Man on a bike - leans into a corner. How?

[mviswanathan]

Please cosider some visibly positive statements in the following para as "just in my opinion"

Consider the system as Rider-cylce combo. The rider can shift the CG of the system by flexing his body. However, it will result is garbageing of CG only in presence of friction beween the wheel and the road. If one coiders a case with zero friction perpendicular to the riding direction, then the body flexing will not unbalance the cycle (please correct me here) and unbalance is required with the non-vertical steering axis for the cylce to turn to balance itself.

As I understood, the original question was, how the CG is changed in an isolated system. But the cycle alone does not form an isolated system due to the reaction on the wheel contact with the road.

May be the following should go to a new thread?
As an extension of this CG shifting question, how does one start swinging sitting on a swing or swinging hanging from gymnastic rings. If one tries to flex the body slowly, one cannot swing. But doing it fast or jerking can start the swing. Does it mean that it has something to do with the slower response of the system to balance itself?

 

[Phrak]

I've spent way to much time on scooter and bicycle dynamics.

Shifting the center of gravity is not the method balance. A bicyle will balance on its own without a rider when in forward motion. It will go into ever-tightening turns, but it doesn't immediately dump over.

But it is possible to balance on a bicycle without forward motion. This is because turning the handlebars changes the contact point of the front wheel. The center of gravity is then to the left or right of the line of contact between front and rear wheels. But contact line change is not the primary mode of balance for a bicycle in motion.

 

[rcgldr]

How does one start swinging ... swing ... hanging from gymnastic rings?

By applying a torque, such as leaning back on a swing pulling the chain, or lifting the legs and/or body away from vertical towards horizontal on the rings. This moves the swing or rings away from directly under the support bar, which results in a component of tension in the chain or straps in the horizontal direction, opposing the torque with a linear force, and the result is a linear acceleration, although a small one.

 

[mviswanathan]

By applying a torque, such as leaning back on a swing pulling the chain, or lifting the legs and/or body away from vertical towards horizontal on the rings. This moves the swing or rings away from directly under the support bar, which results in a component of tension in the chain or straps in the horizontal direction, opposing the torque with a linear force, and the result is a linear acceleration, although a small one ...

If the leaning back action is done slowly, the swing chain and the body take a new orientation, however, with the CG still staying vertically below the suspension point. If you, now lean forward - again a still different oriantation, but still with CG directly below the suspension point. No swinging still.

But when you do the actions faster (I am not explain what one has to do really start swinging, but I could do it), you start swinging. Almost like, you have to give it a jerk to start swinging. Is it that giving a jerk is like Jet action (may be I am confused in this case).

 

[mviswanathan]

The rider can shift the CG of the system by flexing his body. However, it will result is garbageing of CG only in presence of friction beween the wheel and the road.

What I was saying is that, this effective shift of CG with respect to the vertical from the contact point on the road will not happen without the friction perpedicular to the motion. Without this friction, the rider's body flexing will have the opposite shifting of the contact point with the road ( Here, frankly, I am not saying that without friction the system will always remain vertical (CG and contact point), but the immediate effect on the system will be as stated). Well, I require more clarifications. Thanks

 

[rcgldr]

How does one start swinging sitting on a swing or swinging hanging from gymnastic rings.

By applying a torque, such as leaning back on a swing pulling the chain, or lifting the legs and/or body away from vertical towards horizontal on the rings. This moves the swing or rings away from directly under the support bar, which results in a component of tension in the chain or straps in the horizontal direction, opposing the torque with a linear force, and the result is a linear acceleration, although a small one.

If the leaning back action is done slowly, the swing chain and the body take a new orientation ... when you do the actions faster ...

That's because the slower motion is associated with a much smaller torque. The torque is proportional to the rate of angular acceleration, so a faster movement (more angular acceleration) results in more torque, more displacement of the chain or straps and more horiztonal component of linear force opposing the torque, and more linear acceleration. The torque is also proportional to the lever distance, so in the case of a swing, standing on the swing provides a greater effective radius, and probably more maximum torque than when sitting in the swing.

shifting the cg

Getting back to the bicycle, note the bicycle is free to lean to either side and will do so in response to the rider shifting to one side or the other without opposing steering inputs. It's the steering inputs that generate almost all of the side forces at the contact patch of the tires. Initially the bicycle is counter steered directly by steering outwards, or indirectly by the rider leaning inwards, the bicycle leaning outwards, and trail geometry causing the front tire to steer outwards because of the outwards lean angle of the bicycle. The initial counter steering generates an outwards force at the contact patches, which creates an inwards torque, and the bicycle responds with an inwards lean (roll response). The rider and/or trail steering geometry then stop and hold the lean angle with an appropriate inwards steering response. Since the trail geometry is designed to straighten up the bike if the rider does not lean with respect to the bicycle, then a bit of counter steering torque needs to be applied to the handlebars to maintain the lean (this is more noticeable on motorcycles).

 

[David Cuthill]

May I add my $0.02 worth?
Newton's first law says a body continues in a state of rest or uniform motion unless an external force acts.
The man doesn't just lean, he steers the wheel. This internal input is made by the man to the bike-road system, the steering wheel turns, and the motion changes to circular, and there is a force supplied externally from the ground as the straight-line motion changes to circular motion around a distant radial centre. The ground providing a centripetal force to direct the motion around the centre of a circle, or series of circles as the steering column is rotated.
In order to maintain balance in the turn, the man must lean the bike - so that the resultant directs equal and opposite (Newton's 3rd Law) against the external force that is making the direction change. If he doesn't his momentum in the original straight line will cause him to topple over. If he leans too much, he'll fall inside and if he doesn't lean enough, he'll fall to the outside as his momentum tries to continue its straight line.
DC

 

[sophiecentaur]

I could make a few points here.
You can steer a bike easily without holding the handlebars. (You have to whistle and attempt to look very cool at the same time, with your hands in your pockets but I don't think that is part of the Physics of the situation - although getting your weight well to the back seems to help).
You couldn't steer or stay upright on ice for very long.
The castor action of the front wheel is essential for stability. Bikes have been built without it and they are almost impossible to ride.
You can ride bikes with ridiculously small front wheels and they can still be ridden if they have the right castor angle. (Grocer's delivery bikes with a heavy front load in the front basket are a pig to ride, though; the MI of the steering is too high, I think)

 

[YellowTaxi]

I think the OP was saying that on a bike without any steering it should be impossible to make the bike+rider lean in the first place.

it suggests that bikers in real life are mainly using the steering to make the bike lean. Which i think is correct. probably

 

[DannoXYZ]

Coming in a little late, but I may add some info. Yes, it's the steering that initiates the lean and resultant cornering (look up camber-thrust of tyres). A good test is to ride a bike in a parking lot, at about 7-10mph. Then sit back with the hands barely on the bars. Remove one hand and push on the bars with the other hand.

Let's say you remove the left hand and push on the bars with your right hand, aiming the front tyre to the left. Which way does the bike lean and turn? Repeat the test by removing your right hand and pushing on the bars with the left hand (to aim front-wheel to the right).

 

[russ_watters]

Didn't read the whole thread...did anyone mention the fact that the front wheel support isn't vertical..?

...oh phrak hit on that.

 

[rcgldr]

Let's say you remove the left hand and push on the bars with your right hand, aiming the front tyre to the left. Which way does the bike lean and turn?

It leans right, turns left, falls over, ouch. How about aiming the tire left for a brief period to lean right, then not pushing on the right handlebar to allow the steering geometry to aim the front tire right so it corresponds to the proper right steering angle for the right lean?

Countersteering is done to initiate or change lean angle, prosteering is used to turn once the lean angle is established.

 

[cronxeh]

Guys.. I know why Debozo doesn't get it.

The center of mass doesn't change - its the planet Earth!

The biker and the bike are an equal distance away from center of mass, and the angle between them shifts as the biker shifts his weight. If you want an example, sit on the bicycle in the straight position. Now shift your weight to left or right, and when you fall off the bike know that physics owns you.

QED.

 

[SystemTheory]

As someone points out above the initiation and control of a turn (bicycle or motorcycle) is dependent on the speed. One can steer a machine with no hands at higher speeds, but it is nearly impossible to make a U-turn with no hands at low speeds. Low speed turns require steering in the direction of the turn and balance. High speed turns require steering in the opposite direction of the turn and then correcting in the direction of the turn, while adjusting balance.

I rode bikes and motorcycles for years and experimented with all these things, and this is the recollection. Also in a "steer by wire" car the front and rear wheels steer in opposite directions at low speeds for a tight turn, and steer roughly in the same direction at higher speeds. There's more to this steering mechanics than initially "meets the eye."

Personally I would say there is no such thing as an isolated system, since gravity, heat, light interact with a body even if it floats in space. An isolated system is an ideal wherein one imagines there are no external interactions, and this is reasonable when the interactions are negligible. However it is not conventional to regard every system as isolated, and one should respect the conventional definition when making an assertion (which may or may not be a valid alternative way to conceptualize interactions).

 

[espen180]

A (simple) alternative way to look at it is that since there is friction between the bicycle wheels and the road, the rider can exert a torque on the bike with the contact point between the roand and the wheels fixed in the riders rest frame.

 

[rcgldr]

If the leaning back action is done slowly, the swing chain and the body take a new orientation, however, with the CG still staying vertically below the suspension point.

It's easier to visualize this with a person standing on the swing. The person leans back, pushing the swing at his/her feet forwards, and pulling the chain at his/her hands backwards. The forces exerted by the person cancel, but the tension in both segments of the chain above and below the person's hands have a forwards component of force at the persons hands. The tension below the person's hands is countered by the persons compression, but the tension above isn't countered, resulting in forwards component of force in the chain at the person's hands, and a backwards component of force in the chain at the supporting bar. If the supporting bar is fixed in place (attached to the earth), the result is a forwards movement of the person and swing (and a tiny movment of the Earth backwards).

As someone points out above the initiation and control of a turn (bicycle or motorcycle) is dependent on the speed.

and the steering geometry. The steering geometry can be designed with sufficient trail (distance from contact patch to where steering pivot axis intercepts the ground), to be stable at very slow speeds.

Things are less confusing when you get rid of the extra wheel and only have one wheel, a unicycle. The unicycle oriented web sites never get into these debates. It's accepted that leaning requires countersteering at all speeds. There are various methods of turning though, using arms and/or pedal pressure to control direction and/or turning of the wheel.

I would say there is no such thing as an isolated system.

An isolated system is an abstract concept, so it may not be "real", but the abstract concept can be used to simplify the physics of an interaction.