# 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

## Coordinate system

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. ## Inertia calculation

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)
• Iyy= mi (Xi²+Zi²)
• Izz= 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).

### 8 thoughts on “Vehicle inertia calculation tool”

1. A old, but good database of measurements of these parameters can be found on the NHTSA website. Could be good to validate the spreadsheet results. It can be found here: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDUQFjAA&url=http%3A%2F%2Fwww.nhtsa.gov%2FDOT%2FNHTSA%2FNRD%2FMultimedia%2FPDFs%2FVRTC%2Fca%2Fnhtsa_inertia_database_metric.pdf&ei=7BpbUaiiEIT8yAG4soHwCA&usg=AFQjCNGr9ecwroSpAHmf2_VF_hP3GqC6pQ&sig2=3Yn5oVHescW_myUiDIFbKQ&bvm=bv.44697112,d.aWc

2. sorry your explanations are incomplete, I can’t understand, where did you get that formula?? give me a link or etc,
thank you

1. I’m sorry I have a technical issue with the comments at the moment. I’ll fix it and anyway, you can find additional information in this link: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDUQFjAA&url=http%3A%2F%2Fwww.nhtsa.gov%2FDOT%2FNHTSA%2FNRD%2FMultimedia%2FPDFs%2FVRTC%2Fca%2Fnhtsa_inertia_database_metric.pdf&ei=7BpbUaiiEIT8yAG4soHwCA&usg=AFQjCNGr9ecwroSpAHmf2_VF_hP3GqC6pQ&sig2=3Yn5oVHescW_myUiDIFbKQ&bvm=bv.44697112,d.aWc

Hope this helps!

3. Hi every one,
I’m looking for all the data you’ve used to implement your excel file.
Could you please give me a website with all these datas ?