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:

Coordinate system

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:

CG calculation

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.

Inertia calculation

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).

Tool download

Here is the Excel tool that you can download for free: Vehicle Inertia Calculation English

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    About the Author

    Charlie Constant

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

    2. 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 ?
      Thank you for your help
      sincerely yours

    3. Hi every one,
      Greetings of the day..!!
      Thanks for your Excel sheet….
      I’m looking for Inertia measurement of Engine & transmission only, I don’t have any CAD details of engine.
      So, how I calculate the values of Xi, Yi, Zi . Please provide me the detail procedure of calculation.
      I have only Crane to lift engine, Its weight, what else I have to purchase for this measurement…
      Please gave me your inputs…
      Thanks in advance.

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