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12th November 2024
Amontons’ Laws of Friction

Date

Source: Cycle World

Kevin Cameron has been writing about motorcycles for nearly 50 years, first for <em>Cycle magazine</em> and, since 1992, for <em>Cycle World</em>. (Robert Martin/)Whenever I refer on this site to tire grip being positively related to tire footprint area, well-intentioned persons write in to correct me, saying that tire footprint area makes no difference to friction.Rubber is nonlinear in its response to strain. As an element of tread rubber is pressed against pavement with a moderate force that I will call X, it deforms to produce an area of true contact, Y. If we now increase the load to 2X, the area of true contact between rubber and road does not double. It cannot, for the more we deform rubber, the stiffer it becomes. For that reason, the new area of true contact is less than 2Y, and so it goes as we continue to increase load. This tells us that the most efficient use of rubber in producing friction is to load it lightly, taking advantage of the fact that, pound for pound, we get a better ratio of load-to-friction at the low load end of the curve. And that is why MotoGP riders often find that inflation pressures lower than the tire manufacturer’s 1.8 bar (26 psi) give greater grip and quicker lap times.As the tire heats up from being in the hot slipstream of a bike or bikes ahead, its inflation air heats as well, increasing its pressure and making the front tire’s footprint smaller. As this happens, the rider notices changes in tire grip. First comes locking during braking (which threatens loss of control), and then a tendency for the front end to “close” during turning (understeer), requiring increased steer angle to turn, until the front end slides out.Related: About Wet and Dry Tire GripAs tire temperature increases, the footprint decreases as the pressure rises. (MotoGP/)In my first conversation with Marc Márquez (2013) he described a tire behavior he called “becoming hot and bouncy.” As a tire’s temperature increased and its footprint area decreased from increasing inflation pressure, spinning and sliding increased, adding yet more heat. If this vicious cycle is not stopped, it continues until the tire is useless. But if the rider “rests” the tire (not spinning or sliding) for a lap or two, it may recover and again be capable of competitive lap time. This year’s MotoGP point leader, Francesco Bagnaia, recently described having to rest his tire every other lap while leading a GP (which he won).Another of Amontons’ laws states that sliding friction force is independent of sliding velocity. People have known for many decades that this is not true, as the sliding friction force of tires is observed to peak at a slip rate of about 10 percent of forward speed. This is why dragsters accelerate fastest when the rate of tire spin is controlled.Another point to be made here relates to Honda’s 1992 discovery of the “Big Bang effect” on acceleration. Honda’s GP riders reported that the Yamahas could apply throttle earlier in corners than they could. If the Honda men throttled up at the same point as the Yamaha men, they slid out.At that time, the big difference between Honda’s single-crank V-4 and Yamaha’s dual-crank V-4 was that the Yamaha fired pairs of cylinders every 180 degrees, while the Hondas fired one cylinder every 90 degrees.Honda’s experiments showed that an even greater ability to safely throttle up earlier in corners was produced as all cylinder firings were grouped more closely together. On the NSR500 two-stroke, Honda found best acceleration when two cylinders fired simultaneously, then the other two 67–68 degrees later (also called “close firing order”). Persons present during the testing at once noticed the altered exhaust sound of the Hondas, which became like that of big single-cylinder motocrossers.What was happening was that as the yank from cylinder firing died away, tire sliding velocity (a combination of cornering force plus acceleration force) had almost 300 crank degrees in which to decrease, maybe not to zero, but at least down to values low enough to benefit from rubber’s velocity-dependent friction.A useful revolution in tire grip occurred around 1958 in England, when research conducted with synthetic rubber developed during World War II showed that as rubber’s internal friction was increased, tire grip increased with it. The top speeds of Grand Prix cars dropped slightly on this new kind of tread rubber, but lap times dropped dramatically. Top speed was lost because increased rubber hysteresis (internal friction) increased rolling resistance.The widths of auto racing tires have dramatically increased from dimensions similar to those of production tires to the current Formula 1 widths of 13 inches front/18 inches rear. A possible explanation could be that such large tire footprints are necessary to prevent excessive wear during events of many laps. Yet in drag racing as well, rear tires of tremendous width are used, even though for the Top Fuel class the cars accelerate for only 1,000 feet.Tire size for racing and production motorcycles have grown larger over the years. (MotoGP/)Tires for both production and roadracing motorcycles have grown much larger since the 1972 end of what Dunlop engineer Tony Mills once called “the era of narrow, hard tires.” Back in the days of the late Mike Hailwood, a 45 degree angle of lean was thought radical, but in the MotoGP era (2002–present), lean angle as great as 63 degrees to the vertical have been observed.Science advances by successive approximation. Newton’s laws, which had accomplished so much, broke down in the realm of the very small and at extreme velocities. Einstein amended them. So it is with the ideas of Amontons (c. 1699), which were based upon observations of the friction of sliding wooden blocks. They required amendment when extended to other materials.For a nice compact treatment of this, have a look at https://www.sciencedirect.com/topics/engineering/amontons-law. 

Full Text:


Kevin Cameron has been writing about motorcycles for nearly 50 years, first for <em>Cycle magazine</em> and, since 1992, for <em>Cycle World</em>. (Robert Martin/)

Whenever I refer on this site to tire grip being positively related to tire footprint area, well-intentioned persons write in to correct me, saying that tire footprint area makes no difference to friction.

Rubber is nonlinear in its response to strain. As an element of tread rubber is pressed against pavement with a moderate force that I will call X, it deforms to produce an area of true contact, Y. If we now increase the load to 2X, the area of true contact between rubber and road does not double. It cannot, for the more we deform rubber, the stiffer it becomes. For that reason, the new area of true contact is less than 2Y, and so it goes as we continue to increase load. This tells us that the most efficient use of rubber in producing friction is to load it lightly, taking advantage of the fact that, pound for pound, we get a better ratio of load-to-friction at the low load end of the curve. And that is why MotoGP riders often find that inflation pressures lower than the tire manufacturer’s 1.8 bar (26 psi) give greater grip and quicker lap times.

As the tire heats up from being in the hot slipstream of a bike or bikes ahead, its inflation air heats as well, increasing its pressure and making the front tire’s footprint smaller. As this happens, the rider notices changes in tire grip. First comes locking during braking (which threatens loss of control), and then a tendency for the front end to “close” during turning (understeer), requiring increased steer angle to turn, until the front end slides out.

Related: About Wet and Dry Tire Grip

As tire temperature increases, the footprint decreases as the pressure rises. (MotoGP/)

In my first conversation with Marc Márquez (2013) he described a tire behavior he called “becoming hot and bouncy.” As a tire’s temperature increased and its footprint area decreased from increasing inflation pressure, spinning and sliding increased, adding yet more heat. If this vicious cycle is not stopped, it continues until the tire is useless. But if the rider “rests” the tire (not spinning or sliding) for a lap or two, it may recover and again be capable of competitive lap time. This year’s MotoGP point leader, Francesco Bagnaia, recently described having to rest his tire every other lap while leading a GP (which he won).

Another of Amontons’ laws states that sliding friction force is independent of sliding velocity. People have known for many decades that this is not true, as the sliding friction force of tires is observed to peak at a slip rate of about 10 percent of forward speed. This is why dragsters accelerate fastest when the rate of tire spin is controlled.

Another point to be made here relates to Honda’s 1992 discovery of the “Big Bang effect” on acceleration. Honda’s GP riders reported that the Yamahas could apply throttle earlier in corners than they could. If the Honda men throttled up at the same point as the Yamaha men, they slid out.

At that time, the big difference between Honda’s single-crank V-4 and Yamaha’s dual-crank V-4 was that the Yamaha fired pairs of cylinders every 180 degrees, while the Hondas fired one cylinder every 90 degrees.

Honda’s experiments showed that an even greater ability to safely throttle up earlier in corners was produced as all cylinder firings were grouped more closely together. On the NSR500 two-stroke, Honda found best acceleration when two cylinders fired simultaneously, then the other two 67–68 degrees later (also called “close firing order”). Persons present during the testing at once noticed the altered exhaust sound of the Hondas, which became like that of big single-cylinder motocrossers.

What was happening was that as the yank from cylinder firing died away, tire sliding velocity (a combination of cornering force plus acceleration force) had almost 300 crank degrees in which to decrease, maybe not to zero, but at least down to values low enough to benefit from rubber’s velocity-dependent friction.

A useful revolution in tire grip occurred around 1958 in England, when research conducted with synthetic rubber developed during World War II showed that as rubber’s internal friction was increased, tire grip increased with it. The top speeds of Grand Prix cars dropped slightly on this new kind of tread rubber, but lap times dropped dramatically. Top speed was lost because increased rubber hysteresis (internal friction) increased rolling resistance.

The widths of auto racing tires have dramatically increased from dimensions similar to those of production tires to the current Formula 1 widths of 13 inches front/18 inches rear. A possible explanation could be that such large tire footprints are necessary to prevent excessive wear during events of many laps. Yet in drag racing as well, rear tires of tremendous width are used, even though for the Top Fuel class the cars accelerate for only 1,000 feet.

Tire size for racing and production motorcycles have grown larger over the years. (MotoGP/)

Tires for both production and roadracing motorcycles have grown much larger since the 1972 end of what Dunlop engineer Tony Mills once called “the era of narrow, hard tires.” Back in the days of the late Mike Hailwood, a 45 degree angle of lean was thought radical, but in the MotoGP era (2002–present), lean angle as great as 63 degrees to the vertical have been observed.

Science advances by successive approximation. Newton’s laws, which had accomplished so much, broke down in the realm of the very small and at extreme velocities. Einstein amended them. So it is with the ideas of Amontons (c. 1699), which were based upon observations of the friction of sliding wooden blocks. They required amendment when extended to other materials.

For a nice compact treatment of this, have a look at https://www.sciencedirect.com/topics/engineering/amontons-law.

 

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