Marcus du Sautoy and Formula 1

Marcus du Sautoy, the Charles Simonyi Professor for the Public Understanding of Science at Oxford University, makes an attempt in The Times to find a mathematical perspective on Formula 1. He begins:

This year Formula One teams that agree to race within a strict budget rather than relying on unlimited funds to develop their cars are being rewarded with a number of perks under a scheme called the Kinetic Energy Recovery System [KERS].

Marcus seems to have got his wires slightly crossed here: the opportunity to exploit greater technical freedom in exchange for a voluntary budget cap, does not arrive until 2010, whilst KERS is already available to anyone this year, irrespective of budget. Not an auspicious start then.

However, Marcus then redeems himself by posing an interesting question which does, by analogy, help to explain why the teams with double-decker diffusers have done so much better this year than the teams with KERS alone:

You arrive at an airport for a flight connection but the timing is tight. You discover that your next plane is leaving from the far end of the airport. There is a moving walkway for part of the journey. You’ve got enough energy to do a short burst of running, but otherwise you’ll walk at a constant speed...You want to get to the gate as quickly as possible, so the question is: when should you use your burst of energy? Should you run on or off the moving walkway?

The answer is that the button should be hit off the walkway:

Our twins are walking together towards the walkway when one twin decides to press the boost button to get him to the walkway before his brother. He reaches it D metres ahead of his brother. But as soon as he steps on to the walkway the distance between them begins to increase even more. When the second twin steps on to the walkway he presses his booster. Since both are on the walkway, this will allow him to catch up only D metres on his brother. But his brother is more than D metres away by now.

Marcus thinks that an analogy can be made with the question of whether the KERS boost button should be used on the slow part or the fast part of a circuit, but in practice, it can only be used to benefit on the straights; if used in the corners it would simply result in wheelspin.

The airport scenario does, however, still provide a good F1 analogy in the following sense: more time is spent, per unit distance covered, off the walkway, hence the greatest benefit is gained by hitting the boost button there. Similarly, in Formula 1, more time is spent, per unit distance covered, in the corners than on the straights, hence in terms of lap-time alone, the greatest benefits accrue from improving the cornering characteristics of the cars than by improving straightline speed. As a fresh demonstration of this, the teams which have developed a cornering advantage this year (the double-decker diffuser teams), are significantly faster than those which initially developed only a straightline speed advantage (the KERS teams).