*Bukit Hantu* is probably the most challenging hill in Hulu Langat. Especially if you tackle it from west to east. The ascent is about 3.4 km with an average gradient of 7% and maximum gradients over 10%. The descent is shorter at 2.6 km. That descent comes with a tricky combination of turns in the final 500 metres, where the gradient approaches 10%.

Unsurprisingly, some cyclists come to grief on the final curve and end up off the road to the right. That has happened a few times, just in the past week or so.

Thinking about those crashes prompted me to research the forces acting on a bicycle while cornering. I found a very informative site: physicalcycling.com.

The site takes a deep dive into circular motion, centripetal and centrifugal forces, lean angles and the like. Interested in finding out more about F = mA_{c} = mv^{2}/R? This is the site for you.

The following simplified version is taken from the many pages of information about cornering on the physicalcycling.com website.

From Newton’s Laws, we know the inertial tendency of an object is to continue forward in a straight line (the blue arrow) unless acted upon by external forces. So a cyclist must apply a force to the bicycle to make it turn. The force making the bicycle deviate from its straight-line path to a curved path (the red arrow) is called the Centripetal Force (the green arrow).

The only part of the bicycle touching the ground are the tires. So when you turn your bar, the tires are not only rolling but also “biting” into the road.

This is what is causing you to turn. As your tires continue to roll through the turn, they resist the tendency to slide or skid. You can aggressively turn as much as you want as long as the force on the tires is not enough to cause them to slide out from under you.

The chart below shows the force on the tires, known as Cornering Centripetal Force, for various corner radii and speeds.

## Table 1: Cornering Centripetal Force

The data above assumes an elite cyclist weighing 68 kg and riding a bicycle weighing 7.25 kg. Green implies the tire force is approximately the combined weight of the rider and bicycle or less. A corner with a radius of 7.5 metres can be safely taken up to 32 kph.

Yellow is in the double range. Taking a 7.5-metre radius turn at 40 kph will test the limits of what the tires can handle.

Red is in the No Go range. Taking a 7.5-metre radius turn at 48 kph or faster guarantees a skid and a crash.

When cyclists take a corner, they encounter a force that tries to return the bicycle to straight-line movement. This force is often referred to as the Centrifugal Force. To counter centrifugal force, cyclists lean into the inside of the curve. This creates a counterbalancing torque to that of the centrifugal force and the lean “balances” out the bicycle’s inertial tendency to want to continue in a straight line.

The cyclist instinctively searches for the right amount lean, or lean angle, depending on their mass and speed, and the radius of the curve.

It turns out the amount of weight pushing down on the tires decreases as the lean angle increases. As the weight on the tires decreases, the less traction the tires have. This limits the possible turning scenarios.

The table below shows the lean angle limits for various corner radii and speeds.

## Table 2: Lean Angle

Green denotes safe lean angles. Yellow lean angles test the limits of tire traction. Unsafe lean angles are red.

In summary, the limiting factor in taking a corner successfully on a bicycle is how well your tires grip the road. Go into a corner too fast, or lean too much, and your tires will lose their traction, and you will skid. Paradoxically, both too much weight on the tires and too little weight on the tires will cause a skid.

Another factor that may contribute to crashes on corners is the cornering line. The cornering line is the path taken around a particular curve. For any given corner, there is an infinite number of possible cornering lines. There is also an infinite number of possible cornering lines which do not make the curve. The apex refers to the “peak” of the cornering line located at the centre of the corner.

Three cornering lines are shown in the diagram below. The red cornering line shows what happens when you turn in to a corner too early. The cornering line hits the inside of the turn before the apex. The radius of the cornering line is larger than the radius of the corner. The result is the rider ends up off the road at the outside of the curve. This is not good.

The yellow cornering line hits the apex. But the radius of the cornering line exceeds the radius of the turn. The ride stays on the road while making the turn but ends up on the wrong side of the road. Also not good.

The green cornering line hits the inside of the turn beyond the apex. Note that this cornering line starts in the middle of the road. This cornering line allows an exit from the turn on the correct side of the road. The cornering line also has a radius slightly larger than the radius of the road.

Getting cornering centripetal force, lean angle and cornering line right do not guarantee a successful turn. Road condition is important. The grippiest road type is paved, smooth and clear of sand, gravel and other debris. Debris on the road reduces tire traction.

Braking during a turn also reduces tire traction by adding additional Cornering Centripetal Force to the tires. If your speed and the turn radius put your Cornering Centripetal Force in the yellow zone shown in Table 1 above, braking will move you into the red zone.

Braking during a turn will cause your bicycle to be more upright. As we saw in the discussion about lean angle, this will reduce the counterbalancing torque against Centrifugal Force. The bike will straighten out rather than continue to follow the cornering line.

The road surface on the final section of the *Bukit Hantu* descent is good. The combination of too much speed, the wrong cornering line, and perhaps altering the lean angle either consciously or by braking has to be the reason for the crashes.

Cyclists cannot exceed the limits of cornering physics. Not if they want to