Author Topic: The pivot points and lever arm lengths of bicycle roadholding and handling  (Read 1936 times)

Andre Jute

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I like George's seat of the pants luggage distribution in the thread "40 / 60 weight distribution" at
That's what it always comes down to in the end, even when you know all the theory.

But a glancing familiarity with the theory helps with both the large picture when buying or loading a bike, and the small esoteric details, for instance when riding in crosswinds. However, I've separated these theoretical considerations from that thread so as not to burden those who want only to know that the designer took care of the necessary details (a good reason to buy a Thorn bike!) with a lot of what some may discount as esoterics.

by Andre Jute

Roadholding describes how the bicycle in motion responds to inputs from the rider. Handling describes how the bike responds to, and recovers from, inputs from the road and the environment, or the misjudgement of the rider.

A bike dynamically, at any snapshot moment, has pitch, roll and yaw. Pitch is caused by weight transfer through the Centre of Gravity (CoG) and is a rocking motion in the line of travel, to the front or the back. Roll is lean to one side or the other, perpendicular to the line of travel, of the CoG around the axle line. Yaw is what happens when the front and the rear tyres are not on the same footprint of forward travel and most commonly happens in bends and corners. Yaw can also be caused by a crosswind or simply the force of air being parted by bike, luggage and rider at speed. Yaw operates through the Centre of (aerodynamic) Pressure (CoP).

Note that almost every element of bicycle design and operation I mention has at least two dimensions and many have three, plus dynamic and largely uncontrollable weight transfers, which includes air pressure on top of the weight of the bicycle, luggage and rider. The calculated point "centres" are notional, not really points at all but more diffuse thought and mathematical aids, and the "points" can wander in all dimensions as the bike moves and as different rider and ambient inputs come into play.

The distances that matter are the lever arms dynamically formed by the distance of the Centre of Gravity and the Centre of Pressure from the horizontal line between the axles, and the horizontal distance of the CoP from the CoG. Note that the roll centre is not at ground level* but is a mechanical concept determined from the arms controlling the wheels, which is the only really simple part of bicycle dynamics because they're the axle holders! From there it gets more complicated and an integrated approach takes a computer and heavy thought. (I integrated the whole lot for racing cars back in the days of computers with glass tubes like in your granddad's radio, and just the thought of it gives me an instant migraine.)

Note also that these notional lever arms magnifying dynamic input are not free, even if the bike could be shaped to reduce their length. A bike with the CoG or the CoP or both under the axle line will be lethally unstable, reacting to inputs in exactly the opposite way to that expected by an experienced cyclist. There's a good reason why so many recliners are tricycles. But neither can the lever arms be infinitely long, because adverse forces will also be infinitely multiplied. I expect that the Centre of Pressure on a bicycle should not be behind the rear axle because the tail will start wagging the dog with the weight of the surfaces which form the air resistance in that area. (A bicycle is different from a car in both ultimate speed and the construction of fins to move the CoP backwards, relatively weightless on a car, relatively hefty on a bike.) My own most stable bike has the CoP forward of the rear axle in all its unloaded to loaded modes. Remember that the rider is also part of the side-on aerodynamics of the bike.

If the Centre of Pressure coincides with the Centre of Gravity, or worse, if the CoP is in front of the CoG, the bike will be terminally unstable not only in the slightest crosswind but even in normal riding which creates its own air flow. It is essential that the CoP be behind the CoG for a touring bike and, since the large pressure areas on a bicycle are only the rider and the luggage, this is the rationale for carrying the large-profile luggage on the back of the bike. For maximum stability in crosswinds, the CoP should be well behind the CoG; this is the rationale -- besides heel clearance for pedal operation -- for designing a touring bike on a long wheelbase.

Other elements in the stability of the dynamic bike with input to these motions that together make up roadholding and handling, include the wheelbase length and the wheel sizes, which can lower the CoG and CoP a little and thus make the lever arms  shorter for both inherent and external factors. Other important elements include: The angle of the head tube, measured between the road behind it and the head tube, usually between 68 degrees for a relaxed cruiser and 72 degrees or more for a lively road bike, which affects the steering response. Also the specifics of the fork design, specifically the trail, which is the distance between the notional strike point on the road of the head tube (and therefore the steering shaft) inclination and a perpendicular line dropped from the front axle, which influences over- and under-steer -- you never want perfectly neutral steering because it is unpredictable which way the bike will break away and therefore dangerous. A touring bike is generally designed with considerable understeer for the rider's safety under all ambient and load conditions, while a road bike intended for professional racers will have just enough understeer not to launch its riders into the thorny gorse or the ditch too often.

The final element is the tyres, specifically their compound, construction, tread, inflation, width and rims. This is a much more complicated -- indeed confusing -- matter than is generally understood, in which even in car tyres, which has had hundreds of millions lavished on understanding them, there are still mysterious dark corners.

The short answer about tyres for a tourer is that you should fit the widest rims and tyres your fork will take (the minimum rim width between the retention beads should be at least 40 percent of the tyre's nominal width), that soft sidewalls are more comfortable especially if you fit tyres with stiff anti-flat layers, that tyre inflation should be as low as is safe for your inner tubes and tyres and rims, that unless you're a mud plugger the most efficient tyres have no tread.

Once all that is maximised, the cyclist can tune the tyre pressure to the precise roadholding profile he wants. Generally speaking, a touring bike loaded with whatever luggage a competent designer thought suitable, and distributed as he thought meet, will also have the tyres inflated correctly for safe roadholding and handling by whatever religion you follow (15 percent drop at the rim, fingerspitzengefuehl, electronic manometer, whatever). If the bike turns too slowly for your liking, you can put in a couple of extra strokes of the pump into both tyres to sharpen up the handling.

And here we're back to seat of the pants adjustments, but with better understanding of how they work. Those who want a deeper understanding can ask here or read my DESIGNING AND BUILDING SPECIAL CARS (1985; Batsford, London; Bentley, Boston; various special editions; cover pic at which includes the formulae and mathematical expositions.

* People who tell you the roll centre is at ground level are confusing a useful shorthand for the complicated, counterintuitive truth, which is why their math comes out wrong. But, you will say when you first meet this (again) counterintuitive truth, rims cannot bend in the middle. Only too true. But doing the theory and the math the right way allows for a complication, which I've left off as minor and confusing to a first-approach explanation, to be included: this is the lateral scrub radius (like front tire scrub but at 90 degrees to the line of travel) which does indeed have a lever arm that stretches all the way to the interface between the road snd tyre. The tyre adjusts for the inflexible rim by creeping sideways until the pedal on the tilted bike strikes the road and rider and bike go down. A common practical application for touring cyclists will illustrate why a correct understanding of the pivot (the line between the axles rather than the surface of the road) is important: the makers of the best panniers do not allow the cyclist to put the major part of the load area below the axle line. For a test, fit all you panniers but load them only with water bottles below the axle line, then ride on a ridge with crosswind and discover for yourself how dangerous your bike feels, how much concentration it requires to stay mounted.

E&OE. I'll amend this post as required.

Copyright 2023 Andre Jute
« Last Edit: September 11, 2023, 02:36:16 am by Andre Jute »


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many thanks for this interesting reading.
It makes me glad I moved onto Thorn bicycles about 20 years ago for my fully loaded touring.
Now it is more often a full shopping load!


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Muchas gracias Maestro Andre!