Roll Stiffness and Weight Transfer – What you should know - Hyundai Genesis Forum
 
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Roll Stiffness and Weight Transfer – What you should know

When it comes to lateral performance, sway bars and harder springs are the way to go! At least, that’s what the companies claim. How can you, the buyer, be so sure?

Here’s a common opinion we’ll tackle and try to prove or disprove:
Harder springs will cause the car to roll less, decreasing weight transfer.

Just a little technical preface:

This is a technical read
.

Weight transfer is the phenomenon that takes place as a car corners. Weight is transferred from the inside wheels to the outside wheels in order to stabilize the car’s body motion. As a general rule of thumb, more weight transfer means less grip because the outside tires will slip more under higher load. For a specific amount of lateral g’s, the car must transfer certain a total amount of weight in order to keep it stabilized. How that certain weight is transferred between the front and rear axles, however, is something that can be controlled by modifying certain aspects of the car.

In Miliken’s book Race Car Engineering, Miliken derives an equation which describes the weight transfer of the car under cornering.



W= total vehicle weight (lb)
H= height of CG above roll axis (ft)
Zrf= front roll center height (ft)
Zrr= rear roll center height (ft)
a= longitudinal distance from front axle to cg (ft)
b= longitudinal distance from rear axle to cg (ft)
l= wheelbase (ft)
tf= front track (ft)
tr= rear track (ft)
Kf = front roll stiffness (lb-ft/deg)
Kr= rear roll stiffness (lb-ft/deg)
Ay = lateral acceleration (g’s)
ΔWf = Front weight transfer(lb) [Solve for this!]
ΔWr = Rear weight transfer(lb) [Solve for this!]

Now, it is possible to modify a lot of those parameters of the car through extensive and expensive modifications, but by far the easiest ones to change are the roll stiffnesses. They are most easily changed by swapping out the springs and/or changing the sway bar.

So let’s plug in the values of the Genesis Coupe (2.0T track). I have no idea what the front and rear roll centers are, so I just guessed. It won’t make a huge difference in the numbers, but more importantly it won’t change the ideas I’m trying to get across. Assume I made all the necessary unit conversions. Try doing the math yourself; the calculations are a good mental exercise.

STOCK SETUP
W= 3537 lb (with driver)
H= 12 in
Zrf= 8 in
Zrr= 10 in
a= 53.28 in
b= 57.72 in
l= 110 in
tf= 63 in
tr= 63.6 in
Kf = front roll stiffness 600 ft-lb/deg (I guessed)
Kr= rear roll stiffness 600 ft-lb/deg (I guessed)
Ay = .9g (just to assume a skid pad)
ΔWf = 515.3 (lb)
ΔWr = 542.7 (lb)
ΔWtotal = 1058 (lb
)

Now let’s increase the roll stiffnesses of both axles 3 times the amount by adding springs and thicker sway bars. Let’s try the numbers again.

STIFF SETUP
W= 3537 lb (with driver)
H= 8 in
Zrf= 8 in
Zrr= 10 in
a= 53.28 in
b= 57.72 in
l= 110 in
tf= 63 in
tr= 63.6 in
Kf = front roll stiffness 1800 ft-lb/deg (I guessed)
Kr= rear roll stiffness 1800 ft-lb/deg (I guessed)
Ay = .9g (just to assume a skid pad
ΔWf = 515.3 (lb)
ΔWr = 542.7 (lb)
ΔWtotal = 1058 (lb)


Whattt?!?!?!
It didn’t change at all! Even though we increased the roll stiffness three times the amount with some supreme Eibach springs and Luxon sway bars, the weight transfer between both axles stayed exactly the same. So even though it may feel like the car is cornering better since the body is not rolling as much, no performance is gained nor lost.

If one observes the aforementioned equations closely, the weight transfer is not affected by total roll stiffness, but rather the relative stiffnesses between the axles. So instead of increasing both spring stiffnesses, let’s only increase the stiffness on the front by 2-fold by going to a harder front sway bar.

STIFFER FRONT
W= 3537 lb (with driver)
H= 12 in
Zrf= 10 in
Zrr= 12 in
a= 53.28 in
b= 57.72 in
l= 110 in
tf= 63 in
fr= 63.6 in
Kf = front roll stiffness 1200 ft-lb/deg (I guessed)
Kr= rear roll stiffness 600 ft-lb/deg (I guessed)
Ay = .9g (just to assume a skidpad)
ΔWf = 616.3 (lb)
ΔWr = 442.7 (lb)
ΔWtotal = 1059(lb)
Note: the total weight transfer stayed the same!

So here we see that by going harder in the front, we’ve increased the weight transfer between the front wheels and reduced the weight transfer between the rear wheels. Wait a second!!!! Many tuner companies say a harder roll stiffness on an axle decreases its weight transfer. In this case, however, quite the opposite happened!

To sum up this exercise and referring back to our presumptions:

Theoretical Conclusions
1. Weight transfer is only affected by the RELATIVE roll stiffnesses, not the total roll stiffness. Simply going to harder springs and adding sway bars will not always improve the cornering performance of the car.
2. Harder springs on an axle will INCREASE the weight transfer between the wheels on that axle not decrease it!
3. The total stiffness is simply chosen on the desired ride quality and damping characteristics.


Application:
So let’s say in the case of tracking the car, autocrossing, or even taking an off-ramp enthusiastically, the front tires are losing grip faster than the rear causing the car to understeer. In order to increase the front grip to achieve a more neutral feel, going to a softer front or a harder rear will give the front more grip.

So remember, going harder on an axle (or softer on the opposite axle) will DECREASE the performance of the axle!

Well, that’s it for now until I have time to do more technical write-ups. Think hard about it, and think twice before buying those harder springs and sway bars.

Here’s a couple different cars at hard cornering with different weight transfer setups, and one can see it really depends on the application.


F1 car with a much stiffer front, causing more front weight transfer which lifts the inside front wheel off the ground!


In this case the GTI has a much stiffer rear, causing enough rear weight transfer to lift the inside rear wheel off the ground!


In this case the mustang has the springs set up so both axles transfer the same amount of weight. At hard enough cornering this causes both wheels to lift. This may seem like the optimal setup, but this is not always the case!

That’s it for now, until I have time to do more technical write-ups. So next time that spring set looks tempting to buy, think about the performance gain. Sometimes it's just not there.

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Terps Racing University of Maryland Formula SAE
Aerodynamics and Suspension Design Specialist
Mirabeau Blue 2.0T M/T

Last edited by TheEngineer; 12-08-2010 at 07:11 PM.
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