# Revisiting bicycle physics

The “gyroscope” theory of bicycle stability was debunked over 40 years ago by physicist David Jones. Since then, hobbyists and bike nuts (including Yours Truly) thought bicycles stayed upright via something called the caster effect. Physicists from Cornell, the University of Wisconsin-Stout, Delft University of Technology in the Netherlands and University of Twente in the Netherlands found they can build a “two mass skate” bicycle with no gyroscropic effect and with no trail (for no caster effect) that can stay upright.

As a child, I was taught that bikes stayed upright because the spinning wheels give enough gyroscopic force to impart stability, but experimentalists learned years ago that there’s not nearly enough mass in a bicycle wheel to counteract the mass of a leaning bike and its rider. Physicist David Jones put theory to the test by building a bicycle with counter-rotating wheels to eliminate the gyroscopic effect and empirically determined the gyro is unnecessary for balance.

Since then, the conventional wisdom has been that trail — the fact that the bicycle wheel touches the ground behind the steering axis — creates a caster effect to keep bicycles (and motorcycles) upright. Caster is what keeps the front wheel from wobbling wildly around like you might see on some shopping carts with a broken caster wheel.

This fun video from Science Friday explains some of the background of how the caster effect works, but basically, when a bike begins to tip over, the bike steers itself into lean to automatically bring it upright. As long as the bike is moving at a sufficient speed, the bike will “ghost ride” itself.

These experimenters did the math on bicycle dynamics and learned that the caster effect may not be necessary as well. Traditional models of bicycle stability require second order differential equations to solve, so these physicists created a “two mass model” (TMS) bicycle to simplify the dynamics of bicycle stability. With this model, they learned they could completely eliminate the gyroscopic effect and the caster effect and still have a stable bicycle.

With this model, they place a mass far forward of the front wheel to create their self stable bike. That’s how triathletes ride and might explain why their bikes are so difficult to steer — they’re made for going fast in straight lines.

If you’re interested in the details, PDF of the full paper is available here: A bicycle can be self-stable without gyroscopic or caster effects, by J. D. G. Kooijman (Delft University of Technology, Delft, The Netherlands), J. P. Meijaard (University of Twente, Enschede, The Netherlands), Jim M. Papadopoulos (University of Wisconsin-Stout, WI, USA), Andy Ruina (Cornell University, Ithaca, NY), and A. L. Schwab (Delft University of Technology).

Photos by Richard Masoner. The young woman in the bottom photo is Kimberly Capriotti. She’s a professional fashion photographer in Chicago who takes the lovely pinup photos for the Thought You Knew Us cheesecake calendar project..

• Everett
April 18, 2011 - 6:39 pm | Permalink

Dave Moulton has a good entry today about the new problems introduced with bike design based on this exercise. That’s not to say that this isn’t a neat exercise.

• April 19, 2011 - 4:03 am | Permalink

All manner of support material for the no-gyro no-caster paper are here:

http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/stablebicycle/

• Ron
April 19, 2011 - 3:32 pm | Permalink

Howdy–

Okay, I’m straining my brain here, and maybe I’ll actually do a little research, but didn’t Jones also test a no-trail bike, finding that it was actually rideable? I was also kind of surprised that they controlled for gyroscopic force in this new experiment; as Richard notes, that was debunked years ago.

And, from the media reports I’ve heard, the new experiments still don’t tell us exactly how the bike stays upright. I’m happy about that, as I’m glad to allow for the possibility of non-empirical, metaphysical explanations. I’m no wiccan, but it’s entertaining to think I might have a handle on a little black magic.

Happy Trails,
Ron Georg
Corvallis, OR

• Andy
April 19, 2011 - 4:16 pm | Permalink

Correct me if I’m wrong here, but I believe lowrider bikes that still have a nearly vertical tube angle place the wheel significantly forward of the steering axis, for a huge negative-trail. They would still be ridable, but you surely wouldn’t want to take your hands off or ride fast on them. Here’s an example picture: http://images.ifguk.co.uk/products/1132/1132-large1.jpg

• April 19, 2011 - 5:30 pm | Permalink

Negative trail bikes are certainly rideable, they’re just not self-stable — IOW, you can’t push them riderless and expect the bike to stay upright because that front wheel will swivel around like a bad shopping cart wheel. They require hands on the bars.

• April 19, 2011 - 5:32 pm | Permalink

Thank you Dr Ruina for dropping by my cycling blog. Did I read your
information correctly that caster is a helpful but not necessary part for
bicycle self stability? Thank you!

Richard Masoner
http://www.cyclelicio.us/ is yummy!

April 25, 2011 - 2:01 pm | Permalink

Co-author Papadopoulos here. I wanted to add something in case Andy doesn’t get to it.
It often takes very careful reading to determine what a person did or didn’t show.

>”didn’t Jones also test a no-trail bike, finding that it was actually rideable?”
All his bikes were rideable, and most were rideable no-hands. But that doesn’t show self-stability, which means no rider, or absolutely rigid (non-moving) no-hands rider.
Whatever he showed failing to work was only for his particular bike. There are other bikes, or other speeds, where that same condition (zero trail, or zero gyro effect) IS self-stable.

>”I was also kind of surprised that they controlled for gyroscopic force in this new experiment; as Richard notes, that was debunked years ago.”
Well, no. We were much more careful to exactly cancel the gyro terms, and instead of showing one bike where gyro cancellation leads to instability (that is common), we showed a bike where it didn’t.

>”Negative trail bikes are certainly rideable, they’re just not self-stable — IOW, you can’t push them riderless and expect the bike to stay upright because that front wheel will swivel around like a bad shopping cart wheel.”
Au contraire, mon ami! Our bike had negative trail and no rider, yet — surprise — FOR THIS CASE the wheel did not swivel around. In fact the bike math seems to suggest that negative trail for a bicycle free to lean (i.e. not held upright) the negative trail rarely or never causes the wheel to flip around. That is just an idea that many have held, without testing it.

>”Physicist David Jones put theory to the test by building a bicycle with counter-rotating wheels to eliminate the gyroscopic effect and empirically determined the gyro is unnecessary for balance.”

Well, I think the result was a little less clear. It was easier for him to ride an approximately gyro-canceled bike hands-off than a negative trail bike hands off. But when it came to riderless, both on their own collapsed. So Jones needed a gyro for self-balance OF HIS BIKE.

The conclusion most folks took from a casual read of the Jones paper was not necessarily what the data reported! (No offense meant to anyone — I did it myself for many years until I went through every line of that paper about 10 times.)

April 25, 2011 - 2:01 pm | Permalink

Co-author Papadopoulos here. I wanted to add something in case Andy doesn’t get to it.
It often takes very careful reading to determine what a person did or didn’t show.

>”didn’t Jones also test a no-trail bike, finding that it was actually rideable?”
All his bikes were rideable, and most were rideable no-hands. But that doesn’t show self-stability, which means no rider, or absolutely rigid (non-moving) no-hands rider.
Whatever he showed failing to work was only for his particular bike. There are other bikes, or other speeds, where that same condition (zero trail, or zero gyro effect) IS self-stable.

>”I was also kind of surprised that they controlled for gyroscopic force in this new experiment; as Richard notes, that was debunked years ago.”
Well, no. We were much more careful to exactly cancel the gyro terms, and instead of showing one bike where gyro cancellation leads to instability (that is common), we showed a bike where it didn’t.

>”Negative trail bikes are certainly rideable, they’re just not self-stable — IOW, you can’t push them riderless and expect the bike to stay upright because that front wheel will swivel around like a bad shopping cart wheel.”
Au contraire, mon ami! Our bike had negative trail and no rider, yet — surprise — FOR THIS CASE the wheel did not swivel around. In fact the bike math seems to suggest that negative trail for a bicycle free to lean (i.e. not held upright) the negative trail rarely or never causes the wheel to flip around. That is just an idea that many have held, without testing it.

>”Physicist David Jones put theory to the test by building a bicycle with counter-rotating wheels to eliminate the gyroscopic effect and empirically determined the gyro is unnecessary for balance.”

Well, I think the result was a little less clear. It was easier for him to ride an approximately gyro-canceled bike hands-off than a negative trail bike hands off. But when it came to riderless, both on their own collapsed. So Jones needed a gyro for self-balance OF HIS BIKE.

The conclusion most folks took from a casual read of the Jones paper was not necessarily what the data reported! (No offense meant to anyone — I did it myself for many years until I went through every line of that paper about 10 times.)

• Andy
April 25, 2011 - 2:21 pm | Permalink

The physics in my head seem to think that the nearly zero negative trail with a weight far forward of it is what prevents the wheel from swiveling around in this case. I do find this whole bike test a bit of a moot point, since it’s not a ridable bike. If it were moving at regular cycling speeds (15-20mph) with a rider on the bike, I can’t imagine a negative trail bike being ridden no hands would be a fun experience. My bikes see 30mph everyday, and I don’t imagine I’d be willing to test out a negative trail bike at those speeds.

I’m not sure what the overall purpose of the test here is other than academics trying to prove something exists even though it’s not practical. Are they proposing a new way to build a bike? It doesn’t seem like any benefits come from this design, since centrifugal forces and trail do help a bike feel comfortable and stay upright better.

April 25, 2011 - 3:09 pm | Permalink

You are bringing up a giant philosophical can of worms, at the bottom of which we might find disagreement. Certainly a lot of crummy science has been done with a supposed ‘justification’ of wanting to know. But the results had little or no implications. Yet each of these researchers might defend their work on the grounds of scientific taste. When is research pointless?

One of my favorite scientific pathways is Fizeau measuring the speed of light in the 1850’s. What was the point of it? Well, only when you get real numbers, and see differences in water, do you get a chance to link it up to various physical constants and have something that validates Maxwell’s equations. A whole science and technology came out of people like Fizeau and Faraday that seemed kind of pointless at the time.

With regards to ‘the physics in your head’, well they are in mine too. But I’m not sure they are accurate, because messing around with front cm and trail hasn’t led to a clear wheel-flipping catastrophe.

If you look at Wilson-Jones’s motorcycle paper of 1952, he experimented with negative trail, and found no-hands with modest negative trail was no issue, whereas with 3″ negative trail there were some difficulties. So I think the widespread preconception that negative trail is disastrous may be preventing many from considering little or negative trail, which might be fine, or might even provide certain advantages.

The purpose of this work was to try to achieve understanding, and then relate that understanding to experience and practice. Current belief is that you need trail and possibly spin momentum for self-stability. Not true. That you need a tilted steer axis or front steering for self-stability. Not true. That gravity makes the front wheel steer to the side of a fall if trail is positive. Not true. This is not a recipe for a better bike, but I bet we can improve recumbent handling. And I bet there are bikes just as good as today’s, if not better, that will be built once folks have a better appreciation of the real physics.

So, bottom line, I don’t believe we have perfect bikes today (some are darn nice, others are not) and I hope that understanding could lead to improvement. To achieve that understanding we have to critique existing guidelines, and try to come up with consistent explanations.

PS in case it wasn’t clear, in my previous post when I said ‘Andy’ I meant ‘Andy Ruina’, my co-author to whom I was responding.

• April 25, 2011 - 3:31 pm | Permalink

Hi:

As a generality true for all conceivable bikes in all situations, who knows? But one can’t argue with the empirical fact that if you start with a common bicycle and eliminate the trail that it tends to feel and act less stable. So, at a minimum, trail is an important factor (a parameter that has large effects). And, as an empirical rule it seems reasonable to say that trail tends to help stability. But the main point of our paper, in one way of reading, is in the first sentence of this paragraph.

• Andy
April 25, 2011 - 3:41 pm | Permalink

I didn’t mean to infer “pointless”, more about practicality. We can design riderless bikes and test the physics on them, but they will never be practical in the same way that a bike that I can propel would be practical.

• April 25, 2011 - 5:07 pm | Permalink

Thanks so much for your contributions here, Dr Papadopoulos, and clearing these things up!

Are you any relation to Greg Papadopoulos? (I worked at Sun Microsystems)

• Michael Northcott
September 20, 2011 - 4:27 pm | Permalink

Note that the faster a bike goes the easier it is to keep it stable. Perhaps the movement of the air around the wheels has something to do with it? We still don’t fully understand how helicopters work, so it might take solving one problem to solve the other!

• September 20, 2011 - 4:36 pm | Permalink

Perhaps. Something to think about: people do wind tunnel studies and ride on rollers all the time with bicycles. I’ve ridden slow in high headwinds and fast in fast tailwinds.  Crosswinds affect stability a great deal, but that mechanism is pretty well understood — your front wheel is a weathervane in those conditions!

• Hamish
September 20, 2011 - 9:45 pm | Permalink

I always assumed it was falling down – constantly. And being thrown up.

If I throw a ball through the air would I expect it to suddenly stop and fly off at a 90 degree angle to the direction I threw it?

• September 20, 2011 - 10:19 pm | Permalink

Thank goodness I don’t need to understand second order differential equations to enjoy riding my bike!

• Balazsbagi
September 21, 2011 - 12:30 am | Permalink

Two thoughts come to mind.  If you pushed a bike backwards, with the steering wheel leading and the stationary wheel leading, the bike would fall over almost immediately.  So the front wheel is definitately  causing the steering.  As the bike leans off to one side, the momentum from the rear causes the front tire to push in that direction and correct the movement.

Also, when a tire is leaning over, it makes contact with the road differently – the inside track of the tire has a shorter diameter than the center part of the wheel – perhaps this is helping?

I know that train wheels are camfered so when they go around corners, they ride up onto the camfer on the outside wheel, making a larger diameter, and the inside wheel rides down the camfer, making for a smaller diameter, and this is how you can have two wheels on a single axel turn at different speeds around a corner, much like a differential in a car.

• Balazsbagi
September 21, 2011 - 12:30 am | Permalink

*steering wheel trailing, sorry…

• September 21, 2011 - 1:45 am | Permalink

How can you just dismiss gyroscopic stability like that? It works on something as simple as a coin, and would work on 2 coins joined by a little frame, so why just go ‘Nah’? We know that going too slowly reduces stability, that unicycles have half the stability and anyone experiencing a motorcycle’s speed wobble will tell you that wheels have a huge effect… I don’t care what experiment they did, spinning wheels make the bike stable. If their experiement said something else then there’s something wrong with the experiment.

• Bigyellowmutt
September 21, 2011 - 2:33 am | Permalink

I’m not sure all of the confusion. A bike going straight has a vector of momentum pointing straight. Start to tip the bike right, it’s vector of momentum rotates right. Tip the bike left, it’s vector of momentum rotates left. Slightly, but it does move.

A spinning wheel cannot travel perpendicular to the vector of momentum. The wheel does not give a crap if the bike is designed with trail or not, it’s going to rotate because it cannot travel sideways! It will always pivot to remain parallel with the vector of momentum.

• September 21, 2011 - 7:33 am | Permalink

To add to @d9837d13d4f358c8b4f6e90e071de537:disqus ‘s comment, when the bike tips right and begins to turn it will experience a force acting on it to move to the left, thus helping right the bicycle.  Perhaps intuition just means having a general understanding without knowing the math that proves it.

• The Woo
September 21, 2011 - 2:00 pm | Permalink

Is the editor making a hidden hypothesis with his selection of pictures, that bikes stay upright when in motion because they are trying to impress hot chicks who may want to ride bikes?

• Bigyellowmutt
September 21, 2011 - 9:38 pm | Permalink

Yes, when the bike tips right think of a centrifuge. The bike will want to pivot on it’s fulcrum (the contact patches of the tires) because of angular momentum. This in turn shifts the direction of the vector of momentum, and the pivoting tire rotates accordingly.

When you have more velocity, the vector of momentum is greater and has more influence over the bike to keep it pointing straight (i.e. object in motion wants to stay that way). This is why a bike at speed is more stable… not because of any gyroscopic effect from the wheels.

• Bogothedumbass
May 16, 2012 - 4:52 pm | Permalink

Read the part where the angular momentum hypothesis of stability was debunked in the 70s. The wheels do not have enough mass to keep the bike upright, even if they want to resist falling over.

• Anonymous
October 20, 2012 - 11:25 pm | Permalink

Has anyone ever tried putting a bicycle in a vacuum?

• Anonymous
July 2, 2013 - 9:47 pm | Permalink