Aircraft Technology Development Statistical Project Report

Introduction

Beginning of XX century was marked by the creation of flying clubs in different countries. Every year more and more people are interested in aircraft and look forward to, and when progress will be made in the aircraft. They do not have to wait long. The main aerodynamic version of the aircraft in the period from 1905 to 1908 were as follows: a biplane with a box-shaped wing, front elevator and push the propeller; Biplane (polyplane) without partitions on the wing with a tractor propeller and rear-located plumage; monoplane "normal" circuit with a tractor propeller; wing monoplane with a self-balancing without stabilizing tail; monoplane tandem.
Were unified cabin aircraft: there were pedal connected to the rudder and the lever that controls the elevator and aileron. Thus, the pilot of the aircraft could carry in one hand and feet that it was very important for military purposes (shooting, photographing the terrain and other objects). The layout which has become the standard is now used in modern aircraft. In the prewar years were extended wheel chassis. Rise in winter conditions contributed to the emergence of ski gear, development and testing is carried out in Russia. The first aircraft of similar design was made in 1909. Developments in the field of engine proved to be very effective: by increasing the number of cylinders water-cooled engine is now more powerful and widely used in aircraft construction in Germany, Austria-Hungary and Russia. Using profiles with lower relative curvature improved the aerodynamic performance of many airplanes beginning of the XX century.
The most common types of propellers in the prewar period were screws with solid wood blades and high for the time efficiency. On the body and wings of the aircraft makes a lining of wood or cloth, steel is mainly used in the construction of the chassis, connecting nodes of the wing and fuselage, braces and control wiring. However, as a structural metal material has been used very rarely. The idea of ​​creating an aircraft on the basis of non-motorized aircraft was born in 1902 after a successful test airframe. Fearing competition, Wilbur and Orville Wright kept the project a secret. They built a few months four in-line petrol engine cooling water capacity of 12 horse power is a lightweight version of the car engine. When you create a propeller Wright brothers used their aerodynamic observations. Chain drive, bolted together with the engine, allows several times to reduce the frequency of rotation of the propeller. In general, the design of the aircraft looked like a glider with increased dimensions of the wing surfaces and double rudders. As in the model glider, the rudder is automatically rejected at the time of the wing torsion under which housed runners. As a result of this work was made biplane with two pushing propellers that rotate in opposite directions, and the motor is mounted on the lower wing. Management twist wing pilot by moving the hips, located in front of him lever to turn the motor and elevator control.
After the Second World War the era of jet aviation has begun. The first production commercial jet aircraft became a British De Havilland Comet (January 1951) and the American Avro C102 Jetliner (first flight - September 1949). In 1952, the British state airline BOAC started its regular flights to the "comet". While the aircraft was advances in technology, but he was persecuted constant problems because the square shape of the windows led to cracks due to metal fatigue (was caused by cycles of sealing and cabin decompression) and led to several disasters. A thorough investigation to identify the causes and eventually the problems has been overcome - other models of jet passenger planes stood on the wing.
In the last quarter of the XX century in aviation progress slowed. There were no longer revolutionary results in flight speeds, distances and technology development in this period was mainly in the field of avionics. But there have been achievements in various fields: for example, in 1979 Gossamer Albatross became the first unit, driven by muscular force of man who crossed the English Channel in 1981 Space Shuttle space plane made its first orbital flight (proving that large machine can climb into space, to support livelihoods for several days, re-enter the atmosphere at orbital velocity, and then land on a runway like an ordinary airplanes), in 1986 Dick Rutan and Yeager Gina made a world flight in an airplane without refueling and landing. In 1999, Bertrand Piccard was the first person who orbited the Earth in a balloon.

In this paper we will analyze and discuss the data of aviation accidents from 1944 to 1979.

Data
In this research work we have collected five subsets of the data of fatalities in aviation accidents from 1944 to 1979. Each subset corresponds to a particular month: January, February, March, April and May. The characteristics of the data are the following variables:

Aircraft Type / Registration: model and type of an aircraft.

Fatalities: the amount of fatalities in aircraft accident.
The number of accidents is distributed in the following way:
243 accidents in January
208 accidents in February
225 accidents in March
191 accidents in April
140 accidents in May

Histograms

The following histograms visualize the distribution of Fatalities variable for each subset:
According to the histograms output it is possible to say that all 5 data subsets are positively skewed. The overall characteristics of the data are similar to each other; however, there are some differences.

Descriptive Statistics

Sometimes the researcher poses a more specific problem: how, based on the sample of interest to estimate its numerical characteristics of an unknown distribution without resorting to the approximation of the distribution, i.e. without constructing selective distribution functions, histograms, etc. The basic measures of central tendency and variability are given in the table above.
Sample mean value describes the average value in a data sample. Among the given 5 subsets, the sample mean in January is lower than the corresponding values in other months. Sample standard deviation shows how data is dispersed around the mean. The least standard deviation is in January and the highest is in May. As it was already mentioned above, the data is positively skewed for all 5 subsets and the kurtosis is big, that’s why the distribution of each subset is sharp.

Probability Distribution

For each table of data we give QQ-plots:
If the points are close to a straight line, the distribution of the data is close to a normal distribution. These plots help us to understand the characteristics of distribution and detect outliers. It seems that the distribution of January and April are closer to normal distribution than other months.

Confidence Intervals

The 95% confidence interval form mean is given below in the table. It is obtained from the Descriptive Statistics part:
The interpretation of the confidence intervals is that at 5% level of significance the population mean values of fatalities are between lower bound and upper bound of the confidence interval (for each of 5 months).

Hypothesis Testing

Since the data represents the frequencies of fatalities in different period of times and different aircraft accidents, it is more appropriate to run a non-parametric test and check whether the numbers of accidents are significantly different from month to month.

Expected frequencies are:

The output of Chi-square test gives Chi-square value of 739.979 with a corresponding p-value lesser than 0.001. We have enough evidence to support the claim that the distributions of accidents by month are significantly different.

Regression Analysis

In this chapter we have to develop a regression equation for mean values of the data. As it was reported above, the mean values by months are the following:

Provide a scatter plot of the data:

This association gives the overall trend of the number of fatalities from month to month. There is a positive trend, thus, the number of fatalities is growing from January to May. However, the regression equation is not useful. This is mainly due to the fact that it is based only on 5 observations.

ANOVA

As the final step of this research we will test 5 data subsets for difference in mean values. One-way analysis of variance is appropriate technique to compare mean values of more than 2 samples.
H0: μ1=μ2=μ3=μ4=μ5Ha:not all means are equal

Set level of significance alpha:

a=0.05

The result of the test is below:

The result of the test is F=1.312 with a corresponding p-value of 0.264. Since p-value is higher than alpha of 0.05, we failed to reject the null hypothesis. At 5% level of significance, the mean values are not different.

Conclusion

In this statistical research we have compared and discussed the distribution of fatalities in aircraft accidents between five months of the year. It has appeared that the data is differently distributed from month to month. However, the average number of fatalities is similar for all months. The overall trend of number of fatalities is positive - the number of fatalities is growing from January to May.

Works Cited

Argyrous, George. Statistics for Social and Health Research: With a Guide to SPSS. London: SAGE, 2000. Print.
Davier, Alina A. Von. Statistical Models for Test Equating, Scaling, and Linking. New York: Springer, 2011. Print.
Draper, Norman Richard, and Harry Smith. Applied Regression Analysis. 3rd ed. New York: Wiley, 1998. Print.
Freedman, David. Statistical Models: Theory and Practice. Cambridge: Cambridge UP, 2005. Print.
Moore, David S., and George P. McCabe. Introduction to the Practice of Statistics. 2nd ed. New York: Freeman, 1993. Print.