## Introduction

Designing of an airplane is an intensive process that needs careful consideration of all the components that make up the aircraft. It is important since even a single mishap in even the least of elements can lead to catastrophic results. The window design of an airplane is a critical factor due to the pressurization of the cabin requiring intensive consideration of various aspects that are involved. According to Roskam (2002), a window design should be able to satisfy factors like visibility, optical qualities, and rain resistance among others. Therefore, the size, shape, and distance between the windows need putting considerable thought into the process to ensure that the final design has factored all aspects involved to guarantee safety. Some of the factors considered are stress concentration, fatigue, and the type of materials used. This report will discuss different shapes of windows, determine nominal stress for each corresponding shape and how far away the windows must be to attain the nominal stress level. The report will also seek to find the reason that Boeing 787 has large windows compared to similar planes.

## Determining Nominal Stress

Nominal stress is an important parameter when dealing with the analysis of holes in plates. Nominal stress at the hole in a plate is the stress that would exist if there was assumed to be no redistribution of stresses around the hole (Pilkey & Pilkey, 2008). According to Pilkey and Pilkey (2008), the formula for stress concentration factor taking into consideration the maximum stress and nominal stress is:

Kt=smaxsnom

Where:

Kt = Stress concentration factor

smax = Maximum stress

snom = Nominal stress

## Rewriting the Equation to Determine Nominal Stress

snom=smaxKtFor the circular airplane window with a stress concentration factor of 3 and the maximum stress being 240 MPa, the nominal stress will be:

snom=2403

The nominal stress will be 80 MPa.

For the elliptical airplane windows with a stress concentration factor of 2.3 and the maximum stress being 240 MPa, the nominal stress will be:

snom=2402.3

The nominal stress will be 104.3 MPa.

For the rectangular airplane windows with a stress concentration factor of 4.4 and the maximum stress being 240 MPa, the nominal stress will be:

snom=2404.4

The nominal stress will be 54.5 MPa.

For the triangular airplane windows with a stress concentration factor of 5.5 and the maximum stress being 240 MPa, the nominal stress will be:

snom=2405.5

The nominal stress will be 43.6 MPa.

From the calculations, the nominal stress for the circular, the elliptical, the rectangular and the triangular airplane is 80 MPa, 104 MPa, 54.5 MPa, and 43.6 MPa respectively. It is evident that the higher the stress concentration factor, the lower the maximum attainable nominal stress for the different airplane window designs.

## Determining the Distance needed to Attain Nominal Stress

There are several formulas for determining the nominal stress. These formulas are:

snom=PA

Where:

snom = Nominal stress

P = Force acting on the plate

A = Cross sectional area

Considering the image in figure 7, the formula can be modified to the following:

snom=P(D-2r)t

Where

P = Force acting on the plate

D = Width of the plate

2r = Height of the hole (Diameter)

t = thickness of the plate

Also, when considering a finite plate, the nominal stress is determined using the following formula:

snom=D(D-2r)s

Where

D = Width of the plate

2r = Height of the hole in the plate

In this case, the thickness is usually ignored.

To determine how far the away the windows of different shapes under consideration need to be to attain nominal stress, the former formula of nominal stress will be used. Since the values of the force acting on the plate and the thickness of the plate is unknown, these values will be assumed to aid in the calculations. The force is assumed to approximately 200 KN while the thickness of the plate is assumed to be 1 mm.

### Circular Airplane Window

Equate the nominal value to the equation and replace all the known values in the equation.

80106=200103D-0.350.001

D was determined to be 2.85 m.

Then determine the how far the windows the windows must be to ensure nominal stress was attained, d

The value d can be determined using the following formula:

d=D-0.35

Therefore, d will be:

d=2.85-0.35D was determined to be 2.5 m.

Therefore, the circular windows have to be 2.5 m away so that the nominal stress is attained.

### Elliptical Airplane Windows

Replacing all the known values to the equation.

104.3106=200103D-0.350.001

D was determined to be 2.26 m.

Then determine the how far the elliptical windows the windows must be to ensure nominal stress was attained, d. The distance can be determined using the following formula:

d=D-0.35

Therefore, d will be:

d=2.26-0.35

The value d was determined to be 1.92. Therefore, the elliptical windows have to be 1.92 m away so that the nominal stress is attained.

### Rectangular Airplane Windows

Replace all the known values in the equation.

54.5106=200103D-0.350.001

D was determined to be 4.02 m.

Then determine the how far the windows the windows must be to ensure nominal stress was attained, d. The value can be determined using the following formula:

d=D-0.35

Therefore, d will be:

d=4.02-0.35

The value d was determined to be 3.67 m. Therefore, the rectangular windows have to be 3.67 m away so that the nominal stress is attained.

### Triangular Airplane Windows

Equate the nominal value to the equation and replace all the known values.

43.6106=200103D-0.350.001

D was determined to be 4.93 m.

Then determine the how far the windows the windows must be to ensure nominal stress was attained, d. The value can be determined using the following formula:

d=D-0.35

Therefore, d will be:

d=4.94-0.35

The value d was determined to be 4.59 m. Therefore, the triangular windows have to be 4.59 m away so that the nominal stress is attained.

The distance the windows have to attain in increasing with the decrease in the nominal stress values. This trend means that the distance increases with the increase in the stress concentration factor. It, therefore, implies that for shapes with less stress coefficient factor can be placed close to one another safely than ones with a bigger stress coefficient factor.

## The Points the Maximum Stress Will Act on the Different Window

The windows on aircraft fuselage are reminiscent to gaps on plates. The shape of the window plays a considerable part in the stress concentrations on the window of an aircraft. This fact is because stresses on a plate tend to concentrate on the edges and sharp corners of the gap in the plate. Therefore, having a window with sharp corners and edges will face a lot of stresses on the edges and corners than other parts. We will analyze the stress concentration on the different window shapes.

### Elliptical Airplane Windows

For an oval hole on a plate under stress, the maximum stress is faced by the edges that are in contact with the stress flow lines. Therefore, for the elliptical airplane window stress will concentrate on the edges in contact with the flow stress lines and therefore it is these edges that face maximum stress. Since the nominal stress for the elliptical airplane window is the highest, the edges facing maximum stress are of the smaller radius. Estimating the radius of the edges (Liu, 2005).

Kt=1+2r2r1

Where

Kt = Stress concentration

r1 = Bigger radius (Height)

r2 = Smaller radius

Replacing the known values in the equation to determine r2.2.3=1+2(r2350)

The smaller diameter,r2 whose edges were in contact with the stress flow lines was calculated to be 227.5 mm.

### Rectangular Airplane Windows

A rectangle on a plate along the flow of stresses will face maximum stress at its corners. Therefore, the rectangular window of the airplane will meet a have stress concentration at its corners almost equally. This maximum stress will correspond to the nominal stress. The dimensions of the rectangle will have a height of 350 mm that is assumed to be the breadth as well hence the corners under the maximum stress are 350 mm from each other.

### Triangular Airplane Windows

A triangular hole in a plate under stress usually faces maximum stress at the corners across the flow of stress. Therefore, the triangular window on the fuselage will experience maximum stress at the two angles that are across the stress flow. The maximum stress will correspond to the nominal stress.

### Circular Airplane Windows

A circular hole in a plate facing stress faces maximum stress on the edges in contact with the stress flow lines (Ragab & Bayoumi, 1999). Therefore, the circular airplane window will meet maximum stress on the edges corresponding to the diameter that s stress flow lines. The maximum stress will compare to the nominal stress. The radius of the windows diameter corresponds to the height of the window which is 350 mm.

## The Reason is Windows of a Boeing 787, are Bigger

The Boeing 787 is one of the proofs of the miles technology is gifting the aircraft industry making the plane's technology the leading in the industry according to the Boeing website (2018). The plane gifts a significant upgrade to its predecessors in many areas ranging from weight, the strength of materials used, space, fuel efficiency, better cockpit, and passenger comfort. The plane has a more pressurized cabin with higher humidity. This feature makes the passengers feel like they are cruising at a lower altitude compared to the similar planes, therefore, helping reduce passenger fatigue, headaches, and eye dryness. The feat would not have been possible without proper design input to ensure that the plane could sustain the resulting structural fatigue and corrosion risk (Boykoff, 2011). In the design, one of the critical components that would require careful consideration due to the more pressurized cabin is the strength of the materials used and the window design. A more pressurized cabin would mean increased structural fatigue which could not be sustained by the traditional aluminum alloys that have been used in manufacturing airplanes all along. It is due to this fact that the Boeing 787 comprises about 50% composites.

The window design also is another aspect that needs intensified consideration due to increased pressure cabin to ensure aircraft safety. According to Boykoff (2011), the windows of the Boeing 787 are 19 inches high and about 30% bigger than planes of similar size. This feat has been possible due to the type of materials used. Aluminum is the mainstream material used in the manufacturing of airplane fuselage. This material has the defects in its crystal structure resulting to edge dislocations that ultimately leads to cracks and fatigue failure after that. The use of composite materials reduces this risk. They can do that because fatigue failure occurs slowly in composite materials and therefore they have a longer lifespan. Consequently, the use of carefully made composite materials in Boeing 787 fuselage allows for bigger windows since the materials will withstand increased stresses compared to aluminum. The window is elliptical to provide a larger radius that will reduce the stress concentrations due to the pressurized cabin, a caution that will ensure that the window meets the safety standards required in successful operating of the plane. The resulting passenger convenience due to the bigger windows and plane uniqueness come as secondary factors.

## The Main Factors Affecting Safety of Aircraft Windows

From the discussion, there are vital factors that outrightly affect the safety of the airplane window. The shape of the window and the type of fuselage material are the main factors that affect the aircraft window safety. The shape of the window affects a parameter called the stress concentration factor. This parameter then affects the n...

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