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MORE ON LOOSE IN SWEEPERS/TIGHT IN TIGHT TURNS

What can one do to solve the oversteer (fast) understeer (slow) problem mentioned in this newsletter? [This was last issue, January 2013, last portion.]

Racing a Lotus 7. Open diff and about 150 Hp, Semi Slicks no aero assistance.

It will be apparent from the previous discussion that the causes of this effect are things we can’t do much about. Aero balance is the only really powerful tool we have to attack it with. If our hands are tied regarding that, we are limited to minor tweaks that have small effects and carry some penalties.

Reducing yaw inertia helps, so centralizing whatever masses we can is good. With a production car, there often isn’t much we can relocate. In some cases we have a choice with ballast location, but this often plays off against getting the static weight distribution we want.

Lengthening the wheelbase is good, except maybe for very tight turns, but carries penalties in packaging and weight. Generally we can’t do much to change wheelbase on an existing car.

We can add low-speed damping at the rear, and/or reduce it at the front. This will to some degree free up entry and tighten exit, particularly when steering inputs have to be abrupt. However, using this trick conflicts with the objective of calibrating the damping to make the car ride bumps as well as possible.

Finally, we can simply accept the characteristic and drive around it. That’s what we generally do, with varying levels of awareness that we’re doing it. This involves setting up the car so the driver can live with it in sweepers, and then managing its behavior with throttle and brakes in the slower turns.

I know we have plowed this ground some already in the past but I still haven't been able to get the fog to lift while trying to develop a spreadsheet to calculate lateral load transfer to get a better 'feel' for the contribution of geometric and elastic load transfer contributions to dynamic wedge in just a steady state, flat, constant radius corner i.e. relative wheel load changes to roll center and asymmetric spring changes. Can't wait until I start to lay geometric anti-forces and shock forces in transients on top of this, oh boy. I am really just trying to compile some rough data for all of the setups we tried last season to see if there is a common thread and re-calibrate our baseline for the coming season.

All of this in my world, as always, relates to race cars with beam axles front and rear for oval tracks i.e. left hand turns.

To quote one of your newsletters (July 2008):

I probably should spell out exactly what I mean by the wheel rate in roll, as I have encountered some confusion on this from various quarters. Wheel rate in roll, as I use the expression, is the rate of elastic change in wheel load with respect to linear suspension displacement, when the two wheels of a front or rear pair each move the same amount in opposite directions – in English units, the pounds of load change per wheel when one side compresses one inch and the other side extends one inch. This relates to the angular roll resistance as follows:

K_φ = ½ * K_roll * t² * π/180

K_roll = (2 * K_φ) / (t² * π/180) = 360K_φ / πt²

Or, approximating 180/π to three significant figures:

K_φ = ½ * K_roll * t² / 57.3

K_roll = 2 * 57.3 * K_φ / t²

Where:

K_φ = angular roll resistance, lb-in/deg

K_roll = linear wheel rate in the roll mode, lb/in

t = track width, inches

All of the above is clear for a race car that is symmetric about the chassis centerline i.e. cg and roll axis are considered to be on the chassis centerline and the spring rates left and right are identical.

My question is how do 'you' modify the above as the total vehicle and sprung mass center of gravity moves to the left and you add asymmetrical springing to the front and rear wheel pair?

Every reference work I have seems to fall back to the 'well let's take a symmetric car as an example' and I agree with this approach when first introducing the basics of LLT and the concept of a three mass system. But no one takes the next step completely.

RCVD takes what I believe is a slightly different approach to yours and attempts to introduce a LLT correction, so to speak, for an offset cg. But the example used is combined with banking angle effects, uses their 'simplified' one mass model all while maintaining a vehicle centerline defined by

half rear track width which, for me at least confuses the issue. Even when I take the RCVD equations and use a banking angle of zero I do not get the result I think I should get.

I have a very good understanding of how the four primary torques, unsprung weight, geometric sprung and elastic sprung and movement of the cg due to roll (this one small and usually ignored) that produce TLLT are derived. The conundrum for me is how these torques are distributed out to front/rear tire contact patch load as asymmetries increase.

The continued use of a chassis centerline by RCVD as opposed to the use of the sprung mass centerline as you do in your articles pertaining to asymmetric race car setups also seems to add to my confusion. I like your use of the cg location and definition of the vehicles x-axis along the cg. plane as it clearly shows the difference in the moment arms left to right and how these asymmetries effect car behavior.

If you would could you expand on the above to your method of treating asymmetrical load transfer when the cg is offset and you have asymmetrical springing or if you have already done so point direct me as to where I may find this information.

Actually, when defining wheel rates for the four modes of suspension movement, it is necessary to think in terms of equal absolute amounts of linear displacement at the four wheels. This is normally equivalent to using an origin at the track/wheelbase midpoint, and not at the c.g. when the c.g. is offset, either laterally or longitudinally.

If pure roll, or pitch, or warp, is defined as some combination of equal and opposite displacements at the wheels, then when the c.g. is not central to the wheels and we have spring splits and other asymmetries, pure roll or pitch in terms of displacements at the wheels necessarily implies some vertical translation at the c.g., and/or some change in total wheel load.

In an asymmetrical car, we do get somewhat different K_φ depending on whether we assume rotation about the track midpoint, the spring center, or the c.g. plane. However, in most cases the differences are small. The objective is to come up with a reasonable K_φ, by some method that makes sense to us. With an asymmetrical beam axle setup, it may be convenient to use the spring center as a center of rotation, as that will model a condition where the total load on the axle is constant.

Remember that when we assign a K_φ, or a roll center for that matter, we are engaging in simplifications, for the purpose of avoiding the need to solve large numbers of simultaneous equations using elaborate computer programs. We are not going to get exact modelling of loads and displacements. In most cases, the errors introduced will be small compared to those we’re getting by ignoring tire compliance and aerodynamic forces.