Body Roll and Weight Transfer Continued

[rrsettgast]

This thread is in response to a previous thread: http://www.i-club.com/ubb-files/Foru...ML/001722.html

After reading this thread, I wanted to throw in my opinion. This is a summary of body roll, weight transfer, and roll bars. If you disagree with anything here, please feel free to correct me (just be prepared to back up what you say ):

1) For steady-state cornering there is a total amount of load transferred to the outside wheels of the car. This load depends primarily on the lateral acceleration of the car, and the angle of roll does not really matter.

2) The front and rear axles have a roll stiffness (resisting torque to roll/roll angle). This stiffness is:
K_roll = 0.5*K_spring*(distance between suspension springs)^2 + roll bar stiffness

3) There is somthing called a "roll center" for each axle. This is a point which the body of the car "rolls" about. The line drawn between the front and rear axles is called the roll axis.

4) The load transfer between the left and right wheels for either the front or rear axle is given by:

Front:
LoadTransfer={[h_rcf*Wf] + [h1*Ws*K_rf/(K_rf+K_rr-Ws*h1)]}*[ay/(tf*g)]

Where h_rcf = height of the roll center for front axle
Wf = Static Weight on the front axle
h1 = distance between the center of sprung mass to the roll axis
Ws = Sprung Weight
K_rf = Roll Stiffness of the Front Axle
K_rr = Roll Stiffness of the Rear Axle
ay = lateral acceleration
tf = track width
g = acceleration of gravity

A similar expression can be derived for the rear load transfer by switching the front and rear quantities in this expression.

Comments:
[h_rcf*Wf]
This is the load transfer due to the torque generated by the lateral tire forces. Only way you can reduce this is to lower your roll center.

[h1*Ws*K_rf/(K_rf+K_rr-Ws*h1)]
This is what the disscussion is about. This is the load tranfer relating to "roll". To examine what we can do to "adjust" this load transfer, look at this term: K_rf/(K_rf+K_rr-Ws*h1).
This is essentially a ratio of axle roll stiffness to total roll stiffness (exept for the Ws*h1). This means that the load transfer on the front will be large (and that the rear axle load transfer will be small) if the front roll stiffness is large compared to the rear roll stiffenss. The Ws*h1 is only modified by reducing your hieght of the center of mass of your car, or moving the roll axis.

5) So putting a stiffer rear bar generates more load transfer along the rear axle, and less along the front. You also increase your total roll stiffness, which will help to preserve the original suspension geometry.

6) An increase in load transfer on an axle will decrease the amount of total traction available to that axle.

7) Roll is bad because generally it will generate positive camber.

Randy

[This message has been edited by rrsettgast (edited May 06, 2000).]

[Greg Sharpe]

In response to #6...That was my understanding in the first place.


rrsettgast: Would you mind giving me your opinion on three questions...True or False; There is a significant amount of front end traction gained from using a larger rear bar. True or False; The rear end is losing "total available traction" while using a larger bar(you already answered this). Do those two concepts come together in any consideration of chassis dynamics?

[rrsettgast]

There is a significant amount of front end traction gained from using a larger rear bar.

I guess the amount of traction gained depends on the increase in roll bar stiffness and tires...conditional TRUE

The rear end is losing "total available traction" while using a larger bar(you already answered this).

TRUE

Do those two concepts come together in any consideration of chassis dynamics?

I don't know what you are asking???

Just remember that the above disscussion in for STEADY STATE TURNING, so there are other things that happen from the time you are going straight, until the time you are set into your turn.

Randy

[This message has been edited by rrsettgast (edited May 07, 2000).]

[Pilot]

Randy,

I see nothing wrong with your analysis.

Greg,

Your understanding of the wya the car reacts to roll bar stiffness is correct. I beleive however that you still have the mechanics of the load transfer backwards. A sway bar tansfers load from the outside to the inside. So what happens is:

less load = less grip

what I beleive you are thinking is:

more load = less grip

At least that is what I understood from the previous thread.

So on an RS a stiffer rear bar overpowers that outside rear tire causing a more neutral cornering state by reducing the load on that tire.

quote:
---------------------------------------------
Do those two concepts come together in any consideration of chassis dynamics?
-----------------------------------

YES.

Randy's model is for steady state cornering, but of course vehicle dynamics is much more complex, a car with very high skidpad numbers might not handle well if it doesn't have good "transient response".

Transient Response is a vehicle's response to changes in direction. Cars with very stiff suspension have very fast weight transfer and can change direction very quickly.

So to answer your question changes in roll stiffness (sway bar changes, spring changes, damper changes) change the speed of the weight transfer. Weight will always transfer. The question with suspension tuning and vehicle dynamics is how fast will it transfer? Also what should the weight transfer speed realtionship be bewteen the axles?

[Greg Sharpe]

Then what the heck does #6 mean? Isn't an increase in load transfer just another way of saying that weight is loaded more on the outside tire, while using a larger rear bar? Keep flogging me with this conversation, maybe someday I'll come around!

[Pilot]

Greg,
You are one persistant dude.

When you go into a turn the body wants to lean, the sway bar counteracts the lean taking the load away form the outside and putting it back on the inside.

By taking the load away from the outside tire its grip is reduced so it can't take as much lateral force. With a big rear bar that is what happens and then the rear loses traction before the front cause the rear can't take as much force.

Think about what happens when you drive. When you are on the brakes a little the car turns in better cause it has more weight over the front wheels. When you are on the gas it understeers real bad cause the weight is over the back and the front has no grip.

Same thing with the sway bar. It takes weight away from the outside wheel.

Remeber Vehicle dynamics is all about the management of weight transfer.

[Pilot]

I figured it out!

[Pilot]

I figured it out!

You thought Randy was talking about body roll as load transfer, but body roll is WEIGHT transfer. Sway bar twisting is LOAD transfer.

So the body rolls and transfers WEIGHT, the suspension compresses on one side and extends on the other, the sway bar limits this compression and extension by transferring LOAD from the compressed side to the extended side through a twisting action.

Did that work?

[8Complex]

Ack, I tried to respond to this last night but I was too tired. Now I'm beat cause I ran my first (woo hoo!) autocross today, but I'll put a couple of yen in on this one...

Ok, now theoretically body roll transfers the weight over the outside wheel of the car and you gain more grip because it is being pushed into the ground more. However, this is a different story according to how the suspension moves with the body and how the wheels change angle since the body is rolling so much.

Now, with a sway bar in your suspension on the outside rear tire tries to compress to get more weight over that tire and increase grip, however the sway bar twists and tries to keep the car level. The more it tries to keep the car level, the less weight it is transferring over to the outside wheel since there is less body roll.

I think that is about the easiest explanation I can do on that one - especially since I'm just starting to get the hang of it myself.

[rrsettgast]

Greg,
By "Load Transfer" I mean the change in vertical load on a wheel. So if the car is going in a straight line at a constant speed, the front wheels have an equal vertical load, and the rear wheels have an equal vertical load. As you are in a turn, the Load Transfer is the change (added to the outside wheel, subtracted from the inside wheel) from the straight line load.

Pilot,
No I don't think that is what I meant.
Hmmm. Lets see if I can explain this better. By "Load Transfer" I do mean Weight Transfer. If you look at my equations above, you will notice that there is no mention of the actual amount of "roll". What we are concerned with here is "roll stiffness". Lets look at an example of adding a thicker rear sway bar.

1) A larger rear sway bar adds to the roll stiffness of the rear axle.

2) Increased roll stiffness of the rear axle leads to an increase in vertical load transfer between the inside rear and outside rear wheels, and a decrease in vertical load transfer between the front wheels.

3) The Increase in vertical load on the outside rear tire will increase the amount of grip it has. The Decrease in vertical load on the inside rear tire will give that wheel less grip. The opposite is occuring for the front wheels.

4) Due to the nonlineararity of tire friction, the net result of 3) is that the rear wheels have less total grip, and the front wheels have more grip. Less grip from the rear wheels, and more grip up front = more oversteer.

5) SO the sway bar does not transfer load from the outside wheel to the inside wheel. It is exactly the opposite. Increasing the roll stiffness leads to a load transfer from the inside wheel to the outside wheel!

Randy

[This message has been edited by rrsettgast (edited May 08, 2000).]

[Scooter]

http://www.members.home.net/rck/phor/ http://home.kscable.com/mc2racing/suspension.html

Just a couple sites that talk about this subject.

[This message has been edited by Scooter (edited May 08, 2000).]

[Pilot]

"Actually, the transition from sticking `mode' to sliding mode should not be very abrupt in a well-designed tire. When one speaks of a ``forgiving'' tire, one means a tire that breaks away slowly as it gets more and more force or less and less weight, giving the driver time to correct. "

-Brian Beckman

Ok this means that #5 is incorrect. And also illustrates why the back of a car slides first during trailbraking or trailing throttle maneuvers.

Why? The more the outside suspension compresses the more the sway bar is trying to flatten the car out, by doing this it is removing load from the compressed outside suspension and transferring it to the extended inside suspension. Not the the other way around, which can not happen because the suspension can only extned so far, once it is fully extended there is no more movement form the sway bar EXCEPT that which is occurring on the outside tire where the suspension is still compressing. Therefore the sway bar is taking load from the compressed outside and trying to move it back across that axle.

Why rear sway bar does not add load to the outside tire.

The sway bar is simply two lever arms connected by a torsion spring. When discussing a rear bar what we get is a dynamic load transfer from the outside rear tire to the inside front tire. This is diagonal and explains the purposes of weight jacking.

As I discussed before, weight jacking or corner balancing is the practice of balancing a cars' weight left to right by changing the ride height of the car independantly at each corner. Example: To place more weight on the left front one must lower the ride height there, or raise the ride height of the right rear, the diagnoal.

Sway bars allow this ride height change to occur in a dynamic situation, and only in a dynamic situation. I also stated previously that a properly setup racecar that is also properly balanced (CART, F1, etc) does not use a sway bar because it doesn't need it. The fundamental action of a sway bar is negated by these cars, they instead use on board weight jacking systems. The driver can actually change the diagonal ride height from the cockpit.

[Pilot]

One more thing, you NEVER want to have a sway bar that provides more torsional springing action than your suspension (springs and dampers).

1) It will rip the sway bar mounts off the car

2) It makes the rest of the suspension work poorly

[Pilot]

Randy,
I see what you are saying, one tire cannot take as much lateral force as two tires.

True but is this case it doesn't work because you cannot stop weight transfer from the inside to the outside, so the inside tire does not have any grip UNLESS you are accelerating in which case you have transferred load from the front to the back. In any at the limit steady state cornering maneuver all the load gets transferred to the outside.

Like I said it is all about how fast the transfer occurs. And of course when we are driving the car we often have it braking and turing or accelerating and turning.

The only purpose to limiting body roll is to maintain wheel geometry realtive to the ground.

[rrsettgast]

Pilot,
I think we have a failure to communicate. Think about the mechanics of a sway bar. The ONLY way the sway bar can "prevent" body roll is to transfer load from the inside wheel to the outside wheel, WITHOUT compression of the springs. This is what the sway bar does!!!

Think about laying under your car, and have some big dude push your car so that it rolls to the right. Think about how the sway bar will react. The bar will be twisted so that the right sway arm is bent up, and the left arm is bent down. This implies that the sway bar is transferring load directly from the right wheel and pushing up on the right side of the chassis...which will level the chassis. Opposite for the left. If you are having a har time visulaizing this, go do it!

The tire thing is due to the fact that as you increase weight on a tire, you do not get an equivilent increase in lateral grip. The increase in grip will decrease until you reach the limit of the tire. Therefore, two evenely loaded tires will have more grip than one really heavily loaded tire + one lightly loaded tire.

As for dynamic effects...I think that has more to do with the roll inertia of the car, and the damping rate of the struts.

Randy

[This message has been edited by rrsettgast (edited May 08, 2000).]

[Pilot]

I think I have found the problem, I have once again failed to properly explain myself.

A sway bar provides spring action in two directions. I pushes up on one side and down on the other.

A sway bar increases the spring compression rate on the compressed side of the car in a turn and decreases spring compression rate on the extended side.

"two evenely loaded tires will have more grip than one really heavily loaded tire + one lightly loaded tire."

-rrsettgast

This change in spring rate effects the opposite end of the car. So a stiffer rear bar causes more equal loading of the front tires creating more grip at the front of the car.

What I am trying to get at, and failing miserably at it, is that the rear sway bar affects traction at the front of the car much more than the rear of the car.

Conversly the front sway bar affects traction at the rear of the car much more than it does the front.

So why use a bigger rear bar as opposed to a smaller front bar? To control body roll to maintain tire geometry with the ground which increases traction at both ends of the car.

More roll stiffness = better tire geometry relative to the ground = more grip.

Lastly a sway bar can not actually transfer load from the inside to the outside, it can help to increase spring rate at the outside corner which more effectively loads the two front tires.

In my previous attempts to exlpain this I tried to only talk about the rear of the car for simplicity's sake and it made a big mess, disregard all talk about load transfer from left to right being possible by a sway bar, because it isn't.

The sway bar simply uses the opposing suspension movement on both sides of the car to help increase spring rate at the compressed side.

So Randy yes you are right and I am a fool for attmepting to explain this decrease in relative grip from front to back without discussing the increase in grip at the front.

This was the cause of my explanatory confusion.

Is everybody clear now?

stiffer rear bar = more fornt grip = less understeer

Stiffer front bar = more rear grip = more understeer

[rrsettgast]

Sounds Close Enough You are not a fool, you are just trying to work through some complicated stuff, which is better than not working through it!!

Randy

[Pilot]

Finally!

At least this time I'm much more educated on the subjects at hand, specifically vehicle dynamics and suspension action.

Unlike the tire post where I was trying to assimilate infromation that was in many cases new to me.

Here is a technical trivia:

Did you know?

That if your suspension can continually create more negative camber relative to the road surface as the weight transfers to the outside your tires will continually produce more grip.

This is a catch 22 becuase if this ocurrs you can flip your car! Seen race cars flip? Now you know why!

[8Complex]

"A sway bar increases the spring compression rate on the compressed side of the car in a turn and decreases spring compression rate on the extended side." - Pilot

Oddly enough, I never thought of it that way but it is completely the way it actually is. Very cool.

So let's see... if the front sway bar size would be increased, not as much weight would be able to transfer over to the front outside wheel and it'd be stuck in the back, cauing the rear of the car to push it through the turn. Understeer. Correct?

So really the best way to decrease body roll would be to completely move the suspension up to the next level, stiffer all the way around... Geez, the only thing that kinda sucks about all this discussion is the realization that I have to buy more and more stuff before I get the car handling nice and flat. Oddly enough, I managed to do pretty damn well on my RE92's at the autocross yesterday, they're pretty chewed to hell, though. LOL

[Pilot]

Woo Hoo! Yes that is right!

However you should still get new tires first! Then the suspension.

[Pilot]

Also what 8complex pointed out about how a sway bar changes weight distrubution is what I was trying to explain by saying that the larger rear bar reduces the grip at the outside rear tire. The key is relative grip.

For Greg,
It isn't that the rear bar is overloading the outiside rear tire, it's that the rear bar is increasing the grip at the front of the car.

For Randy,
I just want to make sure we are on the same page here. Do you agree with both of these statements? If not why not?

A sway bar can not actually take load off of or incease load on the outside tire.

However, by increasing the spring rate of the compressed outside suspension it can more evenly load the front tires.

[8Complex]

Ok, just for kicks lets check out suspension costs over hte next (?) year or so...

Current:
Whiteline Rear Sway bar
Rear endlinks (on their way)
Front endlinks (got 'em cheap *shrug*)

Future:
Tires (400-500 - I eat em fast so cheap is the way to go)
Strut braces (320-360)
Struts/Springs (800-1200) - Very much an estimate, still not educated enough to buy these yet anyway.

Man, I'm gonna hafta get a second job just to pay for car parts! LOL

[boxerman]

For simplicity sake lets ignore front to rear weight transfer and only consider the rear wheels.

So the increased load on the outside tire is related to the force of the springs pushing the inside wheel away from the body and sprung weight of the inside wheel and suspension. This is why a very stiff roll bar will lift the inside rear tire, since the entire weight and spring compression (ground seeking force) of the inside wheel is travelling down the sway bar to outside wheel increasing the load. A car that lifts the inside rear tire is not only supporting all the body weight on the outside tire but also the weight of inside suspension. Correct?

Just trying to get these things clear in my head.

Tim

[Scooter]

Don't forget the human factor. I think large amounts of body roll tend to make the average driver uneasy, regardless of how much grip they may have left. I think a lot of people determine whether or not they're taking a turn too fast by the amount of body roll versus the amount of grip left. With reduced body roll usually comes more confidence, despite whether or not grip or handling actually increased. Humans have a pretty sensitive balancing mechanism and it doesn't take much to trip the "we might tip over alarms".

[Pilot]

Boxerman,
Originally I tried to explain this ignoring the diagonal weight transfer, but you can not ignore it. Without it the fucntion of a sway bar, or any part of the suspension for that matter, does not make sense.

I have to go take an exam so I will let Randy examine your last post for correctness.

Scooter,
I am ignoring driver psychology in this discussion, but you are correct about the "tip over alarm" for many drivers.