Effect of the length of a winglet on the lift of an aerofoil

Jason André Dias

Candidate Number: 000040-0062

Physics United World College Of South East Asia

May 2014

Supervisor Frazer Cairns

Word Count: 3996

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Acknowledgements This Extended Essay would not have been at all possible without the guidance and counsel of my supervisor, Fraser Cairns. His support and help throughout the process was of great help. Furthermore my thanks extend to the Design & Technology department for their generous support, especially to Carl Waugh for his guidance in the construction of the wind tunnel, and his provision of department resources. My thanks also go to my family, who were very encouraging throughout. I’d like to also thank my father, for his passion of aviation he passed down to me, inspiring me to write my extended essay in this field.

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Abstract This paper poses the question, how does winglet length effect lift? The purpose of this investigation was to determine the enhanced lift that could be achieved through varying winglet length thereby increasing efficiency. To further investigate the outcomes, the lift data was compared to theoretically determined lift with identical wingspan variation. This assessed the appropriateness of winglet use in the future development of larger yet spatially suitable aircraft. A constructed NACA 0015 aerofoil was placed within a homemade wind tunnel, which operated at a tunnel velocity of 5.05 m s-1 and Reynold’s number of around 32477. The aerofoil had a chord length of 100 mm and was analysed with, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 centimetre winglet attachments. A constant angle of attack of 8° was controlled. It was determined that lift was increased with an increase in winglet length. The initial relationship was linear with some reduction in lift at greater winglet lengths. When comparing lift due to winglet length variance in comparison to wingspan variance it is clear that winglets are at their most effective in increasing effective wingspan at lower winglet lengths. The study concludes that the use of winglets can increase effective wingspan making winglet length an important design factor for large aircraft that brink airport wingspan regulation. Word Count: 219

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Table of Contents Acknowledgements ..................................................................................................... ii

Abstract ....................................................................................................................... iii 1. Introduction .............................................................................................................. 5

2. Aerodynamic Theory ............................................................................................... 6 2.1 Size Effects on Lift ........................................................................................................... 6

2.2 The Lift Equation ............................................................................................................. 6 2.3 The Lift Coefficient .......................................................................................................... 7 2.4 Reynold’s Number ........................................................................................................... 7 2.5 The Downwash Effect ...................................................................................................... 8 2.6 Winglets ........................................................................................................................... 9

3. Apparatus & Instrumentation .............................................................................. 10 3.1 Wing Design ................................................................................................................... 10

3.2 Wind Tunnel Design ...................................................................................................... 12 3.3 Winglets ......................................................................................................................... 13

4. Procedure ................................................................................................................ 14 4.1 Apparatus Set Up ............................................................................................................ 14

4.2 Method ........................................................................................................................... 15 4.3 Variables ........................................................................................................................ 16

5. Experimental Results ............................................................................................. 17 5.1 Table of Results .............................................................................................................. 17 5.2 Graph showing the relationship between lift and winglet length ................................... 17

6. Validity Analysis .................................................................................................... 19 6.1 Calculating the Reynolds Number ................................................................................. 19 6.2 Calculating CL ................................................................................................................ 19 6.3 Comparison of Theoretical and Experimental Results ................................................... 20 6.4 Error Analysis ................................................................................................................ 21

7. Comparison of variance in wingspan against variance in winglet length ......... 22 7.1 Effective Wingspan by Winglet Length ......................................................................... 22 7.2 Calculating lift by wingspan .......................................................................................... 22 7.3 Comparison of lift in winglet & wingspan variance ...................................................... 23

8. Results & Discussion .............................................................................................. 25 8.1 Winglet length and lift .................................................................................................... 25

8.2 Lift comparison of winglet length & wingspan variance ............................................... 26

9. Limitations & Errors ............................................................................................. 27 9.1 Winglet ........................................................................................................................... 27 9.2 Aerofoil .......................................................................................................................... 27 9.3 Wind Tunnel ................................................................................................................... 27

10. Conclusion ............................................................................................................ 28 11. Appendix ............................................................................................................... 29

11. 1 Nomenclature .............................................................................................................. 29 11.2 Table 1 NACA 0015 aerofoil coordinates ................................................................... 30 11.3 Table of Results ............................................................................................................ 31

Bibliography ............................................................................................................... 33

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1. Introduction In an increasingly competitive market, the aviation industry has been extending the frontiers of flight. Ever rising fuel costs, as well as escalating environmental concerns have pushed the industry to further improve fuel efficiency. Airlines and aircraft manufacturers alike are paying millions of dollars in research to reduce fuel costs. The research in this paper focuses on adjusting elements of the wing’s aerodynamic properties to enhance lift, thus creating a more fuel-efficient aircraft. Airport regulations are a limiting factor in the size of future aircraft. The wingspan regulations do vary across airports however the largest allowed wingspan is currently imposed under ‘F’ category “65m up to but not including 80m” (Coorperate Development of Operational Safety and Continuing Airworthiness (COSCAP) 1999, 17). By further investigating the effect that winglet length has on lift and how this determines effective wingspan, we may be able to overcome airport regulations. The wingtip is the structure furthest from the fuselage of the aircraft, it is situated at the very tip of the wing. Its main purpose is reducing the downwash effect. This is caused by the vortices, which occur due to air escaping around the edge of a wing from a region of high pressure under the wing to a region of low pressure on top of the wing (NASA 2008). The effect of this is a reduction in lift. It is approximated that during the climb phase 80-90% of the total reduction is caused by this effect, whilst 40% of the reduction in lift is caused by this effect during cruise. (Ning and Froo 2008). The result of this is known as the “downwash effect” (NASA 2008). The outcome of years of research in this field in the optimization of winglets to most efficiently reduce the lift reduction component produced by the wingtips has led to more efficient fuel consumption as well as giving aircraft manufacturers the ability to produce much larger aircraft. A good example is the Airbus A380, which in fact needs a wingspan of around 90 m to be most efficient. However the design of the wing tip fences (providing a similar effect as wingtips) allows the A380 to generate enough lift placing it within the airport regulations of 80m.) The design of the wingtips allowed the aircraft to achieve an effective wingspan equal to 90 m whilst physically only having a wingspan of 80 m (Burns and Novelli 2008). This paper focuses on the optimization of these winglets in an attempt to understand how they can be modified for optimum efficiency. My research question is:

How does the length of a wingtip effect the lift of an aerofoil? In order for this experiment to be carried out, a wind tunnel, aerofoil and winglets with varying length will need to be constructed. By measuring the change in mass of an aerofoil when winglet length is varied the lift force can be calculated. For the calculation and analysis of factors, Newton’s Laws will be applied as well as other more complex aerodynamic theories including the downwash effect, Reynold’s number calculation and Coefficient of Lift calculations. These will be discussed in sections to follow.

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2. Aerodynamic Theory

2.1 Size Effects on Lift In order to analyse the outcome of winglets, and their benefit on air travel, a constant for the relationship between lift and the wingspan needs to be established. From this we can determine the lift produced based on the span of the wing. Theory states: “Lift is directly proportional to the area of the object” (NASA: C 2010) As we are only analysing the lift produced by an aerofoil, we are only observing the lift that is created by the planform area1. This can be shown: Where: L is Lift (N) S is Planform area (m2) (1.1)

OR Defined by a constant (1.2) In defining k, we will be able to determine the lift associated with varying wingspans.

2.2 The Lift Equation Lift is dependent on a variety of different factors including atmospheric conditions such as air density, viscosity and compressibility as well as object characteristics including the speed at which the object travels, the shape of the body, and its inclination. Some of the more complex aerodynamic factors are included in the Lift Coefficient (CL). Lift is defined be NASA as the following equation (NASA: A 2010) Where: L is Lift (N) ρ is Air density (kg m-3) v is True airspeed (m s-1) S is Planform area (m2) CL is the Coefficient of Lift (1.3)                                                                                                                1 The planform area is defined as, “the area of the wing as viewed from above the wing. It is a flat plane, and is not the total surface area (top and bottom) of the entire wing” (NASA: C 2010)

L = 12ρvSCL

L = k ⋅S

L ∝S

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2.3 The Lift Coefficient The lift coefficient encompasses the more complex dependencies on the flow conditions of lift. Mathematically it is a simple rearrangement of the lift formula. (NASA: B 2009) (1.4) Using a wind tunnel and an aerofoil, the velocity, air density and planform area will be controlled to measure the lift produced. From this we are able to determine the lift coefficient.

2.4 Reynold’s Number Reynold’s number represents the interactions between an object that moves through the atmosphere and the atmosphere itself. The aerodynamic forces that are generated are dependent on speed, shape, mass and the compressibility and viscosity of the gas. These are dependent on various factors including altitude and relative humidity. The Reynolds number is given by the formula: Where: Re is Reynold’s Number l is Characteristic Linear Dimension2 (m) µ is Dynamic viscosity (m2

s-1) k is Kinematic viscosity (kg m s-1)

(1.5) (NASA: A 2009)

                                                                                                               2 Typically the chord length of an aerofoil is used

CL =L

12ρv2S

Re =ρ vlµ

= vlk

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Figure 1.0 – “The Downwash Effect” (NASA 2008)

2.5 The Downwash Effect The effect investigated is known as the downwash effect. The basis of this effect is that when a wing experiences lift, the pressure on above the wing is smaller than the pressure below the wing. At the tip of the wings the air is free to move between these two regions, shown in Figure 1.0 below.

The blue lines illustrate the flow that results from the exchange of air between the area of high pressure below the wing and low pressure above the wing, where the arrowheads show the direction of the flow. The vortices that are formed rotate toward the wing root, and the line marking the centre of the wing tip vortices are known as vortex lines. The downwash that is created from these vortices cause a reduction in the lift of the aerofoil (NASA 2008)

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2.6 Winglets Winglets were designed for the purpose of eliminating the vortices, therefore reducing the effect of the reduction of lift. The study conducted will investigate what effect if any; changing the length of the winglet will have on minimizing the downwash effect and maximising lift of the aerofoil.

As seen above in Figure 1.1, the vortices that usually occur without the use of winglets are not apparent when winglets are used. In this case, the winglets block the ability for the high pressure air to escape from the underside of the wing to the lower pressure area on top of the wing. This minimizes the air that is able to escape around the end of the wing minimizing the downwash effect and therefore decreasing any reduction of lift. From this and the previously mentioned downwash effect, we can infer that as we increase the length of the winglet more vortices will be blocked. We can predict that, an increase in the length of the winglet will lead to an increase in the lift produced. This relationship is yet to be established.

Figure 1.1 – The effect of a winglet (National Geographic 2012)

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3. Apparatus & Instrumentation

3.1 Wing Design In order to create a realistic test for finding the most efficient length of the winglet a realistic model aerofoil was constructed. The University of Illinois Applied Aerodynamics Group – Aerofoil Data site (University of Illinois 2013) was used for realistic real world aerofoil plotting coordinates. This particular aerofoil was chosen specifically for its stability. Stability was important as the materials used in this experiment were not of high-grade quality and therefore stability was favoured to reduce vibrations and other movements of the aerofoil to reduce error. Furthermore the symmetrical nature of the aerofoil reduced complexity in construction. For this investigation a NACA 0015 aerofoil was utilized, developed by The National Advisory Committee for Aeronautics (Jacobs, Ward and Pinkerton 1933) For experimentation a 0.1 m chord aerofoil will be used where α=8.0° ± 0.5°

Figure 1.0 – NACA 0015 (University of Illinois 2013)

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In order to construct the aerofoil coordinates for the NACA 0015, aerofoil data coordinates were used in Adobe Illustrator (Adobe 2012). Five wooden templates of thickness 5 mm were printed and attached to a plywood shaft to form the framework of the aerofoil of span 0.105 m. (All measurements are seen in Table 1.0 below). Following this the wood was wrapped in a card, to provide a smooth finish. This can be seen in Figure 2.1 below.

Table 1.0 – Table of measurements for aerofoil

Chord Length c (m) ± 0.001 m Span s (m) ± 0.001 m Planform Area S (m2) ± 0.002 m2

0.100 0.105 0.011

Figure 2.1 – Diagram of aerofoil chord length and photo of completed aerofoil showing span of 105 mm

100mm  

105  mm  100  mm  

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3.2 Wind Tunnel Design For construction, a number of materials were used including:

• Plywood • Acrylic Plastic Sheets • Thick Drinking Straws • Styrofoam

To ensure that there was laminar flow passing through the wind tunnel a honeycomb structure of straws was produced which acted as a diffuser. This ensured that the air produced by the blower flowed in straight lines before it made any interactions with the aerofoil. Sown in Figure 2.2 below.3

                                                                                                               3 Many of the design ideas implemented for this construction came from an online video, found at http://www.youtube.com/watch?v=i0Q0nx0_Dgc (Punsiri Dam-o 2010).

Acrylic Sheets 700 mm x 115 mm

Plywood Base 700 mm x 110 mm x 5 mm

Hole in plywood – 10 mm

Diffuser - Diameter of each straw: 10 mm.

Figure 2.2 – Wind Tunnel – Finished Construction (Labelled)

Styrofoam – blocking escapable air

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3.3 Winglets The winglets were of very simple design, made from recycled cardboard and cut using a cardboard knife and ruler. The design simplicity is shown in Figure 2.3 below displaying an example of an 80 mm winglet attached to the NACA 0015 aerofoil.

A final constructed version of the above aerofoil is shown in Figure 2.4 below. As seen this is the aerofoil with 80 mm winglets attached.

Figure 2.3 – Plan diagram of 80 mm winglet attached to the NACA 0015 aerofoil.

80 mm

Figure 2.4 – Constructed aerofoil example with 80 mm winglets attached

80  mm    

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4. Experimental Procedure

4.1 Apparatus Set Up The equipment was set up as shown in Figure 3.0 below.

As seen in Figure 3.0 above, a mass balance was set up directly below the aerofoil testing area. The base of the aerofoil structure rested on the weighing scale and measured changes in mass readings. The aerofoil was attached to the pole, with the base lying on the weighing scale where α = 8.0° ± 0.5°. The tunnel velocity was set to 5.05 m s-1 ± 0.01 m s-1. The diffuser represented in Figure 3.0 above is shown photographically in Figure 3.1 below.

Figure 3.0 – Experimentation setup

Figure 3.1 – Photograph showing straw diffuser

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4.2 Method Once the air blower was turned on the mass reading was observed for 30 seconds before the air was turned off again. It was the experimenter’s duty to perceive the correct value and note what error existed during the fluctuations that occurred. This was to be done 6 times for each winglet. The winglet length was varied through 0 mm and 100 mm with 10 mm increments.

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4.3 Variables Independent: Winglet length – this will increase from 0 mm to 100 mm with 10 mm increments Dependent: Mass reading of aerofoil Controlled: The airspeed needs be kept constant throughout all experiments as this has a direct effect on the lift that is produced. At higher airspeeds more lift is produced by an aerofoil, as such a Frederikson Air Blower will be used which is capable of maintaining a wind speed within an error of ± 0.01 m s-1. For this experiment the fan controller was set to a constant airspeed of 5.05 m s-1 ± 0.01 m s-1. Another variable that had to remain constant was the temperature due to its direct effect on the Reynold’s number. If varied, there would be a significant effect on the lift produced by the aerofoil. This variable was hard to control however a temperature probe indicated 23.0 °C ± 0.5 °C which remained constant throughout experimentation. The planform area was another factor that had to remain constant throughout experimentation, it has a direct impact when calculating CL as well as having an effect on the measured lift that is produced on the aerofoil. A single aerofoil was used for all experiments keeping the planform area constant throughout. A planform area of 0.011 m2 ± 0.002 m2 was maintained. The span and chord length of the aerofoil determined this.

The different characteristics of an aerofoil such as chamber size and general shape has great effects on the lift. As such a symmetrical NACA 0015 aerofoil was used for all experiments which provided great stability where lift was 0 when α = 0°. The angle of attack must also remain constant throughout experimentation as it affects the lift that is produced by the aerofoil. The total angle considering the angle of the pole and the angle of the aerofoil attached to the pole is measured to be 8.0°± 0.5°. It was also checked after changing winglets of the aerofoil to ensure that this angle was maintained.

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5. Experimental Results

5.1 Table of Results Winglet Length (m) ± 0.001 m

Average Change in Mass (kg) Lift (N) Wind speed (m s-1) ± 0.01m s-1

0.000 0.0036 ± 0.0002 0.035 ± 0.002 5.05 0.010 0.0041 ± 0.0002 0.040 ± 0.002 5.05 0.020 0.0046 ± 0.0002 0.045 ± 0.002 5.05 0.030 0.0051 ± 0.0002 0.050 ± 0.002 5.05 0.040 0.0055 ± 0.0002 0.054 ± 0.002 5.05 0.050 0.0061 ± 0.0003 0.060 ± 0.003 5.05 0.060 0.0068 ± 0.0003 0.067 ± 0.003 5.05 0.070 0.0076 ± 0.0004 0.075 ± 0.004 5.05 0.080 0.0069 ± 0.0004 0.068 ± 0.004 5.05 0.100 0.0050 ± 0.0004 0.049 ± 0.004 5.05

Table 3.0 – Averaged Results and calculated Lift

Table 3.0 above shows processed experimental data for all attached winglets as well as the lift force, which was calculated afterward. Due to the nature of the final two results, they will not be included in any graphical representations. This will be evaluated in section 8.3 Limits and Errors.

5.2 Graph showing the relationship between lift and winglet length

As seen in Figure 4.0 below, a linear relationship is present between winglet lengths, 0 m and 0.06 m. We can note, that the graph is linear, and has increasingly large error bars. The size of the errors increased due to a corresponding increase in the vibrations and movement when the winglet lengths increased. This was due to air being deflected by the winglets upward and rebounding off the wind tunnel lid causing greater fluctuation in the measurement of mass readings. The effect of this will be assessed in the Limits & Error section.

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Figure  4.0  –  Graph  showing  the  relationship  between  lift  and  winglet  length

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6. Validity Analysis The purpose of the following section is to identify the validity of the results produced through the comparison of the experimental CL and a theoretically modeled CL. Along with experimental data that was recorded, there were a variety of additional recordings that were required for further calculations, especially for calculation of the Reynolds Number for the wind tunnel. The figures noted in Table 4.0 show various climatic and geographic measurements for UWCSEA, Dover on the 15th June 2013. (Date of Experimentation) Air Pressure hPa ± 0.5 1006.0 Temperature (°C) ±0.5 23.0 Elevation above Sea Level (m) ±3 23 Relative Humidity % ±0.5 72.0

Table 4.0 – Weather /Geographic Conditions for Singapore 15/06/13\ (Weather Underground 2013)

6.1 Calculating the Reynolds Number

(1.5)

As seen from the calculations above the Reynolds number for the wind tunnel created stood at the nominal value of 32477.65.

6.2 Calculating CL For a NACA 0015 air foil without winglet modification

(1.4)

This value obtained when: Re = 32477.65 ± 0.02 α = 8.0°± 0.5°

Re =ρ vlµ

= vlk

ρdry =pR ⋅T

ρdry =100600287 ⋅296

ρdry = 1.18 ± 0.01

Re =(1.18)(5.05)(0.1)(1.8348E − 5)

Calculation  for  ρ  

Re = 32477.65 ± 0.02

CL =L

12ρv2S

CL =0.035

12(1.18) ⋅(5.05)2 ⋅(0.011)

CL = 0.21± 0.04

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6.3 Comparison of Theoretical and Experimental Results In order to validate the structural design implementation of both the wind tunnel and the NACA 0015 aerofoil the Coefficient of Lift will be compared under the conditions:

As seen in Table 4.1 above, our final calculation for the lift coefficient value when α = 8.0°±0.5°, and no winglet is attached is 0.21 ± 0.04. The theoretical value calculated using the JavaFoil (Hepperle 2006) software under the same conditions was 0.210. This means that the experimental value for the lift coefficient of the NACA 0015 lies within the theoretical value that was calculated using the software.5 From this comparison we are able to accept that the data collected was valid and actually reflected theoretical calculations for the NACA 0015 aerofoil. A random error of 22% was calculated which originated from fluctuations in mass readings, error on climate data, wind speed and measurement errors on the planform area. A 22% error is quite significant, where the largest part of the error was due to measurement inaccuracy, causing 18% error. This error could have been reduced by increasing the scale of the aerofoil produced, by increasing the size of the aerofoil there would be a reduction in the percentage error calculated. The nature of the experimentation meant however that very high-grade materials and construction techniques would need to be used to minimize error. For example, a completely isolated wind tunnel with no gas seepage, as well as 10 different constructed aerofoils with their winglets constructed as one rather than interchangeable ones. The errors that were confronted in experimentation were very difficult to avoid given available resources.                                                                                                                4 AR given by the formula s

2

A

5 This software enabled us to set, Aspect Ratio, wing size, kinematic viscosity, air density, and vary the Reynolds Number. The aerofoil could be modelled directly into the software using the data coordinates as such enabling us to create an identical wind tunnel situation as the experimentation carried out in the lab. (JavaFoil - Analysis of Airfoils 2006)

α=8.0° ±0.5 Re = 32477.65±0.02 AR = 1.00 4

Experimental

Theoretical

ω ± 0.001 (m) CL CL 0.000 0.21 ± 0.05 0.210 0.010 0.24 ± 0.05 - 0.020 0.27 ± 0.06 - 0.030 0.30 ±0.07 - 0.040 0.33 ±0.07 - 0.050 0.36 ± 0.08 - 0.060 0.40 ± 0.09 - 0.070 0.45 ± 0.1 -

Table 4.1 – Comparison of theoretical and experimental values

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6.4 Error Analysis

- % Error on R R – Absolute Error on R

6.4.1 Multiplication & Division of measured quantities Error Propagation on the calculation of CL

(1.4)

6.4.2 Multiplication with a constant

(1.0)

The errors calculated in this section will be evaluated in the, Limits and Error Section.

δR∂

δCL =δ LL

⎛⎝⎜

⎞⎠⎟ •100 +

δρρ

⎛⎝⎜

⎞⎠⎟•100 + δv

v⎛⎝⎜

⎞⎠⎟ •100 +

δSS

⎛⎝⎜

⎞⎠⎟ •100

δCL =0.0010.035

⎛⎝⎜

⎞⎠⎟ •100 +

0.011.18

⎛⎝⎜

⎞⎠⎟ •100 +

0.015.05

⎛⎝⎜

⎞⎠⎟ •100 +

0.0020.011

⎛⎝⎜

⎞⎠⎟ •100

δCL = 22.08%

L =mg∂L = g ⋅δm

∂L = 9.81⋅0.0002∂L = 0.001

CL =L

12ρv2S

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7. Comparison of variance in wingspan against variance in winglet length

7.1 Effective Wingspan by Winglet Length By increasing the winglet length, we have increased the effective lift that the wing can produce. In order to compare the effect that increasing winglet length had, it will be compared to lift increases resulting from an increase in wingspan. As such, we will be able to analyse the effective wingspan through increase in winglet length.

7.2 Calculating lift by wingspan (1.1)

From this we have calculated our constant in the relationship between the lift produced by our wing and its planform area. Through this we are able to calculate the Lift produced by increasing planform area through the exclusive increase of wingspan. This is shown in Table 4.2 below. Where chord length (c) is constant at 0.1m. Wingspan s (m) Planform Area (S) m2 Lift (N) 0.11 0.011 0.035 0.13 0.013 0.041 0.15 0.015 0.048 0.17 0.017 0.054 0.19 0.019 0.060 0.21 0.021 0.068 0.23 0.023 0.073 0.25 0.025 0.080 Table 4.2 – Lift caused by increase wingspan (s)

L = k ⋅S

k = 0.0350.011

k = 3.18

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7.3 Comparison of lift in winglet & wingspan variance In Table 4.3 below we are able to more easily compare the lift produced at different wingtip lengths and different wingspans.

As seen in Table 4.3 above, the increase in lift with increased winglet length varies similarly to the increase in lift by increasing wingspan. This can be observed in Figure 5.0 below.

Varying Winglet Length Varying Wingspan (Theoretical)

ω ± 0.001 (m) Lift (N) s (m) Lift (N) 0.000 0.035 ± 0.002 0.11 0.035 0.010 0.040 ± 0.002 0.13 0.041 0.020 0.045 ± 0.002 0.15 0.048 0.030 0.050 ± 0.002 0.17 0.054 0.040 0.054 ± 0.002 0.19 0.060 0.050 0.060 ± 0.003 0.21 0.068 0.060 0.067 ± 0.003 0.23 0.073 0.070 0.075 ± 0.004 0.25 0.080

Table 4.3 – Comparison of Lift in winglet & wingspan variance

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Lift - Wingspan

Lift – Winglet Length

Figure 5.0 – Comparison of Lift in Winglet & Wingspan Variance

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8. Results & Discussion

8.1 Winglet length and lift As seen in Figure 3.0 there is a linear relationship between the length of the winglet and lift (force) that was produced. We note that as we increase winglet length, there is a corresponding increase in the lift produced. As discussed previously, the winglets purpose is to reduce the downwash effect, increasing the wings capable lift. As seen in the graph, we are able to partially accept this hypothesis given the results. What we can infer from this is that as the tips lengthen they are able to block part of the vortices produced, which in turn reduces the induced lift reduction causing lift to increase. As a result we can confirm that as the winglet length increases it reduces the downwash effect therefore reducing the reduction in lift caused. We may assume that a certain ‘optimum’ point exists when no more seepage of air from below the wing to the top of the wing is occurring and increasing the winglet length will have no further effect. In Figure 3.0 we do note that, at increased winglet lengths there is tendency for there to be some reduction in the lift as the relationship is not entirely linear. Unfortunately this is not entirely clear due to increasing error.

A representation of the assumed curve is shown above in Figure 4.1. At first there is a linear relationship, where lift increases proportionally to increases in winglet length up to a certain point. After this point there is a plateau suggesting that increases in winglet length no longer provide a corresponding increase in lift.

Lift  (N)  

Winglet  Length  (m)  

Figure 5.1 – Assumed Curve

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8.2 Lift comparison of winglet length & wingspan variance Through further data processing, we graphed the theoretical lift caused by an increase in wingspan. Graphing this in Figure 4.0 above we note a linear relationship with gradient k, as calculated to be 3.18. This constant is used to graph the points to observe an increase in lift as the wingspan increases. Graphed with this, we have added the points of lift against an increase in winglet length. Through this we are able to determine the effective wingspan that an aerofoil has, with a particular winglet length attached. Each red point plotted illustrates lift due to winglet variance and correlates to a blue point showing lift due to wingspan variance. As seen, the gaps between winglet length and corresponding wingspan increase as we increase in the winglet length.

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9. Limitations & Errors

9.1 Winglet The winglets required better construction as the use of recycled cardboard resulted in extrusions on some winglets, which effected vibration and movement of the entire aerofoil that could not be accounted for. This contributed to the 22% random error that was propagated and originated from the initial fluctuations in lift reading that was recorded. The error on mass readings only transmitted a 2.86% error, this comprised of errors originating from the aerofoil and winglets, wind speed frequency, and wind tunnel combined.

9.2 Aerofoil The aerofoil used in experimentation was accurately constructed. It was produced using the Design Technology Laser cutter. The card was carefully pasted tightly to the aerofoil frame to create a smooth surface. Unfortunately where the pole was attached to the aerofoil, there will have been some disturbance in the air flow over this area and therefore caused some error on readings and again would have contributed to the error calculated due to mass fluctuation. Measuring the aerofoil proved to generate the largest error. An 18% error was calculated from the calculation of planform area. To avoid this problem, one of two things could have been done, a more accurate measuring device could have been used, or a larger wing should have been used. By increasing the scale of the aerofoil model, percentage errors begin to decrease although absolute errors remain the same.

9.3 Wind Tunnel The wind tunnel propagated most error on readings when using longer winglet lengths. The problems originated from the size of the wind tunnel, due to the increasing length of the wing tips. As length increased, the winglets neared the ceiling of the wind tunnel. Increasing vibrations were observed as the length of the winglet increased as air travelled along the edge of the winglet toward the ceiling and rebounded back causing down force as well as movement. This can be seen clearly in Figure 3.0 above, where the error bars increase as the length of the winglets increases. The error was generated from the increasing fluctuations on the weighing scale increasing the random error produced. As mentioned above, (shown in Table 2.0) the final two results were heavily affected by this phenomenon causing reductions in the lift rather than increases. Furthermore, the airspeed produced by the air blower caused further fluctuations of mass due to slight variances in wind speed. More concise construction of the wind tunnel, paying close attention to reducing random, lateral movements would have eliminated mass fluctuation on the readings.

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10. Conclusion The research that was conducted on the NACA 0015 aerofoil, had the aim: To investigate how the length of a wingtip will effect the lift of an aerofoil The lift was analysed and compared to theoretical data backing the reliability of the capacity for the NACA 0015 aerofoil. The tests were done in a stable environment in a self-constructed wind tunnel at Re 32,477 and α = 8.0°. It was discovered that a linear relationship exists between the length of the winglet and the amount of lift that is produced on an aerofoil. It was observed that as the length of the winglet is increased, there is a corresponding increase in the lift that is produced by the aerofoil. It was expected that the amount of lift produced by the aerofoil would level at a maximum point, due to the vortices no longer leaking from beneath the wing to atop. This was observed through lift reduction in longer winglets where they became less effective. To further investigate the capacity of increasing the winglet length, the data was compared to data comparing lift to a corresponding increase in wingspan. It was noted from this that at shorter winglet lengths there was comparable lift produced with a corresponding increase in wingspan. At greater winglet lengths there was a reduction in lift produced thus making an increase in wingspan more effective then increase in winglet length. The data is conclusive whereby increasing winglet length, wingspan can be reduced, with lift remaining constant. The data is conclusive; winglet length has a linear relationship to the lift that is produced by the aerofoil. From this, we must begin to consider the costs. Which is more cost effective? Are the use of winglets a comparable lift enhancing mechanism compared to the simple increase in wingspan on a construction cost standpoint?

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11. Appendix

11. 1 Nomenclature c Chord s Span v True airspeed L Lift force CL Coefficient of Lift Re Reynold’s number α Angle of attack ρ Air density g Gravity S Planform area µ Dynamic viscosity k Kinematic viscosity l Characteristic linear dimension m Mass g Gravity6 p Pressure T Temperature R Specific gas constant for dry air 7 ω Winglet length AR Aspect Ratio

                                                                                                               6 Acceleration due to Gravity, g as 9.81 m s-2 (TheEngineeringToolBox.com 2013) 7 Specific Gas Constant (Dry Air) as 287 K-1 kg-1

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11.2 Table 1 NACA 0015 aerofoil coordinates

Upper Surface X Y

1.000000 0.001580 0.950000 0.010080 0.900000 0.018100 0.800000 0.032790 0.700000 0.045800 0.600000 0.057040 0.500000 0.066170 0.400000 0.072540 0.300000 0.075020 0.250000 0.074270 0.200000 0.071720 0.150000 0.066820 0.100000 0.058530 0.075000 0.052500 0.050000 0.044430 0.025000 0.032680 0.012500 0.023670 0.000000 0.000000

Lower Surface X Y

0.000000 0.000000 0.012500 -0.023670 0.025000 -0.032680 0.050000 -0.044430 0.075000 -0.052500 0.100000 -0.058530 0.150000 -0.066820 0.200000 -0.071720 0.250000 -0.074270 0.300000 -0.075020 0.400000 -0.072540 0.500000 -0.066170 0.600000 -0.057040 0.700000 -0.045800 0.800000 -0.032790 0.900000 -0.018100 0.950000 -0.010080 1.000000 -0.001580

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11.3 Table of Results Trial #1 Winglet Length (m)

±0.001m Initial Mass (g) Final Mass (g)

0.000 0 -3.7 ± 0.2 0.010 0 -4.1 ± 0.1 0.020 0 -4.6 ± 0.3 0.030 0 -5.0 ± 0.2 0.040 0 -5.6 ± 0.3 0.050 0 -6.2 ± 0.4 0.060 0 -7.2 ± 0.2 0.070 0 -7.8 ± 0.3 0.080 0 -7.0 ± 0.3 0.100 0 -5.2 ± 0.4 Trial #2 Winglet Length (m) ±0.001 Initial Mass (g) Final Mass (g) 0.000 0 -3.5 ± 0.3 0.010 0 -4.0 ± 0.2 0.020 0 -4.8 ± 0.2 0.030 0 -5.2 ± 0.2 0.040 0 -5.4 ± 0.1 0.050 0 -6.0 ± 0.3 0.060 0 -6.7 ± 0.3 0.070 0 -7.5 ± 0.2 0.080 0 -6.8 ± 0.1 0.100 0 -4.9 ± 0.4 Trial #3 Winglet Length (m) ±0.001 Initial Mass (g) Final Mass (g) 0.000 0 -3.5 ± 0.2 0.010 0 -3.9 ± 0.1 0.020 0 -4.5 ± 0.3 0.030 0 -5.1 ± 0.2 0.040 0 -5.6 ± 0.2 0.050 0 -6.2 ± 0.2 0.060 0 -7.0 ± 0.4 0.070 0 -7.6 ± 0.3 0.080 0 -7.0 ± 0.1 0.100 0 -5.0 ± 0.4 Table 5.0 – Raw experimental data – Trials 1-3

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Trial #4 Winglet Length (m) ±0.001 Initial Mass (g) Final Mass (g) 0.000 0 -3.6 ± 0.3 0.010 0 -4.2 ± 0.2 0.020 0 -4.6 ± 0.2 0.030 0 -5.1 ± 0.1 0.040 0 -5.5 ± 0.2 0.050 0 -5.9 ± 0.3 0.060 0 -6.2 ± 0.4 0.070 0 -7.4 ± 0.2 0.080 0 -7.3 ± 0.2 0.100 0 -5.3 ± 0.4 Trial #5 Winglet Length (m) ±0.001 Initial Mass (g) Final Mass (g) 0.000 0 -3.6± 0.2 0.010 0 -4.3 ± 0.1 0.020 0 -4.5 ± 0.1 0.030 0 -4.9 ± 0.1 0.040 0 -5.2 ± 0.1 0.050 0 -6.0 ± 0.3 0.060 0 -6.6 ± 0.3 0.070 0 -7.3 ± 0.3 0.080 0 -6.7 ± 0.2 0.100 0 -4.7 ± 0.4 Trial #6 Winglet Length (m) ±0.001 Initial Mass (g) Final Mass (g) 0.000 0 -3.8 ± 0.2 0.010 0 -4.1 ± 0.2 0.020 0 -4.4 ± 0.3 0.030 0 -5.1 ± 0.3 0.040 0 -5.6 ± 0.1 0.050 0 -6.0 ± 0.2 0.060 0 -6.8 ± 0.1 0.070 0 -7.7 ± 0.1 0.080 0 -7.0 ± 0.3 0.100 0 -5.1 ± 0.5

Table 5.1 Raw experimental data – Trials 4-6

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