Locating the vehicle centre of gravity is fundamental to vehicle dynamics. It is a point that can be used to describe the motion of a rigid body when it subjected to a resultant force. Its intrinsic effect on vehicle dynamic performance makes it a primary consideration in chassis design and setup.

Obtaining vehicle centre of gravity data is difficult. Measuring the location of the vehicle centre of gravity requires specialized equipment like a K&C machine or a tilt table.

To overcome this challenge, we turn to historical data to inform an estimate. A data driven approach may provide a viable approximation assuming that the architecture of modern passenger vehicles has not changed in the past decades.

In this study, we will explore the National Highway and Traffic Safety Administration’s (NHTSA) Light Vehicle Inertia Parameter Database and the NCAP Rollover Stability datasets to identify trends in vehicle centre of gravity (CG) and static stability factor (SSF).

Vehicle properties

The location of the centre of gravity is a point where the vehicle can be analyzed as a particle. In a rotational analysis, the resultant moments about the centre of gravity eliminates linear-rotational coupling components from the equations of motion.

The vehicle centre of gravity is comprised of longitudinal, lateral and vertical components. These components are defined as relative distances from an axle, the vehicle centre plane and the ground respectively. Of particular interest is the height of the centre of gravity, represented by the following variable.

  • Let \(h\) represent the vertical distance between the vehicle CG and the ground [m]

These values can be presented in their non-dimensionalized form: longitudinal weight distribution, lateral weight distribution and static stability factor. We are specifically interested static stability factor, which will be represented by the following variable.

  • Let \(\textrm{SSF}\) represent the static stability of the vehicle [-]
    • Where \(\textrm{SSF} = \frac{T_{avg}}{2h}\)

We also make reference to the physical geometry of the vehicle, specifically its track width and roof height.

  • Let \(T_{avg}\) represent the average track width of the front and rear axles [m]
  • Let \(H\) represent the maximum vertical distance between the roof and the ground [m]

This analysis focuses on the factors influencing the CG height and SSF. These parameters are highly influential on vehicle dynamic performance and rollover stability.

Dataset

This study makes use of the NHTSA Light Vehicle Inertia Parameter Database and the Rollover Stability Measurements for NCAP from years 2001 to 2020. Both datasets are publicly available from their respective organizations. The combined sanitized dataset consists of 1270 data points and includes model years ranging from 1971 to 2021.

Within this analysis, we refer to two segments of vehicles: cars and trucks. The vehicle body styles in each segment are listed below.

  • Cars: sedans, convertibles, coupes, hatchbacks and wagons
  • Trucks: SUVs, pickup trucks, minivans and commercial vans
info

Charts are implemented using the data visualization library Bokeh. The following tools are available in the toolbar, located on the right side of each chart.

  • Box zoom - click and drag to zoom in to a rectangular region
  • Wheel zoom - scroll the mouse wheel to zoom in and out
  • Reset - restores the plot ranges to their original values

The charts include the following interactive features.

  • Tooltip on hover - mouse over a data point to inspect
  • legend_toggle
    Hide on click - click the legend to hide vehicle types
For the best experience, it is recommended to view this page on desktop.

Centre of gravity height vs. vehicle mass

To begin our analysis, we determine whether there is a correlation between centre of gravity height and vehicle mass.

Bokeh Plot

Two clusters are apparent in this graph representing the difference between cars and trucks. The cluster for cars have a lower mean centre of gravity height than the cluster for trucks. Centre of gravity height has a weak positive correlation with vehicle mass for cars and a slight positive correlation for trucks.

Static stability factor vs. vehicle mass

In this chart, we get the first like-for-like comparison of vehicle static rollover resistance. Static stability factor can be interpreted as the lateral G a vehicle can sustain without tipping over.

Bokeh Plot

We see again the clustering of cars and trucks, with cars typically having a higher SSF than trucks. SSF has a slight positive correlation with vehicle mass for cars, and has no correlation for trucks.

Static stability factor vs. vehicle roof height to average track width ratio

Comparing static stability factor against the ratio between the vehicle roof height and its average track width is interesting because of the vehicle eligibility rules for SCCA Solo events. To minimize the likelihood of a vehicle rollover, section 3.1.A in the rule book stipulates that competing vehicles must have a roof height to average track width ratio of less than one. However, the Solo Events Board (SEB) can alternatively use static stability factor to determine vehicle eligibility. When applying this rule, the SEB requires a SSF of 1.3 or greater.

Bokeh Plot

The ratio of roof height to average track width appears to be a valid proxy for rollover stability. Static stability factor is negatively correlated with the roof height to average track width ratio. All vehicles within the dataset that meet the roof height to average track width ratio requirement have a static stability factor of at least 1.2. This is short of the discretionary SSF threshold of 1.3 outlined in the SCCA Solo rule book. Consequently, this means that vehicles that meet the roof height to average track width ratio criteria are not guaranteed eligibility for these events.

Centre of gravity height vs. model year

In this chart, we shift our attention to identify trends over time. The jitter chart shows the distribution of centre of gravity heights for each model year. It also provides insight into the dataset itself.

Bokeh Plot

Much like the charts before, there is a clear difference in centre of gravity height between cars and trucks. There is no clear trend in vehicle centre of gravity height with respect to time.

Decade Avg. CG Height, Cars [m] Avg. CG Height, Trucks [m]
1970s 0.524 0.736
1980s 0.542 0.662
1990s 0.530 0.667
2000s 0.545 0.679
2010s 0.553 0.667

The NHTSA Light Vehicle Inertial Parameter Database covers model years from 1971 through 1998, but is missing data for much of the 1990s. It is not until 2001 do we see regular CG height measurements published as part of the NCAP program.

Static stability factor vs. model year

As advancements in technology are made over time, we would expect road vehicles to become safer. Observing trends in static stability factor over time will indicate if this is the case.

Bokeh Plot

Industry appears to be taking an incremental approach to improving rollover stability over time. This is most clearly visible in the SUV segment. In the 1970s a typical SUV would have an SSF of approximately 1.1. In the 2010s, the expectation is 1.2 or greater. A similar observation can be made for cars. This is great for road safety and rollover prevention.

Decade Avg. SSF, Cars [-] Avg. SSF, Trucks [-]
1970s 1.337 1.100
1980s 1.343 1.138
1990s 1.355 1.144
2000s 1.397 1.178
2010s 1.407 1.225

Average track width vs. model year

Static stability is increasing over time but centre of gravity height remains stationary. This implies that over time, vehicles have been increasing in track width. We can confirm this insight by looking for trends in average track width over time.

Bokeh Plot

This chart shows that vehicle average track width is indeed increasing over time. This means that gains in SSF are a result of increasing vehicle size, rather than vehicle manufacturers designing for lower centre of gravity heights.

Decade Avg. Track, Cars [m] Avg. Track, Trucks [m]
1970s 1.402 1.617
1980s 1.453 1.501
1990s 1.436 1.524
2000s 1.519 1.597
2010s 1.552 1.632

Final comments

In this study, we identified trends in vehicle centre of gravity height and static stability factor using a data set that spans over five decades. We discovered clustering of the data based on vehicle classification, specifically whether the vehicle was a car or a truck. An increasing trend in static stability factor with respect to time is driven by an increase in vehicle track width.

For performance enthusiasts, choosing a vehicle with the highest possible static stability factor is desirable to minimize the negative effects of load transfer and tire load sensitivity. For HPDE organizers, this dataset can be used to validate the effectiveness of vehicle eligibility rules based on track width and roof height.

The increasing trend in vehicle static stability factor is encouraging. Regardless of whether your interest is in vehicle performance or road safety, the trend is promising for the future of passenger vehicles.

References

  • Ginsberg, J. H. (1998). Advanced engineering dynamics. Cambridge University Press.
  • SCCA® National Solo® Rules (2022). Sports Car Club of America, Inc.
  • Walz, M. C. (2005). Trends in the static stability factor of passenger cars, light trucks, and vans (No. HS-809 868).
  • Heydinger, G. J., Bixel, R. A., Garrott, W. R., Pyne, M., Howe, J. G., & Guenther, D. A. (1999). Measured vehicle inertial parameters-NHTSA’s data through November 1998. SAE transactions, 2462-2485.