To respond to the Do Now, you can comment below or tweet your response. Be sure to begin your tweet with @KQEDEdspace and end it with #DoNowBike

For more info on how to use Twitter, click here.


Do Now

How did you learn how to ride a bicycle or what was the hardest part of learning? What would you change about how today’s bicycles are designed?

Introduction

Learning to ride a bicycle is a strong memory from many of our childhoods. Bicycles have been around since the 1800s, although their design has changed from the earliest models. The Draisienne is one of the earliest two-wheeled machines. Made out of wood, it had two wheels of the same size mounted in a frame and handle bars to steer. There were no pedals, so people pushed themselves along with their feet.

The next model to come along was the Velocipede or Boneshaker in the 1860s. It was similar to the Draisienne, however it had pedals added to the front wheel. The wheels were still made of wood, and later metal. This bicycle earned its name “Boneshaker” from the movement riders received when pedaling over the cobblestone roads present during that time.

The High Wheel bicycle had popularity in the 1880s. With one huge rubber tire in front and a smaller one in back, they were easy to ride and fast, but dangerous. Because of the large front wheel and the rider sitting high up, anything to stop the motion of the front tire, including brakes, often caused the back of the bicycle to flip up and over.

Bicycles more like we are used to today–the Safety bicycles–were developed in the 1890s. With two same-sized inflated rubber tires, pedals in between the two wheels and a chain drive, these bicycles were easy to ride and much more comfortable. They became all the rage. Today there are 1 billion bicycles worldwide. Scientists are now studying the process of how we balance while riding a bicycle with the hopes of designing an even more efficient model.

Resource

KQED QUEST segment The Science of Riding a Bicycle
Riding a bicycle might be easy. But the forces that allow humans to balance atop a bicycle are complex. QUEST visits Davis – a city that loves its bicycles – to take a ride on a research bicycle and explore a collection of antique bicycles. Scientists say studying the complicated physics of bicycling can lead to the design of safer, and more efficient bikes.


To respond to the Do Now, you can comment below or tweet your response. Be sure to begin your tweet with @KQEDedspace and end it with #DoNowBike

For more info on how to use Twitter, click here.

We encourage students to reply to other people’s tweets to foster more of a conversation. Also, if students tweet their personal opinions, ask them to support their ideas with links to interesting/credible articles online (adding a nice research component) or retweet other people’s ideas that they agree/disagree/find amusing. We also value student-produced media linked to their tweets. You can visit our video tutorials that showcase how to use several web-based production tools. Of course, do as you can… and any contribution is most welcomed.


More Resources

Instructables resource How to Build Up a Bike
This is a guide to building up a bike from parts. It should help you get the parts and tools you need to get you pedalling along in no time. It assumes that you have tinkered with your bike, but are not an expert. Hope it helps!

QUEST video How to Build a (Research) Bicycle
View a captioned slideshow about how the research bicycle was built that is featured in the QUEST story The Science of Riding a Bicycle.

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  • Calvin Hulburt

    It seems that science can’t explain how a bicycle stays upright while moving. Perhaps that’s because once they do there will be no more grants to study how one rides a bicycle. Science has long known that when a bicycle tips, the acceleration of the falling mass produces a longitudinal force pushing the bike in the direction of the fall. Engineers have been able to design bicycles to have longitudinal compliance in the front wheel and stiffness at the rear so the bicycle steers into a fall. The rider needs to do very little as the bike is designed to follow where his mass dictates.
    Academics are not scientists and the bicycle is a product of engineering. Before making another highly flawed video, I suggest you look outside the ring of Whipplites.

    • Andrew Dressel

      Oh Calvin,

      Your determination is admirable, but until you make a prediction that can be tested, either by equation or experiment, you are just wasting your time and everyone else’s. In the mean time, science can explain quit well how a bicycle stays up. That’s how the two-mass skate bike ended up with an article in the journal Science: http://science.sciencemag.org/content/332/6027/339

      Someone wondered if a certain bike with no trail and no gyroscopic effect would be self-stable, the equations describing the Whipple model predicted that it would, then they built the physical bike, and it confirmed that prediction. That’s how science works.

      • Calvin Hulburt

        And among this faith based physics crowd we have the cheerleaders who cannot read critically. The experiment mentioned only demonstrated that when a bicycle steers to stay upright the camber force acts to yaw the bike when the slip angle force is removed from the front wheel. The conclusion made was just one of several flaws in that paper.

        • Andrew Dressel

          Hmmm. How do you suppose that slip angle force is removed from the front wheel but not camber force, and are you also asserting that slip angle force is not removed from the rear wheel? How is this implemented?

          Meanwhile, where are the alternate predictions that can be tested instead?

          • Calvin Hulburt

            When a bike falls over the center of mass is forced to move laterally. This modifies the motion of the bicycle so that with each tip the velocity vector swings to either side of the straight ahead position. The trail forces the front wheel into alignment with this vector. Since the plane of the wheel is aligned with the direction of travel the slip angle is zero and there is no force. The slip angle forces arise because the camber force, which is primary, pushes the bike sideways but pushing a wheel sideways quickly generates an opposing force. The front wheel cannot generate this opposing force but the back wheel does because it is fixed with the frame and its plane and direction are different. Because the back wheel is laterally rigid and the front compliant, the bikes design cause the front to move toward a tip while the back contact becomes the pivot. The camber force is the reaction to a lateral acceleration and acts to push the bike sideways. The slip angle forces are control forces that oppose the camber force but by this trick the front of the bike has more lateral motion and yaws into a fall. The value of Koojiman et al is that their design did not use trail but removed the front slip angle by means of the double inverted pendulum which can only work if the bike tips thereby demonstrating that the camber force is what causes the bike to change direction when the front slip angle disappears. The design, I believe, was first conceived as a way to demonstrate that a weight forward of the steering axis caused a bike to steer. This is not a significant factor because the force aligning the wheel with the direction vector is far greater. Nonetheless, it is clear from the paper that the model predicts an unstable design whenever the torques about the steering axis are zero. Since the model does not include the lateral degree of freedom it cannot include the actual steering torque and so stability predictions based on the model are wrong. Since the model is more demanding than nature predictions of what will work will be better than what won’t. Another problem with the model is the need to countersteer which does not occur in reality because leaning modifies the forward direction and the frame will be directed to the outside of the turn. Because the model does not have a lateral variable, it cannot employ the actual method by which cyclists do change direction.

          • Andrew Dressel

            With all the other factors generating moments about the steering axis, such as gyroscopic effect and gravity, why should we suppose that the slip angle is exactly or even near zero? Does this happen on every bicycle at every speed?

            How do you account for bicycles that are not self-stable or that cannot be ridden no-handed? Why isn’t their slip angle magically zero as well.

            How do you account for bicycles that are self-stable, but only above a certain speed?

            All of this is accounted for by the Whipple model, and given the dimensions and mass distribution of a particular bicycle, it can predict with high fidelity if and when that bicycle will be self-stable.

            Do you have a model that can predict anything?

            Why do you assert that the camber force is “primary”, which I am guessing means that it dominates? Have you measured the relative magnitudes of corning force and camber force in a bicycle tire?

            What on earth “double inverted pendulum” are you talking about in the two-mass skate bike?

            What “lateral degree of freedom” does the model not include?

            Finally, are you actually stating now that countersteering does not occur? That is sure that it sounds like you mean when you write “another problem with the model is the need to countersteer which does not occur in reality.” Do you realize that just about everybody and their brother now has autonomous bikes or robots riding bikes? Do you seriously believe that they are all working without countersteering, but that they are just keeping that a secret?

            What’s next? NASA didn’t actually put a man on the moon?

          • Calvin Hulburt

            You seem to wish to distort everything I say into nonsense but I suppose you have your reasons. The notion of a slip angle force is one of vehicle dynamics and not physics so I will state it simply as I can. When the plane of a wheel is not aligned with its forward direction the angle between the velocity and the plane is the slip angle. For small angles the side force generated is proportional to the angle so that up to about five degrees the force increases with the slip angle.When you steer a car you turn the wheel and create a slip angle such that a force pushes on the side of the tire and a yawing moment exists to change the direction of the vehicle. This is the notion of steering that the Whipple equations rely on. The central idea is that the lean angle can be controlled by the steering angle. If a rider is not present the moments that are there to cause the front wheel to steer the bike are the gyroscopic moment, the weight of the front frame center of mass forward of the axis, and the normal force.

            The normal force cannot, in fact create a moment to steer the wheel when it is in line with the frame because there is a balancing moment due to the camber force. When a bike tips gravity is pulling the bike down but the frame forces acceleration to the side. Because of inertia the normal force aligns with the bike frame and the normal force vector rotates with the bike frame.

            The gyroscopic moment is a weak force at bicycle speeds and is dependent on the rate at which the bicycle falls. The angular velocity is determined by the inverted pendulum position. Near upright this is small and this moment is not sufficient to steer the bike. Jones, Koojiman, and others have verified this.

            The third moment is the weight of the front frame forward of the pivot axis. This is a small force as well and with my four variable model it made no significant difference. I verified this with an actual bicycle when I built a center steering front hub with the brake mounted behind the steer axis. This was one of the most stable bikes I had ever ridden and was especially steady on fast down hills.

            You can create a slip angle force by steering as I stated above by changing the plane of the front wheel in relation to the velocity vector. Alternatively, you can change the velocity vector in relation to the plane of the front wheel. This second method is how a single track vehicle keeps itself upright. Listen closely, so i won’t have to explain again why countersteering is not needed. A bicycle can lean. Consider what this means to the direction of the velocity. You are travelling straight ahead and moving laterally as well. The two motions combine so that every time you lean one direction or another the velocity vector swings to either side of forward. When the bike falls to one side the velocity is altered but the wheels are still aligned with the frame. Slip angles are created by altering the velocity in relation to the planes of the wheels. The rear wheel is fixed but the front wheel is not so any slip angle at the front is eliminated because the trail can push the wheel into alignment with the velocity vector. If you watch the front wheel you will see that it faithfully follows the velocity direction.

            When a bicycle steers it is not because a slip angle has been created but because one has been eliminated. The bicycle tips to one side accelerating the mass laterally and the camber force at the roadway pushes the bike in the direction of the acceleration. If the front wheel did not steer the slip angle forces would prevent any significant side motion and the bike would fall over. But the front does steer as I have stated above and when this occurs the camber force acts at the front but not at the back causing the bike to yaw into the fall and recover.

            For some reason, you wish to alter what I have said about countersteering. I am not saying that countersteering will not cause the bike to fall into a turn, I am simply saying that you do not need to counter steer to initiate a turn. You would if the Whipple model were correct but at best it is half correct as it represents only half of the important variables. Perhaps, two fifths as pitch becomes significant in cornering. With countersteering you are pointing the plane of the wheel to one side of the velocity vector. As stated above you can alter the velocity vector by leaning and accomplish the same thing. At the same time you must inhibit steering so that the bike does not simply recover. These are the two methods of changing direction on a bike and both have been employed in RC motorcycles.

            An alternate way to consider the slip angle force is to consider how difficult it is to push a wheel sideways. As the wheel moves the bike will move slightly to the side under a force. The faster the speed, the easier it becomes to push because the force/ angle relationship is fixed but the angle is the ratio of lateral to forward velocity.

            Camber is one of those misunderstood ideas due to auto tire testing and Foale. It is not a property of tires as concerns the bicycle of motorcycle. Employ the simple physics you learned in high school and do a free body diagram of the bike falling over. You will discover that the angular acceleration is position dependent. The force at the road can be determined to be W times the tangent of the lean angle. When the bike is near upright we can regard this angular acceleration as lateral and any lateral acceleration will be associated with this force. There are three ways that a bike can move laterally. It can fall over, move to the side or fall into an arc and accelerate centripetally. By considering the case of an accelerating reference frame you can prove that the accelerations do not add but can only replace one another. This is what happens as a bike falls and recovers. I consider this force primary because it occurs due to the inertia of the bike and its motion while the slip angle force resists and controls this force.

            As an engineer, I have spent spare time building bicycles and once created a model in Quickbasic on my 486 computer. I have been considering taking the time to enter this program into Excel and distribute it so others can make their own assessments of design. For my part I found that the current design is very robust and small variations are not that important. Generally, improving the stability borrows on ease of control.

            I am currently designing an electric powered recumbent with a solar recharge. My plan is that the bike should use the minimum energy possible to arrive at work or shopping, allow the sun to recharge the batteries during the day and have sufficient range to get home. I am hoping for a top speed of 45 mph and a range of thirty miles. Because of aerodynamic considerations there are no pedals.

            I also have plans to build another recumbent. It will be a short wheelbase type with the drive contained in the central frame. It will have hub center steering and an aerodynamic seat design. I have built bikes with linear drives and standard cranks and have a design that better employs the thigh muscles in a seated position. The seat height is just above the knee joint. I have found that this raises the rider enough to easily get on and off and be eye to eye with drivers.

            I see by your silly Moon Landing reference that you believe scientific truth is in what is published and no where else. Science is a method of investigation and the literature is full of flawed ideas, especially on this subject. What does it gain you to predict something based on a flawed model. A broken clock is correct twice a day but relying on it will lead to disappointment. For those that trust authority over science, there is always Wikipedia,

          • Andrew Dressel

            Let’s ignore all the pedantic lecturing for now and get right to testing an assertion you make in paragraph 2:

            “Because of inertia the normal force aligns with the bike frame” and so
            “the normal force cannot, in fact create a moment to steer the wheel.”

            This is only correct if you model the bike as a point mass on a massless rod. In that case, the mass moment of inertia is merely mL^2, where m is the total mass, and L is the length of the rod, and the resulting ground reaction force does always align with the stick.

            Real bikes, however, are not well modeled by a point mass on a massless rod. We can still make a simplifying assumption, and use the inertia of a plate pivoting about an edge. In that case, using m again for the mass and 2L for the height, so that the height of the center of mass is still L, the mass moment of inertia is (1/3)m(2L)^2 = (4/3mL^2).

            I guess the additional 1/3 might not seem like much, but since everything else remains the same, it is enough to cause the resulting ground reaction force to no longer align with the midplane of the plate (our improved simplified bike model). Therefore, in the case of finite trail, a steering moment develops with the lean angle, and my rough calculations show it easily steering the front wheel in the direction of the lean.

            That’s all I have for now, but I’ll keep looking.

          • Andrew Dressel

            Next, let’s skip over paragraphs 3 and 4, for now, and take a look at your assertions about tire behavior in paragraph 5.

            I believe it is a misinterpretation and/or misunderstanding of slip angle and corning force to suppose that a bike rolling to the right will slip to the right, and the front wheel, if it is free to rotate about the steering axis, will therefore steer to the right to eliminate with this slip angle.

            Instead, as Pacejka illustrates with the brush model in chapter 3 of his “Tyre and Vehicle Dynamics”, slip angle is the angle between the direction the wheel is pointing and direction the bottom of the rim is moving as it places tread elements on the pavement. Neither the location nor the velocity vector of the center of mass are mentioned because they are irrelevant to the model. All that matters is the path traced by the bottom of the rim as tread elements come into contact with the pavement.

            Here are Pacejka’s words, edited for brevity, and available on google books on page 93-95 of the second edition:

            “As the tyre rolls, the first element that enters the contact zone is assumed to stand perpendicularly with respect to the road surface. … The tip of the element will as long as the available friction allows adhere to the ground (that is, it will not slide over the road surface). … At the same time, the base point of the element remains in the wheel plane. … The resulting deflection varies linearly with the distance to the leading edge and the tips form a straight contact line that lies in a direction parallel to the wheel speed vector V.”

            Thus, one simplistic way to think about the behavior of a bike rolling to the right as it moves forward is that the center of mass continues in a straight line due to inertia, and the contact patches veer to the left, creating a slip angle to the left of the wheel plane and a cornering force to the right. In the presence of positive trail and the absence of any other factors, this would cause the front wheel to steer to the left.

            Another simplistic way to think about this scenario is that rolling to the right requires a rightward ground reaction force to produce the rightward acceleration of the center of mass. This rightward ground reaction force causes individual tread elements to deflect to the right as the tire rolls forward, and the bottom of the rim to moves to the left as it places subsequent tread elements, and this corresponds with a leftward slip angle and a rightward corning force, as before.

            Of course, a rightward lean also causes the tire to produce rightward camber force. The relative magnitude of these two forces depends on the relative stiffness, corning and camber, of the particular tire on a particular rim at a particular inflation pressure. There is a hypothesis that in a steady-state turn the camber force should be sufficient to align the net ground reaction force with the midplane of the wheel, but physical testing has yet to confirm this conclusively.

            If you have some deeper analysis or physical experimentation that eliminates or at least controls for all the other possible contributors to the resulting moment about the steering axis and records the results from instrumentation, I’d love to see it. Based on what you have written here, however, I believe you are as mistaken about this as you are about the direction of the net ground reaction force.

          • Andrew Dressel

            Let’s set aside the disagreements about what causes the bike to steer in what direction for a moment, and skip down to paragraph 7, which contains this whopper:

            “I am simply saying that you do not need to countersteer to initiate a turn.”

            And let’s get the “he said/he said” stuff out of the way first.

            – On April 5, you wrote “another problem with the model is the need to countersteer which does not occur in reality.”

            – Later that same day, I wrote “are you actually stating now that countersteering does not occur?”

            – And then, on April 6, you wrote “for some reason, you wish to alter what I have said about countersteering. I am not saying that countersteering will not cause the bike to fall into a turn, I am simply saying that you do not need to countersteer to initiate a turn.”

            I have not altered anything you said, nor can I. It is common, however, when one wishes to clarify a point made by another, to restate the point in ones own words to see if the two share a common understanding. To that end, I rephrased “countersteer which does not occur” as “that countersteering does not occur”. I still don’t see the difference, but your follow up certainly does clarify things, and they are worse than I thought.

            Asserting that “you do not need to countersteer to initiate a turn” is probably worse than asserting that “countersteering will not cause the bike to fall into a turn.” because nobody with half a brain would fall for the latter, but the former is a dangerous meme that keeps popping up on various discussion forums.

            So, let’s take a look at the reasoning you give for your bold statement. The most I can find is “as stated above you can alter the velocity vector by leaning and accomplish the same thing.”

            It seems that you are saying, and I’m just paraphrasing here to see if I have it right, that countersteering is not need to cause the lean necessary to negotiate a turn because you can just lean instead. You logic causes the picture of a circle to come to mind.

            Let’s back up and consider all the ways that a bike can be caused to lean:

            1. Wait for random perturbations in air flow or pavement to push it out of the upright unstable equilibrium and hope that it is in the desired direction.

            2. Give the bike an explicit impulse of linear momentum to the side or angular momentum about the roll axis from an external source, such as a cross wind, a bystander, or a guardrail, I suppose.

            3. Perform an acrobatic maneuver “by applying appropriate torques between the bike and rider similar to the way a gymnast can swing up from hanging straight down on uneven parallel bars, a person can start swinging on a swing from rest by pumping their legs, or a double inverted pendulum can be controlled with an actuator only at the elbow.” (from Wikipedia)

            4. Steer the front wheel to one side to cause a roll torque in the opposite direction.

            Which one do you use?

          • Andrew Dressel

            Okay, one more: paragraph 9.

            “Camber” [force? or stiffness?] “is not a property of tires as concerns the bicycle of motorcycle. Employ the simple physics you learned in high school and do a free body diagram of the bike falling over. You will discover that the angular acceleration is position dependent. The force at the road can be determined to be W times the tangent of the lean angle.”

            First, I have no idea what you mean by “Camber” force? or stiffness?, and I suspect neither to you.

            Second, perhaps if you are only using high school physics, I suppose you might find “the force at the road can be determined to be W times the tangent of the lean angle.” If you are using calculus based dynamics, usually taught at the 200 level to mechanical engineering undergrads, you would find a more-sophisticated and accurate result.

            Let’s use the following free body diagram (apparently only available at the bottom of this comment) of a simple point mass on a massless rod. Since the center of mass is not moving in a straight line, normal and tangential coordinates attached to the center of mass are appropriate.

            Then we can sum the forces in the tangential and normal directions, and sum the moments about the pivot point O:
            ΣF_t = f*cos(theta) – N*sin(theta) + m*g*sin(theta) = m*a_t = m*L*theta_dd
            ΣF_n = -f*sin(theta) – N*cos(theta) + m*g*cos(theta) = m*a_n = m*L*theta_d^2
            ΣM_/O = m*g*L*sin(theta) = alpha*I_/O = m*L^2*theta_dd

            The last is a nonlinear differential equation in theta (so, yup, “angular acceleration is position dependent”) that is easy to solve numerically, with ODE45 in MATLAB, for example. Then, with theta, theta_d, and theta_dd for a span of time, it is easy to solve the remaining system of two equations in two unknowns, f, and N, for any time.

            You must mean the horizontal force f by “force at the road”, and this diverges from “W times the tangent of the lean angle” as soon as the lean angle is not zero.

          • Calvin Hulburt

            I agree that you are trying to make me say something I didn’t. I cannot follow your whining about my statement that one does not need to counter steer. In all cases I have said that it is not necessary and explained why. Your constant denial makes me assume that my model of the bicycle is essentially correct and you are simply trying to throw whatever tedious undotted i at it that you can find. Your arguments tend to the typical obscuring of a clear concept by common argument ploys such as making something more complex to confuse the issue, taking a condescending and superior tone, and misrepresenting ideas. This kind of argument is pointless because a discussion should be about getting to truth and you seem be set upon creating a smoke screen of confusion.

          • Andrew Dressel

            I am sorry that you find bike dynamics confusing.

            The only explanations I can find for your absurd assertion that countersteering is not necessary to create a lean are
            “because leaning modifies the forward direction” and “a bicycle can lean.” It seems that you don’t even understanding the purpose of countersteering. Yes, a bicycle can lean, and yes, leaning modifies the velocity vector, but neither of these create the lean in the first place.

            As for my tone, I think I’ve kept it remarkably civil, given how you opened this discussion.

          • Calvin Hulburt

            I do not find this topic confusing. It is quite clear that you are the apologist for a model that would only apply to a bicycle that is already moving to recover because it is complying with its direction of motion. The moments used for steering the bike are the small forces that nuance the bike in recovery. The rigid control philosophy that inspired the steer/lean model is a reflection of a need to control rather than accept that the bike is simply responding to your motion. To assume that you cannot create a lean without countersteering is believing in the model and not reality.

          • Andrew Dressel

            What does this “complying with its direction of motion” even mean?

            Just answer the simple question: how to do you cause the bike to lean if not by countersteering?

          • Calvin Hulburt

            The message of the Whipplites is that they are the keepers of knowledge and we are not to trust our own experience. The truth is there for anyone to discover but to keep a lie alive takes constant vigilance, lest it be overturned by anyone. If you read the benchmark bicycle paper description of why a bicycle can remain upright while moving it goes something like, because of a lot of possible moments about the steering axis and because we are a bunch of real smart scientists and you are not. This sort of bullshit is why people need to question published papers more closely. The model they use is incomplete and even a more complete model would contain many assumptions such as a small angle approximation, the rider being a mass fixed to the bike frame, wheels being thin discs. Math models are useful but they only point the way to behavior and when one believes them to the point that they create a double precision model they are clearly not expert in this area. What this group hoped to achieve by overstating what they had done and misleading the public with articles mouthing their press release, I do not know. What we have is a number of well educated inexperienced people working in an area that few are concerned about. This is a clear area where authority tries to create reality for personal gain. You are in a position where you are trying to defend the lie and you do so by citing authority. This is an authority that tells us that a bicycle is so fixed in its path that we have to counter steer to destabilize it. They also tell us that the bicycle is so unstable that we have to steer to keep it upright.

            The reality of the situation is so simple that anyone can understand it if they set aside the nonsense they have been told. The problem is that most people do not understand what they claim to. They only wish to believe that some authority understands it and they can tell them. One of the tools that authority uses to control our beliefs is to make us doubt our own ability. Doubting ourselves we must trust an authority. This is doubly cemented when the explanation uses terms and methods we are not familiar with. The Whipple model is simply a lie. It is faith based physics. It concerns itself with the lean angle and the steering angle and the faith that one can be controlled by the other. The yaw behavior is the central reason a bike stays upright. It allows friction to keep it on the right path.

          • Andrew Dressel

            Well, I guess that’s that. You can’t or won’t point out a flaw in my math, and so are reduced to name-calling, swearing, and pretending to be part of the down-trodden masses who’s ambitions are thwarted by an authoritarian cabal. Holy Moly!

            The “terms and methods”, with which you appear to be unfamiliar, are straight out of any Introduction to Dynamics textbook used in any Civil or Mechanical Engineering department. Do you mean to rail against all of Mechanical Engineering, too? Good luck with that. Try wearing an aluminum foil hat. I hear it helps.

          • Calvin Hulburt

            When a single track vehicle negotiates a turn it leans, yaws and pitches. There is a simple relationship between pitch and yaw based on the amount of lean but in the upright position the change in direction is purely yaw. Generally, Pitch is ignored for upright analysis as yaw predominates. For this condition my original explanation of slip angle is fine. There is no need to concern ourselves with high lean angles and complex explanations. This is a good area of study but not necessary to explain why a moving bike stays upright.

          • Andrew Dressel

            You reasoning for asserting that “my original explanation of slip angle is fine” is that pitch is negligible? You must be kidding. What on earth does pitch have to do with tire forces?

          • Calvin Hulburt

            Yes, the net ground force is a better term than normal force. This force does align with the frame and your misinterpretation of the physics will not change that. Whether we model the bike as distributed mass or point mass the result is the same. What you have done is mix the two. If we consider the bike and rider as a moment of inertia instead of a point mass it will fall over more slowly because of the greater resistance as you have stated. Therefore the acceleration will be less and your error is to apply that to the simpler concept so that the net result is a combination of a lower inertia value with a lower acceleration. As long as you are consistent in your analysis you will find that the normal force does not produce a steering moment.

          • Andrew Dressel

            I guess you are going to have to point out my mistake more explicitly because I still do not see it. I have not mixed the equations for a point mass with the equations for a distributed mass, and the two different sets produce different results. I have not applied the slower acceleration of the distributed mass to the point mass.

            It appears that this forum does provide a limited ability to attach images, and I have attached an image of the two free body diagrams and the corresponding two sets of equations of motion. As you can see, the first set, for the point mass, agrees with your analysis. The second set, for the distributed mass does not.

          • Andrew Dressel

            I guess you are going to have to point out my mistake more explicitly because I still do not see it. I have not mixed the equations for a point mass with the equations for a distributed mass, and the two different sets of equations produce different results. Nor have I applied the slower acceleration of the distributed mass to the point mass.

            The shape and mass distribution, however, does not enter into the two sum-of-forces equations, and since the weight and applied forces remain the same, so do the equations. The only difference is in the sum-of-moments equation, which produces the slower acceleration.

            It appears that this forum does provide a limited ability to attach images, but every time I do, the entire posting is soon deleted. Instead, I’ve posted it on BadBicycleScience instead. We’ll have to continue this conversation there.

            I look forward to your reply.

          • Andrew Dressel

            Let’s try posting the equations here one more time.

          • Calvin Hulburt

            You certainly have made a simple problem into a complex one. This is the way of the Whipplites. This problem can be understood by simply examining the moments about the pivot point. The positive moment is due to the weight of the bike and is Wr sin theta and this overturning moment is equal to the resisting moment of I times the angular acceleration. Thus you have Wr sin theta minus I alpha equals zero. What we wish to know however is the vertical and horizontal reactions at the road. Think about the meaning of the moment equation. It is not just math but two opposing and equal torques. Since they are equal you can replace the inertial term by Wr sin theta. Hence, you have a frame that is equally loaded with no moment at the contact point. There is only the frame compression acting against the road. This is true for both models. One will fall faster than the other but the higher inertia term creates the same ability to mirror gravity. The angle of the frame then determines the ground load. The bicycle is in modified free fall until it steers so while the mass tries to fall down the frame forces it sideways. We are concerned only with a small angular displacement because we are looking at upright stability. With the simpler case it is easy to relate small angular displacements to lateral ones. We can also ignore small considerations such as the centripetal acceleration. The key to understanding the bicycle is to look at what is happening simply and then applying math.

          • Andrew Dressel

            In other words, you can’t find the mistake. I even numbered the lines to make it easy for you to indicate exactly where it is. Instead, all we get is more arm waving and gibberish. If you want anyone to believe that the net ground reaction force aligns with the frame of a real bicycle, and all the rest of your theory, you are going to have to prove it.

          • Andrew Dressel

            Since it appears that you cannot or will not find the mistake in my derivation, let me see if I can unravel your explanation.

            Turns out I can, and it appears you have made a simple, undergraduate mistake: forget to use the Parallel Axes Theory. All the details are below.

          • Andrew Dressel

            No response to my reply below? That’s a shame. I thought we were finally getting somewhere. Well, when you are ready to get back into this, drop me a line.

  • Leah

    If i could design a bike, i would make it where the rider would have an option to raise or lift the seat. Lmao maybe i would make it where you cant lower it more than what it already is. I would probably make a much more comfortable seat with. It would be the same design just with it being padded. Removable i guess. #DoNowBike

  • Wy Ruby

    testing multiple images upload….

Author

Andrea Aust

Andrea is the Senior Manager of Science Education for KQED. In addition to QUEST, she's had the pleasure of coordinating education and outreach for the public television series Jean-Michel Cousteau: Ocean Adventures and the four-hour documentary Saving the Bay. Andrea graduated from UC Berkeley with a B.A. in Environmental Science and earned her M.A. in Teaching and Multiple Subject Teaching Credential from the University of San Francisco. Prior to KQED, she taught, developed, and managed marine science and environmental education programs in Aspen, Catalina Island and the Bay Area. Follow her on Twitter at @KQEDaust.

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