Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Randy Grein on 01/10/2011 05:01:03
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Randy Grein asked the Naked Scientists:
A while back (4/10) you had a segment investigating bicycle steering, with the traditional explanation of gyroscopic effect being disproven but without a good alternative explanation. I found this to be surprising as it is well understood in motorcycle engineering.
View the bike from the side and concentrate on the angle of the steering head. Draw a line from the steering head at that angle to the ground and compare it to the actual contact patch of the tire. Observe that the contact patch is behind this line. As the bike leans this provides a torque on the steering mechanism (front to back torque) that provides a force that steers the tire into the turn. Changing the steering angle or offsetting the axle forward or back changes the effect, resulting in what is called oversteer or understeer. This is critical in racing as it impacts stability vs the ability to steer faster. Recent experiments with counter-rotating brake disks that reduce or eliminate gyroscopic effect improve steering response without reducing stability. Sadly this is easier to see with illustrations. If my explanation is murky let me know and I will attempt some simple artwork to make it clearer.
A related effect in bicycles and motorcycles is countersteering. A 3 or 4 wheel vehicle steers by turning the front wheels in the desired direction, but a bicycle is more difficult. Most people assume that steering is achieved by leaning, but this is confusing cause and effect. Consider a rider and bicycle viewed from either front or behind. With a single point of contact laterally how to lean? Comparing a running back in American football making a rapid direction change, or cut provides the answer. When running straight the feet are directly underneath, observed from front or behind. When the runner wishes to make a rapid direction change the opposite foot is placed well to the side – that is, to make a right hand cut the left foot is placed well to the left. This causes the runner to begin falling to the right, and the feet subsequently arc in a circle to compensate.
The same effect happens with bicycles and motorcycles. An initial small turn to the left moves the bottom of the front tire left, leaning the bike to the right. The self-correcting geometry of steering described above (often assisted by rider input) turns the wheel somewhat to the right, preventing a crash and steering right. This counter intuitive steering mechanism is why learning to ride a bicycle is so hard.
Great podcast (http://www.thenakedscientists.com/HTML/podcasts/), keep up the good work!
Randy Grein
Bellevue, WA, USA
What do you think?
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Interesting theory Randy, but if you have to turn the handlebars the "wrong way" to initiate a turn, how is it possible to make a turn without touching the handlebars at all? I know this is possible because I've done it often, although not so much in recent times.
(Look Mum, no hands!)
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Great question Geezer! The answer is indirectly. By pushing on the seat or frame tube in the direction you wish to turn the top of the bike bends just a bit at the steering head, which (visualizing from above helps) causes the front wheel to point in the opposite direction. Same thing with pressing on the pedals, or footpegs of a motorcycle, you are just translating a downward push off to the side into a roatational movement about the long axis of the bike.
Of course this is rather inaccurate steering, but it does work. Just be ready to grab the bars in case something goes wrong. (grin) You find this commonly discussed in motorcycle racing, both pavement and off road. Steering at speed requires strong inputs and the peg/knee steering reduces the effort required by steering with the arms. It was more important with older motorcycles with large, heavy front tires and conservative steering geometry. In fact, that was the easiest way to prove the concept of counter-steering. Steering effort was so high that successfully initiating a sharp turn at high speed required a sharp tug on the handlebars that was noticeable by everyone.
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With push bikes, there is no need to turn the steering in the wrong direction. All you do is lean into the turn while holding the steering "straight ahead". Then you make small adjustments to the steering so that your "tilt angle" balances centripetal force against gravity.
Things are probably a bit different with motor bikes because they have a much lower center of mass, and the rider only represents a small amount of the total mass, so it can take quite a lot of force to initiate the lean into the turn, particularly at high speed.
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Really, there is no difference in how, just how hard. Of course, a bicycle with a mass of 10 kg will move much easier than a motorbike of 200 kg or so. The steering is so low effort it takes careful measurements to detect it.
Think of this carefully - on a bicycle, motorcycle, feet or even a tightrope walker you are balancing on a line. How do you lean? Way up in the air you can't just push off against something to the side to lean over because there is nothing there. The only object to push off sideways is the ground. So the tires can push sideways against the ground by turning the handlebars; turn left and the front tire goes left. Your body, thanks to inertia keeps on in the same line and the you are now leaning to the right.
Still don't believe it? Measure it. You could use paint but sand, dirt or even a bit of water on the pavement will show it up. Ride as straight as you can,then steer sharply in one direction, just don't crash. The tracks will show the front wheel initiating in the opposite direction before arcing around the corner. A decent video camera from head on will catch the effect as well when viewed head on; a good sized fender will help show front from back on the front tire and thus which way the wheel turns.
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Randy,
If it's necessary to turn the steering the wrong way, I still don't understand how you can turn a bike without touching the steering at all. Also, your argument that you can't cause the bike to lean without steering the bike contradicts your argument that you can steer a bike without using your hands by "pushing on the seat or frame tube in the direction you wish to turn". If, as you say, there is nothing to push against, that would be impossible.
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Like all good paradoxes this is only apparent. Weight, or seat steering works because there is a joint in the middle - the steering head, and you are using part of the system - your body - to push against another part of the system - the upper part of the bike. Try it and watch the bars carefully. You will see that a pushing the seat or upper frame to the left will cause the steering to point right.
Now I hope that, like all good scientists you don't take my word for it, but test it. I have proposed several experiments to demonstrate the effect, try the experiments and let me know what you think!
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Randy,
I thought you said that was impossible because there is nothing to push against.
It's perfectly clear that we can steer a bike without touching the handlebars, so we must be doing it by transferring our weight. Now that we have proved it's possible to to steer by transferring weight alone, why would we need to turn the handlebars the wrong way?
Are you sure you've thought through this properly, or are you just buying into an urban myth you read on a biker forum [:D]?
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What I said was that you can't 'just lean' the bike. Without having something to push against your body tends to keep going in the same direction (straight forward), so how do you lean? Just try it, I have already given you a number of tests to demonstrate the effect including how this works in the special case of not touching the handlebars. Not testing the theory leaves us pointlessly arguing about thought experiments where errors can creep in unnoticed.
I don't normally bring up credentials, but yes, I have given this a great deal of thought. As a motorcycle racer of some 30 years experience, having taught some hundreds of racing students over that time as a long time bicycle rider and science addict I had to not only convince myself but convince very skeptical audiences. When I started racing counter steering skepticism was common among non racers and failure to understand the real process caused serious problems. As speed increases the cognitive dissonance between what you 'know' to be correct and reality causes people to fight themselves, the bike and physics. Quite a few riders end up off the track convinced that there's something wrong with their steering until another rider demonstrates the correct method on the same bike. We had to first convince the new riders that counter steering was real at low speeds, then how to do it correctly - and finally gradually increase corner entry speed through the day so the technique was ingrained. And make no mistake - at high speeds the steering effort becomes so high that no one could mistake the direction of turning. I do not claim that you should agree with me because I am an expert, simply demonstrating how the theory is well tested.
Of course, you have maintained that the weight of a motorcycle makes all the difference. Fair enough. But consider, that were this true - that a heavy motorcycle must countersteer, but that light bicycle steers in the direction the bars are turned - there would be a crossover point where the weight is too little for countersteering but too light for normal steering. All efforts at control would be in vain and the vehicle would be unrideable. I have raced motorcycles that weight as little as 160 lbs and bicycles up to 50 lbs without finding this instability and have piloted tandems where the combined rider/bike weight far exceeds the combined rider/bike weight of some racing motorcycles (all while deliberately using countersteering). I believe the burden of proof now falls to you. Duplicate the experiments I have given, find a flaw in the data. Develop an experiment of your own that demonstrates the fallacy of counter steering and test it first. That is, after all how science works.
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Randy,
I don't disagree with the motor cycle case, but your argument regarding the bicycle "no hands" case is inconsistent.
You keep saying there is nothing to push your body against, but if that's the case, how is it possible to steer without adjusting the steering using the handlebars? The only thing I can think of that makes it possible is because the rider did something to transfer weight (or centre of mass).
Therefore, if you can steer a bike "no hands" by transferring weight, you obviously are not exerting any force on the handlebars to turn the steering the wrong way. You say no hands is a "special case", but how do we know it's really much different from the "normal case"?
From what I remember of cycling (my bike bit the dust recently) I hardly ever exerted any force on the handlebars at all. The greatest force was applied when pushing hard on the pedals while going up hills, or during rapid acceleration. I suspect the real issue here is that the dynamics of a bicycle/rider is a lot more complicated than the motor cycle.
BTW, it's your theory, so it's not my job to prove it for you.
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Hmm, I thought I had made it clear - the rider pushes against the bike with their own mass. That is, we can consider the bike and rider a two part system. For the rider to push the top of the bike to the left his mass is shifted a small amount to the right. How much depends on the relative masses so of course the effort is much lighter on a 10 KG bike than it is on a 200 kg motorcycle.
We haven't talked about how well this works, and the answer is not well - which is why this can be considered a special case. Normally a rider can steer with precision, stay in a (fairly) straight line, make sharp corners, etc. Hands free is rather less so. A good rider can guide a bike more or less straight and bend it around gentle corners, but the technique is not up to anything demanding.
Finally, this is not 'my theory', it is not necessary or desirable to 'prove' it to all comers. I merely provide some evidence. I did not invent the theory of counter steering, I just use it. A quick google search finds an enormous amount of information on the subject, you can start with http://en.wikipedia.org/wiki/Countersteering , http://koczarski.com/Motorcycles/Counter%20streeing.html , or youtube at . ,
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Ah yes! Thanks for the links. I thought this bit was particularly interesting.
"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."
http://en.wikipedia.org/wiki/Countersteering
The problem with a bicycle is that, whether it is rounding a curve or going in a straight line, it is in a continuous state of falling over (it's in unstable equilibrium). The reason it does not fall over is because the steering automatically shifts the point of contact with the road to counteract the fall.
When you steer a pedal bicycle, rather than turning the handlebars in a particular direction, you actually apply a torque that resists the automatic steering and temporarily prevents it from counteracting the fall. The reason you are never conscious of turning the steering in the "wrong direction" is because there is no need to. What you actually do is prevent the bike from steering itself.
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You're getting close, but still insist that bicycles are a special case. ALL single track vehicles are in a state of unstable equilibrium and use self-correcting steering governed by the front wheel geometry for stability. This geometry is the steering head angle (or rake) and axle offset, defined as the difference between the contact patch and the intersection between the ground and an imaginary line drawn through the steering head. Creating a balance between self correction and ease of turning is still something of an art, balancing the need for easy, quick steering with self correction and feel. Too little rake and trail eliminate feel, the sense of traction at the limit and make the bike (cycle or motor) quite unstable and nervous feeling as it darts here and there, sometimes wobbling out of control as the bike falls into every minor corner. Too much rake and trail lead to the classic 'chopper' look and feel with great stability but difficulty executing all but the most gentle of turns, coupled with a tendency to push, or slide the front tire and a too great a tendency to straighten up. At optimum rake and trail the bike will steer neutrally, steering into a corner with ease and staying at that lean without additional input.
However, you are correct that steering is essentially resisting this self correcting effect. As the bike begins to fall over the self-correction steers the front wheel in the direction of fall, or into the turn - essentially putting the front tire further under the bike to prevent it from falling over. So, to straighten up you steer into the turn, to lean over further you steer away, or opposite the direction of the turn, resisting the self correcting steering. [;)]
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BTW, I think this is what the TNS podcast was all about. These guys are in Holland, so they obviously know their bikes.
http://bicycle.tudelft.nl/schwab/Bicycle/index.htm
http://bicycle.tudelft.nl/stablebicycle/StableBicyclev34Revised.pdf
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Excellent! I knew that neither rotational inertia nor trail were essential to a self-correcting, or self-steering bicycle but it appears (at least at first glance) that rake may be. That one of the researchers found an oscillation in testing that was NOT predicted by their equations is interesting, and points out the value of experiment coupled with theory. Sadly the math they are using is a bit beyond what I can quickly do these days, University was a long time ago. I will review as I have time. Thanks for the links.
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I was about to say they also know their dikes, but I thought better of it.