anti effects and load transfer

[silente]

Hi all,

i have been stuck thinking to that for a while, but still not found i good answer, so i hope you people from the forum can help me.

Does Anti effects (force based calculated or kinematically defined) affect longitudinal load transfer in any way?

I try to explain a bit better what i am after.

Let's say we have a car with a certain wheelbase, cg height (which we assume is not changing it's height when the car accelerates) and a double wishbone suspension both at front and rear axle.
Let's say we are accelerating and beacuse of this the car will see a load transfer from the front axle to the rear.

My understanding of the problem is that this Load Transfer will only be affected by the magnitude of longitudinal acceleration, cg Height and wheel base as:

LT = M x CGh x Long_acc / wb

The anti effect should only change how much of this load is reacted by the springs (so how much squat we have) and how much is going through suspension linkages.
Today anyway i found a paper from a "famous" race car guy stating that anti effects change load transfer magnitude. :O

What is your understanding of this problem?

As a side question, if we still assume that cg height doesn't change (which could well not be the case, but let's stick to that for now) how spring stiffness affects (if it does) the way load is transferred to the rear axle? It is "common knowledge" that softer springs should help in traction, but i don't see any reason (except from CG movement or road irregularities) they should influence load transfer or produce this.

Thanks!

[WilO]

Silente,

My understanding (such as it is) is the same as yours: the magnitude of longitudinal load transfer is based upon the parameters shown in your equation, the 'anti effects' serve to distribute what paths the load transfer takes. Given the spring stiffnesses found in most competition vehicles, I would think that the x and z axis locations of the CG wouldn't move much, but that may be a product of my simplified understanding.
I'd be interested to hear other comments as well.
Wil

[Lycoming]

Load transfer is only dependent on the parameters you listed in that equation, that is, weight, CG height, wheelbase and the magnitude of the acceleration. Your stated understanding is correct, that is, that anti squat/dive just sends a portion of the normal load through the suspension links instead of the springs. Thus, normal load at the tire isn't really changed, but the body pitches less. I'd like to see this paper you read that said otherwise.

Spring stiffness doesn't really affect load transfer between the axles unless your car's pitch mode is so soft that the sprung mass CG movement causes its height to change significantly. Softer springs are said to aid in traction because, generally, it offers the tire itself more compliance and allows it to develop higher tractive forces at the contact patch with all else more or less equal. Others with better knowledge of tires may be able to tell you more about this.

Also, depending on the car, it is possible that stiffer springs will mean a more favorable camber. For example, with double wishbone suspensions, generally under accel, the rear will squat, which will cause the camber on the rear tires to go more negative (if you have front or AW drive, this doesn't matter so much). Thus the tire's longitudinal capability is reduced. If increasing spring stiffness allows significantly less camber change, say because your suspension geometry approximates a swing axle, then that's another way spring stiffness may affect rear end traction. Note that if you have parallel equal length wishbones, your camber won't change under any sort of heave motion.

[silente]

Guys,

thanks for your replies.

It seems that, since front and rear axle are not interconnected (as it happens between left and right for lateral weight transfer), longitudinal load transfer is not really tunable.

The document i am talking about is actually an ebook where the author first develop the same equation i posted above, but saying this is valid only when pitch centers are at ground level.

Than, he shows a second equation where Load Transfer seems to be dependent on the distance between CG and Pitch Center, in a case where a trust force is applied to the wheel to accelerate the car in forward direction (so no torque trasmitted to the suspension components because of the hub bearing).

Unluckily, sometimes it doesn't show the process he used to find these equations, as in this case. So it comes a bit out of the blue, but i was surprised to see that, accordin to this equation, the amount of Load trasnferred from the front to the rear axle (or the load lost at the front, if you want to see the problem in a different way) is dependant on CG to Pitch Center distance.

[GSpeedR]

The equation you've written is valid for a single body system with 1 degree of freedom (Pitch). If we are including kinematic anti-effects such as jacking (which are internal forces) in our analysis then we are dealing with a multi-body problem. However, that equation is again useful if we assume the vehicle has reached a steady-state. The author you are citing is attempting to add multi-body effects to a model that only has 1 degree of freedom; this is why pitch and roll centers are confusing...because they are not based on valid principles. People still find the concept useful (I don't), but you should be wary about what they represent.

This question seems to be very related to the first post I made on this forum: Load transfer delay

[silente]

the model the author shows is actually a 2 DOF one, with front and rear suspension but no track width. He call it bycicle model, but it is not the kind of bycicle model you can find in Race Car Vehicle Dynamics when study cornering, more similar to what Dixon shows in his book on dampers.

He incorporate into the model the concept of Force application Points, in this case he calls them Pitch Centers.

What i don't understand is how they can influence (if they do) longitudinal load is transfer. Since with more antisquat more load is going into suspension linkages, it is clear to me that they could influence how quicly the load is trasnferred, but i don't see how they could influence the amount of load transfer for a (constant) acceleration magnitude.

I guess i am missing something.

Anyway, linkages connected forces (or force application points effects) should be internal to the system, while the input to the overall weight transfer should be external.

[GSpeedR]

It's probably what is commonly called a Pitch-plane model with a single body with Heave and Pitch DOFs. As I said before, anti-effects, or jacking, or FAP effects, etc, are internal forces between the chassis and the unsprung masses and therefore they cannot directly affect steady-state load transfer. Indirectly, as mentioned by others, the chassis CG can move in response to these internal forces and this will change load transfer magnitude.

Do not take an author's word for granted. Create a Free Body Diagram that includes all necessary bodies and write the equations of motion.

[Tim.Wright]

what you originally said is correct.

Are you sure that the author is calculating total load transfer wit h the pitch centre? Maybe he is just calculating the elastic component like you do in the lateral case.

Whether its correct or not is a completely different story. I personally calculate the pitch movements another way. I believe thats the unequal front to rear torque bias for both braking and acceleration pretty much renders the pitch centre as useless

[silente]

Tim,

pretty sure he used that equation to calculate the final load on the wheels.

It really made an alarm to ring in my head!

[Tim.Wright]

Interesting,who was it by the way?

Misconceptions like this are actually more common than you might think in this field. Even Carrol Smith has a few blunders in his books which he freely admitted to.

[silente]

Tim,

you are right but i honestly didn't expect something like that in that book.

It is actually from a very famous guy writing on RCE and owning a company who produce a "non steady state" laptime simulation software.

I am not sure if i missed something in his explanation, since sometimes he really doesn't explain how he got to the formulas he shows and the assumptions he did...very often, redoing the proofs, you have to understand yourself what he assumed.

But in this case it was more or less like this:

with "zero pitch ceneter":

Load Front = Static Load Front - (M x Ax x H/wb)
Load Rear = Static Load Rear + (M x Ax x H/wb)

Which makes perfect sense to me.

Then, considering "Pitch centers" he writes:

Load Front = Static Load Front - (M x Ax x (H - pcr)/wb)
Load Rear = Static Load Rear + (M x Ax x (H - pcr)/wb) + M x Ax x pcr/b

where:

pcr = Rear Pitch center height

b = distance between rear axle and cg in x direction.

Did i miss something?

How, anyway, you guys calculate the suspension geometry effect on longitudinal Load Transfer?

[Tim.Wright]

Ah Danny, OK, is that from his book or from RCE? You could always shoot him a mail, hes usually pretty accessible if you have an intelligent question.

What you have listed there seems a bit strange. Again all I can think is that he is calculating only the elastic load transfer (to use Claude's terminology).

How, anyway, you guys calculate the suspension geometry effect on longitudinal Load Transfer?

My calculations for this are a bit different but I don't want to go too much into detail since it's knowledge I gained during an ongoing work project so I'm being cautious for reasons of confidentiality.

However, what I can say is that I believe the method of anti-X calculation used by the software Adams/Car is the most correct. What I do is actually similar to this. Again I don't want to post any of the equations here, but its very easy to find an Adams/Car user manual online.

The main point is that there are no pitch centres used in these calculations. To me its a useless construct for longitudinal load transfer because it links the behaviour of the front and rear axles together but in reality they are independant in a conventional suspension system.

Sorry I can't be more helpful than that, but my advice is: If you want to properly understand anti geometries and longitudinal load transfer behaviours, you really have to go into detail yourself from first principles because most of what is presented in books and on the internet are not correct in my opinion. Stick with FBD's and static equalibrium equations. Avoid constructs like instant centres and pitch centres until you have proved to yourself that they work.

Tim