Posted by: drracing | December 8, 2017

Suspension kinematics excel tool

Hi everybody,

this is just a short entry, to share a small project i am working on in the last few days. Since it is something i wanted to do since a long time, i really want to spend a few words about it here and, maybe, trace how it progresses.

As the title of this post reveals, i am working on a simple suspension kinematics tool in excel, which is able to calculate the position of each hardpoint, basing on the defined suspension movement and all the most important metrics.
For now i am only focusing on double wishbones, as this is the scheme which is mostly used on the race cars i am interested in, but it should be pretty easy to adapt it to be used for a generic five links geometry, in the future.

The method i used is based on the intersections of spheres in space. Each moving point of a suspension is derived as the intersection of three spheres, with the center of each seating on an hardpoint whose position is fixed or has been already identified in a previous step; the radius of the sphere is either a link length or the distance between the point we want to locate and another point of the same component (see for example a wishbone or the upright).
For the very first point (namely the outer point of the lower wishbone, in my case) we can use two close points (for example the two connection points of the same wishbone to the chassis) and a reference point, which can be placed everywhere and will be afterward used also as the input for each suspension movement. In my case, this point will only move in z (vertical direction), as this is all what we need to simulate how a suspension moves.

The tool can currently calculate the result of each heave and roll movement and of any combination of the two. The approach i used, mainly for convenience, is to assume that the chassis remains fix with respect to the global reference system, while the floor moves with respect to it, either translating, rotating or both.
Roll is assumed to be an equal and opposite movement of the two wheels of an axle, this avoiding any philosophical debate/headache about around which point/axis the chassis rotates.
Each metric is anyway always referred to the “new” ground position, so if for example i input a roll movement, all will be calculated with respect to the ground now seating with an angle with respect to the global reference system.

As the tool is still “work in progress”, it still doesn’t depict any of the components seating “above the control arms”, see for example the pushrod, rocker/bellcrank, spring/damper unit, antiroll bar and third elements. Also, for now i am not yet done with steering, but this is relatively easy to add as an horizontal movement of the steering rack and will most probably be the very next step.

This is how it looks like as of today:

Susp kin tool 1


Susp kin tool 2


Susp kin tool 3


As you may notice, the Roll Center is one of the metrics i identified, but there are also the instant centers (they are anyway necessary to determine Roll Center position) and, more importantly, the n-lines slope. The n-lines are the lines connecting the IC to the Contact patch and, effectively, the lines defining the only direction through which the suspension linkage can carry forces. The instant center can be really thought as the pivot about which the upright rotate around the chassis.
I thought and read a lot about anti roll effects recently and i am more and more convinced that the Roll Center is not really the best way to define how the suspension geometry contributes to the antiroll moment. Although the roll centers are pretty effective and relatively easy to use as a metric to just have a picture about the geometry’s antiroll contribution, if we really want to understand and describe what happens in a real cornering situation, they fall short, above all when they migrate significantly. That’s why n-lines look like a much more effective tool to understand what happens in certain situations. More on this will probably come in a future post.

For now, i simply enjoy my new tool!
I will publish an update to track the progress (hopefully) soon.


  1. I’ve been imagining how to represent such situation on a roll case, great work. Looking forward to see the progress.

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