# Motorcycle tire circumference change with lean angle and acceleration

1. Dec 20, 2011

### dragilla

Hello,

First of all - I love this forum - so many interesting topics!

My question is quite complicated - at least for me. My high level goal is to measure lean angle based on the difference of speeds between the front wheel of the bike vs the 'real speed' (let's just assume I have the accurate speed). I want the lean angle in relation to the tarmac not the ground - that's why I don't want to use accelerometer/gyroscope. I don't care about the sign of the angle - if the lean is to the left or to the right - I just need to know the value - how much is the bike leaned.

The next goal is to make this possible with as simple measurements of the tire as possible. In my application the tires will be changed frequently and possibly different tires will be used so I need to be able to perform quick measurements (like width, height when off the ground, then width height when under load of the bike + maybe some measurement of the profile shape),

I found this document that describes some basics of my problem:
2004_02 A Motorcycle Tire Model for Dynamic Simulations MECCANICA.pdf

But I think it's still too little for me.
The main problem here is to determine a formula for the tire profile shape, as it varies from tire to tire. I tried with a parabolic shape, but that does not match all the tire shapes, some are rounder, some maybe a combination of these two.
The other problem is to determine how the tire flattens under load (consider acceleration/braking forces - I have accelerometer/gyroscope on board, so I know the acceleration and the right direction of it) and how that affects the circumference.

As for the speed measurement I have magnetic sensors on the wheel and a counter, so I just count the pulses in a time period and knowing the circumference I know the traveled distance and thus the speed.

I know this is a complex problem, but I would really appreciate some help as I'm not an expert in the matter of physics and my math skills are 'overdue' (studied math over 10 years ago) - although it comes back to me slowly :)

regards,
--
Luke

2. Dec 20, 2011

### Simon Bridge

What's the difference? Or do you mean you don't want the angle to the horizontal because the road may be on a camber?

The angle of the lean will depend on the radius of the turn, the surface properties, the tire type and material, and the speed. It is not a static property of the tire. Unless you are talking about something else?

The actual geometry of the tire can be determined as the paper suggests - take a photo of it end-on, and fit a cubic spline. You'll want to make a database of different commercial tires likely to be fitted to the model of bike you consider. Similarly, the deformation under different loads can be found for a given tire by putting it under load and photographing it.

You need to consider how closely you want to model reality too.

Of course, if you want to measure the lean of the bike to the road, a laser range-finder on each side of the bike, pointing down, will do this.

3. Dec 20, 2011

### dragilla

Thank you for your answer,

That's what I ment.

I want to measure the actual lean angle, not the theoretical one.

Ok. This might be the best choice, so I will stick to it for now. I will be adding tires as needed.

If I can determine the lean angle with accuracy of +/- .5 degrees then I'm perfectly happy.

Well I would need more than one on each side as they only work in a narrow angle, or I would have to change their angle with the bike's angle change - not really a good idea. Besides such range finders are really expensive.
Besides I need the circumference calculation for different purposes in my application.

regards,
--
Luke

4. Dec 20, 2011

### Simon Bridge

[With range finders?]
Nope - just mount them on either side of the seat pointing down, parallel to the bikes axis - further apart the better (for the measurement). So you only need two.

You could use radar instead - possibly ultrasound, but you'd have to find a frequency not used by the bike. You need something that will sense the road.

You could pull a cart that carries an artificial horizon, and carry one on the bike. The difference is the lean wrt the road.

You could mount a camera close to the rear wheel pointing backwards so the road is visible - as the bike leans the picture does also and the amount the road-surface in the picture leans is also the lean of the bike. A lot depends on the surface and the bike.

You could mount a wheel either side of the bike, in contact with the road, on a hinged arm, as the bike leans the arm bends - you can rig a spring to keep the arm from bouncing too much and a sensor to tell how much bend in the arm.

Be creative!

You can have quick, accurate, or cheap ... pick two.

You can detect the turn by a horizontal accelerometer axially mounted on the bike - this and the speed gives the radius of the turn - with time gives the arclength.

Do you plan to run the bike in circles then?
What is the application?

5. Dec 20, 2011

### dragilla

Actually I am being creative... with my idea. I've already checked all the options that you write of. None of them fits my needs. Either too slow, too expensive or unpractical.

The application is a traction control unit for a road racing bike. I do telemetry at the same time.
I need to compare wheel speeds and to know when the rear is sliding. To do that I have to know the lean because front/rear have different profiles. I could calculate the lean from the accelerometer + gyroscope + gps speed like in DCM applications, but that measures the lean vs the horizon, so I've decided to try co measure the lean using the front wheel and compare the rear wheel speed with the gps speed to check if rear is slipping. There's a lot of other factors but I want to focus on my question :)

I need an Idea how to determine the level of change of the circumference of the tire under changing load (acceleraion/braking). Also If someone could help me understand the whole process behind the document I quoted, maybe on a example, from a photo(photos) to a formula for circumference (lean angle, tire load based on acceleration and wheel radius as variables) then it would be great! :)

I know I'm asking for much, but maybe there are some motorcyclists here that want to help me :)

Last edited: Dec 20, 2011
6. Dec 20, 2011

### Simon Bridge

Then your constraints are too strict.

Good luck.

7. Dec 20, 2011

### dragilla

Ok, I've pictured my tire (attachment 1 - DSC02097.jpg). Then I cut a fragment of it and put points on it (attachment 2 - unloaded.JPG).
I've got. [0, 0], [11, 1], [24, 5], [36, 12], [50, 27], [61, 44], [67, 59] (I used the grid in gimp). What interpolation should I use to get the formula for this?
Cubic spline of course ;) But what I meant was how do I fit those points into a cubic spline if they are not 100% accurate. I should be interpolating a cubic spline that goes through circles with centers at those points and radius of say 2.
I need a method for this... I need to get do an approximate some how, because now all I get is a function that is divided into sections limited by my points :(

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Last edited: Dec 20, 2011
8. Dec 21, 2011

### dragilla

Ok. Nevermind that. I can find a flat track, and use the dcm algorithm to produce a table:
front_tire[speed_difference][acceleration] -> [angle]
rear_tire[speed_difference][acceleration] -> [angle]
This way I can teach my device new tires instead measuring them.
Thanks.

9. Dec 21, 2011

### mender

Another method would be to have an accelerometer acting in the vertical axis of the bike. Find a way to filter out the bumps and you can calculate the lean angle by the g reading.

ETA: I just realized that this wouldn't work if the rider's C of G is offset.

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