Oversteer maths formula

Discussion and support for i2 Standard and i2 Pro applications

Oversteer maths formula

Postby CAPMAGIC on Mon May 02, 2011 6:32 pm

Hi,

I have several questions on the oversteer formula.
edit:
This is the original formula out of i2 (it's the same in Standard and Pro version)

smooth(choose('Corr Speed'[km/h] < 50, 0, sgn('G Force Lat'[m/s/s]) * (('Vehicle Wheelbase'[m] * 'G Force Lat'[m/s/s] / sqr('Corr Speed'[m/s])) - sgn(stat_mean('Steered Angle'[rad] * 'G Force Lat'[m/s/s])) * 'Steered Angle'[rad])), 0.2)

I only adjusted the channel names to the ones we use and filled in the vehicle wheelbase to the vehicle details. On i2 Pro the formula works fine or lets just say it shows a "result".

1. Has anyone experience on using the i2 Pro oversteer formula compared to driver's experience/comments.

2. I want to know how reliable the results of the formula are and in between which range I could say "THIS is now understeering (or oversteering)!"

3. I do supervise another car which only can generate i2 Standard files. When I tried to use the oversteer formula on i2 Standard it refused to work by saying: „Binary operator does not apply to these operands.“
Is this formula too complex for i2 Standard?

Thanks for your answer.

Best regards
Julian
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Re: Oversteer maths formula

Postby PaulGM on Wed May 04, 2011 8:25 am

Julian,

In question 3, what you have found is one of the main differences between i2 Standard and Pro- the availability of what is called "Advanced Maths." In i2 Standard, the most complicated arithmetic you can perform is simple multiplication, division, addition, and subtraction. i2 Pro allows you to actually use the functions included in the aforementioned equation (i.e. Choose, Sign, Smooth, etc.). Oversteer is included as a Global Maths channel in i2 Standard, but only works because it is an internal function; when you include this math under the log file in i2 Standard, you will receive the "Binary operator does not apply to these operands" error.

As for questions 1 and 2, I'll let users speak to those.

Paul Marsh
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Re: Oversteer maths formula

Postby CAPMAGIC on Wed May 04, 2011 7:31 pm

Hi Paul,

thanks for the answer.

Can you give a statement on question 2 too, please?

I mean if this formula is developed by MoTeC, you guys have done it for some reason and you thought of something by doing so.
So you should probably be able to define a true-range for the results of the formula, aren't you?

Thanks for further help.

Best Regards
Julian
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Re: Oversteer maths formula

Postby Holmz on Thu May 05, 2011 10:19 am

CAPMAGIC wrote:Hi Paul,

thanks for the answer.

Can you give a statement on question 2 too, please?
...



Alternatively one (e.g. you) could could simulate the measurements over varius speeds, radii of turn, and levels of oversteer understeer, and run the simulation through the lines of math (?).
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Re: Oversteer maths formula

Postby PaulGM on Fri May 06, 2011 8:16 am

Julian,

The Australian engineers could most likely speak to this further, but here is my understanding-

Actual "Oversteer" or "Understeer" angle, as defined by Milliken and Milliken, refers to the surplus or deficit of wheel angle compared with the Ackermann steering angle (or the wheel angle required to navigate a turn when speed and acceleration effects are negligible).

The Oversteer formula in i2 is only an approximation, as i2 does not understand the relationship between your steering wheel angle and the actual angle of the tires in relation to the vehicle's heading (unless you tell it to). If you were to rewrite this equation using actual wheel angle, then any Oversteer angle could be deemed "Oversteer" and any Understeer angle could be deemed "Understeer," assuming again that speed and acceleration effects on slip are negligible.

However, motion ratios from the steering wheel to the actual wheel and tyre change from vehicle to vehicle, and slip comes into play at higher speeds and accelerations. Therefore, an absolute reference range can't really be supplied for the Oversteer formula, the user has to determine what an appropriate range is for their particular vehicle and conditions.
PaulGM
 

Re: Oversteer maths formula

Postby Holmz on Fri May 06, 2011 6:10 pm

PaulGM wrote:Julian,

The Australian engineers could most likely speak to this further, but here is my understanding-

Actual "Oversteer" or "Understeer" angle, as defined by Milliken and Milliken, refers to the surplus or deficit of wheel angle compared with the Ackermann steering angle (or the wheel angle required to navigate a turn when speed and acceleration effects are negligible).
...


I thought in Millikin^2 it was commanded yaw rate versus realized yaw rate. (pg 162/3 ??)
If you have a steering pot, the wheelbase, etc (or measurements of the tyres angle every so often with respect to steering wheel angle), then you know the turing circle versus steering position.
The turning circle and the speed give you the commended yaw rate.

Not sure how to get the realized yaw rate without a yaw sensor.
...unless one does something with position.


ahh I see it now... The lateral G and yaw position are related.
So this would only be valid when the tyres are pointing in roughly the proper direction, or for relatively small slip angles.
But you would be better off with a yaw position measurement.
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Re: Oversteer maths formula

Postby PaulGM on Tue May 10, 2011 1:57 am

The definition I provided is a simplification with multiple assumpitions (which you noted), which is also echoed in a few other texts, including Ch.7 of Segers' book.

I would agree that the measurement of yaw rates would be more accurate (and slip angle measurement is even more accurate than that), but this calculation is simple to provide to the customer.
PaulGM
 

Re: Oversteer maths formula

Postby CAPMAGIC on Fri Jun 10, 2011 12:22 am

Holmz wrote:Alternatively one (e.g. you) could could simulate the measurements over varius speeds, radii of turn, and levels of oversteer understeer, and run the simulation through the lines of math (?).


Back again, got some other stuff to do and "oversteer" isn't topic #1 on my list.

I'm not so into i2 Pro yet. How do I simulate e.g. a race to get some "simulated log data"?

Thanks in advance.

Greetz
Julian
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Re: Oversteer maths formula

Postby Holmz on Fri Jun 10, 2011 5:24 am

CAPMAGIC wrote:
Holmz wrote:Alternatively one (e.g. you) could could simulate the measurements over varius speeds, radii of turn, and levels of oversteer understeer, and run the simulation through the lines of math (?).


Back again, got some other stuff to do and "oversteer" isn't topic #1 on my list.

Q> I'm not so into i2 Pro yet. How do I simulate e.g. a race to get some "simulated log data"?

Thanks in advance.

Greetz
Julian


A> MATLAB, Python, C.

If you exclude a straight line course/track, then the next simplest track would be a circle.
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Re: Oversteer maths formula

Postby PaulGM on Fri Jun 10, 2011 7:00 am

To create data from scratch and actually save it to its own file, you will need to purchase the i2 API. If you already have a log file and you want to temporarily generate a few channels, you can do so using Plugins or Functions, sample code for both of which can be found in the i2 installation directory under "C:\Program Files\MoTeC\i2\1.0\Samples\Maths." There are also a handful of demo files which come with the installation of i2.
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