Trevitt's Blog: Extreme Lean Angle

Written by  on Friday, 04 October 2013 07:15

A video released by MotoGP last week (See bottom of the page) shows Jorge Lorenzo's Yamaha YZR-M1 in pit lane leaned over on its side to the same angle it reaches on the track - 64 degrees from vertical. It's an incredible sight when shown in this manner; the bike is essentially laying on its side and less than two feet tall. Lorenzo, in street clothes, tries to get into his normal riding position on the prone bike, but without the cornering forces to hold him in position, it's impossible.

In school physics classes, we were taught about the coefficient of friction (symbolized by the Greek letter u), and how it varied from 0 to 1. This value defines the ratio of the force holding two objects together and the friction force required to move the objects relative to each other. This is best visualized by pushing an object over a surface, where the coefficient of friction is the ratio of the object's weight (the force holding it down on the surface) and the force required to move the object along the surface.

If an object weighs 10 kilograms and the coefficient of friction is .5, it will take five kilograms of force to move the object. Something like a curling stone on ice has very little friction, and will slide a long distance with just a slight push. At the opposite end of the spectrum, sliding a rubber eraser across your desk requires a lot of effort, and the coefficient of friction is close to 1.

Do some math, and you can show that the maximum lean angle possible from a motorcycle with what we were told in high school to be the perfect coefficient of friction is about 45 degrees, with some variance depending on the width of the tires and how much the rider hangs off the side. That is a long way from the 64 degrees of a MotoGP bike! Because of the exponential relationship, that much lean angle requires a coefficient of friction close to double that for a 45-degree lean angle. How can this be?

There is much more than simple friction at work here, obviously. One part of the explanation is that we are not dealing with simple surfaces; tires and pavement are not smooth or uniform and the tire's rubber can actually mold itself around the granules of pavement, down to a microscopic level. Now we are not sliding an object along a surface but rather pushing against all the imperfections in each, like cornering on thousands of tiny bankings.

Here is where things get interesting. When we look at the weight of the motorcycle perpendicular to those little bankings and spikes of pavement, the additional centrifugal weight from cornering comes into play and this can be a significant addition. Cornering at 45 degrees generates approximately 1g of cornering force and adds 40 percent to the weight of the motorcycle. If you were able to put scales under the tires of a cornering motorcycle, a bike and rider combination that weighed 250 kilograms when stationary would weigh 350 kilograms when cornering. At least some of this additional weight translates to friction force, allowing more of a lean angle than the coefficient of friction would indicate.

Taken one step further, increased corner speed and lean angle generates more centrifugal force, which in turn works to increase the friction force, which in turn increases potential corner speed and lean angle. In other words, there are certainly diminishing returns but the faster you go, the faster you can go.

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Last modified on Friday, 04 October 2013 13:12
Published in Andrew Trevitt

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