AEROSPACE 305W - AEROSPACE TECHNOLOGY
LABORATORY
Laboratory Experiment #2
2D Lift and Drag Coefficients of Airfoil S805
April 6th, 2015
Christian O’Toole
Course Instructor: Professor Auhl
Lab TA: Brian Imperiale
Lab Partners: Steve Himelfarb, David Irizarry, Matt Flaig, Garret Kolmer
AERSP 305W: Aerospace Technology Laboratory
Section 2
Test Facility: 8 Hammond – Aerospace Engineering Wind Tunnel Lab
Abstract
Airfoil S805 was analyzed in a wind tunnel to study the wake velocity profile and determine the
2D lift coefficient, drag coefficient and pressure coefficients on the upper and lower surface at
various angles of attack. Determining the aerodynamic properties of S805 provided insight into how
lift and drag is produced on a wing. A manometer bank and hot-wire anemometer were used to
determine the pressure distribution and airflow velocity in the wake. Using these tools, the pressure
coefficient around the airfoil was plotted against the chordwise location and a wake velocity profile
was plotted for an angle of attack of 16.95 degrees and -4.0 degrees. At a Reynolds number of
700,000 and angles of attack between -20 and +20 degrees a lift curve and lift coefficients vs drag
coefficients were graphed. Data illustrated the maximum coefficient of lift was about 1.3, an angle of
attack of zero lift was near -3 degrees and the slope of the lift curve in the linear range was
0.1137/deg. The drag coefficient was minimized at about 0.01 and roughly constant for low values of
the lift coefficient. As a whole the experiment was accurate compared to the NREL/SR-440-6971
S805 report making this experiment successful.
I.
Introduction
The objective of the experiment was to determine lift and drag coefficients at an angle of attack
ranging from -20 to 20 degrees on an airfoil classified as S805. The span of the model was 24 inches
long and extended the width of the tunnel making the experiment two-dimensional. The cambered
model had a chord length of 19.685 inches and a max thickness of 2.635 inches as shown in Figure 1.
Figure 1: S805 Airfoil Shape and Maximum Thickness
The 2D S805 model was located in the test section and the wind tunnel speed was set so it
corresponded to a Reynolds number of 700,000. At this Reynolds number the local pressure at
various points on the airfoil’s body was measured through the use of a manometer bank. By using a
36-tube manometer bank the pressure distribution around the airfoil at various angles of attack was
determined. Additionally, the upper and lower pressure coefficient on the airfoil’s surface was
determined by relating the pressure reading of the monometer bank, Pu,l at each port to test section’s
static, P∞ and dynamic pressure, q∞. Equation 1 and Equation 2 represent the formula to determine
the upper, CPu and lower pressure coefficient, CPl, respectively.
C Pu 
Pu .  P
q
C Pl 
Equation 1: Upper Pressure Coefficient
Pl .  P
q
Equation 2: Lower Pressure Coefficient
Furthermore, the 2D coefficient of lift for S805 at angles of attack, α, ranging from 20 degrees to
negative 20 degrees was calculated from the upper and lower pressure coefficient readings given by
the manometer bank. The pressure distribution around the airfoil in addition to the angle of attack, α,
as seen in Equation 3 was used to determine the coefficient of lift, Cl.
( n ) pannels
 ( n ) pannels  C   C Pl. i   x 
 C Pu. i 1  C Pu. i   x 
 x    
 x   
Cl     Pl. i 1






       cos( )









2
2
  c  i 1  c  i    i 1 
  c  i 1  c  i  
 i 1 
Equation 3: 2D Lift Coefficient based on Pressure Distribution and Angle of Attack
In order to determine the airfoil’s 2D drag coefficient for each angle of attack a hot-wire
anemometer was used to measure the flow velocity behind the model. By traversing the hot-wire up
and down the height of the test section, the wake generated by the flow around airfoil’s body was
surveyed. The average velocity near the top and bottom edge of the wake, V o in addition to the local
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velocity, V at each point in the wake was used in a linear approximation with a step size, h of 0.1 to
calculate the drag coefficient based on the chord, c as represented in Equation 4.

2 ( n ) HotW ireRe adings  V V 2 
   * h 
Cd 

 V V

c 
i 1
0 i
 0

Equation 4: 2D Drag Coefficient Determined by a Hot-Wire Traverse in the Airfoil’s Wake
II.
Experimental Procedure
In the first experiment a manometer bank was used to determine the pressure distribution around
the airfoil which ultimately gave insight into the upper and lower pressure coefficient and 2D lift
coefficient of the model. The S805 airfoil was placed in the wind tunnel at the test section as shown
in Figure 2 and the pressure tap ports were connected by tubes to the manometer bank in Figure 3.
Figure 2: Airfoil Placed at the Wind Tunnel Test Section
Figure 3: Manometer Bank
After orientating the airfoil in the test section to a fixed angle of attack and recording the
laboratory condition the flow speed of the tunnel was set so the airflow velocity at the test section
corresponded to a Reynolds number of 700,000. As air flowed over the airfoil the static pressure at
each of the 36 ports on the body was measured by the tilted manometer bank. The pressure
coefficient on the upper and lower surface given by Equation 1 and 2 were determined based on the
manometer bank recordings. These pressure coefficient values were then used to determine the
pressure distribution around the airfoil which gave the 2D lift coefficient for a fixed angle of attack
as shown in Equation 3. This experiment was repeated for each angle of attack which varied from
negative 20 degrees to positive 20 degrees.
Before conducting the experiment to determine the 2D drag coefficient the hot-wire was
calibrated. The velocity measured during this experiment was based on a 4th order polynomial
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calibration curve of the hot-wire. This curve was previously determined by relating a voltage output
to the corresponding airflow velocity at the hot-wire. Since the hot-wire functions based on
convective heat transfer as the airflow increased the temperature changed which caused the hot-wire
to recorded it as a change in resistance. As the minimum velocity increased this temperature change
also increased non-linearly which resulted in a change in resistance defined by a 4 th order polynomial
curve as shown in Figure 4.
Figure 4: Hot-Wire Calibration Curve
To determine the drag coefficient for a fixed angle of attack, a survey of the wake two feet behind
the S805 airfoil was conducted using a hot-wire traverse as shown in Figure 5.
Hot-Wire
S805 Airfoil
Figure 5: Wind Tunnel Test Section set-up with Hot-wire Traverse
The envelope of the wake behind the airfoil was determined based on the measured airflow
velocity of the hot-wire after taking a vertical survey along the height of the test section. The local
velocities recoded in this wake and the average velocity near the start of the wake was used to
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determine the 2D drag. Using the numerical integration method in Equation 4, the drag coefficient
was determined for a fixed angle of attack and repeated for each angle of attack ranging from
negative 20 degrees to positive 20 degrees.
III.
Results and Discussion
For each sections experiment the room’s temperature and pressure were recorded and these values
were used to determine the air density as illustrated in Table 1.
Table 1: Temperature, Pressure and Density Readings by Experiment
In order to visualize the wake formed behind the airfoil for a given angle of attack the wake
traverse distance was plotted against the hot-wire velocity. For each angle of attack the hot-wire
recorded a decrease in velocity within the envelope of the wake. Since the velocity decreased in
relation to the freestream velocity a pressure distribution formed. Behind the airfoil was a region of
low pressure which attempted to suck the airfoil back which ultimately caused a measurable pressure
drag force. Figure 6 and Figure 7 illustrate how the hot-wire velocity in the wake of the test section
varies along the height of the test section for an angle of attack of 16.95 degrees and negative 4.0
degrees, respectively.
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Figure 6: S805 Wake Velocity profile at Alpha = 16.95 Deg.
Figure 7: S805 Wake Velocity profile at Alpha = -4.0 Deg.
As displayed above, at a reynolds number of 700,000 as the angle of attack increased the wake
generated behind the airfoil increased in length. Additionally, the point of lowest velocity recorded in
the wake by the hot-wire was lower for a higher angle of attack. A final point is that the drag
coefficent was greater for an angle of attack greater in magnitude. This drag difference resulted from
a greater pressure distribution around the S805 airfoil for an angle of attack of 16.95 degrees
compared to an angle of attack of negative 4.0 degrres.
The coefficent of pressure was ploted as a function of the point along the chordwise location of
the airfoil to analyze the pressure distribution around the airfoil. Figure 8 and Figure 9 include the
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experimental and published data, respectively for the pressure coefficient on the upper and lower
surface as a function of the chordwise location of the airfoil for an angle of attack of 16.95 degrees.
Alpha = 17.14 Degrees
at Re = 1,000,000
Upper Surface
Lower Surface
Figure 8: Experimental Cpu,l vs x/c for Re. # = 700,000 at α = 16.95 Deg. Figure 9: Published Cpu,l vs x/c for α = 16.95 Deg
Figure 9 and Figure 10 include the experimental and published data, respectively for the pressure
coefficient on the upper and lower surface as a function of the chordwise location of the airfoil for an
angle of attack of negative 4.0 degrees.
Alpha = -4.0 Degrees
at Re = 1,000,000
Lower Surface
Upper Surface
Figure 10: Experimental Cpu,l vs x/c for Re. # = 700,000 at α = -4.0 Deg. Figure 11: Published Cpu,l vs x/c for α = -4.0 Deg
As the angle of attack increased the pressure coefficient between the upper and lower surface
increased in magnitude as long as an aerodynamic stall had not occurred. When flow separation
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occurred the coefficient of pressure dropped near zero. The experimental results corresponded with
the published data for each angle of attack which made the results of the lab accurate. Since a
positive angle of attack resulted in a net negative pressure distribution on the upper surface a positive
lift force was generated. A negative angle of attack had the opposite effect with a positive pressure
distribution on the upper surface resulting in a net vertical force pushing down on the airfoil.
A lift curve was plotted in Figure 12 in order to determine the relationship between angle of attack
and the coefficient of lift. In order to compare these experimental results to accurate values the data
has been aligned next to published data in Figure 13.
Re. # = 700,000
Figure 12: Experimental Cl vs α for Re. # = 700,000
Figure 13: Published Cl vs α for Re. # = 700,000
As displayed in Figure 12 the slope in the linear range of the lift curve was approximately
constant at a value of 0.1137/deg which is similar to the theoretical result of 0.1096/deg. The
maximum lift coefficient value peaked around 1.3 for an angle of attack of 14 degrees and as the
angle of attack increased greater beyond this point flow separation around the airfoil increased. This
decreased the pressure distribution and ultimately the lift force generated on the airfoil. As the angle
of attack decreased to negative values the lift curve followed a similar linear slope until an angle of
attack around negative 9 degrees. At an angle of attack near zero degrees the lift coefficient was not
zero and this was due to the fact that the air foil was cambered. The airfoil geometry resulted in zero
lift for an initial angle of attack near negative 3 degrees. The experimental data followed a similar
pattern to the published data displayed in Figure 13. As the angle of attack increased the published
maximum lift value corresponded to around 1.3, the linear slope of the graph was near 0.11/deg. and
an initial negative angle of attack corresponded to zero lift as indicated by the published results.
In order to determine the relationship between the lift coefficients and drag coefficients
experimental data has been plotted for each angle of attack in Figure 14. Figure 14 has been aligned
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next to Figure 15 which displays similar published data in order to determine the accuracy of the
experimental results.
Re. # = 700,000
Figure 14: Experimental Cl vs Cd for Re. # = 700,000
Figure 15: Published Cl vs Cd for Re. # = 700,000
As displayed by Figure 14, the experimental data represented a vertical drag bucket. The drag
coefficient was minimized at about a value of 0.01 for low values of the lift coefficient. Once the lift
coefficient increased past a value of positive and negative 0.9 the drag coefficient increased sharply.
For an increase in angle of attack a larger amount of drag was observed. The tested results are
deemed accurate since they corresponded to the published data. Figure 15 only includes results below
a lift coefficient value of 1.0, but it still follows a similar pattern for the vertical drag bucket and
value for the minimum drag coefficient for the portion of the plot in Figure 14 below a lift coefficient
value of 1.
Furthermore, the drag coefficient was plotted as a function of the angle of attack as illustrated in
Figure 16 in order to determine the relationship between the two parameters.
Figure 16: Experimental Cd vs α for Re. # = 700,000
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Figure 16 gives insight into how the drag varies as a function of the angle of attack. As the angle
of attack increased further past negative 12 degrees and above positive 12 degrees the drag on the
S805 airfoil increased sharply. This is due to the fact that as the airfoil tilted further in relation to the
streamwise flow the magnitude of the low pressure system in the wake of the airfoil increased.
Additionally, Figure 16 displays the fact that at an angle of attack of zero the drag coefficient was
nonzero at a value near 0.01 which was a result of the airfoil thickness and camber line geometry.
This graph is especially useful since it can be used to determine at what angle of attack the drag
sharply increase which is useful for pilots looking to fly in the most efficient manner.
Finally, the lift coefficient divided by the drag coefficient was plotted as a function of the angle of
attack as illustrated in Figure 17.
Figure 17: Experimental Cl/Cd vs α for Re. # = 700,000
Figure 17 is useful in describing the angle of attack that yields the most efficient lift to drag ratio.
As displayed an angle of attack near eight degrees corresponded with the maximum lift over drag
coefficient. The maximum lift over drag ratio is particular effective in the design of gliders since they
operate as a function of glide angle and Figure 17 can be of use since it illustrates data of that type.
IV.
Conclusions
In conclusion, the two-dimensional experiment analyzed the coefficient of pressure on the upper
and lower surface and the wake of the airfoil for an angle of attack of 16.95 and negative 4.0 degrees.
Additionally experiments on the S805 airfoil were successful in determining lift and drag coefficients
at various angles of attack from negative 20 to positive 20 degrees.
From the recorded data it was determined that the value of the maximum coefficient of lift was
about 1.3 for an angle of attack of 14 degrees. The angle of attack of zero lift was not at zero and
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instead near negative 3 degrees which illustrated the fact that the S805 airfoil was cambered. For
values within the linear range of the lift curve a slope of about 0.1137/deg was examined. Near a
value of 0.01 the drag coefficient was minimized and roughly constant for low values of the lift
coefficient. After the lift coefficient increased past a value of positive and negative 0.9 the drag
coefficient was no longer constant at a minimum value and instead increased sharply. This sharp
increase in the drag coefficient corresponded to an increase in pressure distribution between the
leading edge and trailing edge of the airfoil.
In relation to the NREL/SR-440-6971 S805 airfoil report the experimental results were nearly
identical. At an angle of attack at 16.95 degrees and negative 4.0 degrees the pressure coefficient on
the upper and lower surface was similar to the results in the published data. In each case a net
negative pressure coefficient on the upper surface was found for a positive angle of attack while a net
negative pressure coefficient was found on the lower surface for a negative angle of attack. The
measured and published lift curve followed the same pattern with an initial zero coefficient of lift
near negative three degrees and a linear slope around .11/deg. As the angle of attack increased and
decreased outside this region of linearity the lift coefficient rose to a similar tested maximum
coefficient of lift and then decreased in magnitude for the highest angles of attack. The published
data for the lift coefficient in relation to the drag coefficient corresponded with the measured results
as well. A vertical drag bucket was observed in each plot with a minimum drag coefficient near 0.01.
The published results did not include data points for higher coefficient’s of lift, so for a coefficient of
lift past 1.0 these results could not be compared.
A manometer bank and hot-wire anemometer were used to capture data in the wind tunnel. These
tools were reasonably accurate in measuring data during the experiment because these recorded
values corresponded within a small margin of error to the published S805 report. The manometer
bank precisely displayed the static pressure at each pressure tab around the body of the airfoil. This
pressure distribution around the S805 airfoil ultimately helped determine reasonable values for the
upper and lower pressure coefficient and 2D lift coefficient of the model. The hot-wire anemometer
provided a sensible voltage output corresponding to the airflow velocity in the channel. Data taken
by a traverse of the hot-wire in the wake of the airfoil was effective in computing a reasonable drag
coefficient in comparison to the published results. However error did result from using this tool since
as the experiment continued the temperature in the test section heated up which caused error in the
voltage reading and thus velocity recordings by the traverse. This error was witnessed by a
downward slanting slope of the recorded velocity in the wake.
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Finally, to improve the accuracy of the experiment a pitot-static tube could have been used to
record the pressure in the wake of the airfoil. By using a pitot-static tube it eliminates error in the
hot-wire anemometer caused by a temperature rise in the test section during the experiment.
Additionally, it would have been interesting to see how two-dimensional data of the S805 airfoil
compares with the three-dimensional data. Values for the coefficient of lift, drag and pressure would
have varied since the airfoil spanned the length of the test section and performing a 3D test changes
this parameter so the span is no longer consider infinite.
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