# Braking a motorcycle with a Pillion Passenger

This article is in response to an interesting question on Twitter from BikeSafe Glos, to an earlier blog on tyre grip, as to whether the extra tyre grip from the weight of a pillion would reduce stopping distances?

The short simple theoretical answer is it makes no difference. The physics is as follows:-

The kinetic energy of bike and rider(s) = m times v squared / divided by 2, where m = Mass (Weight) and v = Speed.

The braking force = umgd, where u = coefficient of friction between tyre and road, m = Mass, g = gravity, and d = distance.

When braking, the two equations are equal, so ‘Mass’ cancels out as it’s a multiplier for both sides. So (in theory) weight on its own makes no difference to stopping distances.

The additional grip via the passenger’s weight is balanced out by the increased momentum of the additional rider. This does however seem counter intuitive from experience, so there may be other factors.

The rider often has to cope with the extra weight of the pillion passenger pressing on him or her, which has to be held back via the rider’s arms, legs and crutch against the tank (usually) which can be ‘eye watering’ – for blokes anyway.

What limits stopping distances is also the position of the centre of gravity of bike and rider(s), as modern bikes can flip over forwards like a pedal cycle. This limits braking to about 1 g – where cars can do much better (Formula One cars can stop at >5 g with downforce) with a far lower centre of gravity.

However, having a pillion shifts the centre of gravity backwards potentially allowing a faster rate of de-acceleration without flipping. Sportsbike pillions sit higher, so the effect is less than with other types of motorcycle.

Illustrations from Motorcycle Dynamics by Vittorre Cossalter .

I’ve taken out the effects of wind drag on braking (and no we’re not on commission).

The red line shows the effect of the shift in the centre of gravity rearwards and slightly upwards, as the included angle decreases, meaning that de-acceleration can be greater without flipping. When the angle is 45 degrees the maximum de-acceleration would be 1 g, whereas tyre grip can result in up to >1.3 g, so the location of the centre of gravity is key.

So in theory having a pillion would reduce stopping distances, everything else being equal, but is the theory actually achievable? Front suspension can bottom out with the extra weight transferred forward, the bike becomes less stable as trail reduces further, so it is advisable to change the suspension settings as recommended by the manufacturer for a pillion and luggage if necessary. Some bikes are too likely sprung, like the early AprIlia RSV’S, even for solo riding, so aftermarket suspension mods might help, but always go to a reputable company.

As an aside, is also probably worth pointing out that accident first responders will go looking for a pillion if they find a crashed bike had its rear footrests down, particularly sportsbike crashes in rural locations.

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