Airplane Wing Design Paper Example

Introduction

The process of airplane design is an intensive and extensive one as an airplane is comprised of many complicated components. The significant parts of an aircraft are the fuselage, empennage, the wings, landing gear, and the power plant (engines and propellers). An airplane faces four forces while in operation, these forces are lift force, gravity, thrust, and drag (Vilnius, 2017). Due to this, many factors have to be considered during the design process of an airplane. The Bernoulli's principle is regarded as one of the major reasons for planes to fly. The one component where this principle is mainly applied to the functioning of the aircraft is the wings. Designing of an airplane wing involves consideration of factors like shape, load bearing, the moment of inertia, bending moment, and spar among others. This research paper will dwell on an in-depth discussion the wing design process that will involve the calculation of bending moment and moment of inertia of an airplane wing.

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The Wind design and I Beam Principle

The wing design is a crucial process to come up with a strong wing structure that will be able to support the weight of the engine and propellers, and also contribute sufficiently in generating lift. The wing structure is the component running from fuselage horizontally at some given angle, and it hangs on the side like a cantilever beam. There are different types of wing shape, which are the early cambered airfoil, symmetrical airfoil, supercritical airfoil, double wedge supersonic airfoil, circular arc supersonic airfoil, and the modern asymmetrical airfoil among others (Vilnius, 2017). The wing can also be considered to be solid or hollow depending on the different scenarios.

Despite the different shapes, the airplane wing looks strikingly similar to a beam. In this regard, I beam principle is used during the airplane wing design process. An 'I' beam is a beam with an 'I' cross-section that is very efficient in carrying the shear and bending loads in the plane of the web. It is for this reason that it is borrowed in the design of an airplane wing (Chan, Teng, & Chung, 2002). The 'I' beam principle is incorporated in the wing design in the manufacturing of the spar bars. A spar bar is a structural component of the wing that runs through the wing from the fuselage whose function is to carry the shear and bending forces impacted on the airplane wing.

Case Study

This case study seeks to evaluate the bending inertia and bending moment of a mid-size business jet with a tapered straight wing design. To be able to calculate the moment of inertia and the bending moment in a wing, relevant data regarding the airplane and operating has to be obtained. However, it is imperative to understand various parameters that are desirable in evaluating these considerations in an aircraft wing design. The most critical parameters are discussed below.

Airplane Wing Parameters

To design an airplane, wing several aspects need to be considered. These aspects are the following:

• Wing area (S)

The wing area is obtained from the gross weight and wing loading that also have to be determined.

• S=WW/SLocation

The wing location on the fuselage has to be carefully considered. It can either be located in a high position, low position or mid wing position.

• Aerofoil selection

According to Tulapurkara (2013), the shape, camber and thickness ratio of the aerofoil are critical factors in aerofoil selection. In turn, the aerofoil type selected influences the lift coefficient factor. The airfoil thickness ratio of the chosen airfoil influences the maximum lift, structural weight, the stall characteristics, and the Mach number. This necessitates the selection of the optimum airfoil thickness ratio.

• The aspect ratio (A)

The chosen aspect ratio can either be high or low. The selected aspect ratio affects the lift coefficient and wing weight. A high aspect ratio value increases the wingspan which in turn would mean more hanger space hence poor riding quality during the turbulent weather. Due to these factors, the aspect ratio of the airfoil needs to be optimized.

• Taper ratio (l)

Taper ratio is the ratio between the tip chord and the root chord of the airfoil. It can either be a straight taper or variable taper. Taper ratio usually affects the tip stalling, weight of the wing and induced drag.

• Twist (e)

This is the angle of twist of the wing in degrees.

• Angle of inclination

The angle of inclination of the wing through the lateral axis can either be dihedral or anhedral. Dihedral angle (G) is the upward inclination of the airfoil to the plane through the lateral axis while the anhedral angle is the downward inclination of the airfoil to the aircraft through the lateral axis.

• Wing incidence or setting (iw)

The wing incidence is the angle between the wing reference chord and the fuselage reference line (Tulapurkara, 2013). This angle is essential in minimizing the drag at given operating conditions mostly the drag. The wing incidence angle is chosen such that the wing is at correct attack angle for a given design angle while the fuselage will be at the angle of attack with minimum drag.

• Bending moment

The bending moment of the wing has to be carefully considered to ascertain that it will be capable of withstanding the shearing and bending loads that are impacted on it by the engine propellers and other components attached to it.

• Moment of inertia

The moment inertia of the wing will need to be determined so as to guarantee that the wing will be able to withstand the angular acceleration that it will be impacted on it in during flights.

• Other aspects

Other vital aspects considered during the wing design are sweep, high lift devices, ailerons and spoilers, and aerodynamic coupling among others. A well-functioning airplane wing will be obtained upon a careful consideration of the various parameters of the during the airplane wing design process.

The parameters discussed above informs the considerations for relevant calculations in this case study. Ajith et al. (2017) provided relevant information regarding a small capacity airplane. The data of the plane is as follows:

General design characteristics

• Weight of the wings 2000 Kg
• The load factor 3 g condition.
• Factor of safety applied 1.5
• Designed load limit 6000 Kg
• Designed ultimate load 9000 Kg
• Lift load on wings 4800 Kg
• Load on spar 1800 Kg

The general performance

• Cruise speed 905 Km/hr
• Max speed 950 Km/hr
• Range 9070 Km
• Maximum wing loading 7975.5 N/m2
• Minimum thrust/weight 0.287

The spar bar components in the wing structure are the ones that take up shear force, bending loads and angular acceleration that is impacted on the airplane wing. Therefore, to be able to determine the bending moment and the moment of inertia on the wing, the number and parameters of the spar bar have to be known. For the selected aircraft the length of the spar is 3.6 m. The bending inertia will be determined on the end connected to the fuselage and later the bending moment distribution on the spar bar calculated.

The 'I' Value for the Wing at the Root Calculation

The bending inertia of the wing at the root is also known as the 'I' value. There are several ways of determining the 'I' value. One formula of determining the bending inertia is:

• I=0.0449 C T3 For solid wings
• I=ISolid{1-1-2f3} For hollow wings (non-uniform skin)
• I=ISolid{1-1-2f5^3} For hollow wings (uniform skin)

Where:

• C is chord
• T is thickness
• f is skin fraction

But for the airplane wing under consideration the bending inertia on the spar bar is assumed to be equivalent to that for the entire wing as it is the one carrying most of the forces being impacted on the wing. Therefore, the bending inertia is calculated as follows for the cross section of the spar.

The bending inertia for the above structure is calculated using the following formula:

I=t(H-2t)3+B12(H3-(H-2t)3)On replacing the values for in the formula bending inertia 'I' was found to be 6295156 mm4.

Calculation of Bending Moment

After determining the bending inertia, the bending moment of the spar along its length was determined. Bending moment is defined as the measure of the bending effect as a result of the forces acting on the beam. It is measured in terms of the force and distance. This required first determining the weight loading on different sections of the spar beam. The load distribution along its length was as follows:

Since the spar is attached to the fuselage hanging outwards it is assumed to be a cantilever in the calculation of the bending moment at the different points. The formula for calculating bending moment is:

M=WL Where:

• M is Bending moment.
• W is the weight load at a point.
• L is the distance from the fixed end.

In this regard the bending moment along the wing Calculations are demonstrated in the table:

The bending moment in the wing varies from one point of the wing to the other as it is dependent on distance from the fixed end and the load at the specific point which varies.

Bending Theory

Considering the bending theory, when a beam of an arbitrary cross section will bend if subjected to bending moment (Bansal, 2015). Besides bending, other effects like buckling and twisting may occur. With this in mind, the design of the airplane wings has to be made in a way such that they will able to withstand the various forces that are impacted on them like shear forces, angular acceleration, and bending loads among others. To achieve this the designers, have to incorporate many ways to obtain a strong wing. One of these ways is using materials that have a high strength to weight ratio in making the wing components. Doing this will ensure that there is the obtained wing will be of reduced weight, therefore, there will be reduced forces acting on the wings as a result of gravity forces.

Use of support structures is another way of obtaining a wing that is strong and sturdy. The support structures employed in the manufacturing of airplane wings are the spars and the ribs. As already discussed spars are the main structural members of the wing. They offer the much-needed support to the wing structure as well as absorbing the impacting forces on the wing (Oxlade, 2009). Ribs on the other hand usually extend from the leading edge to the trailing edge of the wing. The use of spars and ribs also ensure that the wing will maintain its aerodynamic shape during functioning for optimum performance of the airplane. Finally, the joint of the airfoil to the fuselage. The joint itself has to be of a high standard to be strong enough to support the wing and its attached components. By using a material of high strength to weight ratio in making the wing structure, incorporating the required support structures during manufacturing and applying the right joint will ensure that a strong, well-functioning wing is obtained resulting to an efficient running airplane.

False Spar

Besides the main spars used for providing support to the wing structure, some wings have another set of spars called the false spar. The airplane used in our case study had the false spar. The false spar was employed in the design for this airplane as they help in supporting the ailerons and flaps. According to United States Engineering Division McCook Field (2005)...