2013/14 F1 Regs…

In light of @SomersF1 recent post on the new F1 regulations for 2013 & 2014 I thought I would gather together some of the technical data I have, and put some words up about one of the areas Matt summarised – aero-elasticity or fluid structure interaction from the world of physics and its implementation in F1.

I will attempt to explain the two separately linked components that come together to create one overall phenomena that the F1 teams are looking to exploit to gain performance.

Most of the examples I have are confidential but I will try to include some generic cases that will help in illustrating the complex mathematics that underlies this useful and burgeoning part of F1 racing car design.

My aim is to open up the physics that take place throughout a race and highlight the advantages that teams can gain by designing in aero-elasticity on the front wing.

Hopefully this will then allow all F1 fans to appreciate and understand another science that pushes car development to its consistent and ever-growing limits.

I will endeavour to get this posted in next couple of days, as usual, time permitting… stay tuned.

 

 

The Winning Identity…

I would like to dedicate this post to @RonF1Etc from F1Etc who sadly died earlier today 25th July 2012. Please feel free to tweet your condolences to #RIPRonF1Etc my thoughts are with your family and friends.

In mathematics there are several ‘equations’ that are considered perfect due to the absolute relationship between each term within the equation. For me personally I have a love for Euler as a Mathematician and also as the creator of THE finest equation that exists (my opinion by the way, I know you all may have your personal favourite).

OK so where am I going with this mathematical rambling…

As in mathematics, Formula 1 has dependency on relationships in order for the team to perform to the best of their ability: the car is functioning as it should, the aerodynamics settings are optimised for each particular track, engine is tuned and ready, the mechanics are primed and practiced in pit stops and any potential failures they potentially could experience and the strategists have done their probability calculations and so on and so on. However, something that occurred to me whilst in a tweeting rally with some fellow F1 folks, was that there is a relationship at another macro level between driver, engine and aero.

Let me explain what I mean by asking the same question I asked on twitter over the weekend: What percentage split would you apportion to the performance of the car during a race between driver/engine/aerodynamics? (please exclude strategists, engineers and any mechanical set-up such as suspension for the time being I will come on to this in a second).

Tyres are a whole different topic on their own which may be covered in a later post!

I recently spoke to an ‘F1 Insider’ on this very topic and its fair to say that we must also consider, as I mentioned above, the strategists who plan for any potential events during a race and try to out-manoeuvre rival teams; this is also closely coupled with what the engineers have done to maximise on the performance over the course of the weekend by fine-tuning the set-up of the car. Finally, that set-up of the car is crucial to how it performs over the course of the practice sessions, qualifying and the race itself. Now to avoid even further complexity I am going to group together these (strategists, engineers & mechanical set-up) with the driver in our split driver/engine/aero.

Again, this is my own opinion but I stated 20% for the driver (including the above), 10% for the engine and the remaining 70% to be down to the aerodynamics. It appeared that I was in a majority [to my surprise] and that a high percentage of people tended to agree with me.

It’s fair to say that the engine is a constant in this equation as the FIA state that it should not be a ‘performance differentiator’ but as I alluded to earlier, behind EACH driver are strategists that formulate a plan of tyre choice and order, pit stop timing and quantity, so a definite variable throughout the race weekend. The engineers who determine the set-up of the car mechanically, for a specific race, condition, suspension etc to try to gain as much performance advantage as is possible, would also not really change outside what has been planned for already.

To provoke some thought from you as readers and fans of F1 what would YOU think that HRT or Marussia (for example) would rather have? Alonso driving or a Ferrari engine?

Or, how is it that Red Bull engineers are more able to extract a good time from their car than the HRT engineers?

So what has this all got to do with maths?

Lets break this down further – taking the aerodynamics in the first instance; engineers/designers etc have increasingly over the years, now compute power gives them opportunity, tuned the aero packages tighter and tighter within the realms of the rules to ensure they are exploiting Newton’s Laws of Motion (as we’ve discussed in a previous blog ) so inevitably the aerodynamics have become more a part of the performance of the car in later years – with the now standard use of Computational Fluid Dynamics or CFD, teams are able to run more and more** aerodynamic variations on the car between each race to optimise the car for the type of circuit (minimal corners, lots of straight line speed requiring low drag or the tight corners and lower speed raising the need for higher-downforce for maximum grip). Fundamentally, the aerodynamics would be a governing variable if this relationship between driver/engine/aero were a mathematical equation so naturally becomes more important in the success of the car.

**the Resource Restriction Agreement or RRA controls and limits the amount of TeraFLOPS for any computer simulations and hours that a wind-tunnel is utilised to try to equalise the potential advantages for each team.

Continuing on with each term in this real world equation is the engine: OK so each supplier has to oblige to regulation but can make ‘some’ tweaks to maximise on performance; however some teams share an engine so realistically there shouldn’t be any powertrain performance difference if this is the case? Again, though, some engines seem to sit more ‘comfortably’ than others and you have aerodynamic distribution, driver style, and so on. We’ve all noticed that drivers nowadays are constantly finding that they have to vary or adjust their driving styles to be successful!

A little like the Navier-Stokes equations perhaps – many terms, many variables, each term effecting the others and each resultant driving the next and the next ad infinitum……. at least until you have a converged solution.

For those interested, the Navier Stokes equations illustrated to the right, describe the motion or movement of a fluid (in this case air) whilst applying Newton’s Laws of Motion – his 2nd law in fact, covered in an earlier post)

Finally, you have the driver: they must have the ability to protect their tyres and have to drive a strategy that has been pre-defined by their team to fulfill the requirements of that race and to try to take advantage over their competitors should the opportunity arise. It’s fair to say that the ability of the driver influences the performance of the car at varying stages of the race, be it tyre degradation or high-temperature in the brakes – so yet more variables!!

Firstly, I do believe that the 24 guys that start a GP are the most talented, focused and highly trained people on the planet and do things that we could never dream of doing; but they are human, kind of and therefore are susceptible to error, lack of concentration (we all have our own thoughts on who this could be), distraction and can never be as consistent as a piece of code or mathematical equation, albeit orders of magnitude more focused & concentrated than all of us could be.

A car is essentially ‘suited’ to a driver and will be set up to suit his (and hopefully soon, her) preferences. A driver can be affected by his opponents and forced into a mistake as there are points or credibility or even a World Championship at stake if concentration slips for a millisecond.

Based on what I have said above, I guess you can say that I have not got you any closer to this golden ratio of what the ideal combination would be to make a perfect team – this is why it is the great sport it is; which is why we have had such an exciting season in 2012; why it’s so difficult to predict the outcome based upon previous seasons. Ideal for the fans though.

The point I am trying to make, looking at this with a logical, mathematical mind is that to be a successful team each component of driver, engine, or aero package has to tuned specifically under its own merit, but also it has to have complete synergy with the other two components to ensure the completion of the race but more importantly faster than any of their competitors, obviously.

I don’t want to go into specific teams and I’m not sure I can – one thing is for sure however, that probability, strategy, technical brilliance and a finely tuned ‘system’ is the key to success but is further governed by mechanical failure, team efficiency (good or bad pit stops) and that other topic we’ve ALL debated, TYRES!

For me, the changes each team make, the specific skills of each driver, the weather, etc make for a fantastic sport and an opportunity for each team to push the others not because of budget but because of engineering and skill. Sadly, budget does play a major part and extensively contributes towards the overall speed of the car – is this unlikely ever to change?

This topic is likely to be discussed over and over and there be no right or wrong answer to the perfect ratio or relationship between driver or engine or aerodynamic package – I’ve sat and puzzled over how I can quantify this with bits of paper strewn across the floor, pieces of string inter-connecting each variable, using algebra and statistics, probability and quadratics to ascertain a common thread, and not really being able to do this consistently, fundamentally telling me to just leave it, sit back and ENJOY it.

Which is what I suggest you ALL do…. F1 is incalculable in a calculable way and sadly not an Euler Identity!

Can you find aerodynamics with a map?

Aerodynamics plays a huge part in any F1 race be it the high downforce requirements of Monaco or the reduced-drag desires of Monza; each race also being at the mercy of the changeable weather conditions as we almost experienced this weekend in the Principality.

All these factors affect the performance of each car in many different ways – we’ve had 6 winners in 6 races in 2012 and in each you can see certain variables creating or assisting with the success, or failure, of the drivers and teams.

Now based on what I have posted about previously, aerodynamics (or at least the maths behind it) is complex enough based upon track requirements, weather, tyres, driver preference etc but you often hear about engine mapping also playing its part [F1 is fundamentally a sport, but if all could see the wizardry, physics and depth of mathematical detail supporting it, you'd think it were of NASA proportions].

So what is engine mapping?

Just before I delve into this, I’d like to state that the aerodynamic configuration for the car is determined by the circuit the car is about to hurtle itself around obeying the laws of motion determining the laws of aerodynamics giving an overall performance for the car. Simple. OK a tiny tweak here and there during a race but fundamentally unchanged.

Engine mapping is not a completely specific and nailed down undertaking and is generally discussed and illustrated in a ‘disconcertingly vague’ way but essentially it is the way the ECU allows and controls the engine to perform throughout a race. So, for example, you could be required to brake at the end of a long straight (low downforce, low drag) into a tight corner (higher downforce) and lift off the throttle, applying the brakes, but the ECU maintains the engine power output – the resultant effect of this is that the aerodynamic configuration is now having to work under completely different conditions as the energy output from the exhaust gases are vastly different and far hotter playing an altered role in the aerodynamic performance of the cars set up.

Similarly you could be safely leading the race and not have to ‘hammer’ the engine in order to maintain your lead, simply ‘cruise’ to the finish line.

This can have both a positive or negative effect on the car and needs to be simulated using CFD solvers to capture the increase in energy output and its effects downstream.

I guess most people would state that engine mapping should be set to ‘fast’ at all times as that is the name of the game – but any alterations can assist with fuel consumption on strategic final laps depending upon position – a final cruise to the chequered flag, as described above: or an adjusted power output to conserve tyre degradation.

Either way any change can play a huge part in the overall aerodynamic performance so (it clearly varies from team to team) a fast setting can aide one driver and visibly inhibit another. A main contributor to this is the position and profile, and indeed the downstream aero path, of the exhaust outlet – greatly effecting rear downforce if toward the centre of the car and providing grip if toward the rear.

For me, in my job, this adds complexity and also pushes the designers and aerodynamicist’s within each team to constantly improve the finer details of the ‘aerodynamic path’ of the airflow on race from start to finish accounting for all eventualities.

The mathematics are able to calculate for change by adding a further source term for energy and as I mentioned above CFD (Computational Fluid Dynamics) is the quickest and most accurate way of carrying this out.

More and more powerful compute clusters used by F1 teams are crunching more and more complex mathematical equations to ascertain whether or not the minute or massive changes created by the use of engine mapping techniques contribute toward the final success of each driver and team.

Also these changes play a knock-on effect on phenomenon such as Fluid Structure Interaction (FSI) – FSI is the interaction of some movable or deformable structure with an internal or surrounding fluid flow.

So in the case of an F1 car, the deformation of a front wing under acceleration or braking…… perhaps more on this again!

Composites… and I don’t mean a number which is a +ve integer that has a +ve divisor other than one or itself, obviously!

Athletes nowadays are so strategically trained and finely tuned that miniscule differences separate the winner and the loser in most speed-based events.

So what happens if that athlete requires the use of equipment to carry out that sporting discipline – such as rowing, the luge or cycling?

The human body is continually pushed and pushed to break records set that appear un-breakable, but regularly are; these athletes train more specifically, eat a very controlled and defined diet and have mathematically calculated rest/sleep patterns to achieve maximum efficiency and power output to be the best, the strongest or the fastest.

So what do you do when this ‘thorough-bred’ strain of human being has to climb onto a bike that doesn’t recognize diet, nor sleeps but is a collection of mechanical components engineered to provide utter and pure performance?

It’s the engineering behind the equipment, in today’s example a road bike, that athletes or more specifically countries employ to ensure that athlete is not ‘held-back’ by defective or drag-laden tools of their trade. Which is where I come in.

So, my directive was simple, make this bike faster whilst its stationary?!? This sounds counter-intuitive, no? So what I mean by this is…… The bike is currently aerodynamic to a certain extent and, whilst being ridden by the athlete experiences a certain amount of drag, slowing the rider down, or creating a greater resistance and therefore requiring the rider to exert more energy to maintain a certain pace. This limits the margin where the athlete exerts an explosive amount of energy at a calculated distance from a finishing line as we regularly see during the Tour de France or Sir Chris Hoy competing for example.

If I can reduce the amount of drag the bike creates, irrespective of the rider (they are a constant in this problem) then this will increase the available margin the rider has to explode into this final phase and provide a better opportunity of victory.

With a greater margin for this ‘pace-change’ this is proven to be proportional to more opportunity to be quicker than your opponent; more importantly more opportunity to win.

The bike I am working on is fully composite woven carbon fibre moulded and shaped based upon many different design variations to produce the most aerodynamic profile to give the rider the better ‘margin’.

The bike essentially, from a distance, to a blind man on a galloping horse, is very similar to a regular road bike, but, as with F1 cars, every component, where possible, is aerofoil shaped to guide and direct the airflow around the bike but more importantly around the rider. The faster the rider goes the faster the rider is able to go…. so that bike and rider become one…. on an F1 car, at certain speeds, this driver and car becoming one starts to create pressures sufficient to start to deform the geometry (or in the case of an F1 car, a front wing) which leads me nicely onto my next topic of Fluid Structure Interaction or FSI…. this is where the maths gets a bit fruity!!

Most simulations are run steady-state (at one specific moment in time) but sometimes its necessary to run transiently (or time-dependent – meaning to run over an allotted time) where geometry or performance changes with respect to time and having varying output data. So for example simulating an F1 car going round a corner; this would require a transient study as the car is constantly changing through a prescribed arc as I have sketched below

As you can see, as the car travels around the corner the axis through the centre of the car changes with respect to the angle of the arc and so creating a change in the physical condition. Therefore, a transient simulation is required. You could undertake a quasi-steady state looking at varying static points along the arc and then interpolating throughout the remainder of the arc. This can also be complicated further by adding variations with respect to sea level as illustrated in the graph at the top left of the sketch.

Anyway back to the FSI….

As the car speeds up and slows down throughout the race the downforce on the various components changes as described in the following simple equation:

From the equation you can see that any change in velocity (V) has a significant effect on the resultant downforce.

So, from what I discussed earlier, imagine the change in speed during a race to be the transient variable input and the output being downforce; if the car accelerates, brakes, accelerates, brakes as they do the downforce on the front wing is constantly changing. So the fluid, in this case air, is causing the front wing (the structure) to move through a cycle or interacting with it, hence fluid structure interaction.

OK now we get to the more advanced stuff….. We all know that the front wing, indeed all the wings, on an F1 car are designed with a purpose in mind – to direct the air along the car to create minimum drag and the most effective downforce so as to allow the car to travel fast down the straights and have maximum grip around the corners.

But if the varying velocity changes the downforce the wing is deflecting constantly giving further changes in airflow characteristics – giving a way around the rules that state flexible wings are prohibited! One successful team managed to exploit this rule last season or so by using this deflection (FSI) as part of the race cycle performance.

The beauty of mathematics is that it is never-ending… you can take the problem further and further and still not exhaust the possibilities….

Can you understand why I love my job?

May the Fourth… of the brakes are able to stop me…

Normally I would try to get this written before the days work kicks off, and that was my full intention. But four of my colleagues, who are US-based, all sent me emails of varying sizes from 5MB to 11MB and today I work from home so only now has my virtual pipe cleared…. Never used to happen with paper :-/

So today I’m tasked with essentially the opposite of what I’ve been prattling on about via this blog and will be mainly slowing things down.

Brake design and simulation appears a simple and obvious discipline given the fundamental requirements are – apply lateral pressure to achieve radial velocity reduction (press the pedal and the car slows down in normal English). The problem isn’t the mechanical process from pressing the pedal which activates the calipers (or whatever mechanism is being utilised) this is simple engineering – the fancy stuff is what happens at point of contact. By fancy stuff I mean the material compounds of the pads and the disc.

For general production cars this is designed for safety but longevity over relatively minimal degrees of negative acceleration (braking). Not easy, but not quite as complex as racing cars.

Given the high excessive rates of acceleration/braking during a race the brakes experience incredible thermal stresses and indeed physical torment, both phenomenon interacting with one another and also each exacerbating each.

To counter this you need, as is commonly done in Judo, to use these aggressive mechanical interactions in their own favour, with added engineering a bit of carbon and a pat on the back from someone old and wise – I’m half of this and to clarify its certainly the former!

So what we do, in the case of an F1 car, is to optimise the cooling towards the discs (which during a race can reach temperatures of 900 degC at the end of sharp braking) and incorporate the airflow to reduce drag and provide additional pockets of downforce onto major components or avoiding bluff-bodies (tyres) this way you maintain a workable temperature on the braking system and gain some 100ths of a second at crucial points around the circuit. Imagine how your neck would feel slowing from 200mph to 45mph from your back door to the bottom of your garden (in an average British semi) let alone what the brakes endure!!!

More later as I am presenting my findings on said brake….