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!