Maths behind your car

Maths behind your car

26.11.2020: The famous professor and YouTuber David Calle explains the formula for aerodynamics, the integral of velocity in curves and the calculation of reaction time

The famous professor and YouTuber David Calle explains the formula for aerodynamics, the integral of velocity in curves and the calculation of reaction time

 Concealed in the volumes of a vehicle there are different formulas, operations and mathematical and physical calculations

 All these formulas guarantee the proper performance of the car and the safety and comfort of its occupants

When you get into your vehicle you usually take your family or friends with you. But they are not the only occupants of the car. Similarly, mathematicians like Pythagoras or physicists like Newton are also travelling companions. SEAT’s Education and Youth Empowerment Ambassador David Calle, a communications engineer, YouTube star and 2017 Global Teacher Prize finalist, gives us an exclusive explanation of three formulas that enable our vehicles to function. A new way of teaching at the service of the automotive world.

Professor, engineer and youtuber David Calle is SEAT’s Education and Youth Empowerment Ambassador

To calculate this reaction distance, a simple rule of three is enough: multiply speed by time

Newton invites us to brake

Who would have anticipated that the apple that fell from a tree near Isaac Newton would trigger one of the most productive careers in physics? His first law, that of inertia, is what leads driving instructors to insist so much on the safety distance.

“If you’re driving and a cat suddenly crosses your path, and you have no choice but to continue without swerving, the only thing you can do is brake”, says David. According to Newton’s first law of motion, every object will remain at rest or in a uniform motion in a straight line unless compelled to change its state by the action of an external force. “And this external force is your foot on the brake pedal”, jokes the teacher.

While reacting we do not yet step on the brake, so we continue to move forward. To calculate this reaction distance, a simple rule of three is enough: multiply speed by time. An average person takes 0.75 seconds to react so, if for example you are going at 120 km/h (33.33 m/s), you will have continued moving for 25 metres no less until you finally hit the brakes. That’s why it’s important not to exceed speed limits and to keep a safe distance, “so you can save the cat”, he laughs.

In these cases, the most important thing beyond braking in time is to detect obstacles on the road well in advance. This is why cars are increasingly giving better visibility, even on night-time trips. The fourth generation SEAT Leon features Full LED headlights that illuminate more brightly and with a range of up to 70 metres, compared to 50 in older models.
Beneath the shapes and volumes chosen for a vehicle there’s the formula of aerodynamics

The faster you go, the more difficult it is to fight against the force of air, so the surface and its forms must work in your favour

Exponential aerodynamics

When the Austrian inventor Edmund Rumpler conceived a car in the shape of a drop of water in 1921, it was foreseeable that aerodynamics would become an obsession for car manufacturers. This science that studies the movement of air is key to vehicle performance. “By optimising aerodynamics, the car will go faster, but it will also be safer and more efficient, since it will reduce consumption and CO2 emissions”, points out Calle.

Rumpler was not off track with his extravagant vehicle: “Indeed, cars with rounded, tapering volumes are more streamlined than those with more boxy shapes, because they enable you to get through the large wall of air in front of you”, says the professor. Even so, beneath the shapes and volumes chosen there must always be a formula to support these decisions: the formula of aerodynamics.

This law of physics basically states that when you double the front surface of an object, you double the resistance that the air exerts on it, but if you double the speed, the resistance quadruples. “This happens because surface and resistance have a linear relationship; while with speed, resistance is related exponentially”, explains the teacher.

Therefore, the faster you go, the more difficult it is to fight against the force of air, so the surface and its forms must work in your favour.

In order to take into account all the data from each and every point of the curve, the integral is the perfect operation
Telemetry, this speed monitoring system, is also applied to safety

Integrals, useful at last.

Let’s be real; in our student days we all struggled more than once with integrals and their relatives, the derivatives. Seriously, what are these calculations good for in real life? “It’s a question I’ve been asked countless times”, admits Calle, “and the answer is on any racetrack.”

In the case of a race between two drivers, if you want to know who has taken a curve faster, the easiest thing to do is to measure the speed of each of the drivers at one or two points of the curve and take the average, “but this would only give us a static image of their speed”, says Calle. In order to take into account all the data from each and every point of the curve, the integral is the perfect operation, since it is just that: a continuous sum of infinite data.

Thanks to advanced telemetry systems, which measure different magnitudes in real time, nowadays obtaining speed data at each point on a curve or racetrack is simple. “With the data, far from having to add them up individually, we only have to take the integral of the whole and the average of the result of each driver will tell us who has won”, explains the professor.

Outside the races, this speed monitoring system is also applied to safety. This is the case with the new SEAT Leon, which features adaptive cruise control (ACC) and a travel assistant that provides assisted driving at speeds of up to 210 km/h.
play icon

Driving by numbers.

These are just three of the many examples of the mathematics behind a car. “We don’t see it, but in the automotive industry there are hours and hours of calculations, operations and formulas to ensure the best performance of a car, and above all, safety”, concludes David Calle.

“And comfort as well: for example, millions of 1s and 0s combine in the console to satisfy all infotainment needs, in binary code”, he adds. “But that’s another story.”

Gemma Solà- photos Seat


26.11.2020 / MaP

More News

South Africa's vehicle exports under threat
South Africa’s important built-up vehicle export programme is under threat from two major fronts. This is one of the strong messages that came out of Messe Frankfurt SA’s recent Hypermobility virtual conference and it was mentioned by several speakers at this annual conference. more >>
Bleak outlook for SA economy predicted
The outlook for the South African economy is bleak and a post COVID-19 recovery will take as long as five years and by that time the local economy will be 8% smaller than it was pre-pandemic. This according to Jeff Gable, the head of Fixed Income Currency more >>
Vehicle dealerships will still play an important role in future mobility environment
A lively panel discussion at the recent Hypermobility 2020 virtual conference concluded that vehicle dealerships will still have important roles to play in the rapidly changing global mobility environment.“We are already changing the way we do busin more >>
Ford Expands its Share in Fleet Vehicle Segment
•    The Ford Transit Custom is the most-driven car in South Africa with a 2019 registration year, according to AutoTrader•    Ford dealerships were able to service and maintain fleet vehicles during COVID-19 lockdown nationwide•    Modern safety features, large payload capacity and efficient, powe more >>
The Audi TTS competition plus - Athletic highlight
New equipment line for the Audi TTS        Coupé and Roadster feature sporty design details in the interior and exterior        Exclusive offer from Audi Sport GmbH: “bronze selection” for Audi TT and TTS more >>
Adventures amid glaciers and volcanoes: A ride in the MINI Cooper S Countryman ALL4 on Iceland's Ring Road 1.
A round trip by car is a good way to experience the diversity of the island state's landscapes in the North Atlantic. The road network is thin and four-wheel drive is highly recommended for some excursions. The MINI Cooper S Countryman ALL4 can prove its talent as a robust all-rounder for any terrain on a tour to discover and explore fjords, lakes, glaciers, geysers and volcanoes. more >>
Honda Civic Type R Trifecta: Fun to Drive, Chance to Win and Give Back all at Once!
    Honda teams up with Omaze to offer one winner the first U.S. market 2021 Civic Type R Limited Edition Serial Plate 001 production model    Omaze prize package includes the Civic Type R Limited Edition and Honda "Racing Spirit" package with exclusive race track experience with Colton Herta    Every donat more >>
Maserati selects Ubigi to offer integrated Wi-Fi on board
Maserati is the most recent FCA brand to offer Wi-Fi on board thanks to Transatel's brand for the connected car: Ubigi. The Ubigi service for Maserati is available on all MY21 models and is to become a staple feature for all cars sold in Europe[1]. Ubigi' more >>
Toyota Camry Hybrid arriving with more dynamic design and updated safety technology
    2.5 litre 218 DIN hp Camry hybrid received a sleek yet stronger design, adding more dynamism and a wider stance     New alloy wheels, new exterior colour and revised interior add sophisticated touches to Ca more >>
Automobili Lamborghini partners with Master & Dynamic on new headphones and earphones collection
Automobili Lamborghini partners with Master & Dynamic, the New York-based premium audio brand, to create a co-branded range of headphones and earphones. The new collection presents MW65 Active Noise-Cancelling Wireless Headphones and MW07 PLUS True Wireless Earphones, incorporating design elements inspired by the iconic Italian super sports cars. more >>
Kia unveils two rugged X−Line Sorento concepts built for the wild
Aggressive Custom SUVs Signal Brand’s Focus on Adventure, Capability and Trail Readiness       Sorento Yosemite Edition aims at exploring high-elevation locales and mountain living    Sorento more >>
FORD New Car Tech Could be Just What Cyclists Want
– a Warning That Helps Stop Drivers ‘Dooring’ Them •    Exit warning system provides visual and audible alerts to road users and occupants•    Current customer clinics will ensure that the technology accommodates road users in different markets•    Ford&rsqu more >>
An icon reborn: The new Lego® Technic™ McLaren Senna GTR is unboxed
    McLaren Automotive and the LEGO Group collaborate on creating LEGO® Technic™ McLaren Senna GTR    830-piece model with authentic and impressive details including opening dihedral doors    Aimed for ages 10 and above, the LEGO Technic McLaren Senna GTR is available from January 1 2021 more >>
Ford to Reveal Custom F−150, Bronco and Bronco Sport During ‘Ford Auto Nights’ SEMA Show Special Webcast
    Ford is revealing custom versions of the 2021 F-150, Bronco and Bronco Sport with Ford Accessories and Performance Parts through the first-ever virtual SEMA show; local Ford dealers are ready to personalize these vehicles for customers    New 2021 Ranger Tremor showcases bolt-on modifications to add even more capability to the mo more >>
Mitsubishi ambassador focuses on what to pack
Before deciding on what off-road vehicle to buy, Mitsubishi Motors ambassador Francois Rossouw says planning your (first) off-road adventure with the family determines what vehicle you are going to need.“So, for that reason, let’s look at what yo more >>
Ford and Department of Basic Education Hand Over First Donated Engine to Port Elizabeth Technical High School
•    Ford Motor Company of Southern Africa (FMCSA) is donating 240 locally assembled engines to technical high schools across South Africa, in partnership with the Department of Basic Education•    Valued at R7.8-million, the engines are produced at Ford’s Struandale Engine Plant in Port Elizabeth, and will be used to more >>
Red Bull MotoGP Rookies Cup Riders for 2021 – Stars guide the way
Following our final Red Bull MotoGP Rookies Cup Races of 2020 we are ready to announce the provisional entry list for the 2021 Rookies Cup.It was an incredible weekend with two sensational Cup races contested in the great spirit of our series. more >>
BMW Group Plant Leipzig prepares for production of a future MINI crossover
- 2023 will see Plant Leipzig launch production of the successor to the current MINI Countryman   - The new model will offer a choice of combustion or electric drive - The current investm more >>
New Golf Alltrack now available to order -Charismatic all-rounder with all-wheel drive
 Confident: the Golf Alltrack with all-wheel drive, increased ground clearance and 200 PS TDI engine makes sure that its passengers reach their destination safely even on difficult terrain  Crossover: the new Golf Alltrack combines the high travel comfort and dynamic performance of a powerful passenger car with the allroad characteristics of a talented more >>
MINI x Paul Smith. Design icons supporting a sustainable future.
    MINI and designer Paul Smith have announced their second collaboration since 1999. Not only are they both British institutions with a strong tradition, they also share a commitment to continuous development and to ensuring their products make th more >>
BMW Group sets new standards for driving simulation.
- #NEXTGen 2020 offers exclusive insights before the new Driving Simulation Centre starts work.Most progressive and diversified installation of its type in the automotive industry Ideal simulation tools for every phase of vehicle development Pioneering building design for seamless simulation experience and maximum customer focus more >>
Nissan refreshes its iconic Micra for 2021
    Updated Micra line-up launches with key specification changes to offer the most premium Micra line yet    New IG-T 92 engine offers reduced emissions and improved fuel efficiency, is it also complaint with Euro6D emissions standards more >>
Flying Spur V8 production and deliveries underway
    V8 version of “world’s best luxury four door grand tourer” now in full production at Bentley’s home in Crewe    Every car crafted at world’s first carbon neutral factory for luxury car manufacture    Ordering open globally as first cars leave Crewe for their new owners more >>
LEVC appoints Modul-System as VN5 conversion partner
    Modul-System announced as first official converter for LEVC’s VN5 electric van    Range of bespoke, custom racking solutions available    Conversion partner will support in multiple markets across Europe    For more information visit more >>
AmericanMuscle Customer Spotlight 2008 Shelby GT500
New Video Features Inspirational Mustang Build   Aftermarket parts retailer, AmericanMuscle (AM) continues its “Custome more >>
SKODA SLAVIA continues to enjoy international attention
› ŠKODA Student Car shines as UK media test SLAVIA at Millbrook Proving Ground; located 80 kilometres north of London   › The name SLAVIA harks back to the company’s earliest days, 125 years ago more >>
Porsche, MHP and Munich Re found the “FlexFactory”
Digital Production as a Service The sports-car manufacturer Porsche, its management and IT consulting subsidiary MHP, and the insurance group Munich Re have founded a joint venture – the &ldqu more >>
Going on a shopping tour in Copenhagen in the MINI Cooper SD Clubman ALL4
Stylish, practical, cool   Denmark's capital is a hotspot for people who appreciate fashion, design and a laid-back lifestyle. Just the right environment for an individualist like the MINI Clubman. With its six doors more >>
SKODA AUTO gains additional capacity within VOLKSWAGEN Group’s production network
› By relocating the manufacture of the next-generation SUPERB from the Czech plant in Kvasiny to Bratislava in Slovakia in 2023, ŠKODA AUTO will free up the capacity in the Czech Republic required for the brand’s plans for growth› The extra capacity will be used to build additional cars of the popular ŠKODA KODIAQ and KAROQ SUVs more >>
Efficient and clean: exhaust aftertreatment for gasoline and diesel engines
   Total exhaust aftertreatment system reduces nitrogen oxide emissions of TDI engines by more than 90 percent        Audi in charge of systems for new V6 TDI engine generation within the VW Group        Gasoline particulate filter completes exhaust gas purification of SI engines more >>
VW Touareg now parks by remote control - Car and smartphone merge into one
 Park Assist with remote control allows the Touareg to be manoeuvred into any parking space  Using a smartphone, the driver can drive the Touareg both into and out of parking spaces  Four ca more >>
Production of Machined Components and Fully Assembled Engines Drives Ford’s Struandale Engine Plant
•    Struandale Engine Plant machines the major 2.2 and 3.2 Duratorq TDCi engine components, comprising cylinder head, cylinder block and crankshaft for locally engine assembly and export•    Powerful but economical 2.0 Bi-Turbo and 2.0 Single Turbo engines produced on state-of-the-art assembly line with numerous fully auto more >>
2021 Acura NSX Celebrates Motorsports and Heritage in Long Beach Blue Pearl
    Long Beach Blue joins Berlina Black and Indy Yellow as latest NSX heritage paint offering       Commemorates Acura’s title sponsorship of the iconic Grand Prix of Long Beach more >>
SEAT: Talent transformation
From the production line to the a line of code     A pioneering SEAT training programme aims to turn 5 production line workers into software developers in 4 months    13 weeks of intensive training and 3 week more >>
Lifestyle on four wheels: the BMW M4 Competition x KITH.
BMW #NEXTGen 2020BMW M GmbH has launched a collaboration with New York lifestyle label Kith to help it sense new trends in a young and influential part of the fashion scene. The BMW M4 Competition x KITH has been co-created with Kith f more >>
BMW Driving Simulation Centre - The new benchmark for the automotive industry .
BMW #NEXTGen 2020When the BMW Group was planning its all-new Driving Simulation Centre, the technology the company decided to use included supercapacitors, direct drive with linear motors and 360-degree projectors. At the same t more >>
BMW Group to become the first premium manufacturer with 5G in series production.
BMW #NEXTGen 2020The BMW iX will now go one step further by becoming the first premium model to be equipped with 5G mobile technology. 5G offers extremely high data bandwidth and low latency – meaning fast data tra more >>
Goodyear releases new wintercommand ultra tire
Premium winter tire now available for purchase at retailThe Goodyear WinterCommand Ultra tire is now available for purchase in the U.S. and Canada. It demonstrates exceptional performance on ice and snow and earned No.1 rankings among leading competito more >>
JMS meets JM Cardesign: Lotus Esprit sports car as a joint project
  A true mid-engine classic from Great Britain, which has been manufactured over a truly long period of 28 years and continuously developed during this time, is the Lotus Esprit with up to 354 hp.     The team from JM Cardesign more >>
2001-2023 copyright