# Angular momentum and turning a bicycle

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• Chenkel
Chenkel
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I've been watching a Walter Lewin lecture about gyroscopes, and I was wondering what makes a bicycle fall toward the inside of a turn.
Hello everyone!

I've been watching the following Walter Lewin lecture, the part that illustrates my question is part 17:19 of the video

Most things have made sense during this lecture, but one persistent question I have is the following: why does the bicycle tilt toward the inside of the curve when you're turning the front wheel? If the momentum of the wheel is pointing to the left, and you make a turn towards the left, the change in the torque, based on the right hand rule, should be vertical, and upwards! So I would expect the bike to tilt towards the outside of the leftward turn using the definitions of angular momentum. I see in reality the bike tilts toward the inner part of the turn, this can be seen in those videos of high powered sports motercycles, where they turn so much, that they literally are inches from the concrete. Maybe I'm missing something, and this tilt into the turn has nothing to do with angular momentum, but something is keeping those bikes from falling over, I'd like to know why, let me know what you guys think, thank you!

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That has to do with centripetal force

This might be of interest: look up "banked curves"

Chenkel
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I have is the following: why does the bicycle tilt toward the inside of the curve when you're turning the front wheel?
It does not. Turning the handlebars to the right when riding upright is a prescription for falling over leftward, to the outside of the turn.

Part of the unconscious trick to riding a bicycle is to make use of this fact. If you want to turn right, you will initially turn the handlebars left. The gyroscopic effect is to create a slight lean to the right. In addition, this "steers the wheels out from under you", creating a greater lean to the right. Finally, this rightward lean will result in gravity working to make the lean angle greater still.

Once the desired lean angle is achieved, the rider turns the handlebars to the right, steering the contact patch under the rightward-turning bicycle to maintain the desired lean angle and cornering radius.

Once the desired heading has (nearly) been achieved, the rider will turn the handlebars even more rightward. This works to counter the lean and restore the bicycle to an upright angle. When the upright angle has been achieved, the handlebars can be normalized.

This is not much of a mental trick when you realize that you do the same thing when walking. You take a step left in order to move right. (Or hold your left foot down extra long to get the tilt started).

The gyroscopic effect is largely irrelevant for a bicycle until one attempts to ride "no hands". Then one manipulates the lean angle of the frame by counter-leaning with the body in order to affect the steering angle. The trail of the contact patch behind the steering axis is also important for this to work well.

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DannoXYZ, sophiecentaur, PeroK and 3 others
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The front wheel rotates around the steering axis, which is tilted aft about 20 degrees from vertical.
The faster the bike goes, the harder turning the front wheel becomes.

Delta2 and Chenkel
Chenkel
The front wheel rotates around the steering axis, which is tilted aft about 20 degrees from vertical.
The faster the bike goes, the harder turning the front wheel becomes.

I just watched the video and it seems to make sense, one thing it left me wondering is where the centripetal force comes from, obviously there's a centripetal force or else the bike would move in a straight line by Newton's first law, but I wonder why this happens.

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I just watched the video and it seems to make sense, one thing it left me wondering is where the centripetal force comes from, obviously there's a centripetal force or else the bike would move in a straight line by Newton's first law, but I wonder why this happens.
If you steer the bike rightward (without falling over), the bike moves in a rightward curve under the force of friction from the road on the tires. That rightward force of friction is the centripetal force.

Chenkel and malawi_glenn
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I just watched the video and it seems to make sense, one thing it left me wondering is where the centripetal force comes from, obviously there's a centripetal force or else the bike would move in a straight line by Newton's first law, but I wonder why this happens.
https://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics#Turning

Chenkel
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When I turn the handlebar to the right, I lean to the right. Otherwise, the bicycle would fall to the left.

Chenkel
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When I turn the handlebar to the right, I lean to the right. Otherwise, the bicycle would fall to the left.
True, but the turn of the handlebar to the right does not cause the lean to the right.

Both are caused by your intent to turn right. Which motivates a set-up that allows both conditions to hold. Which is normally arranged by a turn of the handlebars to the left.

berkeman, Chenkel and Lnewqban
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As a longtime cyclist I found this Veritasium video very interesting and clever.

.

Chenkel
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The Wiki article on counter-steering shows that during the initial counter-steer input (steer outwards to lean inwards) the estimate is that gyroscopic precession accounts for about 12 % of the total leaning torque, while most of the leaning torque, 88%, is due to outwards friction force from the pavement:

https://en.wikipedia.org/wiki/Countersteering#Gyroscopic_effects

Due to trail and|or rider input, the bike will tend to steer inwards as soon after it starts to lean inwards, and as the OP pointed out, this will result in an small outwards leaning torque.

That Wiki section doesn't state what the weight of the motorcycle is, which would affect the percentage of precession induced leaning torque versus friction induced leaning torque.

Due to the relatively small effect of this precession induced lean torque, a rider isn't aware of it (at least I'm not), and the most noticeable effect is angular momentum of the front tire resists any change in steering angle, and this increases with speed. As speed increases, it takes more counter-steering effort to induce lean angle changes. The self-correcting (tendency to return to vertical orientation) effect of trail induced inwards steering in response to lean angle is also opposed by the front wheel's angular momentum, acting as a damper at normal speeds, while at high speeds (around 100 mph), the damping effect is so strong that a bike will tend to hold the current lean angle as opposed to tending to return to vertical.

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berkeman, Chenkel and Lnewqban
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"True, but the turn of the handlebar to the right does not cause the lean to the right."
Isn't that what I said?

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"True, but the turn of the handlebar to the right does not cause the lean to the right."
Isn't that what I said?
When I turn the handlebar to the right, I lean to the right. Otherwise, the bicycle would fall to the left.
Taken at face value, the suggestion seems to be that you first turn the handlebar to the right and then decide to lean to the right in order to avoid a fall to the left.

Possibly this a language difficulty and you intend the rightward lean to be first and the handlebar turn to be second.

How do you go about initiating a lean to the right without using the handlebars to accomplish the feat?

It can be done, but the required maneuver is a lean of the torso to the left. This leans the frame of the bicycle rightward and generates a rightward frictional force of road on tires, thus deflecting the center of gravity of rider plus cycle rightward. It is the same maneuver used by tight-rope walkers.

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Chenkel and hutchphd
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Here's a funny (but life-threatening) story to drive this home...

I'd ridden bicycles and dirtbikes most of my young life (and got my motorcycle permit at 15.5 y/o on a light Suzuki 90 dual-purpose motorcycle that I commuted to school on), and when I finally had finished grad school and gotten a full time job as an R&D EE, I wanted to get a street motorcycle to help ease my commutes in Silicon Valley in Northern California. I found a good deal on a Honda CBR900 at a dealership about 20 miles north via an advertiesement in the weekly Cycle Trader (only hard copy back then!).

So I got a ride to the dealership and purchased the CBR900, put on my new streetbike helmet and headed home. But on the onramp to the southbound 101 freeway at about 30mph, I discovered that I was not able to just turn the handlebars into the corner to follow the onramp. This was really bad, since if I could not follow the curve of the onramp, I would go off the outside of the ramp and crash badly into some trees and oncoming traffic on the adjacent offramp. Very bad, bad.

Thankfully my technical instincts kicked in, and I used pertubations (wiggling the handlebars left and right) to quickly figure out that it was more important to push the right bar to make the bike lean to the right, and I just *barely* made the curve and merged onto the freeway and limped my way home.

I obviously did more reading that weekend and discovered countersteering (duh), and used it skillfully for about the next 5 years until I upgraded to a sportbike and learned about body steering (at Laguna Seca Raceway in Monterey). There are definitely important skills to turning a motorcycle at speed. Less so when it comes to lightweight bicycles and even motocross/dirtbikes.

Stay safe out there folks.

DannoXYZ, Lnewqban, jbriggs444 and 2 others
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"Taken at face value, the suggestion seems to be that you first turn the handlebar to the right and then decide to lean to the right in order to avoid a fall to the left.

Possibly this a language difficulty and you intend the rightward lean to be first and the handlebar turn to be second.

How do you go about initiating a lean to the right without using the handlebars to accomplish the feat?

It can be done, but the required maneuver is a lean of the torso to the left. This leans the frame of the bicycle rightward and generates a rightward frictional force of road on tires, thus deflecting the center of gravity of rider plus cycle rightward. It is the same maneuver used by tight-rope walkers.", which works when they carry a long heavy rod.

You are arguing with a nine year old, not a tightrope walker.
When I first rode a bicycle, I did not do one thing and then decide to do another. I turned the handlebar and leaned at the same time. Then, I found out that I could ride with my hands off the handlebar.
A bit surprising, but satisfying to a nine year old, I then found that if I just leaned to the right, the handlebar would turn to the right and the bicycle would follow. I didn't know about tightropewalker's trick at that time.

Chenkel
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I then found that if I just leaned to the right, the handlebar would turn to the right and the bicycle would follow. I didn't know about tightropewalker's trick at that time.
Your body knew. Your brain still does not. Nothing wrong with that. We can do many things without being able to describe accurately how we do them.

It is impossible to "just lean". You have to push on something. That is conservation of (angular) momentum.

It is possible to make the bicycle lean right. You shift your hips rightward to do it. In response to that right lean, your body will absorb the angular momentum and roll slightly leftward. Meanwhile, the bicycle's front wheel will turn right. At this point if you attempt a right turn, you are doomed to fall. So you don't do any of this.

You know how to ride "no hands". You know how to do it without thinking.

So you start your right turn by shifting your hips leftward. The bicycle leans left while you lean right. The bicycle responds to the lean by steering left. The result is a lean to the right.

You maintain this for just long enough to get the lean angle you want and then shift your hips rightward. The bicycle leans rightward. Your body's rightward lean slows down. The bicycle steers rightward as a result of the lean. You keep the lean angle balanced as you continue with a right turn.

To exit the turn, you shift your hips further rightward, causing a momentarily greater lean angle for the bicycle. The bicycle steers harder into the turn as a result and rights itself. You normalize your hip position and continue riding in a straight line.

Riding "no hands" involves counter-steering just as much as riding "with hands" does.

All of this is just grade-school reverse engineering. My parents blessed us with a ton of acrobatic raw materials in the back yard (spools, barrels, bicycles, vertical and horizontal ladders, ropes, swiings, a huge climbable elm tree (succumbed to Dutch Elm disease), "the crate" (incredibly sturdy home made, hard maple, five sided box with slats a child could fit through), bicycles and a unicycle and adopted a hands off "discover your own boundaries" methodology.

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Chenkel
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Taken at face value, the suggestion seems to be that you first turn the handlebar to the right and then decide to lean to the right in order to avoid a fall to the left.
Did you bother to look at the video??
As a longtime cyclist I found this Veritasium video very interesting and clever.

.

Which says exactly
So you start your right turn by shifting your hips leftward. The bicycle leans left while you lean right. The bicycle responds to the lean by steering left. The result is a lean to the right.
He is exactly correct.

Chenkel
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Things are a bit different on a motorcycle, since we have motors...

Chenkel, hutchphd and jbriggs444