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I am trying to learn about the maxium lean angle of a road bike. I'm looking for measurements and comparisons.

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    I'll have to do my own I guess. I would need to build some kind of a carriage and attach four wheels to it and tug it with a force meter. There's no other way. Lots of money, lots of work... – AzulShiva May 31 '17 at 16:42
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    I suspect that, to the extent that there is any variation in tire material characteristics, it's swamped by road surface variations and, to a lesser extent, tread variations. – Daniel R Hicks May 31 '17 at 16:45
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    And when you're looking at stuff like lean angle you must take into account road roughness and vibration. – Daniel R Hicks May 31 '17 at 16:46
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    It's not that all rubber is equal, I just meant that bicycle tire manufacturers select their rubbers from the same pool as the other guys. Also bear in mind the tire contact patch size. – Mike Baranczak May 31 '17 at 16:58
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    The road surface is also only tangentially positioned to the tires yet you wouldn't go anywhere without it. You're welcome to ride through deep snow and we'll see how far you'll lean there. But topics about tire pressure are ok? Lighten up please darling... – AzulShiva Jun 3 '17 at 6:47
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There absolutely do exist tables of tire friction coefficients; see here for an example -- but friction coefficients may not be exactly what you're looking for.

I don't know of any specific tables that measure lean angle and here's why: we do know some of the factors that affect rolling resistance. They include tire construction materials, type (tubeless, tubular, or clincher), tire width, tire pressure, road temperature, road surface, inner tube material (butyl or latex), rider weight, and, because of interactions between road surface and these other variables, sometimes speed. Because these affect rolling resistance, they will also affect maximum lean angle.

Many of the tables that show rolling resistance coefficients were measured under controlled conditions in a lab, using rollers of known diameter and known surface (smooth or bumpy) driven at a known speed. However, some tables are calculated from field tests on real roads. Although the roller test values and field test values may differ, comparisons made by those who have done both show that the relative ranking of tires is almost always preserved (that is, if tire A has lower resistance than tire B on rollers, it almost always has lower resistance than tire B on the road).

Measuring rolling resistance is possible for interested riders, but it's not easy. It's akin to measuring aerodynamic resistance -- in fact, if one is doing field tests outdoors on real road surfaces, the common methods of measuring aerodynamic drag also provide a measurement of rolling resistance drag. The easiest method for outdoor field tests uses an accurate and precise power meter available but it is also possible to do without a power meter (though at greater effort and time). That said, if you have a power meter and a set of rollers with a front wheel stand, you can measure tire rolling resistance yourself, without the complication of the aerodynamic drag component.

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    Rolling resistance is a very different thing from material coefficient of friction (and lateral force a tire can generate, which is what the OP actually wants to calculate lean angle.) – Argenti Apparatus Mar 16 at 19:00
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    @ArgentiApparatus I suspected so 3 years ago, which is why I didn't answer then. But I decided (after 3 years) that it would be good to point out that measurements of rolling resistance vary not only with material but also with construction, width, inner tube, inflation, and speed, and that we've verified that experimentally -- so lean angle is likely to vary, too. – R. Chung Mar 16 at 19:42
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    Agreed. See en.wikipedia.org/wiki/Cornering_force – Argenti Apparatus Mar 16 at 20:50
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    I don't see how this answer adresses the question. Would a high rolling resistance increase the maximum lean angle or decrease it? For learning about maximum lean angle one would have to discuss the cornering stiffness of tires, the position of the center of gravity in a turn, probably speed, etc. Have a look at badbicyclescience.com/2016/04/22/calvin-hulburts-mistake . See also my comment attached to the original question. – mathieu van rijswick Mar 19 at 11:46
  • @mathieuvanrijswick Oh, I agree. I don't think this directly addresses the underlying question, which is why I didn't offer it years ago. However, the question title asked about coefficient of friction, and that's related to the coefficient of rolling resistance -- and thus, the discussion about the factors that we know affect rolling resistance. I'm happy to delete my answer when a better answer comes along. – R. Chung Mar 19 at 13:53
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I had to dig through my senior year single track vehicle knowledge for this one. It's a little confusing but mathematically the maximum lean angle of a bicycle is theoretically 45 degrees regardless of tires or anything else really. Here is a picture of the math:

enter image description here

Since the largest value possible for inverse sine is 1 the largest possible lean angle would be 45 degrees. This makes sense because if you tried to pull a leaning bicycle upright from the tire contact patch, as soon as you reached 45 degrees this would become impossible.

Yes, MotoGP achieve lean angles of 60+ degrees but there are affects such as angular momentum to take into account and are beyond the scope of this answer.

If you are interested in the maximum lean angle based only on tire adhesion the data from my notes shows tires dropping off around 40-50 degrees camber angle. enter image description here

In terms of tire friction coefficients, these change over the different slip angles and camber angles, the same tire could have many different coefficients based on different angles, speeds, temperetures, pressure, wheel widths, surface conditions and many other factors.

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    Pretty much everything you have written above is either off-topic or complete and utter nonsense. The correct formula for lean angle is wikimedia.org/api/rest_v1/media/math/render/svg/… No, angular momentum has nothing to do with lean angle. Your second diagram compares camber angles and slip angles with lateral forces which is of no relevance. The question is not whether tires could have different coefficients based on different factors. They do. That's what this is about. – AzulShiva Jun 7 '17 at 7:15
  • The formula for obtaining maximal lean angle from a coefficient of friction is arctan(μ). If the coeffficient of friction was 10 you could lean like 85 degrees instead of your proposed 45 degrees. Yes like this: bilder-upload.eu/upload/33a8c1-1496819698.jpg Please do not upvote an answer if you don't understand / didn't read it. – AzulShiva Jun 7 '17 at 7:18
  • I apologize if I did not provide the correct answer. The math I provided was assuming a bike that is stopped in time and treated as a static object, but I might very well have got my trigonometry wrong. Angular momentum only applies to motorcycles because of the higher mass and higher angular velocities of motorcycle wheels. The y-axis on the second image is the coefficient of friction [wheel load / lateral force] (racingcardynamics.com/racing-tires-lateral-force) Your formula only contains v, r and g so would assume infinite friction such as mine. – Michael Machado Jun 7 '17 at 16:08
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    max lean angle and friction coefficient go hand in hand: μ = tan(α) and α = arctan(μ). A lean angle of 40 degrees would require a friction coefficient of 0.84. There is not enough information on the graph to know what it's about. And angular momentum does not affect any vehicles cornering performance however you will find a motorcycle much harder to turn at higher speeds. – AzulShiva Jun 7 '17 at 18:00
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    The thing that is right in this answer is that tires can't be modeled simply by static coefficient of friction, you also have to take tire squirm into account. Sideslip angle is the result of tire deforming on contact when not sliding. – ojs Jun 7 '17 at 19:36

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