How do gyroscopic forces affect a bicycle's stability?

[Avtheangel]

My dad gave me this riddle eight months ago, can anyone help?

Why doesn't a bicycle fall over when its moving.

P.S its not balance , as you can push it and it won't fall over for a while.

 

[rcgldr]

It's because of the steering geometry of a bicycle. The contact patch at the front tire is behind where the imaginary line from the pivot axis of the front tire would intercept the ground. In the case of bicycles and motorcycles, the distance from intercept point back to the actual contact patch is called "trail" (for cars, the equivalent effect is called "caster"). If all other factors are equal, the larger the distance, the slower the speed the bicycle can move and still self correct.

Due to the "trail", when a bicycle is leaned over, the pavement pushes up against the side of the front tire, and since this is "behind" the pivot axis, it creates a torque force that steers the front tire inwards enough that with sufficient speed the bicycle (or motorcycle) will straighten up back to vertical (although not in the original direction). You can hold a bicycle by the rear seat, and lean the bicycle to see that the front tire turns in the direction you lean the bicycle.

At low speeds, steering geometry provides vertical stability. As speeds increase, this transitions into lean stability, because gyroscopic forces resist a change in lean. On a motorcycle at 100+mph, lean stability dominiates, and there's no perceptible tendency to straighten up, and instead a motorcycle at these speeds will tend to hold it's current lean angle. Trying to steer by leaning with your body also ceases to work on a motorcycle at 100+mph, "counter-steering" has to be used instead.

If you're curious about "counter steering", I recommend doing a web search for "unicycle counter steering". I've found a few bad web sites trying to explain how steering works on bicycles and motorcycles, but I've never found a bad website explaining how counter steering works on a unicycle.

 

[wdoe999]

I know I'll start a controversy, but here goes.

From what I can gather, gyroscopic forces play no (insignificantly small) role in keeping a bike up/stable.

This is demonstrated in 2 examples.

1. A person can ride a ski-bob (has skis instead of wheels) as well as a bike.
2. I recall a fellow who tried to make an unridable bike by adding extra wheels that rotated in the opposite direction to cancel any gyroscopic forces. This had no effect on the bikes stability. It was taken one step further where the front caster was completely reversed (unstable) and the rider still had no problems.

Then what is the answer?

The bike's stability comes from 3 elements. There is 1 major active element, and 2 minor passive elements.

The major active element is simply the unconscious ability of the rider to actively steer the bicycle so that it remains underneath him. You don't realize that you are doing this, but you are traveling in a slightly squiggly line as you keep the bike between you and the ground. This is demonstrated by the above examples, especially the one where the rider has no problem riding an unstable bicycle with reverse caster.

The first minor passive element is the caster as was described in an earlier post. The caster will help you by self correcting the front wheel, but it is not necessary. It does help you a great deal if you ride with no-hands.

The last passive element is inertia. Inertia doesn't keep you up, but it does increase the time you have to make corrections. That is, your heavy body that is in the upright position would like to stay in that position (Newton's laws). It won't stay there forever because gravity will eventually pull you over. But it does increase the time you have to make steering corrections to keep the bike underneath you.

This now raises the question about countersteering...

Before I talk about countersteering, I should point out that in addition to turning the front wheel, another way to steer a bike is to lean to one side. When you do this, you are no longer riding on the bottom of the tire, rather you are riding on a combination of the bottom of the tire and the side-wall. The side wall has a smaller radius than the bottom of the tire, so you are essentially riding on a conical wheel. For example, imagine wheel that is in the shape of a toilet-paper roll. Such a wheel will roll straight. Now imagine that one end of this wheel is smaller than the other (conical). This wheel will turn when it is rolled. This is know as camber-thrust and the same thing happens when you lean a bike tire.

Let's say you turn the bike's wheel to the left. At low speed, the bike will go to the left. At high speed, if you were to turn the wheel left, the front end of the bike would begin moving left, while your body would want to keep going straight. The bike will now start tipping to the RiGHT. As the bike leans to the right, camber thrust will make the bike move to the right. Therefore, you want to initiate a high speed turn by slightly moving the wheel in the opposite direction that you want to go. It is very subtle, and you perform a slight countersteer to simply initiate a lean that causes the turn.

 

[Avtheangel]

Thanks, But even if your NOT on the bike , and you push it, how come it doesn't fall over straight away?

Theres one word for it, and its one of a trio thing (e.g Distance - Speed - Time)

What keeps it up in general?

Thank you!

 

[ZapperZ]

People way want to read this answer from Physics Central at the APS website.

http://www.physicscentral.com/lou/2001/bicycles.html

Zz.

 

[wdoe999]

I had interpreted your original question to mean a bike that has a rider. I see you are asking about a riderless bike.

The previous poster is correct that without a rider, the wheel caster becomes the dominant stability factor by causing the front wheel to automatically steer so that the wheels stay under the bike (similar to the help you get from the caster when riding with no hands). Again though, the gyroscopic forces are negligible.

 

[rcgldr]

Gyroscopic forces play no (insignificantly small) role in keeping a bike up/stable.

As I previously mentioned, as speeds increase, gyroscopic forces resist a change in lean angle, resulting in lean stability as opposed to vertical stability. At slow to moderate speeds, the self correcting steering geometry is dominant and there is vertical stability, a bicycle and/or motorcycle have a tendency to become vertical if there is no steering input on the handlebars. At high speeds, like 100+ mph on a motorcycle (not sure what speed this would be on a bicycle), there's virtually no self-correction, and the motorcycle will just hold it's current lean angle if there's no steering input at the handlebars. Also at this speed, body leaning has virtually no effect on turning, and the counter-steering effort to change lean angle is virtuallly the same regardless if the intent is to increase or decrease lean angle.

make an unridable bike - one where the rider has no problem riding an unstable bicycle with reverse caster.

It would be very difficult to ride a bike with negative trail, it would require constant correction.

... countersteering, I should point out that in addition to turning the front wheel, another way to steer a bike is to lean to one side.

Since it's a uni-track vehicle, the center of mass remains constant, so when a rider leans to one side, the bicycle leans to the other side, which then reacts by steering to the side the bicycle is leaned, which ultimately is just an indirect method of implementing counter-steering. As mentioned above, at very high speeds on a motorcycle, leaning doesn't work, only direct counter steering.

Conical wheel

This works fine for a single wheel, but two conical wheels, one in front of the other, and with parallel axis will roll in a straight line (slippage occurs instead of turning). I'll try to find a website that ran this experiement and update this post later.

update - http://www.terrycolon.com/1features/bike1.html

Let's say you turn the bike's wheel to the left .. low speeds

Then the bike will lean right, even at low speeds. Since there's little resistance to counter-steering at low speeds it's not as noticable.

staying upright on a bicycle with no forward or backward movement

This is possible because the trail causes the contact patch to move sideways relative to the rest of the bicycle, so a very skilled rider (like a velodrome racer) can generate corrective torque forces with steering inputs, similar to counter-steering, but the range of movment is very small. Trials riders will sometimes use a free leg to generate corrective torque force balance a trials motorcyle, in addition to hopping the bike around like a pogo stick with two contact patches.


The dynamics of two wheeled vehicles can confuse the issue of counter steering, because of body leaning, gyroscopic effects, ... This is why I find the most accurate information regarding counter-steering is found in web sites that explain the dynamics of unicycles

 

[wdoe999]

Here's a link with some info about the British Scientist who made the URB (Unridable Bicycle).

http://www.geocities.com/CollegePark/Campus/1832/pyfair.html
(hey, it's on the internet so it has too be true, lol).

Another way to demonstrate that gyroscopic forces have virtually no effect is as follows:

Many people have probably performed the experiment where they hold a spinning bicycle wheel to feel the gyroscopic force. It feels neat, but in reality, it is only a few pounds of force. Compare this to the rider and bike that may be several hundred pounds (we're getting fatter). A motorcycle wheel is heavier, but so is the motorcycle.

Another way to demonstrate this is with a toy clown bicycle with tiny wheels. It operates like a big bike, and it clearly has no gyroscopic effects. I rode a ski-bob (that has no wheels) and it operates just like a bicycle, complete with countersteering to initiate a high speed turn.

In regard to the question of whether countersteering causes the bike to lean through gyroscopic forces, or does it lean because the momentum of the riders body keeps him moving forward so as to pull the bike over:
I had mentioned above that the gyroscopic forces are dwarfed by the weight of the rider and bike. It is usually argued that in the extreme case of a motorcycle moving at very high speed, the gyroscopic forces must become significant so as to play a part in countersteering. The difficulty with this argument is that the rider's momentum also increases with high speed and still dwarfs the gyroscopic forces. Therefore the countersteer is only being used to cause the rider's momentum to pull the bike over into a lean.

 

[rcgldr]

Here's a link with some info about the British Scientist who made the URB (Unridable Bicycle).
http://www.geocities.com/CollegePark/Campus/1832/pyfair.html ... "He reversed the front fork to nullify the caster action ... "

If this guy truly reversed the fronk forks, which genenerally decrease trail (they bend forwards) then he increased caster even more, making the bike more stable not less. What is needed is forks that are angled forward enough to place the contact patch in front of where the pivot axis would meet the pavement.

gyroscopic forces have virtually no effect

The effect is significant at high speeds, but it's one that produces a tendency to hold a lean angle, instead of a tendency to reduce lean angle.

Regarding the gyroscopic reactions, say a bicycle or motorcycle gets unbalanced, producing a left roll. The gyroscopic reaction at the tires is a left yaw. At the front tire, the effect is direct, it turns the front tire to the left, at the rear, it yaws the entire motorcycle to the left by causing the front tire to turn left a bit further if there is positive trail at the front tire (since the contact patch is behind the pivot axis of the front tire), and this additional turning of the front tire to the left results in a gyroscopic reaction of a right roll. Note that these reactions only occur during the roll, and stop once the lean angle has stabilized.

It turns out that the gyroscopic reactions provide little tendency to reduce lean angle, probably because these are small compared to the weight of bicycle / motorcycle and rider. Most of the tendency to reduce lean angle is because of trail (or caster) in the steering geometry. However while mass of rider / vehicle remain fixed, gyroscopic reactions increase with speed, which leads me to believe that the gyroscopic roll reactions are much less than the roll reactions from the difference in angle between front and rear axis, most noticable in high speed turns.

high speed cornering

I'm re-thinking this issue. I know from personal experience that the higher the speed, the more counter steering effort it takes to produce a roll. Obviously momentum in the motorcycle is going to resist any change in direction, but the centripital acceleration corresponds to lean angle regardless of speed (assuming a coordinated turn), so I'm not sure how much of a factor momentum is regarding the increase in counter steering effort due to increase in speed.

My guess is that the gyroscopic roll reaction to counter-steering is much less than the actual roll reaction due to the steering angle at the front tire, and the gyroscopic reaction is resisting the greater roll rate due to steering as speeds increase.

Getting back on topic, the website I mentioned before includes a pretty good description of how a bicycle works:

http://www.terrycolon.com/1features/bike1.html