The unknown, missed, omitted, and ignored subject on the roll centers, (hence the roll axis height at the sprung c.g.), is it's influence on the sprung roll inertia via Physics 101 Ixx=Ixx_sprung+Msprung*R^2, where R is the vertical distance from the sprung C.G. to the roll axis. Combined with springs, bars & dampers, this produces a measurable change in the roll damped natural frequency. This may seem trivial to most, but knowledgeable vehicle dynamics engineers should realize that while the roll frequency is generally constant with speed (yes, there can be speed effects on stiffness, hence roll frequency changes), the yaw velocity & sideslip natural frequencies are functions of speed & speed^2. If you are familiar the notion of convolution (complex multiplication of system responses), you know that steer produces yaw velocity & sideslip, hence combined into lateral acceleration. These components ALSO then are forcing functions of the roll degree of freedom. So steer doesn't make a vehicle roll unless you have caster in the steered axle. This can have a profound effect on total vehicle response when cross coupling terms (like roll-steer [steer due to roll] and roll-camber [camber due to roll] interact with the lateral acceleration terms. Problems occur when yaw velocity and/or sideslip natural frequencies line up with the roll frequency. Because they are speed dependent, frequency responses can 'hook up', which we call 'Q'. At speed above the 'Q' speed (Q-Speed is where roll & the other frequencies are the same) the SIGNS of the roll-steer & roll-camber functions will reverse, so roll understeer becomes roll oversteer, etc. Most novices throw more damping at the resulting (high speed) problem when the solution is to set these functions, or the roll axis, or the sprung inertia to values which prevent these degrees of freedom from 'Q-ing' up. (Decoupling). Needless to say, the roll axis inclination angle also changes the sprung mass cross-products of inertia, so roll-pitch etc. effects jump into the game. All of this means that the roll centers greatly effect the DYNAMICS of turning as well as the STATICS, as in load transfer, Fy, Mx, and Mz tire force generation RATES. If any of this sounds familiar or makes you think of other 'Q-ing' issues lately, take a pause and re-think 'porpoising': Aero is the forcing function, but the root cause is frequency coupling. Both situations can get so bad, that the responses can become divergent until some displacement limiting constraint is contacted ! BTW: all of this is usually lost in simulation unless you manually adjust the inertias for each situation, or the sim is programmed to correct the sprung inertia values for the roll axis location in play. If you have the capability, switch the roll center locations front to rear, readjust the roll stiffnesses to maintain balance, and examine the time responses. Changes in the cross products of inertia will drastically change the response times & overshoot calculated by the sim.

Really enjoying this series so far, and the articles you’ve put up on your website, although I’m applying what I’m learning to something much smaller (1/12th scale LMP-style RC cars)! Keep up the good work, this is exactly the kind of content we need more of to help young people get move involved in engineering.

What are the negatives of having low roll centers and controlling roll with stiffer roll bars as compared to a high roll center setup? Thanks.