More Practical Steering Linearity

Hope I can express this 'issue' clearly.

When my wheel has less degrees than the AC cars, I'd like the steering linearity to accomodate this more appropriately.

Currently the steering gamma ranges from 1.0 to something large, and is simply an exponent on the steering rack input.

At 1.0, the steering is just multiplied by whatever amount gives the same lock as the car. This is fine.
At higher numbers, the input is taken to an exponent, and then the same process applies. This makes the steering less sensitive around the middle (which is what it's meant to do) but actually goes too far - the ingame wheel starts to turn less than my controller.

Here are some diagrams to hopefully make sense of what I'm saying.

Across the bottom we have the wheel input, normalized for 0 to 1. 0 is dead ahead; 1 is the maximum a 900 degree wheel can turn (450 degrees right). The vertical axis is the output angle of the wheel (up to 540 degrees). A realistic 1080 wheel would be able to turn 20% farther; so that one goes in a straight line but exceeds the maximum wheel turning.

In this plot, the slope of the line is the effective steering ratio - if it's 15:1 on the 1080, then the steeper slope means it's 12.5:1 on the linear 900 degree wheel, and infinity:1 to around 4:1 on the nonlinear.

When you have wheel gamma set to 1.0, it's the red line - at all angles, the wheel turns more quickly than the real thing. When you increase wheel gamma, it's the green line - at low angles it turns less sharply, and then at high angles it turns more sharply than the real thing.
What you can also do, of course, is set your wheel to pretend to be 1080 - then the max it'll actually be able to steer is 900, and the turning circle is larger than on the actual car.

What I'm proposing is a different method of implementing the gamma, that gives both - realistic steering angles to start with, and the ability to hit maximum lock at a lower angle.

The purple is the new function I'm talking about. It's not complicated at all:
If A is the input angle (from 0 to 1)
steer angle = A*450 + A^gamma*90
450 = 900/2 (half of controller's lock)
90 = (1080-900)/2 (half of the difference between controller and car)

The improvement is even more important on lower quality wheels though. Say you have a 200 degree wheel...

By using this formula, you have nearly 20% of lock working at approximately correct steering ratio, rather than it either being entirely too quick (gamma=1) or huge deadzone followed by insanely quick (gamma=3.5)
To recap, in this case, the purple formula, again with A being the normalized input angle, is
steer angle = A*100 + A^gamma*440
100 = 200/2 (half of controller's lock)
440 = (1080-200)/2 (half of the difference)


Also note that if you set gamma=1.0, you have no change to the effective steering ratio compared with the current system. So anyone who's running that will feel no difference.
angle = A*450+A^1.0*90 = A*540 = same as now.

 

It would easier if Kunos tested the steering on a older wheels with 270 degree locks or lower.
then they may understand a bit more what the problem is.