Lab Report v2.0

‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan

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Name: Vignesh Palaniappan

CID: 00637107

Personal Tutor: Dr. Rafael Palacios-Nieto

Due Date: 02-May-2011

Year 1 Lab Report

WIND TUNNELS TESTS ON A MODEL

CESSNA

The purpose of this experiment was to introduce wind tunnel testing; in particular, we examine how

the angle of attack and varying wind velocities affect the lift and drag forces acting on an aircraft. A

model Cessna 172 was tested; it had a wing area of 0.038 sq. m in comparison to a real size area of

approximately 16 sq. m. At both velocities tested, the lift increases as the angle of attack increases

between -2 and 12 degrees and maximum lift is generated at 13 degrees. After this point, drag

becomes prominent and causes the model to stall.

Further evaluations are made to distinguish the relationship between the lift and drag coefficients

and their relationship to the angle of attack. We study the basic forces acting on an aircraft, the

concept of downwash and perform calculations to find the induced drag. An estimation of the

stalling speed of a full scale Cessna is also made and finally as with all wind tunnels, we look at the

errors that affect the quality of the results.


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CONTENTS

INTRODUCTION ....................................................................................................................................... 3

APPARATUS & EXPERIMENTAL PROCEDURE .......................................................................................... 4

THEORY ................................................................................................................................................... 4

WIND TUNNELS ............................................................................................................................... 4

FORCES ON A PLANE ....................................................................................................................... 5

RESULTS & DISCUSSION .......................................................................................................................... 6

INDUCED DRAG ESTIMATION........................................................................................................ 10

STALLING SPEED ESTIMATION ...................................................................................................... 11

SOURCES OF ERROR ...................................................................................................................... 11

CONCLUSION ......................................................................................................................................... 12

REFERENCES .......................................................................................................................................... 12

APPENDIX .............................................................................................................................................. 13

75% ................................................................................................................................................ 13

50% ................................................................................................................................................ 14

NOMENCLATURE

= Lift Coefficient

= Drag Coefficient

= Induced Drag Coefficient

= Aspect Ratio

= Drag-Lift Ratio

= Gradient from specified figure

= Air Density

= Velocity of flow

= Area


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INTRODUCTION Wind tunnel testing is a vital stage in the design process of many industries, regardless of whether

an object is moving or is stationary. It is an excellent way of scrutinizing the airflow round a test

model. For aircraft, it is an opportunity to assess the airworthiness of the plane and identify any

improvements that can be made to optimise performance. Despite CFD and new simulation

techniques, wind tunnel testing has proved over the years to be an aeronautical engineer's most

prized asset. We are able to look at how to increase the lift generated by wing sections or equally

how to reduce the amount of drag acting on the plane.

Road vehicle aerodynamics are of increasing importance as we look to reduce fuel consumption and

we know that the more streamlined the vehicle the less power required to generate movement.

Formula 1 teams rely heavily on using aerodynamic features of their cars to gain leverage against

opponents be it only a few milliseconds and are willing to invest shedloads of money into wind

tunnels and research.

Another beneficiary of wind tunnel testing is high-rise buildings and other large structures such as

bridges and stadiums. For example, a skyscraper like the Burj Khalifa presents a huge surface for the

wind to act upon, if it were not designed properly the building would suffer from violent oscillations

causing the structure to physically deteriorate and possibly collapse. However, by repeating a

process of tunnel testing and modifying the model, a good solution is drawn to reduce the effects of

these winds.

Figure 1 – Lotus F1 Racing Wind Tunnel (Ref.1)


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APPARATUS & EXPERIMENTAL PROCEDURE The tests on the model Cessna were carried out in the Donald Campbell Wind Tunnel at 75% and

50% of the maximum wind tunnel capacity. It is a closed tunnel with a working section cross section

of 0.61m x 1.01m and the circulating air can reach speeds of up to 40m/s. The tunnel was started

and some time was given to allow the air to complete a few cycles ensuring a good free flow was

available. The angle of attack was set to -2 degrees and results were gathered (Lift on model, lift on

tail wire, drag on model and the pressure difference in the working section). The angle of incidence

was altered manually by means of a shaft that was attached to the model, the forces were measured

using force transducers and the pressure was recorded using the Furness Digital Manometer. The

incidence was incremented up 2 degrees, results were taken and the same procedure repeated until

12 degrees. From then on, 1 degree increments were used up to 14 degrees. Flow visualisation was

supplemented by using wool tufts. All the readings were entered in to an existing excel spread sheet

template which automatically generated graphs of lift and drag coefficients versus the angle of

incidence.

Figure 2 – Illustration of the Donald Campbell Tunnel used.

THEORY

WIND TUNNELS

There are several types of tunnel but this particular tunnel is a closed-return type where the model

is placed in the working section and the flow goes round in a complete circuit. The working section is

the section around which the tunnel is built, the tests are run on the model here and this is where

you want close to perfect airflow.

The 'settling chamber 'is in place to straighten the air and to minimise the effect of turbulence. This

usually has screens (wire meshes) and a honeycomb which remove eddies and cross flow

components of the air. When testing, we want the air to come towards the model in only one

direction and the meshes and honeycomb adequately do the job.

Settling

Chamber

Contraction

Diffuser

Working Section


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The 'contraction' before the working section makes the airflow uniform and faster than in the rest of

the circuit. This saves a lot of money since there is no need for a constant high-energy flow over the

whole tunnel. The design of this is crucial since it ultimately determines the flow in the working

section. In this tunnel, two reference static tappings are present in the contraction and the dynamic

pressure is calculated by finding the difference between these two points. This value is also

calibrated against a Pitot-static tube in the test section

The 'diffuser' is where the air coming out of the test section slows down prior to recirculating. The

recovery of static pressure from the kinetic energy is important since it reduces the power required

to drive the wind tunnel.

The advantages of using this type of tunnel compared to an open circuit or open jet is that no dust is

drawn in, the flow isn’t sensitive to external disturbances and the pressure in working section is

fine(less than the atmosphere due to speedy flow). However, this is significantly more expensive and

space consuming. Another point of note is that open jet tunnels have no walls to constrain the flow

in the working section – this is a more 'real' case scenario.

FORCES ON A PLANE

Figure 3 – The 4 main forces acting on a plane (Ref.2)

Moving onto the model, there are two main forces we analyse: the lift and the drag. The lift is the

force acting normal to the resultant of the free stream velocity. The drag is the force acting normal

to the lift opposite to the direction of flight. Airflow around an aerofoil tends to be quicker over the

top and slower over the bottom, this difference in velocity and consequently pressure is the reason

why we get lift. Another thing is that the airflow over the top has less pressure than the airflow

outside the wing therefore meaning the air flows inwards towards the fuselage. The inverse happens

on the bottom where flow is out away from the fuselage. Combining these two flow concepts

together, we are able to understand the formation of wing tip vortices. So in the jet figure above,

the vortex on the left wing will rotate clockwise and the right wing vortex will rotate counter-

clockwise.

http://www.brighthub.com/guides/energy.aspx


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Diagram 1 - the centreline is the fuselage; the flows proceed as shown past the aerofoil. (Ref.4)

Acknowledging the existence of wing tip vortices and their ability to create 'downwash' (a backward

tilting motion of the plane), we know that a part of the lift force acts backwards, this is a component

that contributes to the overall drag on the model and this component is called the induced drag.

As we keep increasing the angle of attack, we should keep increasing the lift coefficient until a

certain critical angle where a further increase would result in a loss of lift, this angle is called the

stalling angle and it varies from aerofoil to aerofoil. The wing disrupts the flow since it produces a

large enough surface for the air to 'hit' against, the air separates and drag becomes more

pronounced.

RESULTS & DISCUSSION The following pages of graphs are presented so that we can observe differences between the tunnel

operating at 50% and 75% capacity. The tables of data obtained while carrying out the experiment

are listed in the appendix. It is easier and more accepted to plot the coefficients of lift/drag rather

than the total lift/drag since they are independent of air density, scale of the aerofoil and the

velocity used in the experiment. Absolute values would make data manipulation rather complicated

and situation dependent.

The lift curves (Figs.4,5) show that a linear relationship exists between the lift coefficient and the

angle of attack up to 13 degrees. The curve peaks at this point (max. lift) begins to fall suggesting

that the aerofoil has stalled. The x-intercept illustrates that at 0 degrees incidence there is a negative

lift coefficient and so there exists negative lift. This is because of the design of the aerofoil; a

symmetrical aerofoil would theoretically produce zero lift at zero degrees.

The drag curves (Figs.6,7) show that the drag is the least at about 3.5-4 degrees(common sense says

that it should be much closer to 0 degrees). In a small region either side of this minimum, the drag

slowly increases, (we can imagine as the aerofoil angles slowly, it increases the area for the air to hit

against – this is regardless of the direction of the attack). Afterwards the drag begins to increase

appreciably especially after passing the stalling angle when airflow separates. Note the connection

between stalling angle and lift/drag curves – changes occur when the aerofoil stalls.


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-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-5 0 5 10 15

Lift

Co

eff

icie

nt

Incidence (deg)

LIFT (50%)

0

0.05

0.1

0.15

0.2

0.25

0.3

-5 0 5 10 15

Dra

g C

oe

ffic

ien

t

Incidence (deg)

DRAG (50%)

0

0.05

0.1

0.15

0.2

0.25

0.3

-5 0 5 10 15

Dra

g C

oe

ffic

ien

t

Incidence (deg)

DRAG (75%)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-5 0 5 10 15

Lift

Co

eff

icie

nt

Incidence (deg)

LIFT (75%)

Figs 4-7 (from left to right) – Lift and Drag coefficient curves vs. the angle of attack for 75% and 50% wind tunnel capacity. The dashed lines show the stalling angle

Stalling angle Stalling angle


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0

0.05

0.1

0.15

0.2

0.25

0.3

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

Dra

g C

oe

ffic

ien

t

Lift Coefficient

Cd vs. Cl (75%)

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

D/L

(D

rag

to L

ift

Rat

io)

Lift Coefficient

D/L vs Cl (75%)

-1.5

-1

-0.5

0

0.5

1

-0.5 0 0.5 1 1.5

D/L

Lift Coefficient

D/L versus Cl (50%)

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.5 0 0.5 1 1.5

Dra

g C

oe

ffic

ien

t

Lift Coefficient

Cd vs. Cl (50%)

Figs 8-11 (from left to right) – Cd and D/L vs. Cl.


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y = 0.0559x + 0.1082 R² = 0.8535

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0 0.2 0.4 0.6 0.8 1 1.2

Dra

g C

oe

ff

Lift Coefficient^2

Cd vs Cl^2 (75%)

y = 0.0716x + 0.1163 R² = 0.7401

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Dra

g C

oe

ff

Lift Coefficient^2

Cd vs Cl^2 (50%)

Figs 12,13 – Cd vs.Cl^2


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Figs. 8 and 9 show the drag coefficient versus the lift coefficient and it is evident that they are

analogous to the drag curves, this is because the lift-angle of incidence relationship is mostly linear

for most of the data points. Only the latter part of this graph is different in that the stalling of the

aerofoil (penultimate point) causes drag to increase rapidly and lift generation to decline. The wool

tufts attached to the model on the aerofoil were oscillating randomly and rapidly instead of being

flat suggesting that the flow had separated at that point.

Figs. 10 and 11 show the drag-lift ratio versus the lift coefficient. The ratio is dependent on the

actual forces and not the coefficients. From any designer's point of view, a major goal is achieving a

low drag coefficient as well as a low drag-lift ratio. Good values influence the green aviation vision of

the future by improving fuel economy and aerodynamic efficiency. From a glider's point of view, a

minute drag-lift ratio is crucial to staying in the air for long periods. For the most part, the ratio lies

between -1 and 1 and so the lift is always greater than the drag. If the lift-drag ratio were plotted

against the angle of attack, it would be evident that the graph rises rapidly up to about 3-4 degrees.

After this, as the induced drag increases appreciably, the ratio is lesser.

Figs 12 and 13 have been plotted with their first and last points omitted so that the linear portion of

the curve is discernable. We use this particular graph to calculate the induced drag acting upon the

aircraft.

The Reynolds numbers for these tests have been calculated to be roughly 146000 at 75% wind

tunnel capacity and 95000 for 50% capacity. These are of importance when we consider scaling up

the model back to its full scale. All of the laws and values are dependent on the Reynolds number

and this must be the same in the tunnel as in the air otherwise all the other calculations end up

useless. This concept of dynamic similarity is extremely valuable and is of utmost importance.

INDUCED DRAG ESTIMATION

We know the following two relations, from this we can derive an equation to calculate the induced

drag coefficient ( ).

( )

( )

(

)

The drag coefficient was an average of all the data points for a scenario. This was done for both

speeds and substituted in. The gradients were calculated by using Excel's 'trendline plotting' feature.

The term AR is the aspect ratio (for the model Cessna AR= 7.52).

AVG DRAG COEFFICIENT: @75% = 0.1485 , @50% = 0.1646 GRADIENT: @75% = 0.0559 , @50% = 0.0716

EVALUATED : @75% = 0.3536 , @50% = 0.3058


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As we now have this coefficient, we can simply find the induced drag force by multiplying by the

area of the wing and the dynamic pressure. The area A=16.2 and the dynamic pressure is given

in the results gathered, we simply have to use the average value

(

) ( )

EVALUATED : @75% = 0.3536 , @50% = 0.3058

AVG DYNAMIC PRESSURE: @75% = 446.75 Pa , @50% = 187.49 Pa

INDUCED DRAG FORCE: @75% = 2557 N , @50% = 929 N

The weight of the aircraft is roughly 10000N and we can see that the induced drag is in the range of

10% to 25% of this value.

STALLING SPEED ESTIMATION

The following equation is used for the estimation of the stalling speed of an aircraft. The term 'n' is

equal to the load factor and represents the ratio between lift and weight. In steady level flight lift is

equal to the weight and so n=1 which is what we will assume when calculating the stall speed. When

aircraft bank or rise sharply, the load factor changes. Weight=W= (1040 x 9.81) N. We use the max

lift coefficient obtained in the 75% capacity experiment (although note that both coefficients are

within 0.05 of each other). This is equal to 1.05.

√

( )

The actual value is 26m/s and this is reasonably close estimation. We must bear in mind the sources

of error that come with using data from wind tunnel testing. The lift coefficient is the one thing that

we had to have determined previously, all the other variables were physical quantities. Instead of

using the value of 1.05 that we determined in the tunnel, if we try = 1.5, = 26.6 m/s.

SOURCES OF ERROR

A difficulty of using models is that they are hard to make accurate, the smaller the more difficult.

Also we need them represent the full size object as closely as possible (especially the exterior

surfaces and physical geometry). The Cessna used here is 1/20th its actual size and the solution to

this problem is to make larger models.

One obvious error in the testing is that the flow in the tunnel is not the same as the free flow

encountered in the sky above. The flow is constrained by the walls; this in turn affects our

measurements and conclusions derived from the experiment. So ideally, we want large

tunnels(working sections) in comparison to the model. It's quite apparent that if we kept making

everything larger (forgetting huge costs) – we would essentially be testing the full scale thing itself!


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Finally, we need to consider the Scale Effect, which says that the simple aerodynamic relationships

for lift, drag, speed squared law and the law of dependence on area and density aren't strictly true

unless certain conditions apply. These conditions are those founded by the Reynolds experiments.

We need to ensure that velocity multiplied by the size value (the 'VL' law) remains the same for both

the model and full-scale flight. We test a 1/20th scale model, so we should be testing at speeds that

are 20 times larger to maintain similarity.

CONCLUSION The wind tunnel testing entailed taking measurements of the lift and drag forces acting on a 1/20th

scale model Cessna at different speeds and angles of attack. It was observed that a linear

relationship existed between the angle of attack and the lift coefficient for low angles of attack. The

maximum lift was achieved at around 13 degrees after which stalling occurred. Beyond this point,

the wool tufts identify the separation of the airflow and the consequent increase in drag.

Figs 10 and 11 illustrated how the drag-lift ratio was always below 1 for positive angles of attack

(which created positive lift coefficients). This indicates how the aerofoil always generates more lift

than drag until stalling. Nevertheless, we already know that at more extreme angles of attack,

induced drag plays a more important role by contributing significantly to the overall drag, the drag-

lift ratio will eventually be greater than 1. Another conclusion that can be drawn from the induced

drag estimations is that as the airspeed goes up, the induced drag goes up.

The estimated stalling speed of 31.8m/s is a guide to the accuracy of this experiment; it is a useful

value since the running conditions were not exactly optimal. It underlines the fact that whatever

model we test, the errors of using constrained flow and scaled objects need to be accounted for

before drawing conclusions from these experiments. In reality, the induced drag is lower than what

we calculated. We need to go through a process of refinement to get the two values closer together.

Also as we can't increase the size of the tunnel, the alternative is to make an even more accurate

representation of the model or to test individual sections of the plane but this can often be costly

and erroneous when we piece information back together.

REFERENCES 1. Motor Sport Circuit Guide [Online], Viewed on 31/03/2011, Available at:

http://www.motorsportcircuitguide.com/cms_images/Lotus_F1_Racing_wind_tunnel_model_C.jpg

2. Royal Aeronautical Society [Online], Viewed on 01/04/2011, Available at:

http://www.raes.org.uk/raes/careers/education/education_planes.htm

3. Greenhalgh, E. S., 01/03/2011, 'Wind tunnel tests on a model Cessna', Aeronautics

Department, Imperial College London

4. Kermode, A.C (1995) Mechanics of Flight, 10th ed, 'Wind Tunnels' pg 45-51, 'Scale effect and

Reynolds Number' pg464-469

5. Cavcar,M., 30/13/2006, 'Stall Speed', Anadolu University, School of Civil Aviation

Available at : http://home.anadolu.edu.tr/~mcavcar/common/Stall.pdf

http://www.motorsportcircuitguide.com/cms_images/Lotus_F1_Racing_wind_tunnel_model_C.jpg

http://www.raes.org.uk/raes/careers/education/education_planes.htm

http://home.anadolu.edu.tr/~mcavcar/common/Stall.pdf


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APPENDIX Cessna gross wing area (S):

0.038 sqr.m Drag correction 0.0174

Barometric pressure:

998.9 m.bar FAI correction 0.997

Temperature: 20.26 deg.C Pitot Correction 0.82

Air Density: 1.186 kg/m^3 Wing Area: 16.2

Weight: 1040 Kg Viscosity 0.0000178 kg/ms

75%

INCIDENCE (deg)

PRESSURE (Pa)

Incidence (corr)

Cd (tunnel)

Velocity (m/s)

Lift (N) Drag (N) Cl Cd D/L L/D Cl^2 Reynolds No.

Re=(pVL)/ visc

NO WIND 0.000

0.00

-2 446.301 -2.338 0.002 27.43 -5.749 2.495 -0.339 0.149 -

0.434 -2.304 0.115 146232.368

0 442.280 -0.118 0.000 27.31 -1.988 2.067 -0.118 0.123 -

1.040 -0.962 0.014 145572.174

2 447.105 2.148 0.000 27.46 2.514 1.897 0.148 0.112 0.754 1.326 0.022 146364.050

4 447.105 4.345 0.002 27.46 5.874 1.843 0.346 0.111 0.314 3.187 0.120 146364.050

6 448.713 6.555 0.005 27.51 9.487 1.901 0.556 0.117 0.200 4.991 0.310 146627.058

8 448.713 8.766 0.010 27.51 13.095 1.996 0.768 0.127 0.152 6.562 0.590 146627.058

10 445.496 10.934 0.015 27.41 15.857 2.393 0.937 0.157 0.151 6.627 0.877 146100.568

12 449.517 13.048 0.019 27.53 17.952 2.755 1.051 0.181 0.153 6.515 1.105 146758.386

13 445.496 14.015 0.018 27.41 17.230 4.101 1.018 0.260 0.238 4.202 1.036 146100.568

AVG Cd 0.1485

GRAD 0.0559

Cdi 0.3533

AVG dynamic pressure 446.75 Pa

INDUCED DRAG FORCE 2556.6 N


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50%

INCIDENCE (deg)

PRESSURE (Pa)

Incidence (corr)

Cd (tunnel)

Velocity (m/s) Lift (N) Drag (N) Cl Cd D/L L/D Cl^2 Reynolds No

NO WIND 0.00 0.00

-2 186.562 -2.404 0.003 17.737 -2.874 1.102 -0.405 0.158 -

0.383 -2.608 0.164 94545.533

0 188.170 -0.107 0.000 17.813 -0.766 0.980 -0.107 0.137 -

1.280 -0.781 0.011 94952.182

2 187.366 2.154 0.000 17.775 1.097 0.897 0.154 0.126 0.818 1.223 0.024 94749.076

4 188.170 4.378 0.003 17.813 2.712 0.852 0.379 0.122 0.314 3.183 0.144 94952.182

6 187.366 6.571 0.006 17.775 4.076 0.883 0.572 0.130 0.217 4.617 0.328 94749.076

8 186.562 8.746 0.010 17.737 5.305 0.914 0.748 0.139 0.172 5.803 0.560 94545.533

10 186.562 10.918 0.015 17.737 6.530 0.983 0.921 0.153 0.151 6.642 0.848 94545.533

12 188.170 13.099 0.021 17.813 7.880 1.498 1.102 0.231 0.190 5.259 1.214 94952.182

13 188.492 14.037 0.019 17.829 7.448 1.911 1.040 0.286 0.257 3.898 1.081 95033.303

AVG Cd 0.1646

GRAD 0.0716

Cdi 0.3058

AVG dynamic pressure 187.49 Pa

INDUCED DRAG FORCE 928.7 N

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