Track portion of a road course

I think you need to ride on the track. I might accept full laps on the track as being their advertised distance (with the standard track measurement that tapes the radii) but any time you get away from that, I think you need to measure.

It would be interesting to know how far off you are. I would suspect that if you could lay down the line on the track that you need to measure you would probably be pretty accurate, but it's hard to stay either 20 cm or 30 cm off of one of those lines on the curves.

There's probably a different coefficient of friction between asphalt and concrete, and certainly between either and crushed limestone. I guess you could try an experiment where you calibrate on 100 meters of the track and see how much different your numbers are. I bet you're not off by very much.

1. Assume you aim to ride 30cm from the inner kerb but make an averaged of 10 cm error round all the bends. (a very generous error allowance) 500m will be 1.25 laps, so 10cm will correspond to 5/4*2pi*10cm = 75cm.

2. I have measured on tracks and for my tyres I think the change of calibration will be less than 0.1%. So 500m might give a max error of 50 cm.

Total error if riding is thus not more than 1.25m. So if this was start/finish of a 5K or longer course then it would easily be covered by the SCPF.

If the course was much shorter than 5k, then perhaps a different approach might be needed. Although one could rely on the track marking if it has been certified, there is still going to be the section from the start lap to the exit gate, and something similar on the return. If I was not allowed to ride on the track surface I would measure these with a steel tape and with the help of an assistant.

Incidentally, I dont think anyone has proved that the coefficient of friction makes a difference, although I do suspect it may possibly make a contribution to the variation in calibration constant on different surfaces. What we do know for sure is that the roughness of the surface has an effect on the calibration constant. I took data on this including on a rubber track over ten years ago.

Aren't the guidelines for building and marking a track much stricter than our own? I think I would trust that the distance between the 200m mark and the finish is 200m more than I would trust our ability to measure it.

Unless the course is entirely on the track it will be necessary to measure the route used to get onto the track. This is unlikely to be recorded in any of the track's layout dimensions. So, if you have to do a little on-the-track measurement, why not take the rest of the lap? I can't see how the measurement can be done without at least SOME actual on-the-track measurement.

As for accuracy of measuring on the track, it's probably no worse than trying to hold a decent line on a long, sweeping curve.

Olympic Marathon Track Measurement

In 1996 a group measurement of the Atlanta Olympic Marathon course was done by a group of 27 riders. Part of the measurement included a full lap of the track.

The curbing had not yet been installed, but there was a peripheral metal perforated drain where the curb would ultimately be placed. We assumed that the outer edge of this drain represented the outer edge of the finished curbing.

Each measurer was invited to submit his own report of the entire measurement. Bob Baumel included a look at the track measurement as part of his report. Below is a chart from it.

Note: In our final analysis, the track was assumed to have a full lap length of 400 meters.

Of these 27 riders, 18 are within the range which would be given by my rough calculation of maximum error quoted in my post above, which for 400m would be 398.97 to 401.03 m, 9 lie outside the range but only just outside, except for DK who presumably had some additional error in his ride.

I think this experimentally demonstrates that if you do decide to ride then the surface and bend is not going to upset the measurement of a 5k or longer race.

quote:

Incidentally, I dont think anyone has proved that the coefficient of friction makes a difference, although I do suspect it may possibly make a contribution to the variation in calibration constant on different surfaces.

The friction coefficient must make a difference. If friction was zero then the weights of different riders would not cause a change in the circumference of the tire. Since we know the rider's weight does make a difference, we know that friction matters.

I did a quick experiment to check this. First I made 4 rides on the 200-meter cal course in front of my house. I then smeared motor oil on my tire and made 4 more rides. The rim readings were:

No oil: 66, 67, 65, 67
average = 66.25

Oil: 65.5, 67, 63.5, 64
average = 64.75

The difference in the readings wasn't big, but I doubt the friction was very different either, since the tire quickly collected dirt and grit on the short ride to the cal course.

Mark,
There must be more to your numbers than you reveal. A change from 66.25 to 64.75 is a change of 2%. This is far higher than anything in my experience, so there is obviously something wrong with you readings. Presumably you have some wheel revolutions which are not stated. What are the readings? Hundredths of a revolution?

Making a guess about this and taking a wheel circumference of 2.1m. I calculate your fractional change to be around 0.015/95 which now comes out at 0.015%.

However, by your own admission your oily tyre picked up grit. This would make the diameter larger and could easily reduce the count by 0.015%. In fact I have experienced something very similar when I was riding up and down a calibration course many tens of times, and in the middle of this exercise. There was a very brief shower which just wetted the cal course. The cal course was very dusty and I was amazed to see my tyre coated with a fine sticky coating of dust. The count immediately dropped slightly (because the tyre diameter was larger). By a few rides later the surface had dried and the wheel had cleaned up. The count was then restored to the the earlier reading. I have got all this data somewhere in my ten year old field note book, which I could pull out if required.

So basically Mark I don't accept your experiment as described as necessarily showing the effect of friction.

I think there are reasons to think that friction could in principle have an effect, and I have certainly observed this on icy roads which is a pretty extreme situation. However I am fairly certain that the roughness of the surface is the major cause of calibration in most situations.

quote:

Originally posted by Mark Neal:
The friction coefficient must make a difference. If friction was zero then the weights of different riders would not cause a change in the circumference of the tire. Since we know the rider's weight does make a difference, we know that friction matters.

Oh, and by the way you have described the effect of weight incorrectly. More weight on the front wheel has to be supported by the contact patch between the pneumatic tyre and the road increasing in area. The pressure in the tyre remains constant to the first approximation, and this pressure operating over a larger area supports the increased weight.

When the contact area is increased by squeezing the tyre under the increased weight, the tyre is squeezed and the wheel hub gets closer to the ground. This reduces the effective rolling radius of the wheel. All this happens irrespective of the value of the coefficient of friction between the tyre and the road.

Sorry. My numbers were in hundredths of a revolution.
No oil: 99.66, 99.67, 99.65 99.67
Oil: 99.65.5, 99.67, 99.63.5, 99.64

By definition, the only thing that will change the effective rolling radius of a tire is a change in the perimeter of the tire. (I should have said perimeter and not circumference before). The hub moving closer to the ground does not, by itself, change the effective rolling radius. If the road surface applies no force in the circumferential direction of the tire (frictionless case) the stress and strain in the tire in the circumferential direction does not change. Actually, the strain will change slightly due to Poisson's effect, but this will be very small compared to changes that would be caused by friction forces in the circumferential direction. Since there is no change in the strain in the circumferential direction, there is no change in the perimeter.

Well, I guess our tyres and surfaces must be very different, or at the very least our understanding of what happens is very different.

This is what I think happens with my tyre on roads here:

1. The flat patch of tyre in contact with the road does not slide over the road. (If it did I think I would come off the bike too easily when going round a corner.)

2. Since I have assumed it does not slide it does not matter what the coefficient of friction is, because by my assumption the coefficient of friction is large enough to prevent any tyre slip.

3. Now it is just a matter of geometry to show that effective rolling radius is equal to the distance of the axle from the ground.

(Of course you are correct in saying the longitudinal circumference of the tyre has to change in this case - it does - because the length of the flat contact patch is less than the arc of the tyre if it where free and not compressed into the patch. Yes there are friction forces which act to compress the rubber in opposition to the air pressure acting on the curved surface which expands it. These friction forces do exceed the coefficient of static friction, otherwise my tyre would be slipping - This is why rubber is used for the tyre and a textured asphalt for the road -a high coefficient of friction which can provide the forces without any slipping occurring.)

2. Since I have assumed it does not slide it does not matter what the coefficient of friction is, because by my assumption the coefficient of friction is large enough to prevent any tyre slip.

The normal force, and therefore the friction force, the road exerts on the tire is not constant under the entire contact patch. At the center of the patch the friction force is high and the tire does not slip. At the edges it is low, and it does slip. How much of the edge slips depends on the friction coefficient. And how much slips affects how much the tire's perimeter changes. It's not a matter of either the whole thing slips or it doesn't.

3. Now it is just a matter of geometry to show that effective rolling radius is equal to the distance of the axle from the ground.

Here's one of many references online that contradicts the above statement.

http://tinyurl.com/5fl5wk

It's a commonly held belief that is simply not true. Consider a tire that is infinitely stiff in the circumferential direction, but has no bending stiffness. You can still flatten it but you can't change it's effective rolling radius.

quote:

Originally posted by Mark Neal:
The normal force, and therefore the friction force, the road exerts on the tire is not constant under the entire contact patch. At the center of the patch the friction force is high and the tire does not slip. At the edges it is low, and it does slip. How much of the edge slips depends on the friction coefficient. And how much slips affects how much the tire's perimeter changes. It's not a matter of either the whole thing slips or it doesn't.

This is not a correct model for my bicycle tyre which has a thin flexible tyre with only about 1 to 2 mm of thickness including the rubber tread, so in my model I regard it as a thin membrane (like the membrane of a toy balloon.) The patch of tyre in contact with the ground is roughly oval shaped. There is no curvature of the tyre over the whole of this contact patch, so the streeses in the tyre membrane act only the the plane parallel to the ground. This means the whole of the air pressure in the tyre has to be supported by the ground pressing upward on the tyre over the whole contact patch. The pressure is constant, so the upward force per unit area is everywhere the same. The force per unit area does not fall off at the edges as you claim. Provided you are not riding on ice there is no need for any slipping, the frictional force will not exceed the limit given by the coefficient of friction.

If I had a tyre which was not like a membrane but for example had a very thick tread and walls that were very stiff, then I would get different characteristics, perhaps somewhat closer to what you describe. And to a very limited extent just at the point of contact I accept that my simple model may be incorrect since the assumption of a thin membrane is clearly inappropriate when I have a tyre and tread say 2mm thick which will need a force to bend it. but if the contact patch is several cms long then I would have thought the edge effects can be neglected to the first approximation.

quote:

3. Now it is just a matter of geometry to show that effective rolling radius is equal to the distance of the axle from the ground.

Here's one of many references online that contradicts the above statement.

http://tinyurl.com/5fl5wk

It's a commonly held belief that is simply not true. Consider a tire that is infinitely stiff in the circumferential direction, but has no bending stiffness. You can still flatten it but you can't change it's effective rolling radius.

Unfortunately the URL you give is to a google books limited view of a book. I find it hard to make a definitive judgment - but I do note that it is referring to motor bicycle wheels of which I have no direct experience. Do they have much thicker treads? Are the inflation pressures relatively low like a car tyre? They are certainly much greater cross-section and wall thickness than my bike tyre so may operate somewhat differently.

The reference gives a very interesting formula for calculating the rolling radius, but the extract unfortunately does not say how this is modeled or empirically derived. The formula says Rolling radius Ro lies between the wheel radius R and the axle to ground distance H, which I can easily accept, but I dont think a bicycle tyre would be Ro=R-(R-H)/3, I think it is going to be more like Ro=R-(R-H)/n, where n is only slightly larger than 1.

Have you got a better reference which is applicable to the well inflated bicycle tyre? I had a look at about 100 google hits, but mostly it is rubbish you find. many years ago I asked the technical director of a Formula 1 tyre manufacturing company for a good book. He could not give me a good reference.

Your model of the situation means that there would be ZERO dependence on friction. Not a small dependence, ZERO. Either the tire completely sticks or it doesn't. Do you really think that is the case?

I think with all your google hits you have discovered, as I did a while ago, that the effective rolling radius is not a matter of simple geometry. I found entire papers devoted to calculation and emperical measurement of the effective rolling radius. Of course all of them concerned automotive tires. I don't think it's likely that either of us will find many papers about bicycle tires. I doubt there's much funding out there for research into bicycle tires, at least not for the rather esoteric topic of effective rolling radius.

If you are really interested I can see if I can dig up the references I do have.

Mark,

I agree my model implies zero dependence on friction. But my model assumes that the tyre is a perfect thin membrane, which it is not. It is about 2mm thick and forces will be needed to bend that thick membrane at the point the tyre meets the ground. I have neglected this in my model. It is in this region within 2 or 3 mm of the front edge of the contact point and at the rear edge, that the bending force and quite possibly also the friction forces (and possible slipping) may cause small deviations from my simplified model.

During my google search yesterday one of the hits I found was my own paper written 10 years ago! It is on the web at http://www.coursemeasurement.org.uk/measurers/report/mnsurfpt3.pdf This morning I have reread it. Although there is a lot of detail which readers will find quite hard to follow, it is relevant to extract one quote from my conclusions:

quote:

I have arrived at a new understanding of the rotating deformed tyre. There are two contributions to the effective rolling radius and hence to the calibration constant. The axle-ground separation is the dominant parameter. In one sense it is determined by the deformation of the tyre as calculated in this article. In another sense it is caused by the circumferential compression of the tyre in contact with the road. There is a circumferential compression as each element of the tyre contacts the road, and there is further compression as it passes under the axle. Without this compression the effective rolling radius would equal the unloaded radius of the tyre. It appears to me that this basic geometrical result is not dependent on the surface roughness.

You will also see from the paper that in my struggles to understand this whole topic I did indeed assume that the coefficient of friction between the tyre and the ground was high enough such that no slipping occured. If I am wrong about this assumption then motorbike tyre model which you describe may be more appropriate.

It is amazing how a night's sleep sharpens one's appreciation of a problem. This morning I realised I had experimental data which supported my model of a thin elastic membrane over the stiffly belted model of the motor bike tyre:

My measuring wheel has a radius R of about 350mm. When I compare the calibration constant which is obtained when riding and with that when pushing my bike I find it increases by about 1%, so the effective rolling radius when riding, Ro, will be 350-3.5 = 346.5mm.

Taking the motorbike tyre equation mentioned above of Ro=R-(R-H)/n where n=3, we see this would give (R-H)=3.5*3 = 10.5 mm, so my front axle should get 10.5 mm closer to the ground when I put my weight on the bicycle. Without doing the experiment I know the compression of the tyre is a lot less than this, so clearly for my tyre at its normal operating pressure of 80psi, n is smaller than 3.

I now realise I can probably measure the value of n using the above mentioned calibration constant change of 1% if I actually go out today and directly measure H when I put my weight on the tyre. Hopefully this will determine whether my thin elastic membrane model, or the stiff tyred motor bike model is more appropriate.

I am afraid we have probably highjacked Jim's thread far too much with this discussion which has moved far off his original topic. If we continue I suggest it should be on a new thread which measurers not interested in such arcane discussions can safely ignore!