Rudranath Ghorai

GDGWI ID: 120232

Programme: BBA – BS (2012-2015)

Module: MNGT213

Module Leader: Kim Menezes

Word Count: ~2000

MNGT213

COURSEWORK

PROJECT

1

RESEARCH OBJECTIVE DOES HAVING A CAR WITH A BIG ENGINE DISPLACEMENT MEAN THAT IT WOULD PROVIDE BETTER ACCELERATION?

INTRODUCTION

A car engine uses small controlled explosions to create the power needed to move the

vehicle. All car engines use a four stroke combustion cycle. The four strokes are intake,

compression, combustion and exhaust.

Power is generated when these strokes repeat in quick succession. All parts of the

combustion cycle take place within an enclosed car engine.

The core part of an engine, the pistons, are enclosed in cylinders. When the pistons are

moved up & down by the crankshaft, the vehicle is put into motion.

Engine displacement is the volume swept by the pistons in the cylinders. It’s generally

measured in cubic inches (cu in), litres (L) or cubic centimetres (cc).

The engine displacement can be calculated with the formula given below:

Displacement = (π/4) x bore2 x stroke x number of cylinders

The acceleration of a car is found out by the time taken by the car to reach from 0-100

km/h.

DATA DESCRIPTION

A sample of the world’s fastest cars were handpicked. Engine displacements were given

for each car & I had to manually find the acceleration i.e. time taken by the car to reach from 0-

100 km/h.

For the assignment, I found the engine sizes in different measurement units, so in order

to achieve consistency, I converted them into cc. “Car” denotes the make & model of the car,

“Time” is the time taken by the car in seconds to reach from 0 km/h to 100 km/h & “Engine

Displacement” denotes the engine capacity in cubic centimetres.

The car names are qualitative nominal data whereas engine displacement & time are

quantitative ratio data. The data collected is cross-sectional data.

ANALYSIS

The data used in the assignment has been analysed with IBM SPSS & Microsoft Excel.

Using the data, necessary tables & graphs were created to support the purpose of the analysis.

The scatter plot diagram illustrates the degree of co-relation & regression between the two

variables, engine displacement & time. The histograms illustrate the frequency of time & engine

displacement.

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Car Time (seconds) Engine Displacement (cc)

Bugatti Veyron 16.4 Super Sport 2.7 7993

Chevrolet Corvette C6 ZR1 3.4 6200

Dodge Viper SRT-10 2.3 7996

Ferrari 430 Scuderia 4.25 4300

Ferrari 458 Italia 4.3 4424

Ferrari 599 GTO 3.54 5999

Ferrari Enzo 3.8 6000

Ferrari F12 Berlinetta 2.8 6262

Gumpert Apollo Sport 4.15 4260

Jaguar F-Type V8 S 3.6 5000

Koenigsegg Agera R 3.5 4998

Koenigsegg CCX 3.65 4800

Koenigsegg CCXR 3.95 4700

Koenigsegg CCXR Edition/Trevita 3.6 4800

Lamborghini Aventador 2.46 6498

Lamborghini Gallardo LP560-4 3.4 5243

Lamborghini Murciélago LP640 3.1 6200

Lamborghini Superleggera 3.7 5243

Lamborghini SuperVeloce 2.9 6496

McLaren F1 3.35 6100

McLaren MP4-12C 4.79 3800

Mercedes-Benz CLK GTR 3.47 6063

Mercedes-Benz SLR McLaren 3.85 5400

Mercedes-Benz SLS AMG 3.3 6200

Nissan GT-R R35 4.63 3799

Pagani Huayra 3.5 5980

Porsche 911 GT3 4.58 3600

Porsche 911 Turbo S 5.1 3596

Porsche 918 Spyder 4.05 4600

SSC Ultimate Aero TT 3.2 6350

Observations Time (seconds) Engine Displacement (cc)

Mean 3.630666667 5430

Median 3.57 5321.5

Mode 3.4 6200

Standard Deviation 0.667646062 1155.104026

Variance 0.430892889 1289789.8

Range 2.8 4400

Minimum 2.3 3596

Maximum 5.1 7996

Sum 21.89920562 1323888.404

3

25 3.275 4556

Percentiles 50 3.6 5243

75 4.125 6200

First Quartile 3.275 4556

Third Quartile 4.125 6200

Mode 3.4 6200

IQR 0.85 1644

From the above data we can see that the mean for the engine displacement is 5430 &

median is 5321.5. The minimum value is 3596 cc for Porsche 911 Turbo S & the maximum value

is 7996 cc for Dodge Viper SRT-10. The range is 4400, standard deviation is 1155.104026 &

variance is 1289789.8.

Similarly, for time, the mean is 3.630666667 & median is 3.57. The minimum value is

2.3 seconds for Dodge Viper SRT-10 & the maximum is 5.1 seconds for Porsche 911 Turbo S. The

range is 2.8, standard deviation is 0.667646062 & variance is 0.430892889.

Since both the variables possess extreme values, the best way to go about computing the

range would be by using Inter-Quartile Range (IQR).

The reason why we use IQR is because it excludes extreme values on both ends & takes

into consideration only the middle 50% values.

IQR for Engine Displacement: 6200 – 4556 = 1644 cc

IQR for Time: 4.1 – 3.275 = 0.825 seconds

The range for engine displacement was 4400 & IQR comes out at 1644 cc & for time,

range was 2.8 & IQR for it comes out 0.5 seconds. We can see that there is a considerable

difference between the ranges & IQRs of both the variables.

For engine displacement, the mode is 6200 cc (Chevrolet Corvette C6 ZR1, Lamborghini

Murciélago LP640, Mercedes-Benz SLS AMG) & for time, it’s 3.1 seconds (Lamborghini

Gallardo LP560-4 & Ferrari 599 GTO).

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After taking a close look at both the histograms, we can conclude that the time histogram is right skewed & the engine histogram is left skewed.

For variable “time”, the majority of data lies in between 3-4 seconds & for variable

“engine”, the maximum data lies in 6000-7000 cc. One thing to note over here is that in the engine histogram, there is no data between 6500-7500 cc however there is one observation at 7500+ cc.

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Engine

Frequ

ency

% Valid

%

Cumulative

%

Valid

3596 1 3.3 3.3 3.3

3600 1 3.3 3.3 6.7

3799 1 3.3 3.3 10.0

3800 1 3.3 3.3 13.3

4260 1 3.3 3.3 16.7

4300 1 3.3 3.3 20.0

4424 1 3.3 3.3 23.3

4600 1 3.3 3.3 26.7

4700 1 3.3 3.3 30.0

4800 2 6.7 6.7 36.7

4998 1 3.3 3.3 40.0

5000 1 3.3 3.3 43.3

5243 2 6.7 6.7 50.0

5400 1 3.3 3.3 53.3

5980 1 3.3 3.3 56.7

5999 1 3.3 3.3 60.0

6000 1 3.3 3.3 63.3

6063 1 3.3 3.3 66.7

6100 1 3.3 3.3 70.0

6200 3 10.0 10.0 80.0

6262 1 3.3 3.3 83.3

6350 1 3.3 3.3 86.7

6496 1 3.3 3.3 90.0

6498 1 3.3 3.3 93.3

7993 1 3.3 3.3 96.7

7996 1 3.3 3.3 100.0

Total 30 100.0 100.0

Time

Frequency % Valid

%

Cumulative

%

V

a

l

i

d

2.30 1 3.3 3.3 3.3

2.46 1 3.3 3.3 6.7

2.70 1 3.3 3.3 10.0

2.80 1 3.3 3.3 13.3

2.90 1 3.3 3.3 16.7

3.10 1 3.3 3.3 20.0

3.20 1 3.3 3.3 23.3

3.30 1 3.3 3.3 26.7

3.35 1 3.3 3.3 30.0

3.40 2 6.7 6.7 36.7

3.47 1 3.3 3.3 40.0

3.50 2 6.7 6.7 46.7

3.54 1 3.3 3.3 50.0

3.60 2 6.7 6.7 56.7

3.65 1 3.3 3.3 60.0

3.70 1 3.3 3.3 63.3

3.80 1 3.3 3.3 66.7

3.85 1 3.3 3.3 70.0

3.95 1 3.3 3.3 73.3

4.05 1 3.3 3.3 76.7

4.15 1 3.3 3.3 80.0

4.25 1 3.3 3.3 83.3

4.30 1 3.3 3.3 86.7

4.58 1 3.3 3.3 90.0

4.63 1 3.3 3.3 93.3

4.79 1 3.3 3.3 96.7

5.10 1 3.3 3.3 100.0

Total 30 100.0 100.0

6

The above scatter plot diagram illustrates a negative bivariate linear regression. It means that there are two variables, “engine” is the independent variable & “time” is the dependent variable & collectively they have a negative slope.

The dependent variable “time”, on the Y-axis is to be predicted whereas the independent

variable “engine” on the X-axis is the predictor. Correlation is a measure of the degree of relatedness of two variables.

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We can further elaborate our findings with the help of a hypothesis test.

The simple linear regression model is:

Variables Entered/Removeda

Model Variables

Entered

Variables

Removed

Method

1 Engineb . Enter

a. Dependent Variable: Time

b. All requested variables entered.

Model Summary

Model R R Square Adjusted R

Square

Std. Error of the

Estimate

1 .916a .839 .833 .27252

a. Predictors: (Constant), Engine

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1

Regression 10.847 1 10.847 146.054 .000b

Residual 2.080 28 .074

Total 12.927 29

a. Dependent Variable: Time

b. Predictors: (Constant), Engine

Coefficientsa

Model Unstandardized Coefficients Standardized

Coefficients

t Sig.

B Std. Error Beta

1 (Constant) 6.506 .243 26.768 .000

Engine -.001 .000 -.916 -12.085 .000

a. Dependent Variable: Time

Expected Time: 6.506 - .001 x Engine Displacement

8

Assuming a 95% confidence interval, α = 0.05. Since the p value is less than α ie. 0.05,

we can reject H0. This proves that the engine displacement does influence the acceleration of a

car.

Since R2 = .839, we can state that 83.9% of the variation in time taken for a car to go

from 0-100 km/h is explained by the regression of the time taken to reach 0-100 km/h on the

engine displacement.

From the linear equation above, we can derive that for every increase in engine

displacement size, the estimated time for a car to go from 0-100 km/h will decrease by 0.001

seconds.

Another interesting aspect about this analysis is that the standard error is 0.000. This

means that the engine size is a major determinant of time taken by the car to reach 0-100 km/h.

However there are certain values that do not fall on the regression line. This could be due

to an array of other factors such as mass of the car, brake horsepower (bhp), torque, number of

cylinders, make of engine, etc.

In the case of Lamborghini Aventador, it weighs 1,575 kg & Bugatti Veyron 16.4 Super

Sport weighs 1,888 kg. Aventador gives an acceleration of 2.46 seconds whereas Veyron gives an

acceleration 2.7 seconds given the fact that Veyron has an engine displacement of 7993 cc

whereas Aventador has an engine displacement 6498 cc. Even though the Veyron has a more

powerful engine, Aventador has a lighter chassis & that gives an edge in terms of acceleration.

This is a clear example which shows how much a car’s weight has influence on its acceleration.

From Newton’s formula, Force = Mass x Acceleration, shifting sides, the formula

becomes, Acceleration = Force/Mass.

So when mass of a car increases, it has an inverse effect on the acceleration & hence

acceleration reduces.

CONCLUSION To sum it up, the engine displacement of a car plays a major role in the rate of

acceleration of a car, however it is not the only factor on which acceleration is dependent.

Other factors which affect acceleration is the type of engine. In the case of a diesel

engine, it tends to have a slow pickup & then it gives a sudden push. However, a petrol engine

gives a full pickup since the very moment you press the throttle. Aerodynamics of a car also play

a major role in the acceleration of a car.

Lastly, the weight of the car also plays a major role. As said previously, Aventador &

Veyron had an engine displacement of 6498 cc & 7993 cc respectively but due to the weight

differences & Aventador had a better acceleration over Veyron considering the fact that the

latter had a more powerful engine.

9

From a personal point of view, there was a steep learning curve associated with learning

how to use IBM SPSS. I had to spend hours on YouTube learning SPSS & then figuring out how

to read the regression chart it threw at me.

New programs to explore, bundled with a lot of new statistical terminologies did make

the whole process a bit too overwhelming, but the entire experience of learning something &

knowing someday it’s going to help you in the near future made up for all of the hard work that

went into this assignment.

It’s every car aficionado’s dream to own at least one of the cars mentioned in the

observation set. The fact that owning even one of the cars would require millions of dollars,

keeps me daydreaming about them.

Till then, it’s safe to say, “Speed thrills, but kills.”

BIBLIOGRAPHY TopCarRating. (2013). The fastest cars in the world. The highest speed. Top rated

maximum speed of supercars.. Available: http://www.topcarrating.com/topspeed.php. Last

accessed 25th Nov 2013.

TheSuperCars. (2013). Fastest Cars In The World: Top 10 List 2013-2014. Available:

http://www.thesupercars.org/fastest-cars/fastest-cars-in-the-world-top-10-list/. Last

accessed 25th Nov 2013.