Post on 21-Feb-2015
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
1
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.
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
2
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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
3
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)
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
4
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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
5
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.
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
6
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.
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
7
-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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
8
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.
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
9
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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
10
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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
11
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!
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
12
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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
13
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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
14
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