[Univ of Cambridge] [Dept of Engineering] Trinity College Clock

A bike with a reverse-spinning wheel
on the insignificance of the gyroscopic effect when riding a bicycle

Dr Hugh Hunt
December 2006

For fun stuff on spinning things go to
Dynamics movies page

How do we manage to stay up on a bike? Gyroscopic forces are not important for the stability of a bicycle - as you can see if you read on below - but they help us to control the bike when riding with no hands. More important than anything is "the trail". The front wheel makes contact with the pavement at a point that lies behind the point where the steering axis intersects with the pavement - and the distance between these is called the trail. The trail is not zero because the steering axis is tilted and the front fork is bent. The trail works to stabilize a bike in much the same way as castors work on a tea trolley. When you lean to the right, say, on your bicycle force at the contact point on the pavement will push the front wheel to the right. This helps you to steer effortlessly and it allows for hands-free steering through leaning slightly left or right. The gyroscopic effect helps but the trail is the more important factor.

The photos below catalogue an experiment which proves that the gyroscopic effect is small. It is helpful when considered alongside a New Scientist "Last Word" contribution of 9 December 2006 Like falling off... and there's more New Scientist backpage discussion at (Continued) where the importance of the "trail" is covered.

Here I am pictured riding an ordinary bike, but with an extra wheel attached to the front axle. The tyre has been removed to give a little clearance from the road and some copper cable (earthing cable with green insulation) wound around the rim in its place to replace the moment of inertia due to the tyre.

The "extra" wheel can be spun up by hand, before you start riding, at any speed you like, even several times the speed of spinning of the "actual" wheel. It can be spun either forwards or backwards and what is so clear is that it really makes no difference to the "ride" of the bike. The bike is just as easy to ride whether the extra wheel is spinning or not, forwards or backwards, fast or slow.

So this begs the question: "How do we stay up on a bicycle"?

The way we stay upright on a moving bike is by active control through steering. This is why we have to learn to ride a bike. If, as learners, we find ourselves falling over to the left then we learn to steer the bike to the left, which generates forces that tilt us back upright again, thereby putting the wheels back under our centre of gravity. Beginners are very wobbly, but as we become expert the corrections become smaller and we can ride in a straight line.

The faster we ride, the smaller the steering adjustment needs to be, simply because the bike moves much further in a given time. When riding very slowly the steering adjustments required are very large. When completely at rest, active steering can do nothing for us.

A good analogy is to ask, "Why is it easier to hop (or pogo-stick) along a straight path than it is to stand still on the ball of one foot?" The reason is that we use each hop to generate correcting forces and also to put our foot down in a new place that is closer to where we need it to be in order to maintain our balance.

It is worth adding here that some bikes are easier to ride than others, and this is all to do with the "trail" described above, and many other parameters such as the hight and width of the handlebars, the height of the seat and the mass of the rider.

Also note that a bike with no rider can stay up much more easily - as many of the bloggers responding to this article have said. This is because the bike is now much lighter and the centre of gravity is much lower. So the forces acting to cause the bike to fall over are smaller. This means now that both "trail" and gyro effects are much more significant in the overall dynamics of the bike and it stays up more easily.


It is almost certain that gyro effects are important at the initial stage of steering manoeuvres. Many riders (especially motorbike riders) tell me that they notice the effect of "counter steering" above a certain speed. This is where any movement of the handle bar to the right (say) causes the bike initially to fall to the left. This is exactly as would be expected from the gyroscopic effect acting on the front (steering) wheel). The more sudden the steering manoeuvre the more pronounced will be the effect - because the gyro effect is a couple (a moment, a torque - call it what you like) that results from the rate of change in direction of the angular momentum of the wheel. The larger the change of angular momentum, and the shorter the time over which the change takes place then the bigger the gyroscopic couple. But what happens after the initial gyroscopic transient is then no longer gyroscopic - you're then down to the effect of the trail and other steering geometry effects. The bike with the reverse-spinning wheel shown below would not exhibit any counter-steering effect because the front wheel has no net angular momentum.

My point is that gyroscopic effects are not needed to keep you from falling over when you are riding in a straight line. I am not saying anything about what happens when you actively wish to steer away from straight ahead.


Misconception 1: Some people think, incorrectly, that the gyroscopic effect exists because a wheel is spinning and that two spinning wheels must increase the gyroscopic effect - just like two heaters in a room are hotter than one. But the direction of the gyroscopic couple depends on the direction of spin and anyone who has tried this out by holding a bike wheel will know this. This means that two bike wheels spinning in opposite directions will produce couples in opposite directions and these will cancel.

It is the purpose of the experiment described on this page to show that because this cancellation makes no difference to the ridability of the bike then gyroscopic effects can't have been important in the first place.


Here is another photo that shows that it is easy riding even if the extra wheel is spinning backwards to cancel out (or even reverse) all gyroscopic effects.

Let's do the math - some simple sums show clearly why the gyroscopic effect is unimportant:

When riding quite fast at 12 mph, ie 6 m/s, a typical bike wheel (diameter 600 mm, circumference 2 m) rotates 3 times per second, which is a spin rate of
       ω = 20 radians per second.
its peripheral mass, around m = 1kg, is concentrated at the rim, ie at a radius of r = 300 mm. The moment of inertia J is therefore
      J = m r2 = 0.1 kg m2 (near enough).
Suppose I am falling over and I try to use the gyroscopic effect to help push me upright again. Consider some pretty frantic wobbling of the handlebars back and forth sinusoidally at a rate of, say, fhandle=1.6 wobbles per second (equivalent to an angular frequency of wobbling w handle= 2 p fhandle = 10 radians per second) and at an amplitude of, say, +/- 6 degrees (ie Θ handle= 6/180* p = 0.1 radian) . The wobbling motion is therefore
       θ handle = Θ handle sin(ωhandle t),
and differentiating this gives a peak handle wobbling speed of
       Ω = ωhandle Θ handle = 10 * 0.1 = 1 rad/s .
and this is the forced precession rate of the front wheel acting as a gyroscope. At its peak, the couple required to achieve this precession motion, due to gyroscopic effects, is
      Θ = J ω Ω = 0.1 * 20 * 1 = 2 N m
The bike and I weigh, say, 100 kg = 1000 N, so the gyroscopic effect will only help me if I don't tilt more than 2 mm from being perfectly upright (1000 N * 0.002 m = 2 N m). This doesn't give me much safety margin.

Note that 12 mph is quite speedy for most ordinary riders: at slower speeds the gyroscopic effect is even less significant. I know that the racing cyclists amongst you reading this will think that 12mph is very slow - but please bear in mind that this web page is inteded to be read and understood by all cyclists, and most families on their sunday outings would rarely reach 12mph. The point I'm making is that even at relatively modest speeds a bike will stay up - and it's not gyro effects that are resposible.


Misconception 2: Anyone who has held a bike wheel in their hands and has felt the huge gyroscopic effect will swear that the forces are huge - so large that they simply must be important when riding a bike. But consider this: when holding the axle of the bike wheel in my fingers I notice that the force is big but it can't possibly be more than a few kg at best - ie a few percent of my body weight - because my fingers are not all that strong. So when I ride a bike the gyro effect at the ends of the forks is only a few kg - nothing compared with the 100 kg or so that the combined weight of the bike and rider exert. This is effectively saying the same thing that was deduced by calculation above, ie that gyro effects are there but small compared with other things.
Misconception 3: The gyroscopic effect holds a bike up so you can ride a bike with the handlebars locked. NO! Try it. You fall over immediatly. The easiest way to do this is with a rope. Tie your handlebars to the cross bar and then tournequet the rope really tight. You will have trouble even getting started. Get someone to push you along, or ride down a hill. Be prepared to fall!
Gareth Ryder, as usual, has been very helpful.

This close-up photo shows the extra wheel. You can see that the tyre has been removed (this gives a little clearance from the road) and in its place some earthing cable has been wound around the rim so that the moment of inertia of the wheel is roughly the same as it would be for a wheel with a tyre.

Note that the forks on all bicycles are inclined, and curved. This geometry means that if I tilt to the left the steering automatically turns the bike to the left, thereby putting the wheels back underneath me. This automatic corrective contrivance is essential for a bike to be ridden "hands free". It is this geometry that works wonders for us, and the gyroscopic effect is a smaller consideration.


This is the neat little brass adapter that Gareth made up for me to allow the extra wheel to be attached to the front axle (I should have cleaned it up a bit before taking this photo!)


References

I'm not the only one to have done these experiments and calculations and to have reached the same conclusions. Take a look at the work of the following people:
David Jones who was the first to make a bike with a reverse-spinning wheel - his URB Mark I (URB = UnRidable Bike) and whose experiment is the obvious inspiration for my own. The link here is to a Physics Today reprint of his article from 1970.
Richard Klein Introducing Precession and Gyroscopic Issues, whose experiments "reinforce previous conclusions that gyroscopic contributions for conventional bicycles are of relatively minor importance".
Karl Anderson "Many people assume that the gyroscopic action of the front wheel is solely responsible for keeping a bicycle upright. In fact, its effect is minor. "
Ryan Heller "The consensus is that there is only a very small gyroscopic force in the front wheel which riders can take advantage of when riding with no hands"

And if you want the full works, with all the equations, then you must visit:
Jim Papadopoulos and Andy Ruina and others, Cornell bicycle research, with papers such as "Linearized dynamics equations for the balance and steer of a bicycle".
Arend Schwab, Delft University of Technology, with instrumented bikes and nice videos of bicycles being ridden on a treadmill.


(For other gyroscopic things: go to Gyro and boomerang page

and for all sorts of video clips on spinning things go to: Dynamics movies page

and for other stuff: go to Hugh Hunt's Cambridge University home page )