Math is essential to all aspects of automobile design and function. It is used in drafting blueprints, measuring part dimensions, determining production ratios and assembly line speeds, calculating horsepower, tire size, and fuel efficiency. Advanced applications include using equations to optimize aerodynamic body shapes in Formula 1 cars and exploit principles like Bernoulli's equation to increase speed. The presentation provides many examples of how mathematical concepts are applied throughout the automobile manufacturing process and in everyday car functions like odometers and speedometers.
Investigations of Drag and Lift Forces Over the Profiles of Car Using CFDijsrd.com
Aerodynamic characteristics of racing car are of significant interest in reducing racing accidents due to wind loading and save the fuel consumption. This work outlines the process taken to optimize the geometry of a vehicle. Vertices and edges of car were imported into GAMBIT and a computational domain is created. An unstructured triangular mesh was then applied. The goal is to obtain a better flow around the car model to lower the coefficient of drag force; the work is carried out in a ANSYS CFD FLUENT program towards a converged solution. These practices are helpful to redesign existing vehicles in order to improve handling and increase fuel efficiency. In the present work an attempt has been made by considering three models of car by varying speed of vehicle, the pressure coefficients and drag coefficients are obtained.
This document contains 4 questions related to optimal assignment problems. Question 1 involves assigning 4 machines (M1, M2, M3, M4) to 5 vacant places (A, B, C, D, E) based on location costs to find the optimal schedule. Question 2 involves allocating 5 jobs (A, B, C, D, E) to 5 employees based on the time each will take to minimize total man-hours. Question 3 involves assigning 5 types of garments to 5 tailors to maximize total profit. Question 4 involves assigning 5 batting positions to 5 batsmen based on their average runs to maximize total runs scored.
Mathability awaken the math genius in your child☁ Sourabh Kumar
This document provides an introduction to the author Shakuntala Devi and discusses math ability or "mathability".
It begins by introducing Shakuntala Devi as an internationally renowned mathematical genius and discusses how she spends her time working to establish an institute for mathematics education. It then discusses the concept of "mathability", which it defines as an attitude and acquired skill that can enhance problem solving and intelligence potential. The author aims to clarify misconceptions about mathability and demonstrate how it is a skill that can be nurtured in children and adults.
Volumetric efficiency calculating your cars volumetric efficiencyZulkarnian Nasrulllah
1) Volumetric efficiency is a measurement of how close the actual air flow into an engine is to the theoretical maximum air flow, given the engine's displacement. It is affected by various losses within the engine.
2) To calculate a car's volumetric efficiency, one must log engine speed, mass air flow rate, and intake air temperature data using a scan tool. These values are used to find actual air flow, which is divided by theoretical air flow to yield a percentage for volumetric efficiency.
3) Theoretical air flow is calculated based on engine displacement, maximum rpm, and whether it is a 2-stroke or 4-stroke engine. Actual air flow comes from mass air flow rate multiplied by air
Twin Turbocharging Inline Six Internal Combustion EngineRobertBeneteau
Design project to twin turbocharge an inline six BMW M3 engine using mathematical computations and engine simulations to increase the power output upwards of 500 horsepower.
Design and performance Analysis of a 5 Speed Manual Transmission System for I...IRJET Journal
This document summarizes a research paper that analyzed the design and performance of a 5-speed manual transmission system for an Indian drive cycle. The researchers obtained various gear ratio sets by varying final drive ratios, intermediate gear ratios, and gear stepping. They then used ADAMS CAR software to simulate the performance of the transmission designs under different conditions. Their results showed that increasing the final drive ratio from 4.467 to 4.8 improved acceleration performance by providing more wheel torque in first gear. They also found that increasing the first gear ratio from 3.72 to 4.2 further enhanced acceleration. The optimal transmission design was selected based on achieving the best acceleration performance.
Sheet1ASU - CON 243NameRoss DodenhoffHomework Chapter 2Student IDP.docxbagotjesusa
Sheet1ASU - CON 243NameRoss DodenhoffHomework Chapter 2Student IDProblem StatementYour company has just been awarded a large contract that would be well suited for Caterpillar 740B Articulated Haul Trucks. A local rental yard said that they will rent you the trucks for $13,200 per month plus 7.0% sales tax not including any operating costs. What would it cost to purchase the trucks instead of renting them? The purchase price including sales tax and attachments is $575,000. The project will last 5 years and you are not sure that you will have work for the trucks after this project therefore you need to plan on selling them at the end of 5 years for 40% of the original purchase price. According to the schedules that the project managers have put together it appears that you will be able to get 1,800 hours of utilization per year on the trucks during all five years and they also anticipate 50 minute efficiency working hours. According to the Chief Financial Officer of the company your cost of money is 6% and the annual insurance amount on each truck will be 0.5%. Your tire sales person says that a set of 6 tires will cost $25,000, last 3,800 hours and the average repairs will be about 15% of the purchase price over the life of the tires. The preventative maintenance schedule that your fleet is on has PM1 oil changes completed every 250 hours with oil, lube and filter cost at $15.00 per gallon, repair and maintenance cost is $5.00 per hour and your throttle load factor for articulated trucks is 60%. Because they are trucks and will not be scraping the ground they do not have any high wear ground engaging items to wear out. Use the product specifications included with this assignment to determine the Gross Flywheel Horse Power, engine crankcase capacities and any other information that you may need. Diesel fuel is $2.50 per gallon for red dyed.Question 1(16 POINTS)What is the Average Annual Investment for this machine?Question 2(24 POINTS)What is the ownership cost per hour?Puchase Price-salvage value-cost of tires+cost of capital+overhead=Ownership expensePurchase Price= 575,000Salvage Value= 230,000Cost of Tires= 25,000Question 3(36 POINTS)What is the operating cost per hour?Question 4(8 POINTS)What is the total cost per hour to your company if you were to own this machine? Question 5(8 POINTS)What is the total cost per hour to your company if you were to rent this machine? Question 6(8 POINTS)For only this project, would it be more economical to rent or buy this machine? Explain why.Question 7(BONUS POINTS)In considering owning vs renting, what is the breakeven point in hours (i.e. how many hours would you need to utilize the equipment before it becomes more economical to own the machine)?
740B
Articulated
Truck
Engine
Weights
Engine
Model
Tier
4
Interim/EU
Stage
IIIB
Cat®
C15
ACERT™
Rated
Payload
39.5
tonnes
43.5
tons
Gross
Power
–
SAE
J1995
365
kW
489
hp
Body
Capacities
Net
Power
–
ISO
14396
361
kW
484
hp
Heaped
SAE
2:.
- The document discusses external aerodynamic analysis of heavy commercial vehicles (HCVs) using computational fluid dynamics (CFD) simulation and wind tunnel testing.
- It aims to study the coefficient of drag of HCVs with different shapes and heights of wind deflectors. Three-dimensional models of the HCV are created in CATIA and analyzed in ANSYS-CFX to compare flow patterns and drag forces.
- The simulation results will be validated through subsonic wind tunnel testing of scaled physical models, which will also utilize smoke flow visualization and surface pressure distribution measurements.
Investigations of Drag and Lift Forces Over the Profiles of Car Using CFDijsrd.com
Aerodynamic characteristics of racing car are of significant interest in reducing racing accidents due to wind loading and save the fuel consumption. This work outlines the process taken to optimize the geometry of a vehicle. Vertices and edges of car were imported into GAMBIT and a computational domain is created. An unstructured triangular mesh was then applied. The goal is to obtain a better flow around the car model to lower the coefficient of drag force; the work is carried out in a ANSYS CFD FLUENT program towards a converged solution. These practices are helpful to redesign existing vehicles in order to improve handling and increase fuel efficiency. In the present work an attempt has been made by considering three models of car by varying speed of vehicle, the pressure coefficients and drag coefficients are obtained.
This document contains 4 questions related to optimal assignment problems. Question 1 involves assigning 4 machines (M1, M2, M3, M4) to 5 vacant places (A, B, C, D, E) based on location costs to find the optimal schedule. Question 2 involves allocating 5 jobs (A, B, C, D, E) to 5 employees based on the time each will take to minimize total man-hours. Question 3 involves assigning 5 types of garments to 5 tailors to maximize total profit. Question 4 involves assigning 5 batting positions to 5 batsmen based on their average runs to maximize total runs scored.
Mathability awaken the math genius in your child☁ Sourabh Kumar
This document provides an introduction to the author Shakuntala Devi and discusses math ability or "mathability".
It begins by introducing Shakuntala Devi as an internationally renowned mathematical genius and discusses how she spends her time working to establish an institute for mathematics education. It then discusses the concept of "mathability", which it defines as an attitude and acquired skill that can enhance problem solving and intelligence potential. The author aims to clarify misconceptions about mathability and demonstrate how it is a skill that can be nurtured in children and adults.
Volumetric efficiency calculating your cars volumetric efficiencyZulkarnian Nasrulllah
1) Volumetric efficiency is a measurement of how close the actual air flow into an engine is to the theoretical maximum air flow, given the engine's displacement. It is affected by various losses within the engine.
2) To calculate a car's volumetric efficiency, one must log engine speed, mass air flow rate, and intake air temperature data using a scan tool. These values are used to find actual air flow, which is divided by theoretical air flow to yield a percentage for volumetric efficiency.
3) Theoretical air flow is calculated based on engine displacement, maximum rpm, and whether it is a 2-stroke or 4-stroke engine. Actual air flow comes from mass air flow rate multiplied by air
Twin Turbocharging Inline Six Internal Combustion EngineRobertBeneteau
Design project to twin turbocharge an inline six BMW M3 engine using mathematical computations and engine simulations to increase the power output upwards of 500 horsepower.
Design and performance Analysis of a 5 Speed Manual Transmission System for I...IRJET Journal
This document summarizes a research paper that analyzed the design and performance of a 5-speed manual transmission system for an Indian drive cycle. The researchers obtained various gear ratio sets by varying final drive ratios, intermediate gear ratios, and gear stepping. They then used ADAMS CAR software to simulate the performance of the transmission designs under different conditions. Their results showed that increasing the final drive ratio from 4.467 to 4.8 improved acceleration performance by providing more wheel torque in first gear. They also found that increasing the first gear ratio from 3.72 to 4.2 further enhanced acceleration. The optimal transmission design was selected based on achieving the best acceleration performance.
Sheet1ASU - CON 243NameRoss DodenhoffHomework Chapter 2Student IDP.docxbagotjesusa
Sheet1ASU - CON 243NameRoss DodenhoffHomework Chapter 2Student IDProblem StatementYour company has just been awarded a large contract that would be well suited for Caterpillar 740B Articulated Haul Trucks. A local rental yard said that they will rent you the trucks for $13,200 per month plus 7.0% sales tax not including any operating costs. What would it cost to purchase the trucks instead of renting them? The purchase price including sales tax and attachments is $575,000. The project will last 5 years and you are not sure that you will have work for the trucks after this project therefore you need to plan on selling them at the end of 5 years for 40% of the original purchase price. According to the schedules that the project managers have put together it appears that you will be able to get 1,800 hours of utilization per year on the trucks during all five years and they also anticipate 50 minute efficiency working hours. According to the Chief Financial Officer of the company your cost of money is 6% and the annual insurance amount on each truck will be 0.5%. Your tire sales person says that a set of 6 tires will cost $25,000, last 3,800 hours and the average repairs will be about 15% of the purchase price over the life of the tires. The preventative maintenance schedule that your fleet is on has PM1 oil changes completed every 250 hours with oil, lube and filter cost at $15.00 per gallon, repair and maintenance cost is $5.00 per hour and your throttle load factor for articulated trucks is 60%. Because they are trucks and will not be scraping the ground they do not have any high wear ground engaging items to wear out. Use the product specifications included with this assignment to determine the Gross Flywheel Horse Power, engine crankcase capacities and any other information that you may need. Diesel fuel is $2.50 per gallon for red dyed.Question 1(16 POINTS)What is the Average Annual Investment for this machine?Question 2(24 POINTS)What is the ownership cost per hour?Puchase Price-salvage value-cost of tires+cost of capital+overhead=Ownership expensePurchase Price= 575,000Salvage Value= 230,000Cost of Tires= 25,000Question 3(36 POINTS)What is the operating cost per hour?Question 4(8 POINTS)What is the total cost per hour to your company if you were to own this machine? Question 5(8 POINTS)What is the total cost per hour to your company if you were to rent this machine? Question 6(8 POINTS)For only this project, would it be more economical to rent or buy this machine? Explain why.Question 7(BONUS POINTS)In considering owning vs renting, what is the breakeven point in hours (i.e. how many hours would you need to utilize the equipment before it becomes more economical to own the machine)?
740B
Articulated
Truck
Engine
Weights
Engine
Model
Tier
4
Interim/EU
Stage
IIIB
Cat®
C15
ACERT™
Rated
Payload
39.5
tonnes
43.5
tons
Gross
Power
–
SAE
J1995
365
kW
489
hp
Body
Capacities
Net
Power
–
ISO
14396
361
kW
484
hp
Heaped
SAE
2:.
- The document discusses external aerodynamic analysis of heavy commercial vehicles (HCVs) using computational fluid dynamics (CFD) simulation and wind tunnel testing.
- It aims to study the coefficient of drag of HCVs with different shapes and heights of wind deflectors. Three-dimensional models of the HCV are created in CATIA and analyzed in ANSYS-CFX to compare flow patterns and drag forces.
- The simulation results will be validated through subsonic wind tunnel testing of scaled physical models, which will also utilize smoke flow visualization and surface pressure distribution measurements.
Motion Control Technical Paper - Spring 2016Matthew Emge
This document provides an overview of a senior design project to create a quasi-autonomous vehicle for competition. The vehicle uses an Ackerman steering system with two motors and custom encoders. The mechanical design includes 3D printed parts for the steering linkages and gearing system. Eight sonar sensors provide obstacle detection. The vehicle will compete in events like tug-of-war, obstacle courses, and "seek and destroy" using color detection software. A Raspberry Pi controls high-level functions while PIC microcontrollers handle lower-level sensing and motion control. The project aims to demonstrate skills in electrical, mechanical, and software engineering through the design and implementation of the competitive robot.
This document analyzes vehicle performance data to develop mathematical models for predicting fuel economy and selling price. Regression analysis was used to determine factors that significantly predict fuel economy and price. For fuel economy, significant factors were weight, acceleration, year, number of cylinders, manufacturer, and country of origin. For price, significant factors were year, weight, manufacturer, country of origin, and acceleration. The models allow the company to understand consumer preferences and price vehicles competitively.
Today parking a car on side of the road is major problem. Every time while parking and removing car from the parking space consumes fuel and space. Also we have to leave some space in the front and back side of car so that removing it outside would be easy. We also have to reverse car several time while parking and crashes occurs sometimes. So to overcome this problem we designed a prototype showing transverse car parking mechanism. The mechanism is attached with the car from the bottom side which will lift the car on four small sized wheels by means of pneumatic or hydraulic system and then it moves transversely. The four auxiliary wheels can flip inside so that when we are not using mechanism the ground clearance of the car will be unaffected. This type of mechanism can also use as in-built jack to replace damaged wheels. This type of mechanism will be very much useful for people in emergency cases like removing car from the road in case it’s not starting and this mechanism will work on the battery.
Nicholas Love worked on the powertrain system for the UTSA Formula SAE team from 2015-2017, taking on increasing responsibilities each year. In 2015, he helped with basic tasks and tuned the engine control unit. In 2016, as Powertrain Lead he designed an intake manifold using simulation software that improved horsepower by 25%. In 2017, he optimized the intake design using carbon fiber to reduce weight by 7.5 pounds while increasing power. He also designed exhaust manifolds both years to meet sound requirements.
This document outlines a student project to convert a standard road car to a race car. It includes an abstract, table of contents, list of team members, and sections on electronic configuration, ECM tuning, spark plugs, high tension leads, fire extinguisher, cut-off switch, and conclusion. The goal is to prepare the car to race at a track day by modifying components like tires, brakes, engine, and adding safety elements. The student focuses on electronic modifications like reprogramming the ECM to boost performance, upgrading spark plugs and leads, and adding a fire suppression system and cut-off switch.
IRJET- Design Optimization of a Formula Student SuspensionIRJET Journal
This document discusses the design optimization of a formula student suspension system using simulation tools. It begins by explaining the importance of accurately predicting vehicle performance through simulation given the non-linearities involved. It then describes analyzing tire data in MATLAB and using a tire model in MSC ADAMS simulations. Suspension geometry is designed in Solidworks and analyzed in ADAMS through quasi-static and dynamic simulations to optimize characteristics like bump steer, roll steer, and camber gradient. The use of computational tools helped optimize the vehicle dynamics and suspension design through reduced iterations, calculations, and time.
Team Contract 1- Team’s purpose· To enhance the look of the.docxmattinsonjanel
Team Contract
1- Team’s purpose:
· To enhance the look of the mousetrap car.
· To make the mousetrap car light as much as we can.
· Find a way that makes it go as far as it can.
· Apply the rules of acceleration on the project.
2- Roles of each team member:
a) J A: Is the leader who will track the progress of the project and maintain timelines, Set goals of the team members meetings.
b) F A: Is going to be the financial officer who will manage the team’s expenses, create the team’s budget and find the errors of the budget.
c) B A: He is going to be the procurement and the liaison of the team
- Procurement: get to know about the purchasing system.
- Liaison: keeping the team members updated about the project.
3- The team will handle the leadership/facilitation/management activities through communicating and set meeting in regular bases and discuss each other’s ideas to decide if it helpful or not.
Group meeting
Twice a week
Gather parts
[3 weeks]
Brain storming
[ 1 week]
Outline and planning
[2 weeks]
Receive the project description
1 day
Project design
[ 3 weeks]
2nd Performance test
[ 1 day ]
1st performance test
[2 days]
Review design
[3 days]
Presentation
Preparation
1 week
Competition –Final project completed
Final tests for the mousetrap car
[1 day]
Distance travel testing
[2 days]
ME101
Design Project Description
OBJECTIVES:
Conceive, Design, Implement, Operate a vehicle in modern team-based environment. The vehicle will be powered solely by the energy of one standard-sized mouse trap, (1 3/4" X 3 7/8"), and will enter a two-event competition:
1) traveling the longest linear distance, and 2) traveling a 5-meter linear distance in the shortest amount of time.
KEY MILESTONES:
· 3/13/15: Team Contract and Biography
· 3/27/14: Team Project Management Plan
· 4/3/15: FRDPARRC Sheet
· 4/24/15: Paper-copy of Team Presentation
· 5/1/15: Contest
· 5/8/15: Team Presentations
DEFITIONS AND REGULATIONS:
By definition, a vehicle is a device with wheels or runners used to carry something, (e.g., car, bus, bicycle or sled). Therefore, launching a ball, (e.g., marble) from the mousetrap will be ruled illegal.
1. The device must be powered by a single Victor brand mouse trap (1 3/4" X 3 7/8") .
2. The mousetrap can not be physically altered except for the following: 4 holes can be drilled only to mount the mousetrap to the frame and a mousetrap's spring can be removed only to adjust the length of the its lever arm.
3. The device cannot have any additional potential or kinetic energy at the start other than what can be stored in the mousetrap's spring itself. (This also means that you cannot push start your vehicle.)
4. The spring from the mousetrap cannot be altered or heat treated.
5. The spring cannot be wound more than its normal travel distance or 180 degrees.
6. Vehicles must be self-starting. Vehicles may not receive a push in the forward direction or side direction.
7. The vehicle must steer itse ...
IRJET- Design and Development of Centralized Tyre Pressure SystemIRJET Journal
This document describes the design and development of a centralized tire pressure system. The system uses a centralized compressor connected to the tires via hoses and rotary joints. The rotary joints allow air to be channeled to the tires as they rotate. Sensors monitor tire pressure and valves control inflation. The goals are to automatically maintain proper tire pressure, improving fuel efficiency and safety. A prototype was developed using off-the-shelf components like a compressor, pressure sensors, solenoid valves and 3D printed parts to demonstrate the concept.
Final Year Paper-Designing the 2016 RMIT Aero Package - Hashan MendisHashan Mendis
This document summarizes a student project to design an aerodynamic package for a Formula SAE race car. The objective was to maximize points gained in competition by increasing downforce. An analytical approach was used to determine that a coefficient of lift (Cl) of 1.7 across events could gain 38 points. A decision matrix determined resources should focus on front and rear wings. Simulations in ANSYS evaluated wing profiles and validated the design could achieve the target Cl of 1.8 in a straight line with center of pressure 10% forward of the center of gravity, improving handling over the previous car design. The package was able to increase downforce as required while keeping the competition position of RMIT University.
The document discusses David Beck's intern project analyzing the Denver RIP track operations using simulation modeling. It describes the current base model of the track, which includes creating cars and assigning repairs, holding cars until a carman is available, and recording repair times and outcomes. An alternative expeditor model is proposed, adding a track for simple expedited repairs estimated to take 30-60 minutes. Simulation results suggest the expeditor model could increase daily car releases from 11.5 to 18.9 cars. Safety mitigations like fall protection would need to be implemented on the additional track.
1. The document describes a computational fluid dynamics (CFD) study of the aerodynamic performance of a Bentley Continental GT's outer body shape.
2. CFD simulations were conducted on the base model and with the addition of individual aerodynamic aids (air dam with front splitter, rear wing) and in combination.
3. The results showed that the combination of air dam, front splitter, and rear wing produced the greatest downforce while increasing drag only slightly, making it the most aerodynamically efficient configuration.
This document summarizes an automated parking system called the Auto-Park System provided by JGT Auto Parking Sdn Bhd. It is a fully automated parking solution that saves space compared to conventional parking structures. It uses electric motors and conveyor systems to store vehicles efficiently without engines running, reducing noise and emissions. The system offers benefits like being environmentally friendly, safe, secure, space-saving, portable, low maintenance and modular. It also guarantees high performance levels and aims to provide a reliable and cost-effective parking solution for applications like vehicle storage, residential and commercial developments, valet parking and public parking.
IRJET- Automatic Air Inflation in Vehicle TyreIRJET Journal
This document describes a proposed automatic air inflation system for vehicle tires. The system uses sensors to monitor tire pressure and a control unit to automatically inflate tires when pressure drops. It can maintain proper tire pressure even while the vehicle is in motion. Benefits include improved safety, fuel efficiency, and tire life by ensuring consistent tire inflation. The proposed system uses off-the-shelf components like a pressure sensor, microcontroller, display, solenoid valves, and an air compressor. It works by using the sensor to detect pressure drops and the controller to open or close solenoid valves to inflate tires or release excess air as needed to maintain the programmed pressure setting.
Design and fabrication of variable steering ratio mechanism for light Motor v...sushil Choudhary
To facilitate easy and proper steering of the vehicle while negotiating a turn, as per the requirements of driver in
different situations like hair pin bends in hilly regions, sudden turns in highways and city streets or in sports car
during race events an improved steering system is needed to address these problems. The steering arrangement
used in a normal automobile was investigated and to solve the above problems a variable steering ratio
mechanism was designed and fabricated, with the aim to determine if incorporation of variable steering ratio
mechanism will make an improvement in the steady and transient state handling of the automobile. The size of
the pinion gear and the number of teeth on the gear determine the rack-and-pinion steering ratio. The steering
wheel must be turned one revolution to turn the front wheels one sixteenth of a turn, the steering ratio is 1 to
1/16. Reversing the numbers gives a ratio of 16 to 1, or 16:1. This steering ratio is always fixed. A variable
steering ratio mechanism was fabricated by using constant mesh type gears from Bajaj-Super and steering
mechanism from Tata-Nano. Gear housing using wood is created and gear shifting arrangement incorporated. It
was observed that on engaging the 1st gear steering ratio is increased to 9.92:1. On engaging the 2nd gear
steering ratio is increased to 7.20:1, On engaging the 3rd gear steering ratio is increased to 4.96:1 On engaging
the 4th gear steering ratio is increased to 3.52:1. The effort required for steering is increased due to these ratios
as energy is lost due to friction. This mechanism can only be practical if used in conjugation with power assist.
This document provides an introduction to automotive technology. It discusses the basics of automobile construction including frames, bodies, engines and the four-stroke cycle. The major systems of a vehicle like the fuel, electrical and cooling systems are identified. Different automotive body types such as sedans, hatchbacks and sport utility vehicles are also described. The purpose of this section is to give readers foundational knowledge of automotive parts and systems to pursue entry-level jobs or study more advanced automotive topics.
1. The document describes the development of a MATLAB software for optimizing the design of a brake for a mini bike.
2. An existing brake design is analyzed and mathematically modeled. The model relates key brake parameters like force, torque, pressure to dimensions of the brake drum and brake lining.
3. The existing design is optimized by taking the maximum allowed width of the brake lining (25mm) rather than the calculated width (20mm). This reduces the size of the brake drum from 200mm to 180mm, lowering weight. It also increases the area of the brake lining.
1. The document describes the development of a MATLAB software for optimizing the design of a brake for a minibike.
2. An existing minibike brake design is analyzed and mathematically modeled. The model relates key brake design parameters like pressure, width of brake lining, drum radius, to torque output.
3. The existing design is optimized by taking the maximum allowed width of brake lining (25mm) rather than the calculated width (20mm). This reduces the required drum size from 200mm to 180mm, lowering weight while maintaining torque output.
Development of Software Using Matlab for Design Optimization of Brake for Min...iosrjce
Mini bikes are normally preferred by for their light weight. Hence attention needs to be focused on
weight while configuring each and every key element like brake, gear box,engine, clutchs etc. Design
optimization of brake for one such mini brake has been taken up in this work. To start with, mathematical model
of the brake has been established so as to bring out the relation between key parameters of the design and the
same has been used in the later stage so as to formulate the optimization strategy. Configuring the brake by
choosing restraining value of width of brake lining in place of choosing restraining value of size of brake drum
yielded to reduction of volume and hence weight. Optimized design lead to increased area of lining which in
turn will reduce dissipation of energy per unit area. Accordingly it has bagged additional merits like reduction
in operating temperature and wear. Further a general purpose software has been developed using MATLAB for
design optimization of brake. For accomplishing this, formulation has been transformed in form of a code in
MATLAB. Programme has been written with interactive mode of operation which means upon executing the
programme it prompts the user to enter the value of inputs and subsequently it generates the outputs.
The document provides details about Team Exergy's electric kart including descriptions of the kart's chassis, steering mechanism, suspension system, brake mechanism, purchased parts, transmission, and body work. The chassis is designed to provide a safe space for the driver while meeting competition requirements. Key components include the roll cage, steering linkage, disc brake, PMDC motor, lead-acid batteries, and fiber reinforced body panels. Calculations and cost estimates are provided for each major system.
The document describes a project to optimize car performance through interpolation of design values. It provides vehicle specifications for a BMW 740li, including dimensions, engine specs, and transmission ratios. Formulas are given for calculating forces, velocity, acceleration, resistance and other parameters. Linear interpolation, Newton's interpolating polynomial, and spline methods are used to predict unknown performance values and optimize design parameters like weight and frontal area. The goal is to improve acceleration and fuel efficiency through analysis and design changes.
Concentrated solar power systems can concentrate sunlight up to 10,000 times using a dual axis tracking system or a ball lens system. This increases efficiency by 35% over traditional solar panels. The total cost of a residential solar system ranges from $15,000 to $60,000, with equipment, installation, permitting, and ongoing maintenance and monitoring accounting for the various expenses. The area of solar panels needed to generate a given power output can be calculated based on the solar irradiance, conversion efficiency, and desired wattage. While solar power has advantages like being renewable and reducing greenhouse gases, disadvantages include the initial cost and challenges of energy storage.
Maths in Green Cars - Ingenious Inventorsenrich_ed
The document discusses the use of mathematics in green car technology. It provides examples of how mensuration is used to calculate the number of solar panels needed based on the roof area. Statistics and charts are used in car production and energy production analysis. Geometry is applied to the shapes of solar panels, car parts, and other components. Angles are important in areas like solar panel installation, car design, mirror adjustment, and inspection. The presentation aims to show how mathematics is integral to green car technology.
Motion Control Technical Paper - Spring 2016Matthew Emge
This document provides an overview of a senior design project to create a quasi-autonomous vehicle for competition. The vehicle uses an Ackerman steering system with two motors and custom encoders. The mechanical design includes 3D printed parts for the steering linkages and gearing system. Eight sonar sensors provide obstacle detection. The vehicle will compete in events like tug-of-war, obstacle courses, and "seek and destroy" using color detection software. A Raspberry Pi controls high-level functions while PIC microcontrollers handle lower-level sensing and motion control. The project aims to demonstrate skills in electrical, mechanical, and software engineering through the design and implementation of the competitive robot.
This document analyzes vehicle performance data to develop mathematical models for predicting fuel economy and selling price. Regression analysis was used to determine factors that significantly predict fuel economy and price. For fuel economy, significant factors were weight, acceleration, year, number of cylinders, manufacturer, and country of origin. For price, significant factors were year, weight, manufacturer, country of origin, and acceleration. The models allow the company to understand consumer preferences and price vehicles competitively.
Today parking a car on side of the road is major problem. Every time while parking and removing car from the parking space consumes fuel and space. Also we have to leave some space in the front and back side of car so that removing it outside would be easy. We also have to reverse car several time while parking and crashes occurs sometimes. So to overcome this problem we designed a prototype showing transverse car parking mechanism. The mechanism is attached with the car from the bottom side which will lift the car on four small sized wheels by means of pneumatic or hydraulic system and then it moves transversely. The four auxiliary wheels can flip inside so that when we are not using mechanism the ground clearance of the car will be unaffected. This type of mechanism can also use as in-built jack to replace damaged wheels. This type of mechanism will be very much useful for people in emergency cases like removing car from the road in case it’s not starting and this mechanism will work on the battery.
Nicholas Love worked on the powertrain system for the UTSA Formula SAE team from 2015-2017, taking on increasing responsibilities each year. In 2015, he helped with basic tasks and tuned the engine control unit. In 2016, as Powertrain Lead he designed an intake manifold using simulation software that improved horsepower by 25%. In 2017, he optimized the intake design using carbon fiber to reduce weight by 7.5 pounds while increasing power. He also designed exhaust manifolds both years to meet sound requirements.
This document outlines a student project to convert a standard road car to a race car. It includes an abstract, table of contents, list of team members, and sections on electronic configuration, ECM tuning, spark plugs, high tension leads, fire extinguisher, cut-off switch, and conclusion. The goal is to prepare the car to race at a track day by modifying components like tires, brakes, engine, and adding safety elements. The student focuses on electronic modifications like reprogramming the ECM to boost performance, upgrading spark plugs and leads, and adding a fire suppression system and cut-off switch.
IRJET- Design Optimization of a Formula Student SuspensionIRJET Journal
This document discusses the design optimization of a formula student suspension system using simulation tools. It begins by explaining the importance of accurately predicting vehicle performance through simulation given the non-linearities involved. It then describes analyzing tire data in MATLAB and using a tire model in MSC ADAMS simulations. Suspension geometry is designed in Solidworks and analyzed in ADAMS through quasi-static and dynamic simulations to optimize characteristics like bump steer, roll steer, and camber gradient. The use of computational tools helped optimize the vehicle dynamics and suspension design through reduced iterations, calculations, and time.
Team Contract 1- Team’s purpose· To enhance the look of the.docxmattinsonjanel
Team Contract
1- Team’s purpose:
· To enhance the look of the mousetrap car.
· To make the mousetrap car light as much as we can.
· Find a way that makes it go as far as it can.
· Apply the rules of acceleration on the project.
2- Roles of each team member:
a) J A: Is the leader who will track the progress of the project and maintain timelines, Set goals of the team members meetings.
b) F A: Is going to be the financial officer who will manage the team’s expenses, create the team’s budget and find the errors of the budget.
c) B A: He is going to be the procurement and the liaison of the team
- Procurement: get to know about the purchasing system.
- Liaison: keeping the team members updated about the project.
3- The team will handle the leadership/facilitation/management activities through communicating and set meeting in regular bases and discuss each other’s ideas to decide if it helpful or not.
Group meeting
Twice a week
Gather parts
[3 weeks]
Brain storming
[ 1 week]
Outline and planning
[2 weeks]
Receive the project description
1 day
Project design
[ 3 weeks]
2nd Performance test
[ 1 day ]
1st performance test
[2 days]
Review design
[3 days]
Presentation
Preparation
1 week
Competition –Final project completed
Final tests for the mousetrap car
[1 day]
Distance travel testing
[2 days]
ME101
Design Project Description
OBJECTIVES:
Conceive, Design, Implement, Operate a vehicle in modern team-based environment. The vehicle will be powered solely by the energy of one standard-sized mouse trap, (1 3/4" X 3 7/8"), and will enter a two-event competition:
1) traveling the longest linear distance, and 2) traveling a 5-meter linear distance in the shortest amount of time.
KEY MILESTONES:
· 3/13/15: Team Contract and Biography
· 3/27/14: Team Project Management Plan
· 4/3/15: FRDPARRC Sheet
· 4/24/15: Paper-copy of Team Presentation
· 5/1/15: Contest
· 5/8/15: Team Presentations
DEFITIONS AND REGULATIONS:
By definition, a vehicle is a device with wheels or runners used to carry something, (e.g., car, bus, bicycle or sled). Therefore, launching a ball, (e.g., marble) from the mousetrap will be ruled illegal.
1. The device must be powered by a single Victor brand mouse trap (1 3/4" X 3 7/8") .
2. The mousetrap can not be physically altered except for the following: 4 holes can be drilled only to mount the mousetrap to the frame and a mousetrap's spring can be removed only to adjust the length of the its lever arm.
3. The device cannot have any additional potential or kinetic energy at the start other than what can be stored in the mousetrap's spring itself. (This also means that you cannot push start your vehicle.)
4. The spring from the mousetrap cannot be altered or heat treated.
5. The spring cannot be wound more than its normal travel distance or 180 degrees.
6. Vehicles must be self-starting. Vehicles may not receive a push in the forward direction or side direction.
7. The vehicle must steer itse ...
IRJET- Design and Development of Centralized Tyre Pressure SystemIRJET Journal
This document describes the design and development of a centralized tire pressure system. The system uses a centralized compressor connected to the tires via hoses and rotary joints. The rotary joints allow air to be channeled to the tires as they rotate. Sensors monitor tire pressure and valves control inflation. The goals are to automatically maintain proper tire pressure, improving fuel efficiency and safety. A prototype was developed using off-the-shelf components like a compressor, pressure sensors, solenoid valves and 3D printed parts to demonstrate the concept.
Final Year Paper-Designing the 2016 RMIT Aero Package - Hashan MendisHashan Mendis
This document summarizes a student project to design an aerodynamic package for a Formula SAE race car. The objective was to maximize points gained in competition by increasing downforce. An analytical approach was used to determine that a coefficient of lift (Cl) of 1.7 across events could gain 38 points. A decision matrix determined resources should focus on front and rear wings. Simulations in ANSYS evaluated wing profiles and validated the design could achieve the target Cl of 1.8 in a straight line with center of pressure 10% forward of the center of gravity, improving handling over the previous car design. The package was able to increase downforce as required while keeping the competition position of RMIT University.
The document discusses David Beck's intern project analyzing the Denver RIP track operations using simulation modeling. It describes the current base model of the track, which includes creating cars and assigning repairs, holding cars until a carman is available, and recording repair times and outcomes. An alternative expeditor model is proposed, adding a track for simple expedited repairs estimated to take 30-60 minutes. Simulation results suggest the expeditor model could increase daily car releases from 11.5 to 18.9 cars. Safety mitigations like fall protection would need to be implemented on the additional track.
1. The document describes a computational fluid dynamics (CFD) study of the aerodynamic performance of a Bentley Continental GT's outer body shape.
2. CFD simulations were conducted on the base model and with the addition of individual aerodynamic aids (air dam with front splitter, rear wing) and in combination.
3. The results showed that the combination of air dam, front splitter, and rear wing produced the greatest downforce while increasing drag only slightly, making it the most aerodynamically efficient configuration.
This document summarizes an automated parking system called the Auto-Park System provided by JGT Auto Parking Sdn Bhd. It is a fully automated parking solution that saves space compared to conventional parking structures. It uses electric motors and conveyor systems to store vehicles efficiently without engines running, reducing noise and emissions. The system offers benefits like being environmentally friendly, safe, secure, space-saving, portable, low maintenance and modular. It also guarantees high performance levels and aims to provide a reliable and cost-effective parking solution for applications like vehicle storage, residential and commercial developments, valet parking and public parking.
IRJET- Automatic Air Inflation in Vehicle TyreIRJET Journal
This document describes a proposed automatic air inflation system for vehicle tires. The system uses sensors to monitor tire pressure and a control unit to automatically inflate tires when pressure drops. It can maintain proper tire pressure even while the vehicle is in motion. Benefits include improved safety, fuel efficiency, and tire life by ensuring consistent tire inflation. The proposed system uses off-the-shelf components like a pressure sensor, microcontroller, display, solenoid valves, and an air compressor. It works by using the sensor to detect pressure drops and the controller to open or close solenoid valves to inflate tires or release excess air as needed to maintain the programmed pressure setting.
Design and fabrication of variable steering ratio mechanism for light Motor v...sushil Choudhary
To facilitate easy and proper steering of the vehicle while negotiating a turn, as per the requirements of driver in
different situations like hair pin bends in hilly regions, sudden turns in highways and city streets or in sports car
during race events an improved steering system is needed to address these problems. The steering arrangement
used in a normal automobile was investigated and to solve the above problems a variable steering ratio
mechanism was designed and fabricated, with the aim to determine if incorporation of variable steering ratio
mechanism will make an improvement in the steady and transient state handling of the automobile. The size of
the pinion gear and the number of teeth on the gear determine the rack-and-pinion steering ratio. The steering
wheel must be turned one revolution to turn the front wheels one sixteenth of a turn, the steering ratio is 1 to
1/16. Reversing the numbers gives a ratio of 16 to 1, or 16:1. This steering ratio is always fixed. A variable
steering ratio mechanism was fabricated by using constant mesh type gears from Bajaj-Super and steering
mechanism from Tata-Nano. Gear housing using wood is created and gear shifting arrangement incorporated. It
was observed that on engaging the 1st gear steering ratio is increased to 9.92:1. On engaging the 2nd gear
steering ratio is increased to 7.20:1, On engaging the 3rd gear steering ratio is increased to 4.96:1 On engaging
the 4th gear steering ratio is increased to 3.52:1. The effort required for steering is increased due to these ratios
as energy is lost due to friction. This mechanism can only be practical if used in conjugation with power assist.
This document provides an introduction to automotive technology. It discusses the basics of automobile construction including frames, bodies, engines and the four-stroke cycle. The major systems of a vehicle like the fuel, electrical and cooling systems are identified. Different automotive body types such as sedans, hatchbacks and sport utility vehicles are also described. The purpose of this section is to give readers foundational knowledge of automotive parts and systems to pursue entry-level jobs or study more advanced automotive topics.
1. The document describes the development of a MATLAB software for optimizing the design of a brake for a mini bike.
2. An existing brake design is analyzed and mathematically modeled. The model relates key brake parameters like force, torque, pressure to dimensions of the brake drum and brake lining.
3. The existing design is optimized by taking the maximum allowed width of the brake lining (25mm) rather than the calculated width (20mm). This reduces the size of the brake drum from 200mm to 180mm, lowering weight. It also increases the area of the brake lining.
1. The document describes the development of a MATLAB software for optimizing the design of a brake for a minibike.
2. An existing minibike brake design is analyzed and mathematically modeled. The model relates key brake design parameters like pressure, width of brake lining, drum radius, to torque output.
3. The existing design is optimized by taking the maximum allowed width of brake lining (25mm) rather than the calculated width (20mm). This reduces the required drum size from 200mm to 180mm, lowering weight while maintaining torque output.
Development of Software Using Matlab for Design Optimization of Brake for Min...iosrjce
Mini bikes are normally preferred by for their light weight. Hence attention needs to be focused on
weight while configuring each and every key element like brake, gear box,engine, clutchs etc. Design
optimization of brake for one such mini brake has been taken up in this work. To start with, mathematical model
of the brake has been established so as to bring out the relation between key parameters of the design and the
same has been used in the later stage so as to formulate the optimization strategy. Configuring the brake by
choosing restraining value of width of brake lining in place of choosing restraining value of size of brake drum
yielded to reduction of volume and hence weight. Optimized design lead to increased area of lining which in
turn will reduce dissipation of energy per unit area. Accordingly it has bagged additional merits like reduction
in operating temperature and wear. Further a general purpose software has been developed using MATLAB for
design optimization of brake. For accomplishing this, formulation has been transformed in form of a code in
MATLAB. Programme has been written with interactive mode of operation which means upon executing the
programme it prompts the user to enter the value of inputs and subsequently it generates the outputs.
The document provides details about Team Exergy's electric kart including descriptions of the kart's chassis, steering mechanism, suspension system, brake mechanism, purchased parts, transmission, and body work. The chassis is designed to provide a safe space for the driver while meeting competition requirements. Key components include the roll cage, steering linkage, disc brake, PMDC motor, lead-acid batteries, and fiber reinforced body panels. Calculations and cost estimates are provided for each major system.
The document describes a project to optimize car performance through interpolation of design values. It provides vehicle specifications for a BMW 740li, including dimensions, engine specs, and transmission ratios. Formulas are given for calculating forces, velocity, acceleration, resistance and other parameters. Linear interpolation, Newton's interpolating polynomial, and spline methods are used to predict unknown performance values and optimize design parameters like weight and frontal area. The goal is to improve acceleration and fuel efficiency through analysis and design changes.
Concentrated solar power systems can concentrate sunlight up to 10,000 times using a dual axis tracking system or a ball lens system. This increases efficiency by 35% over traditional solar panels. The total cost of a residential solar system ranges from $15,000 to $60,000, with equipment, installation, permitting, and ongoing maintenance and monitoring accounting for the various expenses. The area of solar panels needed to generate a given power output can be calculated based on the solar irradiance, conversion efficiency, and desired wattage. While solar power has advantages like being renewable and reducing greenhouse gases, disadvantages include the initial cost and challenges of energy storage.
Maths in Green Cars - Ingenious Inventorsenrich_ed
The document discusses the use of mathematics in green car technology. It provides examples of how mensuration is used to calculate the number of solar panels needed based on the roof area. Statistics and charts are used in car production and energy production analysis. Geometry is applied to the shapes of solar panels, car parts, and other components. Angles are important in areas like solar panel installation, car design, mirror adjustment, and inspection. The presentation aims to show how mathematics is integral to green car technology.
This document discusses the role of mathematics in electric vehicles. It provides examples of how math is used to calculate the electricity needed to recharge a car, the car's range based on the charge, and performance metrics like price, maintenance costs, range and charging time. The document also summarizes the benefits of electric cars, including lower fuel costs, reduced emissions, and fewer mechanical parts requiring maintenance compared to gas-powered vehicles. However, it notes that high battery costs, limited driving range, and long recharging times remain barriers that have prevented more widespread adoption of electric cars.
The document describes the Gravity Light, a lamp that generates electricity through gravity. It works by using the potential energy from lifted weights to power an electric motor and LED light. This provides lighting for 15-30 minutes. It has benefits over kerosene lamps by reducing fire risks and hazardous gas emissions. Its low cost of $5 makes it accessible for the 1.5 billion people without electricity access. It promotes green technology by using renewable gravitational potential energy without batteries.
This document discusses embracing technology in the classroom, known as Classroom 2.0. It outlines how technology can be used to enable collaboration through networking, continuing professional development, and international cooperation. Technology raises the school's profile and provides engaging tasks and resources for assessment of learning. Specific examples discussed include pupils and staff collaborating remotely on projects in real time, international cooperation between schools in different countries, generating personalized codes for tasks, and using Twitter for reflection and feedback.
1) The document provides information about the formation and evolution of the universe from the Big Bang to the formation of galaxies and stars over billions of years.
2) It includes data on different types of galaxies like spiral, elliptical, and irregular galaxies with their diameters, luminosities, and examples. Spiral galaxies tend to be larger in diameter and luminosity.
3) Information is given on distance measurements in space like light years and parsecs. The brightest stars near Earth like Sirius, Vega, and Rigel are listed with their apparent and absolute magnitudes.
This document discusses the role of mathematics in medicine. It provides several examples:
1. Doctors and nurses use math every day to calculate dosages, interpret medical scans like CAT scans, and analyze medical data.
2. Medicines are identified based on their shape, size, and other geometric properties that can be described using basic shapes.
3. Numbers and units are crucial in medicine for tasks like counting pills, measuring weights and volumes, and statistical analysis.
4. Concepts like ratios, proportions, percentages, and statistics are applied when administering medications and analyzing medical trends.
5. Advanced math underlies technologies like MRI machines that provide crucial medical images.
This document discusses the relationship between mathematics and music. It provides group member names and then discusses how mathematics is involved in many aspects of music including rhythm, tuning, frequency, intervals, and chords. It explains concepts like time signatures, note values as fractions, frequency of notes, ratios between intervals, equal temperament, and the mathematical relationships that make music sound pleasant.
Math is essential to all aspects of automobile design and function. It is used in drafting blueprints, measuring part dimensions, determining production ratios and assembly line speeds, calculating horsepower, tire size, and fuel efficiency. Advanced applications include using equations to optimize aerodynamic body shapes in Formula 1 cars and exploit principles like Bernoulli's equation to increase speed. Overall, mathematics permeates every stage of the automobile manufacturing process and is crucial for safety, performance, and profitability.
Mathematics, including calculus, is an important subject in electrical engineering programs. Calculus is generally divided into two parts: differential calculus, which deals with rates of change, and integral calculus, which deals with accumulation. Differential calculus is concerned with how one variable changes with respect to another. Integral calculus calculates quantities such as areas, volumes, and surfaces bounded by curves through integration.
A presentation demonstrating the power of twitter in Education not only as an Assessment for Learning tool but also for CPD, international cooperation, engaging tasks and networking. Download for links and full twitter interactivity including AfL tools.
2. Objective of this project
Whether you realize it or not, maths is a fundamental function
of life and we use it on a daily basis. We use math for everything
from balancing our check book, to computing fuel mileage, to
purchasing aftermarket goodies, to counting the number of cars
ahead of you at the stoplight. Even more impressive is that it's
the only universal language in the world. So this project will give
us an insight about the coolest things in which maths is involved.
3. Maths plays a pivotal role in automobiles. Everything about
a car is based on mathematics. From degree of design to
wind resistance, performance, engine size and
adjustment, power outputs , Bolt holes , part sizes , and
even the Pounds of air in the tires. Everything is measured
and torqued to a specific mathematical formula. From
drawing board, to assembly line, it all depends on maths.
4. In cars , mathematics is involved in-
1. Time and distance
2. Geometry
3. Statistics
4. Angles
5. Ratio and proportion
6. Mensuration
1.Drafting
Artists and car designers who draw models of cars for
production need to understand perspective to make
their drawings and blueprints look right. This includes
a knowledge of angles and line lengths, as well as
different geometric shapes. Car wheels, for
instance, are really circles, hood tops are arcs, and
windows are quadrilaterals.
5. 2.Parts
Each part of an automobile has to fit together like a glove, or the
automobile won't work properly or be safe. Math is used to measure
every part and to make sure those parts are the right size to come
together as designed. This includes everything from the dimensions
of screws to the width of the frame.
6. 3.Pricing
Auto manufacturers want to make a profit on the cars they sell, so
they have to keep track of the cost of every single part. Math is used
to calculate which parts manufacturer can deliver the best price on
needed parts and materials. It also is used to determine the final cost
of the vehicle. If parts cost x dollars and labour costs y, and the
company wants to make a profit percentage of z, for example, then
the company would use the following formula to determine the sell
price: total cost = (x+y)z+(x+y)
7. 4.Production Ratio
Math is used to determine how many cars can be produced an
hour, day, week or month. If an auto manufacturer receives an order
from corporate to increase production by x cars a day, for example, the
speed of the assembly line has to be adjusted by a particular percentage
to accommodate the total number of cars needed. All of the robots of
the assembly line would need to have their speeds adjusted through
their programming or manually by the same percentage.
8. 5.Assembly
Much of the assembly of cars now is done with the help of robots and
other technology. The robots are controlled by specialized computer
programs, and these programs must specify exact parameters for
operation. They must tell the robot, for instance, to hoist a part x number
of feet, apply x pounds of pressure, and distribute x gallons of paint per
square inch. Additionally, the assembly line must be built under exact
dimensions, so there is ample room for assembly to occur safely and
efficiently---if a robot arm needs to swing back and forth, for
example, the robot needs to be positioned to have a certain number of
feet in clearance.
9. 6.Production Time
Certain aspects of auto manufacturing must occur under specific time
parameters. Paint, for instance, has to cure for a specific amount of
time. Math is used to determine how long that time needs to be under a
specific temperature given the chemical composition of the paint.
10. 7.Horsepower & Torque
Maths is used to calculate the horsepower and torque of a car . If
we know either the horsepower or torque figures at a given
rpm, it's easy to calculate the missing figure by simply plugging in
the numbers.
For example-
Torque x RPM / 5,252 = Horsepower
415 x 4,000 / 5,252 = 316
Horsepower x 5,252 / RPM = Torque
316 x 5,252 / 4,000 = 415
11. 8.Selecting a Carburetor
Maths is also involved for selecting a carburetor. There is a simple
formula that makes the selection process easier. We need to take the
maximum rpm and multiply it by the engine displacement. Next divide
that number by 3,456 and multiply it by 0.85. For example, if you plug
in a maximum 6,000 rpm and a 350ci displacement, you end up with
516 cfm.
Street 350 ci
6,000 rpm x 350 / 3,456 x 0.85 = 516 cfm
12. 9.Measuring Displacement
To calculate cubic-inch displacement, we need to know the bore and
stroke of the engine, the number of cylinders, and the handy constant of
0.7854, which is a shortcut representing a portion of the volume
equation of a cylinder-3.1417 (pi) divided by 4.
Displacement = bore x bore x stroke x 0.7854 x number of cylinders.
If the bores are 4,stroke is 3.48 and number of cylinders is 8,then-
Displacement = 4.00 x 4.00 x 3.48 x 0.7854 x 8 = 349.84 ci
13. 10.Tire Diameter and Gear Ratio
Big tires may be cool, but swapping taller or shorter tires affect the final
drive ratio. Taller tires effectively change the rear gear ratio, making it
"taller" or numerically less. Shorter tires create the opposite effect.
Imagine you're building a Pro Street show car and it is already set up with
3.08 gears based on a typical 26-inch-tall tire. Obviously, the car will look
killer with a set of monster 33-inch-tall Mickey Thompson tires, but this
swap to the much taller tires instantly transforms the final drive ratio from
3.08 to 2.42!
Effective Gear Ratio = (original tire diameter / new tire diameter) x gear
ratio= 26/33 x 3.08= 2.42
14. 11. Different tyres in different cars
Maths is used for making tyres of different shapes. A cars tyres are
designed to grip the road surface while supporting the car’s weight and
also to stabilize the ride and help steering. Different driving conditions
and different vehicles call for a wide range of tyre designs and all this is
done through Maths.
15. 1. Bias Tyres- These tyres are used in normal cars and are of normal
shape. They give the tyres a smooth ride and are treaded. Maths
is used to give the tyres their shape and is also used to estimate
how much treading should be done.
2. Bus and lorry tyres- Maths is used to make these tyres thinner
than normal tyres so that they can survive long distance driving.
BIAS TYRES BUS TYRES
16. 3. Dump trucks- In these cars, the tyres are large and wide.
4.Tractor tyres- Maths is used to create and make an estimation of
their oversized treads. It also gives them a different shape and makes
them thinner than normal tyres.
5.Special Tyres for driving on snow- Maths is used to give large and
boxy treads to car’s tyres. Also the tyres are made up of special
rubber that stay flexible in the cold . For this , automobile engineers
need to use maths to calculate how much rubber in a proper ratio
should be added to cars.This is the same for treads.
Tractor tyres Tyres for driving on snow
17. 1.Odometer- It is an instrument (usually on the instrument panel of a
car) that records distance travelled by the car. Thus maths is involved in
the functioning of the odometer.
2.Speedometer- A speedometer or a speed meter is a gauge that
measures and displays the instantaneous speed of a land vehicle .
Without maths we would not get an idea of the distance travelled or
speed of the car. Thus maths plays a vital role here too.
3.Radios -Signal processing is one of the most important mathematical
fields that supports the design and effective operation of radio in cars.
Speedometer and Odometer Radio in cars
18. A Formula 1 car - named for the special formula fuel that it burns has a
much more powerful engine than a passage car. The increased power
comes from the engine’s greater capacity- that is the total volume of
the combustion chambers in its cylinders.In a passage car , engine
capacity may be 1000 cubic centimeters or else. F1 cars have 3 times
that capacity and develop 500 horsepower , which is 4 or 5 times the
horsepower of an ordinary car.
19. To make the additional horsepower of F1 cars more effective , the car’s
body is aerodynamically designed(use of shapes) to minimize air
resistance. Racing cars need to be extra wide for secure road contact and
traction. It also needs to be given a special racing suspension which adds
stability and helps the car to grip the road firmly.
20. 1.Body of F1 cars is moulded for excess speed (use of shapes and maths)
The low , wide body of a racing car, made of lightweight but strong carbon
fiber is designed to make use of the airflow the car creates at high speeds. The
sloped front end and rear spoilers make the air press down on the car and
keep it from becoming airborne.
2.Use of maths in the cockpit
Maths is also used in the cockpit of F1 cars. It is 850 mm long, 350 mm wide at
the pendals,450mm wide at the steering wheel and 520mm at the rear half .
Maths is also used to calculate and show the fuel level, water temperature , oil
pressure and other information which appears at the gauges in the cockpit.
21. Bernoulli principle
The Bernoulli principle has a big role in the operation of the
aerodynamic surfaces of an F1 car. The Bernoulli principle is expressed
by an equation, which states that for a given volume of fluid, the total
energy remains constant. This means that when a fluid is in relative
motion, the energy is split into the ‘parts’. The sum of these parts will
not exceed a certain value, which will remain constant as long as the
external conditions do not change..
22. The three parts of the total energy are:
1) The pressure energy within the fluid.
2) The movement of the air (kinetic energy)
3) The potential energy of the air (in this case, elevation)
This can be written as:
p + 1/2 r v2+ rgh = some constant
p = Pressure
r = Density of fluid
v = Velocity of fluid
g = Acceleration due to Gravity
h = Height of fluid above some reference point
23. Our average track is fairly level, so a race car will not have enough change in
elevation to make the potential energy a variable, so we take this potential
energy as a ‘constant ’and therefore are able to remove it from the equation.
This leaves us with:
p + 1/2 r v2 = some (other) constant
We can rewrite this as:
p+q=H
p = static Pressure
q = 1/2 rv2 = dynamic pressure
H = some (other) constant
This basically means that if the dynamic pressure increases, the static pressure
has to decrease and if the dynamic pressure decreases, the static pressure will
increase. This means that if we speed up a fluid, the pressure will fall.
24. We would like to acknowledge many people without whom this
project would not me possible-
1.Mr.Richard Davies and Mrs.Kamalika Bose for coming out with the
idea of ‘Jugaad’ and providing us with a platform for showcasing
our talents.
2.Mrs.Priya Madan, our maths teacher for constantly helping us.
3.Kieron Williams and Katie Vince , our team mates for constantly
communicating with us.
4. My pal-Sanjay Banerjee for doing half of the research.
5.Last,but not the least we would like to thank ourselves for finding
time to make this project against all odds.
25. Conclusion
• Cars play an important role in our life.
• We were able to understand the importance
of maths in cars.
• Maths is an universal language.
• We were able to know about cars through
maths .
• Lastly its all because of project jugaad we
were able to know so much.
26. A presentation by – Raunak Das and Dynamic Researchers
Team members-Raunak Das(digital engineer , also
researcher),Sanjay Banerjee(chief researcher),Katie
Vince(Group Leader), Kieron Williams(communication
director.)