# If a rolling coin can change direction without a turning torque, then why does a self-steering bicycle front wheel need one to change direction? [closed]

There are many posts/questions discussing the physics of a bicycle front wheel. The ones trying to understand the self-turning motion all try to find where the torque comes from that turns the front wheel. What if we are looking for the wrong thing and a torque isn't needed to change the front wheel's rolling direction?

There is still no scientific consensus on how the front wheel of a bicycle automatically turns into the direction of the lean/fall. Some say it is a result of one or a combination of the following: caster effect, gyroscopic precession, camber thrust, etc. There is even an argument for the weight of the forward extending handlebars creating the wheel turning torque when the bike leans. What we are looking for is the mechanical source that creates the torque which turns the front wheel. But what if a wheel can change rolling direction without a direction changing torque and it is simply the geometry of the wheel in motion that creates this change in rolling direction?

A rolling coin that is leaning/falling constantly changes rolling direction without a wheel turning torque. This is exactly what a bike’s front wheel does when the bike rolls and leans/falls. If you look at the instantaneous horizontal velocity components of the curved path rolling coin, you will see that these velocities are always parallel. If they weren't parallel then that would be evidence of a vertical axis torque.

Looking at a straight rolling wheel: The side view shows that the instantaneous velocities of every part of the wheel are perpendicular to an axis through the contact point. If we look from the top, we see that the horizontal components of all non-zero velocities are parallel at any instant in time.

When a single wheel rolls and falls: The rolling falling wheel (we’ll call it a tumbling wheel) is just a wheel rolling at an angle to its wheel plane. The top view reveals the same as above - the horizontal components of all non-zero velocities are parallel at any instant in time.

Below, the tumbling wheel rolls 90 degrees: Looking from the top, the wheel plane goes through a clockwise change in orientation on a horizontal plane (the road) by 30 degrees from stage 1 to stage 7. There is also a clockwise rotation on a vertical plane of 90 degrees. Attach a bicycle to it and it looks like the bicycle front wheel turned 30 degrees as the bicycle rolls forward and falls/leans. Looking at the geometry in motion; the front wheel does not turn and thus does not have any component of rotational velocities on a horizontal plane. Those velocities are all parallel at any instant in time. The front wheel changes rolling direction without any wheel-turning torque.

This tumbling motion can also be observed when a wheel/disc is rolled onto a rotating turntable. The wheel/disc keeps changing rolling direction and we perceive it to be turning but it is not in the way we think. It is constantly tumbling into a different rolling direction, which is toward the direction the wheel/disc leans, as a result of oncoming turntable surface that is not parallel to the wheel plane (rolling direction).

When a bike rolls and falls/leans, the front wheel tumbles and creates the torque that turns the attached fork through to the handlebars. The geometry of the bicycle, more specifically the head tube angle, must allow the unconstrained motion of the tumbling front wheel.

The images below show the bicycle front wheel following the same motion of the above tumbling wheel images and it looks to us like the bicycle wheel is turning but we know it is not.

To allow the front wheel to tumble, the bike’s head tube angle has to be within a certain range. Below shows which angles work and which angles do not work.

The figures below show a stationary bike with different head angles as the wheel is turned and is compared to the tumbling wheel below each figure.

Starting with head angles the don’t allow the front wheel to tumble:

Fig 1 -NO- A 100 degree head tube angle creates a counterclockwise rotation on the vertical axis plane. This head angle does not allow the wheel to tumble.

Fig 2 -NO- A 90 degree head angle does not allow rotation on a vertical plane.

Fig 3 -NO- A 0 degree head angle does not allow the change in orientation on a horizontal plane.

Fig 4 -YES– A 45 degree head angle allows the dual plane clockwise rotation (change in orientation). The vertical plane rotation and degree of lean are very closely matched through each stage. This tells us that, to a varying degree of freedom, any angle between 0 and 90 will allow a wheel to tumble.

We see the front wheel turn when the bike rolls and falls. When the bicycle corners and the front wheel is fixed we do not see the front wheel turning. But when we examine the instantaneous horizontal component velocities (see below), we see that these velocities are in different directions and are perpendicular to a turn center axis. This is the definition of rotation/turning of a rolling wheel. The ironic thing is that cornering vehicle wheels are actually turning. It’s just imperceptible. When you are cornering in your car and the orientations of the front wheels are fixed, all four wheels of the car are rotating on a vertical axis which is why they individually travel along curved paths. There is a torque at each wheel that constantly turns them which is created by a mechanism that is common to most self-guided vehicles such as airplanes, boats, snowmobiles, bicycles, etc. The video link below describes this cornering mechanism.

https://youtu.be/-UIir0wNIEI

• Bicycles typically have a curved front fork to increase the castor effect. I notice that your bicycles do not. Might this not be part of the problem? Commented Oct 8, 2023 at 18:28
• Thanks, but I don't think caster effect has an influence on why the wheel changes travels direction. Commented Oct 10, 2023 at 13:57
• Hello @Qmechanic. The PSE website has many many posts/questions discussing the physics of a bicycle front wheel. The ones trying to understand the self-turning motion all try to find where the torque comes from. My question asks “what if there isn't a torque needed?”. Please read my description. Please allow this question exploring nature to be allowed. Commented Oct 12, 2023 at 12:10
• Qmechanic merely edited your question; it was closed by the votes of three regular users in accordance with our review process. The amount and size of pictures in this question makes it rather hard to read, and really it is not clear what sort of answers you expect to the question "what if there isn't a torque needed?". physics.SE does best with clear, specific questions, while this seems to be more of a somewhat vague discussion prompt for your ideas about rolling motion and torques. Commented Oct 12, 2023 at 12:50
• This seems like a lecture that begins with a rhetorical question, not an actual question seeking an answer
– Dale
Commented Jul 21 at 21:01