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.
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‘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
THEORY ................................................................................................................................................... 4
‘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
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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
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
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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.
‘Wind Tunnel Tests on a Model Cessna' by Vignesh Palaniappan
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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
‘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).