My name is Andrew Dressel, and I teach mechanics at Milwaukee School of Engineering and University of Wisconsin-Milwaukee. My PhD dissertation was on “measuring and modeling the mechanical properties of bicycle tires.” My LinkedIn profile is available here.
In hopes of reducing the amount of bad bicycle science in the public domain, I am attempting to catalog it here. I have tried contacting the authors and publishers directly, but usually get no reply. Perhaps if they find themselves profiled here, they will correct their content.
If you believe I am mistaken, or if you know of an example of bad bicycle science that I have not yet covered, please let me know.
Bad Bicycle Science 
Hi Andrew,
I have found your thesis on tire dynamics as a free download, but for me it’s over my head to understand the stability diagrams and criteria. I hope you are right that the knowledge is useful for optimizing bicycle design. I am skeptical because a lot has to do with cornering, which is relevant about 5% of the time riding on the bike. Moreover, unlike car drivers, bicycle riders do steer the vehicle themselves and have honed their handling skills in countless hours of exercise.
There is an aspect of tires that is of direct interest 95% of the time: ride comfort. So here is a simple question with three mutually exclusive answers. To each answer I add a tentative explanation in soft scientific language. I hope you are able to assess the answers with the good and the bad science.
I am interested in road-induced vibrations on a ‘regularly’ rough hard surface’, e.g. chipseal, cobbles or even rumble strips, but not incidental defects like potholes. Suppose we have two tires of the same built and materials but different widths. The tires are pumped to the same inflation pressure and used on the same bike riding at the same speed. Which of the following answers & explanations is correct?
A. The wider tire causes more road induced vibrations to the rider. Explanation: at equal pressure the areas of the contact patches are roughly the same. On a rough surface, where the tire stands on the crown of the texture, the number of contact points for both tires are the same. The shape of both footprints is approximately elliptical. The wider tire has a shorter footprint in the driving direction and wider in lateral direction. This implies that the residence time on a contact point is shorter for the wider tire. Vibrations are caused by changing the contact points in time ; the level of vibrations will be proportional to the speed of changing contact points, or inversely proportional to the residence time. Hence wider tires cause stronger road-induced vibrations
B. The wide tire and the narrow tire have the same level of road-induced vibrations. Explanation: when the footprints are the same, the number of contact points is the same and the averaging of surface roughness is the same.
C. The wider tire causes less road induced vibrations. Explanation: vibrations are causes by the variation in the depth that the tire sinks into surface cavities. Statistically, the number of holes in which the footprint can penetrate will decrease with the shortest axis of the elliptical footprint, which is the lateral direction. Hence as the footprint gets broader, the vibrations will decrease
Mathieu van Rijswick
Eindhoven – The Netherlands
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Mathieu,
What an excellent question, and I wish I had a ready answer for you. Instead, all I can think of is how I would set up an experiment to try to find the answer. As for your three candidate answers, the first thing I want to do is check the literature because I suspect that plenty of research as been done on vibration in automobile tires. A first glance, however, suggests that the published research is mostly about road noise, not vibration experienced by the passengers. Let me think about it further.
Andrew.
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Andrew,
Thanks for the reply. I also thought about it further and did a comparison of a 700×23 tire and a 700×28 mm tire at 8 bar under a static load. That is how far I trust my mathematical and physical skills.
I calculated the tire drop as a function of the load, using the elliptical contact patch approximation and neglecting the stiffness of the carcas:
– area A = F/Pt ; (F=normal force ; Pt=pressure)
– area A = pi^2 x a x b
– long axis a = 2 x sqrt(2xRwxs) ; (Rw=wheel radius)
– short half axis b = 2 x sqrt(2*Rt*s – s^2) ; (Rt=tire radius)
– tire drop s
You can solve the tire drop s from this set of equations.
For the same load, the tire drop of the 28 mm tire (i.e. 20% wider than 23 mm) is about 10% less than for the 23 mm tire. The slope of the Force vs Tire Drop curve for the 28 mm tire is about 10% higher. Hence the spring ‘constant’ for the 28 mm tire is about 10% higher.
When I dropped the pressure in the 28 mm tire to 7.0 bar, the Force vs Tire Drop curve of the 28 mm tire almost coïncides with that of the 23 mm tire at 8.0 bar.
I try to add a chart, but I don’t think if it can be handled by your text editor.
So the wider tire is stiffer at the same pressure and if road induced vibrations are filtered by this ‘air spring’, they should be higher. Also, as the tire drop is less, the maximum suspended travel in the positive vertical direction is less.
These results confirm some statements that I read in the technical journals. For example, in http://velonews.competitor.com/2012/03/bikes-and-tech/technical-faq/tech-faq-again-bigger-tires-roll-faster_209888 “When I swapped my 700x23s for 25s they beat the snot out of me…”. My results are not nearly as drastic, but the direction is OK. In http://www.conti-tyres.co.uk/conticycle/road_tyres/GP4000sII/WideRaceTyreTest_TOUR_Magazine_2014.pdf a comparison of 23, 25 and 28 mm tires at 7.5 bar is made “Wide tyres simply felt to hard with this racing pressure. Wider tyres, according to the result of the comparative rides, need about 0.5 bar less pressure than the next-widest tyre class to achieve a ride which feels subjectively similar..” Well, this agrees remarkably close to my result of 1.0 bar drop for 28 mm to get the same force-travel curve as for 23 mm.
My questions:
– This is a purely static analysis. Do you feel that dynamic properties are also involved, as in my original ‘explanation’ for answer A?
– I am interested in damping coefficients of this air spring for vertical travel. Can I read them somewhere in your thesis? You fitted the coefficients in the Pacejka magic formula, but I don’t know how these relate to the above.
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Mathieu,
Thank you again for your detailed comments. It will take me a little time to understand all that you have written. If you would like to communicate offline, in order to send charts and graphs, you can reach me via email. I shouldn’t list my actual email address here, to avoid spam and physhing schemes, but if you search for me at uwm.edu, my wife and I are the only Dressels there.
Andrew
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