Performance and Energy System Report

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UNIVERSITY OF SOUTHERN CALIFORNIA DEPARTMENT OF AEROSPACE AND MECHANICAL ENGINEERING

AME-409: SENIOR DESIGN PROJECT

SPRING 2014

MKL-1 Sport Hybrid

Performance and Energy System Report

Marshall Ly

[email protected]

Date Submitted:

March 17, 2014

Your cover page art

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Table of Contents

Table of Figures 3

Abstract 4

Introduction 5

Transportation Problem 5

Technology Background 6

General Requirements 9

Style Design 10

Design Target 10

Major Parameters and Dimensions 11

Performance 12

Power Requirement 12

Powertrain Design 16

Drivetrain Design 22

Power Curve and Acceleration Performance 23

Energy System 25

Comparison and Discussion 30

Conclusions 32

Recommendations 33

References 34

Appendix 36

Appendix A: White’s Method Diagrams and Data 36

Appendix B: Power Required Curve Data 38

Appendix C: Battery Types Information 39

Appendix D: Final Power Required Curve Data 40

Appendix E: Acceleration Curve Data 40

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Table of Figures

Figure 1: Cumulative CO2 Emissions from 1900-1999, Sources of US CO2 emissions in 1997 5

Figure 2: 2014 Tesla Model S 6

Figure 3: The Toyota FCV Prototype 7

Figure 4: The 2014 McLaren P-1 8

Figure 5: 3-View Drawing of the MKL-1 10

Figure 6: Free Body Diagram of All Forces Acting on the Car 12

Figure 7: Standard Variation of Coefficient of Tire Rolling Resistance versus Velocity 13

Figure 8: Power Required Curve Graph 14

Figure 9: Overall Powertrain Function Structure 17

Figure 10: First Decomposition of the Overall Powertrain Function Structure 18

Figure 11: Dual Hybrid Function Structure 18

Figure 12: P/E Ratio Chart 20

Figure 13: The 1996 Lotus Elise 21

Figure 14: Simplified Engine Speed versus Brake Horsepower Graph 22

Figure 15: Final Power Required Curve Graph 23

Figure 16: Acceleration Curve 24

Figure 17: BSFC Chart 26

Figure 18: MKL-1 Energy Schematic 29

Figure 19: The 2014 Porsche Carrera 30

Table 1: Summary Table of Electric, Fuel Cell, and Hybrid Cars 9

Table 2: Fuel Economy Improvement and Driving Performance of the 3 Hybrid Systems 16

Table 3: Hybrid Drive Mode Requirements 17

Table 4: Morphology Chart with 2 Chosen Solutions 19

Table 5: Gear Ratio Design 22

Table 6: Mission Scenario Description 27

Table 7: MKL-1 and Carrera Key Performance Comparison 31

Table 8: MKL-1 and Carrera Economic and Efficiency Factor comparisons 31

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ABSTRACT

This report outlines the design process of the MKL-1 – a dual hybrid sports car designed

to deliver the high performance capabilities of a high end internal combustion engine sports car.

After establishing key general requirements, it was possible to design the exterior styling, overall

performance, and energy system in order to meet the requirements. Once the MKL-1 was

compared to the 2014 Porsche 911 Carrera, an established rival in the sports car market, it was

possible to draw several conclusions before addressing key areas which could be improved.

The calculated 0-60 mph acceleration time of 4.72 seconds exceeded the general

requirement goal of 8 seconds and also the target goal of 5 seconds. This acceleration time was

on par with the Carrera despite having only 186 hp compared to the Carrera’s 350 hp. This was

due in large part to the significantly lower weight of the MKL-1, which was 2700 lbs compared

to the Carrera’s weight of 3957 lbs. In addition, the fuel consumption rating of 29 MPG

exceeded the 23 MPG rating of the Carrera, demonstrating how the MKL-1 has favorable fuel

economy compared to many similar sports cars. In summation, the lower cost of the MKL-1, its

higher fuel economy, and its emissions friendly dual hybrid drive make it a competitive

alternative to established sports cars in the market today. In this sense, the main goal of the

MKL-1 was accomplished.

A major area which was identified for improvement was the power to weight ratio, which

was calculated to be 0.069 hp/lbs. By increasing the power available by using a more powerful

engine with a lower power to weight ratio than the previous engine, it is possible to increase the

power to ratio to a higher number. In addition, lighter materials could be used to reduce the

weight to improve the ratio. By increasing the power to weight ratio, it is possible to decrease the

0-60 acceleration time, which is desired to improve the acceleration performance of the car. In

addition, the MKL-1’s fuel efficiency of 29 MPG is relatively low for a hybrid car in general,

and it was also targeted as a key area for improvement. Increasing the MPG rating of the car will

help make the MKL-1 stand out more amongst the established sports car market, and this will

help to make the MKL-1 a more attractive and emissions friendly option.

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1. INTRODUCTION

1.1 Transportation Problem

The geography, population density, and widespread traffic of Los Angeles County all

combine to make for a significant transportation and smog problem. The basin geography of Los

Angeles basin exists because of its location on a low lying coastal plain surrounded by deserts

and high mountains.1

As a result of this basin, the general air circulation in the area is limited.

The vast amounts of emissions from the auto exhausts of millions of cars combined with the

city’s weather and atmospheric conditions create an ideal environment for smog to be created.

The poor air quality that results from the smog is mostly due to the fact that the emissions from

cars are weakly dispersed in the Los Angeles basin, and this has been a major concern in the area

for several decades. The vast amount of cars in the area, the widely dispersed nature of the city,

and the very minimal public transport services available to the populace create transportation and

emissions problems. As of 2000, a transportation study of the Los Angeles basin reported that

only 6.6% of commuters in Los Angeles County utilized public transportation.2 In addition, it

was reported that 30% of commuters made daily commutes of more than 40 miles, 35% made

commutes of 20-40 miles, and only 35% made commutes of less than 20 miles. In general, the

CO2 emissions from cars have increased drastically in the last 20 years. From 1900 to 1999, the

United States has been the greatest contributor of CO2 emissions, as seen in Figure 1a. As seen in

Figure 1b, a significant majority of the CO2 emissions in the US are a direct result of emissions

from transportation.

a b Figure 1: a) Illustration of Cumulative CO2 Emissions from 1900-1999; b) Illustration of sources of US CO2

emissions in 19973

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1.2 Technology Background

A solution to the problem of car emissions, along with the heavy oil dependence of the

United States in general, is the implementation of vehicles which utilize alternative fuels. Three

major types of technology utilized in such cars are electric, fuel cell, and hybrid power. In

general, cars which utilize this technology use much less or no gasoline at all compared to

internal combustion engine vehicles, and fewer volatile emissions are produced from these

vehicles as well.

Battery-powered electric, or simply electric, cars are propelled by one or more electric

motors, which are in turn powered by electrical energy provided by batteries or other energy

storage devices. Electric cars only depend on batteries – no use of gasoline is required to power

these cars. The major benefit of electric cars is that they do not produce emissions or pollutants

from tailpipe exhaust like typical internal combustion engines do. Volatile pollutants like soot,

carbon monoxide, lead, ozone, and greenhouse gases are not emitted and the amount of CO2

emissions from electric cars are greatly reduced. A typical electric vehicle made in 2008 emits

115 grams of CO2 per kilometer driven compared to a typical US gasoline powered vehicle

which emits 250g of CO2 per kilometer driven.4

Another benefit to electric cars is that their

electric motors can provide high power to weight ratios, which may be appealing to consumers

who desire high performance vehicles. The Tesla Model S, shown in Figure 2, is an example of a

high performance electric vehicle. While pricing for the more expensive Model S Signature

Performance model starts at $105,400, it has a very fast 0 to 60 mph acceleration time of 4.2

seconds.5 Some cons of electrical vehicles include higher prices, the lack of established

infrastructure to recharge batteries, and limited ranges.

Figure 2: The 2014 Tesla Model S

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Fuel cell electric vehicles utilize a fuel cell in order to power their motors. Fuel cells are

used to convert chemical energy into electric energy from a chemical reaction with oxygen.

Typically, hydrogen is used in these reactions. A major difference between electric motors

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powered by batteries and those powered by fuel cells is that they can be refilled with hydrogen

instead of being directly recharged with electricity. Fuel cell vehicles which use hydrogen

produce zero emissions, and they also are considered fundamentally more efficient that

combustion systems.7 At fuel-to-electricity efficiencies of 40-60 percent, fuel cell systems are

able to achieve much higher efficiencies than steel engines that are only around 20% efficient.

When it comes to noise, they are also very quiet since they do not have as many moving parts as

combustion engine vehicles, with typical decibel outputs around the same volumes heard during

a typical conversation between people at about 60 decibels. Currently, there are no fuel cell cars

available to the public for commercial sales, but there are forklifts and material handling vehicles

which currently use the technology. Similarly to electric vehicles, a major concern to the mass

production of fuel cell cars is that there will need to be a new implementation for the refueling of

hydrogen based fuel cell vehicles. Another criticism is that the technology will take much too

long to be implemented before it is able to make any significant impact. Several prototypes of

fuel cell vehicles have been released by several major car companies with the intention to sell

them in 1 to 3 years’ time. An example of such a prototype is the Toyota FCV shown in Figure 3,

which is scheduled to be released in 2015.

Figure 3: The Toyota FCV prototype

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Hybrid vehicles utilize two or more discrete power sources to propel the vehicle. The

most common type of hybrid combines an internal combustion engine (ICE) with one or more

electric motors. These hybrids are referred to as hybrid electric vehicles, or HEVs. While HEVs

still use gasoline for power, they use electric motors to help with the burden so that they can

achieve better fuel economy than ICE vehicles. Technologies such as regenerative braking,

where a vehicle’s kinetic energy is converted into electric energy in order to charge the battery,

are implemented in HEV systems to improve their overall efficiency. In addition, numerous

HEVs have an idling feature where the ICE is idle and restarted when needed so that more

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energy is conserved. Emissions from hybrid cars are also lower than ICE cars since smaller

gasoline engines are typically needed to power cars which also have power from their electric

motors. There are 3 major types of HEVs: parallel, series, and dual. In parallel hybrids, the ICE

and electric motor are connected to the transmission and can transmit power to drive the wheels

at the same time. In a series hybrid, only the electric motor is used to drive the drivetrain, while

the ICE is used as a generator to power the electric motor and to recharge the batteries. Dual

hybrids combine the benefits of both series and parallel hybrid drives, and are more efficient

overall at the price of a higher overall purchase cost. As of December 2013, over 7 million HEVs

have been sold worldwide, with the United States being the largest market of all.9 Hybrids

continue to be a popular alternative to ICE vehicles, with several types of vehicles being

developed for consumers from all walks of life. An example of a high performance sport hybrid

is the McLaren P-1, shown in Figure 4. Using a 3.8 Liter turbocharged V8 ICE combined with

and electric motor, the P-1 possesses a total power of 903 bhp and can deliver an incredible 0 to

60 mph acceleration time of 2.7 seconds.10

Figure 4: The 2014 McLaren P-1

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A general comparison of the electric, fuel cell, and hybrid technologies can be seen in

Table 1. Of the 3, Hybrid HEV cars are arguably the most well-rounded. While HEVs are not

zero emission vehicles, their emissions are still low, and they come at a much more reasonable

cost than the others. They offer good acceleration performance, and they also offer a good range

without needing to charge. In terms of overall performance for price, HEV technology made the

most sense for the MKL-1.

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Category Electric Fuel Cell Hybrid (HEV)

Emission Zero emission Zero emission Low

Acceleration Low Good with booster

battery

Good

Range Short with long

charge time

Good with no charge Good with no charge

Cost Fairly expensive Very expensive Reasonable Table 1: Summary Table of Electric, Fuel Cell, and Hybrid Cars

After considering all 3 alternatives, it was decided that the MKL-1 would utilize hybrid

technology. A high performance hybrid car represents the most feasible and attractive market, as

the hybrid market continues to become more popular and demanding of the 3 technologies. In

recent years, prestigious companies such as McLaren, Porsche, and Mercedes-Benz have all

created high performance hybrids which produce lower emissions, are more fuel efficient, and do

not sacrifice overall performance in order to do so. By designing the MKL-1 as a high

performance hybrid, it will be entering a competitive and emerging market which shows much

promise for the future. Of the 3 major hybrid types, the dual hybrid was chosen in order to reap

the benefits of both series and parallel hybrids. This specific decision will be discussed in more

detail in section 3.2, in which the decisions made for the powertrain design of the car are

explained.

1.3 General Requirements

When designing the MKL-1, several general requirements were established as the bare-

minimum specifications for the car. It is important to keep in mind that the established minimum

requirements were not meant to be standards that needed to be reached. Rather, they were simply

established as minimums which were kept in mind to be exceeded (especially for the

performance specifications). The MKL-1 was designed to be a sport car that was practical and

emission-mindful. With such goals in mind, the minimum general requirements of the vehicle

are as follows:

Acceleration from 0-60 mph in 8 seconds

Maximum speed of 100 mph

Freeway cruise speed of 60 mph

Minimum zero emission range of 30 miles at 60 mph

Total range of 400 miles at 60 mph

Minimum smog emissions

Minimum energy consumption

Utilizes currently available technologies

Attractive and marketable compared with current vehicles

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2. STYLE DESIGN

2.1 Design Target

The MKL-1 was designed to be a sport vehicle which gave a genuine sports car feel

while being a hybrid. A modern and sporty look was desired, along with the expected high

performance of ICE sports cars. While an aggressive feel was desired, elegant and smooth

characteristics were also desired to give the car an air of controlled aggression. In conjunction

with high performance specifications, the goal of having a very light and well balanced car for

good handling was also established. Ultimately, a perfect balance of high performance and

elegance was desired in the design of the MKL-1. These characteristics would not be sacrificed

for the reduced emissions and efficiency of its hybrid system. Instead, the car would be designed

to exude the stimulating effects of a sports car in spite of its hybrid system. The final 3-view

design is shown in Figure 5.

Figure 5: 3-View drawing of the MKL-1 showing length, height, and width parameters

From the 3-view drawing, it can be seen that all the aforementioned goals of the car’s

design were met. A sporty-look is created from some aggressive features of the car, including the

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front of the car and its spoiler. Smooth curves apparent in the front, on the side, and at the top of

the car help to create a smooth elegance to compliment the car’s aggressive look. The fact that

the car is a hybrid does not distinguish the MKL-1 from other sports cars. In fact, the lower

emissions and higher overall efficiency of the car will help distinguish the MKL-1 from the rest

of the pack.

2.2 Major Parameters and Dimensions

For the MKL-1 to be nimble and well balanced, it was necessary to have a design with a

low center of gravity, a well-balanced chassis, and a relatively light overall weight. As such, the

height of the car was chosen to be a relatively short 4’4” so that the center of mass of the car was

lower to the ground for sharper handling. A short length of 13’ was chosen so that the car could

react very quickly to changes in direction without risk of major oversteer or understeer. A base

of 5’4”, which is relatively wide given the height and length of the car, also aids in quick steering

and ensures sport-performance handling. An estimated weight of 2700 lbs was targeted as a light

and realistic goal. Although the electric motor and dual hybrid system will add more weight to

the car, several parts of the car will be designed with strong and light materials such as carbon

fiber to ensure that its weight is kept at a manageable number. An estimate of the frontal area, A,

of the car can be found through the equation:

(1)

where b is the width of the base and h is the height of the car. For the MKL-1, the frontal area

was calculated to be 18.72 ft2.

In summary, the parameters and dimensions of the car are as follows:

Height of 4’4”

Length of 13’

Width of 5’4”

Estimated Weight of 2700 lbs

Frontal Area of 18.72 ft2

The calculated frontal area of the MKL-1 was then used to calculate the overall aerodynamic

drag, CD of the vehicle. This process will be described in section 3.1.

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3. PERFORMANCE

3.1 Power Requirement

In order to calculate the total power required to propel the MKL-1, the forces acting on

the car must first be analyzed. Figure 6 illustrates the forces which typically act upon a car in

motion.

Figure 6: Free body diagram of all forces acting on the car

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FT represents the total force acting upon the car, G is the gravitational force, D is the

aerodynamic drag, R is rolling resistance, and α is the angle of incline. All of these quantities are

related by the following equation:

(2)

where m is the mass of the car, V is its velocity, and g is the gravitational constant which is

approximately equal to 9.81 m/s2 or 32.17 ft/s

2. To simplify the calculation of , it can be

assumed that the car is on a flat road with its acceleration held constant. (2) then becomes

(3)

Thus, the total force FT that the MKL-1, or any car in general, must overcome is only dependent

on D and R. D can be found through

(4)

where represents the drag coefficient of the car (typically 0.24-0.6), is air density (1.225

kg/m3 at 15

◦ C at sea level), and A is the frontal area of the car which was calculated earlier.

Meanwhile, R is given by

(5)

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where is the rolling coefficient of the car (typically 0.01-0.03).

Determining the actual values for and requires considerable resources – resources which

were not available to be used on the design of the MKL-1. In this stage of the design process, a

full scale model of the MKL-1 was not available to be tested in a wind tunnel to test for or for

the shrouding trailer technique needed to test for . Instead, estimates were made to acquire

these values.

For an individual car, can be estimated using the White method. The White method involves

matching specific components of the car’s exterior to different variations of the specific

component in a chart shown in Appendix A. drag ratings. The 9 components include the front

end plan view, the windshield plan view, the roof plan view, the lower rear end plan view, the

front end side elevation, the windshield peak side elevation, the rear rook/trunk side elevation,

the cowl and fender cross-section front elevation, and the underbody. Each of the components

has a drag rating associated to them, and the sum of the total drag ratings is used to estimate .

The individual drag ratings for each component of the MKL-1 can be seen in the Drag

Coefficient Estimate Table in Appendix A. Using White’s method, is given by

(6)

For the MKL-1, the drag coefficient was calculated to be 0.284, which is considered reasonably

low for any car in general.

As for , an estimate of 0.015 was made based on typical driving speeds and the wheel base of

the MKL-1. The relationship between and V can be seen through the graph in Figure 7.

Figure 7: Standard variation of coefficient of tire rolling resistance versus velocity V13

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After using and to calculate D and R using (4) and (5) respectively, it was then possible to

calculate the power needed for drag, Pd, and the power needed for rolling, Pr, for given velocities

of the MKL-1. Pd is given by

(7)

Similarly, Pr is given by

(8)

Next, the total power required, Pt, is given by simply adding Pd and Pr. Hence, the following

equation:

(9)

Now, , , and can all be plotted against velocity on a Power Required Curve graph shown

in Figure 8. It was then decided that the maximum speed of the MKL-1 would be 150 mph,

which is a top speed typical of many sports cars. The spreadsheet used to create the graph can be

seen in Appendix B.

Figure 8: Power Required Curve graph

0 50 100 150 200 250

0

10

20

30

40

50

60

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160

km/h

kW

Po

we

r (h

p)

Velocity (mph)

Pr Pd Pt

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In order to calculate the maximum wheel power and the maximum engine power required

for the MKL-1, the power of acceleration, power at max speed, and power at incline must first be

identified.

Power of acceleration, Pa, is given by

(10)

(10) can be rewritten as

(11)

where is 60 mph, is the car’s 0 to 60 mph acceleration time, and is

, or 30 mph.

The target for the MKL-1 was a minimum of 5 sec, so this parameter was used to calculate a

of 94.5 kW, or approximately 126.7 hp.

The power at max speed, Pmaxspeed, can be found by simply observing the Power Required Curve

graph in Figure 8. The total power required at the max speed of 150 mph was found to be 103.2

kW, or approximately 138.4 hp.

The power at incline, Pi, is determined by observing Pd and Pt at the cruising speed of 60 mph.

Using an incline angle of 5◦, is given by

(12)

for the MKL-1 was calculated to be 114 kW, or approximately 193 hp.

The maximum wheel power, , is then found by choosing the highest value from Pa,

Pmaxspeed, and . Hence,

(13)

In this case, highest value, so the value of is 193 hp for the MKL-1.

Now, the maximum engine power required can be calculated using the following

equation:

(14)

For the MKL-1, the drivetrain loss was estimated to be 0.18 based on percentage losses from the

accessories, axle, and drive of both the ICE and Electric motor. Using this drivetrain loss,

was calculated to be 139 kW, or approximately 186.4 hp.

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3.2 Powertrain Design

Since it was decided that the MKL-1 would be a hybrid HEV, the decision between

series, parallel, or dual series/parallel had to be made. To do so, the pros and cons of each system

needed to be outlined and compared. A summary of the fuel economy improvement and driving

performance offered by the 3 hybrid types can be seen in Table 2.

Fuel Economy Improvement Driving Performance

Hybrid

Type

Idling Stop Energy

Recovery

High

Efficiency

Operation

Control

Total

Efficiency

Acceleration Continuous

high output

Series Superior Excellent Superior Superior Unfavorable Unfavorable

Parallel Superior Superior Unfavorable Superior Superior Unfavorable

Dual Excellent Excellent Excellent Excellent Superior Superior Table 2: Fuel Economy Improvement and Driving Performance comparison of series, parallel and dual

hybrid systems

Ultimately, the dual hybrid system was chosen with the established high performance goals in

mind. As a well-rounded drive, the dual drive excels over the series and parallel drives

individually. The dual system has the benefits of both series and parallel drives. As seen in Table

2, the dual system does not have any unfavorable characteristics in terms of fuel economy or

driving performance. The dual hybrid allows for maximum usage of the engine and motor, which

is important considering the high performance aspirations of the car. While the dual hybrid may

be more complex while also adding the most weight to the car, the car will already be designed

to be very light so that the added weight from the drive will not have any major effects. The dual

hybrid is also considerably more expensive than the other hybrid dives, but the MKL-1 is

designed to be a high performance car where cost is not the main priority. Cost is certainly

something that will be managed, however, the principles of the car’s design mean that high

performance will not be something that is sacrificed for lower cost.

Next, the following objectives were outlined for the powertrain:

Provide propulsion to the rear wheels (rear-wheel drive)

Charge the battery from wheels when braking

Start and stop the gasoline engine

Only use motor drive at low speed when battery is charged to improve efficiency

With these objectives in mind, the hybrid drive mode requirements were then established. The

roles of the gasoline engine and electric motor along with when the battery is charged at various

modes are outlined in Table 3. When the car starts, all the engine and motor both start. At

cruising velocity, the engine is engaged while the electric motor is generating energy and the

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battery is recharging. For zero emission cruise, the engine is cut and the motor is engaged. At

the same time, the battery is used to power the motor. In acceleration, the engine is chiefly used,

the motor aids in the propulsion, and the battery assists with the wide open throttle. In braking,

the engine is cut while the motor is in a phase of regenerative braking. When the car is stopped,

the engine idles, the motor is turned off, and the battery is generating energy. Overall, much of

the energy is used efficiently and effectively within the dual hybrid system. The dual hybrid

system adequately accomplishes the goal of delivering high performance capabilities while

maintaining its overall efficiency.

Mode Start Cruise Zero

Emission

Cruise

Accelerate

(Full

Throttle)

Brake Stop

Gasoline

Engine

Mode

Engine

Start

Vehicle

Propulsion

Fuel Cut Vehicle

Propulsion

Fuel Cut Idle

Electric

Motor

Mode

Motor

Start

Generation Vehicle

Propulsion

Assist with

Propulsion

Regenerative

Braking

Off

Charge

Battery

Engine

Start

Generation

for

Recharging

Power

Motor

Assist with

Wide Open

Throttle

Regeneration Generation

Table 3: Hybrid drive mode requirements

In order to define a functional diagram for the hybrid powertrain system of the MKL-1, it

is necessary to first start with the basic functions of any powertrain system. Namely, the

powertrain must take the materials of fuel and air with a desired power signal and generate

propulsion by converting into mechanical energy, exhaust, and output power signal respectively.

This is described as the overall powertrain function structure and can be seen in Figure 9.

Figure 9: Overall powertrain function structure

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Next, the “generate propulsion” box in Figure 9 could be decomposed and broken down as

shown in Figure 10. The fuel is stored and then converted into mechanical energy. The

mechanical energy is then transmitted and applied. Energy is lost during these processes, and this

is shown in the figures. In addition, a braking signal was added to the functional diagram.

Figure 10: First decomposition of the overall powertrain function structure

Finally, the final dual-hybrid powertrain structure can be created as shown in Figure 11. There

are now 7 function blocks total in the diagram with the addition of the distribution of electrical

energy, the storing of electrical energy, and the conversion from electrical energy to mechanical

energy.

Figure 11: Dual hybrid function structure

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In order to determine which functions are fulfilled by which mechanisms, several motors,

engines, and batteries were researched to develop a morphology chart where several

combinations could be made, as shown in Table 4. The choices of combinations were narrowed

down to two options. Solution 1 included an electric motor, gasoline engine, and lithium ion

battery, while solution 2 included an electric motor, diesel engine, and lithium ion battery. In the

end, it was decided that solution 1 would be used for the MKL-1. The lithium ion battery is

currently utilized in several high performance hybrids due to its high performance output and

light weight, and the electric motor is the most conventional and effective of the 4 motors for the

MKL-1. Gasoline was chosen over diesel in the end because of higher performance

characteristics and much cleaner emissions.

Functions 1 2 3 4

Convert Electricity

to Mechanical

Energy

Electric Motor Capacitor Drive

Motor

Piezo Quartz Motor Linear Motor

Convert Fuel to

Mechanical Energy

Gasoline I.C. Diesel I.C. Methanol I.C. Natural Gas Turbine

Store Electrical

Energy

Lithium Ion battery Lead Acid Battery Nickel Metal

Hydride Battery

Table 4: Morphology Chart with 2 chosen solutions

A lithium ion battery typically has an energy density of 150 Wh/kg and a power density

of 300W’kg. This information, along with more information on the battery can be found in

Appendix B. The battery power/energy (P/E) ratio is given by

(

)

[

] (15)

In this case, the battery P/E ratio is simply 2. Similarly, the P/E ratio of the motor is given by

(

) [

]. In order for the motor to operate properly, the following inequality must be

satisfied:

(

) (

) (16)

It is desirable to have the minimum required battery power, Emin, on board along with the

maximum required power Pmax, however, the minimum required battery calculated may not

supply enough power for the motor with . To deal with this problem, (16)

becomes

(

) (

) (17)

where

It is then possible to calculate by rearranging (17) via

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(

) (18)

The inequality in (17) suggests possible but undesirable solutions. Increasing is

accomplished by adding more batteries, and decreasing to decrease means

sacrificing performance – both are highly undesirable. As a hybrid solution, it is possible to add

engine power to the equation, hence the equation

(19)

From (19) it can be seen that can now be reduced by subtracting by

instead of directly decreasing . Letting y equal the battery P/E ratio and x equal

to , the following inequality can be formed

(20)

A graph of x versus y can then be created. In addition, the calculated P/E ratio of 2 of the battery

can be placed as a constant line. The intersection of these two lines can be used to determine the

power split between the engine and motor. The graph can be seen in Figure 12.

Figure 12: P/E ratio chart

It can be seen that the intersection occurs at about 2/3 of . Thus, the power split between the

engine and motor for the MKL-1 is 2:1. This ratio is common among sports hybrids, as it allows

the majority of the load to the engine rather than the motor. This allows for faster acceleration

performance, and this is a highly desirable feature for the MKL-1. In addition, the smaller

amount of energy required by the motor means that a smaller and lighter motor will suffice in

0

1

2

3

4

5

6

7

0 20 40 60 80 100 120 140

Bat

tery

P/E

Power (kW)

P/E = 2.0

Min. Engine Power Max Motor Power

P(max)=139 kW

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supplying the rest of the necessary power. As per the ratio, there will be a minimum engine

power of 92.67 kW/124.3 hp and a maximum motor power of 46.3kW/62.1 hp to account for the

approximate maximum power of 139 kW/186.4 hp.

With the minimum engine power and maximum motor power now known, it was possible

to select a specific engine and motor to be used in the MKL-1. After considerable research, it

was determined that the engine used on the 1996 Lotus Elise was the best fit. It is an inline 4

cylinder engine with a displacement of 1.8 that is able to produce 118-125 hp, which meets the

requirements of the engine that is needed. The 1996 Lotus Elise was able to have a relatively

quick 0-60 mph time of 5.8 seconds because of its light weight.14

In a way, the Elise had very

similar goals to the MKL-1, as it was designed as a nimble and quick lightweight sports car. The

car’s braking, cornering, and fuel consumption were improved because of its light weight. As

seen in a picture of the Elise in Figure 13, the exterior helped to inspire some of the lines seen on

the MKL-1. The similar sporty look with smooth elegant characteristics can be seen, and it was

only fitting that the MKL-1 would utilize the same engine as the Elise.

Figure 13: The 1996 Lotus Elise

15

It was also decided that the Azure AC90 motor would be used. This motor offers approximately

330 Nm of torque and up to 50 kW/67hp, which adequately covers the motor power requirement

of 62 hp. The motor does add significant weight at approximately 286 lbs, however it offers

high-end performance which is necessary for the MKL-1. The diameter of the engine is 1’3”, and

the length is 1’6”.

22

3.3 Drivetrain Design:

A drivetrain is needed for a car to deliver the power generated from its engine. Since

speed increases linearly with power, a gearbox can be used to deliver the maximum engine

power to different gears without having to achieve maximum speed. This linear relationship can

be seen in the simplified brake horsepower versus engine speed graph in Figure 14. While in

reality the relationship is not perfectly linear at the lowest and highest engine speeds, a linear

relationship can be assumed to simplify the calculations for the gear ratios of the car.

Figure 14: Simplified engine speed versus brake horsepower graph

16

In order to design the gear ratios for the MKL-1, it was first necessary to calculate the

differential ratio for the engine, R. The relationship between road speed, engine speed,

differential ratio, and gear ratio is shown via the equation

(21)

where V is road speed, D is the tire diameter, N is engine speed, and G is the gear ratio of a given

gear. For the MKL-1, the tire diameter was chosen to be 26 in. At the maximum speed of 150

mph, G is equal to 1, and the maximum N is 6000rpm for the MKL-1. Using these values, it was

possible to calculate R as 3.09. It was then possible to use this ratio to create the gear ratios

shown in Table 5.

Gear Max Speed(Mph) Gear Ratio

1 25 6.00

2 50 3.00

3 75 2.00

4 100 1.50

5 125 1.20

6 150 1.00

Table 5: Gear ratio design table

23

For the transmission of the MKL-1, a 6-speed manual was chosen. Many high-end sports cars

today use automatic transmissions or paddle shifting manual transmissions to simplify the

process for drivers, however, this is not the goal for the MKL-1. A manual transmission ensures

the driver gets a genuine feel for the road and also a genuine feel for the car. The MKL-1 is

designed for savvy drivers who still wish to get the most enjoyment and thrill from driving, and

it is for this reason that a conventional 6-speed manual transmission will be utilized. By having 6

speeds instead of 5, the car will have faster acceleration times and better fuel efficiency.

Numerous sports cars today use 6-speed transmissions because of its performance benefits.

3.4 Power Curve and Acceleration Performance

After successfully designing the gearbox, it was now possible to analyze the available

power for the MKL-1. Once the available power of the engine, P(engine). and motor, P(motor)

were both calculated, it was then possible to find P(total) by simply adding the two together.

Hence,

(22)

For given velocities of the MKL-1, it was then possible to plot all 3 curves onto the power

required curve previously shown in Figure 8 to create Figure 15. The spreadsheet used to create

the graph can be seen in Appendix C.

Figure 15: Final power required curve graph

0 50 100 150 200 250

0

10

20

30

40

50

60

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140 160

km/h

kW

Po

we

r (H

P)

Velocity (mph) Pr Pd Pt P(motor) P(engine) P(total)

24

From the legend, it is clearly indicated which curves represent Pr, Pd, Pt, P(engine), P(motor),

and P(total). It can be seen that the available power P(total) exceeds the total power Pt, which is

desirable for the purposes of faster acceleration. For the 6 peaks of P(engine), it can be seen that

the gears efficiently achieve the maximum power for faster acceleration. When creating Figure

15, it was assumed that there was no major loss in power or energy when changing gears. While

this is an unrealistic assumption, it was necessary to do this to simplify the graph, and the results

shown are adequate for the needed estimates to design the MKL-1.

In order to evaluate the acceleration performance of the MKL-1, the speed performance

must first be estimated before an acceleration speed curve can be created and analyzed. For a car

to accelerate, the power required to overcome drag and rolling resistance must be exceeded.

Thus, the excess power available which is not being used to overcome drag and rolling

resistance, Pe, can be used by the car to accelerate. Thus Pe is simply given by

(23)

For each incremental 1mph step i, (23) can be re-written as

(24)

The acceleration of the car, , is related to through the equation

(25)

where

(26)

Now, the time it takes to accelerate to a given speed can be found by

(27)

It is now possible to create an acceleration curve, shown in Figure 16. The relationship of

velocity versus time of the MKL-1 is shown.

Figure 16: Acceleration curve of the MKL-1

0

20

40

60

80

100

120

140

0 5 10 15 20 25

Ve

loci

ty (

mp

h)

Time (s)

25

The data used to create the curve can be seen in Appendix D. When it comes to acceleration

performance, the measurement of a car’s 0-60 time is commonly used as the gauge. From the

data, it was determined that the MKL-1’s 0-60 time was a very impressive 4.72 seconds. This

time is well below the 5 second goal that was established. In terms of its 0-60 time, the MKL-1 is

on par with several high end sports cars on the market today, and this is a testament to several of

the design aspects of the car. The major factors which affect acceleration are weight, power

available, and the power to weight ratio. The MKL-1’s light weight was key in the car’s great

acceleration performance, and the total power available in the car ensured that the car passed the

test of a sub 5 seconds 0-60 time with flying colors. In addition, the car’s low CD ensured that the

overall drag the car needed to overcome was significantly low, and this helped to improve the 0-

60 time.

4. ENERGY SYSTEM

In addition to the performance analysis in section 3, the analysis of how energy is

created, converted, used, and lost within a car is crucial. In general, the energy required to move

an object is determined by the power needed to move the object along with the time it takes to

move the object a given distance. To estimate the energy required to move a car, it is necessary

to make some simplifications for some common circumstances which the car will encounter. For

a vehicle cruising at 60mph, its energy usage can be determined via

(28)

and can be found by examining the power required graph that was

previously shown in Figure 15, or directly by evaluating equations (7) and (8) at .

There is also the case of when the vehicle is traveling at up an incline of 5o . This

is found by

(29)

It is understood that the car will not always be at a steady cruise, as it will need to accelerate to

reach certain velocities. As a standard, the 0-60 acceleration energy will be calculated. This will

be explained in more depth later in the section.

The fuel required to provide energy to the car in any scenario is given by

(30)

where Drivetrain Loss is the same value of 0.18 from the previous section, Time is the time

elapsed in hours, and BSFC is the Brake Specific Fuel Consumption. BSFC is a number that is

determined by a car’s specific engine, and it determines the required amount of fuel that is used

per a given amount of time. Typically, the BSFC of a car ranges from 0.3 to 0.8 kg/hr depending

on the phase at which the car operates. The BSFC increases at high engine speeds due to

increased friction, and it increases at low speeds due to the increased amount of time for heat

losses from the gas to the cylinder and piston wall in the engine. BSFC decreases as compression

ratio decreases, as a result of higher thermal efficiency. It is possible to improve BSFC by

26

reducing the engine size to help reach the optimum operation line. This is a very important

concept, as the engine is very inefficient when functioning at low engine speeds.

When the engine is in cruise, the batteries which supply the motor will be fully charged, so the

fuel needed by the motor will be dependent on its BSFC. This amount of fuel is given by

(31)

where the Generation Loss is the percent lost by the generator when it is supplying power, and

is the energy of the motor. In the case of the MKL-1, it is estimated that the generation

loss is 20%. is given by the equation

(32)

BSFC is dependent on the engine load of the vehicle and the engine speed of the vehicle. To

solve for the engine speed at a given velocity, gear ratio, differential ratio, and tire size equation

(21) can be rearranged as

(33)

It is now possible to estimate the BSFC of given driving situations via the BSFC chart shown in

Figure 17 below.

Figure 17: BSFC Chart

From this chart, it is possible to estimate the BSFC numbers for cruise, hill climb, and urban

driving. The engine load is estimated to be 30%, 40%, and 5% for cruise, hill climb, and urban

respectively. In addition, it was determined that the engine speeds foe each condition were 2400

rpm, 3200rpm, and 2000 rpm for cruise, hill climb, and urban. By matching the estimated engine

load percentage and engine speeds, it was possible to determine the BSFC numbers as

400g/kWh, 350 g/kWh, and 800 kw/h for cruise, hill climb and urban.

With the BSFC’s estimated, it was now possible to create the following Mission Scenario Table

in Table 6.

27

Table 6: Mission Scenario Description Table

Phase

Speed

(mph,

*km/h)

Time

(min,

*sec)

Distance

(mile,

*km)

Power

Usage

(kW)

Engine

Speed

(RPM)

Engine

Load

(%)

Engine

BSFC

(g/kWh)

Engine/

Motor

Energy

Split

(%/%)

Energy

Usage

(kWh)

Energy/Cycle

No. of

Cycles

Total

Energy Usage Total

Time

(min)

Total

Range

(mile,

*km)

Engine

(kg)

Motor

(kWh)

Engine

(kg)

Motor

(kWh)

Acceleration 0-60 4.36* 0.072 X X 100 X 100/0 X X X 2 X X X X

Deceleration* 60-0 5 0.083 X X X X 0/100 X X X 0 X X X X

Cruise 60 30 30 25 2400 30 400 50/50 6.25 1.25 3.125 9 11.25 28.13 270 270

ZEV Cruise 60 15 15 25 X X X 0/100 6.25 X 6.25 3 X 18.75 45 45

Hill Climb (5o) 60 5 5 50 3200 40 350 60/40 4.17 0.88 1.67 2 1.76 3.34 10 10

Urban 30 30 15 10 2000 5 800 25/75 5 1 3.75 5 5 18.75 150 75

Totals 18.01 68.97 475 400

28

In order to calculate the mile per gallon (MPG) fuel efficiency of the car, the total fuel needed

must first be calculated. This is calculated via the equation

(34)

From Table 6, it can be seen that the total Engine Fuel Needed is 18.01kg, the total Motor

Energy Usage is 68.87 kWh, the Generator Motor Loss is 20% as mentioned earlier, and

is 400 g/kWh. Thus, the was calculated to be 52.5 kg, or

13.87 gal. Dividing the total range by the Total Fuel Needed, a fuel efficiency of 28.8 MPG was

achieved for the MKL-1. The fuel efficiency rating is good when considering the high

performance outputs that were established as goals for the MKL-1. While hybrids like the

Toyota Prius typically have higher MPG ratings, they are designed to be as fuel efficient as

possible without much regard to the acceleration performance of the car. For the purposes and

design goals of the MKL-1, an MPG rating of approximately 29 MPG is certainly adequate.

In terms of practicality, it makes sense to round the number to 14 gal when designing the fuel

tank of the car. The fuel tank will weigh approximately 77 lbs and have dimensions of 1’3” by

1’3” by 1’3”. It is also important to specify the type of fuel which is recommended for the car.

Like numerous high end cars, it was decided that the best fuel for the car would be premium 91

octane rated unleaded gasoline. To preserve the engine and aid in the performance of the car,

premium unleaded fuel makes the most sense for use in the MKL-1.

For the battery of the car, it was decided that the Lithium Ion Battery used in the McLaren P1

would be utilized. The high density battery weighs just 75 kg, and is capable of being fully

charged with plug-in equipment in only 2 hours. While the battery is capable of being charged

quickly, it was designed to prioritize rapid power delivery, and it is on par with the best batteries

used in cars today. While the battery itself is undoubtedly much more expensive, the cost-benefit

of having a battery is very good as it offers the highest level of performance in today’s market.

With the requirements of the engine, motor, battery, fuel tank, transmission, and tires

established, it is now possible to design the energy schematic. This can be seen on the next page

in Figure 18. The front of the car contains the engine, motor, and transmission, while the back

contains the battery and fuel tank. This set up is a common and conventional set-up for HEV

hybrids, and it offers the best balance for the MKL-1. With this schematic, the weight is

distributed fairly evenly across the entire frame of the car, and this aids in the handling

capabilities of the car. Although the engine is in the front, the car is driven by the rear wheels,

which has long been established as a shared characteristic between traditional sports cars for

decades. Overall, this schematic allows for improved weight distribution, better handling, a

favorable center of mass, and high acceleration performance characteristics. The design is

consistent with all of the established goals of the MKL-1, and it succeeds in providing the driver

with one of the best driving experiences possible.

29

Figure 18: MKL-1 Energy Schematic (Right side is front, Left side is back)

30

5. COMPARISON AND DISCUSSION

It is necessary to compare the MKL-1 to high-end rivals to address the strengths and

weaknesses of the vehicle. In this case, a formidable rival in the 2014 Porsche 911 Carrera was

chosen. While the Carrera is not a hybrid, one of the goals of the MKL-1 was to be on par in

terms of performance with established sports cars in spite of the fact that it was a hybrid. The

Carrera has been a staple of Porsche and sports cars in general for several decades, and it has

amassed a prestige and popularity due to its consistent high performance characteristics and

sporty look. The Porsche Carrera can be seen in Figure 19.

Figure 19: The 2014 Porsche Carrera

17

In terms of overall performance, the Carrera has a slight edge. The Carrera is able to output a

maximum of 350 hp and is able to accelerate from 0-60 mph in 4.6 seconds compared to the

MKL-1’s power of 186 hp and 0-60 time of 4.72 seconds.18

In addition, the top speed of the

Carrera is 179 mph compared to the MKL-1’s top speed of 150 mph. The MKL-1 is 1257 lbs

lighter than the Carrera, however it has a lower power to weight ratio of 0.069 hp/lbs compared

to the Carrera’s ratio of 0.088 hp/lbs. While the Carrera may have the edge in terms of

acceleration and power performance, the MKL-1 is not far behind. In keeping up to par with the

Carrera, the MKL-1 has proven that it can compete with similar established sports cars in the

market. The slightly longer 0-60 time of the MKL-1 was achieved despite having a maximum

power that was 164 hp lower than the Carrera, and this is a testament to the car’s overall

efficiency and resourcefulness. While the MKL-1 was outdone by the Carrera in the performance

department, the MKL-1 was successful in its design goals as it was arguably on par with one of

the most famous and established sports cars in the world despite being a lower-powered hybrid.

The key performance specifications are summarized in Table 7.

31

Specification MKL-1 Carrera

Maximum Power [hp] 186 350

Engine Size [L] 1.8 3.4

Cylinder Configuration Inline 4 Flat 6

0-60 Acceleration [sec] 4.72 4.6

Top Speed [mph] 150 179

Weight [lbs] 2700 lbs 3957 lbs

Power to Weight ratio [hp/lbs] 0.069 0.088 Table 7: MKL-1 and Carrera key performance comparison

When considering economic factors and efficiency, the MKL-1 holds the edge over the Carrera.

The MKL-1 has a higher MPG rating of 29 versus the Carrera’s 23. In addition, the MKL-1 has a

longer range with a smaller fuel tank than the Carrera, with the MKL-1 having a range of 400 mi

with a fuel tank capacity of 14 gal compared to the Carrera’s range of 389 mi and fuel tank

capacity of 16.9 gal.19

Both high performance cars utilize premium unleaded gasoline to aid in

performance and efficiency. The target price range of the MKL-1 is significantly less than the

Carrera at $75,000 compared to $84,300. The key economic and efficiency specifications are

summarized in Table 8.

Specification MKL-1 Carrera

Fuel Consumption

(City/Highway Average)

[MPG]

29 23

Range [mi] 400 389

Fuel Tank Capacity [gal] 14 16.9

Fuel Type Premium Unleaded Premium Unleaded

Price [USD] 75,000 84,300 Table 8: MKL-1 and Carrera economic and efficiency factor comparison

In terms of improvement of the MKL-1, there are several areas that could be addressed. Ideally,

the car should have a higher power to weight ratio. Also, 29 MPG is a relatively low fuel

consumption rating for a hybrid, and that number could be improved. The 0-60 time is

acceptable, however, one could argue that for such a light car, that number should be even less

than what it is. Suggestions for these areas of improvement such as these will be discussed in

depth in section 7.

Ultimately, the MKL-1 is able to offer performance characteristics on par with the Carrera at

generally better economic conditions and efficiency. In this way, the MKL-1 certainly

accomplished its main goal – to compete with high-end sports cars with a hybrid engine. The

MKL-1 offers cleaner emissions due to its dual hybrid system, and its lower price makes it very

intriguing to drivers seeking a thrilling driving experience while being environmentally friendly.

While there are several areas which can be improved, the MKL-1 represents a formidable rival to

the established sports car market, and this new company will continue to learn and grow to

develop better cars. Being a car with a lower price and a better overall efficiency, the MKL-1

could certainly hold its own in a competitive sports car market – even against cult classics such

as the Porsche 911 Carrera.

32

6. CONCLUSIONS

In conclusion, the MKL-1 offers great performance capabilities as a hybrid, and it is

projected that it will be able to hold its own in a highly competitive and established sports car

market. The design of the MKL-1 met all of the minimum criteria that were asked of it, and it

excelled in terms of its overall performance. In being on par in several comparisons with the

Porsche 911 Carrera, the MKL-1 demonstrated that it could challenge the status quo of iconic

sports car of today’s world.

At a relatively lower cost, the MKL-1 is clearly a viable alternative to drivers who are

seeking the complete driving experience at a reduced cost. The well-balanced frame, low center

of gravity, and light weight all help the MKL-1 handle with the precision and acuity of high end

sports cars. While the car has significantly less power available, it is able to accelerate very

quickly because of its lightweight design, and in this way it accomplishes more with less. Its

sleek yet aggressive design certainly captures the imagination, and it can be said that its high

performance capabilities to match make the MKL-1 the complete package. Several design

aspects of the car such as the 6-speed traditional manual transmission and its rear-wheel drive

ensure that the driver is able to connect with the car and the road, rather than having heavy

computer aid or automated features that would interfere with the traditional joys of driving. The

MKL-1 gives the feel of a traditional fun-to-drive, high performance sports car while using a

state of the art dual hybrid system to deliver its power.

The MKL-1 proves that it is possible to enjoy the joys of a sports car while being

environmentally aware and efficient. The lower emissions produced from its hybrid engine

ensure that the car will not leave a large carbon footprint, and it is also considerably fuel efficient

compared to other sports car which offer similar performance characteristics. The MKL-1 is

more than capable of being used as an “everyday” car, with several components inside the car

that are durability tested and capable of operating at low maintenance costs. With its high

performance battery that is able to fully recharge in two hours, the MKL-1 conveniently saves

time and requires fewer trips to the gas station than conventional sports cars do. The MKL-1 has

an excellent balance of components that are efficient, durable, and capable of outputting high

performance on a daily basis.

The MKL-1 is no McLaren P1, nor does it try to be. Instead of being a million dollar car

with some of the world’s best performance characteristics, high maintenance costs, and limited

drivability, the MKL-1 strives to provide drivers with a car that gives ample sports performance,

a great feel for the road, and a car that is able to go the distance at a much more reasonable cost.

In the design of the MKL-1, its established target design was always kept in check. Drivers who

wish to have a fun-to-drive car which gives the complete driving experience will more than

likely appreciate what the MKL-1 has to offer.

33

7. RECOMMENDATIONS

While the MKL-1 succeeds in all of the goals established beforehand, there are several

areas which could be improved in order to provide a better car for the consumers. As a company

that is attempting to establish itself in a market of prestigious car companies, it is imperative that

the car is analyzed with heavy scrutiny to improve its design in an ever-changing sports car

world.

As previously mentioned, the power to weight ratio is relatively low at 0.069 hp/lbs. This

number can be significantly improved in two ways: by increasing the power available in the car,

or by reducing the overall weight of the car. Increasing the power available in the car suggests

the utilization of a larger engine or motor, and this will certainly increase the overall weight of

the car. Because of this fact, increasing the power available is only viable for the MKL-1 if an

engine or motor, which has a high power output has a very high power to weight ratio itself, is

implemented. In this way, the added weight will be utilized most effectively to increase the

power to weight ratio of the car. In addition, the reduction of weight of the car can be achieved

by simply choosing lighter materials for components for the car. Both of these solutions entail

higher costs, and that is something which will need to be managed accordingly to stay relatively

close to the target price range. Seeking to decrease the power to weight ratio is definitely an

option which should be explored further, as doing so will most likely increase the 0 to 60

acceleration time of the car. In terms of overall performance benefits to the MKL-1, decreasing

the power to weight ratio has the potential to significantly improve the car.

In addition to improving the acceleration performance of the car, another area for

improvement is the fuel consumption efficiency of the car. At 29 MPG, the MKL-1 is not as fuel

efficient as typical dual hybrid cars are. While fuel efficiency is not as high of a priority as

acceleration performance, it is definitely a number which should be improved for the future.

Having the car be more fuel efficient while maintaining high performance standards could really

help to separate the MKL-1 from other established sports cars. By decreasing the weight or by

choosing a more efficient motor or engine, it is possible to increase the car’s MPG rating. Again,

this is something which will more than likely come at more expensive costs, and cost-benefit

analysis will be crucial when attempting to improve the car’s MPG. A higher fuel efficiency will

ultimately make the MKL-1 more attractive in a highly competitive market.

Indeed, there is room for improvement for the MKL-1, but this is normal for a company

which is trying to establish its footing. With proper diligence and attention to detail in the

analysis of the car, improvements will continuously be made to improve the car for the sake of

the customer. While the initial design of the MKL-1 exceeded the goals which were established

for it, it is important to always strive for improvements to build the reputation and satisfaction

associated with the company’s brand. The future looks bright for the MKL-1, and hard work will

continue to be allocated to make sure the car is the best that it can be.

34

8. REFERENCES

1) http://www.csun.edu/~hmc60533/CSUN_103/weather_exercises/soundings/smog_and_in

versions/Smog_main.htm

2) Lecture 1, slide 15

3) Lecture 1, slide 8

4) "Wheel to Well Analysis of EVs" (PDF). MIT Electric Vehicle Team. MIT. April 2008.

Retrieved 2009-07-09.

5) Frank Markus (2012-06-22). "2012 Tesla Model S First Drive". Motor Trend. Retrieved

2012-06-22.

6) http://image.motortrend.com/f/roadtests/sedans/1110_2012_tesla_model_s_first_ride/340

71035/2012-Tesla-Model-S-passengers-side-front-three-quarters.jpg

7) http://www.fuelcells.org/base.cgim?template=benefits

8) http://www.extremetech.com/extreme/174503-toyota-is-ready-to-sell-fuel-cell-cars-in-

2015-after-a-decade-of-prototypes

9) Toyota News Release (2014-01-14). "Worldwide Sales of Toyota Hybrids Top 6 Million

Units". Toyota USA. Retrieved 2014-01-15.

10) http://www.zeroto60times.com/Fastest-Cars-0-60-mph.html

11) http://www.topgear.com/uk/assets/cms/788f3f0b-9193-47dc-bde7-

12fae2e77328/Thumbnail.jpg?p=131115_03:09

12) Lecture 9, slide 2

13) Lecture 9, slide 3

14) "Lotus Elise S1 1995 - 2001 Series 1 1.8". Archived from the original on 2008-02-13.

Retrieved 2008-03-06.

15) http://autocognito.com/wp-content/uploads/2012/06/1996-lotus-elise.jpg

16) Lecture 11, slide 6 (figure 14)

17) http://img1.findthebest.com/sites/default/files/844/media/images/2014_Porsche_911_Car

rera_4S_1077044.jpg

35

18) http://www.porsche.com/usa/models/911/911-carrera/

19) http://www.edmunds.com/porsche/911/2014/features-specs.html

The lecture slides which were referenced in references 2, 3, 12, 13, and 16 were created by

Professor Yan Jin. Also, the White’s Method Charts in Appendix A and Appendix C were

provided by Professor Jin.

36

9. APPENDIX

Appendix A: White’s Method Data

37

Drag Coefficient Estimate Table

Category Component Low Dev2 Dev Best Dev

2 Dev High

A Plan view, front end 2 0 0 2 0 0 2

B Plan View, windshield 3 0 0 3 0 0 3

C Plan View, Roof 1 0 0 1 0 0 1

D Plan View, Lower Rear End 2 0 0 2 0 0 2

E Side Elevation, Front End 1 0 0 1 0 0 1

F Side Elevation, Windshield Peak 1 0 0 1 0 0 1

G Side Elevation, Rear Roof/Trunk 1 0 0 1 0 0 1

H Front Elevation, Cowl and Fender

Cross-Section

1 0 0 1 0 0 1

I Underbody 1 0 0 1 0 0 1

TOTAL

SumB-

Stdv:

13

ΣDev2:

0

SumB

:

13

ΣDev2:

0

SumB

+Stdv:

13

38

Appendix B: Power Required Curve Data

D V [mph] V [m/s] V [km/hr] Pr [KW] Pd [KW] Pt [KW] Pr [BHP] Pd [BHP] Pt [BHP]

0 0 0 0 0 0 0 0 0 0

6.039327 10 4.4704 16.0934 0.805631 0.026998 0.832629 1.080369 0.036205 1.116574

24.15731 20 8.9408 32.1868 1.611262 0.215986 1.827247 2.160738 0.289642 2.450379

54.35394 30 13.4112 48.2802 2.416893 0.728952 3.145844 3.241107 0.97754 4.218647

96.62923 40 17.8816 64.3736 3.222524 1.727885 4.950409 4.321475 2.317132 6.638608

150.9832 50 22.352 80.467 4.028155 3.374776 7.40293 5.401844 4.525649 9.927493

217.4158 60 26.8224 96.5604 4.833785 5.831612 10.6654 6.482213 7.820321 14.30253

295.927 70 31.2928 112.6538 5.639416 9.260385 14.8998 7.562582 12.41838 19.98096

386.5169 80 35.7632 128.7472 6.445047 13.82308 20.26813 8.642951 18.53706 27.18001

489.1855 90 40.2336 144.8406 7.250678 19.68169 26.93237 9.72332 26.39358 36.1169

603.9327 100 44.704 160.934 8.056309 26.99821 35.05451 10.80369 36.20519 47.00888

730.7585 110 49.1744 177.0274 8.86194 35.93461 44.79655 11.88406 48.18911 60.07317

869.663 120 53.6448 193.1208 9.667571 46.6529 56.32047 12.96443 62.56257 75.527

1020.646 130 58.1152 209.2142 10.4732 59.31506 69.78826 14.04479 79.5428 93.5876

1183.708 140 62.5856 225.3076 11.27883 74.08308 85.36191 15.12516 99.34704 114.4722

1358.849 150 67.056 241.401 12.08446 91.11895 103.2034 16.20553 122.1925 138.3981

Component SI units US units

fr 0.015 0.015

mass 1224.699 kg 2700 lbs

W 12014.3 N 86869.8 ft lbm/s2

Cd 0.284 0.284

rho 1.225 kg/m3 0.0023769 slugs/ft3

A 1.737286 m2 18.7 ft2

39

Appendix C: Battery Types Data

40

Appendix D: Final Power Required Data

V [mph] V [m/s] V [km/h] P(motor) [kW]

P(engine) [kW]

P(total) [kW]

P(motor) [hp]

P(engine) [hp]

P(total) [hp]

0 0 0 0 0 0 0 0 0

25 11.2 40.2 27.6 92.7 120.3 37.0 124.3 161.3

26.5 11.8 42.6 29.8 92.7 122.5 40.0 124.3 164.3

26.5 11.8 42.6 29.8 49.2 79.0 40.0 65.9 105.9

40 17.9 64.4 46.3 74.0 120.3 62.1 99.2 161.3

50 22.4 80.5 46.3 92.7 139.0 62.1 124.3 186.4

53 23.7 85.3 46.3 92.7 139.0 62.1 124.3 186.4

53 23.7 85.3 46.3 65.4 111.7 62.1 87.7 149.8

75 33.5 120.7 46.3 92.7 139.0 62.1 124.3 186.4

79.5 35.5 127.9 46.3 92.7 139.0 62.1 124.3 186.4

79.5 35.5 127.9 46.3 74.0 120.3 62.1 99.2 161.3

100 44.7 160.9 46.3 92.7 139.0 62.1 124.3 186.4

106 47.4 170.6 46.3 92.7 139.0 62.1 124.3 186.4

106 47.4 170.6 46.3 78.5 124.8 62.1 105.2 167.3

125 55.9 201.2 46.3 92.7 139.0 62.1 124.3 186.4

132.5 59.2 213.2 46.3 92.7 139.0 62.1 124.3 186.4

132.5 59.2 213.2 46.3 82.1 128.4 62.1 110.1 172.2

150 67.1 241.4 46.3 92.7 139.0 62.1 124.3 186.4

159 71.1 255.9 46.3 92.7 139.0 62.1 124.3 186.4

Appendix E: Acceleration Curve Data

V (mph) Vi bar Pei a t (sec)

0 0.00 0.00 0.00 0.00

25 12.50 156.30 55.87 1.34

50 31.25 221.10 31.61 3.71

60 40.00 215.50 25.94 4.72

75 53.13 207.10 17.42 6.24

100 76.56 184.10 10.74 10.05

125 100.78 146.10 6.48 15.67

150 125.39 93.10 3.32 23.82