Category Archives: Bicycle Science

The mystery of the bicycle

When a bike and rider are zipping merrily along, the mystery is that they seem to stay upright with relative ease, but common sense surely tells us that if nothing tangible is holding the bike and rider up — it must be quite possible that they could fall down? That makes sense now, doesn’t it?

In the process of learning to ride a bike, intangible matters such as faith and belief arise, as well as stability and balance in a metaphorical sense.

C. S. Lewis (1944) wrote in Perelandra, page 68, “There is no reason why a man on a smooth road should lose his balance on a bicycle; but he could.”

Our point is that there is a certain mystery about a bike. It seems to be so stable remaining upright, and yet common sense, if we actually examine matters, tells us that nothing visible seems to be holding the bike up. If nothing visible is holding the bike up, then it seems obvious that it might fall — unless we start to believe in the power of the invisible.

What Keeps a Moving Bicycle Upright

Other variations on the same question can be phrased as

•How Does a Bicycle Work?

•What scientific principles keep bikes upright?

•Why is it so easy to ride a bike once you have learned?

•Is there an invisible wall, as hinted by C. S. Lewis in Prelandra, (1944, p. 68) that prevents a bike from falling over?
The answers to these and varied questions can be either short or long. In China tourists are told a joke that a bike falls over “Because it is two-tired.”
A friend who is a retired professor of physics, University of Illinois, quipped that a bike works,
“Because you pedal it.”

These are some of the short versions. A somewhat longer version is provided by visiting the various sub-headings in this “Bicycle Science” section.

As a guide to this section, please be advised that it was written almost like a manuscript. Unless you are going for a specific result, our suggestion is that you start with “Intro” (introduction), and then move on down the line of sub-heading tabs from left to right.

The focus on this “Bicycle Science” section will be to present the almost three decades of bicycle related research (1983 to present) performed by Dr. Richard Klein at the University of Illinois in Urbana-Champaign.

The Naive Bike


In the next quest to determine more about the role of bicycle design as well as front fork geometry, it was decided to construct a bicycle with what we’ll call a naïve front fork. The frame has been modified to move the steering head forward, and to have the head angle be vertical (and thus at 90 degrees). Next, a front fork was created that caused the trail to be zero, that is, the point of contact with the ground coincided with the axis of rotation of the front fork. As a consequence, the friction and contact forces as might ever exist between the tire and the ground will act coincident with the axis of rotation of the front fork. Thereby no moment arm exists to induce any significant ground force generated turning moments on the front fork about the steering axis. We called this the Naïve Bicycle, as the bicycle is naïve in behavior and has no predisposition for the front fork to turn in spite of what the bicycle dynamics might be or even according to how the bike tilts.
Concerning the matter of gyroscopic actions, the use of two 12.5 inch tires mounted, one atop the other, caused a cancellation of all front fork precession as well as gyroscopic effects. Other than rider exerted torques by placing hands on the handlebars, this bike has been designed to have scant front fork torques. As a sticky point, we have not as of yet attended to the detail of counter-weighting the handlebars, so admittedly there would be a slight moment in turns due to the action of gravity tugging on the mass of the handlebars. Our plan is to replace the bent back handlebars with a circular-style steering wheel centered on the front fork axis. We note that the center of mass of the front fork is presently behind the steering axis, and thus if the Naïve Bike were to lean – the tendency of gravity action would be to turn the front fork away from the lean causing destabilization. To preliminarily test this shortcoming, the Naïve Bike has been ridden with the handlebars turned 180 degrees, in essence with forward center-of-mass, and the bike is still rideable. Another possible front fork torque could be argued to be due to aerodynamic actions; however we feel that aerodynamic aspects are not significant.

The experimental findings and significances of the Naive Bicycle are many. First of all, the Naïve Bicycle is easily capable of being ridden, meaning that an array of persons of relatively average abilities can and have ridden this bike. Another way to say it is that the bike has always been capable of having been ridden, as every person trying has been successful. Of course, the rider must keep hands-on. No able-bodied adult sized person has ever failed, and hundreds of persons have ridden this bike. The first inference is that precession is not essential in order for a bicycle to be ridden. The second inference is that front fork geometry and trail, in particular, are not critically imperative in order for a bike to be rideable. Moreover, as illustrated by the Naïve Bike, the combination of zero precession and zero trail of the front fork also result in a bicycle configuration that is easily rideable.

Close examination of the front fork on the Naïve Bicycle will indicate the presence of an additional tire axle slot. In short, the front fork was designed such that the two smaller wheels can be removed, and replaced with a single conventional full-sized front wheel. Doing so then restores the precession effects of the front wheel. Engineering students reported in experimental trials that this bicycle, with zero trail but with a conventional balloon style tire on front, was capable of being ridden “no-hands” by a skilled rider. The inference is that when sufficient gyroscopic front wheel action exists that (1) a controllable front fork torque can be induced based on upper body leaning, which in turn, causes a lean reaction of the frame of the bike, and (2) that the front wheel’s gyroscopic properties are sufficient to prevent or at least make controllable any front fork wobble.

Zero Gyroscopic Bike 2


Zero-Gyroscopic Bike II was built at the University of Illinois by three students in the mid-1980’s. Its purpose was to see if a Zero-Gyroscopic Bike could be designed that could be ridden with “no-hands.”
Once the rideability of Zero-Gyroscopic Bike I was established; that precession wasn’t a superior godhead, another question arose – Is it possible to devise a zero gyroscopic bike that can be ridden no hands? University of Illinois undergraduate students in Mechanical Engineering proceeded to design such a bike to test this hypothesis, called Zero-Gyroscopic Bike II. Emphasis in the design was to use two smaller wheels on the front fork, 12.5 inch scooter tires, and a modified front fork as shown. Moreover, the upper front wheel was mounted onto two slider rods thus permitting adjustment of the center of gravity of the front fork assembly.
This bike, quite similar to Zero-Gyroscopic Bike I, was also found to be quite easily rideable, provided the rider kept hands on the handlebars. Students at the time reported that the Zero-Gyroscopic Bike II bike was rideable “no-hands,” but only for brief instants. With body articulation, one could cause the bike to initiate a turn in the usual manner, but a front fork oscillation (often called a “wobble”) would characteristically result. In essence, the Zero-Gyroscopic Bike II defied being ridden no hands for any appreciable distance. In short, it seemed that the Zero-Gyroscopic Bike II lacked a mechanism to dampen any front fork rotational inertia, with the result that a wobble was frequently induced in the process of riding. In the no-hands mode, it was beyond the rider’s ability to control or dampen the resultant front fork wobble.
Other students in subsequent semesters attempted to modify Zero-Gyroscopic Bike II by adding front fork torsional damping, however the results of that experimental effort had to be curtailed at the time due to cost considerations and the difficulty of fitting the bicycle with the proper hardware for torsional damping. In short, we ran out of available time and resources as this work was performed subject to a class schedule where other priorities took precedence. Until it is experimentally proven (validated) or disproved, we will stand by the following:
Conjecture: A zero precession bicycle of the form of Zero-Gyroscopic Bike II is capable of being ridden in a no-hands configuration provided that the front fork can be fitted with a properly sized and adjusted torsional damping mechanism.

Zero Gyroscopic Bike 1

Zero-Gyroscopic Bike I -- A Fundamental Bicycle Experiment

Zero-Gyroscopic Bike I — A Fundamental Bicycle Experiment

Zero-Gyroscopic Bike I is a clever and yet simple experiment that dispels once and for all the centuries old conventional wisdom that a bike stays upright primarily due to the gyroscopic action of the two rotating tires.
The two additional or upper wheels are positioned on this bike so as to rest on the regular two lower wheels. Based on simple frictional contact between the two respective pairs of wheels, the upper wheels attain essentially equal but opposite rotation when forward motion of the bicycle is initiated. In the process of being ridden, the gyroscopic torques present and associated with spinning wheels will experience a precession cancellation effect whenever the bike rotates (yaws) or leans or when the front fork is turned. That is to say, the precession torques are still present and act on the frame and front fork assembly, respectively, however the double wheel pairs rotating in reverse directions to each other cause all precession torques associated with spinning action to be cancelled. In essence, this bicycle as configured can said to be a zero precession bicycle.
Because “precession” is an action, frequently lay people without sufficient technical background tend to become confused. The gyroscope on the other hand is a physical and familiar thing, so if we speak of gyroscopic action, the lay public tends to have a sense of what is being discussed. Hence, in many of our writings, as well as here, we will refer to bikes with precession canceling or even precession altering characteristics as “zero gyroscopic,” but we admit that this is technically in error. The action of a gyroscope can’t be made to equal zero. Newton’s Laws as well as conservation of angular momentum are stalwart pillars of classical science and mechanics. Instead, we do note that two gyroscopes can be designed to counter rotate on the same shaft or on parallel shafts so as to negate or cancel each other. The result is as if the combination of gyroscopic actions was “zero” but the gyroscopic action is only canceled out by clever design of opposing gyroscopic actions.
The empirical significance of Zero Gyroscopic Bike I is that the argument advocating sole dependence upon the “gyroscopic action” for stabilization of a bicycle is smashed and thrown out the window. Not only is the Zero Gyroscopic Bike I rideable, it is in fact, easily rideable. Hundreds of average persons, and even some fairly novice bicyclists, have ridden this bike. Other than being slightly heavier and bulkier due to the two additional wheels, this bike acts almost indistinguishable in handling as compared to a conventional bike.
Jones was the first, to our knowledge, to experimentally investigate precession cancellation as related to bicycles. We note, however, that UIUC Zero Gyroscopic Bike I, circa 1986, was the first to embody a technique that would cancel the gyroscopic torques at all operating speeds. Moreover, Zero Gyroscopic Bike I cancelled not only the front fork gyroscopic component, but also that associated with the rear tire. Of course, we routinely encounter ardent believers in the right hand rule who claim that our experiments are lacking in validity as the sprockets are still turning and even the legs of the rider, when pedaling, create the equivalent of a rotational gyroscope. Such arguments of desperation of this kind are easily silenced – merely by riding the Zero Gyroscopic Bike I in a coasting mode. Leg action ceases, and the sprockets and chain aren’t moving. The Gyroscopic Bike I is easily ridden while in the coasting mode.
In our archives, for those who doubt or those who just want fun, we have the written transcript of a lengthy interview with a fire and brimstone young Ph.D. in physics, an assistant professor of physics at a major Midwestern land grant university, circa 1985. The “professor” professed and defended the exclusive role of precession and gyroscopic action down to the last minutiae – in asserting that precession/gyroscopic alone was the sole mechanism responsible for keeping bicycles and motorcycles upright. He even went on to say that he’d bet $5 that UIUC Zero Gyroscopic Bike I, as proposed on paper the time of the interview, would be impossible to ride. He added, “Of course, unless one was a Chinese acrobat.” He would bet only the $5 amount as he said that he was too impoverished as a brand new PhD to bet more.
The only significant handling difference discovered in riding trials, compared to conventional bikes, was that the Zero-Gyroscopic Bike I was not capable of being ridden “no-hands.” We hypothesized that the additional front wheel, being extended in an upward and forward position, had caused the mass of the front fork assembly to be increased and also that the center-of-mass was shifted forward (as measured relative to the location of the steering axis). As a consequence, if the Zero-Gyroscopic Bike I were to go into a tilt, we reasoned that the action of gravity caused the front fork to turn excessively into the direction of tilt, and thus the bike was not rideable in the “no-hands” sense.

Precession and Gyroscope Issues

Precession is a scientific word that describes how a spinning wheel reacts if the axis is tipped or rotated in space. Given a tip in the axis of spin, the spinning wheel will exhibit precession meaning that the axis will tend to want to tip in a direction 90 degrees to the initial axis tip. Moreover, the direction of tip is dictated by what physicists and experts in mechanics refer to as the right-hand-rule. This tendency to exhibit precession has to do with the principle of conservation of angular momentum. In lay terms, it means that any spinning object has gyroscopic tendencies, and that the object is more stable about its spinning axis, and yet if forced to tip or deviate, then precession will cause an action in a direction 90 degrees to the initial axis.
Scientists and experts elsewhere have made similar claims regarding how the bicycle is critically dependent upon gyroscopic principles and the right-hand rule so as to remain upright, but we’ll defer from going down that path in the interests of brevity. We will mention experiments to be described later, specifically involving Rear Steered Bicycle I. If gyroscopic arguments constituted the primary stabilization mechanism for a bicycle, then it would appear to matter little if the bicycle was steered by the front wheel, or the rear wheel. The experimental record reveals evidence quite the contrary. Rear Steered Bicycle I has a nearly 20 year history of defying being ridden successfully in spite of exhaustive attempts, in cases including some skilled would-be riders.
A predictable outcome of somebody “scientific” explaining or demonstrating precession with the aid of a weighted wheel and a rotating stool or platform, is to be prone to conclude by saying, “And this is why a bicycle works.” Unfortunately, this scenario is more common than not among high school and university level physics instructors, as many teaching schools have access to a weighted bicycle tire capable of being spun on an axis (a handle), as well as a precision stool for the demonstrator to sit on while holding the spinning wheel, or possibly a rotating platform on which to stand. We state that the wheel used in these “demonstrations” is usually (and unfairly) weighted as the tire used is constructed of solid rubber, and thus with greater mass than, say, a conventional pneumatic tire. A central problem is that these “scientists” failed to do one thing – to test the conjecture or hypothesis with an actual experiment involving a complete bicycle, and where some type of valid control was devised to test the hypothesis.
An English chemist, Dr. David Jones, in the late 1960’s, performed an array of simple bicycle experiments, published in Physics Today on April 1st (Jones, 1970). A dominant feature of one of Jones’ experimental bikes was that he mounted an auxiliary spinning wheel on a bicycle’s front fork that was able to spin clear of the ground. Jones could spin the wheel in either direction and at various speeds, and yet the bike was discovered to be still rideable and independent of the resulting angular momentum magnitudes. Aside from the publication date being April Fool’s Day, Jones went on to shock the world of bicycle and physics aficionados by making several points: (1) In spite of Jones’ efforts to cancel or alter precession and thus gyroscopic action, Jones’ experimental bikes, and in all variations tested, were quite capable of being ridden. (2) Jones sought to discover how to design and build an unrideable bike, but he failed in that quest.
Dr. Richard P. Feynman (1918-1988), Nobel laureate of physics fame made the statement (paraphrased) – “Experiment is the ultimate authority.” In keeping with this spirit, Dr. Richard Klein initiated a number of bicycle related experiments in conjunction with students at the University of Illinois at Urbana-Champaign (UIUC), Department of Mechanical and Industrial Engineering, starting in 1983. Some these UIUC experimental bikes and conclusions are described below.

Rear Steer

This section is the direct continuation of the discussion in the previous section, “Gyroscopic.” We continue our scientific quest to investigate the bicycle.
In the process we will start by introducing a term called “Critical Velocity.” Once we have that definition in hand we will next look at the front fork, and in particular, what forces and torques control the behavior (the turning) of the front fork. The “Critical Velocity” is defined as the velocity at which a bicycle becomes stable in and of its own properties — and without the need for human intervention to otherwise prevent falling over. In short, if a bicycle is traveling at too low of a speed, it will fall over. Once Critical Velocity is reached, the bicycle will remain upright on its own.

This section goes into experimental aspects of a discussion necessary in order to get to the mysterious concept of critical velocity of a bicycle.
Understanding the Front Fork Hierarchical Chain of Command
When a front-steered bicycle is being considered, the torques acting on the front fork have a pecking order or hierarchical chain of importance. Rider applied handlebar torques are dominant and the king. Next in line, but relatively far behind, are the castor-camber forces, these being the results of the ground contact forces which act on the front tire. The third in line, but somewhat close to castor-camber torques in magnitude, is the front wheel’s gyroscopic reaction torque. In essence, it is the castor-camber forces along with precession that cause a bicycle’s front fork to want to turn into the direction of fall or tilt. Gravity, inertial, head bearing friction, and aerodynamic torques also come into play but they are usually lower down yet in order of magnitude.
When a bike is ridden “no-hands” it happens that the king is asleep, and hence the secondary and even lesser torques are allowed to come into play. These secondary and lesser torques are relatively weak, and as such one has to be a little more delicate as well as less aggressive. That is why it is important to ride a bike “no-hands” with a degree of finesse, and that we usually tend to make our upper torso lean moves sufficiently in advance, such as riding a bike “no-hands” when a turn is anticipated.
Another reason why a rider has to be more cautious in the no-hands riding mode is that the human’s neural delay for upper torso movement is approximately 0.3 seconds, whereas the neural delay associated with hand and arm movements is faster, typically 0.1 to 0.2 sec (Weir 1972). Moreover, the use of upper torso leaning is further exacerbated as the dynamic response of the bicycle to body leans is relatively slow as compared to steering control that is handlebar actuated.
As a point of clarification regarding aerodynamic torques, if we would ever elect to use a full cover front wheel, which seldom happens in practice and for good reason, the aerodynamic forces can in certain circumstances be intensified, as well as being destabilizing.
Rear-Steered Bicycles
University of Illinois undergraduate students in the 1980’s went on to conduct additional bicycle experiments. Perhaps the most notable, in addition to fun, is what we call Rear Steered Bike I.

Rear Steered Bike I



Travis Williams, a scholarship athlete at the University of Illinois gives a try on the unrideable challenge bike — under the watchful eye of Dr. Klein. Travis tells us that our prize money is quite safe.

Rear-Steered Bike I has never been ridden, although hundreds of average and even skilled riders have tried. The best attempt made so far occurred in the 1980’s when the bicycle was placed on loan for about one month to the then president of the University of Illinois Unicycle Riding Club. With practice the rider, a skilled unicyclist, was able to eventually remain upright on the bike, but in doing so the rider had to do two things:
1.Configure the chain connecting the handlebars and the rear fork in a conventional circular loop, as opposed to being in a “figure 8” or crossed which is the usual connection configuration. See photo below of the connecting chains in the crossed configuration.
2.The rider ended up riding haphazardly in an open and flat parking lot as opposed to being able to follow a prescribed path.
Being able to follow a prescribed path is one of the requirements in order to qualify for the US$5,000 prize. In addition there are additional requirements, all quite reasonable but nonetheless bike riding challenge requirements must be adhered to. The contribution of John Becker, former University of Illinois graduate student in Mechanical Engineering, is acknowledged as it was through John’s effort that this particular bike was built.
As the photos show, this UIUC bike has been through its share of trials and tribulations. Hundreds upon hundreds of overly optimistic riders have tried for the prize reward — but to no avail! Our money is very safe. We’ve hauled and crated this popular bike to seemingly countless shows and exhibitions across the nation. We never fail to attract attention as well as suckers who think that it’s easy to ride. In short we have tons of fun just laughing as this bike draws would-be riders like a pile of hundred dollar bills flying about in the wind draws all who want to scoop up what then can grab.




Robot Bike

The UIUC Robotic Bike was build in collaboration with students at the University of Illinois. The bike evolved from an idea to a full-fledged prototype over the course of three consecutive semesters circa 1987 and 1988.


UIUC Robotic Bike. We believe that this bike, designed, built, and successfully tested in the era 1988 by UIUC engineering students, constituted the world’s first successful robotic bike. The Robotic Bike operates under the premise that it is above critical velocity, and thus is effectively “no-hands.” The bicycle is “fooled” into thinking that it is in a lean — and the castor-camber effect will turn the front fork into the direction of “lean,” really the lean or camber of the front steering head. The camber angle of the steering head is dictated by a radio controlled servo-system. Note that the Robotic Bike has no handle bars and not even a seat, as it doesn’t require a rider. Affiliate Bill Becoat admires the design and details.


More Details of the design. An automotive window cranking motor, reversible in direction, is driven by a radio circuit, commanded by an external radio signal. The motor drives a chain and sprocket and thereby controls the tilt or “camber” of the front steering head tube. By controlling the camber, the front fork will turn into the direction of camber. This design causes the Robotic Bike to act in an intuitive fashion.


Robotic Bike Drive Mechanism. The Robotic Bike used a friction drive where the driving power came from a 12 volt starter motor used for starting model airplane engines, driven by an appropriate 12 volt battery. Note the chains taped to the rim (wheel) of the rear tire. We found this to be necessary so that the rear portion of the bike would be quasi-stable in inertial space. The rear half of the bike remained where it was, and the front fork cambered or tilted. Without the chain on the rear wheel, the bike would tend to “squat” as the front would tilt one way, and the rear would tilt the other way. This Robotic Bike had to be above critical velocity, which was “fast.” The students were not able to run alongside this bike when it was operating at full speed. We estimated the speed at about 18 MPH. In the sixteen years since its inception, this bike has fallen into disrepair, but we have video tapes of it in action, as well as having been featured on media television programs.

We need to note or comment that hands-on science is fun. Theories are called theories, because they are just theories. When we built experimental bikes, we let the reality of the experiments drive the outcome. This is what the Wright Brothers did, and it is what we did at the University of Illinois. Little details such as the need for chain on the rear tire to increase its gyroscopic stabilization wasn’t obvious in forward vision, but vividly clear in hind-sight.

A colleague at the University of Illinois, Dr. Doug Marriott, had a saying, “Build it wrong, but build it.” Far too many students in today’s world of academia and memorization are afflicted by what we can call, “Paralysis by analysis.”

Torque Wrench Bike

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

The bicycle’s forward speed was measured with a standard bicycle computer.
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.

  • Steer torque was measured by the rider by use of a standard mechanic’s torque wrench affixed to the head of the handlebar stem.
  • 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.
  • 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.