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The fundamentals...

by Peter McLaren

At a time when new MotoGP bikes - with ever increasing technical complexity - are being seen in public for the first time, it's worth remembering that the most important formula in motorsport engineering is actually quite simple.

The formula is Newton's second law of motion: "When an external force is applied to a body of constant mass it produces an acceleration which is directly proportional to the force."

F = m x a

F = Force generated (at the tyre contact patch).
m = Mass (of the motorcycle).
a = Acceleration (of the motorcycle).

The most important of these three is acceleration – since winning a motor race essentially requires the consistent generation of larger acceleration forces than those produced by your rivals.

A racing machine should always be accelerating - speed should never, in theory, be constant. The direction of acceleration will change depending on where the machine is on the racetrack and so whether it is braking (negative a), increasing forward motion (positive a), cornering (lateral a) or most likely a combination of each.

The main job of a rider is to keep the machine as close to its limit of maximum acceleration, in whichever direction - a concept often illustrated with a 'g-g' diagram - for as long as possible. The task of the design team is to keep increasing the acceleration limit, while building a 'user friendly' machine that helps the rider stay near that limit for longer.

A 'user friendly' machine can be complicated to quantify, but acceleration is not - by rearranging, Newton's second law becomes:

a = F/m

This simply means that to increase acceleration, either the force being produced at the tyre contact patch needs to increase or the mass of the motorcycle needs to decrease, or both.

Other factors such as drag and downforce can also be significant in influencing acceleration, particularly in four-wheel racing, but - sticking with the fundamentals shown in the above equation - since mass is dictated by technical regulations (which insist on a minimum weight), force at the tyre is usually the most important factor.

Because of this, tyre performance is usually the limiting factor on most directions of acceleration – hence the benefit of improved rubber compounds, or making better use of existing tyres through chassis, suspension and set-up changes. The dramatic effect tyres can have is easily visible when a one lap 'qualifier' is used.

A notable exception to this rule is normally the straight line acceleration limit, where engine force in higher gears is usually well below the limit that could be achieved by the tyres. In other words, few machines can wheel spin on a straight in top gear in the dry, so more engine performance (even if only in higher gears) is always useful.

So, the next time you read about the latest hi-tech development, it is worth considering how much it will increase the force produced at the tyre, decrease the mass of the bike and/or help the rider get - and stay - closer to the acceleration limit. In terms of going faster, those are the fundamentals.

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