Critical Specifications For Balance

Critical specifications for steady-state balance, and the purpose of anti-roll bars.

Balance is not just tuning for driver comfort.
Imbalance means the car (not the driver) is not capable of reaching the full performance of all of its components.
Balance means using as much of the performance of all four tires as possible.

I encourage rear wheel drive teams to consider configurations that are not 50::50 in all aspects.
Consider configurations that are imbalanced statically and dynamically balanced at speed or under acceleration.
Dynamic balance may be achieved with positive driving torque, negative braking torque, and neutral conditions.
In other words, drivers adjust balance with accelerator, brake, shifting, and steering inputs.

Chassis Torsional Rigidity:

• Series of springs.

  • Front roll stiffness, chassis torsional rigidity, rear roll stiffness.

• Chassis should be stiff enough to not substantially affect overall vehicle roll stiffness.

  • Much stiffer than suspension roll stiffness, see Danielsson and Cocaña, Figs 2.6 and 2.7.

  • https://publications.lib.chalmers.se/records/fulltext/219391/219391.pdf

• Chassis itself is a series of springs, and the softest section will dominate.

• Chassis stiffness graph along length may resemble the shape of tube chassis in side view.

Dynamic Longitudinal Normal Force Targets:
(assuming equal sized tires*)

• Fastest skidpad Front::Rear is dynamically 50::50*

• Fastest acceleration launch (for RWD) Front::Rear is dynamically 0::100

  • Rear traction requirement and available wheel torque both diminishes with speed

• Fastest braking Front::Rear is dynamically 50::50*

  • Take braking front load transfer into account.

  • The higher the braking force and Center of Mass (CoM) height, the further to the rear the static mass distribution needs to be for a dynamic 50:50* balance.

• Front::Rear vehicle mass distribution (always including driver) is a compromise choice between these three states.

Acceleration and Aerodynamic Effects:

• Drag shifts the balance of all vehicles rearward compared to CoM acceleration calculations.

  • Its effect is squared with speed.

  • See Race Car Vehicle Dynamics, Milliken, Fig15.10 p504, 14th printing

• Drag Center of Pressure (CoP) can be assessed as a vertical measurement in the front or rear view.

  • In a wind tunnel, secured at axle height, the drag moment is reacted at the axles instead of the tires.

• CoP Z = CoM Z is a reasonable starting guess for non-aero cars, as well as closed-wheel aero cars.

  • Both drag CoP and CoM are usually near the centroid of area in front view.

• If CoP Z = CoM Z, tractive and braking moments at the CoM correctly calculate axle loads.

  • Any load transfer added to the rear axle is subtracted from the front axle.

  • Even though drag affects acceleration, the moment on the CoM is from tractive or braking force at the tires.

  • Without accounting for drag, using vehicle acceleration for load transfer gives incorrect axle load calculations.

• If CoP Z > CoM Z, drag creates a moment at all times. It can be assessed as either:

  • Drag Force * (CoP Z - CoM Z) / Wheelbase + Tire Longitudinal Force * CoM Z / Wheelbase

  • Drag Force * CoP Z / Wheelbase + Mass * Vehicle Longitudinal Acceleration * CoM Z / Wheelbase

  • These are mathematically equivalent because drag subtracts acceleration from tractive or braking components.

• The Accel+Drag and Decel+Drag traces show the correct load as calculated above.

• Downforce bends all curves upward.

• Large, tall rear wings are likely to cause CoP Z > CoM Z.

• Aerodynamic lift or downforce effects on the front or rear axles are squared with speed

  • At a bare minimum, any team with aerodynamic devices needs to present the total front normal load vs total rear normal load as a function of speed.

  • For a starting analysis, the area coefficient of drag (CdA), area coefficient of lift (ClA), and the front::rear distribution of the coefficient of lift (longitudinal Center of Pressure CoP) can be assumed to be constant.

• Accel+Drag and Decel+Drag show correctly calculated loads.

Nonlinear Tire Models:

• Imagine identical cars going around a skidpad, one is 50kg lighter.

• The outside tires of both cars are loaded and dominant compared to the inside.

  • Lateral mu begins decreasing above a certain normal load.

  • Lateral mu begins decreasing above a certain slip angle.

  • Maximum lateral mu generally requires elevated tire temperatures, decreasing again above a maximum.

• Tire saturation means load, slip, or temperature have reached a point where mu is decreasing.

  • It is rare for the front and rear outside tire to reach saturation at exactly the same time.

  • Front tire saturated first: understeer at the limit. Rear tire saturated first: oversteer at the limit.

• The heavier car will be faster if the lighter car is unable to generate tire temperature without high slip angles.

• The lighter car is faster if the tires can be saturated with normal load.

Distribution of Total Lateral Load Transfer:
Anti-Roll Bars Can Change Front::Rear lateral limits During Cornering

• Anti-Roll Bars (ARB) do not change the total load transfer from inside to outside.

• Anti-Roll Bars (ARB) do not change the total inside+outside load on the front or rear axles.

• Anti-Roll Bar (ARB) changes increase the difference Inside::Outside at one axle, and reduce the difference by the same amount at the other.

• Anti-roll bars increase the roll stiffness for that axle:

  • Under lateral load, more of the total load transfer from inside to outside will be carried by that axle.

  • The amount of roll from lateral acceleration is decreased at that axle.

  • Bump and roll stiffness are more independent, possibly leading to roll bars on both ends.

• Stiffening a roll bar means that axle will reach outside tire saturation sooner.

  • A stiffer roll bar slightly reduces total lateral grip available at that axle.

  • Powerful tuning tool. A smart man said: If I can soften one end to get more grip and balance the car, I'll try that before I give anything up stiffening the other.

  • On the other hand, more roll stiffness may be required to control the position of aerodynamic components when aerodynamic forces are dominant. This is known as aero platform control.

• Fastest skidpad is lateral capability perfectly 50::50* at speed.

  • Including mass, aero, and throttle/brake, and the effects of front and rear roll stiffness.

  • Adjusting a anti-roll bar changes the front::rear distribution at the outside tires based on lateral acceleration.

  • Adjustments: changing the amount of leverage twisting the bar, or changing the deflection of the levers.

  • See image by Evan Mason, https://commons.wikimedia.org/wiki/File:Antiroll_Bar2.svg

• See Race Car Vehicle Dynamics, Milliken, Section 18.4, 14th printing.

*Different size front and rear tires will lead to a different ratio.

Rear wheel drive teams do not need to use equal size tires.
That's how rear-engine Porsches and the Deltawing work.
Mass, tires, aero, and braking power are all closer to 40::60 (911) or 30::70 (Deltawing).