The Geometry of Formula 1

Not only do F1 teams compete inside the track, but also outside it. As a case in point, they challenge each other to see which team builds the most magnificent and welcoming motorhome in the paddock.  As attractiveness is commonly associated with sight, let's take a look at the facades of some of these motorhomes while calculating their perimeters and areas. ASTON MARTIN MOTORHOME Aston Martin motorhome for the 2021 season. Calculate the perimeter and area of its facade. FERRARI 90 YEARS MOTORHOME The Ferrari motorhome for the 2019 Italian GP. How many Ferrari legends can you recognise in this poster? Calculate the perimeter and area of its facade.

A mosaic is a pattern made of small pieces which covers a surface. One of the most common mosaic techniques is the regular tessellation of the plane. A regular tessellation is a pattern exclusively formed by a regular polygon and which fully covers the Euclidean plane without overlapping. Owing to this, they can only be made out of squares, equilateral triangles or hexagons. Now let's take a look at some mosaics we can find in F1 races. THE CHEQUERED FLAG The chequered flag is arguably de most iconic symbol of motor racing, since the waving of it traditionally announces the end of a Grand Prix. As its name indicates, it is a mosaic made out of squares. THE MONACO TUNNEL Even when Monte Carlo held its first motor race back in 1932, the old tunnel was already there. Originally it was way shorter and its roof had a curved shape but, on account of the construction of a new hotel just on top of it, it was exhaustively modified in 1973. Before the remodelling, the interior walls simply h

Not only are F1 circuits unique, but also their sectors! Every track is divided into three sectors and each of them can have completely different configurations. Some sectors can have long straights which demand good traction and top speed, others can have plenty of fast speed corners which demand high downforce, etcetera. To get familiarised with F1 tracks and the cartesian coordinates, let's do a brief activity. Locate in the plane every pair of coordinates which are inside the circuit and indicate in which sector are them. Yellow is for sector 1, red for sector 2 and blue for sector 3. For instance: (4,0) is the main straight and it is in sector 1. (5,-3) is turn 2 and it is in sector 1 as well.  Now it's your turn! Look for more coordinates in the Suzuka Circuit. Have you already found all the coordinates in the Japanese track? Let's try now with the luxurious enclave of Monaco, where every corner has a name. Let's finish with Monza, "The Temple of Speed".

Another aspect of F1 cars in which rotations come into play is the toe. The toe describes the angle of the wheels (yellow broken ray) in relation to the perfect straightforward direction of the car (red ray). We refer to neutral toe when both angles equal 0º (central image), positive toe when the front right tyre has a positive angle of rotation and the front left has a negative one (left-hand side image), and positive camber when the opposite happens (right-hand side image). Last year, toe angle was a hotly-debated topic in the F1 paddock, as Mercedes came up with an ingenious invention which they called DAS (Dual-Axis System). This device allowed the driver to adjust toe angles by pulling the steering wheel backwards or pushing it forwards. Pulling back the steering wheel generates positive toe (as you can see in the gif below) whereas pushing it forwards causes negative toe. DAS was banned for the 2021 season, on the ground of mitigating Mercedes dominance. As it is explained in the

As we saw in the previous entries, angles do have a significant impact on car performance. As a matter of fact, their importance is not limited to the floor of the car but also to other parts such as the front wheels. When we talk about tyre camber, we refer to the lean angle front wheels have (yellow rays) in comparison to the vertical axis of the surface (blue rays).  These transformations can be seen as rotations, if we consider the intersection of the axis and the surface itself as the rotation centre (white dots). A common alternative is to take as a rotation centre the intersection of the middle of the tyre and the steering axis (blue dots). We speak of neutral camber when both angles equal 0º, negative camber when the front right tyre has a negative angle of rotation and the front left has a positive one (just like in the example above), and positive camber when the opposite happens. Finally, here's a very insightful video in case you'd like to understand in depth the us

Unlike other motorsport categories such as IndyCar or Nascar, Formula One has always use to have symmetrical cars. The reason for it is quite simple: all the tracks where teams race have a similiar number of righ-hand and left-hand corners, so it is not worthwhile to build an assymetrical car. Nonetheless, throughout the years, there have been exceptions which that have proven the rule. Here are some examples: LOTUS E22 (2014) With the beginning of the hybrid era, several teams came up with infamous designs in the front end of their cars and Lotus' "twin-tusk" nose was definitely one of the most bizarre. This asymmetrical concept didn't live up to the expectations, since the Enstone-based team went from achieving 315 points, 14 podiums and 1 victory in 2013 to obtain 10 paltry points in 2014. MCLAREN MP4-23 (2008) McLaren used for the first time this asymmetric sidepod layout in the German GP, halfway through the 2008 season. The aim of this modification was to improv

When it comes to designing an F1 car, angles play an important role. One of the areas where they are more decisive is the floor. The higher the rake, the more downforce but the less straight line speed the car will have.  Red Bull has always opted for this solution and it's no coincidence that its cars use to be more competitive in tracks like Monaco, Singapore or Hungary, where it's all about corner speed and traction. In this video from 2018 you will see a comparison between the rake angles of Red Bull, Ferrari and Mercedes. But before watching it, can you guess how many degrees of difference are there between them?

F1 steering wheels have come a long way, especially since the beginning of this century. Let's take a look at them! During the first 40 years, they kept it simple. Steering wheels were basically wooden or padded circunferences with three metal radius which converge on the central point. Towards the end of the 1990s, Ferrari revolutionised the design of steering wheels by adding rectangular paddle shifters and displays which gave drivers shift lights, lap times and much more information. Furthermore, they added plenty of circular and hexagonal buttons on the wheel with different functions: team radio, break balance, gearbox neutral position, etc.  If you want to see these shapes in better detail, click on the  3D version Once the 2010s arrived, steering wheels were no longer circular and grip kept on improving. Additionally, shift lights became circular and smaller: can you spot them? Here's the solution Eventually, with the arrival of hybrid engines in 2014, rectangular display

Helmet designs can also reflect part of the drivers' personality. They can be chaotic, striking, traditional, pragmatic, patriotic, changeable, immutable... to each their own. In any case, plane shapes and colours play a major role in defining their own style, as we are going to see now. LANDO NORRIS Young, cheeky, funny... but fast, really fast. Lando Norris is one of F1's rising stars and his helmet design is inspired in that of his idol, the nine-time MotoGP world champion Valentino Rossi. This special design for the 2021 Monaco GP preserves the essence of the original one but adds a few tweaks to it, like those aviator goggles, which were an indispensable part of the drivers' outfit during the 50s and 60s. How many elements of the Eucledian geometry can you glimpse in this helmet? FERNANDO ALONSO Passionate, relentless and perfectionist. "Magic" Alonso has always been proud of being both Asturian and Spaniard, and it shows. The helmet above is the one he used

Geometry is here, there and everywhere... and the sophisticated world of Formula 1 is no exception.  Let's start from the basics and see how many plane shapes can you spot in the logos of the 10 teams which take part in the 2021 F1 championship.  ALFA ROMEO In the logo of this legendary Italian team there are two perpendicular lines, a big circunference & small-sized circles. Can you see them? Tell us their colours to prove it. ALPHA TAURI In the logo of Red Bull's sister team we can see a circunference... ALPINE In the logo of Fernando Alonso's new team we can find concurrent lines, as well as a transversal one, a paralelogram and an isosceles triangle. Can you identify them? Are there any perpendicular lines? ASTON MARTIN In the logo of this luxurious British car brand, very well-known for the James Bond saga, we can spot a rectangle and several concurrent lines. Among them, are there any perpendicular? Use your protractor again to prove it. FERRARI The world's mo