Tuesday, September 22, 2009

7 Dynamic Stability Of Bicycle Design : Part 4

"Trail can be found by supporting the bike on a flat surface in an upright position for measuring purposes. A centerline is run down through the head tube until it hits the flat surface. A vertical line is then dropped from the front axle until it hits the ground. The distance between these two points on the ground is the trail. The comfort range of trail is 50 to 65 millimeters. Beyond these limits in either direction, it would be considered less desirable."

- A quote from Chapter 1 : Frame Geometry, The Paterek Manual for Bicycle Frame builders

Question : Why do we know what we know about the comfortable range of bicycle design parameters and ride desirability? How do we know it? Can such claims be applicable to all bikes with any rider in general? What does science say about these statements?

Continued from Part 4

In the previous post, I presented a mathematical bicycle model to you (validated by research) and a computer program called JBike6 that uses this model to calculate the bicycle's stability eigenvalues. We also explored an important point that this model is, regardless of complexity, still simple in terms of being a riderless model not accounting for the frictional properties of the tires. Hence, whatever results you see in the JBike6 is only so true as long as you consider a riderless bike with other simplifying assumptions established.

Interestingly, Jim Papadopoulos (thanks Jim!) pointed out to me in a comment to the previous post that in terms of ridden bikes, he surmises that JBike6 might apply best to recumbents (where the rider is secured to a seat) with extremely hard tires, ridden no-hands. So its applicability is not lost.

So what is the bottom line of all this mess? What I've been trying to convey to you through this series is that studying a bicycle is a difficult and complex task. The bicycle really is a complex vehicle. Why do we know what we know about the bicycle dynamics, and how do we know it?

Some of us like to think we know bicycles and like to give out general rules of thumb for design so as to get a self-stable bike. Now this could be true for the particular bike design being considered but the point is, it may not be true for different designs and different people. A different bicycle with a differently sized rider can have totally different dynamics.

Hence, it turns out that when someone makes general claims about bicycle design that he thinks he or she knows will work for all bicycles, that's just an unvalidated statement in a true scientific sense. They're what's called an anecdote. Anecdotes come through hearsay or someone's personal experience with building something. However, the state of the art in bicycle science has yet to concretely come out with the unifying principles behind why a rider controlled bicycle, any bicycle, behaves the way it does.

Science has a long way to go before establishing the truth behind general statements about parameter changes and their effect on ride characteristics as applicable to all bicycles of any design. Science also has some ways to go in studying complex modes of motion in bicycles that we talked about in Part 2, particularly the dangerous ones such as high speed wobble that can bring harm and loss of property to the owner.

While I leave you with these thoughts, I'd like to present some research by one of my readers, Jason Moore. Jason is working towards his Phd in Mechanical and Aerospace Engineering at UC Davis. He's currently a Fulbright Visiting Scholar and Researcher at the Bicycle Dynamics Laboratory at Delft University.

Jason and his advisor, Prof. Mont Hubbard, employed the same validated bicycle model we've been talking about and studied the dynamics for the design parameters of an old Schwinn bike he owns. The model was then used with a physical parameter generation algorithm to evaluate the dependence of four important design parameters on the self-stability of a bicycle. These parameters were :

1) Front wheel diameter
2) Head tube angle
3) Trail
4) Wheelbase

In the end, the duo were able to generate interesting results through graphs that showed how changing the above four parameters independent of each other affected bicycle stability in weave and capsize critical velocities.

Their research paper was featured in Engineering of Sport, the journal of the International Sports Engineering Association. The graphs show definite parametric dependence of bicycle stability. Most interestingly, their results disagree with the general claims made by the Paterek (shown at the beginning of the post) about the comfortable limits of trail by showing an increasing stable speed range with increase in trail, provided this increases was kept within reasonable limits.

With Jason's permission, attached below are 8 pages of the paper titled Parametric Study of Bicycle Stability. Please click on them to expand and read. This is also available to read via Google Books Online. See this link.

Finally, if you have any questions about bicycle stability that bothers you, please ask away and I guarantee you'll receive an adequate reply from Jason, Arend Schwab or Jim Papadopoulos, as they all read this blog.

Thanks for sticking along on this journey!

* * *

The Engineering of Sport 7 : Proceedings of the 7th International Sports Engineering Association Conference. Biarritz, France. June 2-6, 2008.


  1. There doesn't seem to be a link to an enlarged image for the last page.

  2. Thanks. I just corrected that.

  3. I may be wrong here, but I'm not sure it's fair to say that any of the findings contradict what Paterek said.

    I think that most likely Paterek is not talking about a bike's self-stability, but rather how well the bike handles for an experienced rider. Surely the two are not the same.

    (FWIW, I'm not convinced that Paterek's range of trail is correct for all bikes, but I don't think that the findings about self-stability have the direct relevance to his claim as this post seems to suggest.)

  4. Tris : Stability and the modes of bicycle motion, as we talked about in Part 3, is a steering phenomenon too. One of the most talked about parameters associated with steering stability is trail. Without positive trail, there's no caster phenomenon.

    Paterek could be right from experience and principles. On the other hand, Jason et. al studied the bicycle TEHY HAD (that's important) for its parameters and found no correlation between Paterek's statement on the prescribed range for trail and what they found in their study, as you can see from the graphs on trail vs stability range.

    In hindsight, too much stability is certainly bad for a bike and Paterek maybe right, but his definition of a "comfort" zone is ambiguious. But he does not have a scientific definition of what he means by comfort so its pretty ambiguous and open to interpretation. Certainly, comfort is better with a more stable bike and if that's the case, then a higher stable speed range with trail means more comfort in straight line motion right? Atleast this is what I feel. You can disagree with me.

  5. I think we probably agree then. I was just under the impression that you were treating Paterek's claim as though it were talking about exactly the same thing as Jason et al and coming up with different values.

    That was a fantastic series - and a great blog as a whole. (I should have said this in the first comment.)

  6. Paterek is talking about bike handling, where as our studies are about bike stability. There are generally some types of relationships between stability and handling. I would claim that most of the time stability does not equal good handling but that isn't necessarily true. Fighter jets, race cars and other highly maneuverable vehicles tend to be designed such that they are either unstable or on the verge of stability. The key is to find that relationship and it is super tough because the human is in the loop and handling is very subjective.

  7. Thanks Jason. Paterek is likely talking about bike handling I agree. And with respect to stability in systems, I can think of one good application where stability would be prime. Let's think of the robot designed to study and take measurements on a planet. It'll land on the planet with the help of a parachute and some distance before it lands, the chute deactivates. The robot's airbags will cushion the landing. Now the chute must be stable enough to limit oscillations of the robot while descending. Too much of an oscillation angle will increase the motion of the robot in descent. If this is not controlled, the airbags of the robot could puncture when they hit the surface. Mission failed! :)


Thank you. I read every single comment.