How to calculate center of gravity

This article was published in the July 2021 edition of NTEA News.

From an NTEA member
I’m building a truck and need to determine if its center of gravity is within limits set by the OEM. How do I perform these calculations?

The three-dimensional location of a vehicle’s center of gravity (CG) determines how weight is distributed in each dimension. For example, the horizontal position will determine how much of the total weight will be on the front versus rear axles, whereas the lateral position will dictate any side-to-side bias of weight on all axles. Along with the CG’s vertical position, this physical characteristic effects the vehicle’s dynamic performance, braking and handling, which is why OEMs establish dimensional limits to ensure vehicles will meet different Federal/Canadian Motor Vehicle Safety Standards (F/CMVSS) and other performance requirements.

OEMs have different limitations for allowable CG dimensions with which multistage manufacturers need to compare their calculated values. A completed vehicle’s vertical CG position is a commonly published limit, usually relative to the ground or sometimes to the top of the chassis frame. On light vehicles, there may be additional vertical limits for just a combined body and added equipment CG, which influence crash performance of various F/CMVSS.

While the physics behind calculating vehicle CG dimensions are the same, it’s important to first review the chassis OEM’s incomplete vehicle document (IVD). These documents are the basis for determining vehicle compliance to applicable F/CMVSS, so guidance they provide will be specific to the vehicle you’re building and based on the OEM’s own testing/development/analysis for meeting different safety and emissions standards. Since weight and CG location factor into many of these standards, any CG limitations will be included and/or referenced in the different conformity statements contained in the IVD.

OEMs may include their own formulas for these calculations. While CG calculations are part of an overall weight analysis, OEM guidance may only require calculation of one or two CG dimensions. For example, maintaining actual weights within the gross vehicle weight rating (GVWR) is an important initial step in determining chassis suitability for a particular application, which does not require calculating CG location. Or, an OEM may only specify a limit for the vertical CG component in order to compare it to their established braking system limit. Other OEM calculations may include an acceptable range for a completed vehicle’s vertical CG position, dependent on the horizontal position. These calculations can be based on an OEM’s background math that already takes a number of factors into account, so following the calculation methods in the IVD is critical in determining values to compare to specified limits — even if calculation methods look different than the traditional balance of moments equations for determining the three CG dimensions.

Additional guidance may be provided in OEMs’ body builder information, so be sure to review those materials, along with the corresponding chassis IVD, for specific references. As an example, completed vehicles, like pickups, do not come with an IVD — but manufacturers still have the same considerations for F/CMVSS compliance when performing box removal and other altered stage operations. Pickup box removal guidelines often share the same criteria as the incomplete version of the same pickups offered by the OEM with pickup box delete. So, while body builder information and the IVD for box-deleted pickups may cross-reference and provide the same CG limitation and calculation methods, caution is required to ensure a pickup model being considered for box removal is included as part of the OEM’s guidance for that model year.

Remember, determining a vehicle’s CG position alone is not the purpose of these calculations, but rather part of an overall weight analysis for F/CMVSS and emissions compliance, bridge weight limitations, towing considerations and basic chassis suitability for an application.

Find center of gravity and weight calculator tools at ntea.com/weightcalculator.