocity of the air stream

allows us to assume that we are in a laminar

fluid leading to the following relation:

The turbulent flat plate is obtained by

using the smaller between the cutoff Reynold

number and the flight Reynold number. Fig 12 – Lifting surface correlation factor for wing subsonic

The effect of surface roughness on the skin friction values is

determined using the cutoff Reynolds number. The type of

surface of the F-16 is a camouflage paint, so the roughness height

value is 1.20 .

With the ratio /k ( in inches) and the previous table, we can

find the cutoff Reynolds number .

Now, we have to compare the cutoff Reynolds number with the

flight Reynold numbers. First, we will calculate the Reynolds

number at sea level and at 140 mph : , then

at Mach 0.8 :

Thus, we use the cutoff Reynolds number in the two cases to

calculate which is equaled at 5.42 .

Fig 14 – Averaged skin friction coefficient versus Reynolds number

The zero lift drag coefficient of the body is primarily due to skin-friction at subsonic speeds and can be

calculated like this:

where

These coefficients are referenced to the maximum cross-section area .

is given by:

3 http://www.scribd.com/doc/57786879/14/NACA-Airfoils

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After computation we have,

To compute we use the

relation.

Fig 15 – Body terminology

Finally, we find that

The external stores, the canopy and other protuberances create

an additional drag . The following table gives us the

experiment drag of those items.

We can see the effect of such protuberances on the drag. These

data must be corrected for the appropriate . We don’t take

into account these drag in this project.

To complete our drag estimation, we finally take into account

the drag due to the tail. However, as not enough information is

available, we will assume that the tail surfaces are scaled wings.

So, their similar aerodynamics lead to:

Thus, we find that

III. Design of the experiment

A. Dependent and independent variables

In this experiment, the independent variables are the angle of attack of the 1/48 scaled model of the F-16

and the Reynolds number Re. The dependent variables are the Lift coefficient and the Drag coefficient

B. Methods for measuring each variable The force at each location is measured by using a pressure transducer system. The acquisition device then

analyzes the voltage difference in the transducer and displays the normal and axial forces. The free stream

velocity and the Reynolds number are also displayed on the wind tunnel computer screen. Measurement of the

angle of attack is done by using a protractor mounted to the bottom of the 1/48 scaled model of the F-16..

C. Equipment and instrumentation

This experiment is done by the use of a 1/48 scaled model of the F-16 Falcon built by General Dynamics for

the US Air Force. Its dimensions are a 20.3 centimeters wing span, 29.8 centimeters max length. It is mounted in

the wind tunnel by fastening it to the sting balance which is designed to be a perch for the F-16 model. The

model positioning system is a series of parallel arms mounted to a gearbox, itself mounted to the yaw table. Both

yaw and pitching angle can be adjusted manually. The model positioning system allows for pitch adjustment

from +20° to -20° and yaw adjustment from +30° to -30°.

The wind tunnel is provided with electronic instruments consisting of two solid-state differential pressure

transducers and a three-component sting balance. In order to take measurements, the instruments are provided

with a data acquisition system.

The axial and normal forces were found using an AeroLab Wind Tunnel. This wind tunnel is of the Open

Circuit type with a test 12” x 12” x 24” test section. There are four major components. First, the contraction has

a contraction ratio of 9.5:1 (the volume of air coming in is compressed 9.5 times). The contraction has a low

turbulence level of 0.12% and ensures high performance. Second, the test section is where the model is hanging

to a sting carried by two vertical arms. Third, the diffuser is crucial to improve the test section flow quality. This

shallow angle diffuser helps to eliminate diffuser effects. Finally, the fan housing is a double-walled structure.

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The inner wall is made of perforated steel and the outer wall is made of structural fiberglass. Between these two

walls is a layer of sound-absorbing fiberglass batons. The computer built into the wind tunnel will be reading all

of our data, and capturing it when instructed.

Being an open-circuit design, the wind tunnel draws air from the surrounding environment. This entering air

first passes through a matrix of parallel passages. Because the passages are hexagonal in shape, this matrix is

referred as “honeycomb”. The honeycomb is 10,16 cm long and serve to straighten the flow – to eliminate most

flow angularity. Because the honeycomb does a little to eliminate small eddies, the tunnel is equipped with two

turbulence-reducing screens immediately downstream of the honeycomb. They are made of 0.009 inch (0.23mm)

stainless steel wire spaced at 20 wires per inch (2.54cm). Small eddies in the air are broken into yet smaller

eddies by the screens. Comparatively speaking, smaller eddies dissipate faster than larger eddies. Eddies passing

through the test section are termed “turbulence”. The screens also serve to reduce axial velocity variation.

Together, the honeycomb and screens smooth the air before it enters the contraction.

The speed of the airstream is sensed through holes drilled into the walls of the test section static pressure is

sensed through holes drilled into the walls of the test section entrance ( one pressure orifice in the middle of each

surface ). These holes are then plumbed together to form a manifold termed a static pressure ring. This ring

provides the average static pressure of the disturbed flow. For numerical applications, we will assume that the

atmospheric pressure is the wind tunnel total pressure.

D. Range for each variable The angle of attack will be varied from -20° to 20°, with a 5° increment. We take 5 different measurements of a

single configuration. The tests consider only 5 airstream velocity values at – 75,100,125 and 140 mph. For each

experiment, we will then get 8 data points.

IV. Results

A. Theoretical results

This curve shape seems to be in ad equation

with common drag-polar. Nevertheless, we do

not know the value of the “break and

that’s why we cannot be sure of the curve

shape for high .

The two curves of this graph are nearly similar

despite the difference of the airstream speeds.

According to this result, we will assume that, in

a subsonic airstream flow, the airstream

velocity does not have a significant influence

on the F-16’s drag polar

Fig 17 -

B. Experimental results at different speeds The acquisition device of the Aerolab wind tunnel gives both the normal and the axial forces in pound-force

(lbf) for every angle of attack.

The lift and drag forces come from a projection on the aero axis with the following formulas:

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We used the regular conditions of

pressure and temperature to determine the

lift and drag coefficients, both relevant

values in the lab at the moments of the

experiments.

As the streamlines inside the wind tunnel

are affected by the presence of walls, we

used a correction given by the constructor.

Fig 18 – Experimental drag polars

We can then pretend that the model is flying in a limitless volume of air - as in free flight conditions – and is

not limited by the section of the wind tunnel. With such corrections, we obtain the previous drag polar at several

velocities

C. Published data

The single data we found concerning the drag polar of the F-16 Falcon comes from the book “Fundamentals of

Aircraft and Airship Design” by L.M. Nicolai.

According to these results, the for fighter aircrafts in subsonic flow is around 0.02.

D. Comparison

Finally, we can compare

both the theoretical and

experimental drags polar

to the published data.

First of all, our

theoretical results show

that the drag polar of the

F-16 are almost not

affected by the different

Reynold numbers when

we stay in a subsonic

airstream. Indeed, all

calculated curves have the

same shape and values are

nearly the same. For

Fig 19 – Comparison of the results

instance, we note on the previous theoretical curves that and .

Furthermore, we note that our theory succeeded to foresee our experimental results. Indeed, airspeed velocity

is not a key factor. All our curves from 75 mph to 140 mph have the same shape and values are nearly the same

too. According to our theoretical and experimental results, we will assume that the drag polar at 140 mph is

representative of the drag polar at Mach 0.8.

Finally, we can compare our three curves representing the drag polar at Mach 0.8 and draw some conclusions.

V. Conclusion

We figured out a flight at Mach 0.8 to compare our theory and experiences at the previous published data.

Finally, we have some coherent results.

First of all, the hypothesis that we figured out in our theory are quite relevant as our experimental data are

close to previous published data. Also, we can make express some remarks. Our theoretical curve has the same

shape as both the previous published data curve and our experiment curve but we did not find the same . We

can guess that our approximations and the lack of accuracy of our theoretical method are the reason of this

difference.

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This leads us to doubt about the relevancy of our theoretical study. That’s why, we should have more published

data and be more accurate to validate this theory and our hypothesis. Our project could be extended in two

different ways. The first one could be to study the stability of the F-16 falcon. The second one could be to

analyze the drag and lift with several side slip angles.

Nevertheless, both the theory and the experiment gave us a Drag polar of the aircraft quite close to the published

data. The problem we had at the beginning is due to the limiting speed of the wind tunnel which has been

partially solved as our data are relevant for a higher velocity.

References

[1] Abbot, I.H., et al., Theory of Wing Sections, NACA TR 824, 1945.

[2] Furlong, G.C. and McHugh, J.G., A Summery and Analysis of Low Speed Longitudinal

Characteristics of Swept Wings at High Reynolds Number, NACA RM L52D16, August 1952.

[3] General Dynamics, Fort Worth Report, FZM-5783, Final Technical Report on a Study to Validate

the Integration of Advanced Energy Maneuverability Theory with Tradeoff Analysis, September 15, 1971.

[4] Gersten, K., Calculation of Non-Linear Aerodynamic Stability Derivatives for Airplanes, AGARD

report No. 342, 1960.

[5] Kuethe, A.M. and Schetzer, J.D., Foundations of Aerodynamics,John Wiley and Sons, New York,

N.Y., 1959.

[6] Leland M. Nicolai, Fundamentals of Aircraft Design, San Jose, METS, 1984.

[7] Pitts, W.C., Nielsen, J.N., and Kaattari, Lift and Center of Pressure of Wing-Body-Tail

Combinations at Subsonic, Transonic and Supersonic Speeds, NACA Report 1307, 1959.

[8] Morris, D.N., A summary of the Supersonic Pressure Drag of Bodies of Revolution, Journal of the

Aeronautical Sciences, Vol. 28, No. 7, July 1961.

[9] Simon, W.E., Ely, W.L., Niedling, L.G., and Voda, J.J., Prediction of Aircraft Drag Due to Lift, AF

Flight Dynamics Lab, AFFDL-TR-71-84, Wright-Patterson AFB, OHIO, June 1971.