How Geometry and Math Drive Car Innovation
•Download as PPS, PDF•
5 likes•6,856 views
The document discusses the history and development of cars and transportation. It notes that the first car was invented in 1886 by Carl Benz, sparking innovations that continue today. During the 20th century, cars, trucks and buses became the main means of transportation. The document also discusses how geometry and engineering principles are used in car design and how engines, transmissions, and other systems work together to power and control a vehicle's movement. It questions how braking systems function and envisions future advanced transportation technologies. Overall, the document explores the connections between math, engineering, and the evolution of automobiles and transportation over time.
Recommended
More Related Content
What's hot
What's hot (20)
Similar to How Geometry and Math Drive Car Innovation
Similar to How Geometry and Math Drive Car Innovation (20)
More from Marina Njers
Recently uploaded
Recently uploaded (20)
How Geometry and Math Drive Car Innovation
- 1. CONNECTION THAT MOVES THE WORLD Borna Brlošić Centar izvrsnosti Koprivnica Mentor: Ksenija Varović
- 2. 1886 – The first car was „born” – invented by CARL BENZ, forever changes the way people move and sparks the innovation process that continues to this day; 1893 – the first diesel engine was invented by RUDOLF DIESEL – first truck with build in diesel engine was produced in 1924 • during 20th century cars, trucks and buses has become main means of transport
- 3. Today our life's are interconnected with cars, trucks and buses – they, together with other means of transport, allow us to travel freely so that we can meet new people, discover different cultures and regions
- 4. Let’s take a looktogetherLet’s take a looktogether
- 5. Each car is structured out of:
- 6. Geometry is a ground of all shapes that creates one car – rectangular and square shapes, circles, trapezes and splines
- 7. Geometry is used to determine main characteristics of suspension and steering
- 9. Car needs to have sufficient engine power to prevail all the resistance which appears at certain speed and road conditions.
- 10. Engine power is created by thermodynamic process in cylinder
- 11. Transmission is used for controlled application of engine power.
- 12. G2 G1 G2 G1 Z1 – no of teeth of gear G1 Z2 – no of teeth of gear G2 D1 – clevelage circle diameter gear G1 D2 – clevelage cirlce diameter gear G2 n1 – revolution speed gear G1 n2 – revolution speed gear G2
- 13. Engine torque and engine revolution speed is transferred through transmission onto car wheels
- 14. Through this journey we have: cruising nice and smoothly on different roads and gravel paths and enjoying our ride thanks to great suspension created explosion in combustion engine → force on piston But does anybody know how to stop the carbefore it actually runs out of fuel? with this force we have turned engine crankshaft and created engine torque and power accelerated car by switching gears and pressing the throttle turning right and left with the help of steering unit
- 15. We all like to read what is acceleration time for certain cars, but what about braking distance needed to safely stop the car?
- 16. How do we calculate maximum braking deceleration?
- 17. Self driven cars, smart braking systems, maybe flying cars? Everything is possible; behind all those future achievements of the human kind will always be one basic ground – BEAUTY OF MATH
Editor's Notes
- Ladies and gentlemen's! My name is Borna, and today I will present you how cars and math are connected together and how they move the world. If you will have some questions, I will be glad to answer them after the presentation. Let’s start…
- First car with petrol engine was invented by Carl Benz in 1886.At that point, he didn’t realize what kind of impact it will have on the future. From that point automotive industry started to develop rapidly and change the way how people travel. Only 7 years later, Rudolf Diesel invented first diesel engine which has been mounted in truck for the first time in 1924. Today cars, trucks and buses are normal part of our lives and we use them as main mean of transport.
- We are using cars to travel on work, vacation, into the shopping. With cars we can travel and discover new cultures, meet new people and enjoy in the beauty of our planet.
- Now, when we know little bit about history of the cars and where we use them, let-s see what is the connection between them and math.
- Each and every car has almost similar structure. They all have body as a base, engine to give required power, transmission to transfer engine power into movement, steering unit to give us control over the car, suspension to assure comfort drive and braking system to stop car safely when needed.
- Before it becomes a car, idea which engineers have has been put on a paper as a sketch or rough draft. For that, engineers use geometrical shapes and bodies, splines and geometrical relations to determine size, shape and design of the car.
- Geometry is also used to determine different characteristics of the steering and suspension. On your left picture, you can see how we use circles and trigonometrical rules to determine car turning radius. You can also notice how each wheel travels on a different circle. This cause that they all rotate and travel with different speed. This phenomenon can be explained with definition of the arc. Middle picture shows usage of trigonometry to determine basic elements of each steering system. On your right picture it has shown usage of trigonometry to define the characteristic of the suspension. With different inclination of the steering axle we are defining how the car will react during driving in curve, on bumpy roads or on straight road.
- Geometry is also used to determine different characteristics of the steering and suspension. On your left picture, you can see how we use circles and trigonometrical rules to determine car turning radius. You can also notice how each wheel travels on a different circle. This cause that they all rotate and travel with different speed. This phenomenon can be explained with definition of the arc. Middle picture shows usage of trigonometry to determine basic elements of each steering system. On your right picture it has shown usage of trigonometry to define the characteristic of the suspension. With different inclination of the steering axle we are defining how the car will react during driving in curve, on bumpy roads or on straight road.
- In order to be able to move, car needs to have sufficient engine power to prevail all the resistance which appears during that movement. To determine required power to prevail those resistances we use different physical formulas and equations composed of mathematical operations as adding, multiplication, dividing and polynomial funcitions.
- Engine power is created by thermodynamic process in cylinder – as a result of this process we get force on a piston. When we know the force on piston (F), engine power and torque can be simply calculated by different physical equations related to circle surface, geometrical relation in triangle and multiplication. For this we are using formulas for calculating surface of the circle, trigonometric relations of the triangle to find force on crankshaft, and different ratios to calculate work of the thermodynamicall process.
- Transmission is used for controlled application of engine power. Transmission of the car consists of gears with different diameters – this creates different gear ratios. Gear ratios are directly connected to the relation of the two engaged gears through geometrical relation between diameters of the gears cleavage circles. Revolution speed of the gear shaft is then result of multiplication or reduction of the engine revolution speed.
- Transmission is used for controlled application of engine power. Transmission of the car consists of gears with different diameters – this creates different gear ratios. Gear ratios are directly connected to the relation of the two engaged gears through geometrical relation between diameters of the gears cleavage circles. Revolution speed of the gear shaft is then result of multiplication or reduction of the engine revolution speed.
- Engine torque and engine revolution speed is transferred through transmission onto car wheels On wheels engine torque if than transferred to force on road Wheels revolution speed is than transferred to car speed By switching gears, driver changes gear ratio in transmission and accelerate or decelerate car. Speed of the car depends how many time wheel turns in period of time and radius of the wheel which determine circumference of a circle and distance travelled per one rotation of the wheel.
- Through this jurney until now we have: Created explosion in engine cylinder Transferred this energy into rotation and torque Accelerated car by switching gears and pressing the throttle Turned left/right with steering unit Cruising around nice and smoothly thank to great suspension But does anybody knows how to stop the car before it runs out of the gasoline?
- To stop the car in safe way, engineers invented braking system. In order to determine required characteristics of the braking system, they use braking graphs, formulas and functions. Interesting thing is to see how the braking distance changes in relation to different speeds – if we drive with double speed, we need 4 time distance to stop safely.
- To calculate maximum braking deceleration, we are using square routs, square functions, vectors and trigonometrical relations. On right picture you can see maximum braking forces for various vehicles/plane
- We will see what will future bring to us – who knows? I don’t. But what I can tell you with certainty is that behind all that will be invented stands one basic ground – beuty of math.
- Thank you very much for your attention! I hope that you have enjoyed presentation. If you have some question, I will be happy to answer you.