Weight Transfer in Car Tires, and Suspension

[jonesto95]

I've been looking up how weight transfers between car tires in various forms of acceleration, and I've found some formulas. For linear acceleration, I found this formula on Wikipedia:

ΔWeight = (accel) * (height of center of mass) * (mass) / (wheelbase)

en.wikipedia.org/wiki/Weight_transfer

And I also found this inequality for a turning car, where a car won't roll over as long as

(centripetal force) / (weight + downforce) < (wheel track / (2 * height of center of mass))

accidentreconstruction.com/research/suv/rollovers[1].pdf

However, the second link mentions how it ignores suspension effects, which made me think: How would those effects play into these two equations? In other words, under the same amount of acceleration and/or centripetal acceleration, how would the amount of transferred weight differ between a stiff suspension (high spring constant), and a soft suspension (low spring constant)?

 

[gsal]

Sounds like they are treating the problem in the typical rigid body fashion. With suspension effect, the location of the center of mass will move.

 

[jonesto95]

From what I've been looking at, that does seem to be the only way suspension plays into this. I can only see the CoM moving vertically though. Can it move horizontally (relative to the car axis) along the car, and if so, how?

 

[tduell]

Have a look at "Race Car Vehicle Dynamics" by Milliken and Milliken, if you can. It gives an excellent treatment of the your problem area.

 

[gsal]

Yes, CoM will move vertically and horizontally. When the car is accelerating, the CoM will move back...when breaking, forward...when turning, sideways

 

[jonesto95]

Oh my. I found that book. This thing is amazing, VERY nice find!

 

[tduell]

Good. It has been the 'bible' for many involved in racing for some time. It should answer most of your questions.

 

[rcgldr]

The total cornering load can't be changed, but it can be distributed unevenly between the front and rear tires by making the front or rear end suspension relatively (compared to forward / rearward weight bias) stiffer. The stiffer end (springs and/or roll bar) gets more of a different in weight distribution (greater downforce on the outside tire, less downforce on the inner tire), than the looser end. Since the coefficient of friction of a tire decreases somewhat with an increase in downforce, the stiffer end will have less maximum grip than the looser end of a car, and this is how oversteer / understeer can be tuned with suspension stiffness.