## Chris Hwang, Year 2 Engineering

## Abstract

The winglet, a vertical or angled extension mounted at the tips of each wing as an attempt to control and weaken the generation of vortices that create induced drag, has become popular among modern aircrafts. This project analyzes the aerodynamic performance gains made by winglets. Two variation of a wing-plane (with or without winglet) were designed and simulated on MachUp 4.0. Both wing-planes were tested for their lift coefficient (C_{L}), drag coefficient (C_{D}), and lift-to-drag ratio (C_{L}/C_{D}) at angles of attack from -8.0000 degrees to 12.0000 degrees. The results showed that at nearly every angle of attack, the wing-plane with the winglet had a higher lift coefficient and a lower drag coefficient. The winglet provided an average of 5.4815% across all angles of attack tested. Winglets are an effective way to increase the overall efficiency of aircrafts.

## Introduction

Flight is a utilization of four forces: lift, weight, thrust, and drag. One of the major objectives for the design of an aircraft’s wing is to obtain a high value of lift-to-drag (L/D) ratio. By increasing the lift while reducing the drag, fuel consumption can be optimized; and therefore, the overall efficiency of an aircraft is enhanced (Rabbi et al, 2015).

The wing of an airplane creates a region of lower pressure on the top and a region of low pressure at the bottom in order to generate lift. Consequently, air from the high pressure region flows up to the region of low pressure; thus, produces spiralling vortices at the wingtip that forms an induced drag. Looking at an aircraft from the back, these vortices spiral inward; so, the left wing creates clockwise-spiralling vortices while the right wing creates counter-clockwise-spiralling vortices. These vortices roll off the back of a wing on a downward angle to create an effect known as downwash and plays a major role in the net drag of an aircraft (Hall, 2021). A winglet is a vertical or angled extension mounted at the tips of each wing as an attempt to control and weaken the generation of these vortices. The winglet was originally conceptualized by a British aerodynamicist in the late 1800s. This concept was tested in the wind tunnels of the NASA Langley Research Center by Dr. Richard T. Whitcomb during the 1970s Oil Crisis in the United Sates. Whitcomb’s study showed that the addition of winglets reduced the induced drag by 20%, resulting in a 9% increase of the lift-to-drag ratio (Whitcomb, 1976). These results were confirmed in 1979-1980 when the NASA Dryden Flight Research Center’s test flight of a militarized version of the Boeing 706 jetliner became 6.5% more efficient in fuel consumption by the addition of winglets (Dunbar, 2008). Since then, winglets have become popular on modern aircrafts. This project aims to simulate the aerodynamic performance gains made by winglets by comparing the efficiency of a wing with a winglet to a wing without a winglet.

## Materials and Methods

Two variations of a wing-plane – with a winglet (Fig. 1) or without a winglet (Fig. 2) – were designed and simulated using MachUp 4.0, a web-based software developed by the USU Aero Lab for the purpose of aerodynamic analysis of fixed-wing aircrafts. Both wing-planes utilized the NACA 2412 airfoil design. The winglet with a semispan of 0.4500, a root cord of 0.4000, and a tip cord of 0.1750 was also based off the NACA 2412 and was mounted at the end of each winglet on an 80 degree angle. The two wing-planes were identical in all aspects other than the addition of the winglet itself on one of them in order to ensure that all performance gains or losses came from only the winglet.

**Figure 1. **Wing-plane without winglet

**Figure 2. **Wing-plane with winglet

The performances of the two designs were simulated by MachUp 4.0’s Airfoil Analysis Tool. This analysis tool was limited to linear-analyzation of the wing-planes; so, the two variations were analyzed only at angle of attacks in the linear range (Molland and Turnack, 2007), where the lift coefficient can be accurately predicted using a linear equation such as:

The
lift coefficient () and drag coefficient (_{ }were taken at different
angle of attacks between -8.0000 degrees to 12.0000 degrees. Upon the collection
of data, the performance gains or losses the addition of a winglet provided was
analyzed.

## Results

At
every angle of attack excluding the interval -4.0000 to 2.0000 degrees, the
wing-plane with the winglet produced a higher value of coefficient of lift (C_{L})
shown by Fig. 3 and Fig. 4. Likewise, the wing-plane with the winglet produced
a lower value of coefficient of drag (C_{D}) at most angles of attack. At
-4.0000 degrees, the wing-plane with the winglet produced an equal value of C_{D}
as the wing-plane without the winglet while it produced an increased value of C_{D
}at -6.0000 degrees. However, at every other angle of attack, the winglet
resulted in decreased values of C_{D }as shown by Figure 5 and Figure
6.

The
lift-to-drag ratio (C_{L}/C_{D}) of both the wing-plane with
the winglet and without the winglet are represented by Fig. 7. The table also
shows the % increase of the (C_{L}/C_{D}) for the wing-plane
with the winglet relative to the ratio produced by the wing-plane without the
winglet. At every angle of attack other than -4.0000 degrees that decreased the
ratio by 0.5886%, the winglet produced a higher value of lift-to-drag ratio ranging
from a 0.1472% and 8.7999% percent increase.

**Figure 3.** Graph showing the coefficient of lift (C1) at different angles of attack for wing-plane with and without winglet.

**Figure 4.** Table showing the coefficient of lift at different angles of attack for wing-plane with and without winglet.

**Figure 5.** Graph showing the coefficient of drag (C_{D}) at different angles of attack for wing-plane with and without winglet.

**Figure 6.** Table showing the coefficient of lift at different angles of attack for wing-plane with and without winglet.

**Figure 7. **Table showing the lift-to-drag ratio and the % increase of the ratio at different angles of attack for wing-plane with and without winglet.

## Discussion

Aircraft winglets are a proven method for reducing drag while increasing lift by lessening the effects of wingtip vortices created by the high-pressure air under the wing spilling over to the top of the wing. This particular experiment further demonstrated as this the addition of a winglet produced an average of 5.4815% increase of the lift-to-drag ratio and thus, the efficiency of the aircraft simulated. This increase in efficiency was the direct result of an average increase of 2.0717% in the lift coefficient and an average of 6.2669% reduction in the drag coefficient.

A point of interpretation is that winglets reduce drag more than it increases lift. Furthermore, the winglets become more efficient and useful in higher angles of attack. In a study analyzing the aerodynamic effects of winglets by comparing two variations of a rectangular wing – with or without winglets – resulted in a 15-30 % reduction in drag coefficient and 10- 20 % increase in lift coefficient at the angle of attack of 8 degrees (Patel et al, 2012), further supporting the performance gains made by winglets.

However, it is important to note that the results were strictly computer simulations conducted using MachUp 4.0. Physically building and testing the wing-planes were not possible due to time constraints but doing so would have been a way to analyze the aerodynamic effects of winglets in a more real-world setting and a way to confirm the simulation data. Moreover, there were many unknowns with the conditions in which the MachUp 4.0 analysis tool simulated the wing-planes such as the air pressure and air velocity. Specifying these would allow deeper and more accurate interpretations of results.

In conclusion, the addition of winglets to an aircraft’s wings increases the lift coefficient while reducing the drag coefficient and thus, producing a higher value of lift-to-drag ratio. Therefore, winglets are an effective way to increase the overall efficiency of an aircraft.

## References

Whitcomb, R. T. (1976) “A Design Approach and Selected Wind-Tunnel Results at High Subsonic Speeds for Wing-Tip Mounted Winglets”. *NASA Technical Note. *https://core.ac.uk/download/pdf/42882778.pdf

Hall, N. *Downwash Effects on Lift.* National Aeronautics and Space Administration, 7 May 2021, https://www.grc.nasa.gov/www/k-12/airplane/downwash.html

Molland, A. F., Turnock, S. R. (2007). “Effective Angle of Attack”. *Marine Rudders and Control Surfaces.* https://www.sciencedirect.com/topics/engineering/effective-angle-of-attack

Rabbi, F., Nandi, R., Mashud, M. (2015). “Induce Drag Reduction of an Airplane Wing”. *American Journal of Engineering Research. 4*(6). https://www.researchgate.net/publication/343153378_Induce_drag_reduction_of_an_airplane_wing

Patel, M., Shah, S., Dubey, D. “Analysis of Drag for an Aircraft Wing Model with and without Winglet”. *Indian Journal of Applied Research. 1*(7). https://www.worldwidejournals.com/indian-journal-of-applied-research-(IJAR)/fileview/April_2012_1356947444_ad4c2_File%2027.pdf

Ashrafi, Z. N., Sedaghat, A. “Improving the Aerodynamic Performance of a Wing with Winglet”. International journal of Natural and Engineering Sciences. 8(3): 52-57. https://www.researchgate.net/publication/272175209_Improving_the_Aerodynamic_Performance_of_a_Wing_with_Winglet

Dunbar, B. *Fact Sheets. *Dryden Flight Research Center, National Aeronautics and Space Administration, 3 March 2008, https://www.nasa.gov/centers/dryden/about/Organizations/Technology/Facts/TF-2004-15-DFRC.html

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