To help you while away those long weary hours on the road...

[Guest fatblokeonbike]

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Dear All,

 

Those of you who read the usenet newsgroups will be aware of how fecund they are. The following came, some weeks ago, from rec.bicycles.misc

If you have a newsreader I recommend you subscribe to the group and enjoy. Some items are lengthy, like this one, some are one-liners, some serious, some gloomy, some hilarious, and all to do with cycling. And they always welcome input from newcomers (you can be as anonymous as you wish).

 

(The best newsreader is Free Agent available free from www.forteinc.com and all of usenet is free. As usual, if you have any problems with installating Free Agent or running it, give me a call.)

 

If you don't have Free Agent, [COPY] & [PASTE] this URL into the Address bar of your browser - http://groups.google.com/groups?hl=en&l ... ycles.misc

 

The following was the wrap-it-all-up-and-take-it-on-home type of article which appeared in a thread about why humans can stay upright on a one-track vehicle (thassa bike to you). Anyone who can commit the complete thing to memory and recite all of it at the Presentation Dinner-Dance will get... well, something or other; you'll certainly get certainly some strange looks.

 

Pondering this will give all you disgraceful young street apaches something to think about in between ogling the wimmin.

 

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I certainly don't want this to turn into a long and involved debate about physics or mechanics; but I find it interesting, and I hope that others do, as well.

 

There are several issues involved in the stability of a bicycle, a vehicle like a Skibob, or something like an aircraft or a Segway scooter. Clearly, the balance and skill of the rider (or some other control system) is the most important factor. The original mention of gyroscopes came from PB Walther, who wrote that "Gyroscopic forces give bikes increased stability at higher speeds." That's true. It can't be otherwise.

 

In order to remain upright, a byclcle, or a motorcycle, or a Skibob, or a Segway, needs to achieve balance by keeping its center of mass (including the rider) directly above a line which is formed between the points where wheels, skis, or whatever, make contact with the ground. Or, to be more complete and accurate, the vector sum of all the forces, including gravity, which act on the vehicle and its rider must be directed at that contact line. When riding in a straight line, the only significant force affecting a vehicle's ability to remain upright is gravity. (Except a Segway, whose left and right wheel arrangment makes it unstable in a fore and aft direction and therefore brings wind resistance into play.) Shifting weight slightly is one way to keep the weight directly above the contact line. Another way is to turn the vehicle slightly when it tries to tip, to drive the contact line underneath the center of mass.

 

In real life, however, other forces besides gravity affect a vehicle. Imperfections in the road (or ice, or snow) surface will bump the wheels or skis to one side or another, and will therefore move the contact line out from under the center of mass. Crosswinds will try to move the center of mass away from vertical. Each of these, and many others, must be corrected for by turning the vehicle, or by shifting weight.

 

And, when a vehicle is turning, centrifugal force from the turn adds a horizontal component to the normal downward gravity force vector. This is why it's necessary to lean left or right when the vehicle is turning. The combination of centrifugal force (horizontal) and gravity (vertical) creates a "net force" which isn't perpendicular to the ground; but is slightly angled. The rider must lean to match that angle, or the vehicle will tip over (toward the outside of the turn).

 

On any vehicle I can think of, all of the various forces of instability can be managed by steering or shifting of weight. That's why it's possible to ride a unicycle, which is inherently unstable in every conceivable way. It's also why "unstable by design" aircraft can fly. Their riders (the computerized onboard attitude controls) maintain stability by quick, constant, and subtle adjustment of the control surfaces on the aircraft's wings and tail - the equivalent of controling stability by steering or by shifting of forces.

 

What's special and different about a bicycle (or a motorcycle, which is pretty much the same thing) is that it has problems with stability that most other vehicles don't have; and that it has the advantage of spinning wheels - gyroscopes - to make up for it's key weakness.

 

An airplane is a large surface area which makes contact with the air on which it flies at a very large number of points, and which has control surfaces located at it's extremes. It spreads itself out over a large area, and can apply steering and stabilizing forces at several places, in a whole range of directions, and can therefore manage the forces which act on it with extreme precision. A Skibob contacts the ground (or snow), with two rectangular patches. The skis aren't just points on which the vehicle is balanced. They're flat (sorta) surfaces that work very much like shape of an airplane, or the V-shaped hull of a boat. When turning, or when pushed away from vertical by any force, the Skibob automatically, necessarily, shifts its contact with the snow to the edges of the skis (rather than their centerlines), and thereby moves its contact line in the same direction as the center of mass is moved. That helps maintain stability. Yes, the skis are narrow, and the effect is small; but small adjustments for small forces are all it takes to stay upright, as long as those corrections are applied quickly enough to prevent gross instability.

 

The weakness I mentioned, which bicycles have and other vehicles don't, is that fact that a bicycle touches the ground only at two tiny points. (Yes, there's a small contact "patch" caused by tire deformation; but that's too small to matter.) The line formed between these two points is like a circus performer's high wire. The rider must keep himself directly above that line (by balance and shifting weight), or must keep the line directly underneath himself (by steering corrections), or the bike has no choice but to tip over. Vehicles like Skibobs, or ice skates, or roller blades, make contact with the ground (or whatever surface) in a completely different way. Their blades, or skis, or rows of wheels, each form separate lines of contact with the ground, and the relations of those separate lines to one another can be changed in ways that can add significant stability.

 

Think about an ice skater, gliding down the ice with his blades side by side. Each blade is a line of conact with the ice surface, and each has a length which extends both forward and backward from the skater's center of mass. There's a "control pattern" on the ice that's shaped like the letter "H". The blades of the skates form the left and right sides of the H, and the imaginary left/right line between the centers of the skates is formed by the legs of the skater. The skater can remain upright as long as his or her center of mass is anywhere inside the four corners of the contact pattern. And, stability can be maintained by shifting weight slightly toward one corner or the other. If some force tries to tip the skater to his left, then it's only necessary to exert a little more downard force with the left leg, and the tipping can be counter-acted. If something on the ice interfere's with the skates, and slows them a bit, then the center of mass of the skater will start to move faster than the skates, and the skater will start to fall forward. In that case, the skater needs only to push downward with his or her toes, transfer force to the forward points of the skate blades, and stability can be regained. Falling backward is avoided, of course, by lifting the toes slightly, transferring weight to the skater's heels, and relying on the tail end of the skate blades to transfer that force to the ice, keeping contact with the ice behind the skater's center of mass, and maintaining vertical stability. In other cases, the relationship between the skates can be changed. Sliding one skate out ahead of the other can dramatically extend the fore and aft length of the contact pattern. Spreading the skates wide apart in a side to side direction can make the skater extremely stable against lateral tipping forces. And combinations of those two actions, used in continuous, fluid ways, can allow a skater to remain upright under even very demanding conditions. The net result of all this gives the skater an infinite range of choices about the size, shape, and aspect ratio of the contact pattern, and the arrangment of contact points with respect to his center of mass. It's an incredibly flexible and stable way to move.

 

Roller blades are essentially identical to ice skates. For the purposes of stability, there's no real difference between blades on a low-friction surface, and small rollers on wood or concrete.

 

When a skater glides on just one skate, of course, then all the rules change. The situation is very unstable, since the H shaped contact pattern has now been reduced to a single line where a single blade meets the ice. The only source of stability is the skater's own skill and balance, and the ability to make tiny, subtle, fore and aft adjustments in weight, or slight steering corrections to keep the skate under the center of mass. This is why skating on one foot is so much harder than skating on two.

 

When a skater moves back and forth from one skate to the other - the normal action we think of in terms of skating, the situation is one of relatively high, but constantly shifting, stability. When pushing with the left skate, the skater is actually falling to his or her right. When the fall has progressed far enough, of course, then the right skate is returned to the ice. The fall is corrected, then reversed; and then the skater starts to push right and fall left. The H pattern for contact and stability still exists. Its various parts and pieces are just being used selectively and sequentially.

 

A Skibob, or ski-bike, even if the width of it's skis is ignored, also makes contact with the ground (or snow) in two lines. The lines are arranged fore and aft of the center of mass, and only one of them is steerable, so the inherent stability is smaller than for ice skates; but still greater than for a bicycle. When traveling in a perfectly straight line, the contact lines of the skis don't behave differently than the line between wheel contacts on a bicycle. It's a high wire act with a sligtly wider wire. (Maybe more like a balance beam.) If you turn the front ski, however, then the rules change completely. Now, instead of a single line of contact with the ground (which is all a bicycle ever has), the ski-bike suddenly has two, non-parallel contact lines. It's contact pattern becomes a kind of "T" shape. The rear (stationary) ski forms the vertical stem of the T, and it's front (steerable) ski becomes the top cross of the T, even though it's only slightly angled from the stem, rather than perpendicular to it. This angled shape is inherently very stable. The forward tip of the front ski actually reaches out to one side of the vehicle's centerline, while the trailing end of the forward ski extends the other way, and the entire vehicle suddenly becomes much wider. Instead of balancing on a high wire or a balance beam, the rider of a ski-bike can sit in the interior of a triangle. It's still important to use balance, weight transfer, and leaning into turns, to achive maximum stability; but the vehicle itself makes that easier, and can demand less precision.

 

A bicycle, unless it's flying through the air, or already lying on its side, makes contact with the ground at exatly two points, which form exactly one line, which must be the center of balance (or the focus of all combined force vectors) at all times. There is no way to change the length or width of ground contact. There's no way, short of putting a foot on the ground, for a rider to "spread out" over the ground to become more stable. It's a high-wire act, and can't be anything else.

 

A bicycles's spinning wheels, however, help make things easier. They're gyroscopes, and they resist tipping, turning, or any force which tries to tip or turn their axles.

 

In fact, they don't really resist. What they actually do is translate linear or coupled forces which are perpendicular to the axles into "precessive" forces. If you imagine a bicycle wheel hanging in space in front of you, with it's axle parallel to the floor, and the ends of the axle pointing to your right and left, and the wheel spinning as if it wanted to roll away from you, you can get an idea about how precession works. If you push upward on the right end of the axle, the upward force you deliver will be translated into a force that will make the wheel want to turn left. The right end of the axle will move away from you, the left end will move toward you (a counter-clockwise pivot, if viwed from above); but the right end of the axle won't just move upward (tipping the wheel to your left), even though you pushed that way. If you push down on the right end of the axle, the results would be exactly the opposite. The right end would move toward you, the left end would move away from you, the whole wheel would turn right; but the axle would still be parallel to the floor. If you push forward (away from you) on the right end of the axle, the wheel will want to pivot upward, driving the left end of its axle toward the ceiling. If you pull back (toward you) with the right end of the axle, then the wheel will pivot downward, toward the floor. If you keep pushing in the same direction (any direction perpendicular to the axle), then the whole wheel starts to "precess". As its attitude changes in response to your original push, the relationship between the direction you're pushing and the new position of the wheel causes the translated force to rotate slightly. And as the wheel's attitude continue to change, then so does the translation of forces. In the end, the wheel will twist its axle in a circle, rather than moving in the direction you pushed it. If you've ever watched a kid's toy gyroscope, or any kind of spinning top, twist and wobble on it's way to falling over, you've seen precession in action. Gravity wants to push the top of the toy's axle to the side, just like it would with anything that falls from a standing position. But the gyroscopic effect makes the toy twist and spin, and resist falling over. As the toy's spinning speed slows because of friction, the resistance to falling also decreases. The toy falls more quickly, but also precesses more quickly, and ends up orbiting around the lower tip of its axle at high speed, just before it touches the ground.

 

Bicycle wheels behave the same way. They have to. If you're riding your bike at any significant speed, and if you keep the handlebar perfectly straight, and lean to your right, you're effectively pushing downward on the right end of the wheel's axles. Like in the imaginary experiment described above, the wheel won't want to lean with you; but will translate the downward force, and will pivot clockwise (as viewed from the rider's perspective, looking down at the wheel). The rear wheel can't precess very easily, since it's locked into alignment with the bike's centerline. But the front wheel can move quite easily. The translated force of precession makes the front wheel want to turn right - exactly the way you'd want it to turn to correct for the fact that you're leaning right. Even if you exert no force of your own on the handlebar (but assuming you don't prevent the bar from turning), the gyroscopic action of the wheel will translate leaning forces into steering forces, and will help to keep you balanced. (You won't be going straight, anymore; but you won't fall over.)

 

If you lean to your left, that's essentially the same as pulling upward on the right end of the wheels' axles, and it causes the front wheel of your bicycle to steer left, keeping you upright.

 

And, the heavier your wheels are, and the faster they're spinning, the more forceful they become. At slow speeds, gryoscopic action is small, so the rider's balance and skill at steering make most of the difference. As speeds increase, however, a bicycle will become stable all on its own, and will become harder and harder to tip over. If you lean left and right, the bike automatically resists the leaning action, and necessarily steers to correct. That's a very, VERY nice natural compensation for the fact that you started out on a high-wire.

 

The other main factor that makes a bicycle rideable, in addition to skill in steering, and gyroscopic stability, is the fact that the front wheel is located slightly forward of the centerline around which the fork pivots. This is accomplished with bent forks on some bikes, or with small weldments that place the wheel in front of straight forks, or with some combination of those devices. If the fork on a bicycle were perfectly straight, and if the center of the wheel were directly in line with the fork's pivot centerline, then the fork would still steer the bicycle; but steering corrections to keep the bike upright would be much harder to do. The wheel would need to roll far enough with every correction to get back under the center of mass, every time you leaned or shifted even a little bit. It could do that; but it would take a lot more time, and a lot more rolling, and much more dramatic corrections that you'd care for.

 

With the wheel in front of the fork, however, the wheel isn't just steered in a new direction when you turn the handlebar. It's also swung through a slight arc, and the whole wheel is actually moved a bit to the left or right of the bike. The contact line - that line formed between the contact points where wheels touch the ground - is no longer parallel to the frame of the bicycle. It's now slightly angled; and the wheel contact line can be underneath the center of mass even if the frame isn't. The exact amount of offset between the fork centerline and the front axle makes a huge difference in the way the bike steers, and in how much steering correction is needed, and how much rolling speed is required, in order to correct for tipping forces. In general, though, there is only a very small range of possible offsets that work well and comfortably for a given wheel size. (I have a hunch that the offset should be different for different size wheels; but I've never done the math, so I can't say for sure if that's a good or valid idea.)

 

In one of his posts to this thread, FatBloke described an experimental bike that had an extra wheel/gyro attached to the fork, and also one that had the front wheel trailing the fork bottom. This would truly be an unrideable bike. The extra wheel, described as counter-rotating (probably just driven by contact with the primary wheel, and therefore spinning in the opposite direction), would indeed add to the total gyroscopic effect. But it wouldn't add constructively. As described earlier, the precessive action of a wheel makes it want to turn in the exact direction needed to correct for tipping or leaning. If another wheel were added to the mix, spinning in the opposite direction, then that extra wheel would increase the resistance to tipping with its extra spinning mass, but it would cancel the automatic steering effect. The primary wheel would still want to turn the fork in the correct direction; but the opposing wheel/gyro would want to twist the other way. This, of course, is why it was reported that it was impossible to ride this bike hands-free. Since the rider of a bike doesn't feel the gyroscopic forces directly; but only senses the results in terms of steering and balance, I suspect that this would be a very strange ride. You'd lean slightly to the left or right, intending to turn, and then find that the wheel hadn't responded as it should. You'd have to do a lot more intentional steering than normal. And, that intentional steering would be more difficult, because you'd be trying to twist two gyroscopes instead of just one. Bad news, for sure.

 

And the front wheel which trails behind the fork? Disaster! If normal forks work by swinging the front wheel right when you need to steer right, then a wheel which trailed the fork would swing to the left of the frame's centerline when the rider tried to turn right. The wheel would still be rolling in the correct direction, but that contact line between front and back wheels would now be angled in the wrong direction, and would be moved away from the rider's center of mass, instead of moving under it to maintain stability. This bike could probably only be ridden at very high speeds, so that steering corrections would all be tiny, and so that front wheel roll did nearly all of the contact line adjustment, and so that the off-line swing of the bassackward wheel would be minimized. How you'd get to high speeds without falling and dying is a more difficult question.

 

Over all, the physics and mechanics of a bicyle are astonishingly intricate, considering what a simple and taken-for-granted thing a bicycle is to most people. That's one of the reasons for my interest in bikes, in addition to the fact that I love riding.

 

I've often thought that a bicycle would be the ideal focus of a full year science class for grade-school kids. You could teach manual dexterity and some elementary mechanical skills, and the proper use of basic hand tools for assenmbling and servicing the bike. You could develop some basic knowledge of how mechanical things work, and perhaps a healthy curiosity about countless other things. You could introduce the metric system, and get kids to start thinking naturally in metrics, instead of being stuck with mental coversions all their lives. ("That's right, Johnny. The 12 millimeter box wrench is just slightly bigger than 7/16ths, but not quite as big as a half inch. Hold them up together, or try them on that nut, and you can see for yourself.") You could teach safety, provide fun and exercise, and instill a sense of real, tangible pride about maintenance tasks or riding skills practiced and mastered - skills that kids normally WANT to learn, which is one of the reasons why bikes are so popular in the first place. You could teach road rules and traffic safety ideas that would continue to serve as the kids became older and more active on their bikes, or later learned to drive cars. You could teach a whole world of basic science and math concepts. The relationship between the diameter of a wheel and its circumference is just a funny greek letter in an ordinary math class. But that same concept would become real speed and fun if you could actually ride the problem yourself, instead of just looking at it on a blackboard. The basics of gear ratios and mechanical advantage would be easy, and would be a great head start for kids when they later (if they're lucky) encountered more involved classes in physics and mechanics. There's air pressure in tires, and a whole branch of science that could be introduced from that. And there's the tensile strength of wheel spokes, and the compression strength of a seat tube, and the inherent strength and stability of triangular or tetrahedral shapes in a frame. (No, you're not going to teach the kids structural mechanics; but you can at least get them thinking, and speaking the language, and teach them to look at the world in ways that will make future science education more fun an easy.) And a bike class would be an effortless way to start kids thinking about problems in time and distance. (Remember those godawful math class problems where Sally rode eight miles per hour for 30 minutes, and then rode twelve miles per hour for 90 minutes, and the teacher wanted to know how far Sally rode, and what her average speed was? I hated those problems; but I bet they'd have been a lot easier, and a lot more fun, and a lot more likely to teach me something, if me and Sally had just climbed on our bikes and done the riding and timing.) There's friction and wind resistance, and how come the wheel slows down and stops, even if I spin it real fast? And if you dealt carefully with things like the combinations of pedal rates, and gear ratios, and wheel diameters, all in a fun and interactive context, you could have the little tykes doing real science and mathematics before they ever realized it. And by then it would be too late, of course. They'd already have learned something. And the kids could be healthier, and could get some fresh air to go along with classroom and workshop stuff. They could learn cooperation and teamwork, if the kids outnumbered the bikes in class by maybe two or three to one. (And the cost of cheap bikes would be nothing compared to what many schools now spend on science equipment, even though most of that goes completely to waste.) And...

 

Well... You get the idea. Bikes are cool, and understanding them at every level is good exercise for any brain. And I need to quit typing and get some work done.

 

Cheers, everyone!

 

KG

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As Dave-The-Trike is wont to say "Just thought you'd like to know that...."

 

Yoooors,

 

Iain.