Why you must use the entire width of the track
Filed under: Features, Thoughts on July 18, 2008
Using the entire width of the track is basic race driver theory. From your local kart track to the Silverstone racing academy, it is taught without impunity and in Formula One, millimetre precision demonstrates excellence. And the idea is pretty simple – the more of the track you use, the more you square off the corner and the faster you go.
But you see, I was wondering: how much of a difference does it really make? If I turn into a corner with a foot to spare on my outside, what does that actually cost me?
Setting the scene
The necessary steps to calculate this accurately for any given corner of a race track are far broader than the scope of this article. And what’s more, I won’t cover the maths in much detail and instead concentrate on getting an answer. Therefore, for the purpose of proving the point, we will imagine an arbitrary 90° right-hand turn with a radius (
) of 75 feet.
Our imaginary track has a constant width of 30 feet (known as 
) and the width of our car (
) is 6 feet. In addition to this, we will say that the maximum cornering force of the car (or more to the point, its tyres – known as a) is 1.2g.
First we must calculate the radius of our cornering line (
). For the sake of simplicity, we are using a perfect geometeric apex as opposed to a more technically correct clipping point further through the corner.
To do this we need to know the radius of both the inner (
) and outer () edges of the corner, expressed as:
Using some geometry, we can calculate the radius of our cornering line as:
Finally, we can now calculate the maximum possible cornering speed as follows, using the conversion factor 15/22 to convert from feet per second to miles per hour, and 32.1 to convert acceleration from gees to feet per second squared:
To further demonstrate the point, consider the following Java applet. Adjust the amount of unused track using the slider at the bottom and see for yourself how much potential cornering speed is being wasted. NB: The pink line does not actually move, it is there for completeness.
In our imaginary example, each 2 feet of unused track on the entry to a corner prevents you from carrying approximately one mile per hour. If you can imagine that is replicated five or six times on every lap it immediately becomes significant. What’s more, a realistic non-geometric apex and variable grip levels means that the potential time loss is in fact larger than in this academic example.
So think about it next time you turn-in to a corner – how much of the circuit are you not using? And how much is that really costing you?
References
1. Brian Beckman’s Physics of Racing
Comments
Ham
November 28th, 2008
As well though isn’t it not just the speed you gain but also the added traction and reduced load on the suspension of making a wider turn gives you better acceleration out of the corner?
Take what you’ve calculated and add this effect and I think the difference becomes even more significant. You’ve added speed coming out of the corner, which you carry until the next corner, and the added acceleration. In theory!
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