The study, published open access in the journal Automotive and Engine Technology by Thomas Gerstorfer, Martin Schabauer, and Cornelia Lex, addresses a long-standing tension in vehicle dynamics. Independent wheel suspensions, such as double wishbone or multi-link layouts, allow each wheel to move with a degree of freedom that solid axles do not possess. Describing their kinematics with a single roll center requires assumptions that do not always hold, particularly when the suspension geometry generates vertical forces as a byproduct of lateral tire forces. These so-called jacking forces can literally lift or lower the vehicle body during cornering, changing the ride height and altering the handling balance in ways that a classic roll angle calculation struggles to capture.

The core of the new approach is the principle of virtual work, a classical tool of analytical mechanics. Rather than choosing an arbitrary point around which the body rolls, the researchers model the suspension as a constrained mechanical system in which the geometry itself dictates how lateral tire forces are transmitted to the body. When a tire generates a lateral force, the links and joints of the suspension guide that force along specific paths, and some components of those paths point vertically. By computing the virtual work done by these force components through small virtual displacements of the mechanism, the model captures the geometric load transfer directly, without ever needing to define a roll center height. The result is a description of both roll and heave motion that emerges naturally from the suspension’s constraints.

What makes this modeling strategy particularly attractive is its efficiency. A complete multi-body simulation of a vehicle, with all its joints, bushings, dampers, and compliance elements, can be computationally expensive, requiring detailed parameterization and significant processing time. Such models are indispensable for final validation, but they are cumbersome during early design exploration, when engineers need to sweep through dozens of suspension geometry variants quickly. The Austrian team’s model sits in a sweet spot: it is simple enough to run rapidly, yet it retains physical effects that cruder analytical methods ignore. The authors emphasize that this transient single-axle model, while far lighter than a full vehicle multi-body model, still accounts for phenomena that matter in real driving.

Among those phenomena is aerodynamic downforce. Modern passenger cars and especially performance vehicles generate significant vertical aerodynamic loads at speed, which press the body toward the road and alter the forces flowing through each suspension link. The new framework incorporates downforce explicitly, allowing engineers to see how it interacts with the suspension geometry during cornering. The model also accounts for camber effects, specifically camber thrust, the lateral force generated when a tire leans relative to the road surface. Because independent suspensions change camber as the body rolls and the wheels travel, these effects feed back into the load paths and the resulting jacking forces, and the proposed model handles them within the same virtual work framework.

Another subtle but important capability concerns the left and right sides of the axle. During cornering, the outer tire typically carries more load and generates more lateral force than the inner tire, so the two sides of the axle are rarely symmetric in their force contribution. Classic roll center methods often implicitly assume symmetric behavior, masking the asymmetries that influence how the body actually moves. The new model takes unequal lateral tire forces into account, computing the jacking forces they produce on each side independently. This means characteristics such as ride height changes, including the tendency of some suspensions to squat or lift under sustained cornering, can be determined directly from the model outputs rather than estimated through empirical corrections.

To establish credibility, the researchers compared their approach against two established benchmarks found in the literature. The first was an existing model that does consider the kinematics of independent suspension systems in more detail, providing a like-for-like test of whether the new formulation reproduces known behavior. The second was the classic roll angle calculation, the textbook method that relies on roll center positions and represents the traditional baseline every vehicle dynamics engineer learns. The comparisons served to position the new model within the existing landscape: more faithful than the simplified classic method, yet more efficient than the detailed kinematic alternative.

The decisive test, however, came from validation against a multi-body simulation, the de facto gold standard for suspension and vehicle dynamics analysis. The authors report that the proposed model was able to predict the roll and heave motions of independent wheel suspension systems in an efficient and physically plausible manner, matching the reference simulation without requiring the computational overhead of a full multi-body environment. For engineers iterating on suspension hardpoints, kinematic properties, or force paths, this combination of accuracy and speed is precisely what makes a modeling approach useful in practice rather than merely elegant on paper.

The broader significance of the work lies in its willingness to question a foundational concept. The roll center has been criticized for decades precisely because its definition becomes ambiguous for independent suspensions, and different definitions can yield different predictions for the same mechanism. By sidestepping the concept entirely and grounding the description of load transfer in the actual constraints of the suspension, the Graz researchers offer a formulation that is easier to defend physically and more transparent to interpret. Effects that had to be patched in with corrections under the roll center framework, such as jacking, camber thrust, and aerodynamic loading, arise organically from the virtual work formulation.

For the automotive industry, the implications are practical. Simulation tools built on such models could accelerate the early stages of chassis development, letting teams evaluate ride height behavior, roll characteristics, and geometric load transfer across wide design spaces before committing to expensive detailed simulations or physical prototypes. The work also has educational value, giving students and practitioners a clearer picture of how suspension geometry converts tire forces into body motion. As vehicles grow heavier with batteries and more reliant on aerodynamics and sophisticated chassis control, the demands on suspension modeling will only increase. An approach that captures the essential physics with minimal computational cost, and that has been validated against multi-body simulation, offers a timely contribution to that effort. The full article is available open access under a Creative Commons license, allowing engineers and researchers worldwide to examine the formulation and apply it to their own suspension systems.

Subject of Research: A virtual work-based modeling approach for roll and heave motions of independent wheel suspension systems without roll centers

Article Title: An effective modeling approach for roll and heave motions for independent wheel suspension systems

Article References: Gerstorfer, T., Schabauer, M., & Lex, C. (2026). An effective modeling approach for roll and heave motions for independent wheel suspension systems. Automotive and Engine Technology. https://doi.org/10.1007/s41104-026-00180-2

Image Credits: AI Generated

DOI: 10.1007/s41104-026-00180-2

Keywords: vehicle dynamics, suspension kinematics, independent wheel suspension, roll center, jacking forces, principle of virtual work, roll motion, heave motion, camber thrust, aerodynamic downforce, multi-body simulation, automotive engineering