Checking the rolling radius -6 July 2008

Index

1. Experimental description of measuring the tyre compression under load
2. Links to various web articles

1. Experimental description of measuring the tyre compression under load

Here are pictures of my experimental measurement described in the posting on the course measurement forum

The first is of me loading my bike with my weight while measuring how much closer the front wheel rim gets to the ground:

Below is a picture of the scale showing the pointer attached to the wheel rim giving a reading of 18.4 mm (the zero of the scale was perversely taken as the long ruling opposite the centre of the hole)Under magnification of the original image it was possible to read the scale with a maximum error of about 0.2 mm. I am in position above the bike seat but I have no weight on the seat or the handle bars. I am standing on the books you can see on the floor in the picture above

Now I have placed my weight on the bike and the handlebars in my normal riding position. You see in the picture below that the pointer is now reading 14.5 mm. The tyre has compressed by 3.9mm under my weight. If you look where the tyre is touching the ground, you can see that in the picture below (under load) the length contact point with the ground is decidely longer than on the unloaded picture above. (The two pictures are at exactly the same magnification.) It would be rather difficult to see the actual contact patch unless one were to photograph from below through glass.

An interesting experimental note is that during the setup we had the tyre and scale resting directly on the floow which is a slightly cushioned type of plastic floor covering. Our first reading of deflection under load was only 1mm. Presumably the bike wheel was deforming the floor covering! We sooned fixed that by placing a rigid bit of chip bopard (the white rectangle you can see in the top photo) on the floor and placing both the bike tyre and the scale on this firm base.

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2. A collection of links

• A lot of interesting theory on car tyres and their analysis from an on-line education course on rubber technology by a Scandavian University consortium, likely done under EU funding. The course index conatins general topics on rubber.
• The Physics of racing Brian Beckmans series on how to model racing car tyres -- analyses the MAGIC FORMULA. {H. B. Pacejka and I. Besseling} Worth a look but not yet obvious what can applied to the measurering bike wheel - racing car tyres seem all about aclleration, braking and cornering, none of which appears particularly relevant to bicycle measuring wheel.
• Brush model - The brush model states that the contact patch between the tire and the road is divided into an adhesion region where the rubber is gripping the road and a sliding region where the rubber slides on the road surface. The total force generated by the tire is then composed of components from these two regions.
• Stretched string model
• My thin elastic membrane theory probablywas overtaken by more sophisticated theories over the last century and particularly in the last 50 years incuding the wide application of Finite Element Methods made possible with modern computers. Perhaps we have to go back to papers like F. Whipple, “The stability of the motion of a bicycle,” Quarterly Journal of Pure and Applied Mathematics, vol. 30, pp. 312–348, 1899.in order to find people dealing with such simple theories as thin elastic membranes!
• An amateur measuring bicycle contact patch area Tom's Place
• Bike tyres explained

Page last updated 8 July 2008