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This section titled "Counter-Intuitive" is a direct continuation of the previous scientific quest efforts in the two previous tab sections, "Gyroscopic" and then "Front Fork." In the manner of a triology, the brute force frontal attack or quest will end in a sense with this tab section. The balance of the tab sections within Bicycle Science are intended to start gathering pieces together, and to reflect upon matters, as opposed to assaulting new territory.

Let us now proceed with the third wave or offensive.

The words "counter-intuitive" have been invoked with regard to the bicycle. By counter-intuitive, we mean that a device or object goes or behaves against simple logic or human nature or intuition. Most experiences in life are what we can call intuitive, so when something pops up that is counter-intuitive, it tends to set people back -- as they have to rethink how they look at the world, or at least the object in question. The counter-intuitive nature of the bicycle is responsible for the fact that we can have so much fun with the bicycle and even become preplexed at times. Bear with us, as we will eventually get to the mysterious thing called "critical velocity."

Steady-State Turn Experiments, The Torque Wrench Bike.
An interesting experiment at the University of Illinois focused on using an instrumented bike to ride in steady circular fashion. The objective was to clarify the matters of how much lean and in what direction is needed, as well as what magnitude of handlebar applied torque is required. The bicycle was instrumented, and was ridden on a special marked riding surface so as to be able to measure five important variables:
  1. The bicycle’s forward speed was measured with a standard bicycle computer.
  2. Angle of turn was measured by the rider noting the angle of turn (of the handlebars) by observing a wire’s position affixed to the front fork relative to a common protractor attached to the frame adjacent to the steering head.
  3. Steer torque was measured by the rider by use of a standard mechanic’s torque wrench affixed to the head of the handlebar stem.
  4. Rider’s lean angle relative to the frame was measured using a pivoted rod connected to the back of the rider (in a position along the rider’s spinal cord); and this angle was measured by a voltmeter as the base of the rod was connected to a rotary potentiometer at the rod’s pivot point just beneath and behind the bicycle seat. The potentiometer was energized being connected to a conventional DC battery source (9 volt transistor battery). The voltage proportional to upper torso lean angle was displayed on a standard analog voltmeter affixed to the handlebars in view of the rider. The voltmeter was calibrated to indicate lean angle of the rider’s upper torso relative to the bicycle’s frame.
  5. Lastly, the riding surface was marked with chalk in circles of known radii. This permitted the rider to maintain circular paths of known radii as desired.
The gist of the first experiment was to ride circularly at a given forward speed, and then hold the steer torque at a zero value (thus nulled about the zero value with fine adjustments) while using upper body lean articulation as the primary biasing steering control input. This experiment was repeated for a variety of bicycle velocities and radii. The object was to determine by measurement whether the rider leaned into or out of a turn and how much, as measured relative to the bicycle’s frame. The bicycle’s forward speeds and radii influenced how much and in what direction the rider had to lean.
The second variation on the experiment was to essentially repeat the above experiments except that the rider’s upper torso was maintained in the plane of the frame of the bicycle. The rider applied a steer torque using the torque wrench affixed to the front fork steering head. As the bicycle was ridden in a steady state or continuous circle, the rider observed the indicators of the forward velocity, the angle of steer, and the rider applied torque on the handlebars. At UIUC we performed these experiments almost twenty years ago, and subject to minimal budgets. Hence, fancy computers and data logging devices were not employed, but instead we relied upon the rider observing key variables as measured by eye during riding, and orally shouting out values which were then recorded using a pencil and notebook by an assistant standing by.
The results of the UIUC Torque Wrench Bike experiments were of considerable significance. In order to do justice to the discussion of the results, it now becomes necessary to introduce the concept of critical velocity of a bicycle.
The Critical Velocity of a Bicycle.
Based on both theoretical and experimental findings, we can make the following statements regarding a bicycle. These remarks apply to both bicycles as well as motorcycles; however we will generally use the word “bicycle” in what follows. The theoretical foundations of our remarks include mathematical analysis published in peer reviewed scholarly articles, as well as exhaustive experimental trials at a number of universities (University of Illinois, Lund Institute of Technology -- Sweden, and Cornell University, to name a few). It is assumed that the bicycle is in perfect alignment, where the center of gravity is and remains balanced (in the plane of the frame of the bicycle), and the bicycle is operating on a flat and level surface.
Given a bicycle operated without rider applied steer torque, and assuming the rider remains fixed relative to the frame of the bicycle, the bicycle will or will not remain upright depending upon the velocity (speed) of the bicycle. As the velocity is gradually increased, the velocity at which stability is first manifested is called the “critical velocity.” If the bicycle is stable this implies a tendency to remain upright without the need for rider corrective actions. In general, bicycles below critical velocity will fall over, that is, be unstable assuming the absence of rider applied steering torques or upper body control actions. At speeds above critical, the bicycle will remain upright in a stable configuration. When an object is said to be stable, that means even if small perturbations occur such as side thrusts or small deviations from equilibrium, the property of stability will cause the bicycle, in this case, to return to the upright (stable) position.
A bicycle’s critical velocity can be theoretically determined based on mathematical analysis, or it can be ascertained using experiment. For mathematical treatments the interested reader is referred to Astrom, Klein, and Lennartsson (2005), as well as Weir and Zellner (1978). Using Swedish values for a bicycle’s mass and dimensions with rider, Astrom, Klein, and Lennartsson (2005) determined the bicycle’s critical velocity as 5.95 m/sec.
As for experimental approaches to determine a bicycle’s critical velocity, we will summarize three techniques.
  1. A first and simple test is to push a riderless bike forward and let go. If the bike falls the velocity is generally less than critical. If the bike is pushed forward at a faster speed, and if the bike runs true and upright, the velocity is above critical. At some speed the bicycle may exhibit a weave, especially if it is modestly tapped by a bystander as it passes, then the speed is at critical.
  2. As a second way to test the critical speed, the bicycle may be fitted as described above in the Torque Wrench Bike Experiment (see previous bike experiment section). Without going into too much technical detail, a bike ridden no hands will be at critical speed in steady state turns, thus riding in a circle, if the rider’s center of mass is perfectly in line with the frame of the bike. At speeds below critical the body will have to lean outward, and at speeds above critical the body will lean inward. Again, we are talking about the rider’s upper torso leaning relative to the plane defined by the frame of the bike, not ordinary vertical as defined by gravity. We are also talking above about conditions necessary to maintain steady state turns, which differ from what a rider is required to do in order to enter into or out of a turn.
  3. A third way to experimentally test critical speed is to ride a bike in a continuous circle while keeping the body directly in the plane of the frame of the bike. It helps to ride holding the handlebars lightly, such as with finger tips, or even by using strings to tug on the handlebar grips as needed. Yet another way is to steer the bike by using a mechanic’s torque wrench fitted to the steering head of the stem or neck of the front fork. At critical velocity there will be zero steering torque required. Below critical velocity, the rider will be required to apply a back pressure, that is, to apply a torque opposite to the direction of turning. Lastly, if the bicycle’s velocity is above critical, the rider will be required to apply a steering torque or bias in the direction of the turn.
These experiments and theory related to critical velocity are not necessarily simple, and the good news is that the everyday rider doesn’t really have a need to know or even care. The reasoning lies in the fact that critical velocity is an attribute of a bike ridden or moving with no rider applied steer torque – in essence “no hands.” Once the rider places hands on the handlebars, the dominant mechanism for stabilization is the rider’s reflex movements in applying steering torques, and thus dictating continuously the handlebar position (the direction and amount of steering correction).
In order to be scientifically correct and complete, we need to comment that a second critical velocity exists. This second critical velocity occurs at rather high speed, at which speed the bicycle or motorcycle will once again become unstable in the absence of rider applied steering or upper torso body lean. According to the analysis by Weir and Zellner (1978), this speed for a light-to-medium weight motorcycle occurs at about 140 MPH. The instability is in the form of a very slow roll, or what is referred to as “capsize.” Capsize instability is rarely an issue or concern as it occurs so slowly that the rider has ample time to make steering or body lean adjustments. For bicycles, capsize instability has never been an issue to be concerned with, again because speeds aren’t high enough to cause capsize. Even if speed is sufficient, the instability or capsize action is characteristically slow so that the rider can easily make small corrections as necessary to maintain stability. Capsize instability is associated with higher vehicle speeds. At higher vehicle speeds the rider’s available steering mechanisms are relatively fast as the reaction time of any steering action is enhanced (shortened) due to the higher forward speeds.
In the American Hollywood tradition, we can recall one movie scene involving a motorcycle that remains stable and upright even when subject to pretty severe abuse. In the closing scenes of “Easy Rider,” starring actor Peter Fonda, a character in the movie is violently “removed” from his chopper motorcycle while at highway speed. The riderless motorcycle then continues straight, and even down and through a deep roadside ditch, and out onto an adjacent farm field. Yes, the motorcycle eventually ends up falling over, but we note that its speed by then had diminished to below critical.
Can we design bikes so as to change critical velocity?
The answer is an absolute “yes.” Based on both experiment as well as mathematical theory, we can cause the critical speed to be lower by adding mass to the front wheel. This will cause the critical speed to drop considerably, as the gyroscopic action increases.
In our previous discussions regarding gyroscopic concepts, we focused on the experimental and theoretical body of knowledge that gyroscopic actions are not the sole and dominant reason why bikes remain upright. We never said that gyroscopic actions were harmful. In fact, gyroscopic actions can indeed be helpful at times, especially if we desire a bike with good stability attributes. We acknowledge that gyroscopic action can be helpful, and so if stability is our goal it makes perfect sense to enhance the gyroscopic action. This enhancement is characteristically accomplished by adding mass to rotating components like tires. Also, in the case of motorcycles with engines, the acceleration or deceleration of engine speed can be sensed by the rider, and even used as a controlling variable in cases such as racing and airborne jumps.
A second way to decrease critical velocity is to add mass to the rear wheel, but the decrease in critical velocity will not be as dramatic as when we increase the front wheel’s mass.

A third way to lower a bike’s critical velocity is to increase somewhat both the head angle as well as the trail. Chopper motorcycles, with increased head angle as well as trail, have increased stability along with a reduced critical velocity.

A fourth way is to apply a negative torsional spring action to the front fork. See photo above. On a bicycle this can be done, for example, by attaching a stretched rubber (bungee) cord between the front of the steering neck stem and the seat post. In engineering terms this is what is called an over-centered spring, as the spring will tug the object to be turned in the direction of any turn, and more quickly than if the spring had not been in place. This may seem odd, but the truth is that when a bike is in motion, once the front fork starts to turn, then the turning action with an over-centered spring acting is quicker and the bicycle then responds more quickly. The base contact points steer more quickly in the direction of the turn and the front fork steering moves to restore equilibrium more rapidly. Thus, the bike more quickly comes back into an upright condition of equilibrium.

Should Bikes be Made to be Ultra-Stable?
In practice we seldom need or want bikes to be ultra stable, as the rider is ordinarily capable of augmenting the stability in keeping the bike upright and on path. Moreover, if we make a bike very stable, then the bike becomes less maneuverable. That is why it is so easy to ride chopper motorcycles on the open road going straight, but it becomes more difficult for the rider on a chopper to execute tight maneuvers. When we are using bikes daily and by skilled riders, the present design of bikes is quite satisfactory for most riders.
These remarks regarding stability are consistent with the findings of others. The Wright Brothers understood early on that in order to be maneuverable, and thus controllable, a heavier than air craft should be actually somewhat unstable. Lindbergh flew across the Atlantic in the Spirit of St. Louis which was by design, open loop unstable. Minorsky, in 1922, commented that naval engineers have long known that ships are easier to maneuver if they are somewhat unstable.
What About Recumbent Bikes?
Recumbent bikes, and we are speaking of those with only two wheels, tend to have longer wheel base lengths as well as other parameter changes, with resultant impacts on maneuverability. A discussion of the dynamics of recumbent bikes is beyond our objectives for this web site. We don’t consider recumbent style bikes for children trying to shed training wheels and ride regular diamond-frame shaped bikes.
Conventional diamond-shaped frame bikes are, in our clinical experience, more conducive for the learning child, especially as we necessarily focus on getting the child to use hand movements to maintain balance. Yes, recumbent bikes can also use hand generated steering movements but the lower center-of-mass combined with a longer wheel base mean that steering responses must be faster and with less tolerance for indecision. Recumbent bikes tend to fall (tilt) at faster rates and are less agile as the wheel base lengthens. This becomes evident to us in cases such as when riders accustomed to conventional diamond-frame “safety” bikes often experience difficulty upon first transitioning onto recumbent bikes. It is our belief that recumbent bikes require a higher level of rider skill, not less, and we certainly don’t start beginners out on traditional recumbent bikes. A day may come when we will experiment with a roller equipped recumbent, but until then we are satisfied with the diamond-shaped frame roller trainer for learning children. Improper upper body shifting, which is normally the result of training wheel exposure, needs to be extinguished as a behavior when first learning to ride, and so we need and use bikes with as forgiving attributes as possible. We believe that our Lose The Training Wheels™ adapted roller bikes are superior to anything else out there at present.
The Rocket Bike – Counter Intuitive Concepts
A simple and fun experiment that can be performed with a standard bike involves the use of a rocket. The strategy is to affix a small model rocket onto a handlebar to one side. The intent is that the bike will be pushed forward without rider, and the rocket will be ignited by remote means or by a timer or delay of some sort. When a bike is pushed off in a straight running line, and the rocket ignites, a steer torque is applied to the handlebars. The astonishing result is that the bike does not steer in the direction of the steer torque, but rather in the opposite direction. This astounding fact perplexes many onlookers. In essence, the bike turns in the direction opposite to the applied steer torque. This experiment demonstrates conclusively that the bicycle’s dynamic behavior is counter-intuitive from the perspective of handlebar steering actions.
Even skilled and proficient bike riders are often puzzled by the results of this experiment. The explanation lies in the fact that the rocket creates a steer torque which, yes, momentarily turns the handlebars in the direction as pushed by the rocket. This steering action in turn causes the base of the bicycle to steer in that direction. But now the bike has been forced into a lean because the ground contact support points have shifted by steering action or offset to one side, and – a lean away from the steer direction then results. It is this reversed direction lean, combined with the front fork geometry involving head angle, rake, and trail, which overpowers the rocket force and turns the bike’s handlebars into the direction of the lean – and opposite to the direction of the applied rocket torque.
In engineering terms we say that the bicycle exhibits counter-intuitive behavior. We can mathematically say, using the language of systems theoretic principles, that the bicycle exhibits “non-minimum phase behavior.”
The significance of the bicycle’s non-minimum phase behavior is that the bicycle usually does the opposite of what the intuitive mind would and might expect. As an example, if we want to steer right using handlebar actions as opposed to leaning, we actually steer first in the opposite direction, or to the left. Accident studies show that nontrivial numbers of motorcycle deaths occur in the case of less experienced riders – as when an obstacle or danger appears, the intuitive reaction is to steer away. But, in doing so the motorcycle sets up a lean towards the obstacle and the motorcycle invariantly impacts the object – and hence a serious collision results.
The proper emergency steering action is called “counter-steering,” whereby the skilled rider initiates a turn by turning towards the hazard. This action sets up a lean away from the hazard, and thus the rider can thereafter quickly and safely turn away from the hazard as a proper lean has been established. In addition, skilled motorcyclists will combine this action with an upper torso lean away from the hazard, in that sense “intuitive,” so as to as efficiently as possible extricate themselves from the hazardous circumstance.
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