Phys 426 Lab Demo : Lift and Drag

Makena Chapman and Josie Peou

March 5th, 2025

This lab demonstration will investigate the characteristics of starting vortices around an airfoil as well as looking at lift as a function angle of attack (AOA) and flow speed. In both experiments, a fluid (water or air) will flow over the solid body of the airfoil, this flow will exert a force on the airfoil. Lift is the component of the force that is perpendicular to the direction of flow and drag is the parallel component. We know that for lift to occur there needs to be a pressure gradient, with the pressure under the wing being higher and the pressure above being lower to create an upward force.

When an airfoil initially at rest is accelerated in a fluid, the flow is initially irrotational and there is no circulation around the airfoil. As the fluid begins to move, a boundary layer develops along the surface. Near the trailing edge, fluid in this boundary layer does not have enough kinetic energy to remain attached, leading to flow separation. This creates a shear layer that rolls up into a rotating structure known as the starting vortex, which is shed downstream. According to Kelvin’s circulation theorem, the total circulation in a closed system must remain constant, where circulation is defined as

$$ \Gamma = \oint \vec u\cdot d\vec l $$

This implies that the formation of a starting vortex requires an equal and opposite circulation to develop around the airfoil. The circulation around the airfoil increases flow speed over the top surface and decreases it below, producing the pressure difference that generates lift.

The angle of attack, defined as the angle between the airfoil’s chord line and the incoming flow, strongly influences circulation and vortex formation. A positive AOA produces counterclockwise circulation, while a negative AOA produces clockwise circulation, and at a neutral AOA the flow should have minimal circulation. Changing the AOA shifts the dividing streamline near the trailing edge, making it more difficult for the fluid to follow the sharp geometry of the airfoil, which promotes separation and vortex formation. Additionally, any acceleration or deceleration of the airfoil generates vortices.

Under steady flow conditions, lift can be described by the Kutta–Joukowski theorem, which states that the lift per unit span is

$$ L = \rho U \Gamma $$

where $\rho$ is the fluid density, $U$ is the flow velocity, and $\Gamma$ is the circulation around the airfoil. This relationship shows that lift increases with both flow speed and circulation, and since circulation depends on AOA, lift is also strongly dependent on angle of attack. For this theorem to hold, the Kutta condition must be satisfied, requiring that the flow leaves the sharp trailing edge smoothly and that the rear stagnation point lies at the trailing edge. At large angles of attack, strong pressure gradients can cause boundary layer separation, leading to a turbulent wake and a reduction in lift as the Kutta condition breaks down.

In this lab, it is expected that increasing the angle of attack will strengthen circulation and produce more pronounced starting vortices, with their direction depending on the sign of the AOA. Increasing the flow speed should increase the magnitude of lift in accordance with the Kutta–Joukowski relation. At very high or very low angles of attack, deviations from ideal behavior are expected due to flow separation, resulting in reduced lift.

from IPython.display import Image, display
display(Image("whiteboard.jpg", width=640, height=480))

Procedure

Materials for Vortex Experiment

• Carbon Fiber Airfoil
• Plastic Tub
• Blue Dye
• Pipette
• Camera

First we filled the plastic tub with about 3 inches of water. Then while one of us placed the airfoil at the desired AOA and prepared to slide it through the tank, the other filled the pipette with a small amount of blue dye. The dye is used to help visualize the vortex created by the foil, specifically direction of rotation as well as vortex size and speed. Then placing the tip of the pipette at the trailing edge of the airfoil, we deposited the dye and then slid the airfoil through the water. We repeated this process a few times to get the desired situations we wanted to investigate : Neutral AOA, small positive AOA, large positive AOA, small negative AOA, large AOA, and two trials with the same AOA but pulled through the water at varying speeds. See video in the Results section.

Materials for Streamline Experiment

• Carbon Fiber Airfoil (mounted and adjustable)
• Wind Tunnel Apparatus
• Red Laser
• Smoke Machine
• Lab Computer set up to record data

We started by plugging in the smoke machine to wait for it to warm up, once the orange light on the control was on we were able to press the green button to get smoke. The smoke machine was finicky so we were not able to do as many observations of the streamlines as we had originally wanted. We looked at Large/Small Positive/Negative and Neutral AOA. The results for this portion are shown in the second video in the Results section. Then without the smoke machine on we took more measurements of the Lift and Drag using the sensor connected to the lab computer. The lift is measured by an apparatus below where the air foil is placed which measures how much the airfoil is moved vertically and horizontally. This displacement is used to find the force that the airfoil is experiencing and therefore the lift.We looked at a selection of AOA (Large/Small Positive, Large/ Small Negative, Neutral etc.) all at the same wind speed to see the relationship between AOA and lift. The final set of data we collected was from keeping the AOA constant (we chose a small positive angle) and then experimented with 6 different windspeeds to see the relationship between windspeed and lift. This was all recorded on the lab computer and then used for the analysis show in the results and discussion section.

Results

The Tub Experiment – Starting Vortices

The tub experiment successfully visualized the formation and behavior of starting vortices at different angles of attack (AOA) and flow speeds. As predicted:

Note that our airfoil was dragged in the opposite direction as shown in Figure 1, therefore the directions of the starting vortices were expected to be reversed.

from IPython.display import Video
Video("tubexperiment.mp4", width=640, height=480)

• Neutral AOA produced almost no visible starting vortex. This aligns with theoretical expectations, as circulation around the airfoil is minimal at zero angle of attack.
• Positive AOA generated a clockwise starting vortex downstream of the trailing edge. The clockwise rotation corresponds to counterclockwise circulation around the airfoil, which accelerates the flow over the top surface, producing lift.
• Negative AOA created a counterclockwise starting vortex. This rotation indicates opposite circulation, reducing the effective flow over the top surface and decreasing lift.
• Varying speed of the airfoil affected vortex intensity. At higher speeds, the starting vortex formed more rapidly and rotated more strongly, consistent with predictions from the Kutta–Joukowski theorem: higher flow velocity produces greater circulation and lift.

These observations confirm that starting vortex formation is directly related to both the angle of attack and the speed of the airfoil, demonstrating the relationship between flow separation, circulation, and lift.

Wind Tunnel Experiment – Streamlines and Lift

The airfoil was mounted in a wind tunnel, and streamlines were visualized using a smoke machine and red laser. Lift and drag were measured with a force sensor connected to a computer. The goal was to observe how angle of attack (AOA) and flow speed affect lift, flow attachment, and stall behavior.

from IPython.display import Video
Video("streamlines 1.mp4", width=640, height=480)

Observations – Streamlines:

• Neutral AOA: Streamlines adhered mostly to the top surface of the airfoil, with only minor separation near the trailing edge. Lift was minimal.
• Small positive AOA: Flow left the trailing edge smoothly, satisfying the Kutta condition, producing measurable lift. Circulation increased.
• Large positive AOA (stall condition): Flow began separating from the upper surface, and streamlines no longer left smoothly. Lift decreased, showing that the airfoil entered stall.
• Negative AOA: Streamlines left the trailing edge smoothly, but circulation produced less effective lift in the upward direction.

Lift values were taken as a function of AOA at constant flow speed of 20 m/s to show how lift varies with AOA:

Angle of Attack	Average Lift (N)
Neutral	1.04
Small Positive	1.70
Large Positive	2.60
Small Negative	0.53
Large Negative	-0.53

As we see from this data, the lift increases as angle of attack increases, and decreases as angle of attack decreases.

Lift values were taken as a function of wind speed at constant AOA to show how lift varies with flow speed:

Wind Speed (m/s)	Lift (N)	Drag (N)
11	0.85	0.22
16	1.31	0.30
19	1.52	0.34
21	1.72	0.38
22	1.99	0.43
24	2.10	0.48

from IPython.display import Image, display
display(Image("image.png", width=640, height=480))

A quadratic fit of lift vs. speed yielded a correlation coefficient of 0.9918, while a linear fit was slightly less accurate (0.9893). This confirms that lift increases approximately quadratically with flow speed, consistent with the Kutta–Joukowski theorem.

Disscussion

The experiments completed in this lab demo gave a comprehensive view of how starting vorticies, circulation and and lift interacts with an airfoil. In the tub experiment, the formation of starting vortices was observed at different AOA and flow speeds which provided a clear visual demonstration of the circulation theorem. The results (show in the first video) agreed with what theory predicts : a positive AOA created a counter clockwise starting vortex, negative AOA created a clockwise starting vortex, and the neutal AOA created minimal circulation and no significant vortex. When the the speed of the airfoil was increased the behaviour also agreed with the Kutta-Joukowski theorm as it says that Lift is proportional to the flow velocity and circulation, so as flow speed increases so does circulationa and therefore vorticies will intensify. The results confirm that AOA and flow speed change the circultion around the airfoil and thus are circtial in determining lift.

The wind tunnel experiment demonstraighted the effects of AOA and flow speed on streamlines and Llift. The second video in the results section shows that at small positive AOA, streamlines adhered smoothly to the airfoil surface, leaving the trailing edge cleanly and satisfying the Kutta condition. At the largest positive AOA, flow separation occurred along the upper surface, indicating stall, where the boundary layer no longer remained attached, reducing lift despite increasing AOA. Negative AOA produced downward lift as circulation reversed, confirming that circulation direction determines lift direction. The first table in the Results section show that the relation between AOA and lift is linear. The second table shows the numerical results from recording lift at multiple wind speeds with a constant AOA. The plot below this table has the data points plotted in LoggerPro with a curve fit. We tried both linear and quadratic curve fits and we determined the quadratic fit to be best as it had the highest correlation value.

Combining qualitative observations (vortices and streamlines) and collected data shows that lift generation is controlled by circulation, which depends on both AOA and flow speed, while flow separation limits lift at high AOA. Observed vortices and measured lift validate the expected relationship between flow speed, circulation, and lift.

Improvements for Future Experiments

1. Apparatus Improvements : smoke machine did not work well
2. More accurate angles : somehow adjust the apparatus/airfoil so that the exact AOA is known and can be repeated
3. Larger amount of data collected for the second experiment (more AOA and more wind speeds could give a more accuarte relationship with lift)

Conclusion

Conclusion

These experiments conclusively demonstrate the fundamental principles of lift generation in airfoils through circulation and starting vortices. Starting vortices observed in the tub experiment confirm the circulation theorem, showing that circulation develops around the airfoil in response to vortices shed downstream and the direction of the vortex depends on the AOA. Wind tunnel measurements further confirmed that lift increases with AOA up to stall conditions. Streamline observations showed that the Kutta condition is satisfied at moderate AOA, allowing smooth flow and predictable circulation, but fails at high AOA, resulting in stall. The quadratic relationship between lift and flow speed confirms that circulation increases with velocity, reinforcing the dependence of lift on both AOA and flow speed.

In conclusion these experiments illustrate the relationship between circulation, flow speed, and AOA in lift generation.