# Calculating motorcycle lean angle

motecben
I would like to calculate racing motorcycle lean angle but my trig is very rusty. Data I can supply for the calculation includes 3 axis of G, 3 axis of gyro (rate of change). The gyro drifts with time as all gyros do. I also have 2 wheel speeds and GPS speed available. There are maths functions available for integration and differentiation among others.There would obviously have to be a correction put in for lateral G as the sensor is fixed on the bike.

A further interesting addition would be a compensation for the banking of a track surface. Any help in this area would be greatly appreciated.

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markjenn
motecben said:
I would like to calculate racing motorcycle lean angle but my trig is very rusty. Data I can supply for the calculation includes 3 axis of G, 3 axis of gyro (rate of change). The gyro drifts with time as all gyros do. I also have 2 wheel speeds and GPS speed available. There are maths functions available for integration and differentiation among others.There would obviously have to be a correction put in for lateral G as the sensor is fixed on the bike.
A further interesting addition would be a compensation for the banking of a track surface. Any help in this area would be greatly appreciated.

This is all back of the envelope, but it might be right:

Assuming a flat surface and no skidding, the lean angle of the motorcycle is related to it's speed and the cornering radius as follows:

theta = arctan ( V*V / r*g)

Where g is the gravitational constant.

Now, I think you can also show that the turning radius is related to speed and lateral acceleration as:

r = V*V / a

where a is the lateral acceleration.

Substitute r in the above and you get:

theta = arctan (a/g)

So to pull 1.0 g, then you need to be turning at a 45 degree lean angle. This is the theoretical limit assuming tires can't achieve coefficients of friction greater than 1.0.

So if you really have lateral acceleration, you don't really need anything else (I think) to get lean angle.

Where are you getting (or planning on getting) your lateral G's? Are there any small sensors out there suitable for motorcycles?

- Mark

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motecben
Motorcycle lean angle

Hi Mark and thanks for responding. This was the first time I had used this forum and I posted the same question in 2 separate areas. Yours was the only reply after several weeks!

Yes we have small accelerometers that we can run on bikes from Crossbow in the US. They are very difficult to mount in such a way as to not get too much vibration interference but sometimes we get them to work OK. We can introduce filters that will assist somewhat. The problem that I am not sure whether you have addressed is that the lateral G sensor is fixed on the bike therefore the gravitational pull on the sensor changes direction as the bike leans so there has to be a correction put in somehow?

Thanks again for your thoughts. If you have any more, please continue to post them.