Classic question about the use of a Cantilever beam for designing vehicle structures

Good afternoon everyone! I know it’s been a while since the last post but I’ve been (and still am) very busy with all kind of simulations, tests and writing papers and my doctoral thesis. Hopefully, I’ll manage to write some more articles during the summer! I recently had a conversation with some senior engineers from a F1 team regarding Cantilever beams and some erroneous assumptions which are commonly made, so I wanted to discuss it with you! Hope you enjoy this brief post!

A few weeks ago, I had the chance to speak with three top F1 designers and we had a chat about a certain question regarding the use of the Cantilever beam as a tool to design some vehicle structural components. First of all, let’s remind what this type of configuration is. A Cantilever beam is a structure which is fully constrained at one end, having a vertical load applied at the other end of the beam to study the effect of bending, as illustrated in Fig. 1.

This type of structure is very useful when designing certain components, since they can be simplified to this well-known beam, reducing the number of variables and being able to define simpler design targets. The thing is that usually, in reality, the components usually have some part of its length reinforced (e.g. thicker walls), so two questions arise: why is this non-homogeneous beam common and where should that reinforcement be placed?

We agreed that a lot of people answer very quickly that it should be placed at the free end of the beam, i.e. where the load is applied. According to these people, the reason for this is pretty obvious, since that end will suffer the greatest deflection (I will write another post soon where I derive this and discuss some ways to calculate it by hand!). Hence, if that region was reinforced, the deflection would be smaller and the structure would be better in terms of bending performance. But, is this true? Let’s have a thought.

Consider the structure from Fig.1 and try to analyse it with simple structural mechanics. Firstly, we need to determine the reaction forces and moment at the fixed end caused by load P. Applying equilibrium as shown in Fig.2, the following results are found:

Then, applying equilibrium to a portion “x” of the beam from the fixed end (see Fig. 3), the stress distribution can be easily calculated by applying, once again, equilibrium:

While the axial stress is null and the shear stress is constant along the length of the beam, the bending moment depends on the position. This means that the maximum moment that the structure experiences is located precisely at the fixed end, rather than at the loaded point! Therefore, the fixed end is the region which suffers the most, resulting in designers adding extra material or other types of reinforcements in that area, in opposition to what other people mights have thought! If you don’t believe this, you can always hold a small stick in one had and apply a vertical displacement on the free end with your other hand: the stick will bend and break at the end that you’re holding!

My point with this post is that this simple question can be asked to you in an interview, and you should not jump into the first “logical” response that comes into your mind. Just spend some time thinking about the problem and you’ll see how basic structural mechanics can help you! And you thought you would never use all these basic theories you were taught at university…

Every year, with the start of the Formula 1 season, a lot of people ask about the rules, concepts, technology and history of the sport. For that reason, Stuart Codling recently wrote a new book called “Speed Read F1”, which tries to cover the keys to understand the basics of Formula 1. If you want to find out more about this book, keep reading this review!

Believe it or not, I first heard about this book on Twitter, where a considerable amount of motorsport journalists shared their excitement about the release of this book. I was curious so I decided to check who the author of this book was and I was shocked when I found out that it was written by Stuart Codling, who is a well known automotive and motorsport expert (you can find his articles in prestigious magazines such as “F1 Racing”). After that, there was no doubt I needed to get my hands on this book!

Let me start the review with the structure of the publication. The book is divided in seven sections based on different aspects of the sport: Technology; Drivers; Rivalries; Racing Circuits; Flag to Finish; Staying Alive; Taking Care of the Business. From my point of view, this division is very clever and helpful for new fans and people who just want to learn the basics of something in particular. Although the book is 159 pages long, it is written in a way that encourages the reader to finish it as quick as a Lewis Hamilton’s fast lap. In addition, another thing that I particularly enjoyed is that every subsection counts with three brief paragraphs on the left margin where the reader can find interesting information about something funny, history and a person of interest (always related to the main topic of the subsection).

Now, with regards to the content itself, I must admit that I got hooked from the beginning, which covers all the main technical aspects of the sport… but that may be because of my engineering background and my previous knowledge of F1. Besides, the chapter about rivalries provides amazing facts about old drivers that I never got the chance to see on the track, so I am sure almost everyone will learn at least one new thing while reading this section. Furthermore, another detail that I would like to highlight is that after each chapter, the author includes a glossary. This glossary is a very useful F1 dictionary that new fans will definitely take advantage of, mainly because it explains specific topics in a very simple way. Now you will be able to understand every word you hear during a Grand Prix on TV!

That being said, I must warn you that sometimes there is a bit too much of information in a very reduced amount of words. If you are not used to scientific papers or technical books you may struggle and will probably need to read certain paragraphs a few times. Also, as a non-native English speaker, I found it curious that in the book some words are written in British English whereas others are written in American English, such as “carbon fiber” (American) instead of “carbon fibre” (British). This is nothing bad, don’t get me wrong, but it made me pay more attention whenever I read something like that, especially about materials… And I found something that is not an accurate fact about composite materials. The author, in order to provide some background, gives a definition of carbon fibre that only applies to certain types of composites… I know this is a silly comment, but I am very picky when it comes to materials science!

Overall, I think it is a nice book to read if you are new to the sport or just a casual fan. However, I wouldn’t recommend it to people who have followed Formula 1 for a long time. From my point of view, this book should target an audience which is willing to get involved in this motorsport world. So, if you are one of these new fans, I definitely encourage you to get a copy of the book. After reading it (and it is very easy to read!), “rookies” will be able to speak about most things F1 related with people who have been enjoying the sport for ages. You won’t need to be asking all sort of basic questions anymore!

What is the aim of the front wing in a F1 car?

Have you ever wondered why Formula 1 cars have those extremely complex front wings? Some people may think that these structures are only there for producing downforce, but in reality their function goes beyond that. Do you want to find out more? Well, here’s your chance!

A few years ago I had the opportunity to meet Craig Scarborough during one of his pesentations about Formula 1 at Cranfield University (United Kingdom). For those who are not familiar with that name, Mr Scarborough is a well known expert in motorsport and, just so you know, he’s quite a celebrity on social media (Twitter, LinkedIn…), where he usually shares top quality information about racing and the engineering behind it.

Yesterday, I contacted him after watching his latest video for motorsport.com in which he discusses the function of a front wing with Willem Toet, one of the best aerdynamicist in the world. They use a 3D airflow animation in order to illustrate how the wing of the McLaren MCL-32 works. After asking for his approval, Mr Scarborough was kind enough to give me permission to share the video with the audience of Engineering Breakdown, so here it is! I hope you enjoy it!

(Please note that in order to watch the videos, you need to reproduce them on Youtube, following the instructions).

Things to take into account when making your own convertible car

Last February I participated in the Young Persons’ Lecture Competition, organised by IOM3. In particular, the local heat took place at the University of Surrey. I want to share with you the transcript of my presentation. I have to say that I tried to present a quite complex topic in a very simple way so that anybody without  an engineering background could follow it. Hope you enjoy it!

Abstract: What would happen if you removed the roof of your car? First of all, you would have a convertble vehicle to enjoy that one sunny day we have in England. Second and most importantly, you would probably be the bravest person on earth. Driving on a bad road or even going over a speed bump could have dramatic results. Using simple engineering concepts, logic and a shoe box you will be able to understand why that could happen ad how automotive companies overcome this issue.

Let’s start from the beginning. What is Strength of Materials? It is the science that studies the behaviour of solid objects when they are subjected to stresses and strains. So, first question: what kind of objects? Basically we can have 1D, 2D and… Exactly! 3D elements! Some examples could be a bar (1D), a shell or a plate (2D) and a hexaedron (3D). For this particular topic, I’m going to focus on 2D elements, since the body panels of a car can be considered as very thin shells assembled together.

Geneva International Motor Show 2017

Last month I travelled to Geneva (Switzerland) in order to attend the most important motor show of the year and here you will find some of the best pictures that I took during the event.

For those of you who are not familiar with the automotive world, I should start this post by stating that during the year there are several events known as “motor shows”, where Original Equipment Manufacturers (OEMs) exhibit their new vehicles and technologies. Since not all OEMs go to every event, there are some motor shows which are flagged in every calendar due to their relevance in terms of the companies and public that will be attending. In these terms, the Geneva International Motor Show is considered as the most important event of the year, followed by Frankfurt.

Carbon Ceramic Brakes

Nowadays, if you are lucky enough to be able to afford a sport car, one decision has to be made with regards to the extras: the brakes. Are the famous carbon ceramic brakes that special? Let´s find out some of their features.

Carbon ceramic brakes consist of carbon fibre reinforced silicon carbide. In this case, the matrix is made of silicon carbide (SiC) and silicon (Si), whereas the reinforcement is made of popular carbon fibre. The matrix provides the hardness to the composite material and the fibres are responsible for the fracture toughness.

The main advantage of this type of brake is its capability to absorb extremely high temperatures. Why is this important? Well, sport cars can go fast… very fast. Therefore, there is also a need for reducing the speed of the vehicle as fast as possible. Since the brakes use friction in order to slow the cars down, heat is generated and it can decrease the efficiency of those particular components. Hence, having brake disks which contain modifications in order to withstand those high temperatures, is a must.

In addition, this composite material reduces the weight of brake disks up to 50% when compared to conventional ones. Furthermore, carbon ceramic brakes do not suffer corrosion, which is a major problem for iron brake disks. Apart from that, other merits include: longer life, less dust (in metal brakes, the dust have magnetic properties due to static electricity, resulting in particles which remain on metal parts around the disk) and less noise.

What’s the best way to go over a speed bump?

I’ve noticed that a lot of people try to avoid using the four wheels of the car when they go over a speed bump. Out of curiosity, I asked some of those drivers and all of them gave me the exact same answer: “Because if you only hit the obstacle  with the wheels of one side of the car, you will cause less damage to the vehicle and, besides, it is less uncomfortable for occupants”. Is that true? Let’s find out.

Let´s start from the beginning. The first thing we need to know is that cars have two axles (i.e.front and rear) and each of them has two wheels (i.e. right and left). On the other hand, speed bumpers are road obstacles which are designed to make drivers reduce the speed in certain areas and they are usually as wide as the lane. Why is that? Well, basically bumps are thought to be encountered by the two wheels of each axle simultaneously, creating a scenario known as “vertical symmetric load case”. This situation causes results in a bending moment which is applied to the structure of the car.

However, sometimes we can find some bumps which present a smaller width or even gaps. These are the situations where some drivers decide to vary the direction of the car so that the wheels of one of the sides avoid the contact with the obstacle. Therefore, only one wheel goes over the bump. Hence, the vehicle will suffer an “asymmetric vertical load case”. In other words, the automotive structure will be subjected to a torsional load, which is a worse scenario than the one introduced above since it can cause one of the wheels to lift off. I will show you how a relatively simple approach can be used to prove this statement.