Rear slip angle generation

[Roni]

Hi folks,
I wondering how would we theoretically find the rear slip angle for any formula car. Finding the front slip angle is relatively easy if the cornering stiffness and the steering angle values are known. But using the some other parameters like wheel base and the front axle to CG and rear axle to CG values, is there a theoretical relation which can relate the front and the rear slip angle? Also I am assuming that the yaw velocity/rate cannot be predetermined so can't be used in a theoretical model.
I can relate the front and rear values using yaw rates but how can I assume the yaw rate in this theoretical model?

[Tim.Wright]

You need to explain a bit more what you are trying to do and what data you have available as input and whether you are talking about linear or limit operation.

There's loads of ways to calculate the rear slip angle:

• Put a slip sensor on the rear axle
• Put a slip sensor somewhere else and transform the output using the yaw rate
• Calculate the slip velocity using yawrate and latacc and then integrate it
• Calculate the rear axle lateral force then divide it by the cornering stiffness

[Roni]

Involving yaw without sensors is not possible and i am talking about a theoretical model which should not involve any hardware.
So, i will try to focus on ur last solution "finding lateral force and dividing by cornering stiffness".
Now lets say i have a tire data look up table, here my inputs are my normal load and slip angle (let us ignore SR for now) and my output is Fy. So you see my input is the slip angle through which i am supposed to find the output, the output being Fy.
I want to find the yaw moment so i need both the front and rear Fy and for the Fy, i need two inputs, SA and normal load. Finding SA in front is relatively easy but i m not able to solve for rear!!

[Tim.Wright]

Something doesn't add up here, how are you finding the front slip angle? You would find the rear in almost the same way.

Btw, are you considering steady state cornering (i.e. totaly yaw moment = 0)?

[Roni]

let us assume that the front slip angle peaks Fy at 13degs, and the 34degs is the peak steering angle. now assuming that for a particular situation, my slip angle can be calculated as "slip angle per unit of steer angle", which for example yields a value of 5.7 degrees of slip angle at 15 degrees of steering wheel actuation. even though this is not an authentic method it brings similar results close enough to a situation where my car is acting on the limit. i could find no other way of deciding the front slip angle without involving variable parameters. my primary aim is to compare the front to rear and not to find the exact slip angle. as far as i know deviations from actual value cannot effect a comparative model. i accept that the method is completely unorthodox but i am presently unaware of any other methods.

Also as of now i have taken my rear slip angle to be in some percentage of front. for example say 20% which means for 13 degrees of front slip my rear will have 2.6 degrees of slip. this method is extremely vague and which is why i am searching for a front to rear relation.

I can find my yaw moment once the front Fy and rear Fy is found.

[Tim.Wright]

What exactly is your overall target here? Are you writing a bicycle model? is it dynamic? is it steady-state? Your working has got some big errors in it but without knowing what you are trying to achieve in the end it's impossible to help...

Front slip angle is proportional to steering angle only in the linear range and only for a constant speed. You can't take the slip at peak Fy and use that as your proportionality constant because it's completely outside the tyre's linear range.

However, if you want to insist on using this input you can still calculate the rear slip angle which is a function of the wheelbase, steering angle and yawrate. Once you know the slip angle at one point you are able to calculate it for every point on the chassis.

[Roni]

It is not a bicycle model since i have considered lateral load transfer.
It is a steady state model as i am not considering any longitudinal load transfer.
My primary aim or goal is "to achieve the Fy of both the front and rear so that i can find out the yaw moment" and since i know my cars moment of inertia, i can calculate the yaw accelaration to see if it is zero or not.
Now thats all for the theoretical part.

Thn i can match my theoretical data to the actual one using a yaw rate sensor.
The only issue i am having with my model is generating slip angles, not only for rear but as you have pointed out for the front as well.
The issue is that my yaw rate is supposed to be the ultimate output not the input.

[Tim.Wright]

It's still not clear at all what you are trying to do. If it's steady state then the yaw moment and yaw acceleration is going to be zero. This is an input, not an output.

[misterbeam]

Pretty much what Tim said in his first post, the only thing i can add is that you should also take toe angle into account.

[marcush.]

Optimum slip angle for Maximum grip is depending on the tyre charecteristic (and ist interaction with the road surface)-so we have surely with load Transfer left to right the Problem we have two different vertical loads under cornering for the tyres of the same axle-In consequence you will Need to get the tyre load over slip angle characteristic into your model.

Then you will have to account for toe in toe out dynamically so both tyres will maybe see the same amount of Change in toe but not necesarily with the same effects ..as it is well possible to have the outside wheel go from toe in to more toe in whereas the inside wheel goes from toe out towards toe in...

Thirdly slip angle optimisation is also depending on camber which is also on opposits on a average car (you gain more on the outside than you loose on the inside that´s why more negative camber pays off!-normally).

I could go on certainly and find more significant Inputs into your model...but then as always omit one important one and your model will degrade to a nice exercise and be of no help to improve a race car at the track...