Lateral Force Calculation

[M.logan]

Hi everyone,

I wanted to calculate lateral force acting on the car so this is the procedure I followed :-
Y = ((Cf+Cr)* β)+(1/V*(aCf-bCr)*r)-(Cf*δ)
Where Cf and Cr are the cornering stiffness(tires), Y is Lateral force, β vehicle slip angle, a and b is the distance from front and rear axle to the CG respectively, V vehicle velocity, r is the angular velocity and δ steering angle.
1)Cf and Cr were got from the tire data sheet
2) V – vehicle velocity of about 14.7 m/s
3) a and b from the CG location of our car
4) δ=l/R where l is the wheelbase and R is radius of curvature of the skidpad track
5) r angular velocity = V/R
6) For calculating β
6.1) Using the formulae αr = β – br/V
6.2) αr and αf are the front and rear tire slip angles
6.3) To calculate α r the condition that the car is tilted to an (φ) angle of 60 degrees because this would have similar g’s as in skid pad.
6.4) αr = (W sin⁡(φ))/2Cr
I wanted to know if the procedure followed is correct or not ?

Regards
M.logan
Ashwa Racing
Vehicle dynamics

[Claude Rouelle]

Sorry M.Logan but I do not understand "the car is tilted to an (φ) angle of 60 degrees because this would have similar g’s as in skid pad" What do you mean? What is φ?

[sjfehr]

The coefficient of friction of tires is not linear, but decreases with load, and is further impacted by dynamic load transfer during cornering. Placing the car on the platform is going to result in a much lower gravitational downforce perpendicular to the tires than the car would experience on the skidpad, impacting not only frictional values from the tires, but also impact to suspension geometry through dynamic camber change. Additionally, the front and rear wheels are going to be experiencing different slip angles in a turn vice on a platform, due to the steering angle. Beyond that, the left and right wheels are going to be experiencing different slip angles, as well, depending on skidpad diameter and tire alignment. So you're going to have to calculate what each of the slip angles is in the turn individually based on skidpad radius and all the other parameters of your car (wheelbase, alignment, etc).

This isn't even touching on surface dependencies and aerodynamic forces. In short, while I'm sure you could mathematically predict skidpad performance from a tilting platform (and vice versa), it's so complicated, and entirely reliant on numbers none of the tire manufacturers provide, that at best you're only going to be able to come up with a rough approximation. Would be better to simply test, I think.

[Claude Rouelle]

Sorry M.Logan but I do not understand "the car is tilted to an (φ) angle of 60 degrees because this would have similar g’s as in skid pad" What do you mean? What is φ? You say the car is "tilted?" Is φ the Roll angle....???

Second, If you know the radius (I assume you speak about the FSAE skipad pad) and you know the speed (14.7 /s = 52.9 km/h) I guess you cal already calculate the lateral acceleration so what as the title of your post is "Lateral Force Calculation" what is this about?

Third, If you impose the steering δ you can have several solution for β... unless you impose you yaw moment to be 0. On the skid pad the yaw moment should be 0.

[M.logan]

Thank you Claude
If the car is placed on a platform and titled by an angle of 60 degrees (φ) and I used this approximation so that an estimate of the tire slip angle experienced in skid pad could be calculated.
I also wanted to calculate Yf and Yr front and rear lateral force so I did not use lateral acceleration.
For the estimation of β vehicle slip angle I am still looking for different solutions and looking forward to learn more about it .


M.logan
Ashwa Racing
Vehicle dynamics

[Claude Rouelle]

M.Logan,

"If the car is placed on a platform and titled by an angle of 60 degrees (φ) and I used this approximation so that an estimate of the tire slip angle experienced in skid pad could be calculated."

Sorry But I have no idea of your thought process when you go from the tilt angle to the slip angle. Can you please elaborate?

Claude

[M.logan]

(φ) is the road bank angle (this φ is same as the one on page 134 in Race car vehicle dynamics)
I am making an assumption that when the car is on a banked road with bank angle 60 degrees it would be experiencing the lateral acceleration that it would experience on skid pad from which I could get the tire slip angle ( αr = (W sin⁡(φ))/2Cr ) then the vehicle slip angle from which Yf and Yr front and rear lateral force can be calculated (then estimate lateral force at each tire).

M.logan

[Claude Rouelle]

M.Logan,

Ohhh OK

1. Do you have such road bank angle in FSAE / FS competition?

2, I am making an assumption that when the car is on a banked road with bank angle 60 degrees it would be experiencing the lateral acceleration that it would experience on skid pad. How do you make this assumption?

I am not following your way of thinking....

Look, you know your FSAE skild pad turn radius and you know what is a good skid pad lap time on dry and on wet (FSG) so from there it is easy to calculate what a good lateral acceleration is....

[M.logan]

Claude
I am aware of that there are such road bank angle φ in FSAE the assumption is on the basis that :
M*V^2/R = M*g*tan(φ)
M is the mass of the car, V is the velocity of the car (from skid pad),R radius of the track (from skid pad)
Using the above relation I got an approximation of φ of 60 degrees and the another reason being that I could calculate the rear tire slip angle from αr = (M*g*sin⁡(φ))/2Cr from which i could get β, Yf and Yr.

M.logan

[sjfehr]

Slip angles are related to the dynamic movement of the tire rubber as it deforms under stress and the tire rubber begins to snap back audibly; you're not going to be able to reproduce that on a static platform even if you manage to align the tires perfectly. In a static setting, you're not going the see the profile below, you're going to see symmetrical deformation front-to-rear.

http://www.mgf.ultimatemg.com/group2/suspension/chassis_and_handling/slip_angle2.jpg

Likewise, if you tilt the platform to 60 degrees, you'll have half the downforce on the tires than you would if the car was level. You won't have half the grip, though; the coefficient of friction (and the resultant frictional force) doesn't scale linerally. Half the downforce on the tires is going to give you some value between 0.5x and 1.0x as much friction as the car would on a level surface.

[M.logan]

sjfehr
I agree that the effect cannot be reproduced on the static platform but my concern is that can I use this expression αr = (M*g*sin⁡(φ))/2Cr to calculate the tire slip angle which involves the road bank angle.
It would be great if someone could give some guidance to calculate the lateral force on each tire or slip angle (fom which I can calculate the front and rear lateral force )
M.logan

[Claude Rouelle]

M.Logan,

I still do not understand what you want.

"...my concern is that can I use this expression αr = (M*g*sin⁡(φ))/2Cr to calculate the tire slip angle which involves the road bank angle."

Why and how do you want to do that?

I am traveling and I do not have the RCVD "bible" with me so I do not see the page you refer to but I feel you are attacking the problem by the wrong end.

The lateral tire force is dependent of many things, one them being the tire slip angle. The slip angle is ATAN (Vy/Vx) (in the tire coordinates). What are your tire Vy and Vx on the tilt table?

Also the tire coefficient of friction is very dependent of the tire temperature and the micro roughness of the surface the tire is on. Whether the skip pad in on dry or on wet (FSG), the tire temperature and the roughness on the track can be really different than the ones of the tilt table.

Let me offer to you another thinking avenue...

I suggest you create a simple Excel spreadsheet.

Start with a 2 wheel model and with tire cornering stiffness which are constant (That is not realistic but let's try this way first, at least the result of the exercise will be relevant for small slip angles)

1. Make a choice of a wheelbase, a vehicle mass and mass distribution; that will give you a and b
2. Make a choice of a given front and rear tire cornering stiffness. Allow yourself to have them possibly different
3. Impose a given speed
4. Make a matrix of beta (Car CG slip angle) and delta (steering). Let’s say Beta and Delta from -10 to + 10 degrees by step of 2 degrees
5. For each step of the matrix calculate
- Front and rear tire slip angle
- Front and rear tire lateral grip
- Total lateral force and lateral acceleration at the CG
- Yaw moment
- Corner radius
- Yaw velocity

You can do the same exercise but you impose the radius and you have to find what the speed is.

After that you can imagine to do the same exercise with tire non-linear cornering stiffness.

Then with 4 wheels (and lateral weight transfer).

If you have the guts to create these spreadsheet and make it downloadable on this forum, I promise you to comments on them and help you to understand what it means, how it works and how to use it for in the car design. It could be a long process (probably several days of exchange on this forum / I am not necessarily available everyday) but I guarantee you will learn a lot from it.

Ready for the challenge?

[M.logan]

Claude,
Yes I will do the best I can to get the results.

M.logan

[Edward M. Kasprzak]

Hello M.logan,

According to your original post you are trying to determine the lateral force acting on your car during the skidpad event. The skidpad has a known radius and you have specified a speed.

Assuming steady-state cornering you can calculate your vehicle lateral acceleration ("V squared over R") from the known speed and radius. Newton's second law gets you to the required, total lateral force. To split this between the front and rear tires requires the condition that yaw moment equals zero (a requirement for steady-state). You are using a "bicycle model" of the automobile, so this is straightforward. Furthermore, assuming tires described by constant cornering stiffness values as in RCVD--which is not reality but it *is* a useful assumption while learning the basics--you can back out your front and rear tire slip angles from the front and rear tire forces.

There is no need to impose a roadway bank angle to simulate an applied lateral force on the vehicle. And you don't need slip angles before you determine the tire forces. RCVD page 134 describes straightline running on a tilted roadway, which is not your vehicle operating condition.

[M.logan]

Edward
Thank you for the reply and for calculating lateral force I am using Y = ((Cf+Cr)* β)+(1/V*(aCf-bCr)*r)-(Cf*δ) as this would also be considering the vehicle slip angle and steer angle with which I can fill the matrix .


M.logan

[Edward M. Kasprzak]

And I'm saying you don't need this formula to calculate Y. Use Newton's second law. Then, use this formula to determine β (given your assumption regarding δ). It's a lot easier than trying to determine β first before calculating Y.

[M.logan]

Claude,
This is the link for the calculations : https://drive.google.com/file/d/0B1jP2vKD5yx9SzZDZzNuSWkwMzg/edit?usp=sharing
This file contains


1. Make a choice of a wheelbase, a vehicle mass and mass distribution; that will give you a and b
2. Make a choice of a given front and rear tire cornering stiffness. Allow yourself to have them possibly different
3. Impose a given speed
4. Make a matrix of beta (Car CG slip angle) and delta (steering). Let’s say Beta and Delta from -10 to + 10 degrees by step of 2 degrees
5. For each step of the matrix calculate
- Front and rear tire slip angle
- Front and rear tire lateral grip
- Total lateral force and lateral acceleration at the CG
- Yaw moment
- Corner radius
- Yaw velocity

I was unable to get results for the Front and rear lateral grip and my understanding about lateral grip is that it is the difference between the lateral force and the Traction force but I was unable to quantify it.


M.logan
(The file is on the googledrive and it is available for download as an excel file .)

[Claude Rouelle]

M.Logan,

Can you make the spreadsheet better organized so that we have all the car data on top than a big spreadsheet with the beta horizontally and the delta vertically (or the other way around) and the display of all the output in one megacell splitted in mini cells where we can find the front and rear slip angle, the front and rear tire lateral grip in the tire and chassis coordinates, total lateral force at the CG, the yaw moment, the corner radius and yaw velocity?

Use the same color for the same family of results.

Also avoid to have too much blanks, non used part of the spreadsheet

You also need to clearly explain what your convention are: what is positive and negative lateral acceleration, slip angle, yaw moment etc...

Then please repost it. The first version is no more available anyway.

I can already give you the next steps; same sheet but impose the radius and find the speed etc... then non-linear cornering stiffness and then 4 wheels (with weight transfer and possibly aero forces) but one thing at a time

[M.logan]

Claude,
Thank you for the feedback will follow the instruction in creating the spreadsheet.

M.logan

[M.logan]

Hi Claude,
https://docs.google.com/file/d/0B1jP2vKD5yx9YmxmNFNOb2tjRnM/edit
This is the link for the updated sheet.

M.logan
(The file is on the googledrive and it is available for download as an excel file from the file tab or Ctrl+ S.)

[M.logan]

Hi Claude
1)For the second sheet on imposing a radius of 9.125m and assuming a time of 5 seconds to go around the circle of the imposed radius, V=d/t with d being the distance covered (2*PI*R) and t as 5 seconds velocity will be 11.46 m/sec with this velocity do I have to calculate the remaining parameters ?

2)My understanding about lateral grip is that it is the difference between the lateral force and the Traction force but I was unable to quantify it.
I wanted to know if my understanding about lateral grip is correct ?

Regards
M.logan

[Jay Lawrence]

M.logan,

Can you define lateral grip, lateral force, and traction force?

[M.logan]

Hi Jay,
Lateral force is the force due to lateral acceleration when the vehicle is negotiating a corner.
Traction (tractive) force : the force that arises due coefficient of friction of the tire or the force that is available due to friction that keeps the tire in contact with the ground.
Lateral grip : The force required to ensure that the tire remains in contact with the ground when the vehicle is negotiating a corner.

Regards M.logan

[Claude Rouelle]

M.Logan,

You can have lateral acceleration without being in a corner.

"Traction (tractive) force : the force that arises due coefficient of friction of the tire or the force that is available due to friction that keeps the tire in contact with the ground. In English that means....?

Claude

[jose_90]

You can have lateral acceleration without being in a corner.

Claude

Do you mean in a tilted road? Or something else?

thanks for doing this threads, I'm following it closely and intend to come up with my own spreadsheet


Jose Maria Martin
University of Seville

[Claude Rouelle]

Jose_90,

Tilted road or simply variation of your car side slip speed. Imagine for example some side wind even at constant longitudinal Vx speed, the car could side slip parallel to itself. If Vy is not constant: it is possible to have no signal from the gyro none from the steering but some lateral G. Agree?

[BillCobb]

Since lateral acceleration contains 2 components in the horizontal plane: from turning (Speed x yaw velocity) and from lateral axis translation (Beta dot). One comes from the difference between the front and rear axle forces and moments, the other from the sum of the axle forces. However you do it, in a purely sideslip acceleration, your yaw gyro will read zero, BUT (that's a BIG BUTT), if you are in this mode you are generally in BIG trouble unless you are airborne. There can also be a gravitational component picked up by your transducer as well as a roll induced component, Both of which must be corrected for in measurements of True Grip (no, not John Wayne, that was True Grit, pilgrim).

Also, those familiar with rear steering algorithms, changing lanes using pure sideslip is a really interesting experience. Can cause heart failure in the driver ahead or behind you. The Milliken Camber car could do this as well as GM's 1965 Buick Wildcat Variable Response Vehicle (which I drove and programmed many times). Parking a vehicle with such capability could cause blank stares in pedestrians. Just sayin' ....

[Z]

... changing lanes using pure sideslip is a really interesting experience...

Many "telehandlers", which are sort of Next-Generation farm tractors, have at least three selectable steering modes:

1. Normal front-wheel-steering only, for regular driving.

2. Rear-wheels steer in same direction as front-wheels, for a "crabbing" motion, or, when in a tight place, to take a step sideways (eg. parallel parking).

3. Rear-wheels steer in opposite direction to front-wheels, for very low radius turns.

Mode 2 gives lateral acceleration with no Yaw.
~~~o0o~~~

But getting back to the OP, I would like to thank M.logan for providing incontrovertible proof that the education system has truly, and completely, disappeared down the crapper!


Lateral force is the force due to lateral acceleration when the vehicle is negotiating a corner.
Traction (tractive) force : the force that arises due coefficient of friction of the tire or the force that is available due to friction that keeps the tire in contact with the ground.
Lateral grip : The force required to ensure that the tire remains in contact with the ground when the vehicle is negotiating a corner.

Just think, in a few years time M.logan will be designing your next car... Aaaarrrggghhhhh!!!! :( :( :(

Z

[404namenotfound]

I have to ask why you want to do this and why an approximation is not good enough?

If you're trying to use this as a sort of simulation why is bank angle a factor?

There are some very simple ways to get some approximations for something that is reasonably accurate if you're looking to design a part.

[M.logan]

Hi everyone,
I would like to clarify myself on Lateral force,Traction and Lateral grip.
Lateral force originates at the centre of the tire where it is in contact with the ground lying on the horizontal plane and is perpendicular to the direction in which the wheel is headed if there is no inclination and camber.
Lateral grip :The ability of a tire to maintain its course, or remain under normal steering control, while being subjected to directionally disturbing influences.
Traction is the ability of the tire to grip the road.

M.logan

[BillCobb]

Only railroads have grip by your definition. Ground vehicles don't have flanged wheels.

[Jay Lawrence]

M.Logan,

You are describing the same thing but giving it 3 different names. Forget the word 'grip' for a start, I think it's confusing you.

[M.logan]

Jay
Lateral grip is confusing me can you help me on understanding it ?
Is this description of lateral force better than my first attempt ?
Lateral force originates at the centre of the tire where it is in contact with the ground lying on the horizontal plane and is perpendicular to the direction in which the wheel is headed if there is no inclination and camber.(lateral force can also be called as sideward force)

M.logan

[DougMilliken]

... Lateral force originates at the centre of the tire where it is in contact with the ground...

A good start for definitions is SAE J670e from 1976, "Vehicle Dynamics Terminology". There is a newer version (much longer) available, but the 1976 version is well organized with both contents and index at the end. Note that ISO definitions may be different from SAE. Available from SAE (some student chapters have access to SAE documents) or possibly online?

[Jay Lawrence]

M.logan,

Some research into definitions as Doug suggests will definitely help you, but briefly: a tyre can generate a certain force (N) based on certain conditions applied to it (vertical load, slip angle, camber, temperature, etc.). This force can be used to move the tyre and whatever is attached to it in the desired direction. If you google some tyre friction circles you will probably understand this better.

[M.logan]

DougMilliken
Thank you for the suggestion and will do some research on the definitions and I have found similar documents which give the definitions but I am saving money to buy the SAE J670e from 1976, "Vehicle Dynamics Terminology" document.
And Jay Thank you for the brief explanation.

Regards
M.logan

[rwstevens59]

M.logan,

Perhaps a better buy for your money would be the book 'Tires, Suspension and Handling by Dixon. The copy I have includes all the really pertinent sections of SAE J670e in the appendix as a reprint directly from the standard. i.e. It has not been edited.

The rest of the book by Dixon is a close second to RCVD in terms of content and educational value.

http://www.amazon.com/Tires-Suspension-Handling-Second-Edition/dp/1560918314

Ralph

[M.logan]

Hi Everyone,
I am sharing an excel sheet with front left and right slip angle calculated with varying values of vehicle slip angle and steering angle from -10 to
10 in steps of 2.
I wanted to know which value of vehicle slip angle should be good a approximation for a FASE car with wheel base 1.550m,front track of 1.200m and on a track with radius of 9.125m.

https://drive.google.com/file/d/0B1jP2vKD5yx9VldKajljUm56U2M/edit?usp=sharing

Regards
M.logan

[Claude Rouelle]

MLogan,

Is there a way you can make everything in just one spreadsheet?

Try to have for each beta 2 lines and each delta 2 rows and then a mega cell divided in 4 mini cells with each 4 slip angle.

As both beta and delta input are -10 to + 10 degrees how can the reader know if the horizontal and vertical input are the steering or the chassis slip angle ?

Also why don't you add the rear track as an input?

The weight distribution should be part of the input too.

Try that than I will come with other suggestions

I can see but cannot download your excel spreadsheet therefore cannot check the calculations, if you want me to do that.

[M.logan]

Hi Everyone,

This is the link for the new sheet with updated calculations.

https://drive.google.com/file/d/0B1jP2vKD5yx9VzFMekJtdFZaMFE/edit?usp=sharing

To download the sheet click on file and click on download or Ctrl + S

Regards
M.logan

[M.logan]

Hi Everyone,

Is anybody facing problems to download the file please let me know.

Regards
M.logan

[Claude Rouelle]

M. Logan,

Your calculations are correct.

So now let’s go back in part to the post I made on April 1st

Add as input
- A possible initial toe angle for each of the wheels (be careful with your sign convention)
- Use delta as a steering wheel input (that will speak to your driver and most of us better) and impose a ratio steering wheel angle / outside wheel steering angle
- Add also a ratio inside to outside steering wheel angle. Called that the Ackermann ratio if you want. Make that ratio constant to keep things simple. From there you will be able to calculate the inside and outside wheel steering angle or a given steering wheel angle.
- A given speed.

As output , for each step of the matrix add
- As you have the speed and the radius as input you can now calculate for each given combination of beta and delta) the CG lateral acceleration as well as the front and rear chassis lateral acceleration. Be careful; because of the angle beta, the physical acceleration “in the axis of the radius” will not be the acceleration measured on an accelerometer on the chassis. Which one will you be displaying?
- Front and rear chassis slip angle.
Let’s call front chassis angle the slip angle of the chassis at the point which is at the intersection of the chassis longitudinal axis and the axis going from the LF to the RF wheel centers (with no steering). Same for the rear chassis slip angle at the point which is at the intersection of the chassis longitudinal axis and the axis going from the LR to the RR wheel centers
- The yaw velocity

Once this is made we will “play” with a simplified tire model Fy Vs Fz Vs slip angle. And you will find the #1 issue that students face when they build a Yaw moment Vs lateral G diagram.

But you will also have to calculate the weight transfer: if you have lateral acceleration the Fz on the tire will not remain the same.

But one thing at a time...

Claude

[M.logan]

Claude,
Before I calculate Ay (Lateral acceleration) with varying beta and delta I created my own calculation sheet which is similar to the calculation sheet on page 3 in the Tech Tip : Steering geometry from OptimumG.
In my calculations there was a lot of difference between the recalculated Ay and the Initial Ay.To determine the recalculated Ay I used the formula numbered 5 on page 1 in the Tech Tip, I approximated Fyr and Fyl from the graph of lateral force VS slip angle at certain normal load .(I got the graph from the Tire Data for C-13 Continental tires.) I wanted to know how I can reduce the difference before I calculated Ay with Varying beta and delta.


Attaching the calculation sheet in the link given below and to download the sheet click on file and then click on download or Ctrl + S.


https://drive.google.com/file/d/0B1jP2vKD5yx9eFljNDNzblBfMVE/edit?usp=sharing

[Claude Rouelle]

You make your life and mine (and the one of the readers of this thread) so difficult. I will act towards you as if I was a teacher I will not comment on this spreadsheet calculation until you first clean a few things,

- Always use the same number of digits; the front track is 1.250 m, the rear track is 1.200 m and the wheel base is 1.550 m.
- Cell F2 and G2 should be automatically calculated from E2. If you change the weight distribution you need to change many other cells; that is ridiculous. Make the software USEFUL!
- How was C6 calculated? Where is this 1.4 coming from? Shouldn’t the speed be an input (as I asked you earlier: why did you do it?)
- How were D6 to H6 calculated?
- C7. Where is this 0.2 coming from? What is it? Should it be an input?
- C7 to H7. You make your life difficult. What don’t you use $H$2 instead of recopying the weight on all cells
- Same comment from C8 to H8; why do you need to recopy the front and rear roll stiffness instead of using $I$2 and $J$2?
- Do you really think that an engineer needs to read the roll angle with a precision of 1/1000000 of one degree? 3 decimals would be enough, This apply to many other cells of your spreadsheet
- Write the units of all dimensions you put in the spreadsheet: roll angle, roll moment, vertical load etc…)
- I have no idea how you did calculate C9 to H9 and C10 to H10, Can you explain? If you use 45 % of you vehicle mass I assume you are calculating the front weight transfer but in that case why do you sue the rear roll stiffness?
- Why don’t you calculate the LF, RF, LR and RR tire vertical load?
- C1 and C12; you assume that the turn center is at right on the rear axle axis. Why? Do you think this is correct?
- C13 to H13 and C14 to H 14 Where are the ideal slip angles coming from?
- Line 15 and 16: the steering angle should be an input (as I asked in last post), not an input.
- Where are the number in line 19 and 20 come from?

I am afraid that if I want to help you it will take a long time to teach you many basic things that you should learn on your own by reading good books. But I will keep trying for a while. Try to improve your spreadsheet, answer my questions above and explain how your calculations are made

[M.logan]

Claude,

The sheet with initial toe as the additional input , I am displaying the slip angle and lateral acceleration as output with varying beta and delta and the sheet is available on clicking the first link.
After this calculation is correct, I will add the other inputs which were given on 6th June 2014 and get the required output.

link for the lateral acceleration sheet with varying beta and delta - https://drive.google.com/file/d/0B1jP2vKD5yx9RmlKdXJEWlhQbkE/edit?usp=sharing


The last sheet which I uploaded is similar to the sheet created in the Tech Tip : Steering Geometry by OptimumG .In the sheet I have created and ignored the effects of camber to simplify the calculation.The Ideal slip angles and lateral force (Data on line 19 and 20) have been taken from the tire data (Tire data for C-13 Continental Tires).
In the sheet which I have created there was significant difference in the recalculated Lateral acceleration and the assumed lateral acceleration which is major mistake so wanted to know where I have gone wrong we have to look into the sheet LATER after we are done with the sheet you asked me to make on 06th June 2014 but I am posting the link for the sheet as I have cleaned it up.

link for the tech tip sheet : https://drive.google.com/file/d/0B1jP2vKD5yx9bUxFc2lTb0tYd2M/edit?usp=sharing


Sorry for the confusion.
Regards
M.logan

[M.logan]

Hi Everyone,

I wanted to know if the calculation for lateral acceleration are correct or wrong with static toe as input.
Attaching the calculation sheet in the link given below and to download the sheet click on file and then click on download or Ctrl + S.

https://drive.google.com/file/d/0B1j...it?usp=sharing

Regards
M.logan

[Claude Rouelle]

M. Logan,

1. You do not put yourself in the reader / user of your spreadsheet. How can I know what is Beta and what is Delta, even more when they are all - 10 to + 10 degrees with the same 2 degrees increments? How do I know if Beta is the row or the column? I did mention this earlier but you have not fixed this problem

2. “Slip angle and Vehicle slip angle positive to right” What does that mean? Can’t you choose a clock or anticlockwise reference?

3. J2: What is positive and what is negative? What is toe out and what is toe in? What don’t you have the toe adjustable on the front and the rear? Be careful about the interference of sign convention for your toe and your slip angle. The car coordinate system is not the tire coordinate system.

4. What is the lateral G at the CG? What are the chassis front and rear slip angles? I did ask you to include this in your spreadsheet. You didn’t.

5. It would be nice that you also calculate and display the yaw moment for each combination of Delta and Beta . Make sure you define the yaw moment sign convention

6. I did ask you
a. to use as an input the steering at the steering wheel
b. to use as an input a ratio steering wheel angle to outside wheel steering angle
c. to use as an input a ration outside to inside wheel steering angle
Why didn't you do it?
It would also be nice to display as an output the inside and outside steering wheel angle for each combination of Delta and Beta

Do that first and then we will discuss the problem you have with the difference between the lateral acceleration input and output

[M.logan]

Hi everyone,
The calculation with an input at the steering at the steering wheel,a ratio steering wheel angle to outside wheel steering angle and a ratio of the outside to inside wheel steering angle is available in the sheet.
I was unable to calculate the Lateral G at CG and yaw moment would it be possible if I can get a small hint to estimate the Lateral G at CG and yaw moment (with Varying beta and delta), I would calculate them and re-Upload the sheet.

link : https://drive.google.com/file/d/0B1jP2vKD5yx9V3lTT2s5LUZqM1E/edit?usp=sharing




M.logan

[Claude Rouelle]

M. Logan,

I will have your calculations checked but for now a few questions and recommendations

- On cell Z11 you write Y. What is this? How can I know? Would this be the βCG? if it is βCG how come you don't display its value?

- Didn't I ask to include output of front and rear chassis lateral acceleration? Please put those in the output even with empty cells if you are not sure yet of how to calculate these accelerations.

- It would be good that you add the units in which the R1 to AC1 numbers are expressed.

- If you can calculate the front and rear chassis accelerations and you know the front and rear mass and the distance a and b you should be able to calculate the yaw moment, shouldn't you?

- If you can calculate the front and rear chassis accelerations how come you can't calculate the CG lateral acceleration?

- Why is the yaw moment (and the description of its units) not part of the output? Even if you can calculate it you should leave a cell ready for it in your output


Claude

[Claude Rouelle]

M.Logan,

I had your calculations checked

1) The slip angle equations do not include yaw speed, which is wrong. By the way, the yaw speed is not displayed either, despite I asked it numerous time.

2) I assume the terms Ayf and Ayr calculate the front and rear axle lateral force? If so, they’re wrong. The equation is only using the Right side tires to calculate the axle lateral force when in fact it should the lateral force from both left and right tires for each axle (in the chassis coordinates).

Until all these preliminary calculations are done properly we cannot go to the next steps.

Claude

[M.logan]

Hi Claude

The following is the link to the updated sheet.

https://drive.google.com/file/d/0By_5neHMNARXRW94aE5BTjVMUUE/view


1) The slip angle equations do not include yaw speed, which is wrong. By the way, the yaw speed is not displayed either, despite I asked it numerous time.

We have the formula for slip angle for front tire as

Alpha= Beta + (a*r)/v- steer angle of respective wheel

alpha= slip angle
Beta= Body slip angle
a= distance between cg and front track
r= rotational velocity
v= longitudinal velocity

But v=radius of turn of respective wheel * r

if we substitute, the r or yaw velocity cancels.


2) I assume the terms Ayf and Ayr calculate the front and rear axle lateral force? If so, they’re wrong. The equation is only using the Right side tires to calculate the axle lateral force when in fact it should the lateral force from both left and right tires for each axle (in the chassis coordinates).

I have made the necessary changes to the sheet

I narrowed down the sheet to realistic values and removed the non feasible ones. That has been done in the the other two sheets in the same workbook.

Looking forward to your reply.


M. Logan

[M.logan]

Hi everyone

After contemplating, I realized that although my formulas were correct, I got high slip angles even when longitudinal velocity was put zero. Hence to make the correction, i have included the yaw rate in the formula.

The below link will lead to the updated sheet.

https://drive.google.com/file/d/0By_5neHMNARXUVNyTDllV0djS1E/view?usp=sharing

M. logan

[MCoach]

M.logan,

your spreadsheet has some weight transfer calculation issues. When changing the lateral acceleration to 0.0, this should reveal your static wheel loads. However, they do not correlate to the weight balance you have input. the rear weight balance is an input to your matrix, but not your base wheel loads. Also, your front or rear distribution should be a function of the other. One driving, one calculated. When changing the front weight distribution, it reveals that the effect is acted up incorrectly upon the wheel loads. Rather than one side dropping in load and the other increasing, they will all increase in weight with increasing front input and decrease with decreasing front input.

[BillCobb]

Based on the 10 or so vehicle parameters you've shown (and 2 guessed ones), it should be clear to you (and others) why this technique is fraught with danger:

Your vehicle is oversteering by about 1/4 deg/g at the 44 kph, saved from speenout only by the Ackerman gradient its running at this speed (basically, its wheelbase). The axle sideslip gradients (~1.0 and ~1.25 deg/g; front & rear) are far away from reality no matter what tires, masses, or planet you are operating with. The front and rear slip angle overshoots are above 25% and the system response times are unrealistic, too.

Luckily, your car has something in common with two of my favority vehicles: my boat and my hammock. THAT may be whats' buggered up your load transfer analysis. If you put my hammock ON my boat, its doesn't change anything in your favor.

As is, you are still missing the tire aligning moment (rigid body moments and compliance effects), lateral force compliance effects, the camber kinematics and compliances and the roll steer and camber stuff. It is as we say, a misleading technique with no possible way to validate it.

Instead, try running a true dynamic simulation from a solution to the diff equations, study the transient and steady state responses and ask yourself if it makes any sense. Then you can take your real hardware for a drive, measure or sense just one or two things and compare the results for validation of your efforts. An overlay plot of simulation vs. road test measurements is pretty convincing). This is pseudo steady state analysis with pseudo useful findings, requiring lots of Sudafed for the resulting headache.

(I tried to mimic Z on this one, how'd I do ? [Because I'm not happy until You're not happy].) The Title is purely Me.