Roll center: definition, calculation and worked example

Open this geometry in opensus

The roll center is the point in the front view about which the body rolls, and where lateral tire forces pass into the body through the suspension links. For a symmetric axle it lies on the centreline, at the height where the line from each contact patch through its suspension's front-view instant center crosses the centreline.

Roll center height splits the lateral load transfer between the links and the springs. A higher roll center sends more of it through the links (less body roll, more jacking); a lower one sends more through the springs (more roll). opensus labels it Roll centre in the readout and charts.

Finding it

In the front view, extend the upper and lower arms until they meet. That is the instant center (IC): the point the upright is rotating about at this instant.
Draw a line from the tire's contact patch through the IC.
Where that line crosses the car's centreline is the roll center.

With the contact patch at lateral position $y_{C P}$ on the ground and the instant center at $(y_{I C}, z_{I C})$ :

h_{R C} = z_{I C} \frac{y _{C P}}{y _{C P} - y _{I C}}

The distance $y_{C P} - y_{I C}$ is the front-view swing arm length (FVSA).

Worked example

Take the docs example double wishbone, left corner, in mm. In the front view the upper arm runs from $(280, 330)$ to $(530, 340)$ , the lower arm from $(200, 150)$ to $(550, 120)$ , and the contact patch is at $(600, 0)$ .

Upper arm line, slope $10/250 = 0.040$ :

z = 330 + 0.040 (y - 280)

Lower arm line, slope $- 30/350 = - 0.0857$ :

z = 150 - 0.0857 (y - 200)

Setting them equal gives the instant center at $y_{I C} = - 1206.4$ mm (inboard of the centreline, on the far side of the car), $z_{I C} = 270.5$ mm. The FVSA length is $600 - (- 1206.4) = 1806.4$ mm, so

h_{R C} = 270.5 \times \frac{600}{1806.4} = 89.9 mm

opensus reports the same 89.9 mm. Open the geometry with the button on this page and look at Roll centre in the readout.

Roll center migration

The roll center moves as the car heaves and rolls. In the example it drops 1.32 mm for every 1 mm of bump, from 89.9 mm at ride height to 76.7 mm with 10 mm of bump. A roll center that moves a lot changes the car's balance as it squats under aero load or pitches under braking. In the Kinematics → Heave and Roll charts, Roll centre height shows this directly; in the 3D view, Roll axis draws the axis through the front and rear roll centers and View → Roll centres and force lines draws the construction.

How opensus calculates it

Extending arm lines only works for double wishbones. opensus instead finds the instant center from the upright's actual motion: it solves the suspension a fraction of a millimetre above and below the current position and takes the point whose front-view velocity is zero. That works for MacPherson struts, multilinks and any linkage you build, and includes the effect of the real 3D arm axes rather than a 2D projection. For the symmetric 2D example above the two methods agree exactly.

Setting roll center height: which pivots move it, by how much
Camber gain: set by the same instant center
Anti-dive and anti-squat: the side-view equivalent