Is there a relation that estimates steering wheel angle from the lateral acceleration of the vehicle? If yes, can someone please explain. Thank you.
In practice this is very difficult because of the fact that many modern vehicles have steering gear ratios that are non-linear plus, as you accelerate, the slip angle of the tyre will increase necessitating a non-linear input of steering angle culminating in no additional increase in lateral acceleration as the tyre grip reaches saturation point regardless of increases in steering angle.
In order to generate meaningful data it is necessary to instrument a vehicle - 1. with an instrument to measure steering wheel angle, 2. with an accelerometer to measure lateral acceleration. This is the minimum necessary and usually a speed measuring device is added plus it is advantageous to know the diameter of the circle or radius of the turn you are making. The data generated will only be true for the exact vehicle and ambient test conditions at the time of measurement. Changes to the road surface, tyre specification and ambient temperature can and do alter the results.
Depending on the linearity of the steering gear, results obtained below 0.3 lateral g may be linear but above this the tendency is for an increasingly non-linear relationship between steering angle and lateral acceleration.
For a given vehicle performing a steady state constant radius turn (R) with a constant forward speed (u), the vehicle later acceleration (ay) can be simplified by the squared velocity dived by the turning radius (ay=u^2/R). The turning radius (R) varies with the steering angle in a non-linear relationship, Furthermore, the turning behavior depends up on weight distribution and tire characteristics which results in understeer, neutral steer or oversteer..
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