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Counter steering


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Graphs showing the lean and steer angle response of an otherwise uncontrolled bike, traveling at a forward speed in its stable rangle (6 m/s), to a steer torque that begins as an impulse and then remains constant. Torque to right causes initial steer to right, lean to left, and eventually a steady-state turn to left.
Countersteering is required to turn any tandem 2-wheeled vehicle
A hypothetical curve on dry asphalt

Countersteering is the technique used by single-track vehicle operators, cyclists and motorcyclists, to initiate a turn toward a given direction by first steering counter to the desired direction ("steer left to turn right"). To negotiate a turn successfully, the combined center of mass of the rider and the single-track vehicle must first be leaned in the direction of the turn, and steering briefly in the opposite direction causes that lean. Once sufficient lean is established to sustain the desired turn, the rider, or in many cases the bike itself, then steers into the turn to cause the bike to turn in the desired direction and stop the lean from increasing. This technique does not apply to multiple-tracked vehicles such as trikes and bicycles or motorcycles with sidecars attached.

It is important to distinguish between countersteering as a physical phenomenon and countersteering as a rider technique for initiating a lean (the usual interpretation of the term). The physical phenomenon always occurs, because there is no other way to cause the bike and rider to lean short of some outside influence such as an opportune side wind, although at low speeds it can be lost or hidden in the minute corrections made to maintain balance.

At the same time, the rider technique of applying pressure to the handlebars to initiate a lean is not always necessary, since, on a sufficiently light bike (especially a bicycle), the rider can initiate a lean and turn by shifting body weight, called counter-lean by some authors.[1][2][3] Documented physical experimentation shows that on heavy bikes (many motorcycles) shifting body weight is less effective at initiating leans.[4]

It is also important to distinguish the steering torque and steering angle necessary to establish the lean required for a given turn from the sustained steering torque and steering angle necessary to maintain a constant radius and lean angle until it is time to exit the turn. The initial steer torque and angle are both opposite the desired turn direction. The sustained steer angle is in the same direction as the turn. The sustained steer torque required to maintain that steer angle is either with or opposite the turn direction depending on forward speed, bike geometry, and combined bike and rider mass distribution.

Contents

Bikes vs automobiles

Automobiles steer by imposing a steer angle between the front and rear wheels. Broadly speaking, the response of the vehicle is related to that angle; the automobile is a "position-controlled" system in normal use.

Bikes steer by controlling roll angle. However roll angle is not directly manipulated by the handlebars in the same way as steer angle in an automobile. Rather it is influenced indirectly by applying roll moments to the machine. These roll moments in turn come from side forces at the wheels, which are closely related to steering torques. Thus the bike is a "force-controlled" system in which the actual position of the handlebars is free.

The lean of a bike's wheels causes a turning force in the direction of the lean, called camber thrust, which enables the bike to negotiate turns with substantially less steering angle of the front wheel than an automobile for the same turn radius.[3]

How it works

A single-track vehicle such as a bicycle or a motorcycle is an inverted pendulum—it will fall over unless balanced.

The technique used by cyclists and motorcyclists to initiate turning in a given direction is to first apply a steering torque in the opposite direction. For example, if a turn to the left is desired, it is started by a turn of the handlebars to the right. Under this force the front wheel will rotate to turn right and the front tire will generate forces to the right. The machine as a whole steers to the right briefly and the rear tire also generates forces to the right. Because the forces are applied at ground level, this pulls the wheels "out from under" the motorcycle and to its right. The resulting roll angle to the left causes the tires to then generate camber thrust to the left providing the centripetal forces required to turn left. The geometry of the steering system provides the forces necessary for the front wheel to adopt an angle turned into the turn in a conventional manner[5]. It is often boiled down to "push left to go left".

While this appears to be a complex sequence of motions, it is in fact known unconsciously by every child who rides a bicycle. The entire sequence goes largely unnoticed by most riders, which is why some assert that they don't do it.

It is often claimed that two-wheeled vehicles can be steered using only weight shifts. While this is true for small "trim" inputs to direction, complex maneuvers are not possible using weightshifting alone because even for a light machine there is insufficient control authority.[6] Although on a sufficiently light bike (especially a bicycle), the rider can initiate a lean and turn by shifting body weight,[1], there is no evidence that complex maneuvers can be performed by bodyweight alone [4].

It is also important to distinguish the steering torque necessary to initiate the lean required for a given turn from the sustained steering torque and steering angle necessary to maintain a constant radius and lean angle until it is time to exit the turn. The initial steer torque and angle are both opposite the desired turn direction. The sustained steer angle is in the same direction as the turn. The sustained steer torque required to maintain that steer angle is either with or opposite the turn direction depending on forward speed, bike geometry, and combined bike and rider mass distribution.

Countersteering is necessary to adjust the angle of lean of a bicycle and works in the opposite sense to the handlebar input while conventional steering in the direction of the turn is used in conjunction with camber thrust to negotiate the turn.

Need to lean to turn

A bike can negotiate a curve only when the combined center of mass of bike and rider leans toward the inside of the turn at an angle appropriate for the velocity and the radius of the turn:

<math>\theta = \arctan \left (\frac{v^2}{gr}\right )</math>

where <math>v</math> is the forward speed, <math>r</math> is the radius of the turn and <math>g</math> is the acceleration of gravity.[1]

Higher speeds and tighter turns require greater lean angles. If the mass is not first leaned into the turn, the inertia of the rider and bike will cause them to continue in a straight line as the tires track out from under them along the curve. The transition of riding in a straight line to negotiating a turn is a process of leaning the bike into the turn, and the only way to cause that lean (of the combined center of mass of bike and rider) is to move the support points in the opposite direction first.[7] The rider can shift his weight of course, but any force used to move one way laterally pushes the bike laterally the opposite direction with equal force. That makes the bike lean (and can affect the steering), but it does not change the combined center of mass of bike and rider.

Lean by countersteering

When riding a bicycle or a motorcycle, countersteering is a method of initiating a turn by a small, momentary turn of the front wheel, usually via the handlebars, in the opposite (counter) direction. This moves the pivot point (the wheels' contact patches) out from under the center of mass to establish the lean angle for a turn. While necessary at all speeds, the need to countersteer becomes more noticeable as speed increases.

Hence, to turn to the right, the rider first throws the bike off balance by momentarily pointing the front wheel slightly to the left. The center of mass of the bike plus rider will continue in a straight line, but the contact patches of the tires move to the left with respect to this straight line.

Once lean is achieved

As the desired angle is approached, the front wheel must then be steered into the turn to maintain that angle or the bike will continue to lean with gravity, increasing in rate, until the side contacts the ground. This process usually requires little physical effort, because the geometry of the steering system of most bikes is designed in such a way that the front wheel has a strong tendency to steer in the direction of a lean.

The actual torque the rider must apply to the handlebars to maintain a steady-state turn is a complex function of bike geometry, mass distribution, rider position, turn radius, and forward speed. At low speeds, the steering torque necessary from the rider is usually negative, that is opposite the direction of the turn, even when the steering angle is in the direction of the turn. At higher speeds, the direction of the necessary input torque often becomes positive, that is in the same direction as the turn.[8]

Adjusting or exiting a turn

Once in a turn, countersteering is again required to make changes to its shape. The only way to decrease the radius at the same speed is to increase the lean angle, and the only way to increase the lean angle, is again to momentarily steer opposite to the direction of the curve. To the untrained, this can be extremely counter-intuitive.

To exit a turn, countersteer by momentarily steering further in the direction of the turn. This tilts the bike back upright.

At low speeds

At low speeds countersteering is equally necessary, but the countersteering is then so subtle that it is hidden by the continuous corrections that are made in balancing the bike, often falling below a just noticeable difference or threshold of perception of the rider. Countersteering at low speed may be further concealed by the ensuing much larger steering angle possible in the direction of the turn.

Unconscious behavior

Countersteering is indispensable for bike steering. Most people are not consciously aware that they employ countersteering when riding their bike any more than they are aware of the physics of walking. They have learned to subsconciously apply the required countersteering.

Gyroscopic effects

One effect of turning the front wheel is a roll moment caused by gyroscopic precession. The magnitude of this moment is proportional to the moment of inertia of the front wheel, its spin rate (forward motion), the rate that the rider turns the front wheel by applying a torque to the handlebars, and the cosine of the angle between the steering axis and the vertical.[8]

For a sample motorcycle moving at 22 m/s (50 mph) that has a front wheel with a moment of inertia of 0.6 kgm2, turning the front wheel one degree in half a second generates a roll moment of 3.5 Nm. In comparison, the lateral force on the front tire as it tracks out from under the motorcycle reaches a maximum of 50 N. This, acting on the 0.6 m (2 ft) height of the center of mass, generates a roll moment of 30 Nm.[8]

While the moment from gyroscopic forces is only 12% of this, it can play a significant part because it begins to act as soon as the rider applies the torque, instead of building up more slowly as the wheel out-tracks. This can be especially helpful in motorcycle racing.[8]

No hands

This is how countersteering works when riding no-hands. To turn left, a rider applies a momentary torque, either at the seat via the legs or in the torso that causes the bike itself to lean to the right, called counter lean by some authors.[3] The combined center of mass of the bike and rider is only lowered, of course. However, if the front of the bike is free to swivel about its steering axis, the lean to the right will cause it to steer to the right by some combination of gyroscopic precession (as mentioned above), ground reaction forces, gravitational force on an off-axis center of mass, or simply the inertia of an off-axis center of mass, depending on the exact geometry and mass distribution of the particular bike, and the amount of torque and the speed at which it is applied.[1][9]

This countersteering to the right causes the ground contact to move to the right of the center of mass, as the bike moves forward, thus generating a leftward lean. Finally the front end steers to the left and the bike enters the left turn. The amount of leftward steering necessary to balance the leftward lean appropriate for the forward speed and radius of the turn is controlled by the torque generated by the rider, again either at the seat or in the torso.

To straighten back out of the turn, the rider simply reverses the procedure for entering it: cause the bike to lean farther to the left; this causes it to steer farther to the left, which moves the wheel contact patches farther to the left, eventually reducing the leftward lean and exiting the turn.

The reason this no-hands steering is less effective on heavy bikes, such as motorcycles, is that the rider weighs so much less than the bike that leaning the torso with respect to the bike does not cause the bike to lean far enough to generate anything but the shallowest turns. No-hands riders may be able to keep a heavy bike centered in a lane and negotiate shallow highway turns, but not much else.

Motorcycles

Even more so than on a bicycle, mastering the technique of consciously countersteering is essential for safe motorcycle riding, and as a result is a part of the safe riding courses run by the Motorcycle Safety Foundation and the Canada Safety Council. At the higher speeds that motorcycles commonly attain, it becomes increasingly impractical to steer by taking advantage of the minute and random corrections needed to maintain balance.

Much of the art of motorcycle cornering is learning how to effectively "push" the grips into corners and how to maintain proper lean angles through the turn. When the need for a quick swerve to one side suddenly arises in an emergency, it is essential to know, through prior practice, that the handlebars must be deliberately pressed away on that side instead of being pulled. Many accidents result when otherwise experienced riders who have never carefully developed this skill encounter an unexpected obstacle.

To encourage an understanding of the phenomenon of countersteering, the phrase positive steering is sometimes used, [10][11] and is summed up in a simplified way as "Push the right-hand bar to steer right; push the left-hand bar to steer left".


The Wright Brothers

Wilbur Wright explains countersteering this way:

I have asked dozens of bicycle riders how they turn to the left. I have never found a single person who stated all the facts correctly when first asked. They almost invariably said that to turn to the left, they turned the handlebar to the left and as a result made a turn to the left. But on further questioning them, some would agree that they first turned the handlebar a little to the right, and then as the machine inclined to the left, they turned the handlebar to the left and as a result made the circle, inclining inward.

[12][13]

See also

References

  1. 1.0 1.1 1.2 1.3 Template:Cite journal
  2. Cocco, Gaetano (2004). Motorcycle Design and Technology. Motorbooks. p. 25. ISBN 978-0-7603-1990-1. 
  3. 3.0 3.1 3.2 Foale, Tony (2006). Motorcycle Handling and Chassis Design, the Art and Science (2nd ed.). Tony Foale Designs. p. 4–7. ISBN 978-84-933286-3-4. 
  4. 4.0 4.1 Gromer, Cliff. "STEER GEAR So how do you actually turn a motorcycle?", Popular Mechanics, 2001-02-01. Retrieved on 2006-08-07.
  5. Jones, David (1970). The Stability of the Bicycle (PDF). Retrieved on 2009-03-31.
  6. Evangelou, S, 2004 "The Control and Stability Analysis of Two-Wheeled Road Vehicles", PhD Thesis, Imperial College London
  7. Wilson, David Gordon; Jim Papadopoulos (2004). Bicycling Science (Third ed.). The MIT Press. pp. 270–272. ISBN 0-262-73154-1. 
  8. 8.0 8.1 8.2 8.3 Cossalter, Vittore (2006). Motorcycle Dynamics (Second ed.). Lulu.com. pp. 241–342. ISBN 978-1-4303-0861-4. 
  9. Brandt, Jobst (1997-09-16). What keeps the bicycle upright?. sheldonbrown.com. Retrieved on 2007-10-17.
  10. Jon Taylor & Stefan Bartlett (2009). How to be a Better Rider. Institute of Advanced Motorists. ISBN 978-0956223913. 
  11. Novice Motorcycle Riders to Learn Positive Steering. Biker 24/7 News (29 June 2009). Retrieved on 2009-12-31.
  12. Crouch, Tom D. (1989). The Bishop's Boys. New York: W. W. Norton. p. 170. ISBN 0-393-30695-X. http://books.google.com/books?id=ytw11Bmxcz8C&pg=PA170&lpg=PA170&dq=I+have+asked+dozens+of+bicycle+riders+how+they+turn+to&source=web&ots=I4sE9HF0Lx&sig=aHXI0sA0XwTVmIT1rjCGAJPWAlc&hl=en&sa=X&oi=book_result&resnum=4&ct=result. 
  13. Kelly, Fred C. (1989). The Wright Brothers. Courier Dover Publications. pp. 297–299. ISBN 9780486260563. 

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