4.1 The Shape
The type de Havilland DH-106 Comet 1 was the first mass-produced jetliner in the world.
About five years after the plane's first flight, a plane of the same type crashed near the island of Elba in the Mediterranean Sea (Nelson 1993, p.20). All 35 passengers of British-Overseas-Airways-Corporation flight BA781 lost their lives. After the wreckage was found, extensive and long-lasting investigations were carried out. The tests showed that the accident was caused by loss of the pressurized cabin. As probably already known, an artificially maintained overpressure is generated in the cabin at great heights. The pressure drop was caused by a weak spot in a window. The smallest cracks that had led to material fatigue could be detected under the microscope. In response to the incident, the airline carried out necessary conver-sions on the de Havilland DH-106 Comet 1, including the adjustment of the windows from a rectangular to an oval shape.
Figure 4.1 Fragment of the fuselage of Flight BA781 with the fuselage roof windows (based on Science Museum London 2009)
This case gives reason to investigate the shape of aircraft windows. Due to the high pressure inside the cabin, the fuselage structure is always subjected to tension in the circumferential di-rection. An airplane window is generally nothing more than a hole in the structure. This hole causes the structure to be exposed to higher loads at this point. This is known as the notch ef-fect.
Notch Effect
The notching effect is described by two factors:
The local stress concentration, often called stress increase.
The support effect. This refers to the fact that the material and the present decay method of the stress concentration counteract the stress peaks.
Figure 4.2 Schematically represented stress curve over the cross-section of a sample subjected to tensile loading [Tensile force F, N: nominal stress, k: notch stress] (based on Neuber 1937)
A higher stress is found in the immediate proximity of the notches than at a great distance from them (Figure 4.2); this is referred to as stress peaks caused by the notching effect (Neuber 1937). A rectangular airplane window would have four corners, which in turn always had a notch effect on the structure. The stress increases would be immensely high at the cor-ners of the window (Figure 4.3).
Figure 4.3 FEM visualized stress increases depending on the notch shape (Scherrer 2004)
The rounder the corner is, the smaller stress peaks occur at the workpiece. These increased stresses are caused by the "stagnation" of the force flow at this point. Stress peaks can there-fore be reduced not only by optimizing the notch shape, but also by diverting the force flow correspondingly (Figure 4.4).
Figure 4.4 Simplified illustration of the force flow in a rectangular (left) and round (right) hole
A round window therefore weakens the hull structure not only less because of missing cor-ners, but also diverts the force flow more favourably, so that the stress increases reach smaller values than with a rectangular window. Increased stress concentrations place an overly high load on the structure, which can fatigue the material at these points and cause cracks that can spread extremely quickly, as the case of flight BA781 shows. Especially with a high pressure difference between the cabin and the atmosphere, this can result in the demolition of entire structural parts from the fuselage.
With the new Dreamliner B787, the aircraft manufacturer Boeing relies on a mechanically op-timized shape of round cabin windows.
These are " long-stretched " oval-shaped high-tech windows with the same shape as long holes. The effect Boeing would like to make use of in this context falls under the principle of notch stress separation (Scherrer 2004, pp.54-55). The spatial separation of notch stresses is not an optimization due to adaptation of the shape. Nevertheless, it is an extremely simple process for reducing notch stresses. The increase in stress that occurs with slotted holes is considerably smaller than with round holes.
Figure 4.5 Stress increase as a function of the distance between the two stress concentrations (Scherrer 2004)
max is the maximum stress occurring near the notch and ref is the reference stress, in this case the gross stress of the component. The quotient of the mentioned stresses results in the factor of the stress rise. It is noticeable that even a small extension of the circular hole leads to a significantly reduced stress increase. The latter then approaches asymptotically to the value 2 with ever larger extensions.
4.2 The Hole in the Cabin Windows
The attentive passenger may have noticed that every window in the aircraft consists of several layers of glass and always has a small hole. The spearing of the windows has another physical cause.
In general, an aircraft window consists of three glasses, an outer, middle and inner glass. Only the exterior is connected to the fuselage structure and can be exposed to high stresses, among other things due to the higher load-bearing capacity of its material. The middle and inner screens are embedded into the inside wall of the aircraft by means of plastic seals. Due to the pressure difference between cabin interior and atmosphere, all components of the cabin interi-or wall are highly stressed. The outer and middle glasses cannot bear the high-pressure load, which is why pressure equilibrium must be created between the air space between the inner and middle as well as the air space between the middle and outer glasses (called air gap). The latter is done by drilling a hole in the middle glass. The hole then functions as a vent valve and also prevents humidity accumulation on the windows, so that the passenger has a clear view outside. The inner screen has no technical function. Usually this is a simple plexiglass cover of the window system to protect the passenger from the low temperatures of the other two screens. The hole keeps the air pressure between the middle and outer glasses in equilib-rium, ensures that the pressure inside the cabin remains constant and protects the middle glass in an emergency. The hole in the airplane window is therefore not a defect, but it makes a lot of sense.