Bicycle cornering dynamics

In the first stage, the bike needs to correct its leaning (roll-axis) to approach corner. This is achieved by counter-steer. At this moment, the front wheel has larger 'slip angle' than the rear; or in another word, the front wheel experiences more lateral force (friction) than the rear.

The figure below describes the forces and torque that acts on the bike, with the frame of reference at the centre of combined mass (rider and bike).

Figure 1: Forces (blue) and Torque(red) acting on the bike in the 'counter-steering' step. Left image is top-bottom view, right image is rear-front view of the bicycle. Front wheel create lateral force (friction) that both 'yaw' and 'roll' the bike.

Once the bike starts to roll (counter-clockwise as in Figure 1), rider starts to steer into the direction that they would like to go. The action once again create extra lateral force (friction) on the front tyre, which would create torque in roll-axis (clock-wise, to stop the bike from dropping) and to 'yaw' the bike to the direction rider wish to follow. At first, the front experiences more side-way friction than the rear. However, the rear and the front tyre will create equal lateral force (friction), to 1) stop the bike from rolling (roll-axis), and 2) creating centripetal force that is required for the cornering.

Figure 2: Forces (blue) and Torque(red) acting on the bike at the first step of steering. Left image is top-bottom view, right image is rear-front view of the bicycle.

Bike design

Source: http://calfeedesign.com/tech-papers/geometry-of-bike-handling/

How these measurements affect stability :

Rake and Trail:

Fork Rake is also known as Offset, which more accurately describes what it is: the hub’s offset from the steering axis. Not to be confused with the curvature of the fork blades, which some people think of as “rake”. Straight blade forks can have plenty of offset. Fork offset determines trail when considered with head angle (and the diameter of the wheel). Trail is best thought of as the tire patch “trailing” behind the steering axis. Fork offset for road bikes usually ranges from 40 to 55 mm, generating trail figures from 50 to 63 mm. 57mm of trail is considered by many to be an ideal combination of stability and agility. More trail is nice at high speeds (motorcycles usually have 80 mm of trail) but can feel sluggish at slower speeds.

Head Tube Angle

Also known as the steering axis, this angle influences stability in combination with fork offset by controlling “wheel flop”, or the tendancy for the wheel to turn when leaned. A steep head angle is more upright and takes less effort to turn the front wheel, especially if there is too much rake or too little trail. A shallow head angle will want to turn too quickly when leaned if there is too little trail or not enough offset. So most shallow angle bikes have plenty of fork offset to compensate. Head tube angles range from 71.5 degrees to 74.5 degrees. Generally speaking, with a proper fork rake to yield a trail from 55 to 60 mm of trail, the head angles in this range are fairly stable at high speeds. The steeper head angle bikes are a little more agile, or require less effort to steer. People are usually very good at adapting to various head angle bikes if they have the proper trail.

Wheelbase, Weight Distribution and Front Center

Head angle also influences wheelbase and front center, which affect weight distribution. Ideally, a rider should have 45% of the bike + rider’s weight on the front wheel and 55% on the rear wheel. (easy to check with a bathroom scale) During high speed descents, proper weight distribution will give the rider confidence in the turns. Too much weight on the rear wheel (common with ultra short chainstays) makes seated climbing more challenging by making it harder to keep the front wheel on the ground. A long wheelbase is nice to have at high speeds, but if too long, it makes it harder to maneuver in a group of riders or just interacting with one rider. There is no rule of thumb about proper front center. Weight distribution is the key measurement. Some people worry about toe overlap. Front center is a handy measurement to see if a bike will have toe overlap when comparing to a known bike.

Bottom Bracket Drop

BB drop seems to have settled at 7 cm for most road bikes. It’s low enough to provide a low center of gravity yet it’s high enough to allow pedaling through corners without scraping a pedal. 8 cm is used by some builders and can feel more stabile. But the rider should use low profile pedals and not very long cranks. Pedaling through corners is riskier with a lower BB drop.

Bike specs - Cog dimension and disc brake

Shimano cassette diameter 32.50 mm
6-bolt disc brake diameter 45.00 mm
Usual cog for drilling 6-bolt: 16T, 17T 18T, 20T