One Man's Take on Stabilizing the Unstable

      Bike riders know it's easier to maintain balance the faster you go. But why? Some say it's because wheels are gyroscopes. Others say stability is designed into the bike from what's called trail. Still others say stability comes from forward momentum.

      To know which proposition might be correct it would be helpful to know how we balance in the first place. Intuitively you'd figure riders balance by leaning side-to-side. Though according to basic physics leaning shouldn't help us balance. Newton's third law of motion states "For every action there is an equal and opposite reaction." A rider leaning one way tilts the bike the opposite way, but the center of mass, the balance remains the same. There is a way for you to test this idea to see for yourself. Or if you trust my account of the same test you can save yourself the trouble.

      I inserted a slat of wood up against the front wheel inside the front fork as shown. I tied the back end to the frame below the seat and tied the front to the wheel. Now the front end will not turn and the bike won't roll forward or back. About the only thing you can do with the bike like this is spin the peddles backwards, which won't get you very far.

      Seated on the bike with my feet off the ground, no matter how I leaned or moved it was impossible to balance and stay upright more than about a second or so. Once it started falling one way or the other, no amount of leaning would stop it. Should you try the experiment for yourself, you will see there is no way to balance such a bike by leaning alone.

      This suggests leaning doesn't help balance a bike. Yet bikes don't have slats of wood preventing the front end turning. Bikes change shape, or geometry, as the front end turns. Which means a bike doesn't behave like a simple unchanging object like the bike with the slat of wood. As a result leaning does help a rider balance a bike, just not in the obvious way. Explaining this is what I hope to do with this article.

Part One: Bike Basics

      In theory there are two ways to balance a bike. Method one is moving the support points, which when riding a bike we call "turning." Turn left and the support points move left. Simple enough. Method two is shifting the center of mass. This can't be done by leaning, as we know if we tried the test above. I suppose you could use retro rockets like on a spacecraft, but bikes don't come equiped with retro rockets or anything like.

      Method one is counter-steering as described below. Method two is a lot harder to explain, but is coming up. This second method is all about bicycle geometry, a fancy pants term for the way all the bits and pieces are shaped and arranged on your bike. More importantly, the way the parts get rearranged when you rotate the front end and tilt the bike.

      We begin by looking at bike geometry and motion from the ground up. Bikes fall over because they sit on two points, and as every geometry student knows three non-colinear points determine a plane. Even kindergartners see how a tricycle stands on its own while a bike doesn't. Which is why bikes have kickstands.

Pitch, Yaw and Roll

      We live in a four dimensional world of height, width, length and time. Time gives us opportunity to move things around. Time matters in how fast things are done, too. For now we just look at the other dimensions with time added in, but not much discussed. Within the other three dimensions objects can be said to have three axes of rotation: pitch, yaw, and roll.

      Above: If a bike were floating in space, pitch is tumbling end over end as at the left. Yaw is spinning like a top, middle. Roll is falling over or tumbling side to side, right.

      If you were floating in space peddling, steering, or leaning wouldn't get you very far. Or you could say applying forces from within the system would not change the combined center of mass of bike and rider. Luckily we ride our bikes on Earth so there are outside forces we can work with. These are gravity pulling you down and the ground holding you up, preventing gravity plunging you to the center of the Earth. Combined you get traction which makes riding around on Earth very different than space travel by bike, besides having air to breathe.

      Below: On the ground bikes stand on two support points, the front and back wheels at the contact patches. You have two spots on which to pitch, yaw and roll. These points line up on the roll axis, but not on the pitch or yaw axes. For instance, you can pitch or yaw at the front wheel, or at the rear wheel. Since the contact patches line up on the roll axis the bike rolls on both contact patches at once.

      Having two pitch points and two yaw points stabilizes a bike on those axes because you can't rotate one object on two axes at once. They sort-of cancel each other. As a result it's hard to make a bike tumble end over end, and hard to make it spin like a top. Still, there is nothing to stop it falling over side-to-side on the roll axis.

      If a bike had no moving parts it would be a lot simpler to explain, though fairly useless for transportation. Different moving parts have axes of their own. Importantly the wheels which support the bike on the ground move within the system.

      Above: Each wheel can spin, or actually pitch at the axle. The front end assembly can turn, or yaw at the steering tube. (Though it does more than that, but let's take it one thing at a time.)

      Below: Pitching the rear wheel by peddling doesn't pitch the bike at the rear axle, it moves it forward. You might call it pitch with the axis at the center of the Earth. But this works even if the world were flat, so just call it going forward. Yawing the front wheel doesn't yaw the bike at the front wheel, but turns it with an axis where the axes of the front and rear wheels cross. We call that a co-ordinate turn or tracking, though you need to be going forward for that. The bike's roll axis is between the contact patches front to back.

      Peddling supplies force from within the system to the ground on the stable pitch axis to change the center of mass by moving forward. When moving, steering applies force to the ground on the stable yaw axis to turn the bike. You cannot apply a roll force from within the system on the unstable roll axis to change the center of mass. To stay balanced you're left with the other stable options, pitch (moving forward) and yaw (turning).

Turning, or Circular Motion

      Circular motion, including turning a bike, is from a combination of forward momentum and centripetal force, a force deflecting your forward motion to the side. Combined they create a centrifugal effect directly opposite the centripetal force. The centripetal force is determined by the angle the wheel is turned, how sharp you turn. The centrifugal effect is determined by your speed (momentum) plus the centripetal force. The faster you go, the tighter your turn, the more centrifugal effect.

      Meanwhile, the forces of gravity pulling you down and the ground holding you up are constant. To keep a bike balanced you use gravity pulling one way and centrifugal effect pushing the other to a standoff.

      Above: Momentum (A) is straight ahead moving the bike forward. The centripetal force (B) is at the contact patch pushing into the turn. The centrifugal effect (C) is on the bike and rider pushing out. As the bike is tilted inward gravity (D) is pulling you down. In combination this directs the force down to the ground at an angle. To be balanced, the center of downforce (E) is between the contact patches in line with the roll axis. This applies at upright or any other angle while you turn.

      We're able to move and turn and balance by applying forces from outside the system, gravity and traction. Try riding on ice and you can see how well it works without traction. Try riding in outer space and see how well it works without gravity.

Counter-steering, or Balancing by Turning

      For those unfamiliar with counter-steering, it can be stated as, "turn right to go left." It might sound absurd, but it works.

      This is pretty much the procedure for a left turn: As you approach the turn, without leaning quickly rotate your handlebars right. (It only takes a small rotation, but quicker is better.) The bike starts turning right. Forward momentum creates a centrifugal effect rolling the bike left, which is the way you wanted to turn. At this point the front end turns left, into the turn the way momentum has rolled you. Or at least it'd better if you don't want to crash.

      Below: On the left rider rides straight, momentum (A) is straight ahead, and gravity (B) is straight down. At start of turn in the middle, right front end rotation puts a centripetal force (C) on contact patch to the right. Combined with momentum this creates a centrifugal effect (D) to the left, which combined with gravity rolls the bike left. After rolling left, front end then rotates left and bike starts going left. This reverses the centrifugal effect to the right which is countered by gravity as bike is already rolled left so you maintain angle through the turn.

      If you follow the track of the front wheel, it goes right quickly then left. You might call it "double-turning" instead, though everybody else will still call it counter-steering even though I think double-turning is more accurate.

      In a way the phrase "turn right to go left" is misleading because in the end the front wheel must rotate left to turn left. So really you "turn right to roll left and then turn left to go left." But that's not very short and sweet and probably rather confusing. This technique works going fast or slow, for big or small turns, for wide or sharp turns. It's fairly simple and straight-forward physics.

So Far

      Experience tells us it's easier to balance the faster you go, and very hard at a standstill. At this point you might imagine why, momentum. Without that we create no centrifugal effect to counter falling over on the unstable roll axis. For this reason many suppose the only way to balance is by counter-steering. If you start falling left, a little turn to the left creates centrifugal effect to the right pushing you back upright. All very simple and easy.

      Yet counter-steering doesn't seem to jibe with our everyday experience riding bikes where we lean into turns. It doesn't seem to explain some observations I made and tests I did with my bike. To get into that you'll have to turn the page, or click the link, actually.

Part Two: Observations & Tests

Part One: Bike Basics
Part Two: Observations & Tests
Part Three: The Front End
Part Four: More Bike Geometry
Part Five: How We Ride