Vehicle inertia calculation tool
One of the parameters useful in vehicle dynamics simulation tools is the vehicle inertia (Ixx, Iyy and Izz). These parameters can be measured, but when you can’t measure them (during the conception phase for example) there is a way to calculate them simply without using any CAD software.
An example Excel spreadsheet has been made with a concrete example: the Mercedes CLS 63 AMG
The main objective of this tool is to obtain:
- static mass bias
- coordinates of the center of gravity (CG)
- vehicle’s moment of inertia
- a first approximation of the vertical stiffness and damping
The most important thing in order to get relevant results is the coordinate system and it has to be chosen as follows:
Inputs for the inertia calculation
All vehicle components have to be taken into account if you want to get a precise result (non-suspended mass, engine, gearbox, chassis, passengers, luggage …). For each component, you need to set the CG coordinate and the associated mass.
For motorsport purposes, the ballast can be added to see how the inertia and mass bias are impacted. You can also change vehicle parameters such as the wheelbase to evaluate their influence.
First, we need to calculate the CG location with this equation:
Thus, we can calculate the distance between the vehicle CG and the CG of each component. This value is used to calculate the inertia (kg.m²) caused by each component.
- Ixxi = mi (Yi²+Zi²)
- Iyyi = mi (Xi²+Zi²)
- Izzi = mi (Xi²+Yi²)
The inertia Ix, Iy and Iz is the sum of each component’s inertia.
For the inertia around the Y and X axis, only the suspended mass has to be taken into account, but the inertia around the Z axis is calculated with all the vehicle components (suspended and non-suspended mass).