Investigating The Lift Produced By Aerofoils Biology Essay

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Aerofoils impacted the 20th Century on a massive scale. Before the 20th century no human had piloted a powered aircraft and by the end of it, it was possible to fly half way around the world. Flight has revolutionised the world, it has enabled economies to expand, trading to diversify and changed the way wars are fought. Human migration has changed drastically and cultures mixed all through the development of the aerofoil. An aerofoil is a device that provides a reactive force when in motion relative to the surrounding air. Its concept gives an aeroplane the essential force needed in flight, lift; generated by the properties of the airflow above and below the aerofoil.

An aerofoil works by creating an environment where the pressure above the aerofoil is lower than the pressure below, resulting in a net force acting upwards, lift. There are two ways in which this pressure difference can be generated, either through designing a cambered aerofoil and/or through positioning the aerofoil at an angle to the airflow.

The aim of this experiment is to investigate the effects of changing the angle at which the aerofoils are positioned in the airflow to find the angle of attack which provides the optimum lift for aerofoils.

A History of Flight

The first recorded flight occurred in 1783 with the Montgolfier brothers' balloon on the 4th June in Annonay, France. Their invention of the first practical balloon arose from their trials with paper and fabric bags held over a flame, the hot air filling the bag and causing it to rise. The brothers then demonstrated flight in Annonay market place with a larger paper lined silk balloon; the balloon reached a height of 6,562 feet.

The first passengers to experience flight did so in another Montgolfier hot air balloon on September 19th 1783; in front of Louis XVI, Mary Antoinette and the French Court, a sheep, a rooster and a duck flew for a total of eight minutes. These passengers were soon followed by Pilatre de Rozier and Marquis d'Arlandes in an unteathered balloon in free flight. In early 1784 seven passengers were carried to a height of 3000 feet in a Montgolfier balloon, thought to be powered by 'Montgolfier gas'; merely hot air but thought to be a newly discovered gas lighter than air.

In the late 1700s Sir George Cayley was the first to identify the four forces of flight, weight, lift, drag and thrust and the relationship between them. He was also the first to build a successful human carrying glider. All previous efforts had focussed on mimicking bird flight with flapping wings, these machines, called ornithopters, generated both lift and forward motion at the same time. Cayley was the first to generate plans that resemble today's aircraft with a fuselage, fixed wings, cockpit and rudder controls, he also built various models to demonstrate his ideas.

After studying the way birds glide he noted that they soar for long periods of time through twisting their arched wing surfaces. His designs introduced cambered wings and his trials became the first scientific testing of aerofoils, the source of lift generated in modern aircraft. He even noticed the region of low pressure created above the glider wings which is what causes the lift generated. By 1849 his designs had progressed such that the ten-year-old of one of his servants became the first person to fly a glider successfully, managing a short flight in a Cayley glider.

Fifty years before the first powered flight Cayley designed and constructed a tri-plane glider (shown in Figure 1 .1) with three horizontal wing sections, this was successfully piloted by his coachman over 275 metres before crashing.

Figure 1.1 - The design for Cayley's triplane glider which successfully carried his coachman 275 metres.

In 1901 after many trials, crashes and designs Orville and Wilbur Wright built a wind tunnel in the back of their bicycle shop to test wings that had previously produced 30% less lift than they had calculated. Using balance and spring scales to measure lift and pressure on various different aerofoils. They discovered that much of the data about aerofoils at the time was incorrect and did not take into account important factors affecting flight. They investigated the way the centre of pressure changes with variations in the angle of attack and they found out what the control devices would have to do to give control to the pilot. After testing over two hundred different wing sections the brothers designed their Glider III.

The brothers took the glider to their regular testing ground at Kitty Hawk in North Carolina, America, and over one thousand glides found that the glider worked well and most importantly how they had predicted it to. Now the brothers thought that they were on the verge of a break through in powered flight. In 1903 the Wrights filed for a patent on the design and turned their focus to turning the glider into a flying machine.

Figure 1.2 - The Wright Brother's wind tunnel

They set about trying to add a power source to Glider III and ended up re-designing the whole structure. The motor was to be fixed to the bottom wing of the plane next to the pilot; the propellers, which had also been developed and perfected with the use of the wind tunnel, would push the aircraft rather than pulling it and would rotate in counter directions. For the craft to be a flyer it could not use the dunes at Kitty Hawk to take off, as the gliders did, they needed a mechanism to take off. This was comprised of a car on a length of track on which the Flyer sat, when the flyer reached the correct speed it would then take off and continue into the air. The car was powered by the aircrafts propellers as it was to be a flight completely under the power of the aircraft itself.

The motor itself they had hoped would be designed and built in the automotive industry but a motor with the right specifications never arose and so eventually they had to construct their own with the help of their machinist, Charles Taylor. The engine wasn't quite what they had wanted but they decided to proceed with the testing anyway to avoid further postponements.

After many days of tweaking the machine was ready to be flown and on the 14th December the brothers tossed a coin to see who would get the first flight. Wilbur won and so took his place on the lower wing. On the first attempt the elevator was set too low and so at the end of the car track the flyer crashed nose first into the sand. After three days of frantically trying to fix the aircraft and the weather threatening the flights Orville took his turn in the Flyer. At 10:35 AM on December 17th in front of several witnesses the flyer took off into a twenty-one mile per hour wind with Wilbur running alongside the wingtip to make sure it did not drag along the ground.

Having felt lucky about the day the brothers had placed a camera at the end of the track and instructed a witness, John T. Daniels to close the shutter when the aircraft left the track. From the camera came one of the most famous photographs in the history of aviation. (Figure 1 .3)

Figure 1.3 - One of the most famous photographs in the history of aviation, Orville Wright aboard the Flyer and Wilbur Wright having run alongside the Flyer during take-off.

The Flyer flew for a total of 12 seconds and landed in the sand 120 feet away, the first powered flight in the history of aviation.

The Wright brothers then went back to their home town of Drayton to improve designs and by the autumn of 1905 had flown Flyer III for over half an hour in figure of eight patterns landing back where they had started from.

The development of aerofoils was not greatly investigated until 1915 when the National Advisory Committee on Aeronautics (NACA) stated the need for "the evolution of more efficient wing sections of practical form, embodying suitable dimensions for an economical structure, with moderate travel of the centre of pressure and still affording a large angle of attack combined with efficient action." [1] 

The development of wing designs (Figure 1 .4) up until 1917 had been simply trial and error and it wasn't until NACA published its first work on "Aerofoils and Aerofoil Structural Combinations" when mathematical theory started to be applied to the aerofoil design. One of the problems in the design of wings up until the 1930s was that there was not a wind tunnel large enough to house a full wing, this meant that data could only be recorded on small sections of the wing and then extrapolated out to model a whole wing. This meant that data about the flow of air around the wingtips was not able to be studied until a wind tunnel was available.

Figure 1.4 - Diagram showing the development of aerofoils in the first half of the 20th Century.

Uncertainty and Calibration

Limitations in the accuracy of the measurements occur due to the quality of the instruments being used. Instruments can only measure to a certain resolution, below which the changes in the value being measured are too small to be detected. As the sensitivity of the instruments is increased the precision of measurements increases allowing better, more accurate readings to be recorded.

Calibration of measuring instruments is also required before use in order to avoid systematic error or bias in the readings measured. The deterioration of instruments from their original settings over time can produce readings that differ from the true values by a constant bias. To check for bias uncertainty, a known mass was placed on the balance and checked for consistency, this was also compared to reading taken from other balances. The readings eventually settled and read to within ±0.01g of each other which was sufficient as I would only be reading to one decimal place.

In order to avoid zero error before each reading was taken the fan was switched off and the balance tared, this ensured that readings were taken from the same zero point each time and improved the accuracy of the results.

Whilst taking the results there was quite a lot of continuous fluctuations whilst the balance was settling down, this response time could have caused uncertainty in the results if not accounted for. In order to do this the balance was allowed to settle to within ±0.1g before attempting to take a reading, this also increased the stability of the results taken as this was the greatest source of error due to the non-uniform airflow from the fan.

How Aerofoils Create Lift

In order for something to fly there must be forces acting on the body to counteract gravity, this force is called lift. In aircraft lift is produced by fast moving air passing over an aerofoil, the air moving over the top of the aerofoil moves faster than that travelling underneath. This speed difference creates a difference in pressure which creates the lift needed to fly.

To understand how an aerofoil creates lift it is necessary to consider a few important equations. Equation 3 .1 and Equation 3 .2 shows Bernoulli's equation.

Equation 3.1 - Bernoulli's Equation for viscous flow, where: p = Pressure, ρ = Density of fluid, v = velocity, g = acceleration due to gravity, H = height.

Equation 3.2 - Height remains more or less constant with an aerofoil; therefore Bernoulli's equation can be re-written, independent of height.

Another important equation that is necessary to understand how an aerofoil works is the Continuity Equation, shown in Equation 3 .3

Equation 3.3 - The Continuity Equation, where: ρ = density, v = velocity, A = cross sectional area of flow.

The design of an aerofoil is such that the top surface is curved (as shown in Figure 3 .5) this means that the distance over the top of the aerofoil is larger than the area below. When air is travelling towards the aerofoil it is travelling at a constant velocity, as it hits the leading edge of the aerofoil some of the air passes over the top and some underneath, this point is called the stagnation point. The air which passes over the top of the wing must therefore travel faster than the air underneath as it has to cover a larger distance in the same time. This occurs as the air reaches the trailing edge of the wing at the same time regardless of the route it takes past the wing. From Bernoulli's principle it is therefore possible to see that the pressure must be lower on the top of the wing if the air is travelling faster. The differences in pressure above and below the wing produce the net upwards force which we call lift. (Figure 3 .6)

Figure 3.5 - Diagram showing the dimensions of an aerofoil.

Figure 3.6 - Diagram showing the regions of high and low pressure responsible

For a wing section when the angle of attack varies, the air flow patterns over the wing section change. The lift generated from thin aerofoils starts off with a linear relationship for small angles of attack, and then as the angle increases the relationship becomes more complex. This is because as an object moves through the air, air molecules stick to the surface of the object. This creates a layer of air near the surface of the object called a boundary layer that changes the shape of the object. The air flow over the object is disrupted as the air responds to this boundary layer as it would a physical surface of the object. The boundary layer can also sometimes separate from the physical object and cause larger disruptions to the air flow. This separation effect of the boundary layer is the cause of a wing stall and it occurs when the angle of attack is too large (shown in Error: Reference source not found).

Figure 3.7 - Diagram showing the effect of a wing stall when the angle of attack becomes too large, the boundary layer separates and vortices are created causing turbulence.

Experiment A

Overview

I designed this experiment to introduce the wind tunnel in order to attempt to reduce the effects of turbulence surrounding the aerofoil and create a more controlled environment to test in. Turbulent air from the surrounding environment could create vortices around the wing section disrupting the airflow over the wing and buffeting the wing section. It would cause disturbances in the wing's performance, reducing the effects of lift and so causing inaccuracies in the data.

Diagram

Figure 4.8 - Diagram of equipment setup for experiment A

Method

I set up the equipment as shown in Error: Reference source not found and tared the balance to zero; I then made sure that the balance reading remained at zero to check that the support and balance pan were not in contact with any other equipment as this would have caused large bias (systematic error) and large zero error. After checking for errors I carefully set the angle of the aerofoil to 0° and made sure that the indicator needle was showing 0° on the protractor.

The next step was to check that the readings to be obtained were within the balance's range for negative readings as it was lift that I was going to be measuring. I did this by setting the fan to maximum speed and then altering the angle of attack in rough intervals to ensure that readings across the whole range of angles from 0-90° were suitable.

Now that I had checked all the equipment and conditions for the experiment I was able to start taking results. I reset the aerofoil position and waited for the balance to settle at 0.00g, I then set the fan to the maximum wind speed and recorded readings at 5° increments, each time waiting for the balance to settle. I repeated this process 3 times to have enough readings for an average and then checked to see that the results were consistent and that there was no need to repeat the experiment a further time to obtain better results to eliminate outliers.

The same procedure was then repeated with 3 further wing sections with differing cambers to test the variation in lift provided by a larger difference in upper and lower airflows.

To obtain the lift force in Newtons, the change detected by the top pan balance was then multiplied by the acceleration due to gravity experienced at the Earth's surface (g)

Angle of attack, α

Figure 4.9 - Diagram showing the angle of attack of the wingwhich will be vaired during the experiments.

Results and Observations

Whilst obtaining results it was difficult to read the balance to more than one decimal place as there was so much variation in the last figure, this was to be expected as the air flow over the wing section would be far from consistent with a simple setup as detailed above. Further experiments would have provided attempts to reduce the fluctuations in the air flow around the wing and provide a steadier stream of air flow. This is detailed in later sections on how I would improve the validity of the results in further experiments.

Wing 1

Angle / ° (±1.0)

Average Lift / mN (±0.6)

0

1.6

5

6.2

10

10.1

15

15.0

20

19.9

25

24.5

30

29.7

35

34.3

40

36.9

45

39.6

50

39.6

55

38.9

60

36.9

65

33.7

70

28.4

75

23.2

80

17.0

85

7.8

90

0.0

Table 4.1 - Table showing the average lift in milli-Newtons of a wing section with camber Wing 1 xmm with varying angles of attack (Plotted in Figure 4 .10. See full table in Appendix, Table 7.2)

Figure 4.10 - Plot of data in Table 4 .1 showing the relationship between lift in mN and angle of attack for an aerofoil of camber Wing 1 xmm The uncertainty bars represent ± twice the standard deviation.

Wing 2

Angle / ° (±1.0)

Average Lift / mN (±0.6)

0

2.6

5

5.9

10

11.8

15

16.7

20

21.6

25

26.8

30

32.0

35

36.3

40

38.6

45

38.9

50

37.3

55

37.3

60

33.7

65

29.1

70

24.2

75

17.0

80

9.5

85

2.3

90

0.3

Table 4.2 - Table showing the average lift in milli-Newtons of a wing section with camber Wing 2 xmm with varying angles of attack (Plotted in Figure 4 .11. See full table in Appendix Table 7.3)

Figure 4.11 - Plot of data in Table 4 .2 showing the relationship between lift in mN and angle of attack for an aerofoil of camber Wing 2 xmm The uncertainty bars represent ± twice the standard deviation.

Wing 3

Angle / ° (±1.0)

Average Lift / mN (±0.6)

0

3.3

5

8.2

10

12.1

15

17.0

20

20.6

25

25.8

30

31.1

35

35.3

40

38.9

45

40.5

50

41.5

55

38.2

60

35.3

65

31.4

70

27.5

75

21.9

80

16.7

85

8.8

90

0.7

Table 4.3 - Table showing the average lift in milli-Newtons of a wing section with camber Wing 3 xmm with varying angles of attack (Plotted in Figure 4 .12. See full table in Appendix Table 7.4)

Figure 4.12 - Plot of data in Table 4.3 showing the relationship between lift in mN and angle of attack for an aerofoil of camber Wing 3 xmm The uncertainty bars represent ± twice the standard deviation.

Wing 4

Angle / ° (±1.0)

Average Lift / mN (±0.6)

0

5.9

5

9.5

10

13.1

15

18.3

20

22.6

25

26.8

30

31.4

35

35.6

40

38.6

45

39.6

50

37.3

55

36.3

60

34.0

65

31.4

70

27.1

75

21.6

80

14.7

85

8.5

90

0.7

Table 4.4 - Table showing the average lift in milli-Newtons of a wing section with camber Wing 4 xmm with varying angles of attack (Plotted in Figure 4 .13. See full table in Appendix Table 7.5)

Figure 4.13 - Plot of data in Table 4.4 showing the relationship between lift in mN and angle of attack for an aerofoil of camber Wing 4 xmm The uncertainty bars represent ± twice the standard deviation.

Figure 4.14 - Plot of data in Table 4.5 showing the relationship between lift in mN and angle of attack for aerofoils of different cambers. The uncertainty bars represent ± twice the standard deviation.

Conclusion

From the graphs it is possible to see that the maximum lift was obtained at an angle of attack of between 45° and 50°. This seems to be consistent across all wing sections of differing cambers. There is no obvious stall angle, which occurs where the lift reaches a maximum and then drops rapidly away, explained further in the section How Aerofoils Create Lift. This is surprising as most aerofoils have a stall angle between 15 and 25 but this greatly depends on the speed of the airflow over the wing and the aerofoil design. It would be difficult to explain accurately as to why the results from the experiment differ greatly from the average wing but through measuring the wind speed it may be possible to gain a clearer picture.

The Reynold's number (given in Equation 4 .4) is a numerical value which describes the ratio of the inertial forces (forces to do with the mass of the object) to the viscous forces (the resistive forces provided by the medium through which it is travelling) and the importance of these in given flow conditions. It is used to compare the conditions found in wind tunnel tests on small scale models to the conditions found on full scale wings. It is well known that some characteristics such as the drag and maximum lift coefficients vary with the size of the wing for a given airflow. As a result the wing sections used in wind tunnel tests do not experience the same effects of flow as would a full scale wing, if the wing was to be scaled down by a factor of 4, the flow speed would have to be increased by a factor of 4 to match the Reynold's number in both conditions.

Equation 4.4 - The equation for Reynold's number where ρ = fluid density, V = mean fluid velocity, L = characteristic linear dimension and μ = fluid viscosity. The characteristic linear dimension for an aerofoil is its chord length.

Objects in flow conditions with a low Reynold's number experience laminar flow whilst those with high Reynold's number create turbulent flow with random eddies and vortices.

Laminar flow is a "smooth" uninterrupted flow of air over the surface of the wing. With any type of flow, close to the wing a boundary layer is stationary relative to the wing; as the distance from the wing surface increases, the relative velocity increases. If the boundary layer flows in parallel layers and there are no disturbances causing energy transfer between the layers, the flow is said to be laminar.

From measuring the wind speed and obtaining values for the viscosity and density of air it would be possible to calculate the Reynold's number for the aerofoils being tested and see how these compared to the Reynold''s numbers of full scale wings. Investigating further into this may show that the wind speeds that were tested were too slow to obtain similar airflow over the wing and may give an explanation as to why the angle of greatest lift is so much higher than expected.

Experiment B

Overview

In order to try and observe the effects of the turbulent flow over the wing section I attempted to use methods in the wind tunnel to show lines of flow as they pass over the aerofoil. To show this I attempted to use lines of smoke injected into the wind tunnel test chamber and capture the flow lines using high definition video recordings.

Diagram

Figure 5.1 - Diagram showing the setup for the Experiment B, introducing the smoke to show airflow.

Method

I used a similar setup to that in Experiment A but in order to attempt to straighten the airflow and improve the consistency, I used small sections of drinking straw arranged to create a honeycomb structure placed in the funnel. I then made a small hole in the roof of the wind tunnel and used a gas syringe connected to a thin tube and nozzle to inject a fine stream of smoke into the path of the airflow. This should have shown the flow of the air above and below the wing section and with a high definition video camera positioned to record the flow I would then have played back the video and analysed the flow patterns. I would have looked for the turbulence that occurs when the wing is about to stall and the splitting of the boundary layer (shown in Figure 5.2) which causes the pressure difference to drop and the lift to decrease dramatically.

Figure 5.2 - Image showing the lines of flow at the point of stalling when the boundary layer splits from the wing section [2] 

Conclusion

Attempts to view the smoke as it passed over the wing section were unsucessful, the problems arose when injecting the smoke into the chamber. The smoke used was either not dense enough or simply dispersed far too quickly in the airflow to be picked up by the camera or by eye. To try and improve the visibility of the smoke I increased the intensity of the light used to illuminate the smoke by introducing a strobe light at the end of the wind tunnel. This made the smoke a little visible to the naked eye but still it was not picked up by the camera. If I were to do the experiment again I would try and use dry ice to create the streeamlines and show the flow over the wing. This I think would have a greater contrast to the background and show the lines of flow and the turbulence much more clearly. This would also tell me whether the conditions in the wind tunnel were similar to those found in true flight as it would be possible to see how the flow changes for different angles of attack. When the aerofoil approaches the stall angle of attack the lines of flow separate as they pass over the wing, I could have compared this data with the data recorded in Experiment A and then tested to see whether it was actually the wing stalling which created the loss of lift or if it was another factor. The stall angle of attack for actual wings is usually around 15-25° however the results from Experiment A suggested that this was not the case in this setup.

It would have been interesting to find out whether there was just too much turbulence and disturbance in the air flow for there to be a noticeable point at which the wing stalls. If the wing was in constant turbulent flow there may not have been a point at which it specifically stalled.

Further Experiments

From studying the results in Experiment A I would have liked to perform this next experiment to see what effect the external conditions outside of the wind tunnel would have on the lift. The turbulent air may cause random error to the results which may show fluctuations in the lift created. The airflow over the wing section would be disrupted and so small vortices and currents would be created, affecting the lift generated by the wing section. This kind of turbulence could occur in weather systems were the air currents are rising and falling with different pressure systems created on Earth. Failure of the wing design in a situation like this could have catastrophic effects with loss of control of the aircraft and potentially dangerous situations.

Diagram

Protractor

Figure 6.1 - Diagram of equipment setup for experiment B

Method

I would set up the equipment as shown in Figure 5.1 taking the same precautions to minimise uncertainty in the results, as in Experiment A. I would then proceed to take three sets of results increasing the angle of attack by 5° each time and measuring the lift to one decimal place after the balance had time to settle. Repeating 3 times would improve the reliability of the results and reduce the risk of outliers, the mean of these results would then be taken and plotted to give a graph of the results to show how lift varied with the angle of attack.

Conclusions

From the results I would expect to see a peak at a similar angle but for there to be more variation in the three repeated sets of results. This is because I would expect there to be more fluctuation in the readings taken from the balance due to the extra turbulence created from external conditions.

Appendix

Risk Assessment Table

Hazard

Risk

Level of Risk

Control Measures

Mains electricity supply

Electrocution

Low

Avoid contact with bare wires if present, do not use faulty equipment, do not use equipment when hands are wet

Open backed fan

Entanglement of clothing or equipment in fan blades

Low

Turn off when not in use, make sure all long hair tied back and keep electrical leads etc. clear from rear of fan.

Obstructions

Tripping and falling

Low

Keep work area free of obstructions (i.e. chairs, bags, etc)

Falling Objects

Damage to body parts

Low

Ensure that all heavy equipment (power supplies, fan) are safely on table and steady before starting experiments.

Table 7.1- Risk assessment table for work in the laboratory during experimental work.

Full Results Tables

Angle / ° (±1.0)

Lift / mN (±0.1)

Standard Deviation / mN

Error / mN

1

2

3

Average (±0.6)

0

2.0

2.0

1.0

1.6

0.57

1.13

5

6.9

5.9

5.9

6.2

0.57

1.13

10

10.8

9.8

9.8

10.1

0.57

1.13

15

15.7

14.7

14.7

15.0

0.57

1.13

20

20.6

19.6

19.6

19.9

0.57

1.13

25

25.5

24.5

23.5

24.5

0.98

1.96

30

30.4

29.4

29.4

29.7

0.57

1.13

35

35.3

34.3

33.3

34.3

0.98

1.96

40

39.2

36.3

35.3

36.9

2.04

4.08

45

41.2

39.2

38.2

39.6

1.50

3.00

50

40.2

39.2

39.2

39.6

0.57

1.13

55

39.2

39.2

38.2

38.9

0.57

1.13

60

37.3

37.3

36.3

36.9

0.57

1.13

65

34.3

33.3

33.3

33.7

0.57

1.13

70

28.4

28.4

28.4

28.4

0.00

0.00

75

23.5

22.6

23.5

23.2

0.57

1.13

80

16.7

16.7

17.7

17.0

0.57

1.13

85

6.9

7.8

8.8

7.8

0.98

1.96

90

0.0

0.0

0.0

0.0

0.00

0.00

Table 7.2 - Full results table for the average lift in milli-Newtons of a wing section with camber WING 1 xmm with varying angles of attack

Angle / ° (±1.0)

Lift / mN (±0.1)

Standard Deviation / mN

Error / mN

1

2

3

Average (±0.6)

0

2.0

2.9

2.9

2.6

0.57

1.13

5

5.9

3.9

7.8

5.9

1.96

3.92

10

11.8

10.8

12.7

11.8

0.98

1.96

15

15.7

16.7

17.7

16.7

0.98

1.96

20

20.6

21.6

22.6

21.6

0.98

1.96

25

27.5

25.5

27.5

26.8

1.13

2.26

30

32.4

31.4

32.4

32.0

0.57

1.13

35

36.3

35.3

37.3

36.3

0.98

1.96

40

39.2

38.2

38.2

38.6

0.57

1.13

45

39.2

39.2

38.2

38.9

0.57

1.13

50

38.2

37.3

36.3

37.3

0.98

1.96

55

38.2

37.3

36.3

37.3

0.98

1.96

60

34.3

34.3

32.4

33.7

1.13

2.26

65

29.4

29.4

28.4

29.1

0.57

1.13

70

24.5

24.5

23.5

24.2

0.57

1.13

75

17.7

16.7

16.7

17.0

0.57

1.13

80

9.8

9.8

8.8

9.5

0.57

1.13

85

2.0

3.9

1.0

2.3

1.50

3.00

90

0.0

1.0

0.0

0.3

0.57

1.13

Table 7.3 - Full results table for the average lift in milli-Newtons of a wing section with camber WING 2 xmm with varying angles of attack

Angle / ° (±1.0)

Lift / mN (±0.1)

Standard Deviation / mN

Error / mN

1

2

3

Average (±0.6)

0

3.9

2.9

2.9

3.3

0.57

1.13

5

8.8

7.8

7.8

8.2

0.57

1.13

10

12.7

11.8

11.8

12.1

0.57

1.13

15

17.7

16.7

16.7

17.0

0.57

1.13

20

20.6

20.6

20.6

20.6

0.00

0.00

25

26.5

25.5

25.5

25.8

0.57

1.13

30

32.4

30.4

30.4

31.1

1.13

2.26

35

36.3

35.3

34.3

35.3

0.98

1.96

40

39.2

39.2

38.2

38.9

0.57

1.13

45

41.2

40.2

40.2

40.5

0.57

1.13

50

42.2

41.2

41.2

41.5

0.57

1.13

55

39.2

38.2

37.3

38.2

0.98

1.96

60

36.3

35.3

34.3

35.3

0.98

1.96

65

31.4

31.4

31.4

31.4

0.00

0.00

70

27.5

27.5

27.5

27.5

0.00

0.00

75

21.6

22.6

21.6

21.9

0.57

1.13

80

17.7

16.7

15.7

16.7

0.98

1.96

85

9.8

8.8

7.8

8.8

0.98

1.96

90

1.0

1.0

0.0

0.7

0.57

1.13

Table 7.4 - Full results table for the average lift in milli-Newtons of a wing section with camber WING 3 xmm with varying angles of attack

Angle / ° (±1.0)

Lift / mN (±0.1)

Standard Deviation / mN

Error / mN

1

2

3

Average (±0.6)

0

5.9

5.9

5.9

5.9

0.00

0.00

5

9.8

9.8

8.8

9.5

0.57

1.13

10

13.7

13.7

11.8

13.1

1.13

2.26

15

18.6

18.6

17.7

18.3

0.57

1.13

20

23.5

22.6

21.6

22.6

0.98

1.96

25

27.5

27.5

25.5

26.8

1.13

2.26

30

31.4

31.4

31.4

31.4

0.00

0.00

35

35.3

36.3

35.3

35.6

0.57

1.13

40

39.2

38.2

38.2

38.6

0.57

1.13

45

40.2

39.2

39.2

39.6

0.57

1.13

50

38.2

37.3

36.3

37.3

0.98

1.96

55

37.3

36.3

35.3

36.3

0.98

1.96

60

34.3

34.3

33.3

34.0

0.57

1.13

65

32.4

31.4

30.4

31.4

0.98

1.96

70

27.5

27.5

26.5

27.1

0.57

1.13

75

22.6

20.6

21.6

21.6

0.98

1.96

80

15.7

12.7

15.7

14.7

1.70

3.40

85

9.8

6.9

8.8

8.5

1.50

3.00

90

2.0

0.0

0.0

0.7

1.13

2.26

Table 7.5 - Full results table for the average lift in milli-Newtons of a wing section with camber WING 4 xmm with varying angles of attack

Angle / ° (±1.0)

Lift / mN (±0.1)

Standard Deviation / mN

Error / mN

1

2

3

Average (±0.6)

0

-12.7

-12.7

-11.8

-12.4

0.57

1.13

5

9.8

8.8

10.8

9.8

0.98

1.96

10

26.5

27.5

29.4

27.8

1.50

3.00

15

49.0

47.1

53.0

49.7

3.00

5.99

20

65.7

66.7

67.7

66.7

0.98

1.96

25

82.4

83.4

82.4

82.7

0.57

1.13

30

89.2

90.2

92.2

90.5

1.50

3.00

35

77.5

76.5

77.5

77.1

0.57

1.13

40

87.3

86.3

89.2

87.6

1.50

3.00

45

96.1

95.1

96.1

95.8

0.57

1.13

50

102.0

101.0

101.0

101.3

0.57

1.13

55

105.9

104.9

103.0

104.6

1.50

3.00

60

104.0

102.0

98.1

101.3

3.00

5.99

65

98.1

93.2

90.2

93.8

3.96

7.93

70

85.3

82.4

81.4

83.0

2.04

4.08

75

66.7

65.7

62.8

65.1

2.04

4.08

80

47.1

49.0

51.0

49.0

1.96

3.92

85

26.5

25.5

29.4

27.1

2.04

4.08

90

2.0

2.9

2.0

2.3

0.57

1.13

Table 7.6 - Full results table for the average lift in milli-Newtons of a wing section with camber WING 2 xmm with varying angles of attack with the airflow restricted by the funnel.

Works Cited

'Aviation Timeline'. (n.d.). Retrieved April 23, 2010, from Century of Flight: http://www.century-of-flight.net

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