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.

 

 

Blood is Thicker than Water… but why?

Whilst we are on F1 shut down I thought I would continue the basics behind aerodynamics and how they contribute to the maths, the physics and the design processes that enable the aerodynamicists and designers to create such effective racing cars.

Before I do I wanted to introduce the term viscosity – which I will refer to fairly often over the next few paragraphs. The word “viscosity” is derived from the Latin “viscum”, meaning mistletoe. A viscous glue called birdlime was made from mistletoe berries and was used for lime-twigs to catch birds…!

So, air is a fluid, and therefore it possesses various properties, one of which is ‘viscosity’. You could say that viscosity is kind of like the fluids ‘stickiness’. (This must not be confused or associated with its density). For example, oil is more viscous that water, yet oil is less dense than water because oil floats on water. The more viscous the fluid, the more force is required to push a body through the fluid, so in other words, viscosity resists a body’s motion through a fluid – much like swimming through treacle!

Fluid very often flows around a body as though it were in very thin layers, or laminae as you can see in the figure shown to the right here. So, because of the viscosity of the fluid, the layer immediately adjacent to the body of the surface remains attached to the body due to shear stress. The subsequent layers of fluid adjacent to the ‘attached’ layer are each held back slightly by the slower moving layer beneath, and as a result of the difference in their relative velocities they slide over one another. However, at ‘some’ distance away from the body surface where the interaction with the static layer is no longer felt, there is no relative motion between the layers of fluid, and the fluid as a whole moves past the body at what we term ‘freestream’ velocity.

This gives rise to a characteristic ‘velocity gradient’ in the fluid near the body surface, which, again, is often diagrammatically represented in the figure shown to the right of this text. The area of slow-moving or low-velocity air close to a body’s surface is known as the ‘boundary layer’.

You can find another great blog post on boundary layer and other F1 terms by clicking on F1 Framework

I’ll try to illustrate this with an example that I explained to my wife @MrsF1ss, who now explains the phenomena to other people without the need for me to intervene!

Imagine your car just out of the car wash all clean and shiny – you drive around in glorious sunshine (not something I get the chance to do very often living in Manchester!!) for a few days and notice that the car is already getting dirty and has a film of dust & grime stuck to the surface.

You’d think that driving around at anywhere between stationary and 50 miles/hour would not allow any particles to stick to the surface as they would be blown off, particularly if it were dry and no rain could be used to enhance adhesion.

So this is the science bit – as I explained above, at the surface of the body or car in this example, the shear forces on the air passing close to the car bodywork are reduced in velocity significantly enough to have a finite ‘zone’ that experiences little or no airflow whatsoever so the tiny particles of dust or dirt simply land on the surface of the car and remain undisturbed due to being within the ‘boundary layer’.

The particles continue to build up and over time you will experience you car getting dirtier – for those reading this that experience snow in winter, whilst driving along (and being safe) look closely at the individual snow-flakes as they land on your windscreen and notice their behaviour – again they are within the ‘boundary layer’.

So, I have introduced viscosity (and as above will expand on this in a second), I have introduced boundary layers and alluded to laminae or more commonly ‘laminar’ flow which is only a tiny part of the full story and far too long and technical for one blog post and which precedes turbulent flow, which more of us will be familiar with.

In my next post I will look in more detail the relationship between viscosity, laminar and turbulent flow characteristics and perhaps run through some of the mathematics that underpins it.

But to finish this piece off I’ll expand on viscosity a little further: now the term viscosity refers to a ‘fluids’ stickiness and determines how easy it would be for a body to travel through the fluid; so water has a very low viscosity compared to that of treacle or honey, but how is this considered mathematically?

In general, in any flow regime and as we described above, layers move at different velocities and the fluid’s viscosity arises from the shear stress between each layer that ultimately opposes any applied force.

The relationship between the shear stress and the velocity gradient can be obtained by considering two plates closely spaced at a distance y, and separated by a homogeneous substance.

Assuming that the plates are very large, with a large area A, such that edge effects may be ignored, and that the lower plate is fixed, let a force F be applied to the upper plate.

If this force causes the substance between the plates to undergo shear flow with a velocity gradient u/y (as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid.

The applied force is proportional to the area and velocity gradient in the fluid:

where μ is the proportionality factor called dynamic viscosity.

This equation can be expressed in terms of shear stress .

Thus as expressed in differential form by Isaac Newton for straight, parallel and uniform flow, the shear stress between layers is proportional to the velocity gradient in the direction perpendicular to the layers:

Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained. (Newtonian Fluids only)

I will continue this on the next post advancing with the principle and also the mathematics behind it; I’ll go through Newtonian (water) and Non-Newtonian (blood or custard) fluids and the relationship between laminar flow and turbulent flow and how viscosity plays its part and pull all this together to determine how F1 cars exploit this branch of advanced physics and mathematics.

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!

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?